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9803 | astro-ph9803278_arXiv.txt | We present {\it Rossi X-ray Timing Explorer}\ (\RXTE) All-Sky Monitor observations of the X-ray binary Circinus~X-1 which illustrate the variety of intensity profiles associated with the 16.55~d flaring cycle of the source. We also present eight observations of Cir~X-1 made with the \RXTE\ Proportional Counter Array over the course of a cycle wherein the average intensity of the flaring state decreased gradually over $\sim$12 days. Fourier power density spectra for these observations show a narrow quasi-periodic oscillation (QPO) peak which shifts in frequency between 6.8~Hz and 32~Hz, as well as a broad QPO peak that remains roughly stationary at $\sim$4~Hz. We identify these as Z-source horizontal and normal branch oscillations (HBOs/NBOs) respectively. Color-color and hardness-intensity diagrams (CDs/HIDs) show curvilinear tracks for each of the observations. The properties of the QPOs and very low frequency noise allow us to identify segments of these tracks with Z-source horizontal, normal, and flaring branches which shift location in the CDs and HIDs over the course of the 16.55~d cycle. These results contradict a previous prediction, based on the hypothesis that Cir~X-1 is a high-$\dot{M}$ atoll source, that HBOs should never occur in this source (\cite{oosterbroek95}; \cite{klis94}). | The X-ray binary Circinus~X-1 is unique in its complex temporal and spectral variability. A 16.55~day cycle of flaring is observed in the X-ray (\cite{kaluzienski76}) as well as optical (\cite{moneti92}), IR (\cite{glass78}), and radio bands (\cite{whelan77}). The high degree of stability of the period of this cycle is evidence that it is the orbital period. The onset of flaring has been suggested to be the result of enhanced mass transfer occurring near periastron of a highly eccentric binary orbit (\cite{murdin80}; \cite{oosterbroek95}). The X-ray profile and average intensity of the 16.55~day cycle has varied considerably over timescales of years (see e.g, Dower, Bradt, \& Morgan 1982\nocite{dower82}; \cite{stewart91}; \cite{oosterbroek95}; Shirey et~al.\ 1996, hereafter \cite{shirey96}). Observations with the {\it Rossi X-ray Timing Explorer} (\RXTE) All-Sky Monitor (ASM, 2--12~keV) showed Cir~X-1 in a sustained bright state with a baseline intensity level of $\sim$1.0~Crab (75 c/s; 1060 $\mu$Jy at 5.2 keV) and strong flaring up to as high as 3.5~Crab (\cite{shirey96}). The flaring state began during the day following phase zero (based on the radio ephemeris of \cite{stewart91}) and typically lasted 2--5~days (see Figure~\ref{fig:asm} and discussion below). The ratio of count rates in different ASM energy channels showed dramatic spectral softening at the onset of the flaring state and gradual hardening during the remainder of each cycle (\cite{shirey96}). Similar behavior was seen in \Ginga\ ASM observations folded at the 16.55 day period (\cite{tsunemi89}). Near phase zero, some of the cycles observed with the \RXTE\ ASM also showed brief dips below the 1~Crab level. Observations of dips near phase zero in Cir~X-1 with \ASCA\ (\cite{brandt96}) and the \RXTE\ PCA (\cite{bradt98}) indicate the presence of both a strongly absorbed spectral component and an unabsorbed component. Observations of type~1 X-ray bursts demonstrate that Cir~X-1 is a low magnetic field neutron star (Tennant, Fabian, \& Shafer 1986\nocite{tennant86b}). Additional type~1 bursts have not been observed from Cir~X-1 since the \EXOSAT\ discovery, possibly because the source intensity has been higher during subsequent observations. The rapid X-ray variability of Cir~X-1 at times resembles that of both ``atoll'' and ``Z'' low-mass X-ray binaries (LMXBs) as well as black-hole candidates (\cite{oosterbroek95}). Quasi-periodic oscillations (QPOs) were reported at 1.4~Hz, 5--20~Hz, and 100--200~Hz in \EXOSAT\ data (\cite{tennant87}, 1988\nocite{tennant88}). Based on these data, it has been suggested that Cir~X-1 is an atoll source that can uniquely reach the Eddington accretion rate and exhibit normal/flaring branch QPOs at 5--20~Hz (\cite{oosterbroek95}; \cite{klis94}). Observations made during non-flaring phases with the \RXTE\ Proportional Counter Array (PCA) showed a QPO peak that varied from 1.3 to 12~Hz, flat-topped low-frequency noise (LFN), and a broad peak that varied from 20--100~Hz (\cite{shirey96}). The two QPO frequencies and the cut-off frequency of the flat-topped noise were highly correlated. These QPOs are likely to be essentially the same phenomenon as those previously seen in the \EXOSAT\ observations at 5--20~Hz and 100--200~Hz. In this paper we present additional \RXTE\ ASM observations of Cir~X-1 which further illustrate how its intensity profile varies from one 16.55~d cycle to another. We also present the results of \RXTE\ PCA observations made over the course of one cycle in which the intensity declined unusually gradually from the flaring state to the quiescent level. This slow transition allows us to demonstrate how the time-variability properties of the source are related to its spectral properties. | The combined temporal and spectral-branch properties of the observations presented here suggest Z-like behavior. We identify the 6.8--32~Hz QPOs as horizontal-branch oscillations (HBOs), the 4~Hz QPO as normal-branch oscillations (NBOs), and the strong VLFN as flaring-branch behavior (see discussion below). These identifications of characteristic time-variability patterns then help to identify the tracks in the HID as horizontal, normal, and flaring branches (HB/NB/FB), where each 6 ks observation of Cir~X-1 appears to have captured a snapshot of portions of one or two of the branches. The spectral branches appear to shift around as the flaring gradually subsides, rather than forming a stable Z pattern. It is likely that the shapes of the spectral branches become distorted somewhat during these large shifts. We now describe the inferred properties of each of the spectral branches in more detail. \subsection{Horizontal Branch} HID regions VIII, VII, and VI-1 show a narrow QPO peak or knee at 6.8--7.6~Hz, 11.3--13.1~Hz, and 32~Hz respectively. This frequency range overlaps the 13--60~Hz range of typical horizontal branch QPOs (\cite{klis95}). The associated low-frequency noise and harmonic peak are also typical of horizontal branch power spectra. The broad high frequency peak in Cir~X-1 may be related to the high frequency noise component often observed on the horizontal branch. The HID track for observation VI shows the narrow QPO at 32~Hz on a roughly horizontal segment (region VI-1) and a knee at 37~Hz on the right end of this segment (region VI-2). The apex of region VI-2 brings a transition to the 4~Hz QPO, which is dominant on the downward branch of this track (region VI-3). This is very similar to the HB/NB transition in Z sources. When Cir~X-1 is in ``quiescence'' in observations VII and VIII, the ``horizontal branch'' turns upward and becomes vertical in the HID. For comparison, \RXTE\ PCA observations of Cir~X-1 from 1996 March 10--19 which show a narrow QPO peak at 1.3--12~Hz (\cite{shirey96}) are almost entirely confined to the 12.3--14.7 kcts/s (2--21 keV) intensity range. The HID tracks for those observations lie along a nearly vertical line, and probably represent sections of the ``horizontal'' branch. Observation II may also be on part of the HB, since a weak narrow QPO appears to evolve into a knee and increase in frequency from 22 to 30~Hz as the intensity increases. However, the broad QPO is also weakly visible in PDSs for this observation. The fact that observations II, VI, VII, and VIII all show little variation of the hard color used in Figure~\ref{fig:cchid_all}a suggests that observation~II may be associated with the other HB observations. \subsection{Normal Branch} The 4~Hz QPO is observed when the source intensity rises above the ``quiescent'' 1-Crab level ($\sim$13~kcts/s). It is roughly stationary in frequency (3.3--4.3~Hz when clearly peaked) and broader than the HBO. The feature is easily seen in observations III--VI; at these times the location in the HID moves along diagonal tracks. The $\sim$4~Hz frequency and motion along diagonal tracks in the HID is consistent with the 4--7~Hz NBOs observed at nearly constant frequency on the NB of typical Z sources (\cite{hk89}). We therefore identify the broad 4~Hz QPO as a normal branch oscillation, and the diagonal tracks for observations III--VI as shifted normal branches. The broad QPO component may be also present in the highest intensity observations, as a weak feature in observation II and in the form of a break near the 4~Hz QPO frequency in observation~I. We also note that at the top of the normal branch (regions I-1, III-1, IV-1, VI-2) a knee above 30~Hz is present in addition to the NBO component. A similar broad 4~Hz QPO is present in observations from 1996 March 5--6 made immediately before phase zero of the cycle showing the 1.3--12~Hz narrow QPO. \subsection{Flaring Branch} Beyond the left apex of the normal branch a short upturned branch is observed in HID region~V-3 and possibly III-3. The PDS for these regions are dominated by very low frequency noise, which is typical for flaring branches, and no QPO peaks are obviously apparent. We note that in the well-established Z sources neither NBOs nor HBOs are present on the flaring branch, except for Sco~X-1 and GX~17+2, in which the NBO evolves into a 6--20~Hz QPO (\cite{klis95} and references therein). The left end of the spectral track for observation~V bends upward in the HID shown in Figure~\ref{fig:cchid_all}b, but bends downward in the CD in Figure~\ref{fig:cchid_all}a. This behavior is demonstrated more clearly in Figure~\ref{fig:cchid_56medhard}, which shows CDs and HIDs for observations V and VI. When a broad color (\broadcolor) is used as the ordinate of the diagrams (Figure~\ref{fig:cchid_56medhard}a,b), the track for observation~V turns upward on the left end. When a harder color (\hardcolor) is used as the ordinate (Figure~\ref{fig:cchid_56medhard}c,d), this branch turns downward. The CD and particularly the HID version based on the harder color show the most clear similarity to canonical Z diagrams, with the temporal behavior of observations V and VI being generally consistent with horizontal, normal, and flaring branches. The broad-color HID (Figure~\ref{fig:cchid_56medhard}b) shows evidence for a shift of the normal branch that does not show up in the other three diagrams of that figure. \subsection{Relation to Other Sources} Our observations reveal spectral branches which shift in the CD and HID as Cir~X-1 evolves from a soft, high-intensity state to a hard, lower-intensity state. The ASM light curves and hardness ratios (Figure~\ref{fig:asm}) show that this evolution occurs periodically with the 16.55~day cycle, thus suggesting that the CD/HID shifts may also be periodic. Shifts of the ``Z'' pattern in CDs and HIDs have been observed in the so-called Cyg-like Z sources: Cyg~X-2 (Kuulkers, van~der~Klis, \& Vaughan 1996\nocite{kuulkers96:cygx-2}), GX~5-1 (\cite{kuulkers94:gx5-1}), and GX~340+0 (\cite{kuulkers96:gx340+0}). However, the shifts do not occur periodically in those sources, nor do they have the magnitude of the shifts observed in Cir~X-1. The flaring branch of Cir X-1 turns upward when a soft or broad color is used on the vertical axis. When a harder color is used, this branch turns downward but then bends to the left. In the Cyg-like Z sources, the flaring branch sometimes turns upward or starts toward higher intensity and then loops back to lower intensity (\cite{kuulkers96:cygx-2}; \cite{kuulkers94:gx5-1}; \cite{kuulkers96:gx340+0}; \cite{penninx91:gx340+0}). In some cases, these sources are observed to ``dip'' while on the flaring branch (\cite{kuulkers94:gx5-1}; \cite{penninx91:gx340+0}; \cite{wijnands97}), with tracks which turn down and then to the left, similar to that of Cir~X-1 in Figure~\ref{fig:cchid_56medhard}c. The left end of the horizontal branch in Cir~X-1 turns upward and becomes vertical at low intensity (Figure~\ref{fig:hidqpo}). On this section of the branch, HBO frequencies are low: 6.8--13~Hz in observations VII and VIII and 1.3--12~Hz in the earlier 1996 March observations. A similar effect was reported in GX 5-1 (\cite{lewin92:gx5-1}; \cite{kuulkers94:gx5-1}), in which the HB turns upward at the low-intensity end while HBOs are observed at relatively low frequency (13--17~Hz). In fact, Lewin et~al.\ (1992\nocite{lewin92:gx5-1}) suggested that other Z sources might show such an upward turn of the HB if their intensities and QPO frequencies became sufficiently low. The 5--20~Hz narrow QPO was detected with \EXOSAT\ at an intensity similar to the quiescent level observed by \RXTE. We note that absorption dips are responsible for much of the structure seen in the CD shown for that observation; however, the HIDs show that the narrow QPO occurred on an upturned left end of a horizontally oriented track as in our data (see Figures~2--4, 8, \& 10 in \cite{oosterbroek95}). At higher intensity during the same observation, the narrow QPO was not present, and we note that some of the high-intensity PDSs show hints of a broad peak near 4~Hz. We thus conclude that the behavior observed by \EXOSAT\ during that observation is related to the Z-like behavior we observe with \RXTE. Most of the other \EXOSAT\ observations took place when Cir~X-1 was significantly lower in intensity than the ``quiescent'' level of the current observations. The CDs and HIDs for these \EXOSAT\ observations did not show tracks which could clearly be identified as Z or atoll. Their power spectra were generally dominated by VLFN, typical of atoll sources in the banana state, and sometimes also showed a broad red noise component resembling atoll high-frequency noise (\cite{oosterbroek95}). However, these power-spectral shapes are not unique to atoll sources: power spectra for black hole candidates in the high state are dominated by VLFN, as are those of the current observations on the low-intensity end of the normal branch and on the flaring branch (i.e., regions III-3 and V-3). Cir~X-1 was expected to never show HBOs since atoll-like behavior was taken as evidence that the magnetic field is not strong enough to allow the magnetospheric beat frequency mechanism (MBFM) to operate (\cite{klis94}; \cite{oosterbroek95}). (However, it is also possible that the HBOs are not produced by the MBFM\@.) The results presented here demonstrate both HBOs and NBOs in Cir~X-1 and show no evidence for atoll behavior. Since the atoll-like behavior observed with \EXOSAT\ occurred at lower intensity than in the present observations, it is possible that they do represent a different state of the source. If Cir~X-1 actually can show atoll behavior as well as the Z-like behavior shown here, then we would have new clues to the differences between the two types of sources. Such observations would challenge the hypothesis that differences in both $\dot{M}$ and magnetic field distinguish these two classes. | 98 | 3 | astro-ph9803278_arXiv.txt |
9803 | astro-ph9803108_arXiv.txt | We report on mid-infrared (MIR) continuum and line emission mapping of the nucleus of NGC~253. The data, with a resolution of 1\as.4, reveal a double-peaked arc-like [NeII] emission region. Comparison with published data shows that the [NeII] arc is centered on the nucleus of the galaxy. The brightest [NeII] source coincides with the infrared continuum peak. The interpretation of these results is complicated by the edge-on orientation of NGC~253, but a self-consistent explanation is starformation triggered by dynamical resonances in a barred potential. | The prototypical starburst galaxy NGC~253 is a highly inclined (i=78\deg , \cite{pen81}) disk galaxy at a distance of about 3~Mpc (\cite{tul88}). The view towards its inner region is heavily obscured, and the exact location of its nucleus has been the matter of some debate. The astrometry of the various infrared sources in the central 10\as\ has been discussed in detail by Kalas \& Wynn-Williams (1994, hereafter KW94) in the near-infrared and \cite{ket93} in the mid-infrared. From their $\approx$1\as\ resolution H, K, L, and M observations, KW94 conclude that the brightest source in all the maps (their peak~1) lies at R.A.(1950)=$00^h45^m5^s.62$, Decl.(1950)=$-25^{\circ}33^{\prime}40^{\prime\prime}.2$. This position is in very good agreement with that of the emission peak at MIR wavelengths as determined by Keto \ea\ (1993) at 10~\mm\ from astrometric methods and Pi\~na \ea\ (1992) from low-level contour fitting to published maps with lower resolution. It is safe to assume that the location of peak~1 is independent of wavelength up to 20~\mm , enabling us to adopt the above coordinates for the continuum peak in our maps. Peak~1 is not connected to any of the strong radio point sources found at 2~cm by Turner \& Ho (1985, hereafter TH85) and 6~cm by \cite{ulv91} and \cite{ant88}. The radio sources are highly aligned along the major axis of NGC~253 at P.A. 51\deg . All of them are most likely either radio supernovae or HII regions, based on their spectral index. The only exception is the source TH~2 in TH85, a powerful flat spectrum radio source that they proposed to be the nucleus of NGC~253. TH85 argue that because of its high radio luminosity ($10^4$~\lsol ) and its unique location at the center of a synchroton disk this source probably is a compact synchroton source, similar to those observed in active galactic nuclei (AGNs). It lies close to a secondary MIR peak (peak~2) $\approx$ 2\as.2 northeast of peak~1 (\cite{pin92}, \cite{ket93}). However, as we will show, the radio nucleus is most likely not identical with any characteristic infrared source. This view was strongly supported from 0.5\as\ resolution NIR color maps by \cite{sam94}. Their maps were referenced to other observations by cross-correlation of low level contours and show that the radio nucleus TH~2 coincides with an extinction maximum of $\rm A_V\geq 24$. In addition, KW94 show that the exact position of peak~2 is wavelength dependent in the sense that for J, H, K observations it lies $\approx$ 1\as\ further east than in M-band. The physical nature behind the various infrared sources is uncertain. For example, according to \cite{for93}, the emission of the \brg -line at 2.17~\mm\ is strongest at peak~1. On the other hand, KW94 show that peak~1 has a low PAH-feature/continuum emission ratio. Since PAH emission is usually indicative of ongoing star formation, KW94 argue against peak~1 being an intense starburst which would be the natural explanation for the \brg\ emission. To investigate this matter further, we have observed NGC~253 at MIR wavelengths, both in continuum and line emission. The forbidden $\rm ^2P_{3/2}-^2P_{1/2}$ transition of singly ionized Neon at 12.81~\mm\ traces the photoionization regions of hot stars and thus carries similar information than e.g. \brg , but at a much lower extinction: $\rm A_{2.17\mu m} \approx 2.5\cdot A_{12.8\mu m}$ (\cite{lut96,gen98}). In the next section we will describe how the data were obtained. We also discuss the special observing techniques in the MIR and their implications on data reduction. We present the results of our observations in Sec. \ref{results} and interpret them in Sec. \ref{discussion}. | \label{discussion} \subsection{The bar in NGC~253} From 10\as\ resolution K-band imaging, \cite{sco85} find a prominent NIR bar at P.A. 68\deg . However, the NIR continuum of the central $\approx$ 10\as\ in all high resolution NIR maps (e.g. Forbes \ea\ 1993, KW94, Sams \ea\ 1994) is oriented at P.A. 51\deg , roughly parallel to the major axis of the optical disk. This change in orientation is also visible as an isophote twist in \cite{sco85} and all MIR maps (\cite{pin92,ket93}, Fig. \ref{fig2}). What is the reason for this behavior? From kinematical studies of the CS(2-1) line at 98~GHz, \cite{pen96} have tried to answer this question. They derived a model for the dynamical processes in the center of NGC~253. In short, they find five prominent CS emission spots. The two innermost spots are aligned along the axis of the radio knots, i.e. the major axis of NGC~253. They are separated by $\approx$ 3\as\ and positioned symmetrically on either side of the radio nucleus. Two other knots lie again symmetrically to the nucleus, but are aligned with the large scale NIR bar. Their observations are well explained by a rotating gas torus around the dynamical center of NGC~253. The torus is the response of the viscous molecular gas to the potential of the NIR stellar bar. Gas clouds in the inner $\approx$ 10\as\ move along elliptical $x_2$ orbits whose major axis is aligned perpendicular to the bar (Athanassoula 1992a,b). At the inclination of NGC~253, these orbits appear to be oriented parallel to the major axis of the optical disk as demonstrated in Fig.~5 of \cite{pen96}. The gas clouds outside of $\approx$ 10\as\ move on $x_1$ orbits, their major axis being aligned with the bar. The existence of $x_2$ orbits depends on the presence of at least one Inner Lindblad Resonance (ILR). For the case of NGC~253, \cite{arn95} have shown that there are in fact two ILRs, one at a radius of 25\as, the other close to the nucleus. It is at the inner ILR, where the orientation of the dominant orbits changes from $x_2$ to $x_1$ (e.g. \cite{tel88}). Because of orbit crowding, massive star formation occurs predominantly at the apocenters of the $x_2$ orbits (\cite{ath92b}), oriented symmetrically on either side of the nucleus. Therefore, \cite{pen96} interpret their CS results as evidence for a rotating torus of dense gas around the radio nucleus TH~2. These results are in agreement with observations of other tracers of high density gas like HCN (\cite{pag95}). \subsection{The [NeII] arc - a starformation ring} Based on their model, \cite{pen96} predict that higher resolution line mapping should prove that gas emission from the central 10\as\ (145~pc) of NGC~253 is aligned with the radio knots rather than with the optical disk. In that context, our results provide an independent confirmation of this scenario. Firstly, the [NeII] emission is well aligned with the radio knots (Figs. \ref{fig1} (Plate 1) and \ref{fig2}). Secondly, based on the structure of the [NeII] emission, we also confirm the distribution of the star forming material in a ring around the radio nucleus. The ring has a rotation velocity of $\approx$ 60~km/s as seen in the CS data by \cite{pen96}, the western side moving away from the observer. Unfortunately, our observations are unable to resolve the velocity structure of the [NeII], this has to await higher resolution line mapping, e.g. with a cryogenic Fabry-Perot interferometer. Our data only show weak emission from the southeastern half of the ring. On the other hand, the [FeII] map of \cite{for93} does show emission from this region (their source B). Thus, we favor the interpretation of the double-peaked morphology as a starburst ring with a diameter of $\approx$ 4\as\ (60~pc). The total observed flux from a circular aperture with 1\as.4 (20~pc) diameter centered on peak~1 is $1.7\cdot 10^{-15}$~W/m$^2$. After dereddening with $\rm A_V=24$ (Sams \ea\ 1994) in a mixed case scenario, this corresponds to $7.7\cdot 10^5$\lsol\footnote{We have adopted $\rm A_{12.8\mu m}=0.04\cdot A_V$ (\cite{gen98})}. With the conversion factor $\rm \frac{L_{Lyc}}{L_{[NeII]}} = 64$ (\cite{gen98}), the intrinsic Lyman-continuum luminosity is $4.9\cdot 10^7$\lsol. This value should be used with caution given its uncertainties, but it compares well to other bright star forming regions like the core of 30~Doradus in the LMC (\cite{bra96}) or the brightest SFR in the gaseous ring of IC~342 (\cite{boe97b}). This supports the view that the [NeII] emission probably stems from individual giant molecular clouds (GMCs) that actively form stars and are located in a ring at the ILR. We will extend the comparison to a similar structure in IC~342 in the next section. \subsection{NGC~253 and IC~342 - two of the same kind?} It is interesting to note the close similarities between NGC~253 and IC~342, another nearby late type spiral. B\"oker \ea\ (1997b) describe the dynamical processes in the central 100~pc of IC~342 as derived from NIR integral field spectroscopy. Table \ref{tab1} compares the two galaxies. \begin{table} \dummytable \label{tab1} \end{table} The dynamical processes and the morphology of the molecular gas are almost identical. This was also noted by Paglione \ea\ (1995). One important difference, however, is that IC~342 does not house a central synchroton source. In fact, in the case of IC~342, there is no radio emission from the dynamical center (\cite{tur83}). Rather, it is occupied by a cluster of young red supergiants that dominate the NIR continuum. For NGC~253, there is no obvious NIR component at the location of the radio nucleus, but the edge-on orientation and patchy extinction might complicate its detection. Both the diameter and rotation velocity of the molecular rings are very similar. This adds to the increasing evidence that stellar bars and small star formation rings on scales of 50-100~pc are a common feature in late type spirals. This points to an evolutionary connection between spirals of different Hubble type, as suggested by \cite{pfe94}. | 98 | 3 | astro-ph9803108_arXiv.txt |
1404 | 1404.4371_arXiv.txt | We present $^{12}$CO $(J = 1 \rightarrow 0)$ observations of a sample of local galaxies ($0.04 < z < 0.08$) with a large neutral hydrogen reservoir, or ``H{\sc i} monsters''. The data were obtained using the Redshift Search Receiver on the FCRAO 14 m telescope. The sample consists of 20 H{\sc i}-massive galaxies with $M_{\rm HI} > 3\times10^{10}~M_{\odot}$ from the ALFALFA survey and 8 LSBs with a comparable $M_{\rm HI}$($>1.5\times10^{10}~M_\odot$). Our sample selection is purely based on the amount of neutral hydrogen, thereby providing a chance to study how atomic and molecular gas relate to each other in these H{\sc i}-massive systems. We have detected CO in 15 out of 20 ALFALFA selected galaxies and 4 out of 8 LSBs with molecular gas mass $M_{\rm H2}$ of ($1 - 11$)$\times10^9~M_\odot$. Their {\em total} cold gas masses of $(2 - 7)\times10^{10}~M_{\odot}$ make them some of the most gas-massive galaxies identified to date in the Local Universe. Observed trends associated with \hi, \htwo, and stellar properties of the \hi\ massive galaxies and the field comparison sample are analyzed in the context of theoretical models of galaxy cold gas content and evolution, and the importance of {\em total} gas content and improved recipes for handling spatially differentiated behaviors of disk and halo gas are identified as potential areas of improvement for the modeling. | The total cold gas content of typical present day spiral galaxies like the Milky Way is known to be insufficient to maintain the current star formation rate, and additional mass accretion mechanism such as a ``cold flow" \citep{b13, b14} is needed to account for the observed properties \citep{putman06}. The gas mass fraction for such galaxies are thought to be much higher in the earlier epochs at $z \ge 1$, where the average star formation rate is also believed to be higher \citep{b5, b6, b7}. For example, the detection of extremely gas-rich galaxies both in H{\sc i} at intermediate redshift \citep{b11} and in CO at high redshift \citep{b12} indeed indicate the possibility of gas mass function evolution. This is also supported by the time evolution of co-moving $IR$ energy density in Ultra Luminous Infrared Galaxies (ULIRGs), whose burst of star formation activity requires gas-rich progenitors \citep{b9,cap07,mag11}. It is therefore intriguing that ALFALFA survey \citep{g05} has identified very massive H{\sc i} galaxies in nearby universe, representing local analogs with a large cold gas reservoir at higher redshift. An intriguing question to ask is {\it whether these most H{\scriptsize I}-massive galaxies are also associated with correspondingly large molecular mass and high star formation rate (SFR)}. In many numerical modeling of galaxy formation \citep[e.g.][]{dvd10}, gas accretion rate is directly translated into SFR and stellar mass build-up. However, this connection is likely more complex and is not well established observationally. Indeed, the baryon content of many H{\sc i}-massive galaxies found in the ALFALFA survey appears to be already dominated by gas and not by stars even when only atomic hydrogen is considered. In order to explore the connection between atomic-molecular gas and SFR further, we have conducted CO observations of a sample of galaxies at $0.04 < z < 0.08$ with a large cold gas reservoir ($M_{\rm HI} > 3\times10^{10}~M_{\odot}$), dubbed ``H{\sc i} monsters", using the Redshift Search Receiver (RSR) on the FCRAO 14 m telescope. A set of important questions to be addressed in our study are: \begin{itemize} \item Do the most H{\sc i}-massive galaxies also contain a large quantity of molecular gas? \item What is the maximum cold gas (H{\sc i} $+$ H$_2$) content of normal galaxies in the field? \item What type of galaxies manage to accumulate such a large cold gas reservoir? \item What is the atomic-to-molecular gas mass ratio and is it related to other properties such as stellar mass, surface mass density, and colour? \end{itemize} \begin{figure*} \label{fig_hipro} \centering \epsfig{file=fig_hipro1,width=0.45\linewidth}\epsfig{file=fig_hipro2,width=0.45\linewidth} \vspace{-0.8cm} \caption{Atomic gas mass ($M_{\rm HI}$) as a function of stellar mass (left) and $u$ -- $r$ colour (right) corrected for galactic extinction using the reddening maps of \citet{sch98}. Note that five galaxies among our sample whose SDSS colour is not available are missing on the right figure. H{\sc i} monsters are shown as red circles, H{\sc i} detections from COLD GASS DR2 \citep{as1, as2} as blue triangles (124 out of total 306 DR2 sample), and H{\sc i} non-detections from COLD GASS DR2 as green downward arrows (182 out of total 306 DR2 sample).Four galaxies not covered by the SDSS are not shown here.} \end{figure*} \begin{table*} \centering \caption{General properties of 28 H{\sc i} Monsters} \begin{threeparttable} \begin{tabular}{@{}ccccccccccc@{}} \hline ID & SDSS ID & $D_{L}$ & bt\tnote{a} & $M_\ast$ & $\mu_\ast$ & $D_{\rm 25}\tnote{a}$ & $u$ -- $r$ & $M_{\rm HI}$ & SFR$_{SDSS}$ & SFR$_{IR}$ \\ & & [Mpc] & [mag] & [log~M$_\odot$] & [log~M$_\odot$/kpc$^2$] & [\arcsec] & & [log~M$_\odot$] & [$M_\odot$/yr] & [$M_\odot$/yr] \\ \hline \multicolumn{9}{l}{- 20 ALFALFA sample}\\ AGC174522 & J075654.18$+$143827.8 & 208.41 & 16.26 & 10.71 & 8.72 & 41.51 & 1.84 & 10.52 & 5.43 & 2.43\\ AGC004552 & J084321.39$+$104333.8 & 205.06 & 15.07 & 11.02 & 8.48 & 58.63 & 2.35 & 10.59 & 0.69 & 1.26\\ AGC192542 & J090023.77$+$071828.3 & 260.12 & 17.67 & 9.67 & 7.86 & 22.81 & 1.19 & 10.62 & 3.48 & 1.15\\ AGC192885 & J091458.59$+$044200.7 & 244.67 & 16.05 & 11.12 & 8.91 & 49.91 & 2.53 & 10.59 & 4.58 & 4.53\\ AGC192040 & J094732.80$+$104508.6 & 208.23 & 17.20 & 10.54 & 9.48 & 17.30 & 2.72 & 10.74 & 0.04 & $\le2.5$\\ AGC005543 & J101620.49$+$044919.2 & 202.07 & 15.04 & 11.16 & 8.58 & 37.86 & 2.24 & 10.70 & 0.85 & 2.57\\ AGC005737 & J103353.36$+$111225.3 & 220.00 & 15.24 & 11.20 & 8.55 & 46.57 & 2.50 & 10.59 & 0.24 & 1.24\\ AGC205181 & J104426.09$+$152348.5 & 240.55 & 16.94 & 10.51 & 8.68 & 30.07 & 2.35 & 10.57 & 0.28 & 0.80\\ AGC06206A & J110949.30$+$124617.3 & 186.54 & 14.77 & 10.44 & 8.53 & 41.51 & 1.82 & 10.54 & 4.32 & 5.00\\ AGC215200 & J114914.07$+$153650.7 & 249.40 & 17.50 & 10.57 & 8.78 & 21.29 & 2.09 & 10.52 & 2.36 & $\le3.1$\\ AGC222077 & J120939.10$+$051608.6 & 194.52 & 15.60 & 10.81 & 8.55 & 49.91 & 2.34 & 10.50 & 0.43 & 0.65\\ AGC008585 & J133613.44$+$102841.5 & 237.02 & 15.21 & 11.46 & 8.95 & 52.26 & 2.64 & 10.64 & 0.37 & 1.29\\ AGC230856 & J135638.03$+$121530.6 & 253.44 & 17.02 & 10.28 & 7.94 & 42.48 & 1.75 & 10.54 & 2.68 & 1.24\\ AGC009162 & J141848.49$+$105037.7 & 245.82 & 15.65 & 11.02 & 8.89 & 57.30 & 2.51 & 10.64 & 0.25 & 1.47\\ AGC244246 & J142327.99$+$083542.1 & 247.65 & 16.67 & 11.04 & 9.23 & 36.15 & 2.79 & 10.56 & 0.11 & $\le1.2$\\ AGC714136 & J143407.62$+$080755.7 & 235.15 & 16.29 & 10.94 & 8.72 & 26.80 & 2.11 & 10.57 & 4.43 & 1.21\\ AGC009515 & J144621.37$+$130115.5 & 204.79 & 15.54 & 11.01 & 8.71 & 42.48 & 2.63 & 10.64 & 0.09 & 0.44\\ AGC009727\tnote{c} & J150735.63$+$143252.7 & 194.83 & 15.03 & 10.99 & 8.62 & 60.00 & 2.01 & 10.55 & ... & 2.69\\ AGC262058 & J160322.20$+$150029.4 & 252.52 & 17.39 & 9.78 & 7.86 & 28.72 & 1.56 & 10.62 & 2.10 & 0.48\\ AGC260164 & J160538.07$+$100207.4 & 176.55 & 15.20 & 10.89 & 8.62 & 48.77 & 2.10 & 10.51 & 4.31 & 3.58\\ \multicolumn{9}{l}{- 8 LSB sample}\\ UGC000605\tnote{b c} & ..... & 291.46 & 16.36 & 10.98 & ... & 52.26 & ... & 10.60 & ... & 2.09\\ UGC001941\tnote{b c} & ..... & 200.03 & 16.54 & 11.12 & ... & 80.94 & ... & 10.40 & ... & 0.64 \\ UGC002224\tnote{b c} & ..... & 162.08 & 16.84 & 10.96 & ... & 53.48 & ... & 10.30 & ... & 0.41\\ PGC089535\tnote{b c} & ..... & 194.88 & 16.71 & 10.46 & ... & 47.66 & ... & 10.30 & ... & 0.50\\ UGC005440 & J100535.79$+$041645.8 & 280.45 & 16.96 & 10.70 & 8.35 & 49.91 & 2.15 & 10.80 & 2.14 & 0.91\\ UGC006124 & J110339.49$+$315129.3 & 203.92 & 16.36 & 11.04 & 9.23 & 72.14 & 2.76 & 10.30 & 0.24 & 1.00\\ PGC089614 & J123036.25$+$243448.7 & 297.37 & 17.56 & 10.42 & 8.31 & 32.22 & 2.15 & 10.20 & 1.89 & $\le3.7$\\ PGC042102 & J123659.34$+$141949.3 & 370.95 & 18.27 & 10.84 & 9.04 & 11.97 & 2.95 & 10.60 & 0.08 & $\le7.7$\\ \hline \end{tabular} \begin{tablenotes} \item[a] Data compiled from Hyper-Leda. \item[b] SDSS data not available. \item[c] Stellar masses are computed from K band magnitude. \end{tablenotes} \end{threeparttable} \label{table_properties} \end{table*} In this work, we complement our atomic and molecular gas mass data with available SDSS photometry (DR7; \citealt{sdssdr7}) and MPA-JHU DR7\footnote{http://www.mpa-garching.mpg.de/SDSS/DR7/} catalogue (\citealt{kauffmann03}) to extract information of the sample galaxies such as stellar mass, stellar surface mass density and colour. We also analyze the infrared-derived star formation rate using the 22 \micron\ photometry from the Wide-field Infrared Survey Explorer \citep[WISE; ][]{wright10} in order to account for dust obscured star formation activity. With this information, we compare H{\sc i} monsters with galaxies having similar stellar mass range from COLD GASS survey \citep{as1,as2}, which we adopt as a { \color{black}reference sample to examine whether our H{\small I} monsters are exceptional in their properties}. This paper is organized in the following order. In \S\ref{sample}, we describe our sample selection criteria and general properties of the sample. In \S\ref{obs and data reduction} we describe the observations and data reduction. In \S\ref{results} we present atomic and molecular properties of H{\sc i} monsters compared to the { reference sample}, and discuss our results in \S\ref{discussion}. We summarize our results and discussions in \S\ref{summary}. Throughout this paper, we assume a standard flat $\Lambda$CDM cosmology with $H_0$ = 70 km s$^{-1}$ Mpc$^{-1}$, and we adopt a constant ${\rm CO} - {\rm H_{2}}$ conversion factor of $\alpha_{\rm CO}$ = $3.2~M_\odot$~(K~km~s$^{-1}$ pc$^2$)$^{-1}$, unless otherwise mentioned. The conversion factor we use corresponds to $X_{\rm CO} = 2\times10^{20}$~\xcounits, which is commonly accepted value for MW like normal spirals (\citealt{sm96}). Note that we do not include helium in the calculation in this work. | \label{discussion} In this section, we discuss how the molecular gas and total gas masses of the H{\sc i} monsters correlate with various stellar properties (stellar mass, stellar surface mass density, $u$ -- $r$ colour) and star formation activities. Being most gas-massive galaxies (and gas-richest in most cases) in the Local Universe, these \hi\ monsters offer the most stringent test to various physical correlations identified between gas and stellar properties and could in turn offer valuable insights on physical processes that govern these trends. We also touch on the implications on theoretical studies of cold gas content in galaxies. \subsection{Molecular gas and optical properties} \subsubsection{Stellar mass and colour} \label{Stellar mass and colour} Among the H{\sc i} monsters, $M_{\rm H2}/M_*$ varies significantly over two orders of magnitude, ranging from $\lesssim$0.015 (AGC009515) to 0.345 (AGC222077). The median value of $M_{\rm H2}$/M$_{\ast}$ for the CO detected H{\sc i} monsters is 0.075, which is similar to the average $M_{\rm H2}/M_*$ of the COLD GASS galaxies, $0.066 \pm 0.039$ \citep{as1}. Molecular gas masses of the \hi\ monsters and the comparison sample of COLD GASS galaxies normalized by stellar mass ($M_{\rm H2}/M_*$) are shown along the upper row of Figure~\ref{fig_optgfr}. H{\sc i} monsters are found at the upper end of the normalized \htwo\ mass distribution for a given stellar mass and $u-r$ colour, which is also true for the normalized H{\sc i} mass (bottom panels). This confirms the conclusion from \S\ref{relation_h1_h2} that our H{\sc i}-massive galaxies also tend to have a large \htwo\ gas reservoir. After analyzing the molecular and atomic gas contents of the COLD GASS sample, \citet{as1} have reported that the mean molecular gas fraction $M_{\rm H2}/M_*$ does not strongly depend on stellar mass, stellar surface mass density, or concentration index, while it has a strong dependence on the $NUV-r$ colour. Our analysis of the combined \hi\ monsters and COLD GASS sample shown in Figure~\ref{fig_optgfr} confirms the earlier conclusions by \citet{as1}, including a correlation between $M_{\rm H2}/M_*$ and $u-r$ colour. This correlation indicates that molecular gas content is indeed closely tied to galaxy stellar properties and that a large dispersion in molecular gas fraction as a function of $M_*$ and $\mu_*$ reflects a wide spectrum of star formation history associated with individual galaxies, as indicated by their optical colour \citep[e.g.][]{b4}. This connection between the gas properties and star formation activity is examined further below in section \S~\ref{sec:sfr}. The scatter in the broad trends seen in all six panels of Figure~\ref{fig_optgfr} is systematically smaller for the \hi\ monsters compared with the COLD GASS sample. The tight correlation between $M_{\rm HI}/M_*$ and $M_*$ seen in the bottom left panel is almost certainly due to the sample selection, as the \hi\ monsters represent the most \hi-massive galaxies with a narrow range of $M_{\rm HI}$ (see Fig.~\ref{fig_hipro}). A broad correlation between $M_{\rm HI}$ and $M_{\rm H2}$ (Fig.~\ref{fig_mhimh2}) offers a natural explanation for the systematic displacement of the \hi\ monsters on the higher \htwo\ mass fraction side of the mean trends in the upper panels, while a large scatter in the $M_{\rm HI}$-$M_{\rm H2}$ correlation translates to a larger dispersion in the \htwo\ mass fraction trends. Given the tighter correlation between $M_{\rm HI}/M_*$ and $M_{\rm H2}/M_*$ (right panel in Fig.~\ref{fig_mhimh2}), a better overlap between the \hi\ monsters and the COLD GASS sample is expected in the correlation between \htwo\ mass fraction and $u-r$ colour. Indeed the two samples overlap better, but a small systematic offset persists. As discussed in some length by \citet{as1}, a comparison of CO data from different telescopes can be problematic with possible systematic differences in calibration and aperture correction. The relative calibration between our data and the IRAM 30~m telescope seems quite good, at least for compact sources, as demonstrated by the comparison of the measured CO line integrals for a sample of ultra-luminous infrared galaxies as shown in Figure~5 of \citet{c09}. Stellar disks of some of the \hi\ monsters are slightly larger than the 50$''$ beam of the RSR (see Fig.~\ref{fig_rsrsp}), and the resulting \htwo\ masses may be a slight {\em under-estimate} in some cases. In contrast, the COLD GASS sample galaxies were observed with a beam only 22$''$ in size, requiring an empirical aperture correction in nearly all cases \citep{as1}. The COLD GASS sample and \hi\ monsters overlap better on the redder end ($u-r>2$), and the apparent difference among late type galaxies may reflect either a true systematic shift in balance among atomic, molecular, and stellar mass density (see \S~\ref{sec:sfr}) or a systematic error in the aperture correction by Saintonge et al. among these late type galaxies. \subsubsection{Stellar and gas surface mass density} \label{stellar mass density and conc} \citet{as1} found little dependence between molecular gas fraction ($M_{\rm H2}$/$M_\ast$) and stellar surface mass density ($\mu_\ast$), and this is also seen among the H{\sc i} monsters and the COLD GASS galaxies in Figure~\ref{fig_optgfr}. This is somewhat surprising since \citet{br06} have found a tight correlation between molecular-to-atomic gas mass ratio $R_{mol} \equiv \mu_{\rm H2}/\mu_{\rm HI}$ and the mid-plane hydrostatic pressure $P_{\rm ext}$, which is controlled by the stellar surface mass density $\mu_*$. In Figure~\ref{fig_stdgsd}, we compare $R_{mol}$ and $\mu_*$ for the H{\sc i} monsters and the COLD GASS galaxies, and again no correlation is recognizable for the full sample, contrary to the expectations from the pressure-driven gas phase transition scenario. The H{\sc i} monsters by themselves cluster together with a possible underlying correlation between $R_{mol}$ and $\mu_*$ in Figure~\ref{fig_stdgsd}. Note that the ratio between $\mu_{\rm HI}$ and $\mu_{\rm H2}$ is essentially the molecular-to-atomic gas mass ratio ($=M_{\rm H2}/M_{\rm HI}$) when one characteristic size is adopted for individual galaxies, which is the case here. The grey dashed line is a linear bisector fit to all H{\sc i} and CO detected galaxies in both samples, and the scatters around this line of H{\sc i} monsters and COLD GASS galaxies are 0.27 dex and 0.39 dex, respectively. The dotted line represents a bisector fit only for the \hi\ monsters excluding one outlier - AGC192040, and the correlation seems to be much stronger with $\sigma$ of only 0.14 dex. The outlier, AGC192040 has a compact/red central component with ring-like stellar arms, and its morphology is not typical of a disk galaxy. This system might be the result of recent merging and thus not follow the same pressure-density relation as normal spirals. AGC230856, which appears to be a normal spiral yet with unusually blue colour (the bluest after two least massive galaxies), is also labelled but still included in our statistics. This galaxy is likely to have gone through a distinct evolution from normal spirals and natural to deviate from other gas-massive galaxies in the opposite sense from the AGC192040's case. \begin{figure} \centering \vspace{-0.5cm} \epsfig{file=fig_stdgsd,width=1.0\linewidth,clip=} \vspace{-1.2cm} \caption{Stellar mass surface density $\mu_*$ vs. $R_{mol}=M_{\rm H2}/M_{\rm HI}$. Symbols are same as Figure~\ref{fig_optgfr}. The dashed line is a linear bisector fit to all galaxies in both samples, and the scatter about this broad trend is large, $\sigma=0.39$. The dotted line is a linear bisector fit to CO detections of H{\sc i} monsters excluding two extreme outliers (labeled in the figure), and the scatter among the \hi\ monsters excluding the two outliers is 0.14 dex.} \label{fig_stdgsd} \end{figure} \begin{figure*} \centering \epsfig{file=fig_dengs1.ps,width=0.45\linewidth,clip=}\epsfig{file=fig_dengs2.ps,width=0.45\linewidth,clip=} \vspace{-0.8cm} \caption{Mean atomic gas surface density $\mu_{\rm HI}$ (left) and molecular gas surface density $\mu_{\rm H2}$ (right) of the H{\sc i} monsters and COLD GASS galaxies, which are defined in the same manner as $\mu_*$, following eq.~(1), are shown as a function of stellar mass density $\mu_*$. Symbols and colours are the same as Figure~\ref{fig_mhimh2}. \label{fig_sigmas}} \end{figure*} A clue to the lack of any correlation between molecular mass fraction ($M_{\rm H2}/M_*$) and molecular-to-atomic gas mass ratio ($R_{mol}$) with stellar surface mass density $\mu_\ast$ in Figures~\ref{fig_optgfr} \& \ref{fig_stdgsd} emerges when atomic and molecular surface mass density ($\mu_{\rm HI}$ and $\mu_{\rm H2}$ - computed in the same way as $\mu_{\ast}$) are compared with $\mu_\ast$ as shown in Figure~\ref{fig_sigmas}. A comparison of atomic gas and stellar mass density, shown on the left panel, again shows no correlation, suggesting that these two quantities are independent of each other. Galaxies with different $u-r$ colour separate themselves in stellar mass density $\mu_*$, and the dispersion in atomic gas density $\mu_{\rm HI}$ is equally large across the full range of $\mu_*$. On the other hand, a comparison of $\mu_{\rm H2}$ with $\mu_\ast$ on the right panel shows a clear correlation, indeed suggesting the correlation between the {\em molecular gas density} and the stellar mass density. This correlation becomes significantly tighter when the galaxies are sorted by their $u-r$ colour, suggesting that galaxy colour is an important secondary parameter underlying this correlation between $\mu_{\rm H2}$ and $\mu_{\ast}$. Galaxies with blue colour ($u-r < 2.5$) in particular forms a tight trend with $\sigma \lesssim 0.2$ in dex, while redder galaxies also show a similar trend but displaced in $\mu_\ast$ by a factor of $\sim$5. The absence of any correlation between $\mu_{\rm HI}$ with $\mu_\ast$ and a tight correlation between $\mu_{\rm H2}$ with $\mu_\ast$ with a strong $u-r$ colour dependence shown in Figure~\ref{fig_sigmas} offers a natural explanation for the lack of any correlation between molecular-to-atomic gas mass ratio ($R_{mol}$) with stellar surface mass density $\mu_\ast$ among the COLD GASS sample in Figure~\ref{fig_stdgsd} and the apparent correlation in the same plot for the \hi\ monsters. The former is a trivial outcome of $\mu_{\rm HI}$ being independent of $\mu_\ast$, as $R_{mol}=\mu_{\rm H2}/\mu_{\rm HI}$ should also be independent of $\mu_\ast$, regardless of any correlation between $\mu_\ast$ and $\mu_{\rm H2}$. Given that, the apparent correlation among the \hi\ monsters is somewhat unexpected. It turns out this correlation arises because the \hi\ monsters have a narrow range of \hi\ masses by the sample definition, similar to the apparent tight trend seen between $M_{\rm HI}/M_*$ and $M_*$ in Figure~\ref{fig_optgfr}. In other words, the apparent correlation between $R_{mol}$ and $\mu_\ast$ among the \hi\ monsters also reflects the correlation between $\mu_{\rm H2}$ and $\mu_\ast$. Some of the \hi\ monsters show a slightly elevated level of $\mu_{\rm H2}$ for their given $\mu_*$ and colour (as discussed in \S~\ref{Stellar mass and colour}), but this enhancement is not enough to disrupt the observed correlation. The surface mass densities $\mu_{\rm HI}$, $\mu_{\rm H2}$ and $\mu_\ast$ discussed here are {\em global} averages, normalized by the characteristic size of their stellar disk, and this is an important difference from the quantities considered by \citet{br06} in explaining the physical connection between {\em local} molecular-to-atomic gas mass ratio ($R_{mol}$) with {\em local} stellar surface mass density (or pressure). The observed correlation between $\mu_{\rm H2}$ with $\mu_\ast$ in Figure~\ref{fig_sigmas} suggests that the scaling relation between molecular gas and stellar disk holds well even at global scales, although there is also a clear systematic dependence on the colour (and thus stellar population and possibly spatial distribution). The absence of correlation between {\em globally averaged} $\mu_{\rm HI}$ with $\mu_\ast$ indicates the disconnect in spatial distribution between atomic gas and stellar disk \citep[i.e. $R_{\rm HI}>R_{\rm H2}$, see][]{walter08}, as well as between total \hi\ and stellar mass, as discussed earlier (in \S~\ref{monsters}). % The breakdown of the correlation between gas and stellar surface mass densities on global scales has an important consequence in the modeling of the gas content and star formation evolution in galaxies as we discuss further below. \begin{figure*} \centering \epsfig{file=fig_sfmfr1,width=0.5\linewidth,clip=}\epsfig{file=fig_sfmfr2,width=0.5\linewidth,clip=} \vspace{-1.2cm} \caption{Molecular gas fraction ($M_{\rm H2}/M_*$) as a function of star formation rate (SFR) and specific star formation rate (SSFR=SFR$/M_*$). Symbols and lines are same as Figure~\ref{fig_optgfr}. \label{fig_sfpro}} \end{figure*} \subsection{Gas content and star formation history} \subsubsection{Star formation rate and molecular gas content} \label{sec:sfr} As noted previously by \citet{as1}, the tightest correlation seen among the comparisons of different gas and stellar properties of the \hi\ monsters and the COLD GASS sample is also the tight relation between molecular gas fraction $M_{\rm H2}/M_*$ and $u$ -- $r$ colour (upper middle panel in Fig.~\ref{fig_optgfr}). In the previous section, we found a clear correlation between molecular gas and stellar surface density (right panel of Fig.~\ref{fig_sigmas}) while no correlation is found between $\mu_{\rm HI}$ and $\mu_*$ (left panel), suggesting a physical disconnect between spatial distribution (and/or relevant time scales) of atomic gas and stellar component. Taken together, these observations suggest a close physical link between star formation activity primarily with molecular gas content of galaxies on global scales. Earlier CO surveys have reported a tight correlation between CO and far-$IR$ luminosity among normal and starburst galaxies, and this is interpreted similarly as a scaling relation between the amount of molecular gas and the luminosity from young stars forming within \citep[see review by][]{young91}. To explore this idea further, we have compiled optically derived star formation rate (SFR) estimates from the MPA-JHU DR7 database\footnote{http://www.mpa-garching.mpg.de/SDSS/DR7/sfrs}, which uses the SDSS spectra and photometry and the method described by \citet{brinchmann}. We have also derived $IR$-based estimate of SFR using the WISE 22 \micron\ photometry (see \S~\ref{quantities}). These two different estimates show a good agreement within the SFR range of 0.1 and 10 $M_\odot$ yr$^{-1}$ represented by the \hi\ monsters and the COLD GASS sample, although the dispersion in the correlation is significant ($\sigma \sim 0.3$ in dex). A comparison of molecular gas fraction versus star formation rate and specific star formation rate (sSFR) shows a much tighter correlation with the $IR$-derived quantities (e.g., $\sigma=0.25$, compared with $\sigma=0.38$ for the SDSS). Therefore, we limit our discussion to the $IR$-derived star formation quantities from this point on. Molecular gas fraction and star formation rate SFR track each other broadly, as shown on the left panel of Figure~\ref{fig_sfpro}. Galaxies with a higher SFR tend to have a larger fractional molecular gas content, and the \hi\ monsters are nearly indistinguishable from the comparison COLD GASS sample. The scatter among individual galaxies is still large for both samples ($\sigma=0.27$ for the \hi\ monsters, $\sigma=0.35$ for the whole sample), but this correlation is clearly seen spanning all galaxies of different types and colours (red galaxies to the bottom left and blue galaxies to the top right). Specific star formation rate is even more tightly correlated with the molecular gas fraction (see the right panel), having the smallest value of $\sigma=$ 0.13 dex for the \hi\ monsters and $\sigma=$ 0.25 dex for the entire sample. Most H{\sc i} monsters follow the same relation as the COLD GASS galaxies, although the systematic offset from the { reference sample} is visible again (see below). % A tighter correlation between $M_{\rm H2}/M_*$ and sSFR, rather than with SFR, is somewhat unexpected, but this appears to be a different realization of the linear scaling relationship between the amount of molecular gas and the amount of young stars that are forming within them. Since specific star formation rate is by definition SFR normalized by $M_*$, the correlation seen on the right panel of Figure~\ref{fig_sfpro} is the correlation between $M_{\rm H2}$ and $SFR$, both normalized by $M_*$ to remove the distance dependence. This correlation shows the smallest dispersion among all comparisons of physical quantities we have examined for the \hi\ monsters and the COLD GASS sample, and this is likely the most fundamental relation that threads all types of galaxies represented in this study. The small systematic offset seen between the \hi\ monsters and the { reference sample} on the right panel of Figure~\ref{fig_sfpro} is surprising, given the tightness of the correlation ($\sigma=0.13$). Besides the \hi\ monsters, several other COLD GASS galaxies are also offset from the main trend, in the manner that can be interpreted as having a SFR 2-3 times {\em smaller} for their given molecular gas mass. As discussed in \S~\ref{Stellar mass and colour}, this offset may largely reflect the sample selection of galaxies with the largest cold gas content. However, we already established no physical link between \hi\ content and SFR (\S~\ref{stellar mass density and conc}), and a {\em lower SFR for given molecular gas mass among the H{\small I} monsters} requires a different explanation. % Cold gas content and consumption is only a quasi-static balance among gas accretion from the halo to the disk, star formation, recycling of the star-gas cycle, and feedback \citep[e.g., ][]{bau10}. Small changes in the physical condition may swing this balance between $M_{H2}$ and $SFR$, for example, as seen among the \hi\ monsters, or the very condition that has led to the large \hi\ reservoir may simultaneously lead to the shift in the balance as observed. These are only conjectures at the moment, but this issue may deserve a further attention in future studies. \begin{figure*} \centering \epsfig{file=fig_ssfrt1.ps,width=0.45 \linewidth,clip=}\epsfig{file=fig_ssfrt2.ps,width=0.45 \linewidth,clip=} \vspace{-0.8cm} \caption{Molecular gas depletion timescale $\tau_{dep,\rm H2}$= $M_{\rm H2}$/SFR (left panel) and total cold gas depletion timescale $\tau_{dep,\rm HI+H2}$ = ($M_{\rm HI}+M_{\rm H2}$)/SFR (right panel) as a function of specific star formation rate. Symbols and colours are the same as Figure~\ref{fig_mhimh2}. Long dashed line represents the Hubble time of 14 Gyr. The dotted line on the left panel corresponds to the constant molecular gas depletion time in nearby disk galaxies by \citet{bigiel11}.} \label{fig_ssftim} \end{figure*} \subsubsection{Total and molecular gas consumption/depletion time} \label{sec:tausfr} One of the main motivations for conducting this study was testing whether a larger neutral atomic gas content (``reservoir") automatically translates to a larger molecular gas mass and a higher SFR, as commonly formulated in cosmological simulations of galaxy growth and cold gas content evolution \citep[e.g., ][]{obr09a,bau10,fu10,lagos11}. Our new CO survey of \hi\ monsters confirms that galaxies with the largest \hi\ content in the Local Universe also tend to have the top end of the range of molecular gas content among the galaxies of similar stellar mass and colour (see \S~\ref{relation_h1_h2}). However, H{\sc i} monsters are {\em not} more efficient in forming stars for their abundant molecular gas mass. In fact, they may be systematically {\em less} efficient in turning their molecular gas into stars, as discussed in the previous section (\S~\ref{sec:sfr}). This in turn means that the time scale for consuming their entire molecular gas reservoir at the current star formation rate should be longer for the H{\sc i} monsters. As seen on the left panel in Figure~\ref{fig_ssftim}, molecular gas depletion time ($\tau_{dep,\rm H2}\equiv M_{\rm H2}/$SFR) is broadly correlated with specific star formation rate with a large scatter. At a given specific star formation rate, H{\sc i} monsters have a systematically larger value of $\tau_{dep,\rm H2}$ than the { reference sample} COLD GASS galaxies. The median values of the molecular gas depletion time are 2.0~Gyr and 4.3~Gyr for the CO detected COLD GASS galaxies and H{\sc i} monsters, respectively. The ``constant" molecular gas depletion time of 2.35 Gyr in nearby spiral galaxies derived by \citet{bigiel11} (dotted line) runs approximately through the middle of the data points. While the Bigiel et al. report an apparent scatter of $\sim 0.2$ in dex (see their Figure 2) for their spiral galaxies, the spread in $\tau_{dep,\rm H2}$ for the COLD GASS and \hi\ monsters is several times larger than this scatter in the mean relation and has a systematic dependence on sSFR. A short molecular gas depletion time (compared with the Hubble time, long dashed line), especially for the COLD GASS sample, {\em requires} a continuous replenishment of cold gas from the surrounding halo if their current SFR were to be sustained \citep[e.g., ][]{putman06}. We also find that the addition of $M_{\rm HI}$ greatly extends the gas depletion time to close to or exceeding the Hubble time, and the gas supply that can fuel the current level of star formation is readily found in the \hi\ phase in many cases. Neutral hydrogen in and around galaxies is widely viewed as the reservoir for supplying gas to mostly molecular gas disk and the associated star formation activity \citep[e.g.,][]{bau10}. The {\em total} cold gas depletion time ($\tau_{dep,\rm HI+H2}\equiv M_{\rm HI+H2}/$SFR, right panel in Figure~\ref{fig_ssftim}) suggests that nearly all \hi\ monsters and a significant fraction of the \hi\ detected COLD GASS galaxies can sustain their current level of star formation for the Hubble time or longer. Numerical studies such as by \citet{b13} suggest that the current gas accretion rate onto DM halo is $\le10\%$ of the peak rate during the first 3 Gyr following the Big Bang. {\em Our analysis shows that the diminished inflow from the $\ge100$ kpc scale halo at the present epoch is not a critical factor in sustaining the current star formation activity in many of these galaxies, and understanding the processes that lead to and regulating the present H{\small I} content may be a more critical step in achieving a better understanding of the evolution of present day galaxies.} The total cold gas depletion time $\tau_{dep,\rm HI+H2}$ for bluer, late type galaxies with sSFR $\ge 10^{-10.5}$ yr$^{-1}$ is mostly shorter than the Hubble time, however, and the most actively star forming galaxies in the Local Universe still require a significant inflow of fresh gas from their halo in order to sustain their current SFR \citep[also true for the Milky Way Galaxy, see ][]{putman06}. \begin{figure*} \epsfig{file=fig_dstfgs.ps,width=0.34\linewidth,clip=} \hspace{-0.5cm}\epsfig{file=fig_mstfgs.ps,width=0.34\linewidth,clip=} \hspace{-0.5cm}\epsfig{file=fig_mstfh2.ps,width=0.34\linewidth,clip=} \vspace{-0.3cm} \caption{Total gas mass fraction ($f_g \equiv \frac{M_{\rm HI}+M_{\rm H2}}{M_{\rm HI}+M_{\rm H2}+M_*}$) and molecular gas mass fraction ($f_{\rm H2} \equiv \frac{M_{\rm H2}}{M_{\rm H2}+M_*}$) as a function of stellar surface mass density ($\mu_*$, left panel) and stellar mass ($M_*$, middle and right panel). Ensemble means and standard deviations for the COLD GASS sample are shown as large empty circles with error bars in the middle and right panel. Symbols and colours are the same as Figure~\ref{fig_mhimh2}.} \label{fig_fgas} \end{figure*} \subsubsection{Molecular and total gas mass fraction} \label{sec:fg} Among the galaxies detected in both H{\sc i} and CO, the gas to stellar mass fraction of the H{\sc i} monsters, $M_{\rm HI+H2}/M_*=0.74\pm0.57$, is more than twice as large as that of the { reference sample} ($0.35\pm0.31$). The difference grows to more than a factor of three when galaxies with \hi\ monster-like neutral gas content ($M_{\rm HI} \ge 10^{10} M_\odot$) are removed from the COLD GASS sample. Cold gas is the dominant component of the baryonic mass budget in some of these galaxies, particularly among the \hi\ monsters. Both molecular gas mass fraction and total gas mass fraction are important in understanding mass build-up history of galaxies. \citet{mcgaugh97} have shown that total gas mass fraction of spiral galaxies is strongly correlated with luminosity and surface brightness and can be reproduced by a simple disk evolution model. McGaugh \& de Blok acknowledged the importance of molecular gas as the main fuel for star formation, but they did not have the appropriate data to incorporate molecular gas into their analysis properly. Instead they modeled the molecular gas content based on the observed trends between $R_{mol}$ and Hubble type \citep{young89}. As shown in the previous section, \hi\ dominates the total cold gas content among local galaxies, and this model-based accounting of molecular gas contribution probably had only a minor impact on the conclusions by McGaugh \& de Blok. The correlation between total gas mass fraction and surface brightness reported by McGaugh \& de Blok is reproduced on the left panel of Figure~\ref{fig_fgas}. A broad trend of a higher gas mass fraction for galaxies with a lower stellar density is present although dispersion in the trend is significantly larger in the new data (compared with their Figure~7). The difference may arise from our using actual \htwo\ masses derived from CO measurements and using $\mu_*$ rather than central $B$-band surface brightness. Colour-tagging galaxies by their $u-r$ colour also reveals that much of the correlation reflects the segregation of galaxies with different colour (i.e., star formation history). One clear outlier in this plot is the \hi\ monster AGC192040, which is an unusual galaxy with a compact, red central stellar component and ring-like stellar arms (see \S~\ref{stellar mass density and conc}). Total gas mass fraction ($f_g \equiv \frac{M_{\rm HI}+M_{\rm H2}}{M_{\rm HI}+M_{\rm H2}+M_*}$) is compared with stellar mass $M_*$ in the middle panel of Figure~\ref{fig_fgas}. Two trends are obvious: (1) total gas mass fraction increases rapidly with decreasing stellar mass; and (2) total gas mass fraction of \hi\ monsters are nearly twice as large as the ensemble average of the COLD GASS sample at a given stellar mass. Both of these trends could have been predicted from Figures~\ref{fig_hipro}~\&~\ref{fig_h2pro} which showed that \hi\ and \htwo\ masses are independent of $M_*$ and that \hi\ monsters have the highest $M_{\rm HI}$ and $M_{\rm H2}$ at a given stellar mass. The \hi\ monsters trace the upper envelop of the gas mass fraction distribution, well above the ensemble mean trend. In fact, most of the \hi\ monsters are more than $2\sigma$ above the ensemble mean, suggesting that they may represent a distinct population. Molecular gas mass fraction ($f_{\rm H2} \equiv \frac{M_{\rm H2}}{M_{\rm H2}+M_*}$), shown on the right panel of Figure~\ref{fig_fgas}, display a rather different behavior from the total gas mass fraction just discussed. Unlike the total gas mass fraction $f_g$, molecular gas mass fraction $f_{\rm H2}$ is a much flatter function of stellar mass, with only a weak systematic trend with $M_*$ is seen. Furthermore, \hi\ monsters mostly {\em follow} the same trend as the COLD GASS sample, rather than standing apart as did for the total gas mass fraction as discussed above, although a few exceptions stand out. This completely different behavior was already seen in the comparison of $\mu_{\rm HI}$ and $\mu_{\rm H2}$ with $\mu_*$ in Figure~\ref{fig_sigmas}, which suggests a close physical link between stellar mass and molecular gas and a disconnect from neutral atomic gas. The nearly linear correlation seen between $\mu_{\rm H2}$ and $\mu_*$ would naturally lead to a flat dependence of $f_{\rm H2}$ on $M_*$ with a mean ratio of 0.05-0.08 across the entire stellar mass range representing late type galaxies. \subsection{Implications on modeling galaxy gas content and star formation rate evolution} \label{sec:theory} Obtaining better understanding of gas physics and cold gas content evolution is a critical next step in connecting galaxy evolution theory with observations of baryonic tracers \citep{yun09,putman09,carilli13}, and this realization has spun a series of recent papers on modeling cold gas content in galaxies and its cosmic evolution \citep{or09,bau10,power10,lagos11a,lagos11}. The weak correlations we found among \hi, \htwo, and stellar mass for the \hi\ monsters and the COLD GASS comparison sample bode poorly for semi-analytic models that incorporate mainly the mean global trends. For example, \citet{lagos11} have shown that modeling gas content through post-processing of a cosmological simulation \citep[e.g.,][]{or09,power10} does a poor job of recovering the local \hi\ mass function, while a self-consistent approach building on the derived merger trees is more successful. A series of tests performed by \citet{lagos11a,lagos11} have also shown that different star formation recipes can lead to drastically different gas masses and molecular fractions, demonstrating the necessity for a certain level of sophistication and care in modeling gas physics. An illuminating lesson is the finding by \citet{lagos11a} that a star formation recipe with a linear dependence on gas density ($\Sigma_{SFR}\propto\Sigma_{gas}$) does a better job of reproducing the observed gas content in local galaxies than a non-linear formulation (e.g., Schmidt-Kennicutt ``law", $\Sigma_{SFR}\propto\Sigma_{gas}^N$). While ample evidence exists for a non-linear dependence of $\Sigma_{SFR}$ on $\Sigma_{gas}$ on sub-kpc scales \citep[e.g., ][]{bigiel08}, we have shown in Figure~\ref{fig_sigmas} that the observed {\em global} dependence is closer to linear, with an additional complication of a colour-dependence. This empirical trend, as well as the tight linear trend between $M_{\rm H2}$ and SFR discussed in \S~\ref{sec:sfr}, suggests that a recipe with a linear dependence should be more effective, regardless of the true underlying physics, when applied on global scales. Another important clue for future modeling studies revealed by our analysis of cold gas content is the clear disconnect between atomic and molecular gas, particularly in relation to stellar mass and SF activities. The strong dependence of total gas mass fraction $f_g$ on stellar mass $M_*$ seen in the middle panel of Figure~\ref{fig_fgas} offers a stark contrast to the nearly constant molecular mass fraction $f_{\rm H2}$ as a function of $M_*$ seen in the right panel. The absence of correlation between {\em globally averaged} $\mu_{\rm HI}$ with $\mu_\ast$ also indicates the disconnect in spatial distribution between atomic gas and stellar disk, as well as between total \hi\ and stellar mass, as discussed in \S~\ref{CO measurement}. This contrasting behavior between atomic and molecular gas demonstrates a clear need to track the gas within the stellar disk separately from the gas in the larger halo. % A disproportional attention given to molecular mass fraction, motivated by the general expectation of a higher $f_{\rm H2}$ associated with a higher star formation rate in galaxies in the earlier epochs \citep[e.g.,][]{daddi10,tacconi10,geach11}, may also be misplaced. While \htwo\ mass clearly correlates closely with far-$IR$ luminosity and {\em current} SFR, \htwo\ is a minor component in the total cold gas content and accounts for less than 10\% of the baryon mass budget in \hi\ monsters and COLD GASS sample. Also seen in Figure~\ref{fig_fgas} is that \hi\ dominates the entire baryon mass budget among some of the galaxies with stellar mass up to $5\times10^{10}M_\odot$, including many of the \hi\ monsters. Focussing on the total baryon mass budget, \citet{mcgaugh97} have shown that {\em total} gas mass fraction is closely tied with the integrated star formation history among disk galaxies, and this implies total cold gas content (\hi+\htwo) is the important parameter in understanding the evolution of galaxies and stellar mass build-up. We confirm the same general trend using a larger sample with a wider range of galaxy types with actual molecular gas measurements. Furthermore, we find the {\em total} gas depletion time to match or to exceed the Hubble time among nearly all \hi\ monsters and a large fraction of COLD GASS galaxies detected in \hi\ and CO. It is widely believed that \hi\ content and total cold gas budget are regulated by gas accretion from the surrounding halo and quenching induced by environment. Future modeling studies should examine the effectiveness of the recipes dealing with halo gas accretion and quenching and the role of the environment in this regard. While little 21cm \hi\ data exists for galaxies beyond $z\sim 0.1$ today to offer a useful test for these studies, ongoing studies such as the Blind Ultra Deep H I Environmental Survey \citep[BUDHIES, ][]{verheijen07,jaffe12} and the COSMOS \hi\ Large Extragalactic Survey \citep[CHILES, ][]{ximena13} should begin to produce blind surveys of cold gas content covering cosmologically interesting volume to $z\sim 0.45$. | 14 | 4 | 1404.4371 |
1404 | 1404.6142_arXiv.txt | New reverberation mapping measurements of the size of the optical iron emission-line region in quasars are provided, and a tentative size-luminosity relation for this component is reported. Combined with lag measurements in low-luminosity sources, the results imply an emission-region size that is comparable to and at most twice that of the H$\beta$ line, and is characterized by a similar luminosity dependence. This suggests that the physics underlying the formation of the optical iron blends in quasars may be similar to that of other broad emission lines. | The geometry of the broad line region (BLR) in quasars can be studied by means of reverberation mapping, where one tracks flux variations in the emission line in response to continuum fluctuations \citep{np97}. The distance range subtended by the BLR gas implies a highly-stratified medium with high-ionization lines, such as \ion{He}{2}\,$\lambda 1640$ and \ion{C}{4}\,$\lambda 1548$, being formed close to the central continuum-emitting source, possibly on scales comparable to the outer optical-emitting accretion disk \citep[and references therein]{rod97,pet99,c13}, and low ionization species, such as \ion{H}{1}, being emitted from larger regions whose size is comparable to the dust sublimation radius \citep{nl93,sug06}. Complicated radiative transfer physics may also affect the apparent size of the BLR \citep{ben10}. Accumulating statistics have shown that the effective area of the BLR scales in proportion to the quasar luminosity \citep{ben09}. This relation has been relatively well established for the Balmer and \ion{C}{4}\,$\lambda 1549$ emission lines \citep{kas00,kas07}, but has not yet been shown to hold in general. Among the most prominent spectral features in the (rest) optical-UV spectra of quasars are the iron emission blends \citep{bg92}: poorly resolved plethora of numerous emission lines predominantly associated with \ion{Fe}{2}, which can only be partially resolved in narrow line objects \citep{vero04}. Despite several decades of intensive research in the field \citep[and references therein]{wam67,sar68,ok76,col79,net80,gr81,kk81,nw83,wil84,bal04,ver04,zh07,bv08,fer09,sh10,do11}, relatively little is known about the physics of these features. For example, it has been argued that collisional excitation, rather than photo-excitation, is responsible for the bulk of the iron emission \citep{col00}, setting its physics apart from the rest of the BLR \citep[but see][]{ves05}. Further, many models including state-of-the-art atomic data and detailed radiative transfer calculations fall short of explaining the phenomenological properties of those blends. Reverberation mapping of this component has proven difficult \citep{ves05,kue08} with only very recent works being able to place the optically-emitting iron blend region around the Balmer line region in a few objects \citep{bia10,bar13,raf13}. Interestingly, \citet{hu08} find that the apparent kinematics of the iron blends differs from that of other emission lines, providing interesting clues about the BLR physics \citep[see however \citealt{sul12}]{fer09}. Here we report new iron blends' lag measurements for the Palomar-Green sample of quasars from \citet{kas00}, and quantify the size-luminosity relation over four decades in luminosity. Our analysis makes use of (and extends) the multi-variate correlation function (MCF) scheme of \citet{cz13}, and is shown to work in cases where reliable spectral decomposition is difficult to achieve. This paper is organized as follows: the MCF scheme is summarized and extended in section 2. Results for the PG quasars are outlined in section 3, with the discussion following in section 4. \begin{figure*} \plottwo{fig1a.eps}{fig1b.eps} \caption{Spectrum, bandpasses, light curves (left panels) and correlation analyses (right panels) for PG\,1700+518. The mean spectrum for PG\,1700 from the \citet{kas00} dataset (solid line), with the quasar composite spectrum of \citet{dvb01} over plotted (dashed line) in the top left panel. The $B$-band transmission curve is also shown, as are the bands from which the light curves used in this analysis are derived (gray for $f_c$ or $f_c^{sp}$, and blue and red for either of the iron blends). Green triangles mark line-free regions used to fit the underlying continuum with second-order polynomials (median fit values are shown as a solid green curve with models deviating by one standard-deviation traced by the dashed green lines). The wavelength region from which information about H$\beta$ has been extracted is marked by a thick horizontal black line (c.f. table 2 in \citealt{kas00}). Spectro-photometric light curves are denoted by gray points and are shown in the bottom-left panel with the pure spectroscopic continuum light curve marked in thick black circles. The blue and red iron-blend light curves are shown in their respective colors, and are arbitrarily shifted for clarity. Two-dimensional (2D) correlation functions are shown in the right panels: left and right columns for the blue and red iron blends, respectively. Filled contours show the correlation function as calculated using the spectrophotometric light curves, with regular contours marking its values as calculated using the spectroscopic data (warmer colors correspond to larger correlation coefficients). Projected correlation functions are shown in the bottom panels with bright/faded colors corresponding to spectrophotometric/spectroscopic data. Red shades show the corresponding analyses with the kernel version of the correlation function (KMCF, whose 2D versions are not shown).} \label{pg1700} \end{figure*} | We reported time-delay measurements for the optical iron blends in three PG quasars. Taken at face value, and noting the slight advantage of the KMCF algorithm in deducing the lag for the blue iron blend, both iron blends appear to originate from regions of comparable sizes. In what follows we define the mean delay for the iron blend region with an uncertainty bracketing the range covered by the various measurements, all of which are assumed to have similar statistical weights (table 1)\footnote{These uncertainties should {\it not} be considered as proper measurement uncertainties.}. Our sample roughly doubles the number of sources with "reliable" lag determinations for the optical iron blends. \begin{figure} \plotone{fig4.eps} \caption{The rest-frame lag-luminosity diagram for the optical iron emission blends in active galactic nuclei (see legend). Dashed line is the least-squares fit to all reported iron measurements ($K=-19.13$ and $\alpha=0.477$; see text). Light shaded red points correspond to results which are insignificant according to the FR-RSS scheme. Red diamonds mark the typical sampling period of the spectroscopic time series for all 17 quasars in the \citet{kas00} sample. Error bars on the measurements presented in this work should not be treated as formal measurement uncertainties (see text). } \label{rl} \end{figure} \subsection{A tentative size-luminosity relation} Figure \ref{rl} shows a size-luminosity diagram for the iron blend in quasars using our results and those reported for the blue iron blend by \citet{bar13}\footnote{The optical luminosity was determined from the continuum model of \citet[see their Fig. 2]{bar13} and using standard $\Lambda$CDM "737" cosmology. We note that \citet{ben13} report a considerably higher luminosity for NGC\,4593 than Barth et al., which could reflect on the source's flux state at that particular epoch.} and \citet{raf13} for low-luminosity objects. If our measurements are in the right ballpark then they imply, for the first time, a size-luminosity relation for the optical iron-emitting region, whose powerlaw index $\sim 0.5$, hence consistent with similar relations for other lines \citep{kas00,kas07}. Specifically, a fit of the form ${\rm log}(R_{\rm BLR})=K+\alpha {\rm log}(\lambda L_\lambda (5100\,{\rm \AA}))$ to the entire data set (see below) yields\footnote{We estimated the uncertainty on the fit parameters using a value randomization (assuming a uniform distribution over the quoted error intervals for each point) random subset selection scheme. The small size of the sample and the uncertainty in the quoted measurement errors do not warrant a more quantitative regression analysis in our opinion.} $\alpha=0.48\pm0.09$ and $K=-19.1\pm4.4$ (c.f. the H$\beta$ size-luminosity relation of \citealt{ben09} who find $\alpha\simeq 0.52$ and $K\simeq -21.3$). To compare the relative sizes of the iron and H$\beta$ emitting-regions, we have remeasured the size of the latter using the prescription employed above, where the H$\beta$ bands follow the definition of \citet[see their table 6]{kas00} and are shown in figures 1-3. The deduced H$\beta$ lags are reported in table 1 and are on average 50\% larger than those determined by \citet[or only 10\% larger if PG\,1700, having the largest lag uncertainties in their work, is discarded]{kas00}. The iron-to-H$\beta$ emission-region size ratio in our sample covers the range $0.9$-$1.5$, i.e., in qualitative agreement with the range of 1.5-1.9 found by \citet[]{bar13} for two low-luminosity sources. Taken together, the results imply an iron emission-region no larger than about twice that of H$\beta$, which is qualitatively consistent with recent theoretical expectations \citep[see their figure 10]{mn12}. It is further possible to consider the other PGs in the \citet{kas00} sample. The analysis method is identical to that carried out in section 3, but the results are insignificant according to our FR-RSS criterion, as described in section 3 \citep[they are, however, significant according to the algorithm of][]{cz13}. Results for PG\,0052+251, PG\,1226+023, and PG\,0804+761 are shown in figure \ref{rl}. The (K)MCF algorithm could not detect a lagging component in the luminous quasar PG\,1704+608, which is consistent with the relatively small contribution of the iron blends to the spectrum of this source \citep[see their figure 1]{kas00}. Insignificant results were obtained for the fainter PG objects, possibly related to the fact that the sampling period is comparable to the expected lag in those sources \citep[and figure \ref{rl}]{lsst}. Our deduced size-luminosity relation for the iron blends needs, however, to be regarded with caution: there are only handful of detections, with the results for some sources being potentially affected by sampling (PG\,2130 and PG\,0052+251). Further, while hard to quantify in the present work, biases inherent to the MCF method with respect to standard cross-correlation techniques may be present, although likely at the $\lesssim$20\% level \citep{lsst}, which is consistent with our findings for the H$\beta$ line. To overcome those problems, better sampling is required, for more luminous sources\footnote{The analysis of available datasets for low-luminosity sources is beyond the scope of the present work, and will not alleviate the uncertainties at the high-luminosity end.}. Our results imply that the iron emitting region is photoionized by the central source also in luminous quasars, and that its size is roughly consistent with that of Balmer lines emission region. This is also in qualitative agreement with the conjecture of \citet{bg92} based on velocity dispersion considerations. These results, however, are not of sufficient quality to test various scenarios for the origin of the iron-line region \citep{hu08,fer09}. Better spectroscopic data for luminous sources, and/or the use of narrow band filters, combined with photometric reverberation mapping schemes could be very useful for testing the relation found here and arriving at a more coherent picture of the BLR in quasars. | 14 | 4 | 1404.6142 |
1404 | 1404.1886_arXiv.txt | {Many aspects of the design trade-off of a space-based instrument and its performance can best be tackled through simulations of the expected observations. The complex interplay of various noise sources in the course of the observations make such simulations an indispensable part of the assessment and design study of any space-based mission.} {We present a formalism to model and simulate photometric time series of CCD images by including models of the CCD and its electronics, the telescope optics, the stellar field, the jitter movements of the spacecraft, and all of the important natural noise sources.} {This formalism has been implemented in a versatile end-to-end simulation software tool, specifically designed for the PLATO (Planetary Transists and Oscillations of Stars) space mission to be operated from L2, but easily adaptable to similar types of missions. We call this tool {\sc PLATO Simulator}.} {We provide a detailed description of several noise sources and discuss their properties in connection with the optical design, the allowable level of jitter, the quantum efficiency of the detectors, etc. The expected overall noise budget of generated light curves is computed, as a function of the stellar magnitude, for different sets of input parameters describing the instrument properties. The simulator is offered to the scientific community for future use.}{} | Recent uninterrupted long-term $\mu$-mag-precision space photometry opened a new era in time-domain astronomy and has led to numerous exoplanet detections, see, e.g., \citet{Moutou2013} for a review of CoRoT (Convection, Rotation and planetary Transits) results and \citet{Borucki2010,Welsh2012,Batalha2013} for results obtained from the {\it Kepler\/} mission. As a by-product, both space missions also implied a goldmine for stellar variability studies \citep[e.g.,][]{Debosscher2009,Sarro2009,Prsa2011,Debosscher2011}. In particular, detailed seismic probing was finally reached and gave new insights into the physics of stellar and galactic structure, pointing out limitations of standard models \citep[e.g.,][]{Degroote2010,Beck2012,Miglio2012,Miglio2013}. Even tests of stellar evolution theory for a wide variety of stellar masses and evolutionary stages, through asteroseismic data alone or combined with ground-based data, became possible thanks to dedicated CoRoT and {\it Kepler\/} asteroseismology programmes \citep[e.g.,][]{Michel2006,Gilliland2010,Bedding2011} and from multivariate statistical studies based on seismic, polarimetric, and spectroscopic data \citep[e.g.,][]{Aerts2014}. Asteroseismology of eclipsing binaries \citep[e.g.,][]{Maceroni2009,Welsh2011,Tkachenko2014,Beck2014} and of exoplanet host stars \citep[e.g.,][]{Gilliland2011,Chaplin2013,Huber2013,HuberScience2013,VanEylen2014} only became possible in the current space photometry era. Despite the availability of these numerous CoRoT and {\it Kepler\/} data sets with long time-base, new projects for similar studies are in development. These new studies are capable of mapping the entire sky rather than just a small portion of it, as was the case for CoRoT and {\it Kepler}. The current paper concerns the PLATO2.0 mission (hereafter simply called PLATO), which was recently accepted as M3 mission in the Cosmic Vision 2015 -- 2025 programme of the European Space Agency (ESA). PLATO is an acronym for PLanetary Transits and Oscillations of Stars and is a mission that will operate from the second Lagrange point (L2) of the Sun-Earth system. PLATO's goals are to study the formation and evolution of planetary systems, with specific emphasis on Earth-like planets in the habitable zone of bright solar-like host stars. PLATO will have the capacity to detect and characterize hundreds of Earth-like planets and thousands of larger planets with the photometric transit technique already used by CoRoT and {\it Kepler}. Up to 1\,000\,000 stars will be observed and characterized over the course of the full mission. Masses, radii, and ages of 80\,000 dwarf and subgiant stars will be measured with sufficient precision to allow for their asteroseismic modelling. The expected noise level for stars with visual magnitudes of less than 11 is 34 ppm per hour, and for stars brighter than 13th magnitude the noise is expected to be below 80 ppm per hour. A unique feature of PLATO compared to previous and other planned space missions is its capacity to measure a fraction of the targets in two photometric bands. In order to achieve its scientific aims, PLATO is equipped with 34 12\,cm aperture telescopes and 136 CCDs (four CCDs per camera) with 4510$\times$4510 18 $\mu$m pixels, to cover about 50\% of the sky, operating in the 500-1000 nm spectral range. Each selected target is assigned a 6$\times$6 pixel window to produce its light curve on board. This on-board processing is required to limit the amount of data to be downloaded to ground for its wide field of view (FoV). Detailed descriptions of the PLATO M3 mission are available in \citet{Rauer2013} and in the Yellow Book submitted to ESA for the selection of M3 \citep{Esa2013}\footnote{http://sci.esa.int/plato/53450-plato-yellow-book/}. PLATO's cameras are high-precision imagers whose expected performance must be carefully assessed from an appropriate overall instrument model. The instrument noise performance cannot be derived from the simple addition of the noise properties of the individual contributors due to the complex interaction between the various noise sources. As is often the case, it is not feasible to build and test a prototype of the PLATO imaging devices. Hence, numerical simulations performed by an end-to-end simulator are used to model the noise level expected to be present in the observations. Such simulations not only allow us to study the performance of the instrument, its noise source response, and the data quality, but they are also an essential tool for the fine-tuning of the instrument design for different types of configurations and observing strategies. The simulator should also allow us to test the scientific feasibility of an observing proposal. In this way, a complete description and assessment of the expected objectives of the mission can be derived. In this paper, we present a formalism, termed {\sc PLATO Simulator}, to model each of the noise sources affecting a space-based high-resolution imager and the mutual interaction of these noise sources. The performance of previous space photometers, such as MOST \citep{Walker2005}, CoRoT \citep{Auvergne2009}, and {\it Kepler} \citep{Koch2010, Caldwell2010} have been tested and evaluated using approaches specifically designed for each of these missions alone, keeping in mind their orbit (low-Earth in the case of MOST (Microvariablity and Oscillations of Stars) and CoRoT and Earth-trailing for {\it Kepler}). Our aim is to provide the scientific community with a tool that is easily adaptable for other high-precision photometric space missions, taking PLATO as the case study to illustrate our simulator. Our approach here is based on previous work developed in this spirit for the MONS (Measuring Oscillations in Nearby Stars) and Eddington mission projects, which never made it to implementation phase \citep[][hereafter termed DAK06]{DeRidder2006}. We have further developed and implemented this formalism in the {\sc PLATO Simulator} end-to-end simulation software-tool, which was specifically constructed for the PLATO assessment and Phase A/B1 studies, but is easily adaptable to other missions. In the following section, we describe each of the noise sources and the algorithms developed to model them, as well as their implementation and interaction. We introduce the {\sc PLATO Simulator} in Sect.\,\ref{sec:package} and, finally, in Sect.\,\ref{sec:application}, we present applications of the simulator to the study of white noise and jitter for the PLATO mission. These results were used to predict the quality of its photometry to assess the transit and stellar variability detection capability and to provide essential feedback for the mission design. | \label{sec:conclusions} We have presented the {\sc PLATO Simulator} software package for the simulation of space-based imaging and photometric analysis with the aim of providing a versatile tool for the modelling of high-precision space photometry. The description of the main noise sources and of the algorithms to transfer these effects to the synthetic images and generated light curves have been presented and demonstrated. We presented some of the results of the application of this tool in the Phase A/B1 study of the M3 PLATO mission of ESA. Although we only include discussions of the jitter effect and of the CCD quantum efficiency as illustrations of the capabilities of the software tool, we used the simulator to assess a variety of instrumental and pointing effects to define the optical design of the mission, its various FoV, the allowable level of satellite jitter, and the performance of the CCD's electronics and derived photometry. The {\sc PLATO Simulator} will be used to carry out future simulations and tests for the ongoing and upcoming Phase B1/B2 of the PLATO mission project. The \href{https://fys.kuleuven.be/ster/Software/PlatoSimulator/}{\sc PLATO Simulator} web site includes a detailed description of all the noise effects and the input parameters to configure those effects, to allow users to perform new simulations. Installation and user instructions are also included, as well as the software environment configuration requirements. We also addressed simulations carried out to evaluate the performance of the extension of the original {\it Kepler\/} mission, termed K2. In that work (paper in preparation), we paid specific attention to the estimation of the expected noise levels due to the pointing stability and possible drift of the spacecraft. This additional {\it Kepler\/} study is an illustration of the versatility of the {\sc PLATO Simulator} and its ease of use for applications to different space missions. | 14 | 4 | 1404.1886 |
1404 | 1404.4430.txt | *{The discovery of the first methane brown dwarf provides a framework for describing the important advances in both fundamental physics and astrophysics that are due to the study of companions of stars. I present a few highlights of the history of this subject along with details of the discovery of the brown dwarf Gliese 229B. The nature of companions of stars is discussed with an attempt to avoid biases induced by anthropomorphic nomenclature. With the newer types of remote reconnaissance of nearby stars and their systems of companions, an exciting and perhaps even more profound set of contributions to science is within reach in the near future. This includes an exploration of the diversity of planets in the universe and perhaps soon the first solid evidence for biological activity outside our Solar System.} \abstract{The discovery of the first methane brown dwarf provides a framework for describing the important advances in both fundamental physics and astrophysics that are due to the study of companions of stars. I present a few highlights of the history of this subject along with details of the discovery of the brown dwarf Gliese 229B. The nature of companions of stars is discussed with an attempt to avoid biases induced by anthropomorphic nomenclature. With the newer types of remote reconnaissance of nearby stars and their systems of companions, an exciting and perhaps even more profound set of contributions to science is within reach in the near future. This includes an exploration of the diversity of planets in the universe and perhaps soon the first solid evidence for biological activity outside our Solar System.} | 14 | 4 | 1404.4430 |
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1404 | 1404.5377_arXiv.txt | It has long been known that three objects (stars, planets, satellites, or some combination), all circling their mutual center of mass at the vertices of an equilateral triangle, are in a state of equilibrium, independent of their individual mass values $m_a$, $m_b$, $m_c$ (Lagrange, 1772). Furthermore, this equilibrium is stable, provided that \begin{equation} m_a m_b + m_a m_c + m_b m_c < M^2/27 , \end{equation} where $M \equiv m_a+m_b+m_c$ is the total mass of the system (Routh 1875). The latter criterion requires that one body be $\gta$ 26 times more massive than the other two combined (see Dobrovolskis, 2013, hereinafter referred to as Paper 1). Such configurations are known as Trojan systems, and their effects on the reflex motion of the parent star are well understood; see Paper 1 for a review. It is less well known that any number $N > 1$ of secondaries can be in equilibrium while sharing the same circular orbit around their primary; the case where they all have the same mass has been studied most. For small $N$, there are numerous equilibrium configurations, some stable, and some unstable. All such configurations affect the the radial velocity variations and reflex motion of the parent star, and some produce no reflex motion at all! This paper examines the effects of such co-orbital systems of planets on the reflex motions of their primary stars, and also on tides and transits. These effects are significant because they affect the interpretation of radial velocity and astrometric data. Most techniques currently used to analyze such data assume that no two planets share the same orbital period. Thus exoplanets with the same period can effectively ``hide'' from detection. | 14 | 4 | 1404.5377 |
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1404 | 1404.2282_arXiv.txt | This paper presents one of the first environmental analyses of the locations of the class of `interacting transients', namely type IIn supernovae and supernova Impostors. We discuss the association of these transients with star formation, host galaxy type, metallicity, and the locations of each event within the respective host. Given the frequent assumption of very high mass progenitors for these explosions from various studies, most notably a direct progenitor detection, it is interesting to note the weak association of these subtypes with star formation as traced by H$\alpha$ emission, particularly in comparison with type Ic supernovae, which trace the H$\alpha$ emission and are thought to arise from high mass progenitors. The radial distributions of these transients compared to type Ic supernovae are also very different. This provides evidence for the growing hypothesis that these `interacting transients' are in fact comprised of a variety of progenitor systems. The events contained within this sample are discussed in detail, where information in the literature exists, and compared to the environmental data provided. Impostors are found to split into two main classes, in terms of environment: SN2008S-like Impostors fall on regions of zero H$\alpha$ emission, whereas $\eta$ Carina-like Impostors all fall on regions with positive H$\alpha$ emission. We also find indications that the Impostor class originate from lower metallicity environments than type IIn, Ic and IIP SNe. | Studies of the host galaxies and local environments of supernova (SN) explosions have been integral in our understanding of the progenitors of these explosions. Initially host galaxy studies found the almost exclusive presence of Core-Collapse Supernovae (CCSNe) in star-forming galaxies \citep[e.g.][]{vanden05}, implying young stellar progenitors. The more central locations of type Ibc SNe compared to type II SNe also led to the suggestion that these events arise from higher metallicity environments \citep[e.g.][]{bois09,ande09}. These examples demonstrate the power of using host galaxy analysis, and studying the local environments of SNe, in constraining the progenitors of these explosions. These type of analyses will be utilised throughout this paper to concentrate on a sample of transients generally accepted to be interacting with a dense circumstellar medium (CSM), namely type IIn supernovae (SNIIn) and SN Impostors. The progenitor systems of these `interacting transients', and the cause of the dense CSM, may arise through a variety of routes. In this introduction we will discuss both types of transients in this sample, SNIIn and Impostors, the features which appear common to both groups, and the possible subgroups within the classes. \subsection{SNIIn} The IIn class is rare within the CCSN group ($\sim$7~per cent according to \citealt{li11}), and the nature of the explosions remains very uncertain, with the class being characterised principally by narrow lines in the spectrum \citep[e.g.][]{kiew12}. The class was originally defined by \citet{schl90}, though he also stressed that a fundamental progenitor characteristic was required for the objects to be a truly distinct class, something which remains elusive. This initial paper not only characterised the objects as having narrow spectral features, but also having a blue continuum and slow evolution (at least spectroscopically), characteristics of the group which remain prominent \citep{kiew12}. The source of the narrow emission lines is generally accepted to be the result of interaction between the supernova ejecta and a dense circumstellar medium immediately surrounding the explosion. This interaction creates hard emission which photo-ionises the surrounding unshocked material, resulting in an H$\alpha$ excess \citep[e.g.][]{chug91}. As SNIIn have been explored in more detail, the narrow spectral lines have been found to have multiple components; a `narrow' line (typically a few hundred kms$^{-1}$) caused by the photoionisation of the unshocked wind surrounding the progenitor, and an `intermediate-width' line (a few thousand kms$^{-1}$) from dense post-shock gas (e.g. \citealt{smit08}; \citealt{kiew12}). These compare to typical broad lines in SN ejecta with widths of 10,000 - 20,000 kms$^{-1}$ \citep{smit08}. \subsubsection{SN2005gl} The only robust direct detection of a SNIIn progenitor was made for SN2005gl \citep{galy09}. The detection of a star at its location, and the subsequent disappearance, indicated that the progenitor was a luminous blue variable (LBV) star with a mass likely to be in excess of 50 M$_{\odot}$ \citep{galy09,smar09}. The calculated mass loss rates and wind speeds of well-studied SNIIn seem to reflect this progenitor channel with only LBV stars predicted to be able to reach high enough mass loss rates, yet with smaller wind speeds in general than Wolf-Rayet (WR) stars \citep[e.g.][]{kiew12,tadd13}. The lack of information available about the variability of the star pre-explosion does lead to some debate as to whether the pre-explosion observations of SN2005gl, which give rise to the high mass estimates of the progenitor, were taken during a quiescent period. Little is known about the long term variability of LBVs, though recent work by \citet{ofek14} has studied type IIn SNe detected by the Palomar Transient Survey \citep{law09,rau09} and found that half of IIn show at least one outburst up to $\sim$120 days prior to explosion, with multiple outbursts common over the preceding year. An example of this is the type IIn SN2010mc which experienced a huge mass loss event 40 days prior to explosion \citep{ofek13a}. Studies have also shown LBVs to have major outbursts on timescales of years \citep[e.g.][]{past10,szcz10} which suggest that there is a chance that the progenitor of SN2005gl was serendipitously in outburst on the single pre-explosion image. Should the LBV have been in outburst when the one pre-explosion image was taken, it is possible that the quiescent star had an actual intrinsic brightness 3 magnitudes lower \citep{hump94} and consequently the mass would lie in the range of 20-25 M$_{\odot}$ according to the models of \citet{groh13b}. There is more controversy over the assumption of LBV progenitors for SNe, not least because stellar evolution models have until recently been unable to end a star's lifetime in the LBV phase (e.g. \citealt{maed08}, though see \citealt{hirs10} for some possible scenarios). Stellar evolution models instead require the LBV star to lose the hydrogen envelope before becoming a WR star and then exploding \citep{dwar11}. However, \citet{groh13} found from their rotational stellar evolution models coupled with atmospheric models, that stars in the mass range 20-25 M$_{\odot}$ exploded in the LBV phase. Although no post-explosion spectra were computed, \citet{groh13} speculated from the surface abundance measurements pre-explosion and position of the star on the HR diagram, that explosions of stars of 20 M$_{\odot}$ are likely to be classified as type IIb rather than IIn SNe. However, the increased mass loss of the 25 M$_{\odot}$ stars is likely to produce a H-rich, dense CSM, and the interaction of the SN with this CSM could produce a type IIn SN. Aside from the case of SN2005gl, \citet{dwar11} argues that the assumptions of LBV progenitors may be flawed. The mass loss equations assume wind mass-loss rates and velocities to be constant with time \citep{dwar11}. An LBV phase, with numerous eruptions prior to explosion (required in order to have the dense medium for the ejecta to interact with), does not have a constant wind mass-loss rate. The one certainty regarding the progenitors is the need for a dense CSM (see \citealt{ofek14a} for a discussion). The assumption has traditionally been that this must be due to LBV-type eruptions, but \citet{dwar11} argue that it is possible that the dense CSM was produced over a longer timescale prior to the eventual eruption of the progenitor star, meaning an LBV could have progressed into its WR phase before explosion. Alternatively a clumpy CSM could produce a similar result, where interaction with a dense clump could cause narrow lines in the spectrum, but not represent an overall high-density CSM (see \citealt{dwar11} for a detailed discussion). The general consensus in the literature, however, appears to be that the most likely candidate progenitors of SNIIn are LBV stars, though there are likely to be several different progenitor types even within this small but diverse class. The SNIIn class has therefore proved mysterious. Aside from the defining narrow emission lines, the objects within the class show diverse features, particularly light curves (LCs), and over time it has been discovered that many of the objects are not true CCSNe at all and have hence been reclassified. \subsubsection{Type Ibn SNe} A rare ($<$1 per cent of all CCSNe; \citealt{past08,smit12}) subclass of transients have been termed type Ibn \citep{past07}; these appear to be type Ib/c CC-explosions embedded within a He-rich envelope \citep[e.g.][]{past08}. SN2006jc is often referred to as the prototype for this group \citep[e.g.][]{matt08}, but several others have been observed (e.g. SN1999cq, \citealt{modj99}; SN2000er, \citealt{chas00}; SN2002ao, \citealt{mart02}). These events have been suggested to be a distinct class of CCSNe \citep{fole07}, but more recent analysis has suggested that they are more likely SNIb/c explosions occurring in a high density CSM, formed either by pre-explosion mass loss of a very massive ($<$100M$_{\odot}$) single star, or an LBV and WR binary system \citep[e.g.][]{past07,past08}. They have distinctive spectroscopic characteristics showing strong signs of CSM interaction in the form of narrow lines, but these tend to be dominated by He rather than H \citep[e.g.][]{past08,smit12}. More recent events found to exhibit these characteristics (e.g. SN2011hw, \citealt{smit12}) indicate that the class may be a span a large range, with some events showing more H emission, which could occur if the progenitors exploded at different points along the transition from an LBV to a WR \citep{smit12}. The recent work of \citet{gorb13} obtained the earliest ever observations of a type Ibn SN, iPTF13beo, whose light curve showed a double peak structure. \citet{gorb13} interpret this as a massive star exploding in a dense CSM with the initial peak powered by SN shock breakout in the CSM, followed by the second peak representing the SN radioactive decay. However, this massive star origin has been complicated by recent observations of the type Ibn SN Pan-STARRS1-12sk which was found in an elliptical brightest cluster galaxy containing no star formation \citep{sand13}, suggesting that some of these events may have older stellar progenitors. \subsubsection{Thermonuclear IIn} A group within the IIn class has been identified as thermonuclear explosions within a dense hydrogen-rich environment \citep[e.g.][]{deng04,dild12}, a hybrid of the SNIa thermonuclear class, yet showing SNIIn features (notably the presence of hydrogen), often referred to in the literature as Ia-CSM \citep[e.g.][]{silv13}. The WD within the system explodes as an SNIa when it reaches the carbon ignition point and then interacts with a dense CSM producing type IIn-like emission lines (e.g. SN2002ic; \citealt{hamu03}, although see \citealt{bene06} for a possible massive star origin for these systems). The origin of this dense CSM is still unclear as is the percentage of the currently classified SNIIn which may actually belong to this group. \citet{silv13} studied SNIIn detected by the Palomar Transient Factory (PTF; \citealt{rau09, law09}) and found that $\sim$10 per cent of explosions classified as SNIIn were more likely to be thermonuclear supernovae, interacting with a dense CSM. They also find the SNIa-CSM in their sample to have a range of magnitudes in the {\it R}-band of --21.3 to --19, i.e. brighter than most CCSN events. Several SNIIn events have been reclassified as SNIa-CSM due to their similarity to previous explosions, most notably SN1997cy \citep{germ00,tura00}. However, this has been questioned by \citet{inse13} who intensively followed one of these events, SN2012ca, and found its nebular spectrum to be consistent with a core-collapse explosion. \subsection{Impostors} Some explosions showing narrow emission lines, originally classified as SNIIn, have later been re-classed as SN `Impostors' when it has become clear that the progenitor stars have survived (e.g. SN1954J, \citealt{smit01}; SN2009ip, \citealt{berg09,mill09}). SN Impostors are thought to originate from the eruption of an LBV star, such as $\eta$ Carina, however, the eruption is non-terminal and hence not a true SN (e.g. \citealt{vand02}; \citealt{maun06}). Usually these events are much fainter than true SN explosions and so are distinct from the SNIIn group, however, the range in photometric properties of both the SNIIn and Impostor classes are so diverse that this may not always be the case (see \citealt{kiew12,tadd13} for the wide range of absolute magnitudes and decline rates of the SNIIn class). \subsubsection{2008S} When SN2008S was discovered \citep{arbo08} it was classified as a SNIIn due to the narrow Balmer emission lines \citep{stan08} though some of the spectral features seen and the faint peak magnitude of the explosion led to some speculation that the event was actually a SN Impostor \citep{stee08}. Given its proximity, it was hoped that the progenitor star might have been directly detectable, but pre-explosion images obtained on the Large Binocular Telescope found nothing (upper limits M$_{U}$$>$--4.8, M$_{B}$$>$--4.3, M$_{V}$$>$--3.8; \citealt{prie08}). A point source was detected at the location of SN2008S in archival infrared {\it Spitzer} observations \citep{prie08}. The detection implied that the progenitor was a dust enshrouded $\sim$10~M$_{\odot}$ star, much lower than assumed SNIIn progenitor masses. The literature now agrees that this event was a SN Impostor rather than a true SN eruption \citep[e.g.][]{bond09,smith09}. It has come to define a group of SN Impostors which have lower masses than generally expected from LBV eruptions \citep{thom09}, which are usually accepted to be the progenitors of SN Impostors, and are often heavily dust enshrouded \citep{smith11c}. \subsubsection{2009ip} SN2009ip was incorrectly classified as a SN during its 2009 outburst; the progenitor star was known to have had previous S Dor-like outbursts (see \citealt{smit13} for an account of the star's pre-discovery variability), and was detected on pre-explosion images, taken 10 years prior to the 2009 discovery, as a massive LBV star (50-80 M$_{\odot}$; \citealt{smith10}). The star had another outburst in 2010 \citep{drak10}, and in 2012 had an outburst followed by re-brightening \citep{marg12}. It is still debated whether this most recent explosion is the transition into a true CCSN explosion. \citet{maue13} presented photometric and spectroscopic follow up of the event, which showed a SNII-like broad P Cygni profile in the Balmer lines, spectral lines with velocities typical of SN explosions and a peak magnitude of $\sim$--18. However \citet{fras13} find no evidence for nucleosynthesised material in late time spectra and the extensive multi-wavelength photometric and spectroscopic follow up of the event presented in \citet{marg13} shows the latest explosion to be consistent with another outburst of the LBV progenitor. \citet{smit13}, however, interpret the near infrared excess seen in the 2012 outburst of SN2009ip as the recent outburst propagating through previous episodic LBV outbursts which have deposited a dense CSM, and they conclude that the 2012 outburst was a true SN explosion. The work of \citet{maue14} also argues that the latest explosion was a true SN with the ejecta having $\gtrsim$10$^{51}$ ergs of kinetic energy, which is hard to reconcile with a progenitor having survived the explosion. The environment of SN2009ip is very unusual, as the star is located outside the main disk of the galaxy. \subsection{This Paper} The well-studied SNIIn explosions to date tend to be biased towards high-luminosity or `unusual' events \citep{kiew12}, which also means that any implications drawn from these events on the progenitors of the whole class could be flawed. Recently \citet{tadd13} presented the results of the follow up of five type IIn SNe from the Carnegie Supernova Project. Most of these were from targeted surveys and hence from bright, nearby spiral galaxies, with high extinction in only two cases, a highly inclined galaxy, and a SN close to the central regions of its host. \citet{tadd13} conclude that from their mass-loss equations, LBVs are still the most likely progenitor of this group. In this paper, we conduct a study of the environments of CSM-interacting transients, in the form of type IIn SNe and SN Impostors. These events were selected by their presence in the Asiago SN Catalogue with an SNIIn classification, or through a literature search for Impostors. Events were not selected according to the amount of interaction observed, or by the types of galaxies in which they are present. We only require the host galaxies to have recession velocities less than 6000~kms$^{-1}$ and to have major to minor axis ratios less than 4:1, in order that our host galaxy analysis techniques are robust (see \citealt{habe12} for more detail). We present a new analysis of the radial distribution within their host galaxies of the resulting sample of interacting transients, and updated results for their respective association with H$\alpha$ emission. The total sample of events studied is 26 probable IIn and 13 probable impostors, although we can only analyse the detailed environment of 37 of these as explained below. We also carry out a robust analysis of the selection effects involved in both SNIIn and Impostor studies. In Section 2 we present an analysis of the host galaxies within this sample, along with the positional information of the interacting transients in terms of the {\it R}-band and H$\alpha$ emission. Section 3 will analyse the association of the transients with star formation, as traced by H$\alpha$ emission. In Section 4 the selection effects within the samples of SNIIn and SN Impostors are explored. Section 5 discusses the individual events contained within these samples and conclusions are drawn in Section 6. Throughout this paper comparisons will be made between the SNIIn and Impostor, or interacting transient class, and the SNIIP and SNIc classes (all CCSN subtype samples are presented in \citealt{habe12,ande12} and SNIa samples in Anderson et al., in prep.). These comparison samples include SNe in all star-forming host galaxies (i.e. not just in undisturbed hosts, see \citealt{habe12}), however, it is emphasised that no events have been selected due to the interacting nature of their hosts, with all host galaxy classifications carried out after the SN analysis. The SNIIP and SNIc sub-types fall at the extremes of the currently understood mass sequence of CCSNe progenitors. The masses of SNIIP progenitors have been well established through direct detection methods (see \citealt{smar09} for a review) to lie within 8 and 20 M$_{\odot}$. Although the true mass range for type Ic SNe is unknown, the class as a whole are thought to result from the explosions of progenitors with much higher Zero-Age Main Sequence masses, even if these progenitors are within binary systems, both from their association with star formation \citep[e.g.][]{ande12,kunc13}, and through high mass stellar evolution models \citep[e.g.][]{geor12}. | This paper has presented the most comprehensive host galaxy environment study of interacting transients (SNIIn and SN Impostors) to date. Following a discussion of the selection effects involved in this study, which are more likely to affect the SN Impostor sample than that of the SNIIn sample, we draw the following conclusions: \begin{itemize} \item The host galaxies of interacting transients trace the normal star formation in the local Universe, whereas SNIc appear to have more massive hosts. \item The host galaxies of SN Impostors appear slightly less luminous than CCSN-hosts, and correspondingly have lower metallicities. \item Inferred local metallicities at the sites of SN Impostors are lower than SNIc, SNIIP and SNIIn sites. SNIIn appear to have slightly more metal-rich sites than SNIIP. \item There is a lack of interacting transients in the central regions of host galaxies. The sole event which falls in the central 20 per cent of host galaxy {\it R}-band light is known to be an SNIa-CSM event, therefore no massive progenitors of interacting transients are found in the central regions of their host galaxies. \item The radial distributions of interacting transients and SNIc (with the highest mass progenitors) are very different (KS; P$<$0.1 per cent), with the former tending to lie in the outer regions of their hosts, while the latter are strongly centrally concentrated. \item A pronounced difference between interacting transients and SNIc is also seen in the association with ongoing star formation. Unlike the SNIc, the interacting transients do not trace H$\alpha$ emission, and therefore ongoing star formation (KS; P$<$0.1 per cent). \item All SN Impostors designated SN2008S-like within this sample fall on regions with zero H$\alpha$ emission, whereas those classed as $\eta$ Carina-like fall on positive values, with an average NCR$_{H\alpha}$ of 0.157. Impostors also show higher association with lower mass progenitors, traced by near-UV emission. \end{itemize} | 14 | 4 | 1404.2282 |
1404 | 1404.5836_arXiv.txt | We show the way of dark matter and dark energy presentation via ansatzs on the kinetic energies of the fields in the two-component chiral cosmological model. To connect a kinetic interaction of dark matter and dark energy with observational data the reconstruction procedure for the chiral metric component $h_{22}$ and the potential of (self)interaction $V$ has been developed. The reconstruction of $h_{22}$ and $V$ for the early and later inflation have been performed. The proposed model is confronted to $\Lambda CDM$ model as well. | \numberwithin{equation}{section} \newcommand{\ph}{\varphi} \newcommand{\prt}{\partial} The later-time cosmic acceleration of our Universe is strongly supported by observational data. Namely observations of supernovae type Ia\cite{Suzuki:2011hu}, the data from Baryon Acoustic Oscillations (BAO)\cite{Percival:2009xn} and Cosmic Microwave Background (CMB)\cite{Komatsu:2010fb} measurements confirm that the Universe is expending with an acceleration at the present time and about 70\% of the energy density consists of dark energy in a wide sense\cite{tsuji-10}, i.e. as the substance which is responsible for an anti-gravity force. In the range with well--known $\Lambda$CDM model, which potentially provides correct description of the Universe evolution but suffers from fine--tuning and coincidence problems, some alternative models were proposed. We will pay attention to the models with presence of scalar fields included in quintessence, phantom and quintom \cite{cosats06,DarkEnergy1103,Padmanabhan,QuintomReview} models. A chiral cosmological model (CCM) as a nonlinear sigma model with a potential of (self)interactions\cite{chervon12qm} has been already used extensively in various areas of gravitation and cosmology\cite{ch97gc,ch02gc,brochesush} and in particular for description of the very early Universe\cite{bcmk12qm,Beesham} and inflation\cite{chzhsh97plb,chekos2003}. A CCM can be applicable as well to the late-time Universe with dark matter and dark energy domination as it was shown in \cite{panche11}. The purpose of this article is to put into use the two-component CCM as the model where the dark energy content of the Universe and also the dark matter component are represented by two chiral fields with kinetic and potential interactions\cite{chervon12qm}. By considering a target space metric in the form % \begin{equation}\label{tsm} ds_{\sigma}^2=h_{11}d\varphi^2 +h_{22}(\varphi,\chi)d\chi^2,~~~h_{11}=const. \end{equation} we prescribe a kinetic interaction between chiral fields $\varphi$ and $\chi $ as a functional dependence $h_{22}$ on the fields. The potential interaction will be included into standard potential energy term of the action. There are no enough indications from observations about kinetic interactions between dark sector fields. Therefore we always deal with the problem: what is the functional dependence for the chiral metric component on the fields? First idea is to attract some results from HEP, for example, to consider SO(3) symmetry (by taking $h_{22}=\sin^2 \varphi $) and/or others symmetries for a chiral space. % From the other hand one can use some testing kinetic interactions\cite{brochesush,panche11}. Thus we can state that there is no evidence for some preferable functional form of the kinetic interaction contained in the functional form of the $h_{22}$ chiral metric component. To avoid this problem we develop here % the reconstruction procedure for the chiral metric component $h_{22}$. We ascribe a certain desirable behavior on the kinetic energy of the second chiral field $\chi $ and it becomes possible to determine both the target space metric component $h_{22}$ and a (self)interacting potential $V$ depending on the first chiral field $\varphi $. So we can restore a functional dependence the $h_{22}$ and $V$ on the scalar field $\varphi $ using observational data. Unfortunately it turns out that the procedure could not be applied for the entirely Universe evolution and we have necessity to consider separately the early and late epochs of the Universe evolution. It will be shown also that a CCM describes dark energy and dark matter in the unified form under special restrictions on the chiral fields (ansatzs). Therefore to include into consideration the present Universe with accelerated expansion it needs to take into account baryonic matter and radiation in the range with a two-component CCM. Making confrontation of proposed model predictions with observational data we found the way of a reconstruction of a kinetic interaction term $h_{22}$ and the potential $V$ in an exact form. This reconstruction is based on the procedure of finding the best--fit values % matching to the astrophysical observations. The structure of the article is like follow. In section 2, we give the basic model equations and discuss their properties including the exact solutions for a pure CCM (without matter and radiation). We derive the Friedmann equation for the proposed model with the aim to make comparison with $\Lambda$CDM in section 3. In section 4, we give the details of a fitting procedure outline. We present the way of the reconstruction of the kinetic coupling and potential in section 4. The early and recent Universe approximations are discussed there as well. Section 6 is devoted to the background dynamics of a CCM. Finally in section 7, we discuss the obtained results and consider perspectives for the future investigations. | \numberwithin{equation}{section} Fig.\ref{ris:mu} shows good agreement of supernovae data with $\sigma$CDM model taken with the best--fit parameters values. This fact confirm the validity of proposed model, i.e., $\sigma $CDM model does not contradict to observational data and may serve as a good dynamical alternative to $\Lambda$CDM. In fig. \ref{ris:contours} the confidence contours are depicted. We keep only positive values of parameter $\tilde{B}$ in order to prevent a crossing of the phantom divide. One can see from the evolution of the individual densities $\Omega_i$, deceleration parameters $q$ and effective equation of state parameters $\omega_{eff}$ (figs. \ref{ris:Omega}, \ref{ris:q} and \ref{ris:omega_eff}) that accelerated expansion takes place earlier in the Universe supported by $\sigma$CDM. Also one may notice that radiation/matter domination transition occurs earlier in $\Lambda$CDM model. These observations are in the full agreement with a smaller total matter amount including cold dark and baryonic components in $\sigma$CDM model in comparison to $\Lambda$CDM model. The graphical comparison (see fig. \ref{ris:q} and fig. \ref{ris:omega_eff}) of the $a_{\Lambda\mathrm{CDM} acc}$ and $a_{\sigma acc}$ (taken from the scale factor values corresponding to $-1/3$ and $0$ crossing) gives us clear evidence for equality of the transitions to accelerate expansion in corresponding models. This observation is concluded from $q$ and $\omega_{eff}$ values and has been already mentioned above. From fig. \ref{ris:early} one can conclude that the early Universe approximation holds for $a=10^{-5}$ up $a=5\cdot 10^{-5}$ scale factor values. The recent Universe approximation depicted on fig.~\ref{ris:recent} is true from $a=0.8$ to $a=1.2$ values. Let us remind that validity of the early and recent approximations comes from confrontation of $H_0(\ph - \ph_{early})$ and $H_0(\ph - \ph_{recent})$. The deviation for approximated and exact $\tilde{H}$ is associated with the lost of domination of DE for the early times. In conclusion it needs to stress that we first time reconstructed from observations the kinetic interaction between DM and DE in the form of chiral metric component $h_{22}$ for $\sigma$CDM. Also we have hope that the reconstruction techniques presented here may be useful for exact solution construction because of obtaining $h_{22}$ from observational data. | 14 | 4 | 1404.5836 |
1404 | 1404.0234_arXiv.txt | {Moderately r-process-enriched stars (r-I; $+0.3 \le \hbox{[Eu/Fe]} \le +1.0$) are at least four times as common as those that are greatly enriched in r-process elements (r-II; $\hbox{[Eu/Fe]} > +1.0$), and the abundances in their atmospheres are important tools for obtaining a better understanding of the nucleosynthesis processes responsible for the origin of the elements beyond the iron peak.} {The main aim of this work is to derive abundances for a sample of seven metal-poor stars with $-3.4$~$\leq\hbox{[Fe/H]}\leq$~$-2.4$ classified as r-I stars, to understand the role of these stars for constraining the astrophysical nucleosynthesis event(s) that is(are) responsible for the production of the r-process, and to investigate whether they differ, in any significant way, from the r-II stars.} {We carried out a detailed abundance analysis based on high-resolution spectra obtained with the VLT/UVES spectrograph, using spectra in the wavelength ranges 3400~-~4500~{\rm \AA}, 6800~-~8200~{\rm \AA}, and 8700~-~10,000~{\rm \AA}, with resolving power R $\sim$~40\,000 (blue arm) and R $\sim$~55\,000 (red arm). The OSMARCS LTE 1D model atmosphere grid was employed, along with the spectrum synthesis code Turbospectrum.} {We have derived abundances of the light elements Li, C, and N, the $\alpha$-elements Mg, Si, S, Ca, and Ti, the odd-Z elements Al, K, and Sc, the iron-peak elements V, Cr, Mn, Fe, Co, and Ni, and the trans-iron elements from the first peak (Sr, Y, Zr, Mo, Ru, and Pd), the second peak (Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb), the third peak (Os and Ir, as upper limits), and the actinides (Th) regions. The results are compared with values for these elements for r-II and ``normal'' very and extremely metal-poor stars reported in the literature, ages based on radioactive chronometry are explored using different models, and a number of conclusions about the r-process and the r-I stars are presented. Hydrodynamical models were used for some elements, and general behaviors for the 3D corrections were presented. Although the abundance ratios of the second r-process peak elements (usually associated with the main r-process) are nearly identical for r-I and r-II stars, the first r-process peak abundance ratios (probably associated with the weak r-process) are more enhanced in r-I stars than in r-II stars, suggesting that differing nucleosynthesis pathways were followed by stars belonging to these two different classifications.} {} | The heavy elements (those beyond the iron-peak elements) are primarily formed by the capture of neutrons. This process takes place through the slow (s) or the rapid (r) process, where the addition of a neutron is considered slow or rapid relative to the time for $\beta$ decay to take place (which differs from isotope to isotope). The main s-process is thought to occur on a relatively long timescale in asymptotic giant branch (AGB) stars (see, e.g., Herwig 2005, Sneden et al. 2008). The r-process instead occurs on a rather short timescale, typical of supernovae explosions (e.g., Winteler et al. 2012; Wanajo 2013) or other brief events, such as neutron star mergers (e.g., Goriely et al. 2011; Korobkin et al. 2012; Rosswog et al. 2014; Wanajo et al. 2014). In the early evolution of the Galaxy, matter may have been enriched in heavy elements through the r-process alone, as first suggested by Truran (1981) (see also Roederer et al. 2010, 2014, and references therein). To date, full understanding of r-process nucleosynthesis and the astrophysical sites that account for its operation remain unclear (e.g., Wanajo \& Ishimaru 2006; Kratz et al. 2007; Langanke \& Thielemann 2013). The best sources of information to constrain this process are the abundances of very and extremely metal-poor stars, since they contain the nucleosythesis products from early generations of stars and are essentially unaltered by later production events. Beers \& Christlieb (2005) classified metal-poor stars in terms of their metallicities and the enhancements of carbon and the r- and s-process elements. Metal-poor stars that are enhanced in the neutron-capture elements provide a unique opportunity to study the r-process in the early Galaxy {\it in situ}, even for extremely metal-poor stars ($\hbox{[Fe/H]} < -3.0$). In the absence of enhancement of the neutron-capture elements, most species would be too weak to be detected in high-resolution spectra. Two classes of metal-poor stars were defined by Beers \& Christlieb (2005) according to their enhancement in r-process elements -- the moderately r-process-enhanced stars, with $+0.3\leq\hbox{[Eu/Fe]}$\footnote{We adopt the notation [A/B]~=~log(n$_{A}$/n$_{B}$)$_{star}$~-~log(n$_{A}$/n$_{B}$)$_{\odot}$, where {\it n} is the number density of atoms.}~$\leq+1.0$ and $\hbox{[Ba/Eu]}<0$, designated as r-I stars, and the highly r-process-enhanced stars, with $\hbox{[Eu/Fe]}>+1.0$ and $\hbox{[Ba/Eu]}<0$, designated as r-II stars. According to Beers \& Christlieb (2005), the r-I stars appear to be, on the whole, at least several times as common as their more extreme counterparts, the r-II stars. In the context of the Hamburg/ESO R-process Enhanced Star survey (HERES) (Christlieb et al. 2004; Barklem et al. 2005, hereafter B05), 253 metal-poor halo stars in the metallicity range $-3.8<\hbox{[Fe/H]}<-1.5$ were studied. The spectra were obtained with the VLT/UVES spectrograph, using a slit width of 2'', yielding a resolving power R~$\sim$~20\,000, and a typical signal-to-noise ratio S/N~$\sim$~50 per pixel, covering the wavelength region 3760~-~4980\,{\rm \AA}. Based on these observations, B05 identified 8 r-II and 35 r-I stars, showing that the r-I stars are, in fact, more than four times as common as the r-II stars. Barklem et al. (2005) (and others before) suggested that the pattern of the neutron-capture elements of r-II stars, including the reference stars CS~22892-052 (McWilliam et al. 1995; Sneden et al. 1996, 2000, 2009) and CS~31082-001 (Cayrel et al. 2001; Hill et al. 2002), closely followed the scaled solar system r-process abundances for elements beyond barium (except for Th and U). In stars of lower r-element enrichment, such as the r-I stars, B05 noted that the lighter element abundances (in particular Sr, Y, Zr) are generally higher than expected from the solar pattern. Moreover, r-II stars were found to occupy a narrow metallicity range, centered on $\hbox{[Fe/H]}\sim-2.8$, with a small scatter ($\sim$ 0.16 dex). The r-I stars, on the other hand, were found to occur across a wide metallicity range. From the data of B05, the abundance ratios from [C/Fe] to [Zn/Fe] appeared to be the same in the r-II, r-I stars, and normal metal-poor stars (those without CNO or neutron-capture enhancements). These results have been strengthened, with only a few exceptions, by high-resolution spectroscopic observations of additional metal-poor stars in recent years. Based on the analysis of a sample of metal-poor stars with $-3.4$~$\leq\hbox{[Fe/H]}\leq$~$-2.4$ classified as r-I stars, the purpose of the present paper is to perform a detailed comparison of the abundance ratios of elements for the r-I and r-II stars, and thereby gain a better understanding of the nature of the r-process and the likely astrophysical site(s) with which it might be associated. In Sect. 2, the observations and reductions are reported. Sect. 3 describes the abundance determinations. In Sect. 4, the results are provided, followed by a discussion in Sect. 5. Conclusions are given in Sect. 6. \section {Observations and reductions} Seven r-I stars were selected from the list of B05, with $\hbox{[Fe/H]}\leq-2.3$, since, at higher metallicity, enrichment of the interstellar medium from which these stars were born with s-process elements contributed by AGB stars becomes more of a problem (see, e.g., Fran\c{c}ois et al. 2007). We also discarded the carbon-enhanced metal-poor (CEMP) stars, since many of these stars have been enriched in C and heavy s-process elements, because of mass-transfer from an AGB companion. The atmospheric parameters of the selected stars (from B05) are given in Table~\ref{atm_barklem}, along with their reported [Eu/Fe], [Ba/Eu], and [C/Fe], the abundance ratios upon which their original classification was based. The seven r-I stars were observed with the VLT/UVES spectrograph in November 6~-~10, 2007. The blue and red arms were centered on 3900\,{\rm \AA} and 8600\,{\rm \AA}, and the spectra were obtained with a 1'' slit, a resolving power of R $\sim$~40\, 000 and R $\sim$~55\,000, respectively, with about five pixels per resolution element. Spectra in the wavelength ranges 3400~-~4500~{\rm \AA}, 6800~-~8200~{\rm \AA}, and 8700~-~10,000~{\rm \AA} were obtained. The log of observations is given in Table \ref{log}. Standard data reductions were performed, employing the UVES pipeline in the ESO~-~GASGANO environment, including flatfield correction, bias and dark subtraction, cosmic-ray removal, spectral extraction, and wavelength calibration with comparison arc-line spectra taken before or after each exposure. In the frame of the Large Program (LP) ``First Stars'' (PI: R. Cayrel), some 35 very metal-poor giants were analyzed based on very high-quality high-resolution spectra. The abundance patterns from C to Zn are presented in Cayrel et al. (2004), and also (for very metal-poor main-sequence turnoff stars) in Bonifacio et al. (2009). Fran\c{c}ois et al. (2007) derived the abundance patterns of the neutron-capture elements for many of these stars. Among the giants, six r-I stars and three r-II stars (CS~31082-001, CS~22953-003, and CS~22892-052) were studied in detail and were added to the present sample of r-I stars for the purpose of discussion. The relative abundances of the heavy elements for CS~31082-001 come from Hill et al. (2002), Barbuy et al. (2011), and Siqueira-Mello et al. (2013), for CS~22953-003 they were taken from Fran\c{c}ois et al. (2007), and for CS~22892-052 from Sneden et al. (1996, 2000, 2009). For the star CS~30315-029, we also used a spectrum obtained during the LP ``First Stars,'' in the regions centered on 3960\,{\rm \AA} and 5730\, {\rm \AA}, to measure the Ba lines. For the other six stars, we derived Ba abundances from the HERES spectra. \begin{table*} \caption{Atmospheric parameters, radial velocities, [Eu/Fe], [Ba/Eu], and [C/Fe] taken from Barklem et al. (2005). Our set of stars were chosen with {\bf $\rm+0.3 \le [Eu/Fe] \le +1.0$} and $\rm[Ba/Eu]<0$.} % \label{atm_barklem} % \centering % \begin{tabular}{cccccrrrr} % \hline\hline % \noalign{\smallskip} \hbox{Star} & \hbox{\Teff} & \hbox{log$g$} & \hbox{[Fe/H]} & \hbox{$\xi$} & \hbox{V$_{\rm r}$} & \hbox{[Eu/Fe]} & \hbox{[Ba/Eu]} & \hbox{[C/Fe]}\\ % \noalign{\smallskip} \hline % \noalign{\smallskip} & \hbox{(K)} & \hbox{[cgs]} & \hbox{} & \hbox{(\kms)} & \hbox{(\kms)} & \hbox{} & \hbox{} & \hbox{} \\ \noalign{\smallskip} \hline % \noalign{\smallskip} \hbox{CS 30315-029} & 4541 & 1.07 & $-$3.33 & 2.06 & $-$169.2 & $+$0.73 & $-$0.31 & $-$0.52 \\ \hbox{HE 0057-4541} & 5083 & 2.55 & $-$2.32 & 1.67 & 13.4 & $+$0.62 & $-$0.74 & $+$0.09 \\ \hbox{HE 0105-6141} & 5218 & 2.83 & $-$2.55 & 1.66 & 3.8 & $+$0.68 & $-$0.50 & $+$0.11 \\ \hbox{HE 0240-0807} & 4729 & 1.54 & $-$2.68 & 1.96 & $-$98.8 & $+$0.73 & $-$0.53 & $-$0.43 \\ \hbox{HE 0516-3820} & 5342 & 3.05 & $-$2.33 & 1.48 & 153.5 & $+$0.67 & $-$0.77 & $+$0.30 \\ \hbox{HE 0524-2055} & 4739 & 1.57 & $-$2.58 & 1.95 & 255.3 & $+$0.49 & $-$0.42 & $-$0.33 \\ \hbox{HE 2229-4153} & 5138 & 2.47 & $-$2.62 & 1.79 & $-$139.6 & $+$0.45 & $-$0.73 & $+$0.28 \\ \noalign{\smallskip} \hline % \end{tabular} \end{table*} \subsection{Radial velocities} For each spectrum, Table \ref{log} lists the measured geocentric ($\rm RV_G$) and barycentric ($\rm RV_B$) radial velocities, along with the mean $\rm RV_B$ for each star. These measurements were made with the blue spectra; a precision of about 1\,\kms was achieved. Comparison to the values given by B05 shows good agreement, within the error bars. Consequently, our sample stars do not present any indication of binarity. \subsection{Measurement of equivalent widths} The spectra were normalized, corrected for radial-velocity shifts, and combined to produce the final average data. We measured the equivalent widths (EW) of a set of weak iron and titanium lines in their neutral and ionized states. The EWs were measured with a semi-automatic code, which traces the continuum and uses a Gaussian profile to fit the absorption lines. The central wavelength of each line was left as a free parameter, and the full width at half maximum (FWHM) was computed as well. For blends on the blue or the red wing, this part of the line can be excluded from the computations. The EWs of the Fe and Ti lines used in this work are given in Table \ref{EW_measurements} along with the corresponding \loggf~values. To check the reliability of the implemented code, the results were compared with those obtained using Fitline (Fran\c{c}ois et al. 2003), an automated line-fitting procedure based on the algorithms of Charbonneau (1995). Fig. \ref{EW_compara} shows a comparison of the EWs obtained with the present method and with Fitline for CS~30315-029, and demonstrates excellent agreement. \begin{figure} \centering \resizebox{80mm}{!}{\includegraphics[angle=0]{EW_compara.eps}} \caption{Comparison of EWs measured for a set of Fe~I lines in CS~30315-029 using the code developed in this work and EWs obtained with the code FitLine.} \label{EW_compara} \end{figure} \begin{table*} \caption{Log of observations: coordinates, date of observation, exposure time, air mass at the beginning and at the end of the observation, geocentric and barycentric radial velocities.} % \label{log} % \centering % \begin{tabular}{cccccccrrr} % \hline\hline % \noalign{\smallskip} \hbox{Target} & \hbox{$\alpha$(J2000)} & \hbox{$\delta$(J2000)} & \hbox{Date} &\hbox{Exp.} &\hbox{Airmass} &\hbox{Airmass} & \hbox{RV$\rm_{G}$} & \hbox{RV$\rm_{B}$}& \hbox{Mean $\rm RV_B$} \\ \noalign{\smallskip} \hline \noalign{\smallskip} \hbox{} & \hbox{} & \hbox{} & & \hbox{(sec)} & \hbox{Start} & \hbox{End} & \hbox{(\kms)} & \hbox{(\kms)} & \hbox{(\kms)} \\ \noalign{\smallskip} \hline \noalign{\smallskip} \hbox{CS 30315-029} & 23:34:26.5 & $-$26:42:19 & 06.11.07 & 3600 & 1.063 & 1.006 & $-$144.95 & $-$169.43 & $-$170.0\\ \hbox{ } & & & 08.11.07 & 3600 & 1.063 & 1.123 & $-$145.39 & $-$170.36 & \\ \hbox{ } & & & 08.11.07 & 3600 & 1.127 & 1.322 & $-$145.23 & $-$170.31 & \\ \hbox{HE 0057-4541} & 00:59:59.2 & $-$45:24:54 & 07.11.07 & 3600 & 1.143 & 1.080 & 30.93 & 14.15 & 13.7\\ \hbox{ } & & & 07.11.07 & 3600 & 1.072 & 1.081 & 30.79 & 13.90 & \\ \hbox{ } & & & 07.11.07 & 3600 & 1.081 & 1.145 & 30.74 & 13.76 & \\ \hbox{ } & & & 07.11.07 & 3600 & 1.146 & 1.281 & 30.89 & 13.82 & \\ \hbox{ } & & & 08.11.07 & 3600 & 1.156 & 1.299 & 30.62 & 13.34 & \\ \hbox{ } & & & 08.11.07 & 3600 & 1.303 & 1.564 & 30.67 & 13.31 & \\ \hbox{HE 0105-6141} & 01:07:38.0 & $-$61:25:17 & 09.11.07 & 4500 & 1.425 & 1.683 & 20.09 & 5.33 & 5.3 \\ \hbox{HE 0240-0807} & 02:42:57.6 & $-$07:54:35 & 07.11.07 & 3600 & 1.095 & 1.233 & $-$96.02 & $-$100.77 & $-$101.8\\ \hbox{ } & & & 08.11.07 & 4500 & 1.232 & 1.631 & $-$95.96 & $-$101.31 & \\ \hbox{ } & & & 10.11.07 & 3600 & 1.641 & 1.290 & $-$96.44 & $-$102.06 & \\ \hbox{ } & & & 10.11.07 & 3600 & 1.287 & 1.120 & $-$96.42 & $-$102.14 & \\ \hbox{ } & & & 10.11.07 & 3600 & 1.117 & 1.050 & $-$96.17 & $-$102.01 & \\ \hbox{ } & & & 10.11.07 & 3600 & 1.045 & 1.069 & $-$96.14 & $-$102.15 & \\ \hbox{ } & & & 10.11.07 & 3600 & 1.070 & 1.175 & $-$95.89 & $-$102.03 & \\ \hbox{ } & & & 10.11.07 & 3600 & 1.178 & 1.408 & $-$95.78 & $-$102.04 & \\ \hbox{HE 0516-3820} & 05:18:12.9 & $-$38:17:33 & 09.11.07 & 3600 & 1.056 & 1.144 & 148.20 & 154.38 & 154.4 \\ \hbox{HE 0524-2055} & 05:27:04.4 & $-$20:52:42 & 07.11.07 & 3600 & 1.007 & 1.013 & 244.19 & 256.32 & 255.4 \\ \hbox{ } & & & 07.11.07 & 3600 & 1.014 & 1.087 & 243.53 & 255.55 & \\ \hbox{ } & & & 08.11.07 & 3300 & 1.030 & 1.116 & 243.65 & 255.31 & \\ \hbox{ } & & & 10.11.07 & 3600 & 1.007 & 1.064 & 243.32 & 254.42 & \\ \hbox{HE 2229-4153} & 22:32:49.0 & $-$41:38:25 & 08.11.07 & 2700 & 1.076 & 1.137 & $-$113.97 & $-$139.92 & $-$138.5\\ \hbox{ } & & & 09.11.07 & 2700 & 1.046 & 1.066 & $-$111.74 & $-$137.66 & \\ \hbox{ } & & & 09.11.07 & 2700 & 1.046 & 1.055 & $-$111.94 & $-$137.90 & \\ \noalign{\smallskip} \hline % \end{tabular} \end{table*} \begin{table*} \caption{Identifications, magnitudes, and reddening.} % \label{flux} % \scalefont{0.78} \centering % \begin{tabular}{cccccccccc} % \hline\hline % \noalign{\smallskip} \hbox{Star} & \hbox{2MASS ID} & \hbox{($V$)*} & \hbox{($B-V$)*} & \hbox{($V-R_{C}$)*} & \hbox{($V-I_{C}$)*} & \hbox{($J$)**} & \hbox{($H$)**} & \hbox{($K_{S}$)**} & \hbox{E($B-V$)***}\\ \noalign{\smallskip} \hline \noalign{\smallskip} \hbox{CS 30315-029} & \hbox{23342669-2642140} & 13.661$\pm$0.004 & 0.915$\pm$0.007 & 0.569$\pm$0.004 & 1.143$\pm$0.004 & 11.780$\pm$0.020 & 11.209$\pm$0.021 & 11.124$\pm$0.023 & 0.020\\ \hbox{HE 0057-4541} & \hbox{00595927-4524534} & 14.829$\pm$0.005 & 0.699$\pm$0.009 & 0.441$\pm$0.007 & 0.890$\pm$0.007 & 13.376$\pm$0.021 & 12.970$\pm$0.026 & 12.877$\pm$0.031 & 0.016\\ \hbox{HE 0105-6141} & \hbox{01073782-6125176} & 13.516$\pm$0.004 & 0.645$\pm$0.006 & 0.403$\pm$0.005 & 0.856$\pm$0.006 & 12.161$\pm$0.023 & 11.758$\pm$0.022 & 11.663$\pm$0.025 & 0.020\\ \hbox{HE 0240-0807} & \hbox{02425772-0754354} & 14.971$\pm$0.005 & 0.896$\pm$0.012 & 0.524$\pm$0.007 & 1.082$\pm$0.008 & 13.213$\pm$0.022 & 12.707$\pm$0.032 & 12.625$\pm$0.031 & 0.025\\ \hbox{HE 0516-3820} & \hbox{05181291-3817326} & 14.377$\pm$0.007 & 0.615$\pm$0.013 & 0.401$\pm$0.009 & 0.839$\pm$0.009 & 12.937$\pm$0.023 & 12.507$\pm$0.029 & 12.469$\pm$0.027 & 0.026\\ \hbox{HE 0524-2055} & \hbox{05270444-2052420} & 14.013$\pm$0.004 & 0.878$\pm$0.007 & 0.526$\pm$0.005 & 1.076$\pm$0.005 & 12.256$\pm$0.026 & 11.747$\pm$0.026 & 11.623$\pm$0.019 & 0.045\\ \hbox{HE 2229-4153} & \hbox{22324904-4138252} & 13.322$\pm$0.003 & 0.676$\pm$0.005 & 0.420$\pm$0.004 & 0.875$\pm$0.006 & 11.937$\pm$0.025 & 11.497$\pm$0.021 & 11.456$\pm$0.022 & 0.012\\ \noalign{\smallskip} \hline \end{tabular} \tablebib{*: Broadband UBVR$_{C}$I$_{C}$ (subscript ``C'' indicates the Cousins system) from HK and Hamburg/ESO surveys (Beers et al. 2007); **: 2MASS (Cutri et al. 2003); ***: Infrared Processing and Analysis Center (IRSA, Schlegel et al. 1998).} \end{table*} \begin{table*} \caption{Temperatures and errors derived using the calibrations by Alonso et al. (1999) for several colors, and the final temperature adopted for each star. The error on the adopted temperature does not take into account the uncertainty on the reddening.} % \label{temp} % \centering % \begin{tabular}{crcccccc} % \hline\hline % \noalign{\smallskip} \hbox{Star} & \hbox{\Teff($B-V$)} & \hbox{\Teff($V-I$)} & \hbox{\Teff($V-R$)} & \hbox{\Teff($J-H$)} & \hbox{\Teff($J-K$)} & \hbox{\Teff($V-K$)} & \hbox{Adopted \Teff}\\ \noalign{\smallskip} \hline \noalign{\smallskip} \hbox{CS 30315-029} & 4703$\pm$96 & 4523$\pm$125 & 4959$\pm$150 & 4383$\pm$170 & 4622$\pm$125 & 4621$\pm$25 & 4570$\pm$53\\ \hbox{HE 0057-4541} & 5104$\pm$167 & 5069$\pm$125 & 5372$\pm$150 & 5158$\pm$170 & 5153$\pm$125 & 5237$\pm$40 & 5144$\pm$60\\ \hbox{HE 0105-6141} & 5273$\pm$167 & 5176$\pm$125 & 5638$\pm$150 & 5156$\pm$170 & 5167$\pm$125 & 5398$\pm$40 & 5234$\pm$60\\ \hbox{HE 0240-0807} & 4689$\pm$96 & 4656$\pm$125 & 5064$\pm$150 & 4707$\pm$170 & 4847$\pm$125 & 4802$\pm$40 & 4740$\pm$53\\ \hbox{HE 0516-3820} & 5400$\pm$167 & 5244$\pm$125 & 5633$\pm$150 & 5067$\pm$170 & 5302$\pm$125 & 5333$\pm$40 & 5269$\pm$60\\ \hbox{HE 0524-2055} & 4736$\pm$96 & 4725$\pm$125 & 5096$\pm$150 & 4736$\pm$170 & 4734$\pm$125 & 4813$\pm$40 & 4749$\pm$53\\ \hbox{HE 2229-4153} & 5146$\pm$167 & 5097$\pm$125 & 5529$\pm$150 & 4966$\pm$170 & 5218$\pm$125 & 5354$\pm$40 & 5156$\pm$60\\ \noalign{\smallskip} \hline \end{tabular} \end{table*} | We analyzed seven r-I stars and derived the chemical abundances based on high-quality, high-resolution spectra. The results obtained for the lighter element Li show that the stars have undergone the first dredge-up, and for the objects with no Li detectable an extra-mixing event may have occurred. The C abundances obtained confirm that the sample is not carbon-enhanced, per our original selection criterion. For nitrogen, the abundances were derived from the CN and NH lines, and the present values confirm the discrepancy found in the literature between these two abundance indicators. For the $\alpha$-elements Mg, Si, S, Ca, and Ti, the odd-Z elements Al, K, and Sc, and the iron-peak elements V, Cr, Mn, Fe, Co, and Ni, the results obtained in our present sample agree excellently with the values from the literature. There are no differences in the chemical content between r-I and r-II stars (or even the normal stars), in terms of these elements. Hydrodynamics models were also computed for some elements to explore the 3D corrections. The same excellent agreement is obtained among the abundance patterns of the second-peak region elements Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. The results of the r-I stars analyzed reproduce the pattern observed in the r-II star CS~31082-001. The origin of this region is associated with the main r-process, which must operate in the same way to build the chemical content observed in the atmospheres of r-I and r-II stars. The upper limits derived for the abundances of the third-peak elements also agree with the expected values from the r-II abundance pattern. On the other hand, the derived abundances for the first peak region elements Sr, Y, Zr, Mo, Ru, and Pd, some of them as upper limits only, are enhanced with respect to the level observed in the r-II stars. In addition, this overabundance is higher in stars with lower [Ba/Fe] ratios. In other words, the abundance level obtained in r-I stars is between the lowest value derived in r-II stars and the highest one observed in the normal stars. It is important to note that the behavior of [first-peak/Fe] ratios as a function of metallicity [Fe/H] seems to be the same among all the stars (r-I, r-II, and normal stars). Indeed, a constant ratio appears for [Fe/H]~$>$~$-$3, which is the metallicity region of the r-process-element enriched stars, indicating a co-production of iron and the first-peak elements. A weak r-process is claimed to explain the origin of these elements, and several models are available in the literature (e.g., Montes et al. 2007; Wanajo 2013). The comparison between the calculated patterns and the observational evidence can perhaps shed some light on this problem. The thorium abundance derived in CS~30315-029 shows that an actinide boost most likely exists for this star, which currently is the most metal-deficient object with r-process enhancement. Several r-process models were applied to calculate the age of the star based on radioactive chronometry, but the lack of uranium abundance in CS~30315-029 does not permit us to use the ratio U/Th, the only robust radioactive pair in stars with actinide boost. | 14 | 4 | 1404.0234 |
1404 | 1404.5627_arXiv.txt | We present Karl G. Jansky Very Large Array (VLA) observations of the 7~mm continuum emission from the disk surrounding the young star LkCa~15. The observations achieve an angular resolution of 70~mas and spatially resolve the circumstellar emission on a spatial scale of 9~AU. The continuum emission traces a dusty annulus of 45~AU in radius that is consistent with the dust morphology observed at shorter wavelengths. The VLA observations also reveal a compact source at the center of the disk, possibly due to thermal emission from hot dust or ionized gas located within a few AU from the central star. No emission is observed between the star and the dusty ring, and, in particular, at the position of the candidate protoplanet LkCa~15~b. By comparing the observations with theoretical models for circumplanetary disk emission, we find that if LkCa~15~b is a massive planet ($>5$~M$_J$) accreting at a rate greater than $10^{-6}$ M$_J$~yr$^{-1}$, then its circumplanetary disk is less massive than 0.1~M$_J$, or smaller than 0.4 Hill radii. Similar constraints are derived for any possible circumplanetary disk orbiting within 45 AU from the central star. The mass estimate are uncertain by at least one order of magnitude due to the uncertainties on the mass opacity. Future ALMA observations of this system might be able to detect circumplanetary disks down to a mass of $5 \times 10^{-4}$~M$_J$ and as small as 0.2~AU, providing crucial constraints on the presence of giant planets in the act of forming around this young star. | \label{sec:intro} High angular resolution observations at infrared and millimeter wavelengths have mapped in great detail nearby young ($<$5 Myr) circumstellar disks and revealed ``holes'' \citep{Andrews09,Andrews11,Brown08,Brown12,Cieza12a,Hughes09,Isella10a,Isella10b,Isella12,Mayama12,Thalmann10}, asymmetric rings \citep[][]{Casassus13,Fukagawa13,Isella13,Perez14,Vandermarel13}, and spiral structures \citep{Fukagawa06, Garufi13, Grady13, Hashimoto11, Muto12} in the dust spatial distribution. These features suggest that the observed disks are perturbed by low mass companions which remain, to date, elusive. Detecting giant planets and brown dwarfs orbiting at small separation from young stars with disks is indeed challenging. The variability of the photospheric lines in young stars and the presence of optically thick disks, prevent the use of radial velocities and transit techniques, respectively. Furthermore, direct imaging at optical and infrared wavelengths is feasible only if the companions have cleared the surrounding disk regions to expose themselves. However, even in this case, current high contrast cameras can image sub-stellar companions only at angular separations larger than about 0.1\arcsec, which correspond to orbital radii larger than about 15 AU at the distance of nearby star forming regions \citep[see, e.g.,][]{Garufi13,Close14}. Alternatively, detections of sub-stellar companions orbiting within dust depleted cavities have been obtained through near-infrared aperture masking interferometric observations \citep[][]{Biller12, Huelamo11, Kraus12}, which achieve the telescope diffraction limit, e.g., 40 mas for a 10 m telescope at the wavelength of 2~$\mu$m. However, the sparse nature of aperture masking measurements and the fact they provide information only on the closure phase of the Fourier transform of the surface brightness, introduce degeneracies in the reconstructions of the source emission. In this work, we attempt to detect planets in the act of forming by observing the millimeter-wave thermal emission from their circumplanetary disks. Young giant planets embedded in their primordial nebula are expected to be surrounded by circumplanetary disks which regulate the angular momentum of the accreting material and provide the raw material to form moons. In analogy with circumstellar disks, circumplanetary disks are expected to intercept a large fraction ($> 20\%$) of the optical and near-infrared radiation from the central planet and reemit it at longer wavelengths. Attempts to detect circumplanetary disks at millimeter wavelengths have been so far inconclusive. \cite{Greaves08} reported the detection of a compact structure in the 1.3 cm continuum emission from HL Tau's disk at a radius of 65 AU, which is interpreted as the evidence of a circumplanetary disk with a mass of 14 M$_J$. However, the rather low signal-to-noise of the detection and the lack of confirmation from observations at shorter wavelengths \citep{Carrasco09,Kwon11}, cast doubt on the real nature of the observed structure. The target of our observations is LkCa~15, a 2-5 Myr old K5 star \citep[L$_\star$= 0.74 L$_\odot$, M$_\star =1.0$ M$_\odot$;][]{Simon00,Kenyon95} located in the Taurus star-forming region at a distance of about 140 pc \citep[see, e.g.,][]{Loinard07}. The LkCa~15 circumstellar disk has a dust-depleted inner region of about 45 AU in radius \citep{Pietu06, Andrews11,Isella12}. Despite this large cavity in dust, the star is accreting material from the disk at a rate of about $10^{-9}$ M$_\odot$ yr$^{-1}$ \citep{Hartmann98}. \cite{Kraus12} have reported the discovery of a candidate protoplanet, LkCa~15~b, through aperture masking observations. The planet candidate is located at a projected separation of 70 mas, which corresponds to a physical distance of 16 AU if the planet orbit is in the plane of the circumstellar disk. Infrared photometric observations suggest a planet mass between 6 and 10 M$_J$ \citep{Kraus12} Section 2 describes our VLA observations which seek to detect millimeter-wave emission from material orbiting around LkCa~15~b, in addition to any circumplanetary disk within the dust depleted cavity. A simple radiative transfer model for the circumplaneray disk emission is presented in Section 3, and the comparison with the observations is considered in Section 4. A short discussion of our results and the possibility of detecting circumplanetary disks with ALMA is presented in Section 5. | \label{sec:disc} LkCa~15 is surrounded by a gas rich circumstellar disk that accretes onto the central star at a rate of $1.3 \times 10^{-9}$ M$_{\sun}$ yr$^{-1}$, as measured by calculating the accretion luminosity from the ultra-violet excess emission over the stellar photosphere \citep{Hartmann98}. Hydrodynamic simulations of giant planets embedded in gaseous rich circumstellar disks suggest that the amount of material accreting from the circumstellar disk onto a circumplanetary disk might be comparable to the mass accretion rate onto the central star. If circumplanetary disks have a viscosity similar to that of the circumstellar disks, then the mass accretion rate onto the planet should also be comparable to the mass accretion rate onto the central star \citep{Zhu11,Szulagyi13}. This suggests that giant planets orbiting inside the dust depleted cavity might be accreting, in average, at a rate of $10^{-9}$ M$_{\sun}$ yr$^{-1}$, or $10^{-6}$ M$_J$ yr$^{-1}$. This value corresponds to the minimum mean mass accretion rate required to form a giant planet such as LkCa~15~b faster than the average disk dispersal time scale derived from infrared observations \citep{Hernandez08}. Higher accretion rates are predicted during the initial phase of planet formation \citep{Ward10,Shabram13}, while lower values are possible if circumplanetary disks are less viscous than the circumstellar disk. However, this would imply that any giant planet orbiting LkCa~15 has, in practice, accreted the majority of its final mass despite the young age of the system. The non detection of millimeter emission at the position of the candidate young planet LkCa~15~b, and, in general, within the dust depleted cavity in LkCa~15 circumstellar disk, sets upper limits on the mass and radius of possible circumplanetary disks. For $M_{acc} \geq10^{-6}$ M$_J$ yr$^{-1}$, we find that the disk temperature is dominated by the viscous heating released by the accreting material and the 7~mm continuum disk emission is in first approximation independent of the luminosity of the central planet. Under this condition, our observations exclude the presence of disks more massive than about 0.1 $M_J$ and larger than about 1~AU, or 0.4 $r_H$ for a 10 $M_J$ planet orbiting at 16 AU from the central star. Higher mass accretion rates would imply lower disk masses and radii, but, as discussed in the previous section, an increase of four orders of magnitude in the mass accretion rate would lower the constraints on disk mass only by a factor of 10 and the disk radius by a factor of 3. If the dust depleted cavity observed in the LkCa~15 disk originates from the dynamical clearing operated by brown dwarfs or massive planets (e.g.,$>10$ M$_J$), our VLA observations suggest that the mass of their circumstellar disks should be less than a few percent of the planetary mass, unless they have very small radii. The upper limits for the circumplanetary disk mass are derived adopting the dust model employed in the study of the LkCa~15 circumstellar disk emission, which assumes a grain composition as in \cite{Pollack94}, a grain size distribution $n(a)\propto a^{-3.5}$ ranging between 0.5~$\mu$m and 0.5~mm, and a gas-to-dust ratio of 100 \citep[][]{Isella12}. The corresponding mass opacity at 7~mm is $2\times10^{-3}$ cm$^2$ g$^{-1}$. There are however at least two (competing) physical processes that might cause the mass opacity of a circumplanetary disk to differ from that of the parent circumstellar disk. The first process is the filtration, or trapping, of large dust grains at the outer edge of the cavity cleared by the gravitational interaction with massive planets. More precisely, \cite{Zhu11} find that only dust grain smaller than 10-100~$\mu$m might be able to filtrate from the outer disk into the dust depleted cavity. In this scenario, the material accreting onto circumplanetary disks would be depleted by large dust grains and have a gas-to-dust ratio higher than the circumstellar disk material. For example, if all the grains larger than 10~$\mu$m are trapped in the outer disk at $R>45$ AU, then the material accreting onto the circumplanetary disk would have a gas-to-dust ratio of 1000, i.e., 10 times larger than the material in the outer disk. The resulting mass opacity at 7 mm calculated accounting for both the higher gas-to-dust ratio and for the reduced maximum grain size would be $1.6\times10^{-4}$ cm$^2$ g$^{-1}$. However, the dust grains in a circumplanetary disk grains are expected to interact and grow in size similarly to what happens in the innermost regions of circumstellar disks. Actually, grain growth in circumplanetary disks is a key ingredient in current models for the formation of the Galilean satellites \citep[see, e.g.,][]{Canup09}. In this case, if the maximum grain size grows, for example, from 10~$\mu$m to 1 cm, then the 7 mm mass opacity would increase to $1.8\times10^{-3}$ cm$^2$ g$^{-1}$ (now assuming a gas-to-dust ratio of 1000). Given the uncertainties on mass opacity, the constraints in the circumplanetary disk mass set by our observations should therefore be cosidered uncertain by at least one order of magnitude. Future ALMA observations will provide better constraints on the mass and radius of circumplanetary disks orbiting around LkCa~15, and, in general, within disks characterized by large dust depleted cavities. ALMA full array will achieve in a few hours a sensitivity in disk mass 100 times greater than that obtained by VLA observations (Figure~\ref{fig:alma_com}) and an angular resolution sufficient to detect circumplanetary disks orbiting at a few AU from the central star at the distance of 140 pc. Assuming a dust emissivity proportional to $\nu^{1.0}$, ALMA band 7 observations ($\lambda=850$~$\mu$m) will achieve a mass sensitivity of $5 \times 10^{-4}$ $M_J$ in one hour of integration on source. Furthermore, ALMA observations in the other bands, although less sensitive, will allow the measurements of the spectral index of the continuum emission to study the evolution of solids, in a manner similar to that employed to study the grain size distribution in circumstellar disks (see, e.g., the review by Testi et al. 2014). \begin{figure}[!t] \centering \includegraphics[angle=0, width=\linewidth, bb=80 0 260 220, clip=True]{diskemission_comp_ALMA_macc1e-9.pdf} \caption{\label{fig:alma_com} Parameter space for the mass and radius of LkCa~15~b's circumplanetary disk that can be probed at more that 99.7\% confidence level in one hour of ALMA observations in the Band 3 (110 GHz), 6 (230 GHz), 7 (345 GHz), and 9 (650 GHz). The disk emission was calculated by assuming a mass accretion rate of $10^{-6} M_J$ yr$^{-1}$ and a dust opacity emissivity proportional to $\nu^{1.0}$. The gray region corresponds to the region probed by our VLA observations and it is the same as in left panel of Figure 3. } \end{figure} | 14 | 4 | 1404.5627 |
1404 | 1404.5319_arXiv.txt | We present the results of a set of numerical simulations of long-duration gamma-ray burst jets aimed at studying the effect of a variable engine on the peak frequency of the photospheric emission. Our simulations follow the propagation of the jet inside the progenitor star, its break-out, and the subsequent expansion in the environment out to the photospheric radius. A constant and two step-function models are considered for the engine luminosity. We show that our synthetic light-curves follow a luminosity-peak frequency correlation analogous to the Golenetskii correlation found in long-duration gamma-ray burst observations. Within the parameter space explored, it appears that the central engine luminosity profile does not have a significant effect on the location of a gamma-ray burst in the Luminosity-peak frequency plane, bursts from different central engines being indistinguishable from each other. | \label{sec:intro} Ever since the detection of the first Gamma-ray burst (GRB) by \citet{klebesadel73} and with the increase of the number of observed GRBs it has been clear that many of them share some general characteristics and so have even been grouped together in sub-classification groups. For example, depending on their duration GRBs have been classified in either long or short \citep{kouveliotou93}. Strikingly, there are no two GRBs which are exactly the same as the other. Variability is commonly observed \citep{walker00} in GRBs, and a significant fraction of the long GRBs ($\sim$85\%) appear to be the result of several pulses \citep{borgonovo07}. The pre- and post-bursting activity, as well as dormant periods, still remain to be fully understood \citep{drago07}. \citet{fenimore00} discovered a correlation between the variability and the observed peak isotropic luminosity. Thus, it is noteworthy to study the effects that a pulsed central engine has on the prompt GRB emission. The prompt emission of GRBs is characterized by bright, non-thermal spectra, peaking between a few tens of keV up to several MeV \citep{band93,kaneko06,gruber14}. The radiation mechanism responsible for the production of such emission is not fully understood, possibly owing to the great diversity of GRB spectra and light curves. Even though most proposed models are capable of finding a parameter set to fit any GRB spectrum, it has been so far impossible to make a synthesis and formulate a model that can successfully account for the diversity of the observations without requiring an adaptation to each individual burst, and resorting to extreme fine-tuning in some cases. An important tool in the effort of finding common properties among the diversity of burst observations is the sample of correlations among different bursts, such as the Amati, Yonetoku, and luminosity-Lorentz factor correlations (see \citet{amati02, yonetoku04, ghirlanda12} for further details, respectively). In previous publications \citep{laz11,laz13a} we have shown that the photospheric emission model for the prompt GRB emission can reproduce the Amati and luminosity-Lorentz factor correlations without requiring any fine tuning of parameters or any underlying correlation between the properties of the central engine and/or its relativistic outflow. Our simulations showed that the correlations are due to the most part to the observer angle effect: burst seen close to their jet axes appear brighter, have a higher peak frequency, and are produced by faster ejecta compared to bursts observed near the edge of their jets. One lingering uncertainty was, however, the robustness of the observational correlations that we attempted to explain. A significant amount of work has been carried out in trying to establish the role of selection effects in the Amati and Yonetoku correlations, with contradictory results, at best \citep{band05,nakar05,ghirlanda08,butler09,krimm09,kocevski12,heussaff13}. A more robust correlation that is certainly not affected by selection effects is the Golenetskii correlation, discovered by the Konus experiment \citep{golenetskii83} and confirmed more recently with the high-quality Fermi spectral data \citep{ghirlanda10,lu12}. According to the Golenetskii correlation, different time intervals of a single burst aligned along a straight line when plotted in the luminosity-peak frequency plane (for further discussion see \citet{bhat94, borgonovo01, ford95, kargatis94, lu10, norris86, peng09}. The burst spectrum peaks at lower frequencies when the emission is weak but moves to higher frequencies when it is bright. In order to study whether photosphere-dominated bursts obey this correlation, we have carried out three hydrodynamic simulations of relativistic jets from collapsars. Two have engines with highly variable energy output while the third, the control, has a constant engine, analogously to our previous work \citep{mor10}. We note that the fact that photosphere-dominated GRBs obey the Amati correlation does not imply that they should be able to reproduce the Golenetskii correlation. As a matter of fact, we showed that the difference in viewing angle is fundamental in producing the Amati correlation within the photospheric scenario \citep{laz11,laz13a}. In the Golenetskii case, instead, the viewing angle cannot play any role, since the observer is the same throughout the burst. This paper is organized as follows. We first describe the initial setup, and the numerical models in Section~\ref{sec:input}, followed by discussion of the the morphology, photospheric, and observable correlation's from our models in Section~\ref{sec:results}.. Conclusions are given in Section~\ref{sec:conc}. | \label{sec:conc} We presented the results of a set of numerical simulations of long-duration GRB jets followed as they propagate through their progenitor star, reach break-out, and expand outward until reaching the radius at which the spectrum of the advected radiation converge to a constant shape to be eventually released at the photosphere. This is the first time that jets from engines with variable luminosity are studied in such an extended domain. Our simulations allow us to explore whether the photospheric emission of jets from unsteady engines follows the Golenetskii correlation between the time-resolved luminosity and spectral peak. We find that the synthetic light curves and spectra from our three models reproduce the Golenetskii and Amati correlations, lending more support to the scenario in which the bulk of the burst prompt radiation is advected in the outflow and released at the photosphere. One notable exception is the light curve for an on-axis observer in our control model (m3). In that case, the synthetic datapoint for an horizontal line that does not follow the Golenetskii correlation. It appears, therefore, that while all GRBs from variable engines obey the correlation, outliers can be produced by engines of constant luminosity. Our simulations attempted to reproduce the correlation as a pulse-by-pulse phenomenon. The engine was set up to produce short pulses of half a second. Half a second features were detected in the light curves and analyzed as pulses, each pulse providing a single point in the Golenetskii plane. Observationally, the latter correlation is detected also within pulses, i.e., when the signal to noise is so high that a pulse can be split in sub-intervals. Our simulations cannot address this situation, at present. A new set of simulations with longer pulses and higher temporal resolution is planned and will be presented in a future publication. \textbf{Acknowledgements} We would like to thank the anonymous referee for constructive suggestions that led to the improvement of this paper. We thank S.E. Woosley and A. Heger for making their pre-SN models available. The software used in this work was in part developed by the DOE-supported ASC/Alliance Center for Astrophysical Thermonuclear Flashes at the University of Chicago. This work was supported in part by the Fermi GI program grant NNX12AO74G and Swift GI program grant NNX13A095G (DL and DLC). BJM is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1102796. | 14 | 4 | 1404.5319 |
1404 | 1404.2539_arXiv.txt | { Mapping of the near-infrared scattered light is a recent method for the study of interstellar clouds, complementing other, more commonly used methods, like dust emission and extinction. } { Our goal is to study the usability of this method on larger scale, and compare the properties of a filamentary structure using infrared scattering and other methods. We also study the radiation field and differences in grain emissivity between diffuse and dense areas. } { We have used scattered near-infrared (NIR) $J$, $H$, and $K$ band surface brightness observations with WFCAM instrument to map a filament TMC-1N in Taurus Molecular Cloud, covering an area of $1^{\circ} \times 1^{\circ}$ corresponding to $\sim$(2.44 pc)$^2$. We have converted the data into an optical depth map and compared the results with NIR extinction and \emph{Herschel} observations of sub-mm dust emission. We have also modelled the filament with 3D radiative transfer calculations of scattered light. } {We see the filament in scattered light in all three NIR bands. We note that our WFCAM observations in TMC-1N show notably lower intensity than previous results in Corona Australis using the same method. We show that 3D radiative transfer simulations predict similar scattered surface brightness levels as seen in the observations. However, changing the assumptions about the background can change the results of simulations notably. We derive emissivity, the ratio of FIR dust emission to column density, by using optical depth in the $J$ band, $\tau_{J}$, obtained from NIR extinction map as an independent tracer of column density. We obtain a value 0.0013 for the ratio $\tau_{250}/\tau_{J}^{Nicer}$. This leads to opacity or dust emission cross-section $\sigma_e(250 \mu \rm{m})$ values $1.7-2.4 \times 10^{-25} {\rm cm}^2/{\rm H}$, depending on assumptions of the extinction curve, which can change the results by over 40\%. These values are twice as high as obtained for diffuse areas, at the lower limit of earlier results for denser areas. } { We show that NIR scattering can be a valuable tool in making high resolution maps. We conclude, however, that NIR scattering observations can be complicated, as the data can show comparatively low-level artefacts. This suggests caution when planning and interpreting the observations. } | \label{sect:intro} The structure of molecular clouds can be studied via a number of methods. These include molecular line mapping, observations of dust emission at far-infrared/sub-millimetre wavelengths, star counts in the optical and near-infrared (NIR) wavelengths, and measurements of colour excesses of background stars. All techniques have their own drawbacks. For example, line and continuum emission maps are subject to abundance variations (gas and dust, respectively) and variations in the physical conditions, most notably the excitation and kinetic temperatures. Mass estimates based on dust emission can also be biased because of line-of-sight temperature variations, especially in high density clouds where star formation is potential~\citep[see, e.g.,][]{Malinen2011}. The colour excess method provides column density estimates for extremely narrow lines of sight toward background stars. However, the intrinsic colours of the stars are usually unknown and this introduces significant noise, especially at low column densities. A full extinction map is obtained only after spatial averaging. This means that for all the listed methods the spatial resolution is usually some tens of arc seconds or worse. See, e.g.,~\citet{Juvela2006} for a more thorough review of the methods, \citet{Goodman2009} for a comparison of several methods, and \citet{Malinen2012} for a comparison of filament properties derived using NIR extinction and \emph{Herschel} observations of dust emission. Surface brightness caused by scattered NIR light provides another means of studying cloud structure. The first observation of scattered NIR light from molecular clouds illuminated by the normal interstellar radiation field (ISRF) was by \citet{Lehtinen1996}. Later the observations of \citet{Nakajima2003} and \citet{Foster2006} (who also named the phenomenon ''cloudshine'') have shown that it is now possible to obtain large maps of the surface brightness of normal interstellar clouds illuminated by the normal ISRF. NIR scattering can therefore be a new, complementary tool for studying the structure of dark clouds. See, e.g.,~\citet{Juvela2006} for a more complete review of the history of scattered light observations in dark clouds. \citet{Padoan2006} presented a method to determine the cloud column density from the intensity of the near-infrared scattered light. \citet{Juvela2006} analysed the method in more detail using simulations, and developed a method to combine the surface brightness with extinction, to reduce errors caused by wrong assumptions of radiation field or dust properties. Starting with the known properties of the interstellar dust and ISRF, the papers made predictions for the visibility of the cloudshine and for the accuracy of the resulting column density estimates. They also demonstrated, independently of the direct evidence given by the \citet{Foster2006} data, that such observations are well within the capabilities of modern wide-field infrared cameras. The main advantage of the new method is the potentially extremely good spatial resolution. When the $J$, $H$, and $K$ bands are used, the method remains accurate in regions with $A_{\rm V}$ even beyond 10 magnitudes. The same NIR observations provide data for the colour excess method, which means that the results of the methods can be compared at lower spatial resolution. Although both methods depend on near-infrared dust properties, the main sources of error are different. Comparison of the results can be used to study the values and variation of near-infrared dust properties (e.g., albedo and the shape of the extinction curve) and spatial variations in the strength of the local radiation field. Furthermore, correlations between wavelength bands give a direct way to estimate the point at which the contribution of dust emission from stochastically heated grains becomes significant. The level of the emission of these so-called Sellgren grains depends on the radiation field~\citep{Sellgren1996}, but is still uncertain in normal interstellar clouds. On the other hand, the amount of the scattered light depends heavily on the grain size~\citep{Steinacker2010}. These dependencies have implications for models of interstellar dust. \citet{Juvela2008} used scattered NIR light to derive a column density map of a part of a filament in Corona Australis, and continued the analysis in a larger area in \citet{Juvela2009}. They also compared the NIR data with \emph{Herschel} sub-millimetre data in \citet{Juvela2012b}. \citet{Nakajima2008} applied a similar method to convert NIR scattered light to column density. They used the colour excess of individual background stars to calibrate an empirical relationship between surface brightness and column density, instead of an analytical formula, as used in \citet{Juvela2006,Juvela2008}. Scattered surface brightness from dense cores in the mid-infrared (MIR) was reported by~\citet{Pagani2010} and~\citet{Steinacker2010}. \citet{Steinacker2010} named this phenomenon ``coreshine'' as a counterpart to ``cloudshine'', which is also observed in the outer parts of the clouds. In this paper, we study a filament in the Taurus molecular cloud using observations of NIR light of a $1^{\circ} \times 1^{\circ}$ field observed with WFCAM instrument~\citep{Casali2007}. Distance to the Taurus molecular cloud is $\sim$140 pc, making it one of the closest relatively high latitude clouds, and consequently one of the most studied star-forming regions~\citep[see, e.g.,][]{Cambresy1999,Nutter2008,Kirk2012,Palmeirim2013}. In \citet{Malinen2012}, we compared the properties of this filament derived using NIR extinction and dust emission observed with \emph{Herschel}. Here, we construct maps of the diffuse surface brightness, determine the intensity of the NIR scattered light, and derive the optical depth based on scattered NIR light using the method presented in \citet{Padoan2006}. We compare the scattered light images with the other tracers, NIR extinction and sub-millimetre dust emission and, using these results, draw some conclusions regarding the intensity and spectrum of the local ISRF. We also perform radiative transfer modelling to compare observations with the level of NIR and MIR scattered light that is expected using standard ISRF levels and standard dust models. The contents of the article are the following: We present observations and data processing in Sect.~\ref{sect:observations}. We describe the method for deriving optical depth from scattered NIR surface brightness in Sect.~\ref{sect:method}. We derive NIR surface brightness maps and optical depth maps based on observations of dust emission, NIR extinction, and NIR scattered surface brightness and compare the results in Sect.~\ref{sect:results}. We describe radiative transfer modelling of a filament seen in scattered light in Sect.~\ref{sect:models}. We discuss the results in Sect.~\ref{sect:discussion} and present our conclusions in Sect.~\ref{sect:conclusions}. | \label{sect:conclusions} We have used WFCAM NIR surface brightness observations to study scattered light in the TMC-1N filament in Taurus Molecular Cloud. We have presented a large NIR surface brightness map ($1^{\circ} \times 1^{\circ}$ corresponding to $\sim$(2.44 pc)$^2$) of this filament. We have converted the data into an optical depth map and compared the results with NIR extinction and \emph{Herschel} observations of sub-mm dust emission. We have also modelled the filament by carrying out 3D radiative transfer calculations of light scattering. \begin{itemize} \item We see the filament in scattered light in all three NIR bands, $J$, $H$, and $K$. \item In all three NIR bands, our WFCAM observations in TMC-1N show lower intensity than previous results in Corona Australis, indicating a lower radiation field in this area. This reaffirms the previous findings, that the radiation field in Corona Australis is at least three times that of the normal ISRF. \item We derive a value 0.0013 for the ratio $\tau_{250}/\tau_{J}^{Nicer}$ . This leads to values $\sigma_e(250 \mu \rm{m})\sim1.7-2.4\times10^{-25} {\rm cm}^2/{\rm H}$, depending on the assumptions of the extinction curve ($R_V = $ 3.1 or 4.0) which can change the results by over 40\%. These $\sigma_e(250 \mu \rm{m})$ values are twice the values reported for diffuse medium, at the lower limit of the values for denser areas. \item Changing $\beta$ from 1.8 to 2.0 increases the ratio $\tau_{250}/\tau_{J}^{Nicer}$ by $\sim$30\%. \item We see no indication of systematic growth of the $\tau_{250}/\tau_{J}^{Nicer}$ ratio towards the densest filament. However, all the assumptions made in the process may not be valid in the densest part of the filament. Also, some areas of high $\tau_{250}/\tau_{J}^{Nicer}$ ratio can be caused by imperfections in the $\tau_{250}$ and $\tau_{J}^{Nicer}$ maps, due to, e.g., the lack of background stars seen behind the densest filament, instead of real changes in the dust properties. \item 3D radiative transfer simulations predict surface brightness that is in intensity close to the observed values, especially in the $H$ and $K$ bands. In the $J$ band, the model predictions can be over two times larger than observations, if no background correction is made. However, using background correction can change the results notably. \item We see no clear evidence for emission in the $K$ band, in addition to the scattered light, based on the observations and simulations. \item NIR surface brightness can be a valuable tool in making high resolution maps, also at large scales. \item NIR surface brightness observations can be complicated, however, as the data can show comparatively low-level artefacts, that are still comparable to the faint surface brightness. This suggests caution when planning and interpreting the observations. \item It is possible to remove most of the effects of instrumental gradients, provided that they only affect large scales. \end{itemize} | 14 | 4 | 1404.2539 |
1404 | 1404.7293_arXiv.txt | We present a systematic study of the orbital inclination effects on black-hole transients fast time-variability properties. We have considered all the black-hole binaries that have been densely monitored by the Rossi XTE satellite. We find that the amplitude of low-frequency quasi periodic oscillations (QPOs) depends on the orbital inclination. Type-C QPOs are stronger for nearly edge-on systems (high inclination), while type-B QPOs are stronger when the accretion disk is closer to face-on (low inclination). Our results also suggest that the noise associated with type-C QPOs is consistent with being stronger for low-inclination sources, while the noise associated to type-B QPOs seems inclination independent. These results are consistent with a geometric origin of the type-C QPOs - for instance arising from relativistic precession of the inner flow within a truncated disk - while the noise would correspond to intrinsic brightness variability from mass accretion rate fluctuations in the accretion flow. The opposite behavior of type-B QPOs - stronger in low inclinations sources - supports the hypothesis that type-B QPOs are related to the jet, the power of which is the most obvious measurable parameter expected to be stronger in nearly face-on sources. | Quasi-periodic oscillations (QPOs) were discovered several decades ago in the X-ray flux emitted from accreting black hole (BH) binaries and have been observed in many systems. In a Fourier power density spectrum (PDS) they take the form of relatively narrow peaks and appear together with different kinds of broad-band noise (e.g. \citealt{Takizawa1997}, \citealt{Casella2005}, \citealt{Motta2012}). It is now clear that QPOs are a common characteristic of accreting BHs and they have been observed also in neutron stars (NS) binaries (e.g. \citealt{VdK1989}, \citealt{Homan2002a}, \citealt{Belloni2007}), in cataclysmic variable (see e.g. \citealt{Patterson1977}) in the so-called \textit{ultra luminous X-ray sources} (possibly hosting intermediate-mass BHs, e.g. \citealt{Strohmayer2003a}, \citealt{Strohmayer2003a}) and even in Active Galactic Nuclei (AGNs, e.g. \citealt{Gierlinski2008}, \citealt{Middleton2010}). Low-frequency QPOs (LFQPOs), with frequencies ranging from a few mHz to $\sim$20 Hz were first observed with \emph{Ariel 6} in the BH binary GX 339-4 (\citealt{Motch1983}) and observations with \emph{Ginga} provided the first indications for the existence of multiple types of LFQPOs (see e.g. \citealt{Miyamoto1991} and \citealt{Takizawa1997}). Three main types of LFQPOs, type-A, type-B, and type-C\footnote{Type-C QPOs are by far the most common type of QPOs observed in BH binaries. Their amplitude is usually large and they are characterized by a variable frequency ranging the 0.1-30 Hz interval. Type-B QPOs are less common than the type-C QPOs, they are usually observed along the transition form hard to soft in transient BH binaries with frequencies around $\sim$6Hz. Among LFQPOs, type-A QPOs are the least common of all. They usually appear in the soft states of transient BH binaries as broad and weak peaks.}, originally identified in the PDS of XTE J1550-564 (see e.g. \citealt{Wijnands1999}; \citealt{Homan2001}; \citealt{Remillard2002}, \citealt{Casella2005}, \citealt{Motta2011a}), have been seen in several sources. These are distinct from the high-frequency QPOs, found at frequency up to $\sim$450Hz, which we do not consider in this work (but see \citealt{Belloni2012} for a review). The origin of LFQPOs is still unclear and there is no consensus about their physical nature, although their study provides a valuable way to explore accretion around accreting compact objects. Several models have been proposed to explain the origin and the evolution of LFQPO in X-ray binaries. Some of them invoke the effects of General Relativity (GR) (e.g. \citealt{Stella1999a}, \citealt{Ingram2009}, \citealt{Motta2014}), while others are based on different kinds of instabilities (e.g. \citealt{Titarchuk1999}, \citealt{Tagger1999}, \citealt{Lamb2001}). On the other hand, several doubts still surround the origin of type-B QPOs, for which no comprehensive model has been proposed. However, it has been speculated that type-B QPOs are associated with the strong relativistic jets that occurs in BH binaries (BHB) during specific state transitions (\citealt{Fender2009}, \citealt{Miller-Jones2012}). It has been known for a long time that inclination strongly affects the observed properties of AGNs (see e.g. \citealt{Antonucci1993}, \citealt{Urry1995}, \citealt{Risaliti2002}, \citealt{Bianchi2012}). Over the last years, it has become increasingly clear that the same is true for Galactic accreting BHBs. \cite{Ponti2012} found strong evidences that the accretion disk winds observed in the radio quiet soft states of BHBs have an equatorial geometry with opening angles of a few degrees and therefore can only be observed in sources where the disc is inclined at a large angle \textit{i} to the line of sight (\textit{high-inclination sources}, as opposed to \textit{low-inclination sources}, where the orbital plane is closer to perpendicular to the line of sight). More recently, the results by \cite{Munoz-Darias2013} supported the hypothesis that the inclination modifies the q-shaped tracks that BHB in outburst display in a hardness-intensity diagram (HID, \citealt{Homan2001}), which can be at least partially explained by considering inclination-dependent relativistic effects on the accretion disc. Finally, \cite{Corral-Santana2013} have found that obscuration effects similar to those observed in AGN, can be relevant in very high inclination BHBs. However, \cite{Gallo2003} and \cite{Soleri2011} noted that there is no evidence that the hard state radio luminosity is a function of inclination. In this work, we use data collected by the Rossi X-ray Timing Explorer (RXTE)/Proportional Counter Array (PCA) satellite to analyse the effects of inclination on the fast time-variability properties of BHBs. \begin{table*} \renewcommand{\tabcolsep}{0.18cm} \centering \caption{List of black hole transients and outbursts included in this work. In the column \textit{comments} we report some informations about the behaviour of the sources relevant to distinguish between high and low inclination systems. With \textit{high inclination evolution (High-IE)}, \textit{intermediate inclination evolution (Int.-IE)} and \textit{low-inclination evolution (Low-IE)} we refer to high, intermediate and low disk temperatures, respectively, as reported in \citealt{Munoz-Darias2013}. As discussed by these authors, the differences in the disk temperatures can be largely ascribed to the inclination of the disk to the line of sight.With the term \textit{spikes} we refer to flux spikes visible in both the lightcurve and HIDs of most high-inclination systems (see \citealt{Munoz-Darias2013}). The term \textit{winds} or \textit{dipping} in the \textit{comments} column indicate that equatorial winds or absorption dips, respectively, have been reported for that source. }\label{tab:sources} \begin{tabular}{c c c c c c c c} \hline System & Outburst & Inclination$^e$ ($^{\circ}$) & Comments & Ref. & Type-A & Type-B & Type-C \\ \hline Swift J1753.5-01 & 2005-2010 & $\sim$ 40--55 & Failed outburst $^{(d)}$ & 0 & & & 32 \\ 4U 1543-47 & 2002 & $20.7 \pm 1.5$ & Low-IE; & 1 & 2 & 3 & 11 \\ XTE J1650-500 & 2001 & $>$ 47 & Low-IE; & 2 & & 1 & 25 \\ GX 339-4 & 2002, 2004, 2007, 2010 & $\geq$ 40$^{(c)}$ & Low-IE; & 3 & 4 & 23 & 54 \\ XTE J1752-223 & 2009 & $\leq$ 49$^{(a)}$ & Low-IE; & 4 & & 2 & 4 \\ XTE J1817-330 & 2006 & & Low-IE; & & 2 & 9 & 2 \\ \hline XTE J1859+226 & 1999 & $\geq$ 60$^{(b)}$ & Int.-IE (spikes) & 5 & 5 & 19 & 24 \\ MAXI J1543-564 & 2011 & & Spikes; & & & & 5 \\ \hline XTE J1550-564 & 1998, 2000 & $74.7 \pm 3.8$ & high-IE (spikes); dipping; & 6,7 & 1 & 18 & 48 \\ 4U1630-47 & 2002, 2003, 2004, 2005 & & high-IE (spikes); dipping; winds; & 8, 9 & & 6 & 19 \\ GRO J1655-40 & 1996, 2005 & $70.2\pm 1$ & high-IE (spikes); dipping; winds; & 8, 10 & & 4 & 50 \\ H1743-322 & 2003, 2004, 2008 (Jan. and Oct.), & $75\pm3$ $^{(a)}$ & high-IE (spikes); dipping; winds; & 11, 12, 13 & & 42 & 108 \\ & 2009, 2010 (Jan. and Aug.) & & & & & & \\ MAXI J1659-152 & 2010 & & Spikes; dipping; & 14 & & 8 & 40 \\ XTE J1748-288 & 1998 & & Spikes; dipping; & & & & 7 \\ \hline \end{tabular} \begin{flushleft} (a) Assuming that the radio jet is perpendicular to the accretion disk.\\ (b) Inclination $\sim$ 60 degrees if accretion disc does not contribute to the optical luminosity in quiescence.\\ (c) The constrain is placed assuming that the mass of the BH should not be larger than 20 M$_{\odot}$.\\ (d) Failed outburst (see \citealt{Soleri2013}).\\ (e) Inclination measurements come either form the X-rays or from multi-wavelength observations (moslty optical and radio).\\ \textsc{REFERENCES:} (0) \cite{Neustroev2014} ;~(1) \citet{Orosz2002};~(2) \citet{Orosz2004};~(3) \citet{Munoz-Darias2008};~(4) \cite{Miller-Jones2011}; ~(5) \citet{Corral-Santana2011};~(6) \citet{Orosz2011}; ~(7) \citet{Homan2001}; ~(8) \citet{Kuulkers1998}; ~ (9) \citet{Tomsick1998};~(10) \citet{Greene2001}; ~(11) \citet{Corbel2005}; ~(12) \citet{Steiner2012}; ~(13) \citet{Homan2005b}; ~(14) \citet{Kuulkers2013}; \end{flushleft} \end{table*} | We have analyzed a large sample of archival RXTE observations were we detected low frequency QPOs. We assumed that there are no intrinsic differences between the sources of our sample and that the presence of absorption dips in the light-curve of a source corresponds to high orbital inclination. We have shown that inclination has a strong effect on the QPOs. We found that: \begin{itemize} \item Type-C QPOs appear stronger in high inclination sources. \item Type-B QPOs show the opposite behavior, being stronger for low-inclination sources. \item The noise associated with both type-C QPOs is consistent with being stronger for low-inclination sources, while the noise associated with type-B QPOs is consistent with being inclination independent. \end{itemize} Our results suggest that: \begin{itemize} \item type-C QPOs, type-B QPOs and the broad band noise associated with type-C QPOs are geometrically/physically different phenomena. \item type-C QPOs are consistent with having a geometrical origin. In particular, we find that the relativistic precession is the only mechanism that satisfies all our observational constraints and therefore is favoured by our results. \item at variance with type-C QPOs, the associated broad band noise might, instead, correspond to intrinsic brightness variability induced by fluctuations in the mass accretion rate propagating in an hot flow that emits in a non-isotropic way. \item fast transition between type-C and type-B QPOs could be the best trackers in the X-rays of the relativistic ejections typical of most BH transients. \end{itemize} \bigskip \noindent \footnotesize{SEM acknowledges Peggy Varniere, Lucy Heil, Erik Kuulkers and Jari Kajava for useful comments and discussion on this work. SEM and MH acknowledge support from the ESA research fellowship program and from the ESAC Faculty. SEM also acknowledges the Observatory of Rome and Brera for hospitality. TMD and PC acknowledge support from the ESAC Faculty and ESA for hospitality. TMB and SEM acknowledge support from INAF PRIN 2012-6. TMD acknowledges funding via an EU Marie Curie Intra-European Fellowship under contract no. 2011-301355. PC acknowledges support by a Marie Curie FP7-Reintegration-Grants under contract no. 2012-322259. This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center. } \appendix | 14 | 4 | 1404.7293 |
1404 | 1404.2649_arXiv.txt | We present the results of a survey for \CaII~$\lambda\lambda 3934,3969$ absorption-line systems culled from $\sim 95,000$ Sloan Digital Sky Survey (SDSS) Data Release 7 and Data Release 9 quasar spectra. With $435$ doublets identified in the catalog, this list is the largest \CaII~catalog compiled to date, spanning redshifts $z < 1.34$, which corresponds to the most recent $\sim 8.9$ Gyrs of the history of the Universe. We derive statistics on the \CaII~rest equivalent width distribution and incidence (number density per unit redshift). We find that the $\lambda 3934$ rest equivalent width ($W_{0}^{\lambda 3934}$) distribution cannot be described by a single exponential function. A double exponential function is required to produce a satisfactory description. The function can be written as a sum of weak and strong components: $ {\partial n}/{\partial W_{0}^{\lambda 3934}}= ({N_{wk}^{\star}}/{W_{wk}^{\star}}) exp({ -{W_{0}^{\lambda 3934}}/{W_{wk}^{\star} } }) + ({N_{str}^{\star}}/{W_{str}^{\star}}) exp({ -{W_{0}^{\lambda 3934}}/{W_{str}^{\star} } }) $. A maximum likelihood fit to the unbinned data indicates: $N_{wk}^{\star}=0.140\pm0.029$, $W_{wk}^{\star}=0.165\pm 0.020~\textrm{\AA}$, $N_{str}^{\star}=0.024\pm0.020$, and $W_{str}^{\star}=0.427\pm 0.101~\textrm{\AA}$. This suggests that the \CaII~absorbers are composed of at least two distinct populations. The incidence (product of integrated absorber cross section and their co-moving number density) of the overall \CaII~absorber population does not show evidence for evolution in the standard cosmology. The normalization of the no-evolution curve, i.e., the value of the \CaII\ incidence extrapolated to redshift $z=0$, for $W_{0}^{\lambda 3934} \ge 0.3$ \AA, is $n_0=0.017 \pm 0.001$. In comparison to \MgII~surveys, we found that only $3\%$ of \MgII~systems in the SDSS have \CaII, confirming that it is rare to identify \CaII~in quasar absorption-line surveys. We also report on some preliminary investigations of the nature of the two populations of \CaII~absorbers, and show that they can likely be distinguished using their \MgII~properties. | \label{intro} A successful and complete theory of galaxy formation and evolution must not only explain the properties of the luminous components of galaxies, but also account for the properties, kinematics, and evolution of gaseous structures associated with them. Quasar absorption lines (QALs) are an extremely powerful probe of the physical properties and kinematics of the gas in galactic, intergalactic and circumgalactic environments. Since the detection of gaseous structures in absorption is independent of the luminosity of the absorbing medium, quasar spectroscopy has been crucial in providing a wealth of information on the distribution and evolution of matter in the Universe. Without the selection bias caused by galaxy brightness and surface brightness limitations, one can identify structures that are fainter than what traditional imaging studies allow. QAL studies have resulted in the identification of a gamut of intervening gaseous absorbers from the coolest molecular clouds detected in H$_2$ (e.g., Noterdaeme et al. 2008) to the predominantly neutral regions identified as \HI\ damped Lyman alpha systems (DLAs) and low-ionization \MgII\ absorbers (e.g., Noterdaeme et al. 2012, Rao, Turnshek, \& Nestor 2006, Quider et al. 2011, Seyffert et al. 2013), as well as hot ionized plasma in the extended halos of galaxies (e.g., Werk et al. 2014). The resonance transitions for the most common atoms and ions fall in the rest-frame ultraviolet (UV). Consequently, the QALs used to explore and make identifications of these various gaseous components studies have often concentrated on absorbers at moderate to high redshifts where these lines fall at wavelengths accessible to optical ground-based telescopes. Given available time allocations, the option of using space-based telescopes such as the Hubble Space Telescope (HST) to perform large UV QAL surveys is impractical, expensive, and unrealistic. Consequently, large statistical studies of absorption line systems and the gaseous components of low-redshift galaxies that they trace are lacking. One particular class of absorber, which falls at optical wavelengths at low redshift, is that traced by the \CaII~H \& K doublet, i.e. \CaII~$\lambda\lambda3934,3969$. It is a resonance doublet transition of singly ionized calcium from the ground state with rest-frame wavelengths $\lambda=3934.78~\mathrm{\AA}$ (\CaII~K) and $\lambda=3969.60~\mathrm{\AA}$ (\CaII~H). The energy required to photoionize the neutral Ca atom is $6.11~\mathrm{eV}$. However, the energy required to photoionize Ca$^{+}$ is only $11.87~\mathrm{eV}$, a value that is slightly less than the ionization potential of \HI. Thus, Ca$^+$~may not be the dominant ionization state of calcium. Moreover, Ca is a highly refractory element, being among the most depleted in the interstellar medium (Savage and Sembach 1996; Wild and Hewett 2005; Wild, Hewett \& Pettini 2006). Thus, \CaII\ is a rare class of absorber, which nevertheless is an important diagnostic of key physical properties of the gas such as its density, degree of self-shielding, and dust content. Strong \CaII~absorption may preferentially arise in environments where some fraction of the dust grains has been destroyed, and the proportion of gaseous Ca has been enhanced by a large factor due to supernova-driven shocks associated with recent star-formation (Routly \& Spitzer 1952). More recent studies of a handful of \CaII~absorbers (Wild \& Hewett 2005; Wild, et al. 2006; Wild, Hewett \& Pettini 2007; Nestor et al. 2008; Zych et al. 2007; Zych et al. 2009) indicate that strong \CaII~systems preferentially reside in dense, dusty, neutral, metal-rich, molecular $H_{2}$-bearing environments –- the reservoirs for subsequent star-formation. Moreover, measurements (Zhu \& Menard 2013) of the average density profile of \CaII~gas around galaxies out to $\mathrm{\sim200~kpc}$ using cross-correlation analysis of the positions of $\sim 10^{6}$ foreground galaxies with $\sim 10^{5}$ background quasars in the Sloan Digital Sky Survey (SDSS) concluded that most of the \CaII~in the Universe is in the circum- and intergalactic environments, and that the \CaII~content in galaxy halos is larger for galaxies with higher stellar mass and star formation rates. Studies of the extent of rare \CaII~absorbers around galaxies will, therefore, place important empirical contraints on models for the existence of cool gas in the extended regions of galaxies. This includes models of cold accretion (e.g. Dekel \& Birnboim 2006, Kere$\check{\rm s}$ et al. 2009, Stewart et al. 2011, and references therein) and models relying on radiation pressure driving from massive clusters followed by ram pressure driving from SNe (e.g, Nath \& Silk 2009, Murray et al. 2011, Sharma \& Nath 2012, and references therein), which can launch cool gas out beyond 50 kpc. These processes have implications for the fueling and evolution of galaxies (Dav\'e, Oppenheimer \& Finlator 2011; Dav\'e, Finlator \& Oppenheimer 2011, and references therein): cold accretion fuels star formation, while resulting feedback and outflows quench it. Furthermore, such studies are useful in understanding trends in the colors, luminosities, morphologies and orientations of galaxies, as well as the dust-content and metal-enrichment of the IGM/CGM. Since \CaII\ can be detected in ground-based surveys down to $z=0$, the lowest redshift \CaII\ systems allow for detailed studies of the absorbers and their host galaxy environments. In this paper, we present the results from the largest sample of \CaII~$\lambda\lambda 3934, 3969$ absorbers ever compiled. In a blind survey of roughly $95,000$ quasar spectra from the Seventh and Ninth Data Release of the SDSS (SDSS-DR7, DR9), we identified $435$ \CaII~doublets with $W_{0}^{\lambda 3934} \ge 0.15 ~\mathrm{\AA}$. The wavelength coverage of the SDSS spectrum allows us to probe the redshift interval $z < 1.34$, which corresponds to $\sim8.9~\mathrm{Gyr}$ of cosmic history. More importantly, \CaII~gives us ground-based access to the low redshift regime of $z < 0.34$, equivalent to $\sim 4$ Gyrs of cosmic history, unlike any other commonly observed ionic transition. The paper is organized as follows: In \S2 we describe the data reduction process: the continuum fitting and line-finding algorithms, the selection criteria we imposed, and tests for systematic biases. We then present our main results in \S3, where we derive the absorber rest equivalent width (REW) parametrization and evolution and the absorber redshift number density and its evolution, along with results on \CaII~doublet ratios and how the incidence of \CaII~absorbers compares with that of \MgII~absorbers. In \S4, we discuss evidence for two populations of \CaII~ absorbers. We summarize and present our conclusions in \S5. Throughout the paper, we assume a standard $\mathrm{\Lambda}$CDM cosmology with $\mathrm{H_{0}=71~km~s^{-1}Mpc^{-1}}$, $\mathrm{\Omega_{M}=0.27}$, and $\mathrm{\Omega_{\Lambda}=0.73}$ (Spergel et al. 2007; Komatsu et al. 2011). | We have presented the results of a blind survey for intervening \CaII~absorption-line systems using $\sim 95,000$ quasar spectra from the seventh and ninth data release of the SDSS. Our results represent the largest compilation of \CaII~absorbers to date. The rest wavelengths of the \CaII$\lambda\lambda 3934,3969$~doublet resonance transition allow us to probe redshifts $z \lesssim 1.34$, which corresponds to the most recent $\sim 8.9$ Gyrs of the history of the Universe. \CaII~absorbers are considerably more rare than \MgII~ absorbers. However, it is notable that with the orginal SDSS spectrograph, \MgII~absorbers at $z \lesssim 0.4$ are not accessible. Therefore, studies of \CaII~absorbers in quasar spectra are the only absorption-line systems which are generally accessible with SDSS spectra at $z\lesssim0.4$, which is equivalent to the past $\sim 4.3$ Gyrs of cosmic time. Consequently, within the SDSS spectral window \CaII~presents a unique opportunity for ground-based studies of cool, metal-rich gas around galaxies at the lowest redshifts, and such studies can help to constrain models for the existence of cool gas in the extended gaseous halos of galaxies. Our blind survey resulted in the identification of $435$ \CaII~absorbers at rest equivalent width significance levels $\geq5\sigma$ for $W_0^{\lambda3934}$ and $\geq2.5\sigma$ for $W_0^{\lambda3969}$, within the physically-allowable doublet ratio range, i.e., $ 1 - \sigma_{DR} \leq W_0^{\lambda3934}/W_0^{\lambda3969} \leq 2 + \sigma_{DR}$. Of these detections, 251 \CaII~absorbers at $z\gtrsim 0.4$ were found to have associated \MgII~absorption, which is essentially all of them. The sensitivity-corrected $W_0^{\lambda3934}$ distribution cannot be fitted by a single-component exponential function, but a two-component exponential function describes the data well. We find $ {\partial n}/{\partial W_{0}^{\lambda 3934}}= ({N_{wk}^{\star}}/{W_{wk}^{\star}}) exp({ -{W_{0}^{\lambda 3934}}/{W_{wk}^{\star} } }) + ({N_{str}^{\star}}/{W_{str}^{\star}}) exp({ -{W_{0}^{\lambda 3934}}/{W_{str}^{\star} } })$, with $N_{wk}^{\star}=0.140\pm0.029$, $W_{wk}^{\star}=0.165\pm 0.020~\textrm{\AA}$, $N_{str}^{\star}=0.024\pm0.020$, and $W_{str}^{\star}=0.427\pm 0.101~\textrm{\AA}$. This suggests that the \CaII~absorbers are composed of at least two distinct populations (Figure 7). The \CaII~absorber incidence was found to not evolve in the standard cosmology, implying that the product of integrated \CaII~absorber cross section and their comoving number density has remained roughly constant over the last $\sim 8.9$ Gyrs. The normalization of the no-evolution curve, which is also the incidence extrapolated to $z=0$, is $n_0=0.017 \pm 0.001$ for the sample with $W_{0}^{\lambda 3934} \ge 0.3$ \AA. Furthermore, we have demonstrated that the incidence of \CaII~absorbers relative to the more common \MgII~absorbers in quasar spectra is about $3$ to $10$ times smaller, depending on the REW threshold used for the comparison (Figure 15). Finally, we performed some investigations to determine if we could use available \CaII~absorber properties, specifically doublet ratio and \MgII\ information, to isolate the ``weak'' and ``strong'' populations of \CaII~absorbers. While it was not possible to do this using the \CaII\ doublet ratio, we did find that \MgII\ information could be used to isolate the two populations (Figures 16 and 17). \nocite{*} | 14 | 4 | 1404.2649 |
1404 | 1404.5775_arXiv.txt | Previous estimates of the solar flare abundances of Si, S, Cl, Ar, and K from the RESIK X-ray crystal spectrometer on board the {\em CORONAS-F} spacecraft were made on the assumption of isothermal X-ray emission. We investigate the effect on these estimates by relaxing this assumption and instead determining the differential emission measure (DEM) or thermal structure of the emitting plasma by re-analyzing RESIK data for a {\em GOES} class M1.0 flare on 2002 November~14 (SOL2002-11-14T22:26) for which there was good data coverage. The analysis method uses a maximum-likelihood (Withbroe--Sylwester) routine for evaluating the DEM. In a first step, called here AbuOpt, an optimized set of abundances of Si, S, Ar, and K is found that is consistent with the observed spectra. With these abundances, the differential emission measure evolution during the flare is found. The abundance optimization leads to revised abundances of silicon and sulfur in the flare plasma: $A({\rm S}) = 6.94 \pm 0.06$ and $A({\rm Si}) = 7.56 \pm 0.08$ (on a logarithmic scale with $A({\rm H}) = 12$). Previously determined abundances of Ar, K, and Cl from an isothermal assumption are still the preferred values. During the flare's maximum phase, the X-ray-emitting plasma has a basically two-temperature structure, with the cooler plasma with approximately constant temperature (3--6~MK) and a hotter plasma with temperature $16-21$~MK. Using imaging data from the {\em RHESSI} hard X-ray spacecraft, the emission volume of the hot plasma is deduced from which lower limits of the electron density $N_e$ and the thermal content of the plasma are given. | Observations of solar soft X-ray spectra are essential for the diagnostics of hot plasmas associated with flares and active regions. The fluxes of emission lines and continua depend sensitively on electron temperature or rather, since the plasma is not in general isothermal, the distribution of emission measure with electron temperature. For rapidly varying conditions, X-ray spectra can also be used to find the plasma's ionization state or the presence of nonthermal electrons. If combined with images taken at similar energy ranges, lower limits of electron densities and the energy content of the emitting plasma can also be found. The RESIK (REntgenovsky Spektrometr s Izognutymi Kristalami: \citet{jsyl05}) instrument, a crystal spectrometer aboard the Russian {\it CORONAS-F} spacecraft, is one of several such spectrometers over the past 30 years or so using a bent crystal geometry with position-sensitive detectors, so that complete spectra over particular ranges can be captured in short time intervals and with much higher sensitivity than is possible with flat scanning spectrometers. RESIK obtained spectra from non-flaring active regions and during numerous flares between 2001 and 2003, the only crystal spectrometer to do so. This period occurred during the latter part of Cycle~23, when the activity levels were higher than at any time since, including the peak of the present cycle (number 24). Consequently, a number of large active regions and flares were observed, and the results already discussed; a catalog of observations is available at http://www.cbk.pan.wroc.pl/experiments/resik/resik\_catalogue.htm. Four spectral bands covered the nominal range 3.4~\AA--6.1~\AA\ with two silicon crystals (Si 111, $2d = 6.27$~\AA) for channels 1 and 2 (spectral ranges for an on-line source 3.40~\AA--3.80~\AA, 3.83~\AA--4.27~\AA) and two quartz crystals (quartz $10\bar 10$, $2d = 8.51$~\AA) for channels 3 and 4 (spectral ranges 4.35~\AA--4.86~\AA, 5.00~\AA--6.05~\AA). Instrumental fluorescence background emission, often a problem with previous solar X-ray spectrometers, was minimized through the adjustment of pulse-height analyzer settings over the mission lifetime; ultimately, for the period 2002 December~24 to 2003 March~23, the fluorescence background was entirely eliminated for channels 1 and 2 and its amount reduced and accurately estimated for channels 3 and 4. To maximize the instrument's sensitivity, no collimator was used; although this introduced the possibility of overlapping spectra from two or more X-ray sources on the Sun, in practice this very rarely occurred. RESIK was intensity-calibrated to a higher accuracy than was possible for previous solar crystal spectrometers (the procedure is described by \citet{jsyl05}), so enabling element abundances to be derived for elements whose spectral lines feature in RESIK spectra. Previously, such analyses (see e.g. \citet{jsyl10a}) have used the assumption of an isothermal plasma for the X-ray emission and with temperature and emission measure given by the flux ratio of the two emission bands of {\em GOES}. The justification for this was that plots of the measured line fluxes during flares divided by the {\em GOES} emission measure ($EM_{\rm GOES}$) against {\em GOES} temperature ($T_{\rm GOES}$) showed points distributed either along the theoretical $G(T_e)$ function or the function displaced by a constant amount. The $G(T_e)$ function is the line emission per unit emission measure as a function of electron temperature $T_e$ calculated, e.g., from the {\sc chianti} atomic database and software package \citep{der97,lan12} for an assumed element abundance. The amount of the displacement gives the factor by which the assumed abundance must be adjusted to give agreement with the measured RESIK line fluxes. A particularly tight distribution of points around the calculated $G(T_e)$ curve was obtained for the case of the \ion{Ar}{17} lines in RESIK's channel~2, and a rather broader scatter of points for K and Cl since the line emission for these low-abundance elements was weak. Thus an argon abundance estimate with very small statistical uncertainty ($A({\rm Ar}) = 6.45 \pm 0.06$ on a logarithmic scale with $A({\rm H}) = 12$) resulted, in close agreement with other argon abundance estimates from solar proxies \citep{jsyl10b}. The RESIK Si and S abundance estimates are based on strong lines of H-like and He-like Si and S seen in RESIK's channels 3 and 4, but the distribution of points given by line flux divided by $EM_{\rm GOES}$ against $T_{\rm GOES}$ was less impressive than that for the \ion{Ar}{17} lines. It was speculated \citep{jsyl12,bsyl13} that the subtraction of crystal fluorescence was not as accurately done as was thought or that the results were affected by some lines occurring very near the end of the range of either channel 3 or channel 4. Here we investigate whether the assumption of an isothermal emitting plasma might instead be more significant in leading to biased results, the thinking being that the temperature derived from the two {\em GOES} channels is more representative of the hotter \ion{Ar}{17} lines than that of the H-like or He-like Si and S ions, an idea described further in Section~3. In this work, we discuss RESIK spectra for the particular case of the M1.0 flare on 2002 November~14 with {\em GOES} soft X-ray maximum at 22:26~UT (SOL2002-11-14T22:26 using the IAU standard flare-naming convention). We first used an iterative procedure (AbuOpt) to derive optimized element abundance estimates of Si, S, Ar, and K, since these elements are represented by lines in RESIK spectra and so their abundances will influence the nature of the RESIK spectra. The optimization is done with a maximum likelihood routine (the Withbroe--Sylwester routine) which determines the differential emission measure (DEM). The optimized abundances of Si and S in particular differ from our previous estimates based on an isothermal assumption. With the Withbroe--Sylwester routine, and with the optimized abundances of Si, S, Ar, and K, the evolution of the differential emission measure (DEM) over the flare duration was then found. With X-ray images of this flare from {\it RHESSI}, estimates of the emitting volume $V$ are made, and from these, lower limits to the electron densities and thermal energy content of the flaring plasma are determined. The physical significance of the new Si and S abundances are discussed in respect of the well known first ionization potential (FIP) effect, in which the abundances of elements with low ($\lesssim 10$~eV) FIP in coronal plasmas are apparently enhanced over photospheric abundances. | One of the primary intentions of this analysis of RESIK spectra and other data for the M1 flare under discussion has been to test a calculation procedure for obtaining differential emission measure using spectral fluxes from the RESIK instrument on {\em CORONAS-F}. Data from this well-calibrated instrument have been used in the past to derive abundances of elements whose lines occur in the RESIK X-ray range (3.4--6.1~\AA), viz. Si, S, Ar, K, and Cl. For flare data we have previously used the approximation that the emitting plasma is isothermal with temperature given by the flux ratio of the two bands of {\em GOES}. This appears to be a good assumption for the case of Ar, K, and Cl abundance determinations, which particularly in the case of Ar have small uncertainties and agree well with abundance determinations from other, unrelated, methods. Previous determinations of the Si and S abundances from RESIK spectra using the same procedure appear to be less accurate: the estimates have larger uncertainties, and the characteristic temperatures of the emission functions of H-like and He-like ions of these elements are significantly less than that from the flux ratio of the {\em GOES} bands. Here we use a procedure (called AbuOpt) in which the abundances of Si, S, Ar, and K are first optimized using the maximum-likelihood, Bayesian Withbroe--Sylwester inversion technique for obtaining differential emission measure from line fluxes is used. The Withbroe--Sylwester routine was then run with optimized abundances to obtain the time evolution of the DEM. The result (shown as a time sequence in Figure~\ref{2D_DEM}) is a DEM distribution with well-defined cooler ($\sim 3-6$~MK) and hotter ($16-21$~MK) components. If the hotter component is assumed to describe the emission seen by {\em RHESSI}, the spatial dimensions combined with the total emission measure of the hotter component lead to estimates of electron density and thermal energy. Compared with recent estimates of $N_e$ from extreme ultraviolet line ratios, these represent lower limits, but give an indication of the physical characteristics of the flaring plasma. Values of element abundances derived from both an isothermal assumption and from the AbuOpt method described here were discussed in \S 3. It appears that our previous estimates for Ar and K based on an isothermal assumption are reliable, having smaller uncertainties, and are preferred values, but for S and Si, the abundance estimates from the present work -- $A({\rm S}) = 6.94 \pm 0.06$ and $A({\rm Si}) = 7.56 \pm 0.08$ -- are to be preferred for the flare analyzed here. Our Si abundance estimate is significantly lower than our estimates from an isothermal analysis of RESIK flare spectra \citep{bsyl13}, viz. $A({\rm Si}) = 7.93 \pm 0.21$ from the \ion{Si}{14} Ly-$\beta$ line at 5.217~\AA\ and $A({\rm Si}) = 7.89 \pm 0.13$ from the \ion{Si}{13} $w3$ line at 5.688~\AA. There are very few determinations of the Si abundance from X-ray flare spectra that our values can be compared with, the only reliable one being that of \cite{vec81} who used the {\em OSO-8} graphite crystal spectrometer to derive $A({\rm Si}) = 7.73 ^{+ 0.19}_{- 0.35}$ from the \ion{Si}{13} $w3$ line and $7.62 ^{+ 0.13}_{- 0.34}$ from the \ion{Si}{14} Ly-$\alpha$ line. An isothermal assumption was used, with the temperature derived from the slope of the nearby continuum which is evident in the spectra from this instrument. Clearly, our present estimates are nearer to the \cite{vec81} values than those from our isothermal analysis. Photospheric abundance estimates \citep{asp09} from 3-D and 1-D LTE analyses, one with non-LTE corrections, give $A({\rm Si}) = 7.51 \pm 0.04$, so abundance estimates from our present X-ray flare result and from the \ion{Si}{14} result of \cite{vec81} are not significantly larger (factor $1.12 \pm 0.2$) than photospheric despite the enhancement expected from the low FIP value for Si (8.15~eV); at any rate the enhancement is less than the factor 4 indicated by \cite{fel92a} and \cite{fel92b}. The S abundance estimate obtained here is only 0.03 different from the determination of \cite{vec81} from the {\em OSO-8} instrument: they give $A({\rm S}) = 6.91^{+ 0.13}_{- 0.19}$ determined from the intense \ion{S}{15} $w, y, z$ lines at $\sim 5$~\AA. Again, our result and the \cite{vec81} result are unexpected on the standard FIP picture for this element which has a FIP (10.4~eV) marginally considered to be high (i.e. more than 10~eV). Recent photospheric estimates range from $A(S) = 7.12 \pm 0.03$ \citep{asp09} to $7.15 \pm (0.01)_{\rm stat} \pm (0.05)_{\rm syst}$ \citep{caf11}. If the uncertainty estimates for all these determinations are to be considered literally, there would appear to be a slight inverse FIP effect for S, i.e. our flare abundance estimate is $0.6 \pm 0.1$ times photospheric. An inverse FIP effect is difficult to reconcile with theoretical models (e.g. \cite{hen98}) with the exception of that based on ponderomotive forces associated with propagating Alfv\'{e}n waves proposed by \cite{lam04,lam09,lam12}. An inverse FIP effect, which is observed in cool main sequence stars \citep{wood12}, can possibly be explained by waves propagating upwards from the chromosphere and reflecting back down as opposed to propagating downwards from the corona and reflecting back upwards. Extreme-ultraviolet spectral lines observed by the Extreme-ultraviolet Imaging Spectrometer (EIS) on {\em Hinode} have recently been used to give Si/S abundance ratios in active regions and other non-flaring features from the intensity ratio of \ion{Si}{10} 258.37~\AA\ line to the \ion{S}{10} 264.23~\AA\ line. The ratio was determined by \cite{bro11} to range from 2.5 to 4.1 (average 3.4) and by \cite{bak13} from 2.5 to 3 for an ``anemone" active region within a coronal hole but up to more than 4 for established active regions. The Si/S abundance ratio from the estimates given here is $4.16^{5.25}_{3.31}$, so on the basis of the EIS results is typical of an established active region. The 2002 November~14 flare occurred in an active region that had recently appeared on the Sun's south-east limb, so its history is not well determined; all one can say is that it was flare-prolific on November~14, with a complex magnetic geometry. The electron densities in this analysis are typical of those estimated from a combination of image data and volume emission measures, but are less than those from density-sensitive spectral line ratios. These are in short supply in the X-ray region, but a number of \ion{Fe}{21} lines in the extreme ultraviolet spectrum seen with the Extreme Ultraviolet Variability Experiment (EVE) instrument on {\em Solar Dynamics Explorer} have recently been identified, enabling electron density to be found as a function of time in two {\em GOES} class X flares \citep{mil12}. These indicate densities of up to $10^{12}$~cm$^{-3}$, a factor 5 higher than the M1.0 flare discussed here. Our estimates of both $N_e$ and the thermal energy are thus likely to be lower limits with undetermined filling factors, perhaps of order 1/25. We plan to use the AbuOpt approach together with the Withbroe-Sylwester DEM analysis method to study element abundances and the thermodynamics of several other flares observed by RESIK to see whether the reduced Si and S abundances found here still hold, and whether any variations in element abundance are related to flare characteristics such as {\em GOES} class. | 14 | 4 | 1404.5775 |
1404 | 1404.5858_arXiv.txt | { Nuclear astrophysics and californium fission neutron spectrum averaged cross sections and their uncertainties for ENDF materials have been calculated. Absolute values were deduced with Maxwellian and Mannhart spectra, while uncertainties are based on ENDF/B-VII.1, JEFF-3.1.2, JENDL-4.0 and Low-Fidelity covariances. These quantities are compared with available data, independent benchmarks, EXFOR library, and analyzed for a wide range of cases. Recommendations for neutron cross section covariances are given and implications are discussed. } | Calculations of integral values at NNDC have been conducted in parallel with the ENDF/B-VII library releases \cite{2006Chad,2011Chad}. These values represent the complementary data sets for nuclear astrophysics, industry, and data evaluation applications. First results on reaction rates and neutron cross sections \cite{2010Pri} have demonstrated a large potential of ENDF/B-VII for applications, such as KADoNiS stellar nucleosynthesis library \cite{2006Dil}. Further interactions with the fundamental and applied science communities have initiated work on the extended list of integral values and their uncertainties \cite{2012Pri,2006Mugh,2007Iaea}. Calculations of nuclear astrophysics and californium fission neutron spectrum averaged cross section ({\it i.e.} californium spectrum) uncertainties are presented in the following sections. | 14 | 4 | 1404.5858 |
|
1404 | 1404.7546_arXiv.txt | Recent results from the AMS-02 data have confirmed that the cosmic ray positron fraction increases with energy between 10 and 200~GeV. This quantity should not exceed 50\%, and it is hence expected that it will either converge towards 50\% or fall. We study the possibility that future data may show the positron fraction dropping down abruptly to the level expected with only secondary production, and forecast the implications of such a feature in term of possible injection mechanisms that include both dark matter and pulsars. { Were a sharp steepening to be found, rather surprisingly, we conclude that pulsar models would do at least as well as dark matter scenarios in terms of accounting for any spectral cut-off.} | The positron fraction, that is, the flux of cosmic-ray positrons divided by the flux of electrons and positrons, has attracted much interest since the publication of the results of the PAMELA satellite \citep{Adriani2009,Adriani2013}. PAMELA has indeed reported an anomalous rise in the positron fraction with energy, between 10 and 200~GeV. These measurements have been confirmed recently by AMS-02~\citep{Aguilar2013}. The intriguing question is what may happen next? The positron fraction must either saturate or decline. In the latter case, how abrupt a decline might we expect? The naive expectation is that a dark matter self-annihilation interpretation, bounded by the particle rest mass, should inevitably generate a sharper cut-off than any astrophysical model. Antiparticles are rare among cosmic rays, and can be produced as {\it secondary} particles by cosmic ray nuclei while they propagate and interact in the interstellar medium. The sharp increase observed in the positron fraction is however barely compatible with the most simple models of secondary production. Various alternatives have been proposed, such as a modification of the propagation model~\citep{Katz2009,Blum2013}, or primary positron production scenarios, with pulsars~(e.g., \citealp{Grasso09,Hooper09,Delahaye2010,Blasi11,Linden13}) or dark matter annihilation~(e.g., \citealp{Delahaye2008,Arkani-Hamed09,Cholis09,Cirelli09}) as sources. The current data and the uncertainties inherent in the source models do not yet enable us to rule out these scenarios. It is however likely that improved sensitivities at higher energies and a thorough measurement of the shape of the spectrum above $\sim 200\,$GeV will be able to constrain the models. This question has been studied in earlier work (see for instance \citealp{Ioka2010,Kawanaka2010,Pato2010,Mauro2014}); here we want to test more specifically the possibility of a sharp drop of the positron fraction. An original aspect of our work is to also convolve our results with the cosmic-ray production parameter space for pulsars allowed by theory. The AMS-02 data presents a hint of flattening in the positron fraction above 250 GeV. Such a feature is expected, as the positron fraction should not exceed 0.5, and hence it should either converge towards 0.5 or start decreasing. We investigate in this paper the following question: what constraints could we put on dark matter annihilation and primary pulsar scenarios if the next AMS-02 data release were to show a sharply dropping positron fraction? A sharp drop could be deemed natural if the positron excess originates from the annihilation of dark matter particles with a mass of several hundred GeV. However, we show in this work that such a feature would be highly constraining in terms of dark matter scenarios. More unexpectedly, we demonstrate that pulsar models could also lead to similar results for a narrow parameter space. Interestingly, we find that pulsars lying in this parameter space happen to be the only ones that would be astrophysically capable of contributing to the pair flux at this level. In this paper, we first describe our method and our assumptions, then we analyse the dark matter and pulsar scenarios respectively. Finally, we discuss our results. | \label{sec:discussion} In the pulsar framework, our parameter scan favours a relatively old (a few hundred kyr old) close-by source (within $\sim 1$\,kpc), capable of supplying at least ${\cal E}_{\rm tot}\sim 10^{47-48}\,$erg into electrons and positrons, accelerated with a hard spectrum. This parameter scan was performed taking into account only propagation arguments. We discuss in this section how likely such a single source scenario is from an astrophysical point of view, in terms of energy budget and given the actual pulsar population. Pair production and acceleration in pulsars happens in several steps: electrons are initially stripped off the surface of the star by strong rotation-induced electric fields and undergo electromagnetic cascading in a yet unidentified region, which could be the polar cap \citep{Ruderman75}, the outer gap \citep{Cheng86}, or the slot gap \citep{Harding06}. The produced pairs are then channelled into the pulsar magnetosphere, and can either escape following open field lines \citep{Chi96}, or reach the pulsar wind nebula (PWN), a shocked region at the interface between the wind and the supernova ejecta, where particles can be further accelerated to high energies. Most pulsars are born with rotation periods $\sim 300\,$ms \citep{Lorimer2008}, which implies a rotational energy budget of $\sim 10^{46-47}\,$erg. Unless a fair fraction of the supernova ejecta energy is injected into particle kinetic energy, it is thus difficult to account for ${\cal E}_{\rm tot}\sim 10^{47-48}\,$erg required to fit the observed flux for the majority of pulsars. Pulsars that could supply this amount of energy should thus be rare sources, either because they need to spin faster, or because the conversion of the ejecta energy into particle kinetic energy has to be highly efficient. As long as the pulsar wind is embedded in the supernova remnant, the accelerated pairs lose energy adiabatically via expansion and radiatively via interactions with the magnetic and radiative fields. \cite{Blasi11} shows however that accelerated pairs can escape in the interstellar medium if they are liberated after the pulsar escapes the parent supernova remnant. This event typically occurs $50$\,kyr after the initial blast, as can be estimated by assuming an average birth kick velocity of the pulsar. Thus pulsars younger than this age would be naturally ruled out as contributors to the rising positron flux, as they would not have escaped the remnant yet, and accelerated particles would be trapped. On the other hand, older pulsars cannot contribute to the high-energy end of the spectrum either, because of propagation effects (Fig.~\ref{fig:pulsars}). Positrons produced by these sources would pile-up at intermediate energies (channel ii, mentioned in section~\ref{sec:method}). From Fig.~\ref{fig:carre}, one can see that the bulk of the more distant pulsars $\gtrsim 1\,$kpc demand that an (unreasonably) large energy budget be channelled into cosmic rays. A typical pulsar beyond 1\,kpc can contribute at a level of $<1\%$ of the flux of a more nearby pulsar, and hundreds of sources would be needed to reach the same level of flux as one pulsar at a distance closer than 1\,kpc. Note also that most of these far away pulsars have an injection cut-off $E_{\rm c}$ that is lower than the observed cut-off. This surprising fact can happen because the injection cut-off has been set as an exponential function, and this means that some cosmic rays are also accelerated to higher energies. However this would also mean that these pulsars will become much brighter in the future when the cosmic rays with energies below the cut-off will finally reach us. This makes these source even more unlikely to explain a sharp drop of the positron fraction. {The anisotropy of the positron flux $A$ should be stronger than that of the positron ratio $\Delta$ on which AMS-02 set an upper limit of 0.036 and hence could be more constraining if detected. However it is not clear that even in the case of a bright source dominating the signal that it would be strong enough to impose a strong conclusion. The energy dependence of $A$ could help as we expect the anisotropy to increase together with the flux in the case of a single pulsar dominating the signal, whereas if the dark matter halo were to dominate, the anisotropy could decrease while the flux increases. This is all the more true if the propagation parameters are close to those of \textit{min}, as this would increase the energy dependence of the anisotropy. The direction of the anisotropy could also be useful if the pulsar or pulsars responsible for the signal are not in the direction of the Galactic Center. Indeed the pulsar scenario would ultimately be satisfactory only if the brightest pulsar is actually identified and detected.} Finally, the energy spectrum injected by a single pulsar depends on the environmental parameters of the pulsar. The toy model of unipolar induction acceleration in pulsars would lead to a hard spectral slope of index $\sigma \sim 1$ \citep{Shapiro83}. More detailed models by \cite{Kennel84a} suggest that the pair injection spectrum into the pulsar wind nebula should present a Maxwellian distribution due to the transformation of the bulk kinetic energy of the wind into thermal energy, and a non-thermal power-law tail formed by pairs accelerated at the shock. Hybrid and particle-in-cell (PIC) simulations show indeed such a behaviour (e.g., \citealp{Bennett95,Dieckmann09,Spitkovsky08}), and the latest PIC simulations indicate a relatively hard spectral slope $\sigma \sim 1.5$ \citep{Sironi11} due to acceleration by reconnection in the striped wind. All these arguments demonstrate that the narrow parameter space pointed out by our scan is astrophysically justified a posteriori. Because such sources should be rare, it is consistent that not more than one of them would be currently operating. The dots in Fig.~\ref{fig:novuple} confirm indeed that existing pulsars present in the allowed parameter region are scarce. \\ | 14 | 4 | 1404.7546 |
1404 | 1404.6540_arXiv.txt | We demonstrate the presence of an extended and massive circumgalactic medium (CGM) around Messier 31 using archival \hst\ COS ultraviolet spectroscopy of 18 QSOs projected within two virial radii of M31 ($R_{\rm vir} =300$ kpc). We detect absorption from \siiii\ at $-300 \la v_{\rm LSR} \la -150$ \km\ toward all 3 sightlines at $R \la 0.2 R_{\rm vir}$, 3 of 4 sightlines at $0.8\la R/R_{\rm vir}\la 1.1$, and possibly 1 of 11 at $1.1< R/R_{\rm vir}\la 1.8$. We present several arguments that the gas at these velocities observed in these directions originates from the CGM of M31 rather than the Local Group or Milky Way CGM or Magellanic Stream. We show that the dwarf galaxies located in the CGM of M31 have very similar velocities over similar projected distances from M31. We find a non-trivial relationship only at these velocities between the column densities ($N$) of all the ions and $R$, whereby $N$ decreases with increasing $R$. Singly ionized species are only detected in the inner CGM of M31 at $<0.2 R_{\rm vir}$. At $R<0.8 R_{\rm vir}$, the covering fraction is close to unity for \siiii\ and \civ\ ($f_{\rm c}\sim 60\%$--$97\%$ at the 90\% confidence level), but drops to $f_{\rm c}\la 10$--$20\%$ at $R\ga R_{\rm vir}$. We show that the M31 CGM gas is bound, multiphase, predominantly ionized (i.e., \hii\,$\gg$\,\hi), and becomes more highly ionized gas at larger $R$. We estimate using \siii, \siiii, and \siiv\ a CGM metal mass of at least $2\times 10^6$ M$_\sun$ and gas mass of $\ga 3 \times 10^9\,(Z_\sun/Z)$ M$_\sun$ within $0.2 R_{\rm vir}$, and possibly a factor $\sim$10 larger within $R_{\rm vir}$, implying substantial metal and gas masses in the CGM of M31. Compared with galaxies in the COS-Halos survey, the CGM of M31 appears to be quite typical for a $L^*$ galaxy. | The circumgalactic medium (CGM), loosely defined as the diffuse gas between the thick disk of galaxies and about a virial radius of galaxies is the scene where large-scale inflow and outflow from galaxies takes place. The competition between these processes is thought to shape galaxies and drive their evolution \citep[e.g.,][]{keres05,dekel06,cafg11,putman12}. Observations of the properties of the CGM are therefore critical to test theories of galaxy evolution. Recent discoveries using high quality ultraviolet observations show that the CGM is a pivotal component of galaxies with significant mass of baryons and metals \citep[e.g.,][]{wakker09,chen10,prochaska11,tumlinson11,churchill12,kacprzak12, kacprzak14,werk13,werk14,lehner13,stocke13,peeples14,werk14,liang14,bordoloi14}. Observations of the CGM at $z>0$ typically provide only average properties of the CGM along one sightline \citep[in some rare cases, 2--3 sightlines, e.g.,][]{keeney13}, and therefore the CGM properties such as gas kinematics, metal mass distribution, and ionization states as a function of galaxy geometry and properties are not well constrained. One way to alleviate in part this issue is to determine the properties of the CGM for similar type or mass of galaxies with sightlines piercing their CGM at various impact parameters. This is the strategy used in the COS-Halos survey \citep{tumlinson13}. With a controlled sample of $L^*$ galaxies, the COS-Halos survey provided strong evidence for extended highly ionized CGM by demonstrating that typical star-forming $L^*$ galaxies have \ovi\ column densities $N_{\rm OVI} \ga 10^{14.3}$ \cmm, while more passive $L^*$ galaxies show weaker or no \ovi\ absorption in their CGM \citep{tumlinson11}. While this experiment has been extremely fruitful \citep{thom11,thom12,tumlinson11,tumlinson13,werk13,werk14,peeples14}, the COS-Halos galaxies have enough spread in their properties that even collectively they do not mimic a single galaxy. With several tens of QSO sightlines going through the Milky Way (MW) CGM \citep[e.g.,][]{savage03,sembach03,wakker03,wakker12,fox06,shull09,lehner12}, the MW would appear a perfect candidate for a ``zoom-in'' experiment, i.e., in which we can study the CGM along different sightlines of a single galaxy. However, our understanding of the MW CGM has remained somewhat limited by our position within the MW disk. The high-velocity clouds (HVCs, clouds that have typically $|v_{\rm LSR}|\ge 90$ \km\ at $|b|\ga 20\degr$, e.g., \citealt{wakker01} ) that cover the Galactic sky were thought to possibly probe the extended MW CGM. Their distances are now largely determined (\citealt{ryans97,wakker01,thom06,thom08,wakker07,wakker08,lehner10,smoker11} for \hi\ HVC complexes and \citealt{lehner11}; \citealt{lehner12} for the diffuse ionized HVCs, iHVCs), but this created another puzzle since they place most of the \hi\ HVCs and iHVCs within 5--15 kpc of the sun, not at 100--300 kpc, the expected size of the MW CGM, and hence the HVCs only represent a comparatively very small mass (since $M\propto d^2$). Only the Magellanic Stream \citep[MS, e.g.,][]{putman98,bruns05,nidever08,fox14} is more distant, possibly extending to 80--200 kpc \citep{besla12}, providing some indirect evidence for an extended corona around the MW \citep[e.g.,][]{stan02,sembach03,fox13,fox14}. The high \ovi\ column density found by COS-Halos is another element that shows that the iHVCs do not probe the extended MW CGM since $N_{\rm OVI}$ for the MW iHVCs is on average a factor 5 times smaller \citep[see the results in][]{sembach03,fox06}. Only if the entire MW thick disk and halo absorption is integrated, would $N_{\rm OVI}$ in the MW approach $10^{14.3}$ \cmm\ (i.e., by combining the results of \citealt{savage03} and \citealt{sembach03}). This would mean that most of the column density of the MW CGM might be hidden in part in the low-velocity gas often associated with the thin and thick disks (see \citealt{peek09} and Y. Zheng et al. 2015, in preparation). However, it is also plausible that the MW CGM has properties that are different from $z\sim 0.5$ $L^*$ galaxies. Studies of the gas content of nearby galaxies offer major advantages over both the MW and higher redshift galaxies. Nearby galaxies span a large angular extent and can be studied over multiple lines-of-sight and offer a direct mapping between the stellar distribution and the gas content. This experiment has been conducted for the Large Magellanic Cloud (\citealt{howk02}; \citealt{lehner07}; \citealt{lehner09}; \citealt{barger14}; N. Lehner et al., 2015 in prep.), showing in particular the presence of large-scale outflows from a sub-$L^*$ galaxy feeding in metals the CGM of a $L*$ galaxy (the MW). The $L^*$ galaxy that can be observed with the most detail is the Andromeda Nebula (M31). The stellar disk and halo of M31 have been subject to intense study \citep[e.g.,][]{brown06,mcconnachie09,gilbert12,gilbert14,dalcanton12}, with well-determined local and global properties, including its inclination \citep{walterbos87}, stellar and virial masses \citep{geehan06,marel12}, dust and ISM disk mass \citep{draine14}, rotation curve \citep[e.g.,][]{chemin09}, and its galaxy satellites \citep{mcconnachie12}. These studies all imply that M31 is fairly typical of massive star-forming galaxies,which has undergone several major interactions with its satellites \citep[e.g.,][]{gordon06,putman09}, and possibly in a phase of transformation into a red galaxy \citep{mutch11,davidge12}. The specific star-formation rate of M31, sSFR\,$\equiv {\rm SFR/M_\star} = (5\pm 1) \times 10^{-12}$ yr$^{-1}$ \citep[using the stellar mass M$_\star$ and SFR from][]{geehan06,kang09}, places M31 just between the passively evolving and star forming galaxies in COS-Halos \citep{tumlinson11}. As we show in this paper, the value of $N_{\rm OVI}$ in the CGM of M31 and the sSFR of M31 are also consistent with M31 being in the ``green valley''. Parallel to this intensive observational effort, there is also a major theoretical effort to understand the two massive galaxies, the MW and M31, of the Local Group (LG) \citep{richter12,garrison14,nuza14}. With this large amount of empirical results, M31 could become a benchmark for assessing the validity of the physics implemented in these simulations. This requires to have also knowledge of its extended diffuse ionized CGM. Both deep and shallower observations of the \hi\ 21-cm emission have reported detections of \hi\ clouds mostly within 50 kpc \citep{thilker04,westmeier05,westmeier08}, and at farther distances along the M31--M33 axis \citep{braun04}. The \hi\ 21-cm emission $49\arcmin$ resolution map in \citet{braun04} gave the impression of an \hi\ bridge between M31 and M33, but subsequent deep Green Bank Telescope (GBT) $9\farcm1$ resolution observations show that they appear to be small concentrations of \hi\ with $\sim 10^5$ M$_\sun$ on scale of a few kpc \citep{lockman12,wolfe13}. As for the MW, these \hi\ clouds might only be the tip of the iceberg and \hi\ alone does not provide information on the gas-phases, the metal content, and hence the total metal and baryon masses of the gas in the CGM of M31. We therefore mined the \hst\ Cosmic Origins Spectrograph (COS) archive for high resolution UV QSO spectra with sufficient signal-to-noise (S/N) to search and model the weak metal-line absorption features that may be signatures of the diffuse CGM gas of M31. Our search radius is within about 2 virial radii of M31. We adopt throughout a distance of 752 kpc and a virial radius of $R_{\rm vir} = 300$ kpc for M31 \citep{riess12,marel12}.\footnote{We emphasize that the exact definition of CGM and even $R_{\rm vir}$ is far from settled, as recently discussed by \citet{shull14}. For example, the overdensity $\Delta_{\rm vir}= 18 \pi^2 = 178 \approx 200$ of a collapsed object to estimate $R_{\rm vir}$ is often calculated assuming a ``top-hat'' model in an Einstein-de Sitter cosmology, but this value changes with the adopted cosmological models (e.g., \citealt{klypin02} adopted $\Delta_{\rm vir} = 340$; see discussion in \citealt{shull14}). For ease of comparison with previous studies and in view of the distribution of our targets we choose for this paper $R_{\rm vir} = 300$ kpc for Andromeda. As we show in this paper, the gas that we associate with the CGM of M31 is at velocities consistent with the material being gravitationally bound to M31 (even beyond $R_{\rm vir}$), which implies that the extended CGM gas of M31 is bound.} In \S\ref{s-sample}, we describe in detail how the sample was selected, while in \S\ref{s-assoc} we present several arguments that point to an association to the diffuse CGM of M31 for the absorption at $-300 \la v_{\rm LSR} \la -150$ \km\ observed along some of the sightlines in our sample . In \S\ref{s-prop}, we determine the properties of the M31 CGM, including its kinematics, ionization, covering fraction, and baryon and metal masses. We discuss the implications of our findings in \S\ref{s-disc} and finally summarize our results in \S\ref{s-sum}. \begin{figure*}[tbp] \epsscale{1} \plotone{f1.eps} \caption{Distribution of our targets in our adopted (circles) and rejected (squares) samples used to probe the CGM of M31 (right ascension increases from right to left, declination increases from bottom to top, see Table~\ref{t-data}). All these these sightlines were observed with COS G130M and/or G160M and some were also observed with \fuse. Targets with UV absorption at LSR velocities $-300 \le v_{\rm LSR} \le -150$ \km\ associated with the CGM of M31 are shown in red. Note that the sightline HS0058+4213 is near the $0.2 R_{\rm vir}$ boundary. Overplotted is the \hit\ 21-cm emission map around M31 adapted from \citet{braun04} where the lowest contour has $\log N_{\rm HI} = 17.5$ in the $40 \arcmin$ beam, with 0.5 dex increment between contours (this provides in our opinion a better representation of the \hit\ distribution around M31 according to recent GBT observations, see \citealt{lockman12,wolfe13}). The yellow crosses show for reference the targets from the COS G140L M31 program where low ions (e.g., \mgiit) were detected only within the \hit\ disk contour (i.e., $R \le 32$ kpc, see \citealt{rao13}). The two MW stars in blue are distant halo stars, allowing us to determine that absorption at $v_{\rm LSR}\ga -170$ \km\ traces MW gas. We also indicate the position of the Local Group barycenter with the green cross. \label{f-map}} \end{figure*} | \label{s-disc} Prior to this work, the CGM of M31 beyond its optical radius has been only explored with deep \hi\ 21-cm emission observations at a sensitivity of $\log N_{\rm HI} \ge 17$ \citep{thilker04,braun04,lockman12,wolfe13}. Within about 50 kpc ($0.2 R_{\rm vir}$), \citet{thilker04} found low $N_{\rm HI}$ filamentary gas within $\sim 80$ \km\ of M31 systemic velocity, i.e., with a velocity separation similar to that seen in the UV data presented here (see Fig~\ref{f-vm31}). They derived a total mass for the \hi\ gas observed through the GBT $9\farcm1$ beam of $3$--$4 \times 10^7$\,M$_\sun$. At $R>50$ kpc, the $49\arcmin$ Westerbork \hi\ survey by \citet{braun04} suggested a filament of \hi\ gas between M31 and M33, but this structure has dissolved into very small clouds of diameters less than a few kpc and masses of a few $10^5$ M$_\sun$ when observed with the GBT \citep{lockman12,wolfe13}. While the \hi\ mass is still poorly constrained, it is evident the mass of the M31 CGM is dominated by the diffuse ionized gas (see \S\ref{s-metal}). Our sample is still small within $R_{\rm vir}$, but each sightline with its pencil beam shows detection of M31 CGM gas for at least \siiii, with most showing absorption from multiple ions (\siii, \siiii, \siiv, \cii, \civ, \ovi). It would be of course important to fill the radial and azimuthal spaces with more COS observations of QSOs behind the CGM of M31 in order to confirm these results and more accurately characterize its physical structure. Nevertheless the present observations provide already strong evidence that the CGM of M31 is filled with multiphase, diffuse ionized gas (see \S\ref{s-cover}). We do not detect any \oi\ absorption in any of the QSO spectra piercing the CGM of M31, which puts stringent limits on the ionization level, \hii/\hi\,$\ga 93$--$97\%$ (see \S\ref{s-ion}), consistent with the small covering fraction of \hi\ detectable with 21-cm emission observations. Although deep \hi\ emission observations with $\log N_{\rm HI} >17$ reveal only the tip of the iceberg of the CGM, it will be critical that future radio \hi\ surveys can achieve this type of sensitivity with a good angular resolution in order to bring to light the spatial distribution of the \hi\ gas beyond the optical radii of galaxies. The present COS UV sample provides therefore the first strong evidence in the LG for CGM gas beyond 50 kpc \citep[see][]{lehner12}. As displayed in Fig.~\ref{f-vlms}, the associated components with the CGM of M31 are found at $-300 \la v_{\rm LSR} \la -150$ \km\ ($-7 \le v_{\rm M31} \le +110$ \km). As shown in Fig.~\ref{f-vm31}, the comparison with the velocity distribution of the dwarf satellites suggests that some of the absorption observed at $-121 \le v_{\rm M31} \le -34$ \km\ ($-450 \la v_{\rm LSR} \la -300$ \km) is a mixture of the MS and M31 CGM components, where the absorption is dominated by the MS (see \S\ref{s-velm31}). We also find that $\sqrt{3} v_{\rm M31}< v_{\rm esc} $ (see Fig.~\ref{f-vm31} and \S\ref{s-kin}), implying that the gas is bound to M31 even at large $R$. These results could suggest that the CGM of the MW might be similarly large, but to characterize it will be difficult, since in view of our findings for the M31 CGM, the MW CGM absorption may also be dominated by low-velocity halo clouds (LVHCs, $|v_{\rm LSR}| \la 90$ \km), where the absorption is strongly blended with the MW disk and low halo. Except for the MS, most of the HVCs and iHVCs have been indeed found to be within 5--15 kpc (see, e.g., \citealt{thom08,wakker08,lehner11,lehner12}, and also \citealt{richter12} who found a characteristic radial extent of 50 kpc for the \hi\ HVCs of the MW and M31 using a model with a radial exponential decline of the mean \hi\ volume-filling factor). The LVHCs may be the best candidate for an extended MW CGM \citep{peek09}, along with some of the very high-velocity clouds not associated with the MS \citep{lehner12}. We determine that the baryonic mass of the weakly and highly ionized CGM gas of M31 is at least about 30\% of the total baryonic mass of M31 (see \S\ref{s-metal}), but this does not include the hot $\ge 10^6$ K CGM coronal component. The ubiquitous detection of high ions in our sample suggests the presence of hot ($>10^6$ K) diffuse gas surrounding M31 within its virial radius and possibly beyond (see \S\ref{s-ion}) if the production mechanisms of the high ions are dominated by thermal instabilities in the hot corona or interfaces between the cool (\siii, \siiii) and putative hot gas (see \S\ref{s-ion}). In cosmological simulations, substantial amounts of \ovi\ are produced through collisional ionization in the CGM of galaxies as it transistions from cooling of hot gas \citep{oppenheimer12,cen13,ford13,ford14}, although some of the \ovi\ could be photoionized in very low densities at impact parameters $\ge 100$ kpc ($\ge 1/3 R_{\rm vir}$) \citep{ford14}. \citet{cen13} show that collisional ionization dominates the production of strong ($N_{\rm OVI}> 10^{14}$ \cmm) \ovi\ absorbers. For M31 we only find $N_{\rm OVI} <10^{14} $\ \cmm\ beyond $R_{\rm vir}$ (see Fig.~\ref{f-nrho} and \S\ref{s-ion}). The hot galaxy coronae are one of the fundamental predictions of galaxy formation models \citep{white78,white91}, but their direct detection has been very difficult. Progress has been made recently with the detection of diffuse X-ray emission that appears to extend to about 30--70 kpc around a handful of massive, non-starbursting galaxies \citep{anderson11, bodgan13a,bodgan13b} or in stacked images of galaxies \citep{anderson13}. The mass estimate for these hot halos at these radii are about a few times $10^9$ M$_\sun$, which is comparable to the mass found in the cooler ($< 10^5$ K) gas of the CGM of M31 (see \S\ref{s-metal}), and hence the total mass of the CGM of M31 including all the gas-phases could be as large as $\sim 10^{10}$ M$_{\sun}$ within 50 kpc. Beyond $50$ kpc, the CGM is too diffuse to be traced with X-ray imaging, even though a large mass could be present. Extrapolating to about the virial radius, \citet{anderson11} estimate that the hot halo mass of the massive spiral galaxy NGC1961 might be about $10^{11}$ M$_{\sun}$ (the stellar mass of NGC1961 is $\sim 3$ times that of M31), a factor 5 larger than the mass of the cool CGM of M31 for the volume within $R_{\rm vir}$ (see \S\ref{s-metal}). For the MW, \citet{gupta12} argue that the mass of the $2\times 10^6$ K CGM out to 160 kpc could be as high as $10^{11}$ M$_{\sun}$. However, there is still a large disagreement on the interpretation of the X-ray observations and their implications for an extended hot MW CGM \citep{gupta12,gupta14,wang12,henley14,sakai14}. The most recent estimate for the MW implies a smaller mass for the $2\times 10^6$ K MW CGM gas of about $4\times 10^{10}$ M$_{\sun}$ within 50 or 240 kpc \citep{miller15}. Based on these X-ray observations, a substantial mass of the M31 CGM could also be present in its hot ($>10^6$ K) diffuse corona. \begin{figure} \epsscale{1.2} \plotone{f8.eps} \caption{Comparison of the total column density of \ovit\ versus the specific star-formate rate of the galaxy between M31 and the COS-Halos program \citep{tumlinson11}. For M31, we only consider the sightline with $R =25$ kpc since the COS-Halos targeted galaxies with $R\le 150$ kpc. \label{f-ovi}} \end{figure} Our results echo the findings from the COS-Halos survey of $L*$ galaxies at $z\sim 0.2$ \citep{tumlinson11,werk13,werk14,peeples14}. In Figs.~\ref{f-werk} and \ref{f-ovi}, we reproduce two COS-Halos figures with our M31 results included. Fig.~\ref{f-werk} was already presented in \S\ref{s-metal}, which shows a similar distribution for $N_{\rm Si}$ as a function of $R/R_{\rm vir}$ between the COS-halos and the present study, which implies similar masses for their cool (probed by \siii, \siiii, \siiv) and warm-hot (probed by \civ\ and \ovi) ionized CGM. The typical dark matter halos of the COS-Halos galaxies is $10^{12}$ M$_\sun$, similar to M31 \citep[e.g.,][]{marel12}. In Fig.~\ref{f-ovi}, we show $N_{\rm OVI}$ against the specific star-formation rate of the COS-Halos galaxies and M31.\footnote{As for Si, the total amount of \ovit\ could be larger if some of the \ovit\ absorption of the CGM of M31 is blended with the MS or the MW. However, for \ovit, the total column would only increase by about 0.3 dex.} M31 is right between the COS-Halos passively-evolving and star-forming galaxies where star-forming systems have typically $\mlnovi \ga 14.3$. The column density of \ovi\ through the M31 CGM is therefore consistent with the transition observed between the COS-Halos passively-evolving and star-forming galaxies, providing additional evidence -- independent of that based on its colors -- that M31 might be indeed transitioning from a blue to a red galaxy \citep{mutch11,dalcanton12}. We emphasize that although the mass and luminosity of M31 are comparable to the COS-Halos galaxies, their environments might be quite different: M31 lives in a galaxy environment with close by companions (M32, M33, MW, etc.) while the COS-halos galaxies were selected to be fairly isolated. The influence of the MW (750 kpc from M31) on the CGM within 300 kpc of M31 may be thus be relatively small. While the M31 CGM has properties similar to other $L*$ galaxies, we find CGM masses at least about 5--6 times larger than estimated for the sub-$L*$ galaxies at $z \sim 0$ \citep{bordoloi14}. The origin of this diffuse ionized CGM gas is an open question. The distribution and composition of the CGM gas have been addressed in several high-resolution cosmological hydrodynamic simulations with various level of star formation and feedback prescriptions \citep[e.g.,][]{klypin02,joung12,cen13,nuza14,ford14}. Notably, despite the various treatments and different levels of the feedback in these simulations, there is some agreement regarding the distribution of the baryons in the CGM between these simulations and with our empirical results as we now outline. One of the basic requirement of all these simulations is that a large fraction of the baryons are in the CGM of galaxies. For example, the $\Lambda$CDM-models of the Milky and M31 by \citet{klypin02} requires that 1/4 to 1/2 of the baryons within the virial radius of the halo must not be in the disk or bulge of the MW and M31 in the absence of any feedback, which is consistent with our empirical results (see \S\ref{s-metal}). \citet{cen13} predicts that over half of the gas mass within 150 kpc of red or blue galaxies is in the cool phase of the CGM. \citet{nuza14} studied the gas properties in the CGM of MW and M31 analogs using a cosmological simulation of the LG. They find masses for the cool CGM within $0.2 R_{\rm vir}$ and $R_{\rm vir}$ that are consistent with our results. The covering fraction of the CGM gas with $\log N_{\rm HI}>15$ (i.e., tracing some of the ionized gas reported in our work) in their simulation appears also to be broadly consistent with our observations, being close to 1 at $R\la 0.4R_{\rm vir}$ and then progressively decreasing to $\la 0.3$ at $R\ga R_{\rm vir}$. It is worth noting also that in their simulation as well as the more general simulations of galaxies at $z\sim 0$ \citep[e.g.,][]{cen13,ford14}, the cool CGM dominates the mass of the CGM within $0.2 R_{\rm vir}$ (by a factor $\sim 4$ relative to the mass of the hot gas), but there is a turnover at larger radii where at $R_{\rm vir}$ the mass of the hot gas is a factor 3 larger than the mass of the cool gas. While we cannot observe the hot gas associated with the CGM of M31, we find that the gas becomes more ionized and more highly ionized at $R>0.8 R_{\rm vir}$ than at $R<0.2 R_{\rm vir}$ (see \S\ref{s-ion}). \citet{ford14} specifically investigated the distribution of similar ions studied in our work and find that the covering fractions of the low (e.g., \cii) and high (\civ, \ovi) ions are all typically high (near 100\%) at $R<0.2 R_{\rm vir}$ and drops much more rapidly at higher impact parameter for the low ions than the high ions, again consistent with our empirical results (see \S\ref{s-prop}). The similarity in the distribution of the column densities of \civ\ and \siiv\ with $R$ in the simulations of \citet{ford14} (see their Fig.~7) and our observations (see Fig.~\ref{f-nrho}) is striking, with a comparable trend and magnitude in the variation of $N$ with $R$ (only \civ\ and \siiv\ are common in both studies). In the Nuza et al. and Ford et al. cosmological simulations, the CGM gas belongs to the ambient medium rather than being associated with satellites. \citet{ford14} also show most of the metal mass comes from recycled accretion at any $R$ (i.e., gas that was once ejected in a wind at least once before), but this is different for the baryons where if the total mass at $R<0.2 R_{\rm vir}$ is largely dominated by recycled accretion, at $R>0.2 R_{\rm vir}$ the ambient gas (i.e., gas is not going to accrete onto a galaxy and that have never been in a wind by $z \sim 0$) dominates the total mass. This comparison between cosmological models and our observations is extremely encouraging and demonstrates that a larger sample of targets observed with COS that populate in particular the $0.2 \le R/R_{\rm vir}\la 1$ region of the M31 CGM would make M31 a perfect testbed for theories of galaxy formation and evolution. With our present sample, we cannot accurately assess how the surfaces densities of the different ions change with $R$ (with an absence of data points at $0.2<R/R_{\rm vir}<0.8$) or azimuthal angle (e.g., to determine how the surface densities and kinematics vary along the major and minor projected axes of M31). This would also help us to better understand the origins of the metals and baryons in the CGM of M31. | 14 | 4 | 1404.6540 |
1404 | 1404.1967_arXiv.txt | Using high-resolution, high signal-to-noise echelle spectra obtained with Magellan/MIKE, we present a detailed chemical abundance analysis of both stars in the planet-hosting wide binary system \hda\ + \hdb. {Both stars are G dwarfs, and presumably coeval, forming in the same molecular cloud. Therefore we expect that they should possess {the same} bulk metallicities.} {Furthermore, both stars also host giant planets on eccentric orbits with pericenters $\lesssim$0.2 AU. Here, we investigate if planets with such orbits could lead to the host stars ingesting material, which in turn may leave similar chemical imprints in their atmospheric abundances.} We derived abundances of 15 elements spanning a range of condensation temperatures (\tc\ $\approx$ 40--1660~K). {The two stars are found to have a mean element-to-element abundance difference of {$0.04\pm0.07$ dex}, which is consistent with both stars having identical bulk metallicities.} {In addition,} for both stars, the refractory elements (\tc\ $> 900$ K) exhibit a positive correlation {between abundance (relative to solar)} {and} \tc, {with similar slopes of $\approx$1$\times$10$^{-4}$ dex K$^{-1}$.} The measured positive correlations {are not perfect; both stars exhibit a scatter of $\approx$5$\times$10$^{-5}$ dex K$^{-1}$ about the mean trend, and certain elements (Na, Al, Sc) are similarly deviant in both stars.} {These findings} are discussed in the context of models for giant planet migration that predict the accretion of H-depleted rocky material by the host star. {We show that a simple simulation of a solar-type star accreting material with Earth-like composition predicts} {a positive---but} {imperfect---correlation between refractory elemental abundances and \tc.} {Our measured slopes are consistent with what is predicted for the} {ingestion} {of 10--20 Earths} {by each star in the system.} {In addition, the specific element-by-element scatter might be used to distinguish between planetary accretion and Galactic chemical evolution scenarios.} | \label{s:intro} Exoplanet surveys like NASA's {\it Kepler} mission are discovering planets in a variety of environments, e.g., systems with multiple stellar components, which suggests that planet formation mechanisms are remarkably robust. An important result in attempts to understand these planet formation mechanisms is that giant planets are found to be more prevalent around solar-type stars that are typically enriched in metals by $\sim$0.15 dex relative to similar stars that have no detected giant planets~\citep[e.g.,][]{2005ApJ...622.1102F,2010ApJ...720.1290G}. This evidence indicates that giant planet formation is most successful in metal-rich environments. Beyond overall metallicity, investigations of abundance patterns in elements besides Fe in planet-hosting stars have uncovered evidence that planet hosts may be enriched or depleted (relative to the Sun) with elements of high condensation temperatures (\tc\ $\gtrsim$ 900 K, i.e., the refractory elements that are the major components of rocky planets) depending on the architecture and evolution of the their planetary systems. There are at least two planet formation processes that may alter stellar surface abundances: (1) the accretion of hydrogen-depleted rocky material~\citep{1997MNRAS.285..403G}, which would result in the {\it enrichment} of the stellar atmosphere, and (2) H-depleted rocky material in terrestrial planets may be withheld from the star during their formation, which would result in the {\it depletion} of heavy elements relative to H in the stellar atmosphere~\citep{2009ApJ...704L..66M}. For the enrichment scenario,~\citet{2011ApJ...732...55S} suggest that stars with close-in giant planets ($\sim$0.05 AU) may be more enriched with elements of high condensation temperature (\tc). {This is thought to be a result of giant planets which form in the outer planetary system migrating inward to their present close-in positions.} As they migrate, they can push rocky material into the host star~\citep[e.g.,][]{2008ApJ...673..487I, 2011A&A...530A..62R}. For the depletion scenario, \citet{2009ApJ...704L..66M} and \citet{2009A&A...508L..17R} propose that the depletion of refractory elements in Sun-like stars may correlate with the presence of terrestrial planets. Certainly there are processes other than planet formation that may alter stellar atmospheric abundances, but these effects can be mitigated by simultaneously considering a pair of stars that have experienced essentially the same evolution and environments over the course of their lives, {such as stars in wide binaries.} Indeed, wide stellar binaries known to harbor planets are {valuable} laboratories for studying the connection between how planets form and the chemical compositions of their host stars. Since most binary stars are believed to have formed coevally from a common molecular cloud~\citep[][and references therein]{2011ASPC..447...47K}, planet-hosting wide binaries are particularly valuable, because both stars can be presumed to have the same age and initial composition. {In fact, \citet {2004A&A...420..683D,2006A&A...454..581D} studied the differential Fe abundances for a set of 50 wide binaries. They found that only one binary pair possessed a $\Delta$[Fe/H] $>$ 0.09~dex, while for the majority of the systems they found $\Delta$[Fe/H] $<$ 0.03~dex. Thus, for components of wide binaries where at least one star possesses a planet, it is reasonable to expect that any significant difference in their present-day chemical abundances is most likely due to some aspect of the planet formation process.} For example, the investigation by~\citet{2011ApJ...737L..32S} of 16\,Cyg (a triple system that includes a wide binary pair of two nearly identical stars, plus the secondary hosts a giant planet at $\sim$1.7 AU while the primary does not) found that \cyga\ and \cygb\ were chemically identical (However, we should note that \citet{2011ApJ...740...76R} found that \cyga\ is more metal rich than \cygb\ by {$0.041\pm0.007$ dex}, but \citet{2012ApJ...748L..10M} found that the two stars are chemically identical). The authors speculated that one possible reason \cygb\ formed a giant planet, while \cyga\ may not have, is because \cyga\ itself has a resolved M dwarf companion (the tertiary in the system). This third star may have truncated the primary's circumstellar disk and inhibited planet formation \citep[e.g.,][]{1996ApJ...458..312J,2005MNRAS.363..641M}. Since the two stars must be the same age, and in addition they were found to be chemically identical, the authors were forced to consider {the properties of the system described above, which} could have led to these two stellar twins failing to form planetary systems with similar architectures. The 16\,Cyg wide binary was an ideal first system for this kind of comparison study, because the component stars have almost identical physical properties, i.e., their masses are nearly equal. This minimizes systematic errors that may arise from analyzing two stars with drastically different basic stellar properties~\citep{2011ApJ...737L..32S}. Ascertaining how planet formation may influence the composition of host star atmospheres could revolutionize target selection for future exoplanet surveys. If chemical abundance patterns can identify a star as a planet host, then a single high-resolution spectrum$-$instead of solely relying on large, time-intensive monitoring surveys$-$will permit selection of probable planet hosts among nearby stars in our Galaxy. Furthermore, if particular chemical signatures indicate the existence of specific kinds of planets, such as terrestrial planets, considerably more targeted searches for Solar System analogs would be possible. The goal of this series of papers is to study the interplay between planet formation and the chemical composition of the host star by directly comparing the chemical abundances of each stellar pair in planet-hosting wide binaries. {This paper presents the analysis of detailed abundance trends in the two stars comprising the \hdab\ system.} {\hda\ and \hdb\ are a common proper motion wide binary with an angular separation of $252''$ and a projected physical separation of $\sim9,000$ AU {\citep{2007A&A...462..345D,2009A&A...494..373M}}. They are both solar-type stars with spectral types of G1.5V and G9.5V, {and apparent V magnitudes of 7.36 and 8.48}, respectively~\citep{2006AJ....132..161G}.} For \hdab\, we present the investigation of the only known binary system where both stars have detected {planets.} \hda\ has a Jupiter-mass planet on a very eccentric ($e\sim0.97$) orbit at $\sim$1.4 AU~\citep{2006MNRAS.369..249J}, {and} \hdb\ hosts two moderately eccentric ($e\sim0.1-0.3$) Neptune-mass planets within $\sim$0.3 AU {(M. Mayor 2013, private communication)}. {Therefore, {\it if} the formation and evolution of planetary systems with different architectures affect the host star composition in distinct ways, studying systems like \hdab\ allows us to discern which aspects of their architectures play the most important roles.} In Section~\ref{s:data}, we describe our observations, reductions, and spectral analysis. In Section~\ref{s:results}, we summarize the main results, {including the finding that both stars in \hdab\ exhibit similar positive trends between refractory elemental abundance and \tc.} In Section~\ref{s:disc}, we discuss the results in the context of previous studies and a simple calculation that predicts how the accretion of Earth-like rocky planets would affect refractory elemental abundances as a function of \tc. {We find that the observed trends between refractory elemental abundance and \tc, and the element-by-element scatter relative to the mean trends, are consistent with the ingestion by both stars of 10--20 Earths}. Finally, in Section~\ref{s:conc} we highlight our main conclusions. | \label{s:conc} We have performed a detailed chemical abundance analysis of the planet-hosting wide binary \hdab, which is presently the only known wide binary where both stars have detected planets. {The mean element-to-element abundance difference between the two stars is $0.04\pm0.07$ dex, signifying that their bulk metallicities are identical, as expected for a binary system.} Both stars show {modestly} significant ($\sim$2$\sigma$) positive trends with \tc\ among their refractory elemental abundances. {We cannot definitively rule out that these trends may be the result of Galactic chemical evolution. However,} {given the orbital characteristics of the stellar binary, and the fact that both stars have eccentric giant planets that approach within $\lesssim$0.2 AU, models of dynamical interactions between binary stellar companions and models of giant planet migration} indicate that the host stars could have accreted rocky planetary bodies that would have initially formed interior to the giant planets. This is also consistent with previous studies that found positive trends with \tc\ in field stars with close-in giant planets. {According to our simple model for the accretion of Earth-like planets, the slopes of the weighted fits to these trends are consistent with \hda\ accreting $\sim$10~\ME\ and \hdb\ accreting $\sim$20~\ME\ of material with Earth-like composition. Our model also predicts that there should not be a perfect correlation between refractory abundances and \tc\ {for stars accreting H-depleted, rocky planetary material}.} {Three elements (Na, Al, and Sc) are similarly discrepant with both the fit to the simulated data and the fit to the observed data.} Therefore, the scatter in the [X/H]-\tc\ correlation is not necessarily due solely to {observational noise}, {but may in fact be a signature of the accretion of refractory-rich material driven by the inward migration of the giant planets orbiting these stars}. {Indeed, the specific character of the element-by-element scatter might be used as a strong discriminant between the planetary accretion and Galactic chemical evolution scenarios.} As we investigate other planet-hosting wide binaries, we hope to further {refine these} insights into abundances trends {and their relation to the planet formation process}. | 14 | 4 | 1404.1967 |
1404 | 1404.3686_arXiv.txt | We explore the impact of obliquity variations on planetary habitability in hypothetical systems with high mutual inclination. We show that large amplitude, high frequency obliquity oscillations on Earth-like exoplanets can suppress the ice-albedo feedback, increasing the outer edge of the habitable zone. We restrict our exploration to hypothetical systems consisting of a solar-mass star, an Earth-mass planet at 1 AU, and 1 or 2 larger planets. We verify that these systems are stable for $10^8$ years with N-body simulations, and calculate the obliquity variations induced by the orbital evolution of the Earth-mass planet and a torque from the host star. We run a simplified energy balance model on the terrestrial planet to assess surface temperature and ice coverage on the planet's surface, and we calculate differences in the outer edge of the habitable zone for planets with rapid obliquity variations. For each hypothetical system, we calculate the outer edge of habitability for two conditions: 1) the full evolution of the planetary spin and orbit, and 2) the eccentricity and obliquity fixed at their average values. We recover previous results that higher values of fixed obliquity and eccentricity expand the habitable zone, but also find that obliquity oscillations further expand habitable orbits in all cases. Terrestrial planets near the outer edge of the habitable zone may be more likely to support life in systems that induce rapid obliquity oscillations as opposed to fixed-spin planets. Such planets may be the easiest to directly characterize with space-borne telescopes. | The habitability of a world depends on a host of properties, from observable quantities like its mass and distance from the parent star to those that are difficult if not impossible to measure: atmospheric composition, surface reflectivity, ice, water distribution, etc. In the case of stars as massive as our Sun, detecting Earth-mass planets in any orbit is difficult with modern technology. In the last decade, attention has turned primarily to the discovery of rocky planets orbiting in the habitable zone (HZ), a shell around a luminous object in which an Earth-like planet could support liquid water on its surface \citep{Dole64,Kasting93,2013ApJ...765..131K}, as these worlds are best-suited for the development and sustainment of life as we know it. In its latest revision \citep{2013ApJ...765..131K}, the HZ is calculated for a highly idealized case, in which many properties of the star, planet, and planetary system are ignored. Following the identification of possible processes that can impact habitability \citep{SuperHab2014}, we explore how gravitational perturbations from additional planets can affect the climate. We find that in many cases, these perturbations can extend the outer edge of the HZ, thereby increasing the number of planets in the galaxy that are potentially habitable. While the vast majority of work on habitability has used a replica of the Earth to determine orbits that are potentially habitable, there are notable exceptions. Some studies explored the habitability of synchronously rotating planets \citep{Joshi97,Joshi03,Pierrehumbert11,Edson11,Wordsworth11, 2013ApJ...771L..45Y} . Others \citep{Abe11,Zsom13} considered planets that are much drier than the Earth. Several studies \citep{WilliamsPollard02,WilliamsPollard03,Spiegel10,Dressing10} varied the eccentricity and obliquity of an Earth-like planet and found that larger values tend to increase the globally averaged temperature on a planet, while holding the semi-major axis constant. While these studies made great strides in understanding the Earth's climate's sensitivity to rotation rate, obliquity, and eccentricity, aside from \citet{Spiegel10}, they largely ignored that the latter two properties evolve with time due to gravitational perturbations from other bodies. The Earth maintains a relatively constant axial tilt either due to the presence of the Moon, as suggested by \citet{1993Natur.361..615L}, or due to the inherent stability of Earth's axis, as indicated by \citet{2012Icar..217...77L}. However, as illustrated by \citet{1998PhDT........23W} and \citet{1998pslv.conf..415W}, changes in the architecture of our solar system - such as moving Jupiter inwards - can result in dramatic variations in the obliquity of the Earth even with the presence of a Moon. Still, It has been suggested that the relatively small variations in Earth's obliquity result in a stable climate conducive to the development of life. Adding to this stability is the fact that the orbital eccentricity remains smaller than about 0.05 due to the approximately circular orbits of the large planets of the Solar System. It is possible small obliquities and circular orbits are not a requirement for habitability. \citet{WilliamsPollard03} used General Circulation Models (GCMs) to determine how different obliquity variations affect the Earth's climate. They found that Earth-like planets with high obliquities were no more likely to experience extreme runaway greenhouse or snowball Earth events, making them just as habitable as Earth. Later \cite{Spiegel10} examined how large eccentricity oscillations affect the climates of rocky exoplanets. They found that in some cases, planets could break out of a snowball event during periods of high eccentricity. It is the goal of the current study to build on these previous results and explore self-consistent models of the climates of planets that experience rapid, large amplitude, and possibly chaotic oscillations of eccentricity and obliquity. Orbit-induced seasonal effects like the ice-albedo feedback determine the limit of the outer edge of the HZ. As the surface temperature drops, volatile ices such as CO$_2$ and water can condense on the surface. The high albedoes of their solid phases inhibit a planet's ability to absorb solar radiation reducing the temperature further. Mars, if it possessed sufficient surface water, would have been in danger of falling prey to these snowball episodes. Geological evidence exists for these episodes in Earth's past \citep{1998Sci...281.1342H}. For the Earth, a dynamic CO$_2$ recycling system works to offset the negative effects of these events on timescales of millions of years \citep{Walker81}. As the planet cools, weathering rates slow down and lock CO$_2$ in the atmosphere. As the CO$_2$ builds up, the greenhouse effect increases, eventually melting the ice. On early Mars, as now, such robust CO$_2$ cycling could not have been enough to resurrect the planet from these snowball events. From seasonally resolved modeling, it seems that other factors, in particular orbital and obliquity variations, would have to play a role \citep{Paper1}. Mars' obliquity has probably undergone significant evolution in the past \citep{1993Natur.361..608L} due to gravitational torques by the other planets in the Solar System, a property which may have permitted at least episodic liquid water at the surface. With this solar system context in mind, we turn our attention to predicting the habitability of exoplanets. We do not anticipate the photometric and spectroscopic data needed to characterize extrasolar planets until the launch of the James Webb Space Telescope in $\sim 2017$. Spacecraft like Kepler and ground based radial velocity surveys are already returning data that can pin down, through computational analysis, important orbital parameters that impact the climate such as eccentricity, timing of perihelion passage, and the evolution of the spin axis of the planet. Through the coupling of these data to N-body simulations and simple, fast climate codes, a more comprehensive picture of the HZ of a system can be obtained. This type of analysis can be used to prioritize future characterization observations, which are likely to be challenging, expensive, and based on precious little information. In this study we find that planetary system architecture --- that is, the distribution of masses and orbits of the other planets in the system --- can play a significant role in defining the extent of the habitable zone. The rotational evolution of the bodies in our Solar System can be accurately modeled because the masses and orbits of the planets are extremely well measured. For exoplanets, the situation is more difficult. Radial velocity surveys \citep[e.g.][]{Butler06} are only able to place a lower bound on mass, and cannot measure the relative inclination between orbital planes. Kepler can constrain inclinations \citep{Fabrycky12}, but is heavily biased toward the discovery of planets in coplanar configurations. While these systems are analogous to our Solar System, we note that the one system for which astrometry (which is not biased toward any particular inclination) has measured a mutual inclination, $\upsilon$ Andromedae \citep{2010ApJ...715.1203M}, the relative inclination is 30$^\circ$. Moreover, studies that predict the large eccentricities of exoplanet orbits, simultaneously predict large inclinations \citep{MarzariWiedenschilling02,Chatterjee08,Raymond10,Barnes11}. It is possible, perhaps likely, that there exists a population of planetary systems with large inclinations and a potentially habitable planet. These architectures will induce much larger changes in orbital inclination, which in turn induces large obliquity oscillations. The GAIA mission may be able to determine the range of architectures for giant planets \citep{Casertano08,Sozzetti13}. As no rocky planet is currently known to orbit with sibling planets with high mutual inclinations, we explore the phenomena with 17 hypothetical, dynamically stable systems. We find that there is a direct link between the orbital architecture of a planetary system and the possible range of climate conditions on a potentiality habitable planet. We use these models to constrain the orbital conditions of a hypothetical planet and find that orbital and rotational evolution tend to push the outer edge of the HZ out, relative to planets where no evolution occurs. Below, we outline a model that links physically realistic orbital architectures to the spin evolution of a hypothetical Earth-like planet, and finally to its climate. In Section \ref{sec:orbit}, we discuss the motivation behind the systems we have modeled in an effort to obtain a set that spans a range of orbital elements. In Section \ref{sec:obl}, we outline the model used to evolve the spin axis of the planet. In Section \ref{sec:climate}, we present a simplified energy balance model designed to be robust across wide variations of these orbital changes and fast enough that million-year integrations require only second of computational time. We then present the results of these models in Section \ref{sec:results} followed by a discussion in Section \ref{sec:discussion}. | Our simulations show that the evolution of planets' orbit and rotation can increase the maximum separation between a star and a habitable planet by up to 93\%. By controlling for the natural extension due to larger eccentricity and obliquity, we find that their oscillations can extend the outer edge by up to 20\%, and never decrease it. Thus, the number of potentially habitable planets in the galaxy may be larger than previously thought. We interpret our results to mean that planets with large and rapid obliquity oscillations are more likely to be habitable than those with negligible oscillations, such as the Earth. This perspective is at odds with the notion that the stability of the Earth's obliquity is important to the development of life. While it still may be true that rapid oscillations can be detrimental, and certainly at some point obliquity cycles could be too large and rapid, our results clearly show that rapid obliquity evolution can be a boon for habitability. At the least, one should not rule out life on planets with rapid obliquity cycles. Our results are important for future telescopic searches for life, such as the Terrestrial Planet Finder (TPF). Although a final design has yet to be selected, TPF's mission is to directly image potentially habitable planets. These observations depend critically on large star-planet separations in order to disentangle stellar light from reflected planetary light. Our results show that potentially habitable planets can exist at larger star-planet separations than previously appreciated, improving the odds that TPF can discover an inhabited planet. By necessity, our study was based on hypothetical planets. While our model systems are extreme from a Solar System point of view, they were relatively tame by exoplanet standards. Eccentricities larger than 0.9 have been discovered \citep{2001A&A...375L..27N, 2006MNRAS.369..249J,2008A&A...480L..33T}, very large mutual inclinations are implied by the misalignment between some star's rotation axis and the orbital planet of a companion planet \citep{Triaud10,Naoz11}, and eccentricity-inclination coupling can drive large and rapid oscillations, if both properties are large \citep{Kozai62,2007ApJS..168..297T,Barnes11}. Thus, our results should not be viewed as an extreme possibility, but rather as in the middle of a spectrum of spin-orbit coupling. Our approach has been simplified in several important ways. While our N-body simulations are the best representation of possible orbits, our rotational model is simplified. A better approach would be to calculate the direct torques from all the bodies in the system and adjust the angular momentum distribution accordingly. Such a model is much more computationally expensive, but could be incorporated into an N-body model without too much extra computational cost. Our EBM is also highly idealized and future improvements could include ocean/land dichotomies, the physics of glacier advancement and retreat, cloud physics, and ultimately even a 3-dimensional global circulation model. Each of these additions, however, adds free parameters to a model with very few constraints. While these features will improve realism, we will continue to suffer from a dearth of observational constraints. Nonetheless, as we move toward identifying planets worthy of detailed spectroscopic followup, such modeling could provide additional insight for prioritization. While our results demonstrate that planetary system architecture can influence the position of the habitable zone, it remains unclear how robust this influence is. For example, our planets all began with a spin rate of 24 hours and an obliquity of 23.5$^\circ$. How do different choices change the picture presented here? Future work should explore a range of initial conditions and determine if certain architecture always drive the planet into a particular obliquity cycle. If true, then we may be able to characterize a planet's obliquity without direct measurements. While such a study was beyond the scope of this paper, the possibility of tightly constraining obliquity is tantalizing and certainly worthy of a follow-up investigation. Our study suggests that rapid changes in obliquity and eccentricity increase the outer edge of the HZ. We quantify that relationship with linear trends in the enhancement factor with obliquity, but we did not find a threshold to achieve a specific quality that permits significant expansion. We blame the small number of systems we studied for this ambiguity, and leave its identification for future work. We note that prior to running a simulation, it is very difficult to know how the orbital and rotational angular momenta will evolve, thus it could take considerable effort to produce a suite of architectures that suitably cover parameter space. Our study has shown how orbital architecture is a crucial factor when assessing planetary habitability. While previous work has mostly focused on static planetary properties, planets are expected to lie in multi-planet systems and hence the sequence of states must be considered. For the foreseeable future, we will have very few constraints on the properties of potentially habitable planets and we therefore must leverage any information we have. \label{sec:discussion} | 14 | 4 | 1404.3686 |
1404 | 1404.4259_arXiv.txt | {Recently, using the light-travel time effect, planets and sub-stellar companions have been proposed to orbit around binary star systems (aka circumbinary companions) as a result of variations in timing of observed eclipses. For the majority of these systems the proposed orbital architecture features crossing orbital configurations as a result of high eccentricities for one, or both, of the companions. For such systems, strong mutual gravitational interactions are expected, resulting in catastrophic orbital instabilities, or collisions between the proposed components, on very short timescales.} {In this paper, we re-examine the primary and secondary eclipse timings of the short-period and semi-detached binary RZ~Draconis (RZ~Dra), as originally presented in Yang et al. (2010). In their work, the proposed companions have masses of around $\simeq 0.07$ and $\simeq 0.18~M_{\odot}$ with the inner companion on an orbit with moderate eccentricity (0.46) having its apocenter distance crossing the orbit of the outer companion. We show that the companions proposed by Yang et al. (2010) follow highly unstable orbits. In an attempt to find a stable system we have searched the underlying $\chi^2$ parameter space for a best-fit model and carried out an orbital stability study in order to test possible best-fit models. If the binary period changes are truly due to additional massive companions in a hierarchical configuration, they must follow stable orbits.} {For numerical orbital stability calculations we use well-established orbit integration routines. Computations were carried out using large-scale multi-CPU computing environment. Data analysis of times of primary and secondary eclipse is based on the Levenberg-Marquardt least-squares minimisation algorithm using the two-body Keplerian light-travel time effect model.} {Despite the wide variety of potential models tested for the RZ~Dra system in this work, we found very few models that were stable for even one million years, with the vast majority of systems tested falling apart on timescales of just hundreds of years. It seems likely therefore, that the observed timing variations are not solely the result of massive, unseen companions.} {} | A hierarchical \citep{Evans1968} multi-body star system is believed to be formed through one or more formation channels. First, \cite{vandenBerkEtAl2007} considers interaction/capture mechanisms during the formation and dynamical evolution of a globular star cluster. A second mechanism that could explain the existence of such systems is that they could be formed directly from a massive primordial disk involving accretion processes and/or local disk instabilities \citep{LimTakakuwa2006,DucheneEtAl2007,MarzariEtAl2009}. A third mechanism follows a chaotic erosion process of a non-hierarchical star system by angular momentum and energy exchange via mutual gravitational interactions. In the latter case, and considering an initial triple-system, \cite{Reipurth2000} provides a schematic outline of three stages that could produce a close binary system with a circumbinary disk from redistribution of circumstellar material after chaotic interactions. The formation of the tightly bound central binary is followed by the transport of the third member to a wider orbit as a result of conservation of energy. In extreme cases, this can result in the third member being ejected completely from the system leaving a tightly-packed close binary on a quasi-Keplerian orbit. A particular example of a hierarchical multi-body system is a so-called circumbinary system (aka companions on P-type orbits \citep{Schwarz2011}) in which one or more massive objects orbit a binary star system. Such systems has been recently discovered by {\sc Kepler} and the {\sc Planet Hunters} community\footnote{www.planethunters.org} \citep{DoyleEtAl2011,WelshEtAl2012,OroszEtAl2012a,OroszEtAl2012b}. \cite{Ofir2009} presents the results for a search of circumbinary companions based on {\sc CoRoT} data. The planet orbiting the binary PH-1 \citep{SchwambEtAl2013, KostovEtAl2013} is a particularly exotic example of such a system. Here the binary is a member of a quadruple (or quaternary) hierarchical system where two binary pairs form a gravitationally bound star system. Similar in nature though with no evidence of planetary companions is the HD98800 quadruple system \citep{FurlanEtAl2007}. Other types of hierarichical star systems reside in so-called S-type \citep{Schwarz2011} configurations where one body is orbiting one component of a binary pair. Several examples of such systems have been reported in the literature \citep{Neuhauser2007,Chauvin2007}. A {\bf well-known} technique to detect a hierarchical circumbinary systems is to measure and monitor timing variations of the mid-eclipse times of the central binary (aka times of minimum light). {\bf For a detailed description of its application on detecting circumbinary companions of planetary mass we refer the interested reader to \citet{DeegEtAl2000} and \citet{DoyleDeeg2004}. This technique has recently begun to be applied to the excellent timing data collected by the {\sc Kepler} mission, resulting in the recent announcement of the first sub-stellar mass circumbinary companion discovered from that data, orbiting KIC002856960 \cite{LeeEtAl2013a}.} The fundamental principle of the light-travel time effect (LTT\footnote{sometimes also referred to as LITE \citep{BoHe1996}}) makes use of the motion of the binary around the total barycenter of the system. Due to the finite speed of light, the eclipses exhibit delays or advances in the timings of minimum light depending on the orbital position of the binary relative to the observer \citep{Irwin1952,Irwin1959}. This method is particularly attractive as it is observationally time-effective involving only photometric CCD measurements. In recent times, single and multi-body sub-stellar circumbinary companions to known eclipsing binary systems have been proposed using ground-based timing measurements \citep{LeeEtAl2011,LeeEtAl2012,LeeEtAl2013a,LeeEtAl2013b}. The same technique was used to detect candidate circumbinary companions of planetary nature: CM Draconis \cite[CM~Dra, one companion]{DeegEtAl2000}, DP Leonis \cite[DP~Leo, one companion]{QianEtAl2010a, BeuermannEtAl2011}, HW Virginis \cite[HW~Vir, two companions]{LeeEtAl2009a}, NN Serpentis \cite[NN~Ser, two companions] {QianEtAl2009, BeuermannEtAl2010, BeuermannEtAl2013}, UZ Fornazis \cite[UZ~For, two companions]{PotterEtAl2011} and HU Aquarii \cite[HU~Aqr, two companions]{QianEtAl2011}, QS Virginis \cite[QS~Vir, one or two companions]{QianEtAl2010b, Almeida2011}. Recently additional circumbinary companions were proposed utilising the LTT effect: RR Caenis \cite[RR~Cae, one companion]{Qian2012a}, NSVS 14256825 \cite[two companions]{Almeida2013} and NY Virginis \cite[NY~Vir, one companion]{Qian2012b}. However, the existence of the proposed multi-body systems has been cast in doubt as a result of a number of studies of the dynamical stability of their orbital architectures. The proposed companions around HU~Aqr have been studied in detail, and a series of studies have revealed them to be dynamically unfeasible \citep{HUAqr,HinseEtAl2012a,HUAqr2, FunkEtAl2011, FunkEtAl2012, GozdziewskiEtAl2012}. The same is true of HW~Vir \citep{HWVir} and NSVS~14256825 \citep{NSVS,HinseEtAl2014}. Indeed, of those systems studied in this way, the only one to withstand dynamical scrutiny is that around NN~Ser \citep{NNSer,BeuermannEtAl2013}, although a recent study of the evolution of the central binary in the NN~Ser system suggests that it is unlikely that planetary companions on the proposed orbits could have survived the system's post-main sequence evolution intact \citep{Mustill2013}. Furthermore, \cite{HinseEtAl2012b} showed that the two sub-stellar companions orbiting around the SZ Herculis \cite[SZ Her, two companions]{LeeEtAl2012} binary also follow highly unstable orbits. The same situation is also seen for the QS~Vir system where \cite{QSVir} could show that the proposed two-companion system is highly unstable. Finally, \citet{ParsonsEtAl2010} present photometric follow-up observations of a number of eclipsing post-common-envelope binaries where they have been able to rule out previous claims for single-object circumbinary companions (e.g., \citet{QianEtAl2009}, \citet{QianEtAl2010b}). In this work we re-examine the observed timing dataset of RZ~Dra as presented by \cite{YangEtAl2010}. Those authors propose the existence of two additional low-mass dwarfs from two distinct quasi-sinusoidal variations in the times of mutual eclipses. Section 2 presents a dynamical stability analysis of the nominal orbital parameters as derived by \cite{YangEtAl2010}. We then continue and give an outline of our data analysis based on the light-travel time effect and describe the least-squares methodology in section 4, where we present a new best-fit model of the two proposed companions. A dynamical analysis of our new model is presented in section 5 and we finish with concluding remarks in section 6. | Based on measurements of primary and secondary eclipse times \cite{YangEtAl2010} proposed to interpret the timing variation due to two circumbinary companions. The two bodies they propose are very low mass stars with minimum mass $0.07~M_{\odot}$ for the inner and $0.18~M_{\odot}$ for the outer companion. From their best-fit model the inner companion's apocenter distance is at $\simeq 18$ AU and the outer companion's pericenter distance is $\simeq 17$ AU, implying a crossing-orbit architecture. We tested the dynamical feasibility of the proposed best-fit orbits by exploring a large grid of initial conditions using direct $n$-body integrations. The results of our simulations exploring the $(a,e)$-space are shown in Fig.~\ref{original}. All of the tested orbits were highly unstable, and resulted in either the break-up of the system or collisions between the two bodies. We found that the mean lifetimes range between 100 and 1600 years. {\bf In this work we have not considered mutually inclined orbits between the two companions. For the interested reader, we would like to point to the works of \citep{HUAqr,HinseEtAl2012b,QSVir,BD+20,Wittenmyer2014} who investigated the effect of mutually inclined orbits leading to the result of little improvement to the overall dynamical stability. However, the only exception to this finding were those scenarios for which the two planets were placed on anti-coplanar orbits - in other words, where they moved in the same plane, but with a mutual orbital inclination of 180 degrees. This setup predictably led to extremely stable systems whenever the two planets were not placed on orbits that crossed one another (which led to extreme instability). We judge that such an orbital architecture, whilst of theoretical interest, seems highly physically implausible, and so need not be considered further at this time.} We then searched for and determined a new best-fit model using the complete set of timing measurements transformed from HJD to BJD time standard. We found a new best-fit model with parameters shown in Table \ref{bestfitparamtable}. Compared to the orbital parameters given in \cite{YangEtAl2010} our new model assigned higher eccentricities to the orbits of the companions and increased the mass of the outer companion to $0.4~M_{\odot}$. We then tested the our new model parameters for dynamical stability and found life-times of only a few hundred years (Fig.~\ref{neworbits}). On the basis of our dynamical simulations we conclude the two companion hypothesis around RZ Dra does not stand up to scrutiny. At this point we would like to emphasize on the robustness of our stability analysis. First we have carried out tests which demonstrate that the results obtained from HYBRID integrations are reliable. Second, our dynamical setup replaces the two binary components as a single massive object. In that sense our setup considers a system which favours dynamical stability by ignoring the gravitational perturbations from a extra (significant in mass) body. If no stable orbits are found in this simplified system it is generally hard to conceive how stable orbits are ensured by adding an additional pertubing force to the system. From an intuitive point of view adding more perturbing forces will increase the effect and possibility of chaos and hence favours orbital instabilities. Another aspect of replacing the two binary components by a single body is an issue of being consistent with the LTT model which assumes the binary to be a single massinve object. It is clearly important, therefore, to consider what other mechanisms could account for the observed variations. In Fig.~\ref{RZDRABestFitNoSec} we have some indication by an asymmetric distribution of the residuals of additional effects that might be causing a period change. The orbital periods of many binary systems have varied due to some combination of secular and/or cyclical variations. Generally, the quasi-sinusoidal timing variations could be produced by at least three physical causes: (1) apsidal motion in an elliptical orbit of the binary, (2) a light-travel-time (LTT) effect (or several) due to additional companion(s), or (3) cyclical changes of magnetic activity of the component stars with deep convective envelope. The secular variations can be interpreted as being caused by either mass transfer between the two component stars or by angular momentum loss (AML). In case of RZ Dra, because the binary has a circular orbit, the cyclical variations cannot be described by apsidal motion. Further, \cite{YangEtAl2010} ruled out the magnetic activity cycles because the variations of the gravitational quadrupole moment ($\Delta Q$) are two orders of magnitude smaller than typical values of $10^{51} - 10^{52}$ for close binaries. This finding is further supported by a recent study \citep{Lanza2006} which indicates that the magnetic mechanism (Applegate model) is not sufficiently effective to explain the period modulation of close binaries with a late-type secondary. However, the eclipsing pair of RZ Dra is a semi-detached binary with the less massive secondary filling its inner Roche lobe \cite{YangEtAl2010}. In such semi-detached binaries, a secular variation (quadratic term) could be produced through a mass transfer from the secondary to the primary star, AML due to a magnetic stellar wind, or the combination of the two aforementioned mechanisms. The mass transfer cause a period increase (upward parabola), while the AML a period decrease (downward parabola). In this work we considered a quadratic + two-LTT model (see Section 4), but we were not able to convincingly detect either one of these trends in the residuals. However, a secular variation may be hidden in the timing data set and this system may be in a weak phase of mass transfer. We refer to \cite{Erdem2011} who considered a quadratic + 1-LTT model. Furthermore, the presence of systematic residuals shown in Fig.~\ref{RZDRABestFitNoSec} might be due to an apparent phase shift of the real conjunctions due to asymmetrical eclipse minima originating from starspot activity \citep{LeeEtAl2009b}. The effects of starspots on timing measurments of eclipsing binaries were also studied by \cite{WatsonDhillon2004}. At present we can not rule out that most of the timing measurements have been underestimated and hence the plotted errorbars in Fig.~\ref{RZDRABestFitNoSec} could be much larger than stated in the literature. To obtain an idea of the timing uncertainty we scrutinized table 4 in \cite{YangEtAl2010} and noticed the visual recording of the same secondary eclipse (presumably by two observers) on the night of HJD~2,442,984 (July 24, 1976; we refer to the VO ASCII data file available on-line). The first observer measured the secondary eclipse to be at HJD~2,442,984.637 and the second observer measured the same eclipse event to occur at HJD~2,442,984.641. These observations suggests a larger uncertainty since the time of minimum light from the visual observations differ by more than 5 minutes (over 300 seconds). This assumes, of course, that the entry in the corresponding VO file is neither a duplicated entry or typing error. If times of minimum light truely have a precision of 0.003 days, then most of the variation seen in Fig.~\ref{RZDRABestFitNoSec} would be within the noise-level of timing estimates. In general, \cite{Eastman2010} recommend that uncertainties of at least 60 seconds should be used for the timing precision, if the time standard has not been specified explicitly. We therefore encourage future follow-up observations of eclipsing binaries to obtain as precise timing measurements as possible for RZ Dra and other systems mainly characterised via visual measurements of the minima. Several monitoring programs are currently running or in planning \citep{Sybilski2010, PribullaEtAl2012} within the context of searching for circumbinary companions of planetary, sub-stellar and stellar nature. | 14 | 4 | 1404.4259 |
1404 | 1404.1821_arXiv.txt | \noindent It is generally believed that in single-field slow-roll inflation, a large tensor-to-scalar ratio $r > 0.1$ requires inflaton field values close to or above the Planck scale. Recently, it has been claimed that $r > 0.15$ can be achieved with much smaller inflaton field values $\Delta\phi < \mpl/10$. We show that in single-field slow-roll inflation, it is impossible to reconcile $r > 0.1$ with such small field values, independently of the form of the potential, and that the recent claim to the contrary is based on an invalid approximation. We conclude that the result of the BICEP2 measurement of $r > 0.1$, if confirmed, truly has the potential to rule out small-field models of single-field slow-roll inflation. | A few weeks ago, the BICEP2 collaboration reported a discovery of B-mode polarization of the CMB \cite{BICEP}, for which the most obvious explanation would be primordial gravity waves due to vacuum fluctuations of the metric during inflation. Though it is still too early to be sure about this interpretation, the announcement has already generated great excitement due to the many dramatic implications such a detection of primordial tensor perturbations would have \cite{LythBound1,LythBound2,LythBound3,LythBound4,implication1,implication2}. One of these implications is that in slow-roll inflation, a large tensor-to-scalar ratio $r$ requires values of the inflaton field close to or above the Planck scale. The basic idea, known as the Lyth bound \cite{LythBound1,LythBound2,LythBound3,LythBound4}, is that a large tensor-to-scalar ratio requires a steep inflaton potential at horizon crossing, and that in such a steep potential, the inflaton moves over a large field range during the 50-60 e-folds of inflation that are needed to solve the flatness and horizon problems. The argument is often presented for a monotonous slow-roll parameter $\varepsilon$, for which this bound is particularly strong. It is therefore natural to ask whether the Lyth bound can be circumvented by a non-monotonous evolution of $\varepsilon$. In fact, it has been recently claimed that a large $r > 0.15$ could be achieved in a single-field slow-roll model with $\Delta \phi < 0.1 \mpl$ \cite{LythBoundViolation1,LythBoundViolation2}. In this letter we show that requiring single-field slow-roll inflation alone is sufficient to rule out small-field inflation for the large tensor-to-scalar ratio $r \gtrsim 0.1$ implied by the BICEP2 experiment. As an illustrative example, we also explain how the Lyth bound is enforced for the specific inflaton potential used in \cite{LythBoundViolation1}. We close with a summary and a brief discussion of the implications of our result. | In this letter, we have discussed why it is impossible to construct a single-field slow-roll model of small-field inflation (defined as $\Delta \phi \ll \mpl$) that generates $r \gtrsim 0.1$. Making no assumptions beyond single-field slow-roll inflation,\footnote{To be precise, the derivation also assumed that $\Delta \phi \lesssim \mpl$, because our bound is aimed at ruling out small-field models. For super-Planckian field values it is anyway clear that one can generate large $r$.} we arrived at the bound \eqref{eq:MAIN} \begin{align*} \Delta \phi \, \gtrsim \, \frac{ 0.11 }{\braket{\eta - 2\varepsilon}} \sqrt{\frac{r}{0.1}}, \end{align*} which requires that for slow-roll inflation (for which $\varepsilon \ll 1$ and $\eta \ll 1$), the canonically normalized inflaton field must take values close to or above the Planck scale. We also briefly discussed how this bound can be generalized to multi-field slow-roll models, and mentioned two ways in which multi-field models can dodge this bound. We demonstrated that our results hold up for an expansion of the inflaton potential to 4th order, for which it was claimed that large $r > 0.15$ could be realized in small-field slow-roll inflation \cite{LythBoundViolation1}. We explained how $r \gtrsim 0.1$, together with constraints on the scalar power spectrum, forces the potential to be too steep to generate sufficient e-folds of inflation for $\Delta \phi \lesssim \mpl/2$ in such a potential. We hope that this letter removes some of the confusion about the Lyth bound and shows that a measurement of primordial gravity waves with $r \gtrsim 0.1$, if confirmed, truly has the potential to rule out all small-field models of single-field slow-roll inflation. However, it is still early days yet. Apart from a confirmation of the BICEP2 measurement by other experiments, it is necessary to explore other possible sources which could produce or enhance such a signal, e.g.\ primordial magnetic fields \cite{BICEP:magnetic}, gravity wave production from other sources during inflation \cite{BICEP:axion0,BICEP:axion1,BICEP:axion2,BICEP:axion3,BICEP:axion4,tensorsFromSpectators}, phase transitions in the early universe \cite{BICEP:phaseTrans1,BICEP:phaseTrans2}, non-Bunch-Davies initial conditions \cite{BICEP:nonBD1,BICEP:nonBD2,BICEP:nonBD3,BICEP:nonBD4}, topological defects \cite{BICEP:defects1,BICEP:defects2}, other things that have been overlooked, or any combination of these. | 14 | 4 | 1404.1821 |
1404 | 1404.4635_arXiv.txt | { HD 95086 is an intermediate-mass debris-disk-bearing star.VLT/NaCo $3.8~\mu m$ observations revealed it hosts a $5\pm2\,\mathrm{M}_{Jup}$ companion (HD\,95086\,b) at $\simeq 56$\,AU. Follow-up observations at 1.66 and 2.18 $\mu m$ yielded a null detection, suggesting extremely red colors for the planet and the need for deeper direct-imaging data. In this Letter, we report H- ($1.7~\mu m$) and $\mathrm{K}_1$- ($2.05~\mu m$) band detections of HD\,95086 b from Gemini Planet Imager (GPI) commissioning observations taken by the GPI team. The planet position in both spectral channels is consistent with the NaCo measurements and we confirm it to be comoving. Our photometry yields colors of H-L\,'= $3.6\pm 1.0$ mag and K$_1$-L\,'=$2.4\pm 0.7$ mag, consistent with previously reported 5-$\sigma$ upper limits in H and Ks. The photometry of HD\,95086\,b best matches that of 2M\,1207\,b and HR\,8799\,cde. Comparing its spectral energy distribution with the BT-SETTL and LESIA planet atmospheric models yields T$_{\mathrm{eff}}\sim$600-1500\,K and log\,g$\sim$2.1-4.5. Hot-start evolutionary models yield M=$5\pm2$\,M$_{Jup}$. Warm-start models reproduce the combined absolute fluxes of the object for M=4-14\,M$_{Jup}$ for a wide range of plausible initial conditions (S$_{init}$=8-13\,k$_{B}$/baryon). The color-magnitude diagram location of HD\,95086\,b and its estimated T$_{\mathrm{eff}}$ and log\,g suggest that the planet is a peculiar L-T transition object with an enhanced amount of photospheric dust. } | HD 95086 b is a directly imaged planet ($5\pm2$\,M$_\mathrm{J}$, $a_{proj}$ = 55.7 $\pm$ 2.5\, $AU$) discovered by \citet{rameau13a} in L$^\prime$ (3.8 $\mu m$) with VLT/NaCo \citep{lenzen03,rousset03} orbiting the young A8 star HD\,95086 (M$\sim$ 1.6 M$_{\odot}$), a member of the Lower Centaurus Crux subgroup \citep[$17\pm4$\,Myr,][]{pecaut12,meshkat13}. Additional L$^\prime$ images taken later in 2013 confirmed that the object is comoving with its star \citep{rameau13b}. NaCo Ks ($2.18~\mu$m) and NICI \citep{chun08} H-band ($1.65~\mu$m) observations failed to reveal the planet \citep{rameau13a,meshkat13}. However, $5\,\sigma$ lower limits of Ks-L$^\prime=1.2\pm0.5$ mag and H-L$^\prime=3.1\pm0.5$\,mag suggest that the planet may have extremely red colors, similar to the young planets HR 8799 bcde and 2M 1207 b \citep{Chauvin04,Marois08,Marois10a}, which have very dusty/cloudy atmospheres \citep{Barman2011,Currie2011}. Higher contrast near-IR data able to detect HD 95086 b can provide better comparisons with these objects and better constrain its atmosphere. In this Letter, we present detections of HD\,950\-86\,b with the recently installed Gemini Planet Imager \citep[GPI,][]{macintosh14} on Gemini South from public data as a part of GPI commissioning observations \citep{perrin14}. The data (acquired and reduced by the GPI team), their analysis, and the detections are presented in \S\,\ref{sec: obs}. In \S\,\ref{sec: photoastro}, we combine GPI H and $\mathrm{K}_1$ photometry with NaCo L$^\prime$ photometry to constrain the physical properties of HD\,95086\,b. | We reported the near-IR detections of HD\,95086\,b from GPI public commissioning data. We confirmed that the companion is comoving with HD\,95086 and derived the first estimates of its magnitudes with respect to its star: H = $13.1\pm0.9$ and $\mathrm{K}_1$ = $12.1\pm0.5$. While the mid-IR luminosity of HD\,95086\,b is best consistent with an L-T transition object, it has redder near-IR colors than other young, imaged planet-mass companions. This is consistent with a very dusty and low surface gravity atmosphere. Comparison with atmosphere models provide $\mathrm{600\:K \leq T_{\mathrm{eff}} \leq 1500\:K}$ and $\mathrm{2.1\:dex \leq log\:g \leq 4.5\:dex}$. Evolutionary models are consistent with a mass of $5\pm2$\,M$_{Jup}$. However, the models are affected by systematic errors that are difficult to quantify because of the lack of young objects at the L/T transition. More higher precision spectroscopic and photometric data for HD\,95086\,b are required to refine the planet properties. \\ {\small Acknowledgments: we thank the consortium who built the GPI instrument and the data analysis team for developing reduction tools. We are grateful to Dave Spiegel and Adam Burrows for making the warm-start models publicly avaliable. JR, MB, GC, and AML acknowledge financial support from the French National Research Agency (ANR) through project grant ANR10-BLANC0504-01. This research has benefitted from the SpeX Prism Spectral Libraries, maintained by Adam Burgasser at http://pono.\-ucsd.edu\-/$\sim$adam/brown\-dwarfs/spex\-prism. JLB PhD is funded by the LabEx “Exploration Spatiale des Environnements Plan\'etaires” (ESEP) \# 2011-LABX-030. TC is supported by a McLean Postdoctoral Fellowship.} | 14 | 4 | 1404.4635 |
1404 | 1404.5649_arXiv.txt | We present a method for finding binaries among pulsating stars that were observed by the Kepler Mission. We use entire four-year light curves to accurately measure the frequencies of the strongest pulsation modes, then track the pulsation phases at those frequencies in 10-d segments. This produces a series of time-delay measurements in which binarity is apparent as a periodic modulation whose amplitude gives the projected light travel time across the orbit. Fourier analysis of this time-delay curve provides the parameters of the orbit, including the period, eccentricity, angle of ascending node and time of periastron passage. Differentiating the time-delay curve yields the full radial-velocity curve directly from the \textit{Kepler} photometry, without the need for spectroscopy. We show examples with $\delta$\,Scuti stars having large numbers of pulsation modes, including one system in which both components of the binary are pulsating. The method is straightforward to automate, thus radial velocity curves can be derived for hundreds of non-eclipsing binary stars from \textit{Kepler} photometry alone. | \label{sec:intro} The study of binary stars is fundamental to our understanding of stellar structure and evolution. Eclipsing binaries in particular are the major source of the stellar fundamental parameters mass and radius. In close binary systems, deformation of the stars by tidal forces provides observational constraints on our understanding of tidal interaction. Most stars form in multiple systems; probably $\sim$100\:per\:cent do if we include stars with exoplanets. Now we have a second, complementary way to derive stellar fundamental parameters: asteroseismology (e.g., \citealt{aertsetal2010}). The study of pulsating stars in binary systems is therefore particularly important (e.g.\ \citealt{handleretal2002,becketal2014}), but most efforts so far have been limited to eclipsing systems (e.g. \citealt{southworthetal2011,hambletonetal2013,debosscheretal2013,frandsenetal2013,maceronietal2014,dasilvaetal2014}). The clear geometrical information available from the binary observations (light curves and radial velocity curves), combined with the constraints on internal structure from asteroseismology, give us novel insights into stars. Stellar masses, radii and ages are better known than ever before, and physical processes such as convective overshoot, internal rotation, and tidal interaction are now observational sciences. The {\it Kepler} mission provides an unprecedented source of high-precision stellar light curves with nearly continuous data over a time span of 4\,yr for over 150\,000 stars. Obtaining the required radial velocity curves for this many stars from ground-based observations is currently not possible. In this paper we show how radial velocities for pulsating binary $\delta$\,Scuti stars observed with {\it Kepler}'s long-cadence mode (30-minute sampling) can be derived from photometry alone. Our technique can be automated to discover and characterise hundreds of binary stars in the {\it Kepler} data set, particularly for non-eclipsing systems that other techniques do not find. It should even be capable of finding planet-mass companions to pulsating stars that are beyond the reach of other surveys for exoplanets. | \label{sec:conclusions} The long data sets with high duty cycle provided by \kepler\ have allowed the detection of binary companions to pulsating stars through phase modulation (PM) of the pulsation modes. As with the FM method \citep{shibahashi&kurtz2012}, binary information can be extracted from the \kepler\ light curve without the need for spectroscopy. Furthermore, the PM method is easily automated, offers a clear visualisation of the binary geometry, and straightforwardly provides the instantaneous radial velocity curve. The choice of FM or PM analysis is to be made on a case-by-case basis, and the methods are complimentary. While FM performs more satisfactorily for short-period binaries, where PM sampling segments must be short and thus suffer poor frequency resolution, PM is preferable for long-period binaries and produces a more detectable signal than FM for low-frequency pulsations. We have shown that the PM method allows companions to be found in orbits at least as long as the 1400-d \kepler\ data sets. Moreover, companions can be found around very low amplitude ($\sim$$20$\,$\upmu$mag) pulsators, regardless of orbital period. Extrapolating this finding, we infer that planetary companions could be discovered around mmag amplitude pulsators. We will be applying this analysis to the full set of $\delta$\,Sct stars in the \kepler\ archive. | 14 | 4 | 1404.5649 |
1404 | 1404.7366_arXiv.txt | {% Magnetic reconnection is a leading mechanism for magnetic energy conversion and high-energy non-thermal particle production in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas (e.g., microquasars or AGNs) -- a regime where first principle studies are scarce. We present 2D particle-in-cell (PIC) simulations of low $\beta$ ion-electron plasmas under relativistic conditions, i.e., with inflow magnetic energy exceeding the plasma rest-mass energy.\newline We identify outstanding properties: (i) For relativistic inflow magnetizations (here $10 \leq \sigma_\lec \leq 360$), the reconnection outflows are dominated by thermal agitation instead of bulk kinetic energy. (ii) At large inflow electron magnetization ($\sigma_\lec \geq 80$), the reconnection electric field is sustained more by bulk inertia than by thermal inertia. It challenges the thermal-inertia-paradigm and its implications. (iii) The inflows feature sharp transitions at the entrance of the diffusion zones. These are not shocks but results from particle ballistic motions, all bouncing at the same location, provided that the thermal velocity in the inflow is far smaller than the inflow $E\times B$ bulk velocity. (iv) Island centers are magnetically isolated from the rest of the flow, and can present a density depletion at their center. (v) The reconnection rates are slightly larger than in non-relativistic studies. They are best normalized by the inflow relativistic Alfv\'en speed projected in the outflow direction, which then leads to rates in a close range (0.14--0.25) thus allowing for an easy estimation of the reconnection electric field. }% | \label{sec:intro} Magnetic reconnection has been the focus of extended studies since its first introduction by \citet{Giovanelli1947,Giovanelli1948} to explain the sudden release of energy in solar flares. The term itself was coined by \citet{Dungey1958}. It is now the key ingredient for theories of coronal heating, solar flares and jets, and coronal mass ejections in the Sun \citep{Priest1987}, of magnetic storms and substorms in the Earth magnetosphere \citep{Paschmann2013}, and for the behavior of fusion plasmas with, e.g., the sawtooth oscillation in tokamaks \citep{Biskamp2000}. Space physics proofs that magnetic reconnection can quickly convert magnetic energy into kinetic energies (bulk flow, heat, non-thermal particles), with fast variability and high efficiency. Such attributes made it most attractive for high-energy astrophysics to explain, for example, radiation \citep{Romanova1992} and flares \citep{Giannios2009} in active galactic nuclei (AGN) jets or in gamma-ray bursts \citep{Lyutikov2006c,Lazar2009}, the heating of AGN and microquasar coronae and associated flares \citep{Matteo1998,Merloni2001,Goodman2008,Reis2013}, the flat radio spectra from galactic nuclei and AGNs \citep{Birk2001}, the heating of the lobes of giant radio galaxies \citep{Kronberg2004}, the $\sigma$-paradox and particle acceleration at pulsar wind termination shocks \citep{Kirk2003,Petri2007b,Sironi2011b}, GeV-TeV flares from the Crab nebulae \citep{Cerutti2012,Cerutti2012b,Cerutti2013}, transient outflow production in microquasars and quasars \citep{deGouveia2005,deGouveia2010,Kowal2011,McKinney2012,Dexter2013}, gamma-ray burst outflows and non-thermal emissions \citep{Drenkhahn2002,McKinney2012b}, X-ray flashes \citep{Drenkhahn2002}, soft gamma-ray repeaters \citep{Lyutikov2006b}, flares in double pulsar systems \citep{Lyutikov2013}, or energy extraction in the ergosphere of black holes \citep{Koide2008}. As pointed out by \citet{Uzdensky2006}, magnetic reconnection is of dynamical importance in any environment where magnetic fields dominate the energy budget, so that the energy transfer can have dynamical and observable consequences, and where the rates of reconnection are fast, which is known to hold in collisionless plasmas \citep{Birn2001} or in collisional but turbulent plasmas \citep{Lazarian1999,Lazarian2011}. Many of the above mentioned environments are collisionless \citep{Ji2011}, so that fast reconnection must be triggered and sustained by non-ideal terms others than collisional ones, which implies kinetic processes on scales of the order of the electron inertial length or Larmor radius, with particles largely out of equilibrium and possibly comprising high-energy tails. These non-ideal terms can be linked to particle inertia and wave-particle resonant interactions, or to finite Larmor radius effects in magnetic field gradients. Simulation studies thus require full kinetic codes such as Vlasov solvers or particle-in-cell algorithms. Most of the above environments are also relativistic, either because of relativistic velocities (bulk flows or currents), or because the thermal kinetic energy and/or the magnetic energy density exceeds the rest-mass energy of the particles. The latter translates into the magnetization of the inflow, $\sigma_{\ins,s} = B_\ins^2/(\mu_0 n_\ins m_s c^2)$ with $s$ denoting ions or electrons, being larger than unity. This magnetic energy can be transferred to the particles, and as it is larger than the particles rest mass, relativistic particles are expected. The relation $h_{0,\out,s}\Gamma_{\out,s} = 1 + \sigma_{\ins,s}$, with $h_{0,\out,s}$ the enthalpy and $\Gamma_{\out,s}$ the bulk Lorentz factor of the reconnection outflow (see Sect.~\ref{sec:outflows}, Eq.~\ref{equ:outflow_energy_bis}), indeed shows that either relativistic temperatures ($h_{0,\out,s}>1$) or relativistic bulk velocities ($\Gamma_{\out,s}>1$) are obtained for the outflows. The relevant magnetization is thus not that of the plasma, which is low because of the ion mass, but that of each species taken individually. Studies of relativistic reconnection are more scarce than their non-relativistic counterparts \citep[for the latter, see the reviews by][]{Birn2007,Treumann2013}, and they mainly deal with pair plasmas: for relativistic pair plasmas, they include 2D MHD simulations \citep{Watanabe2006,Zenitani2011,Takamoto2013,Baty2013}, two-fluid simulations \citep{Zenitani2009b,Zenitani2009}, test-particle simulations \citep{Bulanov1976,Romanova1992,Larrabee2003,Cerutti2012}\note{Larrabee's paper include a retroaction of the particles on the fields, in an iterative way.}, 1D PIC simulations \citep{Petri2007b}, 2D PIC simulations \citep{Jaroschek2008,Sironi2011b,Bessho2012,Cerutti2012b,Cerutti2013,Zenitani2001,Zenitani2005,Zenitani2008b,Zenitani2007}, and 3D PIC simulations \citep{Zenitani2008b,Zenitani2008c,Sironi2011b,Kagan2012,Cerutti2013b,Sironi2014}. Relativistic reconnection in ion-electron plasmas is less studied. We find a test-particle simulation \citep{Romanova1992}, a resolution of the diffusion equation \citep{Birk2001}, and a discussion by \citet{Sakai2002} in a 2D PIC simulations of laser fusion beams. The focus of the present work is on relativistic reconnection -- as compared to non-relativistic studies -- and on ion-electron plasmas -- as compared to pair plasmas. Our goal is to carve out aspects that are particular to this regime, to shed light on the underlying physical causes, and to ultimately put our findings in the, admittedly speculative, larger astrophysical context of microquasar and AGN disk coronae and magnetospheres, and of other possible environments with ion-electron relativistic plasmas. Part of our results are also of interest for pair plasmas and for non-relativistic cases. In Sect.~\ref{sec:pb_setup} we describe the simulation setup and parameters. Section~\ref{sec:results} presents the results of simulations with antiparallel asymptotic magnetic fields. We investigate the structure of the two-scale diffusion region in Sect.~\ref{sec:inflow}, and explain why we see sharp transitions at the entrance of this region. Next, we turn to the relativistic Ohm's law. In non-relativistic reconnection, non-ideal terms are dominated by thermal inertia, i.e., by the divergence of off-diagonal elements of the pressure tensor. There are, however, PIC studies (see references of Sect.~\ref{Sec:Ohms_law}) suggesting that for relativistic reconnection, thermal inertia can be dominated by bulk inertia. In Sect.~\ref{Sec:Ohms_law} we show that this is the case in our simulations with large inflow magnetization. We demonstrate in Sect.~\ref{sec:outflow_analytical_estimate_harder} that this is to be expected on the basis of an analytical model. Concerning the reconnection outflows, mass and energy conservation imply that relativistic inflow magnetization results in relativistic temperatures and/or relativistic bulk velocities in the outflows, but say nothing on the balance between the two. In Sect.~\ref{sec:outflows} we show that in our simulations, thermal energy largely dominates over bulk kinetic energy. We demonstrate analytically in Sect.~\ref{sec:outflow_analytical_estimate_harder} that this is to be expected for large inflow magnetization, under the assumption that thermal inertia significantly contributes in Ohm's law. This is an important question that has observational consequences. In Sect.~\ref{sec:islands_no_guide_field} we detail the structure of the magnetic islands and of their central density dips and isolated centers. Section~\ref{sec:rec_electric_field} studies the reconnection electric field. The relevant normalization is non-trivial for relativistic setups, and we propose to use the relativistic Alfv\'en speed in the inflow, which leads to rates in a close range. Section~\ref{sec:results_guide_field} highlights differences resulting from the presence of a guide magnetic field. We summarize and conclude our work in Sect.~\ref{sec:ccl}, and discuss applications to astrophysical objects. | Cut along $z$ through the X-point. Left: Run $\wce/\wpe=1$, $\sigma_\lec^\mathrm{hot}=9.9$, same X-point as in Fig.~\ref{fig_wcewpe=1_NT=21300_cutalongX_partNumber_velocity}, $t=142T_\pe=35\omega_\ci^{-1}=875\omega_\ce^{-1}$. % Right: Run $\wce/\wpe=3$, $\sigma_\lec^\mathrm{hot}=89$, $T_\bg=1.5\times10^7$\,K, $B_\mathrm{G}=0$, same X-point and time as in Figs.~\ref{fig:xcf_wcewpe=3_NT=6000_2D_pseudocolor_illustration}, \ref{fig_wcewpe=1_NT=21300_cutalongX_partNumber_velocity} upper-right, \ref{fig:wcewpe=3_NT=6001_Ohms_law}, \ref{fig:wcewpe=3_cut_Z_NT6000_temperature_only}, and \ref{fig:xcf_wcewpe=3_NT=6000_2D_pseudocolor_temperature_NT=6000} ($t=40T_\pe=30\omega_\ci^{-1}=750\omega_\ce^{-1}$). % } \end{figure*} We show in Fig.~\ref{fig:wcewpe=3_NT=6001_Ohms_law} the results for a cut through the X-point, for the simulation with $\wce/\wpe=3$ and $T_\bg=1.5\times10^7$\,K ($\sigma_\lec^\mathrm{hot}=89$). Ohm's law is satisfied everywhere, except at the sharp transitions at the entrance of the electron diffusion region, where the derivatives diverge. Different areas emerge: \begin{itemize} \item The electrons are ideal outside of the ion diffusion region. \item In the ion diffusion region, $|\bar{\b{v}}_\lec\wedge\b{B}|$ decreases linearly. The bulk inertia term $\sum_k\partial_k(n_\lec\bar{p}_k\bar{v}_y)$ rises linearly to compensate. The term $\partial_x(n_\lec\bar{p}_x\bar{v}_y)$ dominates over $\partial_z(n_\lec\bar{p}_z\bar{v}_y)$. The contribution of the former is understandable when looking at $\bar{p}_x$ and $\bar{v}_y$ that increase when we get closer to the sheet in this region (see Fig.~\ref{fig_wcewpe=1_NT=21300_cutalongX_partNumber_velocity} for $\bar{v}_y$). The thermal inertia term $\sum_k\partial_k(n_\lec\delta{p}_k\delta{v}_y)$ is slightly positive, and partly cancels the contribution of bulk inertia. This cancellation is also reported in \citet{Fujimoto2009} and \citet{Klimas2010} for non-relativistic ion-electron plasmas, and in \citet{Bessho2012} for relativistic pairs. Only $\partial_x(n_\lec\delta{p}_x\delta{v}_y)$ contributes, and is negative, which is easily seen when looking at the temperature curves $T_{xy,\lec}$ and $T_{zy,\lec}$ (Fig.~\ref{fig:wcewpe=3_cut_Z_NT6000_temperature_only}). \item In the electron diffusion region, the ${\bar{\b{v}}}_\lec\wedge\b{B}$ term vanishes (because $B$ is very weak and $\bar{v}_{x}=0$). The bulk inertia term is constant, and due only to the term $\partial_z(n_\lec\bar{p}_z\bar{v}_y)$, which is expected to contribute given that $\bar{v}_y\sim\mathrm{cst}$ and $\bar{p}_z \propto z-z_\mathrm{X-point}$ in this region (Fig.~\ref{fig_wcewpe=3_NT=6000_cutalongZ_summary}). The other term, $\partial_x(n_\lec\bar{p}_x\bar{v}_y)$, vanishes because $\bar{p}_x=\mathrm{cst}=0$ in this area. The thermal inertia term $\sum_k\partial_k(n_\lec\delta{p}_k\delta{v}_y)$ contributes as much as the bulk inertia term. Only $\partial_x(n_\lec\delta{p}_x\delta{v}_y)$ contributes, and is negative, which is easily seen when looking at the temperature curves $T_{xy,\lec}$ and $T_{zy,\lec}$ in Fig.~\ref{fig:wcewpe=3_cut_Z_NT6000_temperature_only}. \end{itemize} A cut along $x$ through other X-points in the simulation leads to the same results. Also, a cut along $z$ through the X-point reveals that the results of the electron region hold throughout the center of the current sheet, with a slow increase of the ${\bar{\b{v}}}_\lec\wedge\b{B}$ term as we get near the islands. In summary, non-ideal terms in the ion regions are due to bulk inertia and, in the electron diffusion region, to an interestingly equal contribution of bulk and thermal inertia. For other runs with $\wce/\wpe=3$ ($\sigma_\lec^\mathrm{hot}=27$ to 89), we also find an equal contribution from thermal and bulk inertia. For the most magnetized run, $\wce/\wpe=6$ ($\sigma_\lec^\mathrm{hot}=260$), the contribution of bulk inertia exceeds that of thermal inertia by a factor 1.5 to~3. We show in Sect.~\ref{sec:outflow_analytical_estimate_harder} with analytical estimations that the large magnetization for electrons indeed allows bulk inertia to overreach thermal inertia, with the former scaling as $\sigma^\mathrm{cold}_{\ins,\lec}$ and the latter as $\left(\sigma^\mathrm{cold}_{\ins,\lec}\right)^{1/2}$. This effect is present in our simulations, and not in the references previously mentioned with antiparallel fields, because our background electron magnetization is larger. It is thus a new regime that challenges the thermal inertia paradigm at large electron magnetizations. We discuss the possible consequences in Sect.~\ref{sec:astro_outlook}. \subsection{Outflow: energy content of the exhaust jets} \label{sec:outflows} \begin{table*}[tb] \caption{\label{tab:energy_outflow_flux}Energy content of the outflows. The energy flux due to the bulk flow mean velocity is proportional to $\Gamma_{\out,s}-1$, and the energy flux due to kinetic particle motions and pressure work is proportional to $\Gamma_{\out,s}(h_{0,\out,s}-1)$ (see Eq.~\ref{equ:particles_energy_flux}). Here $B_\mathrm{G}/B_0=0$. Quantities are measured at their maximum value, which is reached at the end of the exhausts along $z$.} \centering \begin{tabular}{c|c|c|cc||c|cc|cc} $\wce/\wpe$ & $n_\mathrm{bg}/n_0$ & $T_{\bg,\lec}$, $T_{\bg,\ion}$ (K) & $\sigma^\mathrm{cold}_{\ins,\lec}$ & $\sigma^\mathrm{cold}_{\ins,\ion}$ & & electrons & & ions & \\ \hline 1 & 0.1 & $1.5\times10^7$, idem & 10 & 0.4 & $\Gamma_{\out,s}-1$ & 0.49 & 31\% & 0.02 & 20\% \\ & & & & & $\Gamma_{\out,s}(h_{0,\out,s}-1)$ & 1.07 & 69\% & 0.08 & 80\% \\ \hline 3 & 0.31& $2.0\times10^8$, idem & 29 & 1.2 & $\Gamma_{\out,s}-1$ & 0.71 & 14\% & 0.065& 22\% \\ & & & & & $\Gamma_{\out,s}(h_{0,\out,s}-1)$ & 4.34 & 86\% & 0.24 & 78\% \\ \hline 3 & 0.1 & $3\times10^9$, $2\times10^8$ & 90 & 3.6 & $\Gamma_{\out,s}-1$ & 0.089& 1\% & 0.056& 9\% \\ & & & & & $\Gamma_{\out,s}(h_{0,\out,s}-1)$ & 15 & 99\% & 0.54 & 91\% \\ \hline 3 & 0.1 & $1.5\times10^7$, idem & 90 & 3.6 & $\Gamma_{\out,s}-1$ & 0.63 & 5\% & 0.13 & 20\% \\ & & & & & $\Gamma_{\out,s}(h_{0,\out,s}-1)$ & 11 & 95\% & 0.5 & 80\% \\ \hline 3 & 0.1 & $2.0\times10^8$, idem & 90 & 3.6 & $\Gamma_{\out,s}-1$ & 0.38 & 4\% & 0.091& 14\% \\ & & & & & $\Gamma_{\out,s}(h_{0,\out,s}-1)$ & 9.7 & 96\% & 0.56 & 86\% \\ \hline 6 & 0.1 & $8.0\times10^8$, idem & 360& 14 & $\Gamma_{\out,s}-1$ & 0.42 & 1\% & 0.19 & 8\% \\ & & & & & $\Gamma_{\out,s}(h_{0,\out,s}-1)$ & 51 & 99\% & 2.2 & 92\% \\ \end{tabular} \end{table*} It can easily be shown (Sect.~\ref{sec:outflow_analytical_estimate}) from analytical considerations that the outflows from the diffusion region should have relativistic bulk velocities and/or relativistic temperatures. In our simulation data, the thermal part always clearly dominates over the bulk kinetic energy part, more strongly for more relativistic cases (Sect.~\ref{sec:outflows_results_simulations}). A refined analytical estimate explains why in Sect.~\ref{sec:outflow_analytical_estimate_harder}. \subsubsection{A simple analytical estimation} \label{sec:outflow_analytical_estimate} As explained in Sect.~\ref{sec:overall_evolution}, bipolar outflow jets are naturally produced from each side of the X-points. They are clearly visible in Fig.~\ref{fig:xcf_wcewpe=3_NT=6000_2D_pseudocolor_illustration}. An estimation of the energy content of these outflows can be easily obtained in steady state, by using the conservation of particle number and of energy. To do so, we consider that the diffusion region for species $s$ has a length $D_s$ (along $z$) and a width $\delta_s$ (along $x$). We generalize the situation to cases where there is a guide field $B_\mathrm{G}$. We denote quantities entering (leaving) this region by a subscript ``in'' (``out'', respectively). Conservation of particle number (Eq.~\ref{equ:conservation_part_number_lab}) gives $n_{\ins,s} v_{\ins,s} D_s = n_{\out,s} v_{\out,s} \delta_s$. The inflow velocity is estimated by the $E\times B$ velocity as $v_{\ins,s} = E_y / B_0$. This assumes that the reconnection electric field is constant inside and outside of the diffusion region, a fact confirmed by our simulations\note{(analytical justification in 2D:...)}, and that particles do $E\times B$ drift up to the very entrance of the diffusion region, which is true in our simulations up to a factor $\sim 2$ (Fig.~\ref{fig_wcewpe=1_NT=21300_cutalongX_partNumber_velocity}). It also assumes that the value of the magnetic field at the entrance of the diffusion region is the asymptotic field $B_0$, while in our simulations $B_z$ has already dropped by a factor $\sim 3$ at this level (Fig.~\ref{fig_wcewpe=1_NT=21300_cutalongX_partNumber_velocity}), leading to an error in $v_{\ins,s}$ of the same order. Regarding energy conservation (Eq.~\ref{equ:energy_relat_lab_all_species}), the inflow energy flux includes the particle energies, and the reconnecting and guide field Poynting fluxes (Eqs.~\ref{equ:energy_flux_fields} and \ref{equ:energy_flux_particles}): $D_sn_{\ins,s}m_sc^2\bar{p}_{\ins,s} + D_sv_{\ins,s} \cdot B_0^2/\mu_0 + D_sv_{\ins,s} \cdot B_\mathrm{G,in}^2/\mu_0$. We assume that in the outflow the energy in the reconnected magnetic field $B_0$ is negligible compared to particle energy, so that the energy flux is $\delta_s n_{\out,s}m_s c^2 \bar{p}_{\out,s} + \delta_s v_{\out,s} \cdot B_\mathrm{G,out}^2/\mu_0$. Equating the two fluxes, combining this with the conservation of particle number, we obtain: \begin{equation}\label{equ:outflow_energy} \frac{\bar{p}_{\out,s}}{\bar{v}_{\out,s}} % = \frac{\bar{p}_{\ins,s}}{\bar{v}_{\ins,s}} + \sigma_{\ins,s}^\mathrm{cold}(B_0) + \sigma_{\ins,s}^\mathrm{cold}(B_\mathrm{G,in})(1-\alpha), \end{equation} with $(1-\alpha) = \left( 1-\frac{n_{\ins,s} B_\mathrm{G,out}^2}{n_{\out,s} B_\mathrm{G,in}^2} \right)$. The guide field is usually merely compressed, so that $1-\alpha\simeq 0$\note{(link this to CGL?)}. Equation~\ref{equ:outflow_energy} is independent of the $\b{p}$ dependence of the distribution function $f_s$. However, some insights can be gained by considering a distribution that is isotropic in the comobile frame, for which we have the result $\bar{\b{p}} = h_0(T) \Gamma \bar{\b{v}}$, with $h_0$ the comobile enthalpy (as defined and pictured for a Maxwell-J\"uttner distribution in Fig.~\ref{fig_kappa_32}), and $\Gamma = (1-\bar{\b{v}}^2/c^2)^{-1/2}$. If, in addition, we neglect the contribution of the guide field, and assume an inflow plasma with non-relativistic temperatures and non-relativistic velocities, Eq.~\ref{equ:outflow_energy} becomes\footnote{We note that the non-relativistic limit of Eq.~\ref{equ:outflow_energy_bis}, with $h_{0,\out,s}\sim 1$ and $\bar{v}_{\out,s} \ll c$, is \begin{equation}\label{equ:NR_outflow_speed} \bar{v}_{\out,s} = \sqrt{2\sigma_{\ins,s}^\mathrm{cold}(B_0)} = \sqrt{2}V_\mathrm{s,A}^\mathrm{in}(B_0), \end{equation} where $V_\mathrm{s,A}^\mathrm{in}(B_0)$ is the non-relativistic inflow Alfv\'en speed with only the mass of species $s$. It comprises only the component $B_0$, so that if there is a guide field, this is the projection of the total Alfv\'en speed onto the outflow direction $\hat{\b{z}}$.} \begin{equation}\label{equ:outflow_energy_bis} h_{0,\out,s}\Gamma_{\out,s} = 1 + \sigma_{\ins,s}^\mathrm{cold}(B_0). \end{equation} We clearly see that for a relativistic inflow plasma, where $B^2/\mu_0 > nmc^2$ and hence $\sigma_{\ins,s}^\mathrm{cold}(B_0)>1$, magnetic reconnection is expected to produce outflows with either relativistic bulk velocities ($\Gamma_{\out,s}>1$), or relativistic temperatures ($h_{0,\out,s}>1$), or both. We also see that since $\sigma_s^\mathrm{cold}\propto 1/m_s$, electrons will be more accelerated/heated than ions, and that relativistic electrons ($\sigma_\lec^\mathrm{cold}>1$) can be expected even at low ion magnetizations ($\sigma_\ion^\mathrm{cold} = \sigma_\lec^\mathrm{cold}\times m_\lec/m_\ion \ll 1$). \subsubsection{Results from simulations} \label{sec:outflows_results_simulations} We first check that the energy estimate of Eqs.~\ref{equ:outflow_energy} and~\ref{equ:outflow_energy_bis} holds in all simulations, which is indeed true up to a factor $\sim 6$. An only approximate correspondence is to be expected because this relation assumes a simple geometry, and no energy exchange between the species. For example, in Fig.~\ref{fig_wcewpe=3_NT=6000_cutalongZ_summary}, for $\wce/\wpe=3$, we measure in the inflow $1 + \sigma_{\ins,s}^\mathrm{cold}(B_0) = 2.1$ for ions and 1.7 for electrons, while we have at the outflow maximal velocity $\bar{p}_{\out,s}/\bar{v}_{\out,s} = 1.7$ for ions and 13 for electrons. These orders of magnitude hold for all cases. A more refined analysis of the energy content of the outflow, split into its thermal and bulk contributions, can be performed. To do so, we decompose the particle energy flux as (see Appendix~\ref{sec:app_measure_relat_1}): \begin{equation}\label{equ:particles_energy_flux} \begin{aligned} n_s \langle &\gamma m_s c^2 \b{v}\rangle_s = n_s m_sc^2 h_{0,\out,s} \Gamma_{\out,s} \bar{\b{v}}_{\out,s} \\ &= n_s m_sc^2 \bar{\b{v}}_{\out,s} \left[1 + (\Gamma_{\out,s}-1) + \Gamma_{\out,s}(h_{0,\out,s}-1)\right]. \end{aligned} \end{equation} On the right-hand side, the first term is the rest-mass energy flux, and is the same as that from the inflow. The second is the kinetic energy of a cold bulk flow of velocity $\bar{\b{v}}_{\out,s}$. The third is the energy transported by thermal motions in the plasma rest-frame and by pressure work, and we will denote it as the enthalpy flux. We note that these definitions match those of \citet{Zenitani2009b}, who performed a similar analysis with two-fluid simulations of relativistic reconnection in pair plasmas. We measure the maximum outflow velocity $\bar{v}_{\out,s}$, deduce the Lorentz factor $\Gamma_{\out,s}$, measure the maximum in momentum $\bar{p}_{\out,s}$, and compute the enthalpy $h_{0,\out,s} = \bar{p}_{\out,s} / (\Gamma_{\out,s}\bar{v}_{\out,s})$. From these values, we estimate in Table~\ref{tab:energy_outflow_flux} the balance of particle energy between each of the terms of Eq.~\ref{equ:particles_energy_flux}. In all cases, a large fraction of the particle energy flux is in thermal kinetic energy, not in bulk flow kinetic energy. For electrons, we see that the thermal part clearly dominates more as one increases the relativistic nature of the inflow (e.g., 69\% in the thermal part for the less relativistic case, 99\% for the most relativistic). This is also the case for ions: from 80\% to 92\% in the thermal part as the ion magnetization increases. The $T_\mathrm{bg,i}=2\times10^8$\,K case is exceptional with 91\% in the thermal energy, but this large fraction is likely explained by interactions with the hot electrons $T_\mathrm{bg,e}=3\times10^9$\,K. We explain why thermally dominated outflows are expected at large inflow magnetization with a refined analytical model in Sect.~\ref{sec:outflow_analytical_estimate_harder}. \subsection{Islands structure} \label{sec:islands_no_guide_field} Turning to the magnetic islands, we emphasize that they are magnetically isolated, have an M-shaped density distribution, and are hot with anisotropic temperatures. After being expelled along $\pm z$ in the outflow, the particles meet the magnetic islands that separate each pair of X-points. The islands are initially formed by the tearing of the current sheet. They then consist only of particles of the current sheet, plus those of the background plasma that were inside the current sheet location. Small at the beginning, they grow by collecting particles from the outflows at their periphery and by merging with other islands. A remarkable property is that particles from the background plasma cannot enter inside the islands: they are scattered by the strong magnetic field structure surrounding the island, and circle around it. Consequently, the particles at the island centers remain the same throughout the whole simulation, even after many island merging events. This matter is explored in more details in Melzani et al. (in prep.). We stress here two main points. First, the trapped particles are heated by the island contraction (which occurs when two islands merge), so that the central temperatures are very high for both species, highly anisotropic (Figs.~\ref{fig_wcewpe=3_NT=6000_cutalongZ_summary} and~\ref{fig:xcf_wcewpe=3_NT=6000_2D_pseudocolor_temperature_NT=6000}), with a dominance of $T_{zz}$. The island centers are also where the currents are the strongest. Second, as we said, most of the inflowing background particles populate a region around the center, and the central part of the island mainly consists of particles originally from the current sheet. As a result, the central part is less dense than the surrounding part, and a cut along $z$ through an island center (Fig.~\ref{fig_wcewpe=3_NT=6000_cutalongZ_summary}) reveals for the particle density a M-shape, with a central dip and two shoulders. This may explain observed density dips at the center of magnetic islands during magnetotail reconnection events \citep{Khotyaintsev2010}, without invoking island merging or particle escape along the flux tube\note{As \citet{Markidis2013} does.}. \begin{figure}[tbp] \centering \includegraphics[width=\columnwidth]{xcf_wcewpe=3_NT=6000_2D_pseudocolor_temperature_NT=6000.jpg} \caption{\label{fig:xcf_wcewpe=3_NT=6000_2D_pseudocolor_temperature_NT=6000} Temperatures for same simulation and time as in Figs.~\ref{fig:xcf_wcewpe=3_NT=6000_2D_pseudocolor_illustration}, \ref{fig_wcewpe=1_NT=21300_cutalongX_partNumber_velocity} upper-right, \ref{fig:wcewpe=3_cut_Z_NT6000_temperature_only}, and \ref{fig_wcewpe=3_NT=6000_cutalongZ_summary} right) Note the different units for ions and electrons. Since $m_\ion c^2=25m_\lec c^2$, the ions are actually hotter than the electrons. } \end{figure} \subsection{Reconnection electric field and reconnection rate} \label{sec:rec_electric_field} \begin{figure}[tbp] \centering \def\svgwidth{\columnwidth} \import{./}{reconnection_rates_no_guide_field.pdf_tex} \caption{\label{fig:reconnection_rates}Time evolution of the normalized reconnection electric field $E_y/(B_0 V^\mathrm{R}_\mathrm{A,in})$, measured at the X-point of various simulations. The velocity $V_\mathrm{A,in}^\mathrm{R}$ is given in Table~\ref{tab:param_magnetization}, and $B_0=0.11$, 0.33 or 0.66 for $\wce/\wpe=1$, 3 or 6 respectively. Time is normalized by the ion cyclotron pulsation, but note that the growth rate of the collisionless relativistic tearing mode is not proportional to $\omega_\mathrm{ci}$ \citep{Petri2007}, hence the different time lags and shapes. In particular for $\wce/\wpe=6$, the time scale of the plot is divided by 3. For pairs, the timescale is $t\wce/25$.} \end{figure} The rate of variation of magnetic field flux across a X-point, $\dif\Phi_{B_z}/\dif t=(\dif/\dif t)\int_{x=0}^\text{X-point}B_z\dif x$, is equal in two-dimensional configurations to the $y$ component $E_y$ of the electric field at the X-point location. In addition, $\dif\Phi_{B_z}/\dif t$ is in part determined by the outflow velocity, because the latter sets the rate at which magnetic field is extracted from around the X-point \citep[see e.g., in a resistive MHD context,][]{Borovsky2007,Cassak2007}. Since in non relativistic setups one expects $\bar{v}_\out \propto V_\mathrm{A}$, the reconnection rate $E_y$ is usually normalized either to $B_0 V_\mathrm{A,0}^\mathrm{NR}$, with $V_\mathrm{A,0}^\mathrm{NR}$ the hybrid Alfv\'en speed of Eq.~\ref{equ:hybrid_NR_Alfven_speed}, or to $B_0 V_\mathrm{A,in}^\mathrm{NR}$, with $V_\mathrm{A,in}^\mathrm{NR}$ the Alfv\'en speed in the inflow of Eq.~\ref{equ:inflow_NR_Alfven_speed}. These normalizations are chosen so that the normalized rate, $E^* = E_y/B_0 V_\mathrm{A}$, stays close to the same set of values. For example it has been shown that it gives identical results when varying the mass ratio (e.g., \citet{Hesse1999}, or \citet{Ricci2002,Ricci2003} for $m_\ion/m_\lec=25,180,1836$ with an implicit PIC code)\footnote{However, going down to $m_\ion/m_\lec=1$ leads to less systematic results. For example, \citet{Fujimoto2009} reports $E^*=0.15$ for $m_\ion/m_\lec=100$ and 0.08 for pairs. \citet{Liu2014} report close rates for $m_\ion/m_\lec=1$ and 25. Here we performed a simulation with $m_\ion/m_\lec=1$, and find a peak reconnection rate $E^* = 0.30$, larger than for $m_\ion/m_\lec=25$ (Fig.~\ref{fig:reconnection_rates}).}. In the following we turn to our relativistic case and ask whether a normalization can be found that confines the range of values for $E^*$ in a narrow range, and relaxes to the above normalization in the non-relativistic case. We argue here that the normalization by the hybrid Alfv\'en speed is not relevant, because it does not depend on the particle number density of the inflow, while the ratio $E_y/B_0$ clearly does. This is seen for the simulation with $n_\bg=0.3n_\cs(0)$, for which $E_y/B_0$ peaks at $0.13c$, compared to the otherwise identical simulation with $n_\bg=0.1n_\cs(0)$, where $E_y/B_0$ peaks at $0.20c$. On another hand, the inflow Alfv\'en speed $V_\mathrm{A,in}^\mathrm{NR} \propto 1/\sqrt{n_\bg}$, and thus leads to closer normalized rates. We consequently exclude hybrid quantities for normalization. In a relativistic configuration the non-relativistic Alfv\'en speed can increase to infinity. However, the ratio $E_y/B_0$ is also the $E\times B$ velocity of the incoming plasma, and cannot exceed the speed of light. The normalizing Alfv\'en velocity should thus also saturate to some value, which is why we choose to normalize the electric field by \begin{equation}\label{equ:rec_rate_normalized} E^* = \frac{E_y}{B_0 V_\mathrm{A,in}^\mathrm{R}}, \end{equation} with $V_\mathrm{A,in}^\mathrm{R}$ the relativistic Alfv\'en speed in the inflow (Eq.~\ref{equ:inflow_R_Alfven_speed}), that cannot exceed $c$. The time evolution of $E^*$ is shown in Fig.~\ref{fig:reconnection_rates}. Several comments can be made. First, the rate $E^*$ is not sensitive to the background plasma temperatures, as can be seen for the simulations $\wce/\wpe=3$, $n_\bg=0.1n_\cs(0)$, no guide field and $T_\bg = 1.5\times10^7$, $2\times10^8$ and $3\times10^9$\,K. This contrasts with the interpretation of \citet{Hesse2007} who attribute a lower rate to a larger inflow temperature. In addition to the temperatures, the magnetization of their simulation also changes, and may also affect the rates. Coming back to our simulations, we note that we use very low background plasma $\beta$ ($<10^{-2}$, Table~\ref{tab:param_magnetization}), and that a weak plasma $\beta$ dependence is expected for higher values \citep[e.g.,][have rates $E^*$ multiplied by $\sim2$ when $\beta$ passes from 0.01 to 1]{TenBarge2013}. Second, the reconnection rate for the simulation with a higher background particle density ($n_\bg=0.3n_\cs(0)$, $E^*=0.18$) remains lower than its counterpart with $n_\bg=0.1n_\cs(0)$ ($E^*=0.23$). This is in line with the pair plasma simulations of \citet{Bessho2012} who found a similar rate for $n_\bg=0.1n_\cs(0)$ ($E^*=0.19$), and a higher rate for $n_\bg=0.01n_\cs(0)$ ($E^*=0.36$). The reconnection rate thus increases with decreasing background plasma density, which is also coherent with the $\beta$ dependence mentioned above. Finally, the normalization leads to very similar values of $E^*$ for the relativistic cases ($\wce/\wpe=3$ or 6), with $E^*=0.17$-0.24, but to a significantly smaller rate for the less relativistic case ($\wce/\wpe=1$), with $E^*=0.14$. More generally, the values for the relativistic cases are larger than those reported in the literature for undriven, symmetric reconnection with zero guide field in \textit{non-relativistic} ion-electron plasmas. We can quote for the peak values of $E^*$ (once normalized in the same way as here): \citet{Birn2001,Pritchett2001}: $0.09$, \citet{Fujimoto2006,Fujimoto2009}: $0.15$, \citet{Daughton2006}: $0.08$, \citet{Klimas2010}: $0.07$--$0.09$, and the theoretical work of \citet{Hesse2009,Hesse2009b} predicting a maximal rate of $0.28$. Our results thus suggest larger rates for relativistic reconnection, a fact already seen in relativistic simulations of pair plasmas with, e.g., \citet{Zenitani2007} ($E^*=0.2$), \citet{Cerutti2012b} ($E^*=0.17$), or \citet{Bessho2012} ($E^*=0.19$ and 0.36). In conclusion, the relativistic Alfv\'en speed of the inflow provides the best normalization for the reconnection electric field, in that it is robust from non-relativistic to relativistic flows. Corresponding rates are in a close range (0.14--0.25), which is higher than the rates found in non-relativistic simulations with the same normalization (0.07--0.15). The rate does not depend on the inflow temperature at low $\beta$, but is nevertheless not universal: it decreases with increasing background particle number density. Generalization to the presence of a guide field is discussed in Sect.~\ref{sec:rec_electric_field_guide_field}. \subsection{Hall field and dispersive waves} \label{sec:Hall} We can see in Fig.~\ref{fig_wcewpe=1_NT=21300_cutalongX_partNumber_velocity} that inside the ion diffusion region, but outside of the electron diffusion region, ions have a small fluid velocity, while electrons still $E\times B$ drift toward their diffusion region. This results in a net current roughly given by $q_\lec n_\lec \bar{\b{v}}_\lec = q_\lec n_\lec \b{E}\wedge\b{B}/B^2$, which is the Hall current. This current continues along the magnetic separatrices in the outflow direction, and is at the origin of a quadripolar magnetic field directed along $\pm\hat{\b{y}}$. This Hall magnetic field, with the quadripolar structure, is present in our simulations. It has a weak intensity (between 1\% and 10\% of $B_0$). The charge separation between electrons and ions (Fig.~\ref{fig_wcewpe=1_NT=21300_cutalongX_partNumber_velocity}) also leads to the creation of a Hall electric field directed along $+\hat{\b{x}}$ in the $x<0$ region and $-\hat{\b{x}}$ in the $x<0$ region. Both the magnetic and electric Hall fields are absent in a simulation with pairs. The difference in the dynamical response of ions and electrons also allows the existence of waves with a quadratic dispersion relation, $\omega\propto k^2$, below ion scales \citep[either whistler waves or kinetic Alfv\'en waves, see][]{Rogers2001}. Observations of the same reconnection rate for any simulation model allowing these waves \citep[PIC, electron-MHD, Hall-MHD, two-fluid with and without electron inertia, hybrid simulations, see ][]{Birn2001,Shay2007,Rogers2001}, as well as theoretical considerations, have led to the thesis that these waves are essential to allow for fast reconnection rates. However, this view is questioned by a number of simulations that do not support quadratic dispersive waves, but still support fast rates \citep[hybrid simulations with no Hall term, pair plasmas, or strong guide field regime, see][]{Karimabadi2004,Bessho2005,Daughton2006,Daughton2007,Liu2014}. It is thus interesting to see whether our simulation data can provide any further insight into the matter. A prediction of the dispersive wave physics is that the reconnection rate is controlled solely by the ion physics, and not by the electrons. According to \citet{Daughton2006}, it should be independent of the electron diffusion region length. Their analysis we could, however, not reproduce because the electron diffusion zone length is, in our case, limited by the standing islands. It cannot stretch to large values, and we are thus unable to conclude in favor or in disfavor of the dispersive wave paradigm. However, we underline that the simulation with $m_\ion/m_\lec=1$ that we performed features an identical (and even slightly larger, Fig.~\ref{fig:reconnection_rates}) reconnection rate than simulations with $m_\ion/m_\lec=25$. It thus points toward a negligible influence of the dispersive waves, or to another mechanism allowing fast rates in pair plasmas. \subsection{Simulation-based scaling analysis} \label{sec:outflow_analytical_estimate_harder} The energy content of the outflows and the balance between thermal and bulk inertia in Ohm's law were explored through the simulations in Sects.~\ref{Sec:Ohms_law} and~\ref{sec:outflows}. The aim of the present section is to investigate these points with a simple analytical model in order to gain physical insight concerning these phenomena, and to extrapolate our simulation results to a larger parameter space. We extend the analytical results of Sect.~\ref{sec:outflow_analytical_estimate}, where particle number and energy conservation allowed an estimation of the quantity $h_{0,\out,s}\Gamma_{\out,s}$ (Eqs.~\ref{equ:outflow_energy} or~\ref{equ:outflow_energy_bis}), by now also using the equation of conservation of momentum (Eq.~\ref{equ:fluid_2}). \subsubsection{Thermal versus bulk electron inertia} We first investigate the relative weight of thermal and bulk electron inertia. At the center of the electron diffusion region, we learn from Sect.~\ref{Sec:Ohms_law} that the reconnection electric field is sustained by electron thermal and bulk inertia, with only the terms $\partial_x(n_\mathrm{e}\langle \delta{p}_{x}\delta{v}_{y}\rangle)$ and $\partial_z(n_\mathrm{e}\bar{p}_{z}\bar{v}_{y})$ contributing to either one of them, respectively. \begin{itemize} \item Concerning thermal inertia, the temperature tensor is defined via Eq.~\ref{equ:def_temperature}, so that $\langle \delta{p}_{x}\delta{v}_{y}\rangle = c^2\Theta_{xy,\lec}/\Gamma_\lec$. We see in Fig.~\ref{fig:wcewpe=3_cut_Z_NT6000_temperature_only} that $\Theta_{xy,\lec}$ is linear in the electron diffusion region. It vanishes at the center because there the distribution function $f_\lec$ is symmetric with respect to $v_x$. It is maximal at the diffusion region edge with a value $\Theta^\mathrm{edge}_{xy,\lec}$. Consequently, we approximate the thermal inertia contribution by $(c^2\Theta^\mathrm{edge}_{xy,\lec}/\Gamma^\mathrm{in}_\lec)/\delta_\lec$, where $\delta_\lec$ is the width of the electron diffusion region. \item For the bulk inertia term, we use the fact that $\bar{p}_{z}$ rises linearly from the center to its maximal value denoted by $\bar{p}^\out_{z}$ over a distance $D_\lec/2$, and that $\bar{v}_{y}$ has a vanishing derivative at the center (Fig.~\ref{fig_wcewpe=3_NT=6000_cutalongZ_summary}). Consequently, it can be estimated as $\bar{v}^\mathrm{center}_{y}\bar{p}^\out_{z}/D_\lec$. \end{itemize} All in all, from Ohm's law (Eq.~\ref{equ:Ohm_fluid_1}), the electric field at the center of the diffusion region is: \begin{equation} \label{equ:Erec_thermal_bulk} \begin{aligned} E^\mathrm{center}_y &= \frac{m_\lec}{q_\lec n_\lec} \left( \frac{\partial}{\partial \b{x}}\cdot (n_\lec\langle \delta\b{p}_\lec\delta\b{v}_\lec\rangle) + \frac{\partial}{\partial \b{x}}\cdot (n_\lec\bar{\b{p}}_\lec\bar{\b{v}}_\lec) \right)_y \\ &\sim \frac{m_\lec}{q_\lec} \left( \frac{c^2\Theta^\mathrm{edge}_{xy,\lec}}{\delta_\lec\Gamma^\mathrm{in}_\lec} + \frac{\bar{v}^\mathrm{center}_{y}\bar{p}^\out_{z}}{D_\lec} \right). \end{aligned} \end{equation} The next step is to use the constancy of $E_y$, that is well respected in the simulations: $E^\mathrm{center}_y = E^\ins_y = \bar{v}_{\ins} B_0$. If we introduce the inertial length in the inflow, $d_\lec^\ins = c\sqrt{\epsilon_0 m_\lec/(n_\lec^\ins e^2)}$, and the inflow magnetization $\sigma^\mathrm{cold}_{\ins,\lec} = B_0^2/(\mu_0m_\lec n_\lec^\ins c^2)$, we ultimately obtain: \begin{equation} \label{equ:Erec_thermal_bulk_bis} \frac{\delta_\lec}{d_\lec^\ins} \left(\sigma^\mathrm{cold}_{\ins,\lec}\right)^{1/2} \frac{\bar{v}_{\ins}}{c} = \frac{\Theta^\mathrm{edge}_{xy,\lec}}{\Gamma^\mathrm{in}_\lec} + \frac{\delta_\lec}{D_\lec}\frac{\bar{v}^\mathrm{center}_{y}\bar{p}^\out_{z}}{c^2}. \end{equation} We now proceed to derive approximate scaling relations for cases where either thermal or bulk inertia dominate the reconnection electric field. \begin{itemize} \item First, if thermal inertia dominates over bulk inertia, then Eq.~\ref{equ:Erec_thermal_bulk_bis} gives \begin{equation}\label{equ:scaling_theta_edge_thermally_dom} \frac{\Theta^\mathrm{edge}_{xy,\lec}}{\Gamma^\mathrm{in}_\lec} = \frac{\delta_\lec}{d_\lec^\ins}\left(\sigma^\mathrm{cold}_{\ins,\lec}\right)^{1/2} \frac{\bar{v}_{\ins,\lec}}{c} \propto \left(\sigma^\mathrm{cold}_{\ins,\lec}\right)^{1/2}. \end{equation} There are thus several factors contributing to $\Theta^\mathrm{edge}_{xy,\lec}$. The diffusion zone width $\delta_\lec$ is dynamically set during the reconnection process. It can be of the order of the particles gyroradius at the center of the current sheet, or of the plasma inertial length at the center of the current sheet. In all our simulations we find that the latter assumption holds throughout time to within a factor 2 (Sect.~\ref{sec:diff_width_2}), and in any case, $\delta_\lec / d_\lec^\ins$ is expected to be of order unity. The inflow speed is set by the reconnection electric field, $\bar{v}_{\ins} = E_y/B_0 = E^* V_\mathrm{A,in}^\mathrm{R}$ with $E^*$ the normalized reconnection rate (which lies in the range 0.1-0.25, Sect.~\ref{sec:rec_electric_field}) and $V_\mathrm{A,in}^\mathrm{R}$ the relativistic Alfv\'en speed in the inflow. For relativistic setups we thus have $\bar{v}_{\ins}\sim E^*c$. The inflow magnetization can be arbitrarily large. It is thus the main actor to produce relativistic temperatures, and thermal inertia scales as $\Theta^\mathrm{edge}_{xy,\lec} \propto \left(\sigma^\mathrm{cold}_{\ins,\lec}\right)^{1/2}$. \item Second, the term corresponding to bulk inertia in Eq.~\ref{equ:Erec_thermal_bulk_bis} can be estimated with the help of Eq.~\ref{equ:outflow_energy} (with $\bar{p}_{\out,s}=\bar{p}^\out_{z}$, $\bar{v}_{\out,s}=\bar{v}^\out_{z}$, and neglecting the guide field): \begin{equation} \frac{\delta_\lec}{D_\lec}\frac{\bar{v}^\mathrm{center}_{y}\bar{p}^\out_{z}}{c^2} = \frac{\delta_\lec}{D_\lec} \frac{\bar{v}^\mathrm{center}_{y}\bar{v}^\out_{z}}{c^2} \left(\frac{\bar{p}_{\ins}}{\bar{v}_{\ins}} + \sigma^\mathrm{cold}_{\ins,\lec}\right). \end{equation} The ratio $\delta_\lec/D_\lec$ is of order $1/10$ in our simulations. If we neglect the term ${\bar{p}_{\ins}}/{\bar{v}_{\ins}}$, which is of order unity for non-relativistic inflow temperatures, we see that bulk inertia scales with $\sigma^\mathrm{cold}_{\ins,\lec}$. \end{itemize} In conclusion, thermal inertia scales at most as $\left(\sigma^\mathrm{cold}_{\ins,\lec}\right)^{1/2}$, and bulk inertia as $\sigma^\mathrm{cold}_{\ins,\lec}$. Consequently, regarding the non-ideal terms in Ohm's law in the electron diffusion region, we expect bulk inertia to outweight thermal inertia at large inflow electron magnetization. \subsubsection{Energy content of the outflows} We now turn to the energy content of the outflows, in order to see whether we can explain their thermally dominated character for relativistic runs. The temperature in the outflows is dominated by $\Theta_{xx,\lec}$ or $\Theta_{yy,\lec}$, which we denote by $\Theta^\mathrm{out}_{\lec}$. We first have to link $\Theta^\mathrm{out}_{\lec}$ to $\Theta^\mathrm{edge}_{xy,\lec}$. The outflow temperature at the center of the diffusion region is roughly constant along $z$ throughout the area of linear increase of $\bar{v}_z$ (Fig.~\ref{fig_wcewpe=3_NT=6000_cutalongZ_summary}), because particles on their way from the X-point to the exhaust mainly turn into the reconnected magnetic field and thus do not really gain thermal agitation, but convert it from one component of $\Theta$ to another. We can thus assume $\Theta^\mathrm{out}_{\lec} = \Theta^\mathrm{center}_\lec$. We now would like to assume $\Theta^\mathrm{edge}_{xy,\lec} \sim \Theta^\mathrm{center}_{xx,\lec}$. This indeed holds for electrons in the case of Fig.~\ref{fig:wcewpe=3_cut_Z_NT6000_temperature_only}. However, this does not hold in all simulations, and $\Theta^\mathrm{edge}_{xy,\lec}$ is between $1/10$ to 10 times $\Theta^\mathrm{center}_{xx,\lec}$. This is due to the different origin of these components: $\Theta^\mathrm{center}_{xx,\lec}$ reflects particles in Speiser orbits going up and down along $x$ with a zero bulk $x$-velocity, while $\Theta^\mathrm{edge}_{xy,\lec}$ reflects the asymmetry of the distribution function with respect to $v_x$ due to the newly entering particles at the edge of the diffusion zone. With the previous remark in mind, we still make the hypothesis $\Theta^\mathrm{edge}_{xy,\lec}\sim\Theta^\mathrm{center}_{xx,\lec}$. Next, if we assume that thermal inertia contributes significantly in Ohm's law, we obtain with the scaling of Eq.~\ref{equ:scaling_theta_edge_thermally_dom}: \begin{equation}\label{equ:theta_out_is_relativistic_simple} \Theta^\mathrm{out}_{\lec} \propto \left( \sigma^\mathrm{cold}_{\ins,\lec} \right)^{1/2}. \end{equation} For relativistic temperatures we have $h_{0,\out,\lec} \simeq 4\Theta^\mathrm{out}_\lec$ (Fig.~\ref{fig_kappa_32}), so that with Eq.~\ref{equ:theta_out_is_relativistic_simple} we see that a relativistic inflow magnetization implies $h_{0,\out,\lec} \propto \left( \sigma^\mathrm{cold}_{\ins,\lec} \right)^{1/2}$. On another hand, energy conservation gives, in its simplest form (Eq.~\ref{equ:outflow_energy_bis} with $\sigma_\lec^\mathrm{cold}(B_0)\gg1$): \begin{equation}\label{equ:outflow_energy_ter} h_{0,\out,\lec}\Gamma_{\out,\lec} \sim \sigma_{\ins,\lec}^\mathrm{cold}. \end{equation} Thus: \begin{equation}\label{equ:outflow_energy_quatro} \Gamma_{\out,\lec} \propto \left( \sigma^\mathrm{cold}_{\ins,\lec} \right)^{1/2}. \end{equation} We finally turn to the ratio of energy fluxes in the outflow. We see with Eq.~\ref{equ:particles_energy_flux} that the flux associated with kinetic bulk energy is $\Gamma_{\out,\lec}-1$. With Eq.~\ref{equ:outflow_energy_quatro} (and for $\Gamma_{\out,\lec}\gg1$), this flux is $\Gamma_{\out,\lec} \propto \left( \sigma^\mathrm{cold}_{\ins,\lec} \right)^{1/2}$. The flux associated with thermal kinetic energy and pressure work is $h_{0,\out,\lec}\Gamma_{\out,\lec}-1$, and with Eq.~\ref{equ:outflow_energy_ter} we have $h_{0,\out,\lec}\Gamma_{\out,\lec}-1 \sim \sigma_{\ins,\lec}^\mathrm{cold}$. The ratio of thermal to bulk energy fluxes is thus $\propto \left( \sigma^\mathrm{cold}_{\ins,\lec} \right)^{1/2}$, meaning that relativistic inflow magnetization inevitably implies reconnection exhausts dominated by thermal energy -- which is what we see in our simulations (Table~\ref{tab:energy_outflow_flux}), even if the scalings derived here do not hold exactly because of the many assumptions involved. In conclusion, we have shown that \textit{under the hypothesis of non-ideal effects sustained by thermal inertia}, relativistic inflow magnetizations produce thermally dominated outflows. The physical reason is that the reconnection electric field $E_y$ is large in the inflow region, so that thermal inertia must be high in order to sustain $E_y$ in the central region, which implies high temperatures. However, we also demonstrated that thermal inertia is not expected to dominate for very relativistic inflows. When this is the case, there is no constraints from Ohm's law on the temperature, and we cannot conclude on the ratio of thermal to bulk energy fluxes. Since this ratio is $(h_{0,\out,\lec}\Gamma_{\out,\lec}-1)/(\Gamma_{\out,\lec}-1) \sim h_{0,\out,\lec}$, a relativistic outflow temperature of the order of $m_\lec c^2$ suffices to give thermally dominated outflows. For our simulations, thermal inertia contributes equally or less than bulk inertia (Sect.~\ref{Sec:Ohms_law}), but still significantly, so that the outflows are thermally dominated. \label{sec:ccl} \subsection{Summary} We investigate magnetic reconnection in low $\beta$ ion-electron plasmas (mass ratio of 25) with 2D PIC simulations, under relativistic conditions, i.e., the magnetic energy of the inflowing plasma exceeds its rest-mass energy. The simulations start from a Harris kinetic equilibrium with no localized perturbation. For diagnostics and analytical models, we use momentum and energy fluid equations based on lab-frame quantities (Appendix~\ref{sec:app_measure_relat_1}). They have the advantage of being valid whatever the particle distribution function, while the usual relativistic fluid equations using comobile quantities are restricted to isotropic comobile distribution functions. For antiparallel reconnection, the structure of the diffusion region has a width (in the inflow direction) $\delta_s$ given by the respective inertial length $d_s$ of the species $s$, measured at the center of the diffusion region. A large inflow temperature increases this width. \note{For all cases with low inflow plasma $\beta$ ($\leq2.5\times10^{-3}$) we find: $0.5\leq\delta_\ion/d_\ion\leq1$ and $1\leq\delta_\lec/d_\lec\leq1.5$. For higher inflow temperatures, and thus larger $\beta$, the width is increased by the large thermal velocity of the incoming particles. This is similar to non-relativistic studies.} At the entrance of the diffusion regions for simulations at low background $\beta\leq 2.5\times10^{-3}$ we find sharp transitions in the fluid quantities that were not reported elsewhere. We argue that they are not shocks. Instead, they occur when the inflowing particles have a thermal velocity far smaller than their bulk $E\times B$ velocity, so that they enter the diffusion region with the same velocity and bounce back at the same location. We stress that these sharp transitions are not a feature of relativistic reconnection, as they depend only on the cold nature of the inflow. However, the phenomenon should be more common in relativistic reconnection because then the inflow bulk velocity $v_{E\times B}\sim E/B$ is large. We explicit the balance of terms in the relativistic Ohm's law for antiparallel reconnection. % The ion diffusion region is dominated by bulk inertia (as defined in Eq.~\ref{equ:Ohm_fluid_1}). In the electron diffusion region, bulk inertia contributes equally or more than thermal inertia. This latter result challenges the thermal-inertia-dominated paradigm that holds for non-relativistic or mildly relativistic antiparallel reconnection. We show analytically % that a significant contribution of bulk inertia is to be expected whenever the inflow magnetization $\sigma_\lec^\mathrm{cold}$ (cold meaning that the temperature is not taken into account, see Eq.~\ref{equ:sigma_s_cold}) of the \textit{electrons} is large, because then bulk inertia $\partial_z\bar{p}_z\bar{v}_y \sim \bar{p}_z c/D \propto \sigma_\lec^\mathrm{cold} / D$ can exceed thermal inertia $\partial_x\delta{p}_x\delta{v}_y \propto (\sigma_\lec^\mathrm{cold})^{1/2}/\delta$. This is a new result that should hold for any large electron magnetization. For the reconnection outflows we show analytically from mass and energy conservation that reconnection is expected to produce relativistic outflow temperatures and/or relativistic outflow bulk velocities. From simulations we find that outflow thermal energy dominates over bulk kinetic energy (from 70\% to 99\%, for simulations with increasing background magnetization). A more refined analytical analysis shows that this is expected if the reconnection electric field is sustained by thermal inertia. If bulk inertia dominates over thermal inertia, as expected at very large inflow magnetization, then our simple analytical model does not allow to conclude on the cold or hot nature of the outflows. Also, our simulations do not probe high enough electron magnetizations to reach this regime: at $\sigma_\lec^\mathrm{cold} = 90$, thermal inertia contributes as 50\% of the reconnection electric field, and this fraction goes down to 25-40\% at $\sigma_\lec^\mathrm{cold} = 360$, which is significant enough for the hypothesis of $E_\mathrm{rec}$ sustained by thermal inertia to hold. For the islands we show that, with or without a guide field, their centers consist mainly of particles initially in the current sheet that were gathered inside the island during the tearing instability, that do not mix with the background plasma even after many island merging events. Particles of the background plasma cannot reach the inner parts because of the strong magnetic field surrounding the islands, and thus circle around the central part. As a result, the central part is less dense than its immediate surrounding. This may explain observed density dips at the center of magnetic islands during magnetotail reconnection events \citep{Khotyaintsev2010}, without invoking island merging or particle escape along the flux tube\note{As \citet{Markidis2013} does.}. Islands are also the hottest parts of the flow, with fully anisotropic temperatures in the antiparallel case, and distributions close to gyrotropic with a guide field.% We argue that the reconnection rates are to be normalized by the asymptotic magnetic field and relativistic Alfv\'en speed in the inflow, projected onto the outflow direction if there is a guide field: $E^*=E_y/(B_0 V_\mathrm{A,in}^\mathrm{R}\cos\theta)$. This leads to rates in a narrow range: $E^*$ peaks between 0.14--0.25. % However, we stress that there is no universal value for $E^*$ as defined here or elsewhere. First, because other studies show that it depends on the inflow plasma $\beta$ (increasing with decreasing $\beta$). Here we find no dependence on the background plasma temperature, but smaller rates for larger particle number densities\note{($E^*=0.18$ instead of $E^*=0.23$ for a three times less dense background)}. Second, we find larger rates for the relativistic setups (0.18--0.25) than for the mildly relativistic case (0.15). These rates are also larger than those reported in the literature for ion-electron non-relativistic reconnection \citep[0.07--0.15 for][]{Birn2001,Pritchett2001,Fujimoto2006,Fujimoto2009,Daughton2006,Klimas2010}. This points toward relativistic reconnection being slightly faster than non-relativistic reconnection. This trend is reinforced by simulations in relativistic pair plasmas \citep[$E^*=0.3$ in our case or, e.g., 0.17--0.36 for][]{Zenitani2007,Bessho2012,Cerutti2012b}. We note that this is against the interpretation of \citet{Hesse2007} of a smaller rate for more relativistic setups. Third, we confirm that a guide field leads to a smaller normalized rate. We explore the consequences of adding a guide magnetic field. The flow structure is strongly disturbed for two reasons: the Lorentz force associated with the guide field, and the relation $E<B$ everywhere. The acceleration region is now defined by the condition $\b{E}\cdot\b{B}\neq 0$. Inflowing ion and electron Larmor radii are smaller than the island scales or magnetic gradient scales, and remain so even after the acceleration phase by $E_\mathrm{rec}$ because this phase conserves the perpendicular-to-$\b{B}$ momentum. Particles thus remain tied to the field lines everywhere, including in the acceleration region where they spend more time before being deviated in the outflows. \subsection{Discussion and astrophysical outlook} \label{sec:astro_outlook} This study may serve as micro-physics input for analyses on larger scales concerning magnetic energy conversion in relativistic ion-electron plasmas, as should be encountered in the coronae of AGN and microquasar accretion flows, in the lobe of radio galaxies, or inside relativistic jets from AGNs or GRBs. We now discuss such applications, and give estimates for key parameters in these objects: magnetic field $B$, electron number density $n_\lec$, magnetizations $\sigma_s^\mathrm{cold}$ (where cold means that only the rest mass energy is taken into account, Eq.~\ref{equ:sigma_s_cold}), with $s=\ion,\,\lec$ for ions or electrons, and Alfv\'en speeds $V_\mathrm{A}^\mathrm{R}$. The properties of magnetic reconnection as studied here depend only on the inflow magnetization and temperatures, regardless of the real values of $B$ and $n_\lec$. This is true at least as long as effects such as pair creation and annihilation, radiative braking, or Compton drag on the electrons, can be neglected (see Melzani et al., in prep, for a discussion on these effects). \subsubsection{Toward a new regime: non-dissipative reconnection?} Our finding of a reconnection electric field sustained equally or more by bulk inertia than by thermal inertia for large inflow electron magnetization ($\sigma_\lec^\mathrm{cold} \geq 90$), and the extrapolation of Sect.~\ref{sec:outflow_analytical_estimate_harder}, indicate that bulk inertia might end up dominating at even larger inflow electron magnetizations. This was also envisioned by \citet{Hesse2007}, and reconnection in such a regime would bear significant differences with the standard picture. However, we nuance the assertion of \citet{Hesse2007} that reconnection would then be a reversible process: as underlined in Sect.~\ref{sec:outflow_analytical_estimate_harder}, the reconnection outflows may be thermally dominated even when bulk inertia dominates Ohm's law. A definite answer to these questions requires very high magnetizations, that we can hardly afford with a PIC code, and that may require relativistic gyrokinetic codes. Highly magnetized environments, such as magnetar magnetospheres \citep[with magnetizations exceeding $\sigma_\lec^\mathrm{cold}=10^{13}$,][]{Lyutikov2013}, pulsar winds near the termination shock \citep[$\sigma_\lec^\mathrm{cold}=10^{13}$,][]{Bucciantini2011,Sironi2011b}, other objects with $\sigma_\lec^\mathrm{cold}\ggg 1$ discussed in what follows, are likely to support this reconnection regime. \subsubsection{Large scale transient outflow production, the example of microquasars} We have shown that the reconnection outflows are thermally dominated, with a bulk Lorentz factor not necessarily increasing with the inflow magnetization and featuring low values (1.63 at most, Table~\ref{tab:energy_outflow_flux}). However, applications to large scale outflows triggered by reconnection events require some care. The outflows studied in the present manuscript originate from the electron diffusion region, and feature ion/electron decoupling. On larger distances, if not bounded by the islands and by our periodic setup, electrons and ions are expected to couple and to follow the ideal MHD dynamic. The scale on which they can propagate is fixed by larger scales than simulated here. On another hand, it is expected and observed \citep{Khotyaintsev2005} that magnetic energy conversion takes place also along the magnetic separatrices far away from the dissipation region, on length scales of hundreds of ion inertial lengths. This conversion occurs through instabilities that produce thermal and non-thermal electrons \citep{Drake2005,Egedal2009,Egedal2012}, and through the complex structure of collisionless non-linear waves (slow shock, compound wave, rotational wave) by which the magnetized inflowing plasma transits to the hot and unmagnetized outflow on MHD scales \citep{Liu2012,Higashimori2012}. It is this large scale outflow that should be identified to the transient reconnection-driven jets in microquasar models \citep{deGouveia2005,deGouveia2010,Kowal2011,McKinney2012,Dexter2013}. In the magnetosphere close to the black hole, \citet{deGouveia2005} estimates on the basis of an analytical model, $n_\lec \sim 5\times10^{15}\,\mathrm{cm^{-3}}$, $B \sim 7\times10^7$\,G, which gives electron and ion magnetizations $\sigma_\lec^\mathrm{cold}\sim 10^5$ and $\sigma_\ion^\mathrm{cold} \sim 60$, and an Alfv\'en speed $V_\mathrm{A}^\mathrm{R} \sim c$. This is clearly in the relativistic case. The energy content of the large scale outflows in this case has not been studied, but we can expect from the collisionless slow shocks, or rotational discontinuities at the separatrices, to produce a thermally dominated outflow. It may not be so for other jet production mechanisms, and could help discriminating in favor or against reconnection scenarios. Another unknown is what becomes of the ambient plasma that is expelled by the first reconnected field lines, ahead of the dipolarization front. In our study, it would correspond to half of a magnetic island, ejected out of the simulation box. The ambient plasma would be the plasma from the current sheet trapped in the island. As we demonstrate, this plasma does not mix with the reconnected plasma and is simply compressed and heated \citep[see][for a 3D case where instabilities imply magnetic to kinetic energy conversion]{Vapirev2013}. In an open configuration, it would be at the head of the large scale outflow. \subsubsection{Plasma heating in AGN and microquasar coronae and in galaxy radio lobes} Photon emission in the hard state of microquasars and AGNs is believed to come from inverse-Compton scattering of seed photons by the electrons of a corona. To achieve this, these electrons must reach temperatures of the order of $10^9$\,K, i.e., $\Theta_\lec = T_\lec/m_\lec c^2 \sim 0.2$. A non-thermal population of electrons is also required by the observation of MeV photons \citep{Poutanen2014}. A proposed mechanism for plasma heating is by magnetic reconnection \citep{Matteo1998,Merloni2001,Reis2013}. The plasma Alfv\'en speed estimated by these authors lies in the range $0.03c$--$0.3c$. Associated electron magnetizations are $\sigma_\lec^\mathrm{cold} \sim 1.7$-180, which is in the range of the present study. A crucial question is the energy distribution between ions and electrons: if most of the magnetic energy goes to ions, and because of the low collisionality of these dilute environments, a large temperature difference can be sustained \citep{Matteo1997}. Our study shows that ions are slightly more heated than electrons: this can be seen with the temperatures of Figs.~\ref{fig:wcewpe=3_cut_Z_NT6000_temperature_only}, \ref{fig_wcewpe=3_NT=6000_cutalongZ_summary}, \ref{fig:xcf_wcewpe=3_NT=6000_2D_pseudocolor_temperature_NT=6000}, and \ref{fig:guide_field_overall_velocities}. More generally, the kinetic energy of the particles trapped in the magnetic islands is distributed as 55\% for ions and 45\% for electrons, and the kinetic energy of the particles from the background plasma that are accelerated when reaching the current sheet is also distributed as 60\% for ions and 40\% for electrons (for details see Melzani et al., in prep.). The energy distribution by acceleration processes far downstream of the diffusion region requires another study. Similar questions arise concerning the heating of the lobes of radio galaxies \citep{Kronberg2004}. There, $n\sim 3\times10^{-6}\,\mathrm{cm^{-3}}$ for the number densities, and $B \sim 5\,\mathrm{\mu G}$ for the equipartition magnetic field with values that can be locally ten times higher, which gives magnetizations $\sigma_\lec^\mathrm{cold} \sim 0.8$-80 and Alfv\'en speeds $\sim 0.02c$-$0.2c$. Our conclusion for the energy repartition between ions and electrons also holds. \subsubsection{Flares and ``mini''-jets in extragalactic jets and in GRBs} Flare-like activity in the GeV-TeV range is observed from extragalactic jets, and may possibly be explained by local reconnection events inside the jet, that produce smaller jets (the reconnection exhausts) which in turn radiate the expected photons \citep{Giannios2009}. This $\gamma$-ray emission region may be located close to the black-hole \citep[$<0.05$\,pc,][]{Giroletti2004}, where $B\sim 0.02$-$0.2$\,G and the plasma magnetization is high. For example, \citet{Giannios2009} take $\sigma^\mathrm{cold}_\ion = 100$, which leads to $\sigma^\mathrm{cold}_\lec = 2\times10^5$ and $V_\mathrm{A}\sim c$. This is in the regime where bulk inertia should dominate in Ohm's law. Also, \citet{Giannios2009} estimate from energy considerations, that the blobs emitted from the reconnection exhausts should be $\sim10^{14}$\,cm, i.e., based on its estimated particle density, $10^{10}$ ion inertial lengths.\note{$d_i=1000$cm with $n=80cm^{-3}$} Here again, the physics far from the dissipation region should play an important role in producing such large scale structures. \subsubsection{Radio emission from extragalactic jets} Another case for relativistic magnetic reconnection is inside jets from AGNs, on scales of 10-100\,kpc. Radio spectra may be explained by radiation linked to reconnection events \citep{Romanova1992}.\note{Romanova uses $B\sim 300\mu G$, $n\sim 10^{-3}cm^{-3}$ -- $\sigma_e = 10$, but with no ref. to observations.} Observations of AGN jets indicate $B\sim 10$-$30\mathrm{\mu G}$, $n\sim 0.8$-$5\times 10^{-8}\mathrm{cm^{-3}}$, and electron magnetizations in the range $\sigma_\lec^\mathrm{cold} \sim 500$-2500 \citep{Schwartz2006}, which implies ion magnetizations $\sigma_\ion^\mathrm{cold} \sim 0.3$-1.3 and Alfv\'en speeds $\sim0.5$-$0.8c$. Again, our results apply in these cases, and in particular the electron magnetizations are in the very relativistic range where bulk inertia should dominate in Ohm's law. \subsubsection{High-energy particle production} The proposed normalization of the reconnection rate, $E^* = E_\mathrm{rec} / (B_0 V_\mathrm{A,in}^\mathrm{R}\cos\theta)$ with $V_\mathrm{A,in}^\mathrm{R}$ the relativistic inflow Alfv\'en speed, leads to $E^*$ in a close range (0.14-0.25) and, because it relies only on inflow quantities, allows for an easy prediction of the reconnection electric field. In particular, the ratio $E_\mathrm{rec}/B_0$ is a key quantity to estimate the time scale of energy dissipation or the maximal energy gain for particles. It is interesting to notice that for very relativistic plasmas, $V_\mathrm{A,in}^\mathrm{R}$ saturates at $c$, so that $E_\mathrm{rec}/B_0$ saturates at $\sim 0.2c$. It may imply that the hardness of the high-energy tails saturates. We explore these matters in a forthcoming paper (Melzani et al., in prep.). Briefly, we find for a given species a power-law tail whenever its background magnetization is relativistic (above a few), with an index depending mainly on the inflow magnetization. \subsubsection{Other complications} We finally point out that the present study is oversimplified in many respects. Magnetic reconnection in magnetized coronae and jets likely often implies asymmetric plasmas from each side of the current sheet, guide fields \citep{Aunai2013,Hesse2013,Eastwood2013}, and also normal fields (along $\hat{\b{x}}$ here) reminiscent from the ambient magnetic field. The last point has been studied in the context of the Earth magnetotail \citep{Pritchett2005b,Pritchett2010,Sitnov2011}. Also, the initial conditions chosen in the simulations are arbitrary and do not necessarily reflect the real environments. Explored alternatives to the Harris sheet include X-point collapse \citep[e.g.,][]{Pahlen2013} or force-free equilibrium \citep[e.g.,][]{Liu2014}, and show little differences with the Harris case. However, three dimensional initial configurations should also be considered, because in a real environment most of the energy dissipation may occur at 3D nulls, involving for example spine-fan reconnection, or at quasi-separatrix layers \citep{Birn2007,Pontin2011}. Few kinetic simulations of such setups exist \citep{Baumann2012,Olshevsky2013}. A related point is the external forcing, i.e., the large scale plasma flow that can increase the magnetic field gradients and trigger reconnection. Studies \citep{Pei2001,Pritchett2005,Ohtani2009,Klimas2010} show that the reconnection rate $E^*$ is then fixed by the boundary conditions, and is thus larger than the spontaneous rate. The timescale of the forcing also proves to be of importance \citep{Pei2001}. These considerations, as well as some of the points made earlier on, highlight the multiscale nature of reconnection in the context of concrete astrophysical objects -- and demonstrate the need for corresponding multiscale simulation studies, a field still in its infancy \citep[e.g., ][]{Horiuchi2010,Innocenti2013} Another central question is the validity of the 2D findings in three dimensions. Magnetic islands then become extended filaments, modulated or broken by instabilities in the third dimension or by a lack of coherence of the tearing instability \citep{Daughton2011,Kagan2012,Markidis2013}. It may imply more mixing of the current sheet particles with those of the background plasma. Concerning the validity of our claims on Ohm's law, 3D PIC simulations in non-relativistic plasmas have shown that anomalous resistivity due to microinstabilities remains a negligible dissipation mechanism in the diffusion region \citep{Liu2013b,Karimabadi2013}, where the reconnection electric field is still sustained by thermal electron inertia. The scaling analysis of Sect.~\ref{sec:outflow_analytical_estimate_harder} should thus remain valid, as well as the conclusion that bulk inertia dominates at high inflow magnetization. | 14 | 4 | 1404.7366 |
1404 | 1404.2543_arXiv.txt | { We report the {identification} of a new wide separation binary (LDS~5606) in the $\sim$20~Myr-old $\beta$ Pic moving group. This M5+M5 pair has a projected separation of 26$''$, or $\sim$1700~AU at a distance of 65~pc. Both stars host warm circumstellar disks and many strong hydrogen and helium emission lines. Spectroscopic observations reveal signatures of youth for both stars and on-going mass accretion in the primary. The properties of LDS~5606 make it an older analog to the $\sim$8~Myr TWA~30 system, which is also composed of a pair of widely separated mid-M dwarfs, each hosting their own warm circumstellar disks. LDS~5606 joins a rather exclusive club of only 3 other known stellar systems where both members of a binary, far from any molecular cloud, are orbited by detected {circumstellar disks}. } | Over the last few decades, astronomers have identified hundreds of stars in young moving groups near Earth (for reviews see \citealt{ZS04,Torres:2008,Malo:2013}). These moving groups have ages of $\sim$10--100~Myr and provide a sample of stars useful for the study of the planet formation environment. Previous work has relied heavily on identification of these stars at X-ray wavelengths with the ROSAT All-Sky Survey (RASS). Recent work has demonstrated that low-mass members can be successfully identified by utilizing the GALEX \citep{Martin:2005} ultraviolet survey \citep{Rodriguez:2011,Rodriguez:2013,Shkolnik:2011}. Among known low-mass youthful stars within 100 pc of Earth, a modest number stand out with special interest because of the presence of both surrounding dust and gas. The first such star to be recognized was the late-K type star TW Hya; the first known member of the $\sim$8~Myr-old TW Hya Association (TWA; see \citealt{Ducourant:2014} and references therein). Relatively recently, \citet{Looper:2010a,Looper:2010b} identified a remarkable pair of dusty mid-M type stars (TWA 30A \& B) that are members of TWA and that exhibit surrounding gas that is both accreting and outflowing. As part of the GALEX Nearby Young-Star Survey (GALNYSS; \citealt{Rodriguez:2013}) we identified a pair of mid-M dwarfs that exhibit strong UV emission and excess mid-infrared emission. As we show in Sect.~\ref{results}, this very dusty binary, {LDS~5606}, is a likely member of the $\sim$20~Myr-old $\beta$~Pic moving group and is an older analog of the TWA~30 binary. Dusty low-mass stars such as these serve as excellent laboratories in which to study the planet forming environment of the most abundant stars in the Galaxy. To date, only a handful of binaries far from molecular clouds or star forming regions are known in which both stars host circumstellar disks. LP~876--10, recently recognized as a widely separated companion (158~kAU) to Fomalhaut \citep{Mamajek:2013}, has now been shown to host a cold circumstellar disk \citep{Kennedy:2014}. The HD223352 triple system hosts a circumbinary disk around the close binary and a circumstellar disk around the $\sim$3000~AU companion, HD223340 \citep{Phillips:2011}. Both systems are older than 100~Myr. At the intermediate age range ($\sim$10--100~Myr) of most nearby young moving groups, only TWA~30 is a known binary hosting a pair of disks. The TWA~30 system is comprised of an M4+M5 pair separated by $\sim$3400~AU \citep{Looper:2010a,Looper:2010b}. Among star forming regions, there are many more cases where both stars in a binary system each host disks. \citet{Monin:2007} conservatively list 40 multiples with pairs of disks (either accreting or not), but argue that more non-accreting disks pairs remain to be discovered in these $\sim$few~Myr-old regions. It is clear that, while binary systems do host disks, these dissipate on faster timescales than around single stars \citep[e.g.,][]{Rodriguez:2012}. The presence of two disks within a $\gtrsim$8~Myr binary is a rare occurrence; LDS~5606 presented here is only the 4th example after Fomalhaut, HD~223352, and TWA30. {LDS~5606 is a 26\arcsec\ binary listed in the Luyten Double Star catalog \citep{Luyten:1997}. Other than an entry in the Washington Double Star catalog \citep{Mason:2001}, this system has gathered little attention since its discovery. Given that both stars have nearly identical 2MASS magnitudes, spectral types, and similar UV and IR excesses, it is difficult to unambiguously designate one or the other as the brighter primary. Hence, we adopt the notation introduced in the LDS and WDS catalogs that the primary star (A) is the western component of the binary (see Fig.~\ref{fig:chart}). Both stars are detected in GALEX yet, curiously, the secondary component (B) was not identified as part of GALNYSS given that its near UV (NUV) emission is stronger than the selection criteria (see \citealt{Rodriguez:2013}), a situation similar that of the actively-accreting TW~Hya.} In this paper, we demonstrate that LDS~5606 is a new member of the $\beta$~Pic moving group. In a related paper (Zuckerman et al., submitted to ApJ), we discuss in more detail the disk and accretion signatures of both stars. \begin{figure}[t] \begin{center} \includegraphics[width=88mm,angle=0]{chart1_v2} \end{center} \caption{2MASS J-band finder chart illustrating the location {and components of LDS~5606}.} \label{fig:chart} \end{figure} | LDS~5606 is a widely separated (26$''$) binary system consisting of two M5 dwarfs. These stars were identified as part of the ongoing GALNYSS program \citep{Rodriguez:2013}, which seeks to identify low-mass members to nearby young moving groups by virtue of their strong ultraviolet emission. Our kinematic and spectroscopic analysis of LDS~5606 place it as a member of the $\sim$20~Myr-old $\beta$~Pic moving group. We estimate a kinematic distance of 65~pc, implying a projected separation of $\sim$1700~AU. Features of youth are seen in the spectra of both stars. In particular, LDS~5606A shows numerous strong emission lines, especially of hydrogen and helium. Both components of LDS~5606 have IR excess at WISE wavelengths suggestive of warm circumstellar dusk disks. As such, the properties of this binary are analogous to the younger ($\sim$8~Myr) TWA 30 binary \citep{Looper:2010a,Looper:2010b}. Both systems exhibit strong emission lines and host circumstellar disks, although the different orientation of these disks may account for the different emission lines observed and for the lack of GALEX detections for TWA~30. To date, only a handful of binary stars located far from molecular clouds are known to host disks around each component. Among stars with ages $\sim$8~Myr or older, LDS~5606 is one of only 4 binary or multiple systems known to host a pair of disks (TWA~30:\ \citealt{Looper:2010a,Looper:2010b}; HD223352:\ \citealt{Phillips:2011}; Fomalhaut:\ \citealt{Kennedy:2014}; and LDS~5606). The unusual properties of the disks around the components of LDS~5606 and the accretion and photodissociation signatures in the spectra are discussed in detail in Zuckerman et al.\ (submitted to ApJ). Identification of systems like LDS~5606 show that additional outstanding members of these young moving groups may yet be found. | 14 | 4 | 1404.2543 |
1404 | 1404.7150_arXiv.txt | We present an algorithm for classifying the nearby transient objects detected by the \gaia{} satellite. The algorithm will use the low-resolution spectra from the blue and red spectro-photometers on board of the satellite. Taking a Bayesian approach we model the spectra using the newly constructed reference spectral library and literature-driven priors. We find that for magnitudes brighter than 19 in \gaia{} $G$ magnitude, around 75\% of the transients will be robustly classified. The efficiency of the algorithm for SNe type I is higher than 80\% for magnitudes $G\leq$18, dropping to approximately 60\% at magnitude $G$=19. For SNe type II, the efficiency varies from 75 to 60\% for $G\leq$18, falling to 50\% at $G$=19. The purity of our classifier is around 95\% for SNe type I for all magnitudes. For SNe type II it is over 90\% for objects with $G \leq$19. GS-TEC also estimates the redshifts with errors of $\sigma_z \le$ 0.01 and epochs with uncertainties $\sigma_t \simeq$ 13 and 32 days for type SNe I and SNe II respectively. GS-TEC has been designed to be used on partially calibrated \gaia{} data. However, the concept could be extended to other kinds of low resolution spectra classification for ongoing surveys. | The study of transient phenomena is a field of increasing interest: for example, the observations of type Ia Supernovae (SNe) have lead to the discovery of the accelerated expansion of the Universe (\cite{1999ApJ...517..565P}, \cite{Riess1998}) and have played a fundamental role in the discovery of Dark Energy. Furthermore the investigation of transient phenomena at multiple wavelengths have lead to a better understanding of SNe progenitors \citep{2009ARA&A..47...63S} and modelling of the explosion mechanisms. The era of large transient surveys has just begun with, for example, the Palomar Transient Factory (PTF, \cite{Rau2009}), Pan-STARRS \citep{2002SPIE.4836..154K}, and Catalina Realtime Transient Survey (CRTS, \cite{CRTS2011}). \gaia{}, the ESA cornerstone mission \citep{GaiaPerryman}, whilst primarily an astrometry mission, will have a significant ability in revealing the transient universe. \gaia{}, will provide highly accurate parallaxes for over a billion stars. In addition, it will provide a wealth of additional information about each star: full six dimensional astrometric parameters; and astrophysical parameters such as effective temperature, surface gravity, metallicties and reddening. Since \gaia{} will observe each point of the sky around 70 times on average, it will, over the nominal mission length of 5 years, detect many thousands of new transient events. Indeed \gaia{} is expected to discover between 6000 and 7000 new SNe (\cite{Belokurov2003}, \cite{Altavilla2012}), thus several SNe each day, down to a limiting magnitude of \gaia{} $G$=20 which for SNe events corresponds to a redshift limit $z \lesssim 0.14$. The \gaia{} photometric science alerts system \citep{Wyrzykowski2012} will perform the detection, classification and dissemination of the alerts on transient events to the scientific community. The alerts system will process all data from \gaia{}, on a daily basis, as soon as the data is downloaded. In the simplest case, it will issue alerts based on flux changing by more than a defined magnitude threshold. GS-TEC is a standalone module using the \gaia{} photometric and spectrophotometric data allows the alerts system assign a classification type and a classification probability to each alert. This module is one of the three different classification modules that the photometric science alerts intends to use for classification purposes. The spectroscopic classification result provided by GS-TEC will be published along with photometric data (lightcurve of the event as detected by Gaia) and environment of the transient based on catalogue search. However, it will be the only one providing information on SNe subtypes and their parameters. The description of the full photometric science alerts pipeline and first results is aimed to be released in a separate paper. The alert stream will be non-proprietary and will be distributed via public on-line services. The time to release the alerts is still to be determined, but it will take between 24 and 48 hours since the on-board observation. Its main goal is to provide information to enable targeted selection for follow-up and to filter the objects according to their scientific relevance. At this point it becomes essential to provide a reliable classification algorithm that can provide information on the nature of the event, e.g. AGN, variable star, SNe (plus its type), in addition to providing parameters, such as redshift, or epoch to maximum brightness for the case of slowly evolving objects like SNe. Other type of events such as Cataclysmic Variables or Tidal Disruption Flares are also relevant for Gaia classification scheme, however, the (almost) lack of broad features in their spectra makes them a difficult target for a low resolution spectral classification only. Therefore, in the present context they will be considered as part of the black body-like population, which is included in the classification. The importance of having a real-time automated detection and classification framework has been already pointed out by the teams of PTF: \cite{Brink2013} and \cite{Bloom2012}, and Catalina \citep{Djorgovski2011} synoptic surveys. An average night may receive several hundreds of potential alerts, which need to be processed in nearly real time in order to characterize them and select the most interesting targets for rapid follow-up. This paper describes the classification algorithm developed to enable the prototyping of SNe events from \gaia{}, where the primary information source is the \gaia{} low resolution spectrophotometric data. The paper has the following outline: Section~\ref{sec:gaia-bprp} summarizes the most relevant characteristics of \gaia{} Blue Photometer (BP) and Red Photometer (RP), Section~\ref{sec:library} describes the assembly of the reference spectral template library, Section~\ref{sec:algorithm} summarizes the method employed. Sections~\ref{sec:results} and~\ref{sec:pessto} contains the results of applying the classifier on ground-based observations of transient objects. The discussion of the results is contained in Section~\ref{sec:discussion} whilst summary and conclusions are presented in Section~\ref{sec:conclusions}. | \label{sec:conclusions} We have presented an algorithm for processing \textit{Gaia} low-resolution spectrophotometric data that is capable of estimating the main class of a transient event and some of its non-intrinsic parameters, such as the redshift and epoch of the explosion. The algorithm has been tested on a set of ground-based observations which presented high heterogeneity among types and epochs. The conclusion from the current work are summarized as follows: \begin{itemize} \item \textit{Gaia} low-resolution spectrophotometric and broadband photometric data, coupled with realistic priors, carries enough information to be used for classification of transients; \item GS-TEC has proven to be an efficient independent module to obtain accurate information on transient class and parameters particularly for SNe having standard spectral shapes and strong features; \item the efficiency of classification is 85\% at the bright end for SNe type I and 76\% for SNe type II. However, it decreases to 60\% and 48\% respectively for magnitude 19. Class purity is 98\% and 90\% at the bright end for SNe type I and SNe type II, then it decreases to 95\% and 84\% for objects at magnitude 19; \item redshifts for both main types of SNe can be predicted with an accuracy $\sigma_z \lesssim 0.01$; \item the main source of confusion at bright magnitudes are variable stars. However, this should not be a major problem since nearby SNe are a minority, and they will be promptly discovered and characterized by ground-based observing facilities; \item for fainter magnitudes the highest confusion comes from within similar SNe types, the group SN I and SN II, as they have similar spectral features and which cause confusion at low signal-to-noise. Providing a more general classification type increases our confidence in the result. \end{itemize} Ground-based surveys that collaborate with \textit{Gaia} will benefit from our module as it will provide additional information on the transient object nature, which may enable more efficient filtering of alerts and therefore better resource allocation for follow-up. \begin{figure} \hspace{-1cm} \subfigure{\includegraphics[width=1.2\columnwidth]{figure14a.pdf} } \caption{Performance of redshift parameter estimation for the PESSTO dataset. Estimated values for redshift are plotted against the true values from the spectral archive. } \label{fig:parameters_pessto} \end{figure} | 14 | 4 | 1404.7150 |
1404 | 1404.5964_arXiv.txt | Recent statistical analysis of two extragalactic observational surveys strongly indicate a sublinear Kennicutt-Schmidt (KS) relationship between the star formation rate (\sigsfr) and molecular gas surface density (\sigmol). Here, we consider the consequences of these results in the context of common assumptions, as well as observational support for a linear relationship between \sigsfr\ and the surface density of dense gas. If the CO traced gas depletion time (\tmol) is constant, and if CO only traces star forming giant molecular clouds (GMCs), then the physical properties of each GMC must vary, such as the volume densities or star formation rates. Another possibility is that the conversion between CO luminosity and \sigmol, the \XCO\ factor, differs from cloud-to-cloud. A more straightforward explanation is that CO permeates the hierarchical ISM, including the filaments and lower density regions within which GMCs are embedded. A number of independent observational results support this description, with the diffuse gas comprising at least 30\% of the total molecular content. The CO bright diffuse gas can explain the sublinear KS relationship, and consequently leads to an increasing \tmol\ with \sigmol. If \sigsfr\ linearly correlates with the dense gas surface density, a sublinear KS relationship indicates that the fraction of diffuse gas \fdiff\ grows with \sigmol. In galaxies where \sigmol\ falls towards the outer disk, this description suggests that \fdiff\ also decreases radially. | \label{introsec} As observations reveal that stars form predominantly in the molecular component of the interstellar medium (ISM), the physical conditions of the H$_2$ gas undoubtedly influence the star formation process. For example, the star formation {\it rate} (SFR) is directly related to the {\it amount} of molecular gas. This fundamental property is supported by observations, often through the detection of the CO ($J=1-0$) rotational line as a molecular gas tracer, and some combination of stellar UV, \Halpha\ from HII regions, and dust thermal emission in the infrared (IR) due to heating from young stars \citep[e.g][and references therein]{Kennicutt&Evans12}. Though the trend of increasing SFR with higher CO luminosity is unambiguous, quantifying such correlations, as well as the associated theoretical interpretations \citep{Maclow&Klessen04, McKee&Ostriker07}, remain a subject of considerable debate. One formulation of the correlation between the surface densities of the star formation rate \sigsfr\ and molecular gas \sigmol\ is the power-law ``Kennicutt-Schmidt'' \citep[hereafter KS,][]{Schmidt59, Kennicutt89} relationship: \begin{equation} \Sigma_{\rm SFR} = a \Sigma_{\rm mol}^{N_{\rm mol}}. \label{KSlaw} \end{equation} The surface densities in Equation \ref{KSlaw} are estimated by employing conversion factors, such as the \XCO\ factor for translating the CO luminosity to \sigmol\ \citep[see][and references therein]{Bolatto+13}, and an appropriate factor for estimating \sigsfr\ from the star formation tracer \citep[see references in][]{Kennicutt&Evans12}. The correlation between \sigsfr\ and the total gas surface density, including the contribution of HI, exhibits larger scatter \citep{Bigiel+08, Schruba+11}\footnote{The scatter is dependent to some extent on the observed scale \citep[][]{Onodera+10, Schruba+10, Kim+13, Kruijssen&Longmore14}.} further indicative of a more direct link between star formation and the molecular component\footnote{Note, however, that H$_2$ or CO are not strictly necessary for star to form, as C$^+$ can also be an efficient coolant \citep{Krumholz+11, Krumholz12, Glover&Clark12}.}. Estimates of the KS parameters $a$ and the index \Nmol\ in Equation 1 range from super-linear \citep[$\sim$1.5, ][]{Kennicutt89, Liu+11, Momose+13}, linear \citep{Bigiel+08, Leroy+13}, to sublinear (\citealt{Shetty+13}, hereafter SKB13, and \citealt{Shetty+14}). \citet{Kennicutt89, Kennicutt98} measured an index $\approx1.4\, \pm$ 0.15 from unresolved observations over entire galactic disks, covering a range over five orders of magnitude in gas surface density. These observations included both normal spirals as well as IR starbursts, and considered the total HI + H$_2$ gas surface densities. One interpretation for a KS index of $\sim$1.5 is that the primary mechanism in the star formation process is the free fall collapse of molecular clouds \citep[][]{Elmegreen94, Kennicutt98}. For a recent review of explanations of the KS relationship, see \citet{Dobbs+13}. However, recent resolved extragalactic observations on 100 $-$ 1000 pc scales demonstrated a tighter molecular KS relationship with lower indices. The analysis of the STING and HERACLES surveys advocated for a linear KS relationship, with significant variations between galaxies \citep[][]{Leroy+08, Leroy+09a, Leroy+13, Bigiel+08, Schruba+11, Rahman+11, Rahman+12}. The interpretation of a linear KS relationship is that CO is primarily tracing star forming clouds with relatively uniform properties, including \sigsfr. A direct consequence of this description is that the depletion time of the CO traced gas is constant and approximately 2 Gyr, both within and between galaxies. Evidently, there is no consensus on either the precise KS parameter estimates, or the associated interpretation. Two recent statistical analyses of STING and a sub-sample of HERACLES by SKB13 and \citet{Shetty+14} have indicated that the data actually favor a sublinear KS relationship for both ensembles, as well as for most of the individual galaxies. Those works developed and applied a Bayesian fitting method that included a treatment of uncertainties, and provides parameter estimates for each individual galaxy as well as the population. SKB13 explained the advantages of a hierarchical Bayesian method for fitting the KS relationship, and demonstrated its accuracy over common non-hierarchical methods \citep[see also][]{Kelly07, Gelman&Hill07, Kruschke11, Gelman+04}. Other recent efforts favor a sublinear KS relationship as well. Using \Halpha\ observations of M51 at 170 pc scales, \citet{Blanc+09} infer a sublinear KS relationship, \Nmol\ $=$ 0.82 $\pm$ 0.05. Additionally, \citet{Ford+13} estimate \Nmol\ $\approx$ 0.6 in M31 from observations at a comparable scale. Finally, \citet{Wilson+12} find that the ratio of integrated CO ($J=3-2$) to IR luminosity increases with CO ($J=3-2$) luminosity (see their Fig. 5), suggesting \Nmol\ $<$ 1. How can we interpret this emerging evidence for the sublinear KS relationship? The standard interpretation is that CO ($J=1-0$) traces ``clouds'' or ``giant molecular clouds'' \citep[GMCs, e.g.][]{Dickman+86, Solomon+87}. Several theories have attempted to explain the index of the KS relationship, assuming that GMCs constitute the basic star forming unit, and that these GMCs are ``virialized'' \citep[e.g.][]{Krumholz&McKee05}. These assumptions, however, face difficulty if the CO line is not solely a cloud tracer, but rather also delineates more diffuse molecular gas distinguishable from the densest star forming regions. SKB13 attribute the sublinear KS relationship to the presence of CO outside of star forming regions, perhaps in a diffuse but pervasive molecular component. This description is consistent with a complex, hierarchical ISM consisting of shells, filaments, low density ephemeral wisps, besides the well-known high density star forming clouds. In this work, we explore this further and consider how and/or to what extent common assumptions about GMCs can withstand a sublinear KS relationship. In the next section, we discuss gas depletion times. Then, in Section 3 we provide three explanations for a sublinear KS relationship, including the presence of the diffuse molecular component and its role in estimating star formation efficiencies. Subsequently, in Section 4 we describe independent observational investigations revealing diffuse molecular gas. We then provide a description of this component in the hierarchical ISM in Section 5, and additional associated implications in Section 6. We conclude with a summary in Section 7. | \label{summarysec} We have examined possible physical interpretations of the sublinear KS relationship \citep[SKB13][]{Blanc+09, Ford+13, Shetty+14}. In Section \ref{diffclouds}, we indicated that if CO uniquely traces star-forming clouds, then cloud properties such as the volume density or star formation efficiency must differ between clouds. Similarly, we discussed variations in the \XCO\ factor in Section \ref{diffXco}. The third possibility, considered in Section \ref{diffgas}, is the presence of substantial amounts of diffuse molecular gas which also contributes towards the total CO luminosity. As the star formation rate is expected to be linearly correlated with dense gas, then the resulting KS index \Nmol\ depends on \fdiff. Galaxies with \Nmol\ $<$ 1, such as M51, have \fdiff\ (dense gas fractions \fden) increasing (decreasing) with \sigmol. Accordingly, we expect \fdiff\ to drop at larger radii where \sigmol\ decreases. Since the KS relationships are different between galaxies, the \fdiff $-$ \sigmol\ correlations also correspondingly vary. Indeed, observations including higher level CO transitions as well as \thCO\ indicate the presence of substantial amounts of CO in a diffuse component consisting of \apgt\ 30\%. This phase may exist in the form of low mass \paplt 10$^4$ \msun) clouds, or as a hierarchical and pervasive medium. Quantifying the amounts of gas in the various phases is necessary for understanding the timescales associated with star formation. We suggest that the sublinearity in the KS relationship is directly due to the dominant contribution of diffuse CO gas, with large \fdiff. This results in a long CO depletion time, which in the case of M51, varies from $\sim$1.7 to \aplt 3 Gyr for 25 \aplt\ \sigmol\ \aplt\ 200 \msunpc. If collapse only occurs in dense gas at a constant timescale, then for galaxies such as M51 with \Nmol\ $\approx$ 0.7 the fraction of CO traced gas currently forming stars is only of order 0.1\% or less. Future observational analysis, including other ISM tracers, should further reveal the role of the different phases, including the timescales and efficiencies in the phase transitions towards the formation of stars. | 14 | 4 | 1404.5964 |
1404 | 1404.3897_arXiv.txt | We reconsider the topological interpretation of magnetic helicity for magnetic fields in open domains, and relate this to the relative helicity. Specifically, our domains stretch between two parallel planes, and each of these ends may be magnetically open. It is demonstrated that, while the magnetic helicity is gauge-dependent, its value in any gauge may be physically interpreted as the average winding number among all pairs of field lines with respect to some orthonormal frame field. In fact, the choice of gauge is equivalent to the choice of reference field in the relative helicity, meaning that the magnetic helicity is no less physically meaningful. We prove that a particular gauge always measures the winding with respect to a fixed frame, and propose that this is normally the best choice. For periodic fields, this choice is equivalent to measuring relative helicity with respect to a potential reference field. But for aperiodic fields, we show that the potential field can be twisted. We prove by construction that there always exists a possible untwisted reference field. | Magnetic helicity $H({\bf B})=\int_V{\bf A}\cdot{\bf B}\,\rmd^3x$ has long been recognized as an important dynamical invariant in ideal magnetohydrodynamics, with applications ranging from laboratory plasmas to astrophysical objects \citep{Brown1999a}. Here ${\bf A}$ is a vector potential for the magnetic field ${\bf B}=\nabla\times{\bf A}$, and it is a fundamental property of $H({\bf B})$ that the integral is independent of the particular gauge chosen for ${\bf A}$, provided that $V$ is simply connected and magnetically closed ($B_n=0$ on the boundary $\partial V$). Analogous invariants exist for other solenoidal vector fields, notably the vorticity in fluid mechanics \citep{Moffatt1969a}. Physically, $H({\bf B})$ may be interpreted as a measure of the average topological linking of the magnetic field lines of ${\bf B}$ \citep{Moffatt1969a,Arnold1986,Arnold1998}. One way to see this is to consider a special magnetic configuration where ${\bf B}$ is confined to two (or more) linked magnetic flux tubes that are closed and untwisted \citep[see, for example,][]{Moffatt1992a}. Another way is to write ${\bf A}$ in Coulomb gauge ($\nabla\cdot{\bf A}=0$), whence, providing that $B_n=0$ on the whole boundary of $V$, it has the expression \begin{equation} {\bf A}({\bf x}) = \frac{1}{4\pi}\int_V \frac{{\bf B}({\bf y})\times{\bf r}}{|{\bf r}|^3}\,\rmd^3y, \label{eqn:bs3} \end{equation} where ${\bf r}={\bf x}-{\bf y}$ \citep{Cantarella2001}. It follows that $H({\bf B})$ may be written as \begin{equation} H({\bf B})=\frac{1}{4\pi}\int_V\int_V{\bf B}({\bf x})\cdot\frac{{\bf B}({\bf y})\times{\bf r}}{|{\bf r}|^3}\,\rmd^3x\,\rmd^3y. \label{eqn:hlink} \end{equation} This is the flux-weighted average, over all pairs of magnetic field lines $\rmd{\bf x}/\rmd s={\bf B}(\bf {x})$, $\rmd{\bf y}/\rmd s={\bf B}(\bf {y})$, of the Gauss linking integral \begin{equation} \label{gl} L({\bf x},{\bf y}) = \frac{1}{4\pi}\oint_{{\bf x}(s)}\oint_{{\bf y}(s)}\frac{d{\bf x}}{ds}\cdot\frac{d{\bf y}}{ds}\times\frac{\bf r}{|{\bf r}|^3}\,\rmd s\,\rmd s'. \end{equation} The Gauss integral is integer-valued and measures the net linking of a pair of closed curves \citep{Ricca2011}. Unfortunately, the gauge invariance of $H$ relies on the condition $B_n|_{\partial V}=0$. In astrophysical situations such as the solar atmosphere, this condition is generally violated. In a seminal paper, \citet{Berger1984ay} showed how gauge invariance may be restored by measuring the helicity with respect to a chosen reference magnetic field ${\bf B}'$ sharing the same distribution of $B_n$ on $\partial V$. This relative helicity, which we shall denote $H_{{\bf B}'}({\bf B})$, is then an ideal invariant under motions that vanish on $\partial V$. It has since been widely applied to the open magnetic fields arising in solar physics \citep[see the review by][]{Demoulin2007c}. This work is motivated by a fundamental question: is there a topological interpretation of relative helicity in open fields analogous to the linking number interpretation of $H$ (Equation \ref{eqn:hlink}) in closed fields? Since the magnetic field lines are no longer closed curves, they no longer have invariant Gauss linking integrals. However, one can construct alternative invariants for pairs of curves stretching between two planes, provided that the end-points are held fixed \citep{Berger1986,Berger1993b}. And indeed we will show in Section \ref{sec:wind} that it is possible to express both $H$ and $H_{{\bf B}'}$ in terms of these ``winding numbers''. The fact that there are multiple ways of defining such invariant winding numbers reflects the fact that neither $H$ nor $H_{{\bf B}'}$ is uniquely defined for an open field. Rather, $H$ depends on the choice of gauge, and $H_{{\bf B}'}$ on the choice of reference field. In fact, we argue in Section \ref{sec:hr} that $H$ is no less meaningful than $H_{{\bf B}'}$ in an open field, despite the fact that the latter has been used preferentially in applications. In solar physics, the non-uniqueness of $H_{{\bf B}'}$ has almost universally been circumvented by choosing ${\bf B}'$ to be the unique potential field ${\bf B}^{\rm p}$ matching $B_n$ on the boundary of the domain. The potential field is well-defined and has the minimum magnetic energy of all fields matching the same boundary conditions. In the case of magnetic fields rooted in a single planar boundary, $H_{{\bf B}^{\rm p}}$ has been shown explicitly to be an average winding number \citep{Berger1986,Demoulin2006}. This physical interpretation has been used to infer the injection of relative helicity into the Sun's corona by tracking the winding of magnetic field lines by their footpoint motions on the photospheric boundary \citep{Demoulin2007c}. However, there are two limitations that prevent $H_{{\bf B}^{\rm p}}$ from being a perfect helicity measure. The first limitation is that, if the boundary conditions $B_n|_{\partial V}$ are changing in time, then the reference field ${\bf B}^{\rm p}$ will itself change in time, and usually in a non-ideal way. This means that the evolution of the relative helicity will mix up both real topological changes in ${\bf B}$ and those simply due to the change of ${\bf B}^{\rm p}$. The second limitation is that, in a domain with more than one boundary where $B_n\neq 0$, the interpretation of $H_{{\bf B}^{\rm p}}$ as measuring the average winding number breaks down. This is shown in Section \ref{sec:hr}. Our central idea in this paper is that these limitations may be overcome by defining helicity not through $H_{{\bf B}^{\rm p}}$, but by fixing a special gauge in $H$. Fixing the gauge of $H$ will always create an ideal invariant that is (trivially) gauge independent. Our main contribution is to show in Section \ref{sec:bs2} how this invariant is physically meaningful. It should be mentioned that several authors have proposed other alternatives to the widely used $H_{{\bf B}^{\rm p}}$. For example, \citet{Longcope2008} have explored different choices of reference field for relative helicity in sub-volumes of the solar corona. \citet{Low2006f} has proposed a ``Lagrangian helicity'' that decomposes ${\bf B}$ at some initial time into a toroidal and a poloidal component, then measures the linking between the two components mapped back to the initial configuration \citep[see also][]{Webb2010a,Low2011h}. This retains a freedom in the choice of the initial toroidal-poloidal decomposition. Closer in spirit to the present paper, \citet{Hornig2006} proposes to define $H$ completely with a particular choice of gauge, namely $\nabla^\perp\cdot{\bf A}=0$ on the boundary (where $\nabla^\perp$ denotes the component of the gradient tangential to the boundary). \citet{Jensen1984w} also imposed a gauge condition - that ${\bf n}\times{\bf A}={\bf n}\times{\bf A}^{\rm p}$ on $\partial V$ - to uniquely define their version of relative helicity, which has the form \begin{equation} H^{\rm JC}=\int_V{\bf A}\cdot{\bf B}\,\rmd^3x - \int_V{\bf A}^{\rm p}\cdot{\bf B}^{\rm p}\,\rmd^3x. \end{equation} Such gauge conditions are also frequently used to simplify the calculation of $H_{{\bf B}^{\rm p}}$ in practice \citep{Demoulin2007c}. For the particular case of a cylindrical domain, \citet{Low2011h} introduced an ``absolute helicity'' that is similarly based on fixing a particular gauge of ${\bf A}$ (related to a toroidal-poloidal, or Chandrasekhar-Kendall decomposition). The geometric characterisation of the helcity in any gauge which we highlight in this study allows for comparison of our fixed gauge measue with these alternatives. It is demonstrated in Section \ref{sec:gen} that all choices expect the one we propose in this paper measure the field-line winding in a manner which is not wholly physically meaningful. The layout of this paper is as follows. We briefly review the standard definitions of $H$ and of the relative helicity $H_{{\bf B}'}$ in Section \ref{sec:prelim}, before introducing an important special gauge in Section \ref{sec:bs2} for fields in a cylinder, which we call the ``winding gauge''. Section \ref{sec:wind} then presents the main contributions of this paper: (i) that $H$ is physically meaningful in any gauge, and (ii) that the winding gauge best captures our intuitive idea of field line winding. In Section \ref{sec:hr} we investigate how the ``winding'' helicity relates to the relative helicity. Conclusions are summarized in Section \ref{sec:conclusions}. | \label{sec:conclusions} To summarize, we have shown that, for open magnetic fields between two parallel planar boundaries, the helicity $H$ has a physical meaning in any gauge: it is the average pairwise winding number of magnetic field lines with respect to some frame field. We have shown how this gauge freedom is equivalent to the freedom of choice of reference field in the commonly used relative helicity for such fields. Moreover, there is a unique choice of gauge that always measures winding with respect to a fixed frame. This is the ``winding'' gauge of Equation \eqref{eqn:bs2}. We propose that the helicity in this gauge ($\Hw$) is a physically-motivated measure of the topological linking in an open magnetic field, that is uniquely defined and does not depend on choice of an arbitrary reference field. In effect, it always measures winding with respect to a straight field. As we have demonstrated in Section \ref{sec:gen}, from a geometrical perspective any other choice is unnecessary as it adds a contribution to the helicity arising form the rotation of the reference frame used to measure winding. This quantity has no physical meaning. Using the relative helicity with a potential reference field may or may not measure the same helicity $\Hw$, depending on the boundary conditions. If it differs from $\Hw$ then the relative helicity measure necessarily includes a contribution due to a rotating reference frame. As a result, we make the following practical recommendation. In magnetic fields having more than one boundary with $B_n\neq 0$, one should calculate $\Hw$, rather than using the relative helicity with potential field as a reference. For a cylindrical domain whose end boundaries $S_0$ and $S_h$ are the same shape, and if the boundary conditions on $B_n$ are the same on both ends ({\it i.e.} are periodic), then the two helicities are equal. This is because the potential field itself then has vanishing $\Hw$ in such a field, meaning that it is untwisted with respect to a straight field. But if these conditions are not met then the potential field will generally have $\Hw\neq 0$, so that the relative helicity does not match $\Hw$. For example, we have shown that this may arise if the boundary conditions are aperiodic (Section \ref{sec:aper}) or if the domain boundary has a complex shape (\ref{sec:coil}). We envisage that the absolute measure provided by $\Hw$ will be particularly useful when analyzing the time evolution of magnetic configurations where $B_n$ on the boundary is changing, or when comparing different magnetic fields. An example of the latter would be the comparison of different magnetic active regions in the solar corona \citep{Valori2012b}. In practical terms, there are several ways to calculate $\Hw({\bf B})$ for a given magnetic field ${\bf B}$. Using \eqref{eqn:rbs}, one can calculate the relative helicity with respect to a reference field known to have vanishing $\Hw$ (for example, Appendix \ref{app:ref} shows how to construct such a reference in the cylinder). Or, one can evaluate the vector potential by numerically evaluating \eqref{eqn:bs2}, then computing $\int_V{\bf A}^{\rm W}\cdot{\bf B}\,d^3x$. But the most straightforward method will generally be to utilize the physical interpretation and calculate $\Hw$ directly from ${\bf B}$ using \eqref{eqn:hbs}, evaluating pairwise winding numbers of field lines. We have implemented this numerically for the examples in Figures \ref{fig:jlpf} and \ref{fig:ref}. It is interesting to observe that there are some similarities between the winding gauge choice and the gauges chosen by \citet{Hornig2006} and by \citet{Low2011h} in their suggested ``universal'' or ``absolute'' helicities. \citet{Hornig2006} fixes $H$ with the gauge condition that $\nabla^\perp\cdot{\bf A}=0$ everywhere on the boundary $\partial V$ (here $\nabla^\perp$ denotes the component of the gradient tangential to the boundary). On $S_0$ and $S_h$, this condition is satisfied by ${\bf A}^{\rm W}$ (this is seen directly from Equation \ref{bsiden}), but it is not satisfied in general by ${\bf A}^{\rm W}$ on $S_s$. \citet{Low2011h} defines an absolute helicity $H$ (for $V$ a cylinder) by taking the gauge \begin{equation} {\bf A}^{\rm CK} = \nabla\times\psi\hat{\bf z} + \eta\hat{\bf z}, \label{eqn:ack} \end{equation} which corresponds to a Chandrasekhar-Kendall representation of ${\bf B}$ for functions $\psi$, $\eta$. Our ${\bf A}^{\rm W}$ may also be written in this form with \begin{equation} \psi = -\frac{1}{2\pi}\int_{S_z}B_z({\bf y})\log|{\bf r}|\,\rmd^2{y},\quad \eta = A^{\rm W}_z. \end{equation} However, Low applies specific boundary conditions to uniquely define $\psi$ and $\eta$, and these are not the same as for ${\bf A}^{\rm W}$ in general (see Appendix \ref{app:low}). Another gauge condition, suggested by \cite{Valori2012b}, is that $A_z=0$; this does not uniquely specify the gauge, and the resulting freedom is used to make $H_{{\bf B}^{\rm p}}\equiv H$. However, we show in Appendix \ref{app:low} that the winding gauge ${\bf A}^{\rm W}$ may have ${A}^{\rm W}_z\neq0$, so in general this measure differs from $\Hw$. We conclude in general that these proposed gauges measure the field-line winding in a non-physical rotating frame, yielding (in general) a different helicity measure from $\Hw$. We conclude with some remarks about the generality of our results. We have assumed that our domain $V$ is simply-connected and lies between two parallel planar boundaries $S_0$, $S_h$. Furthermore, these parallel boundaries are the only part of the boundary where we allow $B_n\neq 0$. These restrictions are necessary so that the winding gauge ${\bf A}^{\rm W}$ is well-defined. In making the restriction that $S_0$ and $S_h$ are planar and parallel, we are essentially identifying a distinguished direction ($\hat{\bf z}$) that is perpendicular to the cross-sections $S_z$ on which ${\bf A}^{\rm W}$ is defined. This distinguished direction is also needed for defining winding numbers ${\cal L}({\bf x},{\bf y})$, along with a choice of coordinate frame $\{\hat{\bf e}_1,\hat{\bf e}_2\}$ on each cross-section. Extending the definitions of ${\bf A}^{\rm W}$ or ${\cal L}$ to a domain with curved boundaries $S_0$, $S_h$ would require choosing a foliation of \emph{curved} cross-sectional surfaces throughout $V$, complicating the definition of what it means for two curves to have non-zero winding number. We hope to address these complications in future. | 14 | 4 | 1404.3897 |
1404 | 1404.6156_arXiv.txt | We quantitatively assess, by means of comprehensive numerical simulations, the ability of broad-band photometric surveys to recover the broad emission line region (BLR) size in quasars under various observing conditions and for a wide range of object properties. Focusing on the general characteristics of the Large Synoptic Survey Telescope (LSST), we find that the slope of the size-luminosity relation for the BLR in quasars can be determined with unprecedented accuracy, of order a few percent, over a broad luminosity range and out to $z\sim 3$. In particular, major emission lines for which the BLR size can be reliably measured with LSST include H$\alpha$, \ion{Mg}{2}\,$\lambda 2799$, \ion{C}{3}]\,$\lambda 1909$, \ion{C}{4}\,$\lambda 1549$, and Ly$\alpha$, amounting to a total of $\gtrsim 10^5$ time-delay measurements for all transitions. Combined with an estimate for the emission line velocity dispersion, upcoming photometric surveys will facilitate the estimation of black hole masses in AGN over a broad range of luminosities and redshifts, allow for refined calibrations of BLR size-luminosity-redshift relations in different transitions, as well as lead to more reliable cross-calibration with other black hole mass estimation techniques. | Mass estimation of supermassive black holes (SMBHs) in active galactic nuclei (AGN) relies on locally-established relations between the SMBH mass and various source observables, such as the luminosity and the velocity dispersion of the broad emission line region, BLR \citep{kas00,pet04,vp06,ben09,den09}. While the adequacy of such relations has been demonstrated for local samples of objects where several independent means for estimating BH masses exist (e.g., via the reverberation mapping technique and the stellar velocity dispersion in the inner regions of the host; \citealt{on04}), it is not clear that this approach is warranted also at higher $z$, where one probes earlier cosmic times, and is sensitive only to the most luminous sources at those epochs \citep{net03}. Further, as quasar\footnote{The terms AGN and quasars are used here interchangeably.} observables in a given spectral band are redshift-dependent, it is not clear that inter-calibration of various phenomenological relations (e.g., between luminosity, the particular emission line probed, and SMBH mass), even if justified, is free of biases \citep{den09}. In this respect, the challenge in SMBH mass estimates at high-$z$ is akin to the cosmological distance scale problem, with more data and better control of systematics required to place them on firmer ground. With upcoming (photometric) surveys that will monitor a fair fraction of the sky to unprecedented depth and photometric accuracy, and with good cadence, the time-domain field of quasar study, and specifically reverberation mapping of the BLR, is expected to undergo a major revision \citep{cd11}. As has been demonstrated in several previous works \citep{ha11,cd11,cd12,c13,cz13,ed12,po12,po13,zu13}, while individual emission lines cannot be resolved using photometric means, their signal can be recovered at the light curve level \citep[see also][]{raf13}, and reverberation mapping is, in principle, possible. In this work we build upon the formalism of \citet{cz13}, and provide more realistic benchmarks for reverberation mapping using broadband photometric surveys, having in mind the characteristics of the {\it Large Synoptic Survey Telescope} (LSST)\footnote{\url{http://www.lsst.org/lsst/scibook}} experiment. Specifically, we are interested in the ability of photometric campaigns in determining BLR-associated time delays in individual sources as well as statistically, in sub-samples of sources. This paper is organized as follows: section 2 describes the model used here for constructing mock AGN light curves in different bands, as well as the analysis technique employed to recover the input line-to-continuum time-delays. Section 3 provides benchmarks for the measurement of the line-to-continuum time-delay under various assumptions concerning the sampling, redshift determination accuracy, filter choice, object properties, and the priors used in the analysis. The discussion, with particular emphasis on LSST-enabled science, follows in section 4, and the summary in section 5. | \begin{figure} \epsscale{1.2} \plotone{fig12.pdf} \caption{Lag determination for the \ion{Mg}{2}\,$\lambda 2799$ emission line in the luminosity-redshift plane. The top row corresponds to a 60\,sec exposure (obtained by combining 4 exposures of 15\,sec each, taken over an interval of 30\,minutes), while the bottom row assumes 15\,sec-exposure visits. Only objects for which $\alpha$ is recovered to within $\pm40\%$ of the input value are considered in the presented statistics, which results in only a fraction of all objects being used. The blue-to-red colors (see color bar) mark the median output-to-input (O/I) lag ratio (left column) in each redshift-luminosity bin, the standard deviation (shown in the middle column as $10^{\rm STD[Log(O/I)]}$), and the fraction of objects that pass our $\alpha$-selection criterion (see text; right column). DDF sampling is assumed in all cases.} \label{Lz_mg2} \end{figure} \begin{figure*} \epsscale{1.17} \plottwo{fig13a.pdf}{fig13b.pdf} \caption{Lag determination for prominent BLR emission features in the luminosity-redshift plane. Colored regions mark the value of the median ratio of the output-to-input (O/I) time delay (the colorbar of figure \ref{Lz_mg2} applies here: green colors mark values of unity while blue/dark-red shades indicate $-/+0.3$\,dex deviations). Only objects for which $\alpha$ is recovered to within $\pm40\%$ of the input value are considered in the presented statistics, which results in only a fraction of all objects being used (this is marked as dark blue contours with values denoting fraction levels). Also shown in white contours are regions in the luminosity-redshift plane including 60\%, 70\%, 80\% ,90\% and 99.99\% of all LSST-selected quasars (this does not include faint AGN). {\it Left panels:} Results for DDF sampling with 4 months' seasonal gaps show that time-lag measurements are S/N bounded at low luminosities and limited by the total lifetime of the LSST survey at high-luminosity and redshifts. {\it Right panels:} Results for UNS, which characterize the bulk of LSST sources, are bounded at the low-luminosity end by relatively poor sampling. Generally, reverberation mapping is feasible in roughly the brightest $10\%$ of the quasar population, with DDF sampling allowing to recover shorter BLR timescales in less luminous sources, especially at low-$z$.} \label{Lz} \end{figure*} We have shown that photometric surveys with quasi-regular sampling in several bands, and with characteristics similar to the LSST, can be used to measure the line-to-continuum time-delay in major emission lines, line blends, and non-ionizing continua from the BLR. Lag measurements show enhanced scatter when the time delay is a fair fraction of the survey lifetime, or when the lag is comparable to the sampling period. Nevertheless, even in such cases, it is possible to reduce the scatter and reach statistically robust results if additional constraints on the value of $\alpha$ (e.g., from independent spectroscopic measurements, or from knowledge of the quasar population as a whole) are incorporated in the MCF analysis. Probing line-to-continuum time-delays on sub-sampling timescales is unreliable, as photometry cannot disentangle line and continuum light curves on short timescales; an exception to this rule is in cases where the lagging signal dominates the flux in the band \citep{cz13,c13}, and provided the light curves are well sampled. Time series whose sampling pattern exhibits many different characteristic timescales lead to considerable scatter in individual lag measurements, especially on timescales comparable to the sampling periods and their harmonics. Here too, it is possible to reject non-physical solutions by employing priors on $\alpha$ so that a statistical measurement of the median lag, in properly defined quasar samples, provides a good estimator for the true lag. The degree to which such filtering can be effectively used depends on the strength of the emission feature probed. Generally, as with spectroscopic reverberation mapping campaigns, regular sampling should be sought as one attempts to reduce the number of sampling timescales in the problem. Good redshift determination leads to more robust lag measurement on a case-by-case basis since preferable filter combinations may be reliably selected, and meaningful priors on $\alpha$ may be set. This also exemplifies the advantage of having follow-up (single-epoch) spectroscopy which can secure the object identification and precisely determine its redshift. Moreover, spectroscopic follow-up can determine the velocity dispersion of the relevant emission lines, thereby providing critical information required for SMBH mass estimates. We find that, even under ideal observing conditions, the recovered median lag may overestimate the true lag, i.e. the centroid of the line transfer function, by $\lesssim 20$\%. This is a direct consequence of the inability of photometric data to disentangle line and continuum light curves on short timescales, whose sum makes up the total signal. The exact value of the bias depends primarily on the line transfer function, which is rather loosely constrained by observations: for transfer functions with a large amplitude at zero time delays (e.g., when line emissivity close to our sightline is considerable, as in edge-on configurations) the bias is more significant. Consequently, the bias is smaller for face-on systems, which may be more relevant to type-I quasars \citep{mai01}. This implies that some statistical information concerning the line transfer function may be obtained using photometric means. Our simulations indicate that photometric reverberation mapping is especially advantageous when large samples are concerned, as the median time delay is less susceptible to sampling-induced noise, redshift uncertainties, and the underlying properties of the power-density spectrum of the quasar. Therefore, good control of systematic effects is essential, especially as far as redshift determination is concerned. Provided large enough samples exist, statistical averaging would lead to BLR size-luminosity relations with unprecedented accuracy for various emission lines, and over a broad luminosity and redshift ranges (see also \citealt{cd11,zu13}, and below). It is worthwhile to consider more specific predictions for the LSST. We first consider the case where the signal per visit is obtained by combining the data of four consecutive (to within $\sim$30\,minutes) exposures of 15\,sec each, which should characterize the majority of LSST data\footnote{See \url{http://www.lsst.org/files/docs/sciencebook/SB_2.pdf}}. Thus, we effectively neglect quasar variations on $\sim$hour timescales, which is reasonable given the red power-density spectra of quasars, the suppressed variability of luminous high-$z$ sources (Fig. \ref{var}), and the considerably longer timescales associated with the BLR. Figure \ref{Lz_mg2} divides the luminosity-redshift space into small [$\delta {\log}(L_{\rm opt})=0.25,\delta z=0.05$] segments, each typically having $\lesssim 10^3$ simulated sources, and shows the statistical properties of the obtained lag solutions for \ion{Mg}{2}\,$\lambda 2799$. The time-delay statistics includes objects for which the recovered $\alpha$ is within $\pm 40$\% of the input value (section 3). The relevant parameter space for measuring the size of the \ion{Mg}{2}\,$\lambda 2799$ emission region is well-defined and forms an envelope that is bounded at low-luminosities by minimal S/N requirements, and by the finite duration of the survey at the high-luminosity end. Within this envelope the recovered lag is within $\pm0.3$\,dex of the input value, with a median value of $\simeq 0.9$ over the relevant phase space. In particular, several trends are observed: in regimes of effective low-S/N (either low source flux and/or small contribution of the emission line to the flux in the band), there is a tendency for a biased lag measurement, by up to 60\%; c.f., the second column of Figure \ref{zerr}. There is also a tendency to somewhat underestimate the lag, by typically 30\%, in cases where it is comparable to the lifetime of the experiment. Discarding those regions near the envelope's rims, typical median lag determination is at the $\sim \pm 20$\% level for the \ion{Mg}{2} line out to $z\sim 2.5$. Taking into account the quasar luminosity function and the LSST selection criteria, some $5\times 10^4$ lags may be determined over the LSST lifetime (see also Table 2) suggesting that \ion{Mg}{2} may have a crucial role in constructing more reliable single-epoch BH mass estimations by cross-calibrating scaling relations used at different redshift ranges. Our calculations imply that the expected scatter in individual \ion{Mg}{2}\,$\lambda 2799$ lag measurements is, typically, $\sim 40$\%, with a tendency for an increased scatter under low S/N conditions (see the middle panels of Fig. \ref{Lz_mg2}). As noted above, these statistics were obtained after screening against erroneous $\alpha$-solutions that, typically, results in only $\sim$ 10\% of the objects being used (right panel of Fig. \ref{Lz_mg2}). Nevertheless, there are regions in the parameter space ($z<1.2$ and $45<{\rm log}(L_{\rm opt})<46$) that are characterized by good S/N, and well-sampled light curves with respect to the BLR extent, for which $\gtrsim 30$\% of the sources lead to robust solutions. We note that it may be possible to further narrow the scatter in individual measurements by testing the robustness of the solutions \citep{cz13}. This, however, is beyond the scope of the present work due to the prohibitively long computation time involved. Reducing the exposure time per visit to 15\,sec instead of 60\,sec, shrinks the parameter space over which reliable \ion{Mg}{2} lag measurements are obtained while maintaining similar lag statistics in regions of the parameter space where such measurements are possible. Specifically, with the S/N reduced by a factor 2, \ion{Mg}{2}\ lag measurements are feasible up to redshift of $\sim 1.7$, instead of $2.5$, and only for the brighter sources, which reduces the number of reliable lag measurements by an order of magnitude for this transition (Table 2). \begin{figure} \epsscale{1.2} \plotone{fig14.pdf} \caption{Lag determination statistics with the LSST. Upper left panel shows the number of objects within the LSST footprint for which a given number of emission-line time delays may be simultaneously determined (using six filters a maximum of five lags are measurable using the formalism adopted here). A total exposure time of 60\,sec per visit is assumed and DDF sampling is considered. Different colors correspond to different lag measurement accuracies; for example, the blue line includes all objects for which the ratio between the absolute difference of the measured to input lag, and the input lag is $<10^{0.7}$ (see legend). Upper-right panel is for UNS sampling, while the lower-left panel assumes DDF sampling but with a 15\,sec exposure time per visit. The bottom-right panel is the total number of time-delay measurements, as a function of the number of DDFs surveyed (see text).} \label{ddfuns} \end{figure} Figure \ref{Lz} shows an analysis similar to the above for several additional major emission lines in quasar spectra, and examines some of their statistical properties using DDF and UNS samplings (60\,sec exposure times are assumed throughout). Clearly, there exists a non-negligible region in the redshift-luminosity plane in which time delays may be determined with good accuracy. For example, in low-luminosity, low-$z$ quasars, the lag-luminosity relation for H$\alpha$ may be probed over $\sim 2$ orders of magnitude in luminosity with a total expected number of H$\alpha$ lag measurements of $\gtrsim 10^4$ (Table 2). For the \ion{C}{4}\,$\lambda 1549$ emission line, the parameter range probed extends to lower luminosities than probed by \citet{kas07}, and is dominated by radio-quiet objects rather than radio loud ones, as in their work. The small blue bump (Balmer continuum) has a similar role to the \ion{Mg}{2} line in the sense that its lag may be quantified over a broad range of quasar luminosity and redshift. Obviously, this spectral feature is of limited use for directly estimating BH masses as there is no kinematic information associated with it. Interestingly, we find that Ly$\alpha$ lag measurements at the peak of quasar activity are facilitated by the effectively narrow and spiky throughput curve of the $u$ band, and are feasible out to $z\sim3$. \begin{table} \begin{center} \caption{Lag measurement statistics in the LSST footprint} \begin{tabular}{llll} \tableline & UNS & DDF$^\dagger$ & DDF$^\dagger$ \\ ID & (60\,sec) &(60\,sec) & (15\,sec) \\ \tableline Ly $\alpha$ & 64000 & 95000 & 7000 \\ \ion{Si}{4}\,$\lambda 1397$ & 150 & 300 & 30 \\ \ion{C}{4}\,$\lambda 1549$ & 8000 &16000 & 1200 \\ \ion{C}{3}$]$\,$\lambda 1909$ & 21000 &45000 & 6500 \\ \ion{Mg}{2}\,$\lambda 2799$ & 46000 &48000 &4300 \\ H$\gamma$ & 2000 & 6000 &300 \\ \ion{Fe}{2}\,$\lambda 4564^\ddag$ &9400 &16000 &900 \\ H$\beta$ & 47000 &110000 &19000 \\ \ion{Fe}{2}\,$\lambda 5305^\ddag$ & 6500 &27000 &4800 \\ \ion{He}{1}\,$\lambda 5877$ & 0 &700 &40 \\ H$\alpha$ & 28000 &73000 &25000 \\ Balmer cont. & 310000 &310000 &50000 \\ Paschen cont. & 14000 &15000 &4000 \\ \tableline Total for all BLR features: &560000 &760000 &120000 \\ \tableline \end{tabular} \end{center} Number of time-delays measured for individual emission features in quasars within the LSST footprint for DDF (using 15\,sec and 60\,sec exposure times) and UNS sampling (60\,sec exposure time). Features for which $>100$ lag measurements may be obtained are included in the table, and measurements for which the measured lag agrees to better than 0.5\,dex with the input value. Typical uncertainties on the quoted figures are at the 10\% level given the model assumptions (but may be of order unity for those transitions with $\lesssim 100$ detection statistics).\\ $^\dagger$ Full coverage of the LSST footprint by DDFs exceeds the LSST resources (see text). \\ $^\ddag$ Approximate wavelengths are quoted for blends (Table 1). \end{table} The fact that the lags of different emission lines may be determined in overlapping luminosity-redshift ranges means that a more reliable BLR-size ladder (in analogy with the cosmological distance ladder) may be obtained using LSST, allowing the cross calibration of different prescriptions for SMBH mass estimation over cosmic time. In this respect, it is interesting to note that for an exponentially-small (but finite) fraction of all quasars, simultaneous lag determination for several transitions may be possible. The number statistics in this case is less secure and may depend on the exponential tails of currently poorly-determined quasar property distributions (e.g., the fraction of objects with extreme variability amplitude). Current predictions for the statistics of multi time-lag measurements within the LSST footprint for different levels of accuracy, and for UNS and DDF sampling (for the latter either 15\,sec or 60\,sec exposure times are considered) are shown in Figure \ref{ddfuns}. Clearly, an exponentially small (but finite) number of sources will have up to 5 time-delays simultaneously determined. The number of such sources is very sensitive to sampling: e.g., the number of quasars with five lag measurements drops by more than an order of magnitude when switching from DDF to UNS sampling. S/N has a smaller effect on the relative number of objects with multi time-delay measurements. Lastly, we consider the total number of reliable time-lag detections as a function of the number of DDFs covered assuming each field consumes 1\% of the LSST resources\footnote{Assuming our definition of a DDF, each field, observed daily, will require four 15\,sec exposures, each with an overhead of 2\,sec of reading time, in six bands. Slewing between adjacent fields will take additional 5\,sec. Together, this amounts to $\sim 400$\,sec per DDF, which is of order 1\% of a full observing night.}. The total sky coverage in $N$ DDFs is then $\simeq 9N$\,sq-deg, and the remaining UNS coverage is then $\simeq 2\times 10^4(1-N/100)$\,sq-deg. The total number of time lag measurements as a function of $N$ is shown in the bottom-right panel of Figure \ref{ddfuns} demonstrating that sheer number statistics prefers UNS over DDF sampling with up to $\sim 500,000$ time delay measurements possible for full UNS coverage of the sky. Note, however, that the sparser UNS will result in the loss of short time-delay information concerning, e.g., accretion disks or high-ionization optical emission lines, such as \ion{He}{1}\,$\lambda$5877 (see Table 2), especially in low-$z$, low-luminosity sources. | 14 | 4 | 1404.6156 |
1404 | 1404.4365_arXiv.txt | Exoplanet searches have discovered a large number of 'hot Jupiters'--high-mass planets orbiting very close to their parent stars in nearly circular orbits. A number of these planets are sufficiently massive and close-in to be significantly affected by tidal dissipation in the parent star, to a degree parametrized by the tidal quality factor $Q_*$. This process speeds up their stars' rotation rate while reducing the planets' semimajor axis. In this paper, we investigate the tidal destruction of hot Jupiters. Because the orbital angular momenta of these planets are a significant fraction of their stars' rotational angular momenta, they spin up their stars significantly while spiralling to their deaths. Using Monte Carlo simulation, we predict that for $Q_* = 10^6$, $3.9\e{-6}$ of stars with the Kepler Target Catalog's mass distribution should have a rotation period shorter than 1/3 day (8 h) due to accreting a planet. Exoplanet surveys such as SuperWASP, HATnet, HATsouth, and KELT have already produced light curves of millions of stars. These two facts suggest that it may be possible to search for tidally-destroyed planets by looking for stars with extremely short rotational periods, then looking for remnant planet cores around those candidates, anomalies in the metal distribution, or other signatures of the recent accretion of the planet. | \cite{tidal_evolution_1973} showed that a planet-satellite system evolving under tidal dissipation has three outcomes: the satellite could spiral inwards to its death, spiral outwards to escape, or approach a tidally locked equilibrium. Ever since the discovery of the first exoplanets, astronomers have studied tidal decay due to exoplanet-star interactions. For example, \cite{51pegasi_tides} studied tidal dissipation in 51 Pegasi b--the first exoplanet discovered around a main-sequence star--and concluded that the planet's orbit is unstable, even though the decay time is longer than its star's main-sequence lifetime. Most of the early exoplanets were similar to 51 Pegasi b--they are hot Jupiters, with high masses and short orbital periods. Tidal decay in planetary systems has been relied on to explain a wide variety of phenomena. For example, it is hypothesized to be responsible for circularizing eccentric orbits--although this is due to tides in the planet, not in the star. The standard theory of hot Jupiter formation suggests they formed outside the ice line and migrated closer to their stars by one or both of two mechanisms: interaction with the protoplanetary disk or with other planets. At this early age, the star's rotation frequency would be faster than the planet's orbital frequency and increasing due to shrinking of the star, so tidal forces would act to push the planet outwards and prevent it from spiralling into the star (\cite{disk_migration_tides}). Tidal decay has also been implicated in the apparent correlation between high obliquity, as measured by the Rossiter-McLaughlin effect, and high stellar temperature. The hypothesis is that higher-mass (and hotter) stars have much thinner convective zones, and are thus subject to much less tidal dissipation. A lower-mass star would have a significant convective zone, causing a massive planet's orbit to significantly evolve towards alignment (\cite{hot_stars_obliquity}). More recently, \cite{albrecht_obliquities} examined a larger set of RM measurements and found that the temperature dependence in \cite{hot_stars_obliquity} still holds. Additionally, they found that obliquity is smaller for hot Jupiters where the expected tidal timescale is short, consistent with a hot Jupiter formation mechanism where the planets' initial obliquity is random. Depending on the tidal dissipation efficiency, massive hot Jupiters close to their stars may spiral in towards the Roche limit and be destroyed in a short timespan, depositing their angular momentum on the star's envelope while leaving behind a small, rocky, low-period core. \cite{short_period_objs} carried out a search for extremely low-period transiting objects in the Kepler dataset and found 13 candidates, with periods from 3.3 to 10 hours and estimated masses from 3-200 Earth masses (with large error bars). The authors suggest the possibility that these objects are the remnants of destroyed hot Jupiters. \cite{teitler_konigl} investigated the phenomenon discovered by \cite{mma113}--namely, the dearth of Kepler Objects of Interest (KOIs) with orbital periods smaller than 2-3 days around stars with rotation periods shorter than 5-10 days. They use a Monte Carlo model to select an initial population of planets and evolve them forward in time, accounting for tidal interaction, magnetic braking, and core-envelope coupling. The authors conclude that the observed distribution of low orbital period, low rotation period systems is qualitatively consistent with the simulated distribution if $Q_*$ is around $10^5$ to $10^6$. At least two examples of tidal destruction may have already been discovered. \cite{potential_engulfment} reports the discovery of BD+48740, a star with unusually high lithium content and with a 1.6 $M_J$ planet in a highly eccentric ($e \approx 0.67$) orbit. The authors suggest that both characteristics--both unusual for an evolved star--can be explained by the recent engulfment of a more inner planet. They also note that current data is not accurate enough to verify this hypothesis. \cite{corot7b} examines CoRot-7b, the first confirmed rocky exoplanet, and suggests that it could have originated as a farther-out gas giant, after which evaporation and tidal decay reduced it to its current state. \cite{planet_death} found that the destruction of a hot Jupiter might be observable on a human timescale. The authors predict that destruction happens at a galactic rate of $0.1-1 yr^{-1}$, and describe 3 qualitatively different scenarios, depending on the planet-to-star density ratio $\rho_p/\rho_*$. If $\rho_p/\rho_* > 5$, the planet plunges directly into the star, creating a EUV/soft x-ray transient that lasts weeks to months and an optical transient lasting days. If $\rho_p/\rho_* < 1$, the planet reaches the Roche radius and stably transfers mass to its star over a timescale of ~1000 years--the most difficult scenario to observe. If $1 < \rho_p/\rho_* < 5$, the planet is disrupted into an accretion disk, which causes an optical transient that lasts weeks to months. Optical transients are expected to be similar to, but distinguishable from, classical novae. This paper takes a parallel course to \cite{planet_death} and estimates the fraction of Sun-like stars in the galaxy that have swallowed a planet and are rotating at extremely short rotation periods ($P < 8h$) as a result. Extreme rotation periods might be good tracers for planet death because few stars, especially on the main sequence, naturally spin this fast. Exoplanet surveys such as SuperWASP (\cite{superwasp}), HATnet (\cite{hatnet}), HATsouth (\cite{hatsouth}), and KELT (\cite{kelt}) have produced light curves of millions of stars to detect planetary transits. Light curves produced by these surveys are ideal for finding short-rotation-period stars. 8h is much shorter than the orbital periods of the planets that the surveys routinely detect, and starspots are not likely to change significantly over 8h, giving a very highly periodic photometric signal. The question of how many stars amongst these millions have detectable rotation periods is addressed in Section \ref{subsec:detectability}. To make this estimate, we need to know the tidal dissipation effiency. Unfortunately, the tidal dissipation efficiency is very poorly known, and proposed values range from $10^6 - 10^{12}$ (\cite{tidal_q_range}). Depending on the value of $Q_*$, the planet could have a significant effect on the star's rotation rate, or it could have a negligible effect for the entirety of the star's lifetime. Data on the circularization of binary stellar orbits seem to indicate $Q_* \approx 10^5$ or $Q_* \approx 10^6$ (\cite{binaries_tidal_circ}). However, \cite{ogilvie_planet_tides} propose that hot Jupiters should have smaller dissipation efficiency than binary stars because the Hough waves they excite are not damped at the center of the star. \cite{penev_sasselov} also argue that there is good reason to suspect that $Q_*$ may not be $10^6$ for planet-hosting stars due to differences in the mechanism of dissipation. For example, the members of a binary stellar system are likely to be tidally locked, whereas most known transiting hot Jupiters do not have enough orbital angular momentum to synchronize their stars' rotation with their orbit. Numerous planets have been used to constrain $Q_*$. \cite{hellier_wasp18} analyzed WASP-18b, the first discovered planet with a period less than 1 day, and found that a $Q_*$ of $10^6$ would mean the planet's remaining lifetime is less than a thousandth of the star's main-sequence lifetime, and that the shift in transit timing would be detectable after only 10 years. It should be noted that WASP-18 is a 1.24 solar mass star, and that tidal dissipation may be less efficient in stars of this high mass due to the absence of a convective zone. \cite{hellier_wasp19} analyze WASP-19b and conclude that likely values for $Q_*$ are $10^7-10^8$, but because the age of WASP-19 is highly uncertain, the best estimate being that it has a 65 percent chance of being older than 1 Gyr with estimates ranging from a few hundred Myr to many Gyr (\cite{wasp19_age}), no firm conclusions can be drawn. \cite{penev_et_al} argue that the distribution of planet orbital periods is inconsistent with $Q_* < 10^7$ with 99 percent probability. Because $Q_*$ is so uncertain, we will run simulations for $Q_*=10^6$, $Q_*=10^7$, and $Q_*=10^8$. This paper is divided into 4 further sections. The first, 'Model', will describe the set of ODEs we use to model the evolution of a stellar system, as well as our choice of parameters for the ODEs. 'Simulation method' will describe the code used to solve these ODEs, the planets chosen for constraining Q, and the distributions of planetary and stellar parameters used to estimate the number of fast rotators. 'Results' has a self-evident name. 'Conclusions' will discuss the possibility of detecting planets as they inspiral into their stars and shortly afterwards. | We have simulated the tidal decay of hot Jupiters for 3 different values of $Q_*$: $10^6, 10^7, 10^8$. We find that, within an order of magnitude, one out of a million Sun-like stars are expected to exhibit rotation periods less than 8h as a result of swallowing a planet. Ground-based exoplanet surveys have examined millions of stars, but only a fraction may exhibit enough variability to find even a very fast rotation period. Thus, we conclude that it is possible for these surveys to detect a fast rotator if $Q_*=10^6$, but unlikely if $Q_*=10^8$ or greater. A very fast rotation rate is a good indicator because 20-80 percent of hot Jupiter deaths (depending on $Q_*$) cause their host stars to spin faster than $P_{rot} < 8h$, and because there are very few other explanations of such a high rotation rate:\\ 1. The star is young (pre-main-sequence or near ZAMS)\\ 2. Tidal interaction in a binary system\\ Scenario 2 can usually be excluded because huge Doppler shifts, anomalous spectra, and/or transits are all easily detectable features of binary systems, where 'easily detectable' is with respect to the ease of detecting a planetary transit. Scenario 1 is harder to exclude because it is extremely hard to date stars. Other observations may enable confirmation that a planet was tidally destroyed. Observing the rocky core is the most direct method, providing that the planet was not destroyed through a direct-impact merger and that the tidal disruption process was not violent enough to destroy the core. If the core is not detectable, there may be detectable changes in stellar metallicity. \cite{metallicity} analyzed the change in stellar metallicity due to accretion of protoplanetary disk material, and found that accretion of a Jupiter-mass planet can cause changes in the relative metal abundances in the star's convective zone that last on the order of tens of Myr. It is not clear whether these changes are practically observable, especially given the broadening of spectral lines caused by the extreme rotation. \newpage | 14 | 4 | 1404.4365 |
1404 | 1404.3259_arXiv.txt | We explore the nature of the small-scale solar dynamo by tracking magnetic features. We investigate two previously-explored categories of the small-scale solar dynamo: shallow and deep. Recent modeling work on the shallow dynamo has produced a number of scenarios for how a strong network concentration can influence the formation and polarity of nearby small-scale magnetic features. These scenarios have measurable signatures, which we test for here using magnetograms from the Narrowband Filter Imager (NFI) on \emph{Hinode}. We find no statistical tendency for newly-formed magnetic features to cluster around or away from network concentrations, nor do we find any statistical relationship between their polarities. We conclude that there is no shallow or ``surface'' dynamo on the spatial scales observable by \emph{Hinode}/NFI. In light of these results, we offer a scenario in which the sub-surface field in a deep solar dynamo is stretched and distorted via turbulence, allowing the field to emerge at random locations on the photosphere. | \label{sec:intro} The Sun is covered in a pattern of ``salt and pepper'' small magnetic features that dominate the star's photospheric magnetic energy budget \citep{Babcock1953}. The generation of large-scale magnetic fields in the interior and on the surface of the Sun is understood to be a consequence of rotational motion, large-scale convection, the transport of magnetic fields to the poles, and the storage of intensely strong magnetic fields at the base of the convection zone, though many important questions remain unanswered \citep{Charbonneau2010}. The origin of magnetic fields on much smaller spatial scales, scales of order the supergranular ($\sim$15--30 Mm) size, granular ($\sim$1 Mm) size, or smaller, is not as well understood. These small-scale magnetic fields are important for the overall magnetic flux and energy budgets of the Sun, and are important in structuring and heating the chromosphere and corona. On one hand, it is possible that the fields seen on these small scales are produced as a consequence of the global, large scale (mean field) dynamo. In this scenario, the convective buffeting of the fields at the surface and in the interior shreds them to smaller and smaller scales, down to (and likely further than) the resolution limit of currently available telescopes. Evidence of this model is given by simulations of magnetoconvection that show invariance across a wide range of scales \citep{SteinNordlund2006} and by observations that the probability distribution of magnetic flux concentrations shows a smooth $-1.8$ power-law distribution over nearly 6 orders of magnitude in magnetic flux \citep{Parnell2009}. On the other hand, it is possible that a shallow near-surface ``small-scale'' dynamo is present, and that even without the global dynamo, magnetic fields would continue to be generated and amplified by the small-scale flows. Recent observational evidence, primarily from \emph{Hinode}, lends some credence to this scenario. Examples include the patterns of horizontal magnetic fields in the photosphere \citep{Lites2008} and the lack of a change in the numbers of weak magnetic features in the quiet sun when measured as a function of the solar cycle phase \citep{Buehler2013}. Several groups have produced impressively realistic-looking simulations that amplify a small seed field into something that looks and behaves like the observed magnetic network \citep[e.g.,][]{Cattaneo1999, VoglerSchussler2007}. However, as \cite{Stenflo2012} recently pointed out, evidence for small-scale dynamo activity in these simulations is not necessarily evidence for small-scale dynamo activity on the Sun, as the results typically depend strongly on the initial conditions or the approximations used. Due to unavoidable computational limitations, current state-of-the-art simulations are forced to operate in a physical regime in which the Reynolds number $Re$, magnetic Reynolds number $Re_M$, and magnetic Prandtl number $Pm$ are (sometimes vastly) dissimilar to the actual properties of the Sun. Thus while the simulations are useful for understanding the size scales, expected magnetic phenomenology, and interaction of any generated fields with larger-scale fields, progress in understanding the existence of and role played by a small-scale dynamo is, for now, best made by observational analysis. There is a third alternative to the problem of the small-scale flux: a small-scale dynamo in which the dual processes of stretching of the seed field and the addition of the new field to the photosphere are not in close proximity to each other-the new field may be observed at an essentially random location with respect to the original field. Such a dynamo could be driven by turbulent convection throughout the full depth of the convection zone without the proximity properties one would expect of a shallow surface dynamo. This possibility is supported by simulations that show cool downdrafts extending through the turbulence of the outer solar layers to the base of the convection zone \citep[e.g.,][]{Stein2003}. If this possibility is correct the cross-scale equilibrium \citep{Schrijver1997} could drive energy flow in either direction: large to small scales, or vice versa \citep[e.g.,][]{VoglerSchussler2007}. We refer to this possibility as a ``spatially nonlocal small-scale dynamo'', where ``spatially'' is meant to distinguish (non-)locality in physical space from (non-)locality in wavenumber space. Dynamos are a mechanism for creating magnetic fields, but in order for a dynamo to operate indefinitely, there must be a way to stem the continued growth of the field. Otherwise, the photosphere would quickly become choked with magnetic fields and convection suppressed, which is obviously not the case as can be seen in any photospheric line-of-sight magnetogram. Very generally, this stemming of the growth of the field may take two forms: in the first, existing magnetic field is removed in cancellation / flux annihilation events; in the second, the production of new flux is suppressed. While the cancellation events have been studied for decades, the suppression of continued generation of magnetic flux (apart from sunspots) is less extensively studied. Two relatively recent examples include the work of \cite{Morinaga2008}, in which convection (and thus presumably dynamo action) was reduced in the presence of small-scale magnetic features such as G-band bright points, and the work of \cite{Hagenaar2008}, in which the emergence rate of large-scale ephemeral regions was found to be reduced in areas of strong unipolar magnetic fields (including but not limited to coronal holes). \subsection{Outline} \label{sec:Outline} In this paper, we bridge the gap between the works of \cite{Morinaga2008} and \cite{Hagenaar2008} and investigate the spatial relationship between existing strong-field regions and the detection of new magnetic features, which we take as a proxy for dynamo action, at intermediate spatial scales. We focus on the areas around supergranular network flux concentrations, and analyze whether the rate of feature birth at a range of distances from the network concentration is significantly larger or smaller than would be expected from a random distribution of events. In addition to occupying an interesting intermediate spatial scale, supergranular network concentrations are an ideal observational target: their field strength and flux is high enough that they might reasonably have a positive or negative effect on any spatially local small-scale dynamo activity, their occurrence is common enough that several will exist in a reasonably-sized dataset, and they are sufficiently long-lived such that the surrounding plasma can be affected by their presence. Our criteria for identifying network concentrations is given in Section~\ref{sec:feature-tracking}. Our goal was to identify whether the rate of detection of new magnetic features has some dependence on the distance from the network concentration. In this work we use the number of features as a proxy for the rate of flux production. This enables us to explore four mechanisms by which the number of features at short distances from a network concentration could be altered. In the case of suppression, for example, fewer features should be found near the borders of the concentration, while more features per unit area should be found further away. Three forms of feature evolution are illustrated in Figure~\ref{fig:Shred-&-stretch}. Shredding (Figure~\ref{fig:Shred-&-stretch}a) involves field lines that are bodily moved away from the network concentration. This results in a decrease of the concentration's flux as the field lines move away, and the features have the same polarity as the network concentration. Stretching (Figure~\ref{fig:Shred-&-stretch}b) involves field lines from below the surface that are stretched and brought to the surface. Such distorted field components would then appear on the Sun as newly-formed small-scale features. Here the flux of the concentration remains the same, the total unsigned flux in the region increases, and the new, nearby features have a mixed polarity. This is the chief mechanism we search for as evidence of spatially local small-scale dynamo action. Canceling (Figure~\ref{fig:Shred-&-stretch}c) involves field lines of opposite polarity to the network concentration that are brought towards it and cancel with it. In this case the flux of the network concentration decreases and the unsigned flux of the region also decreases. \begin{figure} \includegraphics[width=1.0\columnwidth]{f01.pdf} \caption{Three mechanisms which could result in an increase in detected features near a network concentration. a) As the network concentration is shredded, flux is removed from the edge of the concentration, possibly (but not necessarily) in a way that eludes detection, as shown. b) Network concentration field lines below the surface are stretched and brought to the surface. c) Opposite polarity flux impinges on the network concentration and cancels.} \label{fig:Shred-&-stretch} \end{figure} Section~\ref{sec:Methodology} describes the dataset and feature tracking method, the means for identifying network concentrations, and the method used to measure suppressions and enhancements of features around the network concentrations. Section~\ref{sec:results} presents our results. We find no signature of systematic enhancement or suppression of magnetic feature production in the vicinity of the network concentrations. Instead, we find that most measured suppressions and enhancements can be attributed to network concentration evolution, as shown in Section~\ref{sub:NetworkConcEvolution}. Further, we find that there is no statistical tendency for these magnetic features to cluster around network concentrations. Section~\ref{sec:Clustering-Discussion} concludes with a discussion on the implications of these null measurements and the importance of small-scale fields to network concentration evolution. | \label{sec:Clustering-Discussion} The objective of our work was to test various solar dynamo models using observations. This was made possible by automated feature tracking techniques, which enabled the identification of small, weak magnetic features in the vicinity of large, evolving network concentrations. We treated the number of these small weak features as a proxy for the vigor of the flux production process. Through the statistical analyses detailed in Section~\ref{sec:results} we have found, with our sample of seven network concentrations observed with \emph{Hinode}/NFI, that small-scale magnetic features form in a random distribution at least within our observable range of $\sim$12~Mm from the center of the network concentrations. We found no observable tendency for newly-formed features to either cluster around the neighborhood of network concentrations, nor to have their formation rate suppressed there. We conclude that there is no spatially local small-scale dynamo action due to stretching and subsequent emergence of nearby subsurface fields, nor suppression of small-scale dynamo action due to the presence of nearby strong field. Comparing the polarity of newly-formed features to that of the nearby network concentration allowed us to probe the mechanisms of shredding \citep{Schrijver1997} independent from a hypothetical small-scale dynamo. The lack of a spatial locality signature in the polarity of the new feature distribution indicates that shredding plays at most a very minor role in the flux balance of the nearby network. We draw the conclusion that there is no influence of small-scale magnetic feature enhancement from a nearby network concentration. The last two results together rule out every major possibility for a dynamo that is local on these spatial scales, i.e., one that works by stretching or recycling nearby flux, and is therefore dependent on the strength of fields in the neighborhood rather than the global volume of the convection zone. We now return to the two types of solar dynamo mentioned in Section~\ref{sec:intro}: shallow and deep. These are illustrated in the left column of Figure~\ref{fig:two-dynamo}. Our analysis of the location of feature birth rules out local suppression, and our analysis of the polarity of the features excludes shredding and canceling of the network concentration. Stretching at the local level is also excluded, as this would require newly-formed magnetic features to be in relative close proximity to the network concentration, as it would be unlikely that a small sub-surface field could be distorted to any large distance from the concentration itself (see Figure~\ref{fig:two-dynamo}a). Our main conclusion therefore is that there is no spatially local dynamo on the spatial scales observable by Hinode, i.e. that the observed small-scale field is a high- wavenumber manifestation of a large- scale phenomenon. We note that all plausible surface dynamo models have the property of spatial locality, and we are therefore able to exclude the possibility of a surface dynamo. \begin{figure*} \includegraphics[width=1.0\textwidth]{f11.pdf} \caption{Illustrations of the two basic categories of model describing the nature of the small-scale solar dynamo. The left column provides an elementary illustration of the category, and the right column illustrates a scenario in which the sub-surface field beneath a network concentration can become distorted and breach the photosphere elsewhere. a) The dynamo extends to small depths, down to the upper few scale heights of the convection zone. In this case, parts of the sub-surface field beneath a network concentration is most likely to breach the photosphere at a location near the concentration itself. b) The dynamo extends to large depths, through the entire convection zone. In this case, the breaching of the photosphere by the sub-surface field does not necessarily occur near the seed network concentration.} \label{fig:two-dynamo} \end{figure*} This leaves us with the second category, a deep small-scale dynamo, illustrated in Figure~\ref{fig:two-dynamo}b as suggested by \cite{Stein2003,SteinNordlund2006}. A deep dynamo would allow for stretching at much larger distances, and so there would be no preference for small-scale enhancements in the proximity of the network concentration. There would also be no preference for polarity in the proximity of the network concentration due to the random tendency of the subsurface flows to breach the photosphere. \subsection{Limitations of the Result} In many cases, the network concentration appeared to be affected by nearby small-scale magnetic features. This implies that weak fields coming off or onto the network concentration can be just at the limits of visibility in the NFI magnetograms and still have an effect on the parent network concentration. While the effect of a single one of these features is small, this affect from a large number may play an important role in the network concentration evolution. It is important to call attention to the limits of our selected parameter $P$ for comparing the new features with those of the random points. Firstly, even with a purely random distribution, we should not expect the integral of $Px_{tot}$ in Figure~\ref{fig:Px_tot-long} to be zero, because of the uncertainties associated with the factors that went into its derivation. Secondly, $P$ is not effective at identifying polarity concentrations on opposite sides of a network concentration, since it averages over many variables. This is best demonstrated with a movie of NC 1029. If a network concentration had a surplus of like polarity features on one side (perhaps due to shredding) and a surplus of opposite polarity features on the other side (perhaps due to cancellation), and these features happened to be at or near the same distance from the center of the network concentration, then $Px_{tot}$, $Px_{tot}^{+}$ and $Px_{tot}^{-}$ could all be enhanced at the same distance, which would mimic the signature of subsurface field line stretching and emergence. It is therefore necessary to accompany the analysis $Px_{tot}$ with at least a visual inspection of the evolution of the network concentration (the classic balance of case studies vs.\ statistics). It is important to reiterate that the features that one readily sees merging into and fragmenting from the network concentrations are not the same population as those considered in our analysis. This is because we have excluded those features born by ``Fragmentation'' and ``Error'' (see Section \ref{sub:Position-New-Features}), which accounts for a large fraction of the features in the dataset, and an even larger fraction of the strong ones \citep[see][]{Lamb2010,Lamb2013}. Analyzing only these small, weak features allows us to consider only the true small-scale field as observed by \emph{Hinode}/NFI. \subsection{Concluding Remarks} We have conducted a statistical analysis of the birth and polarity of small-scale magnetic features in proximity to strong supergranular network concentrations. We find no observational evidence of a relationship between the network concentration and the number or polarity of features at a given distance from the network concentration. This rejects the spatially local small-scale solar dynamo hypothesis at spatial scales observable by \emph{Hinode}/NFI, and we therefore conclude that the features that dominate the photospheric magnetic landscape are driven by a spatially nonlocal deep solar dynamo. | 14 | 4 | 1404.3259 |
1404 | 1404.6226_arXiv.txt | We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann--Lema\^{i}tre--Robertson--Walker background. We consider cosmological models including the Hilbert--Einstein curvature term and the $N$ degree monomial of the scalar field nonminimally coupled to gravity. The potential of the scalar field is the $n$ degree monomial or polynomial. We describe several qualitatively different types of dynamics depending on values of power indices $N$ and $n$. We identify that three main possible pictures correspond to $n<N$, $N<n<2N$ and $n>2N$ cases. Some special features connected with the important cases of $N=n$ (including the quadratic potential with quadratic coupling) and $n=2N$ (which shares its asymptotics with the potential of the Higgs-driven inflation) are described separately. A global qualitative analysis allows us to cover the most interesting cases of small $N$ and $n$ by a limiting number of phase-space diagrams. The influence of the cosmological constant to the global features of dynamics is also studied. | The assumption that General Relativity is the correct theory of gravity leads to the conclusion that the observable data~\cite{cosmo-obser,PlanckInflation,Planck2013} give the strong support that there exists and currently dominates a smoothly distributed, slowly varying cosmic fluid with negative pressure, so-called dark energy~\cite{DE_rev,DINDE}. The simplest way to describe the dark energy is to add the cosmological constant to the Einstein--Hilbert action. Another popular variant is to consider models with scalar fields~\cite{DINDE,Tsujikawa:2013fta}. Models with scalar fields are very useful to describe the observable evolution of the Universe as the dynamics of the spatially flat Friedmann--Lema\^{i}tre--Robertson--Walker (FLRW) background and cosmological perturbations. That is why scalar fields play an essential role in modern cosmology. The models with the Ricci scalar multiplied by a function of the scalar field are being intensively studied in cosmology~\cite{induced,nonmin-inf,Kaiser1994,HiggsInflation,Cooper:1982du,KKhT, Elizalde,Cerioni,Kamenshchik:2012rs,Gannouji:2006jm,Szydlo, KTV2011,Sami:2012uh,ABGV,KTVV2013,KPTVV2013} (see also~\cite{Book-Capozziello-Faraoni,Fujii_Maeda,NO-rev} and references therein). Induced gravity models, wherein the curvature arises as a quantum effect~\cite{Sakharov}, and models, where both the Hilbert--Einstein term and the scalar field squared multiplied by the scalar curvature are present, have been applied to quantum cosmology~\cite{nonmin-quant} and are being intensively studied in the inflationary cosmology~\cite{induced,nonmin-inf,Kaiser1994,HiggsInflation}. Note that predictions of the simplest inflationary models with minimally coupling scalar fields are in disagreement with the Planck2013 results~\cite{Planck2013} and some of these inflationary scenarios have been improved by adding a tiny nonminimal coupling of the inflaton field to gravity~\cite{GB2013,KL2013}. The Higgs-driven inflation has attracted a lot of attention~\cite{HiggsInflation}. The recent discovery of the Higgs boson~\cite{discovery} makes this model especially attractive. The predictions of this inflation model is very close to predictions of the Starobinsky inflation~\cite{Starobinsky} (see~\cite{BezrukovR2Higgs} for details). The number of integrable cosmological models based on scalar fields is rather limited. The most popular integrable cosmological model is the model with a minimally coupled scalar field and a self-interaction exponential potential~\cite{Lucchin,gen-exp}. In~\cite{Fre}, the general classification of integrable cosmological models based on scalar fields was suggested and studied in great detail. Integrable models with nonminimally coupled scalar fields have been found in~\cite{KPTVV2013}. In this situation it is reasonable to search for asymptotic regimes in the theory under consideration. Note that dynamical system methods are extensively used for analysis of cosmological models with scalar fields~\cite{Szydlo,Sami:2012uh,CapozzelloPhasespaceview,FaraoniDS,GalileonDS,Leon}. Using these methods several different asymptotic regimes have been found, and their stability has been investigated for the simplest case of quadratic coupling in \cite{CapozzelloPhasespaceview} and for other power-law coupling in \cite{Sami:2012uh}. However, as such analysis usually requires transition to expansion normalized variables which can be not smooth in some points, this results in the fact that some solutions can be lost in this procedure. That is why a global analysis of the dynamics in question is an important counterpart to the description of locally stable regimes -- apart from the fact that phase-space diagrams are very useful in visualizing the dynamical picture (especially for the considered two-dimensional problem), we also can be sure that we did not miss some important regimes during local analysis. Note that the phase-space diagrams are actively used to analyze dynamics of a cosmological model with scalar fields (maybe with nonstandard kinetic term) minimally coupled to gravity~\cite{PhantomPhPort,FaraoniMC}. A combination of the phase-space and stability analysis is a systematic way to explore the possible cosmological behaviors. Recently a set of phase diagrams for the theory with a quadratic coupling have been constructed in \cite{CapozzelloPhasespaceview,Szydlo}. In our paper, we consider a more general case. We investigate the dynamics of cosmological models including the Hilbert--Einstein curvature term, a monomial function of the scalar field coupled to gravity and polynomial potentials. Using the analysis of \cite{Sami:2012uh}, it is possible to show that for the case of $\xi<0$ (the only case we consider in the present paper) the form of phase diagrams does not depend on $\xi$ and depends only upon relations between power indexes of the coupling function and the scalar field monomial potential. This allows us to characterize completely the global feature of cosmological dynamics in the model in question using a limiting number of phase portraits. We start with listing known asymptotic regimes from \cite{CapozzelloPhasespaceview, Sami:2012uh} and show how they are incorporated into a global picture by constructing phase-space diagrams. The paper is organized as follows. In Section~2, we examine the Friedmann equations for models with a nonminimally coupled scalar field. In Section~3 we consider de Sitter solutions and analyze their stability with the help of the effective potential. In Section~4 we consider asymptotic solutions for the considering model. We also present Rizmaikin-type~\cite{Ruzmaikin} solutions and the corresponding potentials. In Sections~5 and 6 we use the phase-space diagrams for the global qualitative analysis of the cosmological dynamics. In Section~5 we consider monomial potentials, and more complicated potentials are considered in Section~6. Section~7 is devoted to the conclusions. | In the present paper we have made a global qualitative analysis for the cosmological dynamics with a nonminimally coupled scalar field with power-law coupling functions and potentials. Local analysis provided in \cite{Sami:2012uh} shows that for $\xi<0$ stability properties of asymptotic solutions do not depend on $\xi$ and depend only upon power indices $N$ and $n$ of the coupling function $B$ and the scalar field potential $V$ correspondingly. This allows us to cover most interesting cases of small $N$ and $n$ by a limiting number of phase-space diagrams. We argue that usage of effective potential $V_{eff}$ helps significantly to understand different cases of qualitatively different dynamics. This does not require a full transition to the Einstein frame which can be rather cumbersome. We identify three qualitatively different points of scalar field dynamics realized for $n<N$, $N<n<2N$, and $n>2N$ and two boundary cases of $n=N$ and $n=2N$. The latter is of particular interest because it contains (and generalizes) the Higgs inflation proposal. All fixed points for corresponding dynamics found in \cite{Sami:2012uh} are incorporated into the global phase diagram constructed in the present paper. Some interesting modifications of possible phase diagrams when more general potentials are allowed also have been presented. In particular, we study the influence of the explicit cosmological constant in the action of the theory. It is interesting, that, unlike the minimally coupled case, nonzero $\Lambda$ in the action does not automatically lead to the existence of a de Sitter solution. The opposite is also true - there are theories (for example, with $V=V_0\varphi^2+\lambda \varphi^6$ and quadratic coupling) which have stable de Sitter solutions without a cosmological constant in the action. \medskip \noindent {\bf Acknowledgements. \ } The research of S.V. is supported in part by RFBR grant 14-01-00707 and by the Russian Ministry of Education and Science under grant NSh-3042.2014.2. A.T. is supported by RFBR grant 14-02-00894. The work of A.T. is partially supported by the Russian Government Program of Competitive Growth of Kazan Federal University. | 14 | 4 | 1404.6226 |
1404 | 1404.1630_arXiv.txt | Short-period comet P/2010 V1 (Ikeya-Murakami, hereafter ``V1'') was discovered visually by two amateur astronomers. The appearance of the comet was peculiar, consisting of an envelope, a spherical coma near the nucleus and a tail extending in the anti-solar direction. We investigated the brightness and the morphological development of the comet by taking optical images with ground-based telescopes. Our observations show that V1 experienced a large-scale explosion between UT 2010 October 31 and November 3. The color of the comet was consistent with the Sun ($g'-R_\mathrm{C}$=0.61$\pm$0.20, $R_\mathrm{C}-I_\mathrm{C}$=0.20$\pm$0.20, and $B-R_\mathrm{C}$=0.93$\pm$0.25), suggesting that dust particles were responsible for the brightening. We used a dynamical model to understand the peculiar morphology, and found that the envelope consisted of small grains (0.3--1 \micron) expanding at a maximum speed of 500$\pm$40 m s$^{-1}$, while the tail and coma were composed of a wider range of dust particle sizes (0.4--570\micron) and expansion speeds 7--390 m s$^{-1}$. The total mass of ejecta is $\sim$5$\times$10$^{8}$ kg and kinetic energy $\sim$5$\times$10$^{12}$ J. These values are much smaller than in the historic outburst of 17P/Holmes in 2007, but the energy per unit mass (1$\times$10$^4$ J kg$^{-1}$) is comparable. The energy per unit mass is about 10\% of the energy released during the crystallization of amorphous water ice suggesting that crystallization of buried amorphous ice can supply the mass and energy of the outburst ejecta. | \label{sec:introduction} Periodic comet, P/2010 V1 (Ikeya-Murakami, hereafter V1) was independently discovered by two amateur astronomers in Japan, Mr. Kaoru Ikeya and Dr. Shigeki Murakami, in early 2010 November \citep{Nakano2010a}. They reported the comet to be at magnitude 8--9 at the time of discovery. Later, the orbital elements (semimajor axis $a$=3.083 AU, eccentricity $e$=0.488, and inclination $i$=9.38\arcdeg) showed that V1 is a short period comet with an orbital period of 5.41 years \citep{Williams2010}. Figure \ref{fig:orbit} shows the orbit projected on the ecliptic plane. It has a Tisserand parameter with respect to Jupiter, T$_J$=3.013, slightly larger than 3. Such comets are sometimes classified as Encke-type comets (2P/Encke has $T_J$ = 3.026) rather than Jupiter-family comets, for which 2 $\le T_J<$ 3 \citep{Levison1997}. Despite its short orbital period and considerable brightness at the time of discovery, it is interesting to note that V1 had not been previously detected. To date, there are no published reports to characterize the physical properties of V1. Images taken by amateur astronomers showed interesting features. The comet was enveloped by a spherical cloud and the overall appearance was reminiscent of historic cometary outbursts in 17P/Holmes. To characterize the physical properties, we obtained monitoring observations and compared them with a model based on the dynamics of dust grains. | \subsection{DUST DYNAMICAL MODEL} For a better understanding of the unique morphology on UT 2010 November 9, we created model images of V1 based on a dynamical theory of dust grains. The dynamics of dust grains are determined both by the ejection speed ($V_{ej}$) and by the ratio of radiation pressure acceleration to solar gravity ($\beta_{rp}$). For spherical particles, $\beta_{rp}$ is given by: \begin{eqnarray} \beta_{rp} = \frac{K Q_{pr}}{\rho_d a_d}, \label{eq:eq3} \end{eqnarray} \noindent where $a_d$ and $\rho_d$ are the particle radius and the mass density in the {\it MKS} system, and $K$ = 5.7 $\times$ 10$^{-4}$ kg m$^{-2}$ is a constant. $Q_{pr}$ is a radiation pressure coefficient the value of which depends on grain size, shape, structure and the optical constants of the grain material \citep{Burns1979}. We applied a three-dimensional analysis to match the observed images, following the model in \citet{Ishiguro2007}, \citet{Hanayama2012}, and \citet{Ishiguro2013}. We adopted a power-law function for the terminal speed of ejected dust particles: \begin{equation} V_{ej} = V_0 \left(\frac{\beta_{rp}}{\beta_{rp,0}}\right)^{u_1} v , \label{eq:eq4} \end{equation} \noindent where $V_0$ is the reference ejection speed of particles having $\beta_{rp,0}=1$ and $u_1$ is the power index of the ejection speed. In a real comet the ejection speed will depend not only on $\beta_{rp}$ but also on the location of the dust source on the nucleus, on the shape and porosity of the dust particles and perhaps on the ejection time within the outburst. The random variable $v$ in Eq. (\ref{eq:eq4}) reflects these uncertain factors. It follows the Gaussian probability density function, $P(v)$, \begin{equation} P(v) = \frac{1}{\sqrt{2\pi} \sigma_v}\exp \left[- \frac{(v-1)^2}{2\sigma_v^2}\right] , \label{eq:eq5} \end{equation} \noindent where $\sigma_v$ is the standard deviation of $v$. In our computations, we limited the range $v-1<2\sigma_v$ in order to avoid very fast particles. In addition, we set the minimum ejection speed to zero. The number of dust particles at a given size is written: \begin{equation} N(a_d;t)~da_d = N_0 \left(\frac{a_d}{a_{0}}\right)^{-q}~da_d, \label{eq:eq6} \end{equation} \noindent in the size range of $a_{min}$ $\le$ $a_d$ $\le$ $a_{max}$, where $a_{min}$ and $a_{max}$ are minimum and maximum particle size given by $a_{min}=0.57/\rho_d \beta_{max}$ and $a_{max}=0.57/\rho_d\beta_{min}$, respectively, and $q$ is the power-index of the differential size distribution. We imposed several constraints on the model. First, we considered that all dust particles were released impulsively on UT 2010 November 2, neglecting the possibility of weaker dust ejection before and after this date. This assumption is supported by our synchrone analysis and by the coma photometry as described above. Secondly, we supposed that ejected dust particles are compact in shape and can be represented by $Q_{pr}$ = 1. This is a reasonable approximation for optically large (2$\pi a_d/\lambda\ga$1, where $\lambda \sim$0.64\micron~ is the wavelength) particles but is not strictly valid for optically small particles ($a_d\la$0.2--0.3 \micron) \citep[see, e.g.,][]{Ishiguro2007}. The dust mass density was assumed to be $\rho_d$=1000 kg m$^{-3}$. We also assumed that the dust particles were ejected symmetrically with respect to the Sun--comet axis in a cone-shaped jet with a half-opening angle $w$, implying that the explosion occurred around the subsolar point of the nucleus. Finally, we assumed that, for particles of all sizes, the geometric albedo is 0.04 and the phase coefficient is $\beta$ = 0.035 mag deg$^{-1}$. We examined several key properties with which to constraint our dust model from the observed images. We noticed that the envelope has a more open shape in the anti-solar direction meaning that the width of the envelope was enlarged by increasing ejection speeds even as the envelope was stretched by the solar radiation pressure. Because smaller particles are more susceptible to radiation pressure, the envelope morphology suggests that small particles were ejected with higher speeds (see Figure 3 and 4 (a)). From Eq. (\ref{eq:eq4}), we can derive the power index of the ejection speed for the particles in the envelope, $u_1$=$\log(w_1/w_2)$/$\log(\beta_1/\beta_2)$, where $w_1$ and $w_2$ are the apparent width of the envelope (proportional to the ejection speed projected on the celestial plane). We examined the width and the corresponding $\beta_{rp}$ values from the image taken on 2010 November 9, finding that $u_1$=0.30$\pm$0.05 best fits the observed broadening of the envelope. Separately, we found that the envelope did not extend more than $\sim$4.5\arcmin~in our data. Particles with $\beta_{rp}>$2.5 should have spread to the edge of the field of view in the time since ejection, while particles with $\beta_{rp}<$1 would not match the observed extent. Through a test simulation for hemispherical ejection model (e.g. Reach et al. (2010) section 6.1), we obtained $\beta_{rp}\sim$1.5. In the image on February, there is no obvious gap between the dust tail and the inner coma. From the evidence, we put the upper limits of $\beta_{min}$ $\sim$1$\times$10$^{-3}$. Model images were produced in a Monte Carlo simulation by solving Kepler's equation including solar gravity and radiation pressure. We derived the above parameters to fit the surface brightness of the dust cloud on UT 2010 November 9, where prominent features (the envelope, tail and coma) were detected. We created a number of simulation images using a wide range of parameters as listed in Table \ref{tab:parameter}, and fitted the image from the outer parts to the inner parts. A two-component (i.e.~envelope and tail+coma) model worked well for the fitting. We selected 20 sampling points in the envelope and found the optimum parameter sets first (envelope model). Then we subtracted the best-fit envelope model from the observed intensity, and selected 25 sampling points in the residual image, and derived the best-fit parameters to fit the tail and coma surface brightness (tail+coma model). The best-fit parameters are shown in Table \ref{tab:parameter}. We tolerate intensity differences between the model and observation of up to 10\%, and derived the errors in the Table. Figure \ref{fig:model_image} shows the comparison between the observation and model. We produced the model contour through further tuning of the best-fit parameters within the error range. The distinctive morphology of the dust cloud is successfully reproduced by this two component model. The best-fit parameters suggest that the envelope consists of small particles ($\beta_{rp}$=0.5--1.8 or $a_d$=0.3--1 \micron) with ejection speeds higher than in the coma and tail. The reference speed of particles in the envelope was $V_0$=420$\pm$30 m s$^{-1}$. With the range of $\beta_{pr}$, the ejection speed of the envelope particles turned out to be 290--500 m s$^{-1}$, where we adopted $\sigma_v$=0 to derive the typical speed. On the other hand, the tail and coma consisted of a wide range of dust particles from sub-micron to sub-millimeter ($\beta_{rp}$=1$\times$10$^{-3}$--1.5 or 0.4--570 \micron) in size. Their ejection speeds are estimated to vary from 7--390 m s$^{-1}$. The effective radius, $a_e$, of dust particles in the coma is given by $a_e\approx\sqrt{0.4\times570}$ = 15 \micron. The ejection speed of 15 \micron-particle is 52$\pm$3 m s$^{-1}$ from Eq. (\ref{eq:eq4}), which is fast enough to reach the projected radius of 15,000 km during the time of our observation. This explains why the free expansion model can characterize the observed magnitude profile (Section \ref{sec:free_expansion}). We obtained the power index of $\beta_{rp}$-dependence of the ejection speed, $u_1$ = 0.30$\pm$0.05 in the envelope and 0.55$\pm$0.10 in the tail and coma. Given the uncertainties, it is not clear that the difference between these estimates is formally significant. We note that the value $u_1\sim$ 0.5 is expected of dust particles accelerated by gas drag forces \citep{Whipple1951}. The moderate slope for the envelope particles may suggest that small particles may be largely accelerated to reach the gas velocity. We deduced the total mass of dust and the total kinetic energy by integrating with respect to particle size, as summarized in Table \ref{tab:summary}. The total dust mass is $M_d$=5.1$\times$10$^8$kg. With uncertainties in dust size ($a_{min}$ and $a_{max}$) and its power index ($q$) as well as the photometric error ($m_R$), the derived mass is good to within a factor of four. The dust mass corresponds to a body 62-m in radius assuming mass density of $\rho_n$=500 kg m$^{-3}$. This is $>$0.004 \% of the mass of a $r_n <$ 1850 m spherical body (the upper-limit of the nuclear radius). The total kinetic energy is $E_k$ = 5.0$\times$10$^{12}$ J, or 1.2 kiloton of TNT, with the bulk of the energy carried by the tail and coma particles. Presumably, a comparable or larger energy was carried by gas in the initial explosion. The energy per unit mass is $E_k/M_d \sim$ 1$\times$10$^4$ J kg$^{-1}$. The value is similar to that of 17P/Holmes \citep{Li2011,Reach2010} and is about 10\% of the energy released by the crystallization of amorphous water ice (9$\times$10$^4$ J kg$^{-1}$). The ejected mass could be contained in a surface layer on the nucleus having thickness \citep[see, e.g.,][]{Li2011}, \begin{equation} l = \frac{M_d}{4 \pi r_n^2 f \rho_n}, \label{eq:eq7} \end{equation} \noindent where $f$ is the fraction of the surface area of the nucleus that is ejected. We obtained $w$ =30--35\arcdeg~ to an accuracy of $\sim$10\degr~from our model simulations, which suggests that the active area exists within $w \lesssim$30\arcdeg~ from the sub-solar point. The area of the inferred active region is 2.9$\times$10$^6$ m$^2$, corresponding to $f$=0.07. Substituting these values gives $l >$0.35 m. The ejected mass could be contained within a circular patch of the nucleus surface roughly 1 km in radius and 35 cm thick. \subsection{Dynamical Evolution of the Nucleus} Here we examine the orbital evolution of V1 to attempt to understand its recent history. Dynamical chaos imposes a fundamental limit to our ability to backwards-integrate the motion of any comet; a small error in the initial conditions will grow exponentially on the Lyapunov time. There is additional uncertainty from the (generally poorly known) non-gravitational acceleration, which is induced in comets by recoil forces from the sublimation of ice. The non-gravitational parameters of V1 are not known. In the case of V1, there is in addition a relatively large uncertainty in the orbital elements because these were necessarily determined from observations taken over a short interval (only 80 days). To investigate the past orbit, we consider many `clones', whose initial orbits follow a Gaussian distribution with the average values and the standard deviations provided by the NASA/JPL HORIZONS site (Table \ref{tab:orbital_elements}). Then the clone orbits are calculated and examined statistically. We generated 1,000 clones of V1 using the N-body integration package, Mercury \citep{Chambers1999}, and calculated the orbital evolution over the past 10,000 years. We set the non-gravitational force equal to zero. Figure \ref{fig:orb_evo} shows the orbital evolution of five sample clones. They follow almost identical orbits for about 100 years before present epoch, with perihelion fixed near 1.6 AU. Their Tisserand parameters drop below 3 and become Jupiter-family comets within 100--200 years. Thus, V1 is likely to be a Jupiter-family comet which originated in the Kuiper-belt region. Comets generally become active within $\approx$2.5 AU owing to sublimation. We examined the fraction of V1 clones which existed within 2.5 AU as visible comets. We found that all the V1 clones had perihelion $<$2.5 AU over the last 100 years, dropping to 74\% over 1,000 years and 19\% in 10,000 years. On this basis, it is clear that V1 is unlikely to be a new comet making its first appearance at small heliocentric distances. Therefore, the non-detection of V1 before 2010 is either a result of sky-survey incompleteness (unlikely, given the brightness of the comet) or a reflection of much reduced activity in previous orbits. We conjecture that, until the outburst on 2010 November 2, activity on the nucleus was largely stifled by a dust mantle, leading to low brightness and the non-detection of V1. \subsection{COMPARISON WITH OTHER COMETS} Like V1, 17P/Holmes was discovered (in 1892) because of a dramatic outburst. Another outburst, in 2007, was well observed, revealing a spherical envelope, a detached blob, and a central coma \citep[see, e.g.,][]{Watanabe2009,Reach2010}. Total ejecta mass was estimated to be (1$\sim$610)$\times$10$^{10}$ kg \citep{Altenhoff2009,Reach2010,Ishiguro2010,Li2011,Boissier2012,Ishiguro2013}. The expansion speed on the plane of the sky of the dust envelope particles was 554$\pm$5 m s$^{-1}$ \citep{Lin2009,Montalto2008}. Several other comets are known to have undergone huge photometric outbursts accompanied by circular envelopes. For example, 41P/Tuttle-Giacobini-Kresak experienced an outburst at 1.15 AU, and, before fading underwent second outburst at 1.25 AU from the Sun. It possessed an envelope (probably consisting of dust and gas \citep{Sekanina2008a}) expanding at 300 --700 m s$^{-1}$ \citep{Kresak1974}. 1P/Halley experienced a massive explosion in 1836 at 1.44 AU from the Sun. Similarly, 1P/Halley was enclosed by a circular envelope consisting of dust particles traveling at a speed of 575$\pm$9 m s$^{-1}$ \citep{Sekanina2008b}. Only 17P/Holmes and V1 were observed with modern astronomical instruments (i.e.~CCD) and the others were observed by photographic plates or naked eyes. We summarize the physical quantities of the outburst events at 17P/Holmes and V1 in Table \ref{tab:comparison}. Although the magnitudes and heliocentric distances are different, the maximum speeds are similar to one another. Figure \ref{fig:speed} shows the comparison between the 2010 V1 event (this work) and the 2007 17P/Holmes event \citep{Reach2010,Lin2009}. The dust size was not specified in \citet{Lin2009} and \citet{Montalto2008}, but we regard it as sub-micron particles (i.e.~0.3$^{+0.7}_{-0.2}$\micron) because only such small particles can be accelerated to the highest velocity and remain as sensitive scatterers in optical observations. \citet{Reach2010} provided the speeds for three different populations (core, blob and shell). Although the total dust mass and the kinetic energy of these two events are different, the size--speed relationships are quite similar to one another. Several possible mechanisms have been presented to explain 17P/Holmes outburst; these include vaporization of pockets of more volatile ices such as CO$_\mathrm{2}$ and CO \citep{Schleicher2009,Kossacki2011}, the phase change of water from amorphous to crystalline ice \citep{Sekanina2009}, thermal stress in the nucleus, or the polymerization of hydrogen cyanide \citep{Gronkowski2010}. A plausible trigger is the crystallization of amorphous water ice \citep{Prialnik2004}. From Table \ref{tab:comparison}, most of large-scale outbursts occurred after their perihelion passages, suggesting that a time-lag from conducted heat might trigger these outbursts. The heat diffusion equation can be solved to give the distance over which heat can be transported by conduction, $\delta r = (\kappa P / \pi)^{1/2}$, where $\kappa$ is the thermal diffusivity of the surface materials and $P$ is the period of time over which conduction acts \citep{Li2011}. The applicable thermal diffusivity in comets is uncertain, depending on the unknown porosity of the material. Insulating solids typically have $\kappa \sim$ 10$^{-6}$ m$^2$ s$^{-1}$ while $\kappa = 10^{-7}$ to $10^{-8}$ m$^2$ s$^{-1}$ maybe more appropriate for comets in which porous structure reduces the contact area between grains \citep{Prialnik2004}. If, as seems likely from the clone experiments, V1 has spent $\gtrsim$100 yr inside 2.5 AU, conducted heat would reach a depth $\delta r \gtrsim$ 3 to 10 m beneath the initial surface. Since $\delta r \gtrsim l$ (Equation \ref{eq:eq7}), it is quite plausible, although far from proved, that the outburst was triggered by the action of conducted heat through the crystallization of buried amorphous ice. \clearpage | 14 | 4 | 1404.1630 |
1404 | 1404.2803_arXiv.txt | In this paper, we study a warm intermediate inflationary model with a general form for the dissipative coefficient $\Gamma(T,\phi)=C_\phi\,T^{m}/\phi^{m-1}$ in the context of loop quantum cosmology. We examine this model in the weak and strong dissipative regimes. In general, we discuss in great detail the characteristics of this model in the slow-roll approximation. Also, we assume that the modifications to perturbation equations result exclusively from Hubble rate. In this approach, we use recent astronomical observations from Planck and BICEP2 experiments to restrict the parameters in our model. | In cosmology our concepts concerning the early universe have introduced a new ingredient, the inflationary phase of the universe, which provides an attractive approach for resolving some of the problems of the standard model of the universe, as the flatness, horizon, etc. \cite{R1,R102,R103,R104,R105,R106}. Also, it is well known that inflation provides a graceful mechanism to clarify the large-scale structure \cite{R2,R202,R203,R204,R205} and the observed anisotropy of the cosmic microwave background (CMB) radiation \cite{astro,astro2,astro202,Planck}. Recently, the effects from BICEP2 experiment of gravitational waves in the B-mode has been analyzed in Ref. \cite{Ade:2014xna}. An important observational quantity obtained in this experiment, is the tensor-to-scalar ratio $r$, which $r=0.2^{+0.07}_{-0.05}$ (68 $\%$ C.L.) and takes out the value $r=0$ ( at a significance of 7.0 $\sigma$). Therefore, the tensor mode should not be neglected. On the other hand, warm inflation differs from the cold inflation since evades the reheating period at the end of the accelerated evolution of the universe \cite{warm}. During warm inflation the process of radiation production could take place under strong enough dissipation \cite{warm,taylorberera,taylorberera02,taylorberera03,taylorberera04,taylorberera05, taylorberera06,taylorberera07,taylorberera08,taylorberera09}. In this form, the dissipative effects are important and these emerge from a friction term since the inflaton field is dissipated into a thermal bath. Also, an interesting feature of the warm inflationary model is that the thermal fluctuations constitute a dominant character in producing the primary density fluctuations essential for Large-Scale Structure (LSS) formation \cite{62526,6252602,6252603,6252604,1126}. In the context of the dissipative effects, a fundamental quantity is the dissipation coefficient $\Gamma$. In particular, for the scenario of low-temperature, the parameter $\Gamma$ was analyzed in supersymmetric models. In these models, there is a scalar field together with multiplets of heavy and light fields that give different expressions for the dissipation coefficient, see Refs.\cite{26,28,2802,Zhang:2009ge,BasteroGil:2011xd,BasteroGil:2012cm}. A general form for the dissipative coefficient $\Gamma$, is given by \cite{Zhang:2009ge,BasteroGil:2011xd}. \begin{equation} \Gamma=C_{\phi}\,\frac{T^{m}}{\phi^{m-1}}, \label{G}% \end{equation} where the constant $C_\phi$ is related with the dissipative microscopic dynamics and the constant $m$ is an integer. Various elections of $\Gamma$ or equivalently of $m$ have been assumed in the written works \cite{Zhang:2009ge,BasteroGil:2011xd}. In special, for the value of $m=3$, $C_\phi$ corresponds to $C_{\phi}=0.64\,h^{4}\,\mathcal{N}$ in which ${\mathcal{N}}% ={\mathcal{N}}_{\chi}{\mathcal{N}}_{decay}^{2}$. Here, $\mathcal{N}_{\chi}$ is the multiplicity of the $X$ superfield and ${\mathcal{N}}_{decay}$ represents the number of decay channels available in $X$'s decay \cite{26,27,Berera:2008ar,BasteroGil:2010pb}. For the special case $m=1$, i.e., the dissipation coefficient $\Gamma\propto\,T$ corresponds to the high temperature supersymmetry (SUSY) case. For the value $m=0$, then $\Gamma\propto\phi$ and the dissipation coefficient represents an exponentially decaying propagator in the high temperature SUSY model. For the case $m=-1$, i.e., $\Gamma\propto\phi^2/T$, it agrees with the non-SUSY case \cite{28,PRD}. On the other hand, Loop Quantum Gravity (LQG) is a proceeding of nonperturbative background autonomous approach to quantize gravity \cite{5}. In LQC the geometry is discrete and the continuum space-time is found from quantum geometry in a large eigenvalue limit (see, Refs. \cite{Ashtekar:2011ni,6,7, 8, 9}). Different cosmological models have been studied, in particular the Friedmann-Robertson-Walker (FRW) model \cite{AA}. Here, the loop quantum effect modifies the Friedmann equation by adding a correction term in the energy density, specifically $\rho^2$ at the scale when $\rho$ becomes similar to a critical density $\rho_c\approx 0.82\,G^{-2}$ ($G$ is the Newton's gravitational constant)\cite{SinghMFE, As}. In this way, the effective Friedmann equation becomes \be \label{newfried} H^2=\frac{\kappa}{3}\,\rho\,\left[1-\frac{\rho}{\rho_{c}}\right], \en where $H=\dot{a}/a$ is the Hubble parameter, $a$ is the scale factor, $\kappa=8\pi G$, $\rho$ is the total energy density, $\rho_{c}=\sqrt{3}\,\rho_{p}/(16\pi^2\gamma^3)$ is the critical loop quantum density, and $\rho_{p}=G^{-2}$ is the Planck density. We note that a rigorous numerical test of the Eq.(\ref{newfried}) have been performed recently in Ref.\cite{numMFE}. The inflationary universe model in the context of LQC has been analyzed in Refs. \cite{Singhinf, good}. In particular, the inflationary model has been studied in great detail for power-law and multiple fields in the context of LQC \cite{Ranken:2012hp}, while in the Ref.\cite{Gupt:2013swa} the authors have studied different isotropic and anisotropic space-times for avoiding singularities in LQC. By the other hand, the model of the warm inflation in LQC scenario was studied in Ref. \cite{Herrera:2010yg}, in which the author studied the inflationary scenario described by a standard scalar field coupled to radiation, see also Ref. \cite{nn}. For a review of inflationary LQC models, see Refs. \cite{agre1, agre2,Xiao:2011mv,int1,int2} On the other hand, exact solutions in inflationary models can be obtained from an exponential potential, frequently called power-law inflation. Here, the scale factor has an expansion power law type, where $a(t)\sim t^{p}$, where the constant $p>1$ \cite{power}. As well, an exact solution can be found by using a constant scalar potential which is often called de Sitter inflationary universe \cite{R1}. Nevertheless, exact solutions can also be found from intermediate inflation \cite{Barrow1}. In this inflationary model, the scale factor growths as \begin{equation} a(t)=\exp[\,A\,t^{f}], \label{at} \end{equation} where $A$ and $f$ are two constants; $A>0$ and the value of $f$ varies between $0<f<1$ \cite{Barrow1}. In intermediate inflation the evolution of the scale factor, $a(t)$, is slower than de-Sitter expansion, but quicker than power law, hence the name ``intermediate". This intermediate evolution was originally elaborated as an exact solution, but this model may be best explained from the slow-roll approximation. In the slow-roll approximation, it is possible to obtain a spectral index $n_s\sim 1$ and for the special value of $f=2/3$, the spectral index correspond to Harrizon-Zel'dovich spectrum, where $n_s=1$. Also, the quantity obtained in this model, for the tensor-to-scalar ratio is $r\neq 0$ \cite{ratior,Barrow3}. Thus the goal of the paper is to study an evolving intermediate scale factor during warm inflation in the framework of LQC model together with a generalized form of dissipative coefficient $\Gamma$. We will study the warm intermediate inflationary model in LQC for different values of $m$, and also we will consider this model for two regimes, the weak and the strong dissipative scenarios. In the context of the cosmological perturbations, we will consider for simplicity the procedure of Refs.\cite{good,Herrera:2010yg,g1,nn} for warm inflation in LQC, where the perturbation equations arise only from Hubble rate. Also, we only study the standard inflation scenario, that occurs after the superinflation epoch. For a review of superinflation epoch in LQC, see Refs. \cite{good,g1}. The outline of the paper is the follows: The next section presents the basic equations for warm inflation in the framework of LQC model. In the sections III and IV, we discuss the weak and strong dissipative regimes in the intermediate model. In both sections, we give explicit expressions for the scalar field, the dissipative coefficient, the scalar potential, the scalar power spectrum and the tensor-to-scalar ratio. Also, the Planck and BICEP2 data are used to constrain the parameters in both regimes. Finally, our conclusions are presented in section V. We use units in which $c=\hbar=1$. | } In this paper we have analyzed the intermediate inflationary scenario in the context of warm inflation in LQC. During the slow-roll approximation and considering a general form of the dissipative coefficient $\Gamma(\phi,T)=C_\phi\,T^{m/\phi^{m-1}}$, we have found solutions of the Friedmann equations for a flat universe filled with a self-interacting scalar field and a radiation field in the weak and strong dissipative regimes. In special, we researched the values $m=3$, $m=1$, $m=0$, and $m=-1$. From the warm-intermediate inflationary model in LQC, we have found explicit relations for the corresponding scalar potential $V(\phi)$, spectrum of the scalar perturbations $\mathcal{P}_{\mathcal{R}}$, scalar spectral index $n_s$, and tensor-to-scalar ratio $r$ in the weak and strong dissipative regimes. In order to bring some explicit results we have considered the constraint in the $n_s-r$ plane given by the two-dimensional marginalized constraints (68$\%$ and 95$\%$ C.L.) derived from Planck and BICEP2 in combinations with other data sets. Here, we noted that the BICEP2 data places stronger limits on the tensor-to-scalar ratio $r$ versus $n_s$ compared with the Planck data. Also, we obtained a constraint for the value of the parameter $C_\phi$ analyzed in the weak and strong regimes, and from these scenarios we have found an upper bound for $C_\phi$. Additionally, we observed that when we reduce the parameter $m$ the value of the parameter $C_\phi$ also decreases. In particular, for the strong dissipative regime, we found that for the cases in which $m= 0$ and $m=-1$, i.e., for $\Gamma\propto \phi $ and $\Gamma\propto \phi^2/T $, these models of the warm-intermediate LQC are ruled out from Planck and BICEP2 data, since the spectral index $n_s > 1$, and hence the models do not work. On the other hand, for the weak dissipative regime, the quantum geometry effects in LQC, given by the correction term $\rho/\rho_c$ becomes similar than the reported in the standard LQC scenario. For the strong dissipative regime the results found indicate that the effect of the correction term $\rho/\rho_c$ on the warm inflationary model is marginal. Nevertheless, it cannot be rejected that future experiments uncover it. Our results for both regimes are summarized in Table I. Also, given that the rate $R=\Gamma/3H$ will also evolve during inflation, we may have also models which start in the weak dissipative regime $R <1$ but end in the strong regime, in which $R >1$, or the other way round. In this paper, we have not studied these dynamics. Besides, we should mention that we have not addressed a complex treatment of the scalar perturbations of the effective Hamiltonian in LQC, in this sense, we have considered that the modifications to perturbation equations arise exclusively from Hubble rate \cite{good,Herrera:2010yg,nn,g1}. We hope to return to these points in the near future. | 14 | 4 | 1404.2803 |
1404 | 1404.5338_arXiv.txt | HNC and HCN, typically used as dense gas tracers in molecular clouds, are a pair of isomers that have great potential as a temperature probe because of temperature dependent, isomer-specific formation and destruction pathways. Previous observations of the HNC/HCN abundance ratio show that the ratio decreases with increasing temperature, something that standard astrochemical models cannot reproduce. We have undertaken a detailed parameter study on which environmental characteristics and chemical reactions affect the HNC/HCN ratio and can thus contribute to the observed dependence. Using existing gas and gas-grain models updated with new reactions and reaction barriers, we find that in static models the H + HNC gas-phase reaction regulates the HNC/HCN ratio under all conditions, except for very early times. We quantitively constrain the combinations of H abundance and H + HNC reaction barrier that can explain the observed HNC/HCN temperature dependence and discuss the implications in light of new quantum chemical calculations. In warm-up models, gas-grain chemistry contributes significantly to the predicted HNC/HCN ratio and understanding the dynamics of star formation is therefore key to model the HNC/HCN system. | Isomers are prevalent in the interstellar medium, with many of the currently detected molecules having an isomeric counterpart \citep{Remijan05}. These molecules provide a unique opportunity to probe physical properties of interstellar systems if line emission ratios are regulated by a single or small set of physical characteristics. Many isomers have a dominant species, which is typically the more stable form. For example, both HCO$^+$ and HOC$^+$ are observed in dense molecular clouds and photon dominated regions, but the ratio of HCO$^+$/HOC$^+$ is greater than 300 in these regions \citep{Smith02}. Isomer pairs are often observed in the same environments, indicating connected formation pathways and that energetic differences and selective destruction routes control the ratio. However, favoring the lower energy isomer does not hold for all ratios; the isomer pair HNC and HCN exhibits a ratio of unity at low temperatures \citep{Irvine84, Schilke92, Ungerechts97}. The observed ratio of unity at low temperatures is counterintuitive due to the reactivity of HNC, the metastable isomer of HCN. These isomers have a ground state energy difference of approximately 7240 K \citep{Bowman93}. Because of the relatively high abundances of both isomers and nearly identical dipole moments, implying similar excitation characteristics, this ratio has great promise as a molecular probe. The ratio has been measured in a variety of different sources, from dark clouds \citep{Schilke92} to prestellar cores \citep{Padovani11}, Titan \citep{Hebrard12}, OMC-1 \citep{Schilke92} and other galaxies and their outflows \citep{Aalto12}. A comprehensive survey designed to understand the HNC/HCN abundance ratio, and directed at OMC-1, was performed by \citet{Schilke92} using the IRAM 30m telescope and Plateau de Bure Interferometer in the 90 GHz region. It was found that the HNC/HCN ratio is approximately 1/80 towards Orion-KL but rises to 1/5 at lower temperature regions next to Orion-KL. In the coldest OMC-1 regions, the ratio rises further to unity. The unusual temperature dependence indicates that the ratio must be kinetically controlled \citep{Herbst00}. Understanding the kinetics that determine the HNC/HCN ratio is key to developing HNC/HCN as a widespread tool for probing the thermal history of interstellar regions. The chemistry of the two species was studied by \citet{Schilke92} with a gas-phase astrochemical model to explain the observed HNC/HCN temperature dependence. The most important formation mechanism was found to be the dissociative recombination of HCNH$^+$, forming both HNC and HCN in a 1:1 ratio. This branching ratio has been verified experimentally by \citet{Mendes12}. The same model predicted that the temperature dependence of the HNC/HCN ratio is regulated by the destruction efficiency of HNC with H and O at different temperatures (see also \citet{PineauDesForets90}). At that time, the activation energy barriers for these reactions had not been calculated theoretically, so \citeauthor{Schilke92} set the barriers to be 200 K, which best reproduced observations of OMC-1. Quantum chemical studies of these barriers have now been carried out and the results are used in many astrochemical networks, such as KIDA \citep{Wakelam12}. For the HNC + O reaction, a study by \citet{Lin92} determined the barrier to be approximately 1100 K. The rate coefficient of the HNC + H reaction has been calculated on a number of occasions. \citet{Talbi96} studied this reaction and determined the barrier to be 2000 K, an order of magnitude larger than the barrier presented by \citet{Schilke92}. A more recent barrier is 1200 K (D. Talbi, private communication, 2013). Additionally, it should be noted that the backwards reaction of H + HNC (i.e., H + HCN) has a very high energy barrier of 9000 K, and is therefore not included in our study of the HNC/HNC ratio. In addition to new barrier calculations, recent years have also seen advances in gas and gas-grain modeling of interstellar chemistry \citep{Chang12, Vasyunin13, Garrod13}. Considering the potential utility of HNC and HCN, it is therefore timely to reevaluate our understanding of what regulates this important chemical ratio. Observational advances also motivate a deeper understanding of the HNC/HCN ratio. With the near completion of the Atacama Large Millimeter/sub-millimeter Array (ALMA), its unprecedented spacial resolution and sensitivity will allow for better mapping of many interstellar environments. This is particularly exciting for the HNC/HCN ratio since temperature gradients in the less complicated low-mass star-forming regions occur on small size scales. ALMA also adds the possibility to study extragalactic sources at higher resolution. Detection of HNC and HCN is common in many extragalactic sources and is used as an AGN tracer, distinguishing Seyfert galaxies from starbursts \citep{Aalto02, Costagliola11}, however current single-dish telescopes and small interferometers are not able to resolve small-scale behavior of the HNC/HCN ratio in these sources. To study the HNC/HCN temperature dependence anew and determine the important chemical pathways in light of recent progress, a variety of models were used to simulate the ratio. Specifically, the influence of the H + HNC barrier, initial H atom abundances, and the influence of dynamics were investigated as the major drivers for the HNC/HCN chemistry. Models using the most recently calculated H + HNC barrier of 1200 K will be the focus of our studies. The models used are described in Section 2, with the results and a discussion following in Sections 3 and 4. The results are evaluated against the published HNC/HCN observations in OMC-1 \citep{Schilke92}. | The chemistry of HCN and its higher energy isomer HNC is reproduced quite well in cold dense interstellar sources by gas-phase ion-molecule chemistry. Both the individual abundances and the abundance ratio of near unity are fit by a chemistry in which the formation of HNC and HCN is primarily via the dissociative recombination of HCNH$^+$, initially predicted by \citet{Herbst73}, while reactions with H$_3^+$, H$_3$O$^+$, and HCO$^+$ are the dominant molecular destruction mechanisms. For sources at higher temperature, the HNC/HCN abundance ratio decreases rapidly, an unusual occurrence since one would expect the higher energy isomer to increase in abundance. Indeed, the temperature dependence of the ratio implies that the ratio is governed by kinetic rather than thermodynamic considerations. The temperature dependence of the HNC/HCN abundance ratio has been studied most carefully in the source OMC-1 \citep{Schilke92}, and we have endeavored to simulate this temperature dependence with up-to-date gas-phase and gas-grain chemical networks. But what reaction or reactions can lead to the unusual HNC/HCN temperature dependence? The gas-phase formation and destruction pathways for the chemistry of the HNC/HCN ratio are shown in Figure \ref{pathway_gas} for chemical times up to $ 2 \times 10^{5}$ yr. In addition to the low temperature ion-molecule processes, there are a number of destruction mechanisms for HNC involving neutral reactant partners. The only reaction that appears to be of importance in reducing the HNC/HCN ratio at times representative of dense clouds in static systems is the reaction between HNC and atomic H, which is known by a number of quantum chemical calculations to have an activation energy barrier, although the different calculations yield a wide divergence of results between the earliest calculation \citep{Talbi96} and more modern ones (700 K, 1200 K) (D. Talbi, private communication, 2013). Even with the lowest calculated barrier (700 K), our gas-phase model calculations fail to reproduce the extent of the diminution of the HNC/HCN ratio with increasing temperature unless it is assumed that a much larger abundance of atomic hydrogen is present than in standard ion-molecule calculations. Indeed, a chi-squared analysis shows that for a density of $ 2 \times 10^{5}$ cm$^{-3}$ and a time scale of $ 2 \times 10^{5}$ yr, the maximum barrier consistent in a statistical sense with the HNC/HCN data is 600 K, at a rather high H atom initial fractional abundance of 0.1. If a more realistic upper limit for the fractional abundance of H of 10$^{-2}$ is utilized, we obtain a maximum barrier of near 500 K. With a more standard theoretical fractional abundance of 10$^{-4}$, this maximum barrier is slightly higher than 300 K. None of these values are even close to the most recently calculated barrier of 1200 K. We have not been able to improve upon these results by variation of parameters such as the elemental abundances, the lifetime of the source, and its density nor have we been able to do better with a full-fledged gas-grain chemical simulation at a constant temperature. The inclusion of a warm-up in the gas-grain chemical simulations provides some information on how dynamics affect the system. Depending on the warm-up time-scale, different and complicated temperature dependences for the HNC/HCN ratio are calculated, due, in part, to the enhanced importance of indirect gas-grain interactions, specifically the influence of formaldehyde. H$_2$CO forms on grain-surfaces via the hydrogenation of CO. Once H$_2$CO has desorbed, it reacts with HCNH$^+$ to form HCN, a reaction that was studied experimentally by \citet{Freeman78}. The analogous reaction to form HNC is quite endothermic, and does not occur. In our chemical simulations, the reaction becomes important between 30 - 40 K, explaining the dramatic decrease in the HNC/HCN by an enhancement in the HCN abundance. Additionally, a second, direct gas-grain process occurs in this temperature range through the desorption of HCN and HNC from the grain surface. The contribution to the 35 K dip arises because of the large abundance of HCN on the grain surface compared with HNC. Following this initial decrease around 35 K, the HNC/HCN ratio increases in all warm-up models; however, the rate of the increase varies depending on the warm-up time scale. This is again primarily due to the H$_2$CO reaction and time effects. With the shortest warm-up time scale investigated of 5 $\times$ 10$^4$ yrs, very little time is spent at each temperature. Therefore, the chemistry that occurs at higher temperatures is still influenced by the lower temperature chemistry. However, as the warm-up stages get longer, the amount of time that each temperature has experienced increases, resulting in the lower temperature chemistry proceeding further before the onset of the higher temperature chemistry. As the warm-up timescales for each temperature increase, they approach the time scales used for the static models and the dip becomes negligible, analogous to the static model results. The chemistry of the HNC/HCN ratio after the dip is identical to that determined by the important reactions found in the static models, as displayed in Figure \ref{pathway_gas}. With all of the results from the gas-phase and gas-grain models, we can infer from the inability to reproduce the observed temperature dependence of the HNC/HCN ratio using static models that one or more of the following inferences must be true: \begin{enumerate} \item the H + HNC barrier is lower than the most recent calculated value of 1200 K. \item the reaction networks are not complete. \item the observations are heavily influenced by short dynamic timescales and therefore gas-grain chemistry, consistent with the complicated nature of the source. \end{enumerate} Through lowering the H + HNC barrier from the calculated value of 1200 K, this reaction becomes an increasingly efficient destruction mechanism. Differences between the empirical and theoretical barrier values could elucidate whether other processes, such as tunneling, are occurring in interstellar environments. The barrier discrepancies also suggest that we might need to update or are missing some important reactions for this chemistry. For example, the HNC + O reaction was found to be important for the HNC/HCN ratio by \citet{Schilke92}, but was last calculated by \citet{Lin92}. Since this time, quantum chemical methods used to determine barriers have advanced so that a recalculation of the barrier or a laboratory study of this reaction might be worthwhile. The inferences obtained from static models may not represent the situation satisfactorily. It is also plausible that the dynamics of the observed system can produce variations of the observed HNC/HCN ratio. Indeed, with astrochemical warm-up models, the effect of warm up the chemistry on the HNC/HCN ratio is quite evident, although strongly dependent on the rate of the warm-up. The dynamic models indicate that reasonable models of the HNC/HCN dependence on temperature with barriers higher than 200 K might exist. However, these models only incorporate the warm-up phase of a collapse, omitting any variations in the density. Further exploration of this effect on the chemistry of the HNC/HCN ratio is necessary to fully understand observed results if a system is known to be dynamic. The comparison between the observations of \citet{Schilke92} and our simulations for the HNC/HCN abundance ratio in OMC-1 has also been affected by new calculations by \citet{Sarrasin10} of rotationally inelastic collisions involving HCN and HNC with He. These collisional calculations indicate that HNC/HCN abundance ratios greater than unity in cold cores inferred from prior collisional rates \citep{Green74} are likely to be too high and should be reduced to unity for sub-critical gas densities, close to our calculated values at 10 K. For the HNC/HCN results of \citet{Schilke92}, which even at low temperatures (20 K) are less than unity, the new collisional results are likely to push the ratio somewhat lower, although the density is closer to critical, and slightly increase the disagreement between theory and observation. The agreement could be improved by an additional low temperature destruction mechanism for HNC and might be indicative of tunneling under an activation energy barrier, a process not currently included in the gas-phase portion of our models. Finally, while our model to explain the HNC/HCN ratio in OMC-1 determines the important chemical parameters for this ratio, the region that was studied by \citet{Schilke92} might not be the ideal source for comparison. In addition to our use of older observations which incorporate now out of date collisional rates, as mentioned above, OMC-1 and the region around OMC-KL are not quiescent, with an energetic outflow, which might cause shocks \citep{Allen93}. Although, through combining multiple studies of other clouds, a similar temperature dependence of the HNC/HCN ratio is still observed (e.g.\citet{Ungerechts97, Bergin97, Pratap97, Liszt01, Jorgensen04, Padovani11}), this is also non-ideal. New observations of the HNC/HCN ratio in more quiescent sources with resolvable and known temperature structures, such as protostars and protoplanetary disks, would be ideal laboratories to develop the HNC/HCN ratio as a robust temperature probe for a variety of different interstellar regions. \begin{figure}[hp] \centering \includegraphics[width = 0.5\textwidth]{HNC_HCN_scheme.pdf} \caption{HNC and HCN reaction pathways for 10 to 100 K at 2 $\times$ 10$^5$ yrs. Green indicates formation, red indicates destruction, and black represents both formation and destruction with bold lines drawing attention to the most important reactions.} \label{pathway_gas} \end{figure} | 14 | 4 | 1404.5338 |
1404 | 1404.5879_arXiv.txt | The claimed detection of the BICEP2 experiment on the primordial B-mode of cosmic microwave background polarization suggests that cosmic inflation possibly takes place at the energy around the grand unified theory scale given a constraint on the tensor-to-scalar ratio. i.e., $r\simeq 0.20$. In this report, we revisit single-field (slow-roll) composite inflation and show that, with the proper choice of parameters and sizeable number of e-foldings, a large tensor-to-scalar ratio consistent with the recent BICEP2 results can be significantly produced with regard to the composite paradigms. | 14 | 4 | 1404.5879 |
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1404 | 1404.7798_arXiv.txt | \footnotetext{\textit{$^{a}$~IRAM, 300 rue de la Piscine, 38406 Saint Martin d'He\`res, France. E-mail: [email protected]}} \footnotetext{\textit{$^{b}$~LERMA-LRA, UMR 8112, Observatoire de Paris and \'Ecole normale Sup\'erieure, 24 rue Lhomond, 75231 Paris, France}} \footnotetext{\textit{$^{c}$~Centro de Astrobiolog\'ia, CSIC-INTA, Carretera de Ajalvir, Km 4, Torrej\'on de Ardoz, 28850 Madrid, Spain}} \footnotetext{\textit{$^{d}$~LUTH UMR 8102, CNRS and Observatoire de Paris, Place J. Janssen, 92195 Meudon Cedex, France}} Molecular lines are used to trace the structure of the interstellar medium (ISM) and the physical conditions of the gas in different environments, from high-z galaxies to proto-planetary disks. However, the interpretation of molecular observations for most of these objects is hampered by the complex source geometries, and the small angular sizes in the sky compared with the angular resolution of current instrumentation, that prevent us from resolving the different gas components, and hence to know which specific region each molecule actually traces. Therefore, in order to fully benefit from the diagnostic power of the molecular lines, the formation and destruction paths of the molecules must be quantitatively understood. This challenging task requires the contribution of theoretical models, laboratory experiments and observations. Well-defined sets of observations of simple \textit{template} sources are key to benchmark the predictions of theoretical models. In this respect, the Horsehead nebula has proven to be a good template source of low-UV field irradiated environments because it is close-by ($\sim400$~pc), it has a simple geometry (edge-on) and its gas density is well constrained. Moreover, in contrast to other Galactic photo-dissociation regions (PDRs), like the Orion Bar and Mon R2 which present large radiation fields ($\chi\simeq10^4-10^5$), the Horsehead is illuminated by a weaker radiation field ($\chi\sim60$) and thus better resembles the majority of the far-UV illuminated neutral gas in the Galaxy. Furthermore, the dust grains in the Horsehead have temperatures of $\simeq20-30$~K, which is not enough to thermally desorb most of the ices. The Horsehead therefore offers a clean environment to isolate the role of photo-desorption of ices on dust grains. Observations by the Infrared Space Observatory (ISO) and Spitzer have shown that dust grains are covered by ice mantles in the cold envelopes surrounding high-mass protostars\citep{gibb2000,gibb2004}, low-mass protostars \citep{boogert2008,pontoppidan2008,Oberg2008,bottinelli2010} and in isolated dense cores \citep{boogert2011}. These studies revealed that the ice mantles consist mostly of \hho{}, CO$_2$ and CO, with smaller amounts of \chhhoh{}, CH$_4$, NH$_3$ and \hhco{}. More complex prebiotic molecules, such as glycine (NH$_2$CH$_2$COOH) could also form on the ices around dust grains. Although their exact formation is unclear, it is believed that the simplest prebiotic molecules have an interstellar origin \citep{garrod2013,elsila2007}. Indeed, numerous amino acids, which are the building blocks of proteins, have been found in meteorites \citep{glavin2013}. In addition, glycine, which is the simplest amino acid, has been detected in samples returned by NASA's Stardust spacecraft from comet Wild~2 \citep{elsila2009}. Despite controversial detection claims \citep{snyder2005,jones2007,cunningham2007}, glycine or other more complex amino acids have not been detected in the interstellar medium yet. The most complex molecules detected in the interstellar medium so far, are glycolaldehyde\citep{hollis2000} (CH$_2$(OH)CHO), acetamide\citep{hollis2006} (CH$_3$CONH$_2$), aminoacetonitrile\citep{belloche2008} (NH$_2$CH$_2$CN), and the ethyl formate\citep{belloche2009} (C$_2$H$_5$OCHO). This shows the high degree of chemical complexity that can be reached in the interstellar medium. \TabObsMaps{} Simpler, but still complex organic molecules, such as methanol (\chhhoh{}), ketene (\chhco{}), acetaldehyde (\chhhcho{}), formic acid (HCOOH), formamide (NH$_2$CHO), propyne (\chhhcch{}), methyl formate (HCOOCH$_3$), and dimethyl ether (CH$_3$OCH$_3$), are widely observed in hot cores of high-mass protostars \citep{cummins1986,blake1987,bisschop2007}, and also in hot-corinos of low-mass protostars \citep{vandishoeck1995,cazaux2003}. The complex molecules observed in protostars have been classified in three different generations by \citet{herbst2009}, depending on their formation mechanism. The zeroth generation species form through grain surface processes in the cold ($<20$~K) pre-stellar stage (\eg{}, \hhco{} and \chhhoh). First generation species form from surface reactions between photodissociated products of the zeroth generation species in the warm-up ($20-100$~K) period. Finally, second generations species form in the hot ($>100$~K) gas from the evaporated zeroth and first generation species in the so called hot-core phase. Although it is clear that grain surface processes play an important role in the formation of complex molecules, the exact formation mechanism of most complex molecules is still debated. \TabAbundances{} \FigMaps{} \citet{bisschop2007} observed several complex molecules toward seven high-mass protostars, and classified them as cold (T$<100$~K) and hot (T$>100$~K) molecules based on their rotational temperatures. The hot molecules include \hhco{}, \chhhoh{}, HNCO, \chhhcn{}, HCOOCH$_3$ and CH$_3$OCH$_3$, while the cold molecules include HCOOH, \chhco{}, \chhhcho, and \chhhcch. The cold molecules are expected to be present in the colder envelope around the hot-core. \citet{oberg2013} studied the spatial distribution of complex molecules around a high-mass protostar and found that \chhco{}, \chhhcho{} and \chhhcch{} are indeed abundant in the cold envelope. They classified them as zeroth order molecules because their formation must require very little heat. Complex organic molecules may trace other environments than hot cores and hot corinos. They are also present in the cold UV-shielded gas. \citet{bacmann2012} detected CH$_3$OCH$_3$, CH$_3$OCHO, \chhco{} and \chhhcho{} in a cold ($\Tkin\sim10$~K) prestellar core. These observations challenged the current formation scenario of complex molecules on dust grains, because the diffusion reactions that lead to the formation of species are not efficient on dust grains with temperatures of $\sim10$~K. \chhhcho{} and \chhco{} have also been detected in the dark cloud TMC-1 \citep{matthews1985,irvine1989}. \chhco{} and \chhhcho{} have also been detected in a $z=0.89$ spiral galaxy located in front of the quasar PKS1830-211 \citep{muller2011}. In this paper, we present the results of an unbiased line survey performed with the IRAM-30m telescope in a classic star forming region, the Horsehead nebula. We describe the observations in section~\ref{sec:obs}. In section~\ref{sec:results} we present a summary of the recently published results of the line survey. In section~\ref{sec:complex} we present new unpublished results about the first detection of complex molecules in a PDR. We discuss these observations in section~\ref{sec:discussion} and conclude in section~\ref{sec:conclusions}. | \label{sec:conclusions} We have carried-out an unbiased spectral line survey at 3, 2 and 1mm with the IRAM-30m telescope in the Horsehead nebula, with an unprecedented combination of bandwidth, high spectral resolution and sensitivity. Two positions were observed: the warm photodissociation region (PDR) and a cold condensation shielded from the UV field, located less than $40''$ away from the PDR edge. The results of this survey include 1) the detection of \cfp{}, which can be used as a new diagnostic of UV illuminated gas and a potential proxy of the \cp{} emission associated to molecular gas; 2) the detection of a new species in the ISM, the small hydrocarbon \ccchp{}, which confirms the top-down scenario of formation of the small hydrocarbons from PAHs and photo-erosion; 3) the detection of \hhco{}, \chhhoh{} and \chhhcn{}, which reveals that photo-desorption of ices is an efficient mechanism to release molecules into the gas phase; 4) and the first detection of the complex organic molecules, HCOOH, \chhco{}, \chhhcho{} and \chhhcch{} in a PDR, which reveals the degree of chemical complexity reached in the UV illuminated neutral gas. Complex molecules are usually considered as hot-core tracers. The detection of these molecules in PDRs shows that they can survive in the presence of far-UV radiation, and their formation could even be enhanced due to the radiation. This opens the possibility of detecting complex molecules in other far-UV illuminated regions, such as protoplanetary disks, in the future. From this work we conclude that grain surface chemistry and non-thermal desorption are crucial processes in the ISM and therefore must be incorporated into photochemical models to interpret the observations. | 14 | 4 | 1404.7798 |
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1404 | 1404.4614_arXiv.txt | Current data from the Planck satellite and the BICEP2 telescope favor, at around the $2 \sigma$ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running $\alpha < 0$, the curvature perturbation amplitude has a {\it maximum} on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on $n_{\rm S}$ from Planck, this corresponds to an upper bound of the running $\alpha < - 4 \times 10^{-5}$, so that even tiny running of the scalar spectral index is sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In single-field inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as $10^4$ e-folds. | Inflation \cite{Guth:1980zm,Linde:1981mu,Albrecht:1982wi} has emerged as the standard paradigm for modeling the behavior of the very early universe. In addition to explaining the flatness and homogeneity of the cosmos, inflation predicts the generation of perturbations from quantum fluctuations in the early universe \cite{Kazanas:1980tx,Starobinsky:1980te,Sato:1981ds,Sato:1980yn,Mukhanov:1981xt,Mukhanov:2003xw,Linde:1983gd,Hawking:1982cz,Hawking:1982my,Starobinsky:1982ee,Guth:1982ec,Bardeen:1983qw}, a prediction which has been tested to high precision in measurements of the Cosmic Microwave Background (CMB). The temperature anisotropy of the CMB has been measured in exquisite detail by the Planck satellite \cite{Ade:2013kta,Ade:2013zuv,Ade:2013uln}, and recent measurement of the CMB polarization by the BICEP2 telescope has provided clear evidence of primordial gravitational waves consistent with the predictions of inflation \cite{Ade:2014xna}. The Planck and BICEP data are consistent with the simplest inflationary models. An example is inflation in a quadratic monomial potential, $V(\phi) \propto \phi^2,$ which predicts a tensor/scalar ratio $r \simeq 0.15$, consistent with BICEP2 constraints, and a scalar spectral index $n_{\rm S} \simeq 0.96$, consistent with Planck constraints. Such ``large-field'' inflationary models have field excursion $\Delta\phi > M_{\rm P}$ during inflation, where $M_{\rm P}$ is the reduced Planck Mass. Such potentials have the interesting property that, for field values $\phi \gg M_{\rm P}$, the amplitude of quantum fluctuations in the field becomes larger than the classical field variation, so that the field is as likely to roll {\it up} the potential as it is to roll down the potential. Therefore, in a statistical sense, inflation never ends: there will always be regions of the universe where the field has fluctuated upward, rather than downward, and inflation becomes a quasi-stationary, infinitely self-reproducing state of eternal inflation \cite{Vilenkin:1983xq,Guth:1985ya,Linde:1986fc,Linde:1986fd}. In this paper we consider the question of whether the BICEP2 data {\it imply} eternal inflation. We focus in particular on the fact that Planck + BICEP2 weakly favor a scale-dependent spectral index, a so-called {\it running} of the primordial power spectrum. Such running of the power spectrum would rule out all simple monomial potentials, requiring a more complex (and more finely tuned) inflationary potential. We find that for even a small negative running, of order $\alpha \sim 10^{-4}$, eternal inflation is prevented, even in cases where inflation continues for many e-folds. Therefore, it is premature to conclude that the large tensor signal favored by BICEP2 is consistent only with models leading to eternal inflation. The paper is organized as follows: Section \ref{sec:running} considers the current evidence for running of the spectral index. Section \ref{sec:eternal} discusses the relationship between eternal inflation and the amplitude of the curvature perturbation spectrum. Section \ref{sec:limit} discusses suppression of eternal inflation in the case of negative running of the curvature power spectrum. Section \ref{sec:conclusions} presents a summary and conclusions. | \label{sec:conclusions} In this paper, we consider the viability of eternal inflation in light of the results from the Planck and BICEP2 observations of the Cosmic Microwave Background. Current data weakly favor nonzero running of the scalar spectral index $n_{\rm S}$, mostly as a result of the suppressed scalar power observed on large angular scales in the Planck data. The suppression of low-$\ell$ modes in the CMB, compared to expectations from the standard $\Lambda$-CDM cosmology, may be due either to negative running, or may have another more exotic origin. In this paper, we consider eternal inflation in a scenario with nonzero running, and show that a negative running of the scalar spectral index on superhorizon scales serves to suppress eternal inflation. Assuming a constant running, we derive an upper bound \begin{equation} \alpha < - 4 \times 10^{-5}. \end{equation} For running below this bound, the primordial power spectrum is less than unity on all scales larger than the current horizon, and eternal inflation is prevented. In a more realistic case where higher-order terms such as running-of-running become significant, it is still the case that, as long as the curvature perturbation remains smaller than order unity, eternal inflation does not occur. In single-field inflationary models, negative running eventually results in a breakdown of slow roll and therefore a finite duration for inflation. We show that negative running is consistent with as many as $10^4$ e-folds of inflation, without the onset of eternal inflation, in contrast to the case of no running, for which eternal inflation will occur given around $1000$ e-folds of inflation. Can we really know what occurs very early in the inflationary epoch? Eternal inflation requires a curvature perturbation spectrum of at least order unity to occur, $P\left(k\right) \geq 1$ (which itself raises concerns about the effect of gravitational backreaction \cite{Martinec:2014uva}). It is therefore clear that the portion of the potential that produces observable density fluctuations ({\it i.e.} around 60 e-folds before the end of inflation) cannot give rise to eternal inflation, since CMB normalization requires $P\left(k\right) \sim 10^{-10}$. Eternal inflation occurs on the portion of the potential where the inflaton field rolls prior to producing these perturbations, which corresponds to length scales larger than our current horizon size. For example, in an $m^2 \phi^2$ potential, with $m\sim 10^{13}$ GeV, eternal inflation only takes place high up in the potential, at $\phi > 100 M_{\rm P}$. Since we do not have observational access to superhorizon length scales, and therefore the physics of very early stages of inflation, any conclusion we might reach contains an inherent element of speculation: It may be that such high regions of the potential are never probed, for example in the case of non-negligible spatial curvature \cite{Kleban:2012ph}. In this paper, we have not {\it proven} that eternal inflation does not occur. We have argued that it is not inevitable, even in single-field inflation, and current data in fact hint that we may be in a situation where eternal inflation is suppressed, even on far super-horizon scales. | 14 | 4 | 1404.4614 |
1404 | 1404.4422_arXiv.txt | We investigate potential $\gamma-\gamma$ absorption of $\gamma$-ray emission from blazars arising from inhomogeneities along the line of sight, beyond the diffuse Extragalactic Background Light (EBL). As plausible sources of excess $\gamma-\gamma$ opacity, we consider (1) foreground galaxies, including cases in which this configuration leads to strong gravitational lensing, (2) individual stars within these foreground galaxies, and (3) individual stars within our own galaxy, which may act as lenses for microlensing events. We found that intervening galaxies close to the line-of-sight are unlikely to lead to significant excess $\gamma-\gamma$ absorption. This opens up the prospect of detecting lensed gamma-ray blazars at energies above 10~GeV with their gamma-ray spectra effectively only affected by the EBL. The most luminous stars located either in intervening galaxy or in our galaxy provides an environment in which these gamma-rays could, in principle, be significantly absorbed. However, despite a large microlensing probability due to stars located in intervening galaxies, $\gamma$-rays avoid absorption by being deflected by the gravitational potentials of such intervening stars to projected distances (``impact parameters'') where the resulting $\gamma-\gamma$ opacities are negligible. Thus, neither of the intervening excess photon fields considered here, provide a substantial source of excess $\gamma-\gamma$ opacity beyond the EBL, even in the case of very close alignments between the background blazar and a foreground star or galaxy. | 14 | 4 | 1404.4422 |
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1404 | 1404.2424_arXiv.txt | We present results from imaging of the radio filaments in the southern giant lobe of Centaurus\,A using data from GMRT observations at 325 and 235\,MHz, and outcomes from filament modelling. The observations reveal a rich filamentary structure, largely matching the morphology at 1.4\,GHz. We find no clear connection of the filaments to the jet. We seek to constrain the nature and origin of the {\it vertex} and {\it vortex} filaments associated with the lobe and their role in high-energy particle acceleration. We deduce that these filaments are at most mildly overpressured with respect to the global lobe plasma showing no evidence of large-scale efficient Fermi\,I-type particle acceleration, and persist for $\sim2-3$\,Myr. We demonstrate that the dwarf galaxy KK\,196 (AM\,1318--444) cannot account for the features, and that surface plasma instabilities, the internal sausage mode and radiative instabilities are highly unlikely. An internal tearing instability and the kink mode are allowed within the observational and growth time constraints and could develop in parallel on different physical scales. We interpret the origin of the {\it vertex} and {\it vortex} filaments in terms of weak shocks from transonic MHD turbulence or from a moderately recent jet activity of the parent AGN, or an interplay of both. | \label{sect:introduction} From studies of both high- and low-power radio galaxies over the past three decades, considerable observational evidence has emerged for inhomogeneous, filamentary lobes, e.g., Cygnus\,A \citep{PER84}, 3C\,310 \citep{BRE84}, Hercules\,A \citep{DRE84, GIZ03}, Fornax\,A \citep{FOM89}, Pictor\,A \citep{PER97}, 3C\,353 \citep{SWA98}, M\,87 \citep{OWE00, FOR07}, NGC\,193 \citep{LAI11}, B2\,0755+37 \citep{LAI11}, with the bulk of the observations being conducted with the Very Large Array (VLA) in the GHz regime. The filamentarity has implications for the internal structure of the lobes. However, no consensus exists on whether the magnetic field in the lobes has a low filling factor and electrons are uniformly distributed, or the electron population tracks the magnetic field enhancements closely. Positionally varying magnetic field strength was claimed for lobes of a number of Fanaroff-Riley class\,II (FR\,II) \citep{FAN74} sources (e.g. \citealp{HAR05, GOO08}), in contrast with the western giant lobe of the source Fornax\,A\footnote{Morphologically, Fornax\,A is FR\,II class by the original \citep{FAN74} definition; in terms of luminosity, it is on the boundary FR\,I/FR\,II.}, for which a positionally varying electron energy spectrum is favoured \citep{SET11}. \begin{figure*} \includegraphics[width=1.0\textwidth]{GMRTfil-fig1.eps} \caption{Combined ATCA and Parkes 1.4\,GHz continuum image at $60\times40$\,arcsec angular resolution of the southern giant lobe of Centaurus\,A, indicating the {\it vertex} and {\it vortex} filaments and the position of the dwarf galaxy KK\,196. The radio galaxy core and the inner lobes are beyond the north edge of the image. The artefact protruding to the northern part of the giant lobe originates from the bright inner lobes. The artefact centred on RA\,$\hms{13}{23}{04.2}$, DEC\,$\dms{-44}{52}{33.3}$ is the background quasar PKS\,1320--446 at a redshift of $z\sim1.95$, the artefact on RA\,$\hms{13}{18}{30.02}$, DEC\,$\dms{-46}{20}{35.2}$ the background quasar MRC\,1315--460 (PMN\,J1318--4620) of $z\sim1.12$ and the artefact on RA\,$\hms{13}{19}{21.59}$, DEC\,$\dms{-44}{36}{46.7}$ the background source MRC\,1316--443. Adapted from \citet{FEA11}.} \label{fig:fig1} \end{figure*} Filamentary structure does not necessarily imply turbulence, but magnetohydrodynamical (MHD) turbulence implies filamentary structure in synchrotron emission (e.g. \citealp{EIL89, HAR13, WYK13}). MHD turbulence amplifies and transports magnetic fields which in turn control lobe viscosity, conductivity and resistivity, as well as the acceleration and propagation of cosmic rays (e.g. \citealp{LEE03, JON11}). The presence of turbulence might in some cases be akin to a development of plasma instabilities. Various types of instabilities, promoting growth of filament-like features, could develop inside or on the surface of a radio lobe. Hydrodynamical (HD) instabilities, such as Kelvin-Helmholtz (KH), Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) are relevant since they can lead to flow patterns that naturally filament and can amplify ambient magnetic fields (e.g. \citealp{JUN95, RYU00}). MHD instabilities such as the resistive tearing instability, the sausage mode and the kink mode are also apposite, as are radiative instabilities. Utilising the Australia Telescope Compact Array (ATCA) and the $64$\,m Parkes telescope for imaging at 1.4\,GHz with $49$\,arcsec angular resolution, \cite{FEA11} have discovered intricate filamentary features associated with the northern and southern giant lobes of Centaurus\,A (Fig.\,\ref{fig:fig1}). Centaurus\,A is the nearest (3.8$\,\pm\,$0.1\,Mpc; \citealp{HARR10})\footnote{At that distance, $1$\,arcmin corresponds to $1.1$\,kpc.} Fanaroff-Riley class\,I (FR\,I) radio galaxy, hosted by the massive elliptical galaxy NGC\,5128. Due to its luminosity and proximity, Centaurus\,A is an outstanding testbed for models of jet energetics, particle acceleration, and the evolution of low-power radio galaxies in general. Centaurus\,A's northern jet (angular size $\sim4.0$\,arcmin) and its immediate surroundings, the bright inner lobes ($\sim5.5$\,arcmin each) and the northern middle lobe ($\sim33$\,arcmin) have been extensively studied (e.g. \citealp{TIN98, MOR99, HAR03, KRA03, HAR06, CRO09, KRA09, MUL11, NEF14}; Israel et al., in preparation). However, Centaurus\,A's proximity to Earth has hampered for a long time comprehensive investigations of its giant (i.e. outer) lobes ($\sim4.3^{\circ}$ each), whose substructure has been mapped only recently in the aforementioned work by \cite{FEA11}. Topics of great current interest are the ages of the giant lobes and the lobe particle content and pressure. \cite{HAR09} and \cite{YAN12} have determined radiative ages of Centaurus\,A's giant lobes: the former obtaining $\sim30$\,Myr based on synchrotron ageing fitting the single-injection Jaffe-Perola model \citep{JAF73}, the latter $\la80$\,Myr reasoning that ages significantly larger than a few tens of Myr are not consistent with the observations of gamma-ray inverse-Compton emission. The above values would imply that the giant lobe front ends expand at respectively $\sim0.030$ and $\ga0.011c$, i.e. faster than Centaurus\,A's inner lobes ($\sim0.009c$, \citealp{CRO09}), in discord with expectations. The dynamical age calculations by \cite{WYK13} give $\sim560$\,Myr based on buoyancy arguments, and the estimates by \cite{EIL14} give $\sim500$\,Myr$-1.5$\,Gyr relying on dynamical models of the growth of the giant lobes. Giant lobe thermal electron content evaluations also show an inconsistent picture: $n_{\rm e,th}\sim1\times10^{-4}$\,cm$^{-3}$ gauged independently from X-ray and radio observations \citep{STA13, SUL13} versus $n_{\rm e,th}\sim5.4\times10^{-9}$\,cm$^{-3}$ based on entrainment calculations \citep{WYK13}. The preceding value, which is similar to the thermal content of the Centaurus\,A intragroup medium, $n_{\rm th}\sim1\times10^{-4}$\,cm$^{-3}$ \citep{SUL13, EIL14}, would make Centaurus\,A exceptional among lobed radio sources, which normally show cavities associated with the lobe (e.g. \citealp{BIR04, WIS07, CAV10}) implying that the internal densities of the lobes are below those of the intragroup/intracluster medium. Giant lobe pressure estimates vary from $p_{\rm th}\sim8.0\times10^{-14}$\,dyn\,cm$^{-2}$ \citep{STA13, SUL13, STE13} and $p_{\rm th}\sim9.0\times10^{-14}$\,dyn\,cm$^{-2}$ \citep{FRA14} which are close to the minimum pressure of the lobes, to $p_{\rm th}\sim3.2\times10^{-13}$\,dyn\,cm$^{-2}$ \citep{EIL14} and $p_{\rm th}\sim1.5\times10^{-12}$\,dyn\,cm$^{-2}$ \citep{WYK13}. \cite{HAR09}, \cite{SUL09}, \cite{SUL11}, \cite{WYK13} and \cite{EIL14} have considered MHD turbulence in Centaurus\,A's giant lobes. \cite{WYK13} have argued for mildly sub-Alfv\'enic turbulence in those lobes which allows for the existence of relatively long-lived filaments\footnote{MHD simulations (e.g. \citealp{JON11}) indicate that this is also true for trans-Alfv\'enic and mildly super-Alfv\'enic turbulence. Filaments last roughly an eddy turnover time for the scale of the eddies that stretch them.}. A detailed description of the ensemble of the filaments has been offered by \cite{FEA11}, and \cite{STA13} and \cite{WYK13} have drawn some attention to the prominent filamentary features in the southern giant lobe, the {\it vertex} and the {\it vortex} (see Figs.\,\ref{fig:fig1}\,--\,\ref{fig:fig4}), whose nature and origin are as yet ill-constrained. The {\it vertex} (Largest Angular Size, LAS, $\sim\!34$\,kpc), at $\sim\!2^{\circ}$ from the core and $\sim0.5^{\circ}$ from the position of the background point source PKS\,1320--446, is slightly curved and shows variations in surface brightness. The {\it vortex} (LAS $\sim\!53$\,kpc), at about $\sim2.5^{\circ}$ from the core and lying immediately interior to the western part of the lobe, has been likened \citep{FEA11} to the mushroom-shaped structure seen in the eastern giant lobe of the FR\,I radio source M\,87 \citep{OWE00}. \cite{FEA11} have proposed a number of explanations to be origin of the filaments in Centaurus\,A: the {\it vertex} and {\it vortex} might derive from an enhanced jet activity, from KH instabilities at the lobe-intragroup interface, or from the passage of the dwarf irregular galaxy KK\,196 (AM\,1318--444), a Centaurus group member at $3.98\pm0.29$\,Mpc \citep{JER00, KAR07}, through the lobe. To gain more insight into physical processes occuring in radio galaxies's lobes, it is essential to have access to multifrequency observations, including very-low frequency bands. We have chosen to use the Giant Metrewave Radio Telescope (GMRT) to study the properties of the {\it vertex} and {\it vortex} filaments at 325, 235 and 150\,MHz. At these frequencies, the field of view of the GMRT is large enough to fit the combined {\it vertex}\,--\,{\it vortex} region in one or two pointings. The combination of short and long baselines (ranging from $\sim\,100$\,m up to $\sim\,25$\,km) enables the detection of, and separation between, large structures of the angular size of the filaments and compact radio sources along the same line of sight. The GMRT has no baselines that sample the largest scales of radio emission from the giant lobes, which are therefore naturally surpressed. Besides the intrinsic delicacies of handling low-frequency radio data and imaging diffuse, extended radio emission, processing these observations is particularly challenging. As observed from GMRT, the {\it vertex} and {\it vortex} filaments are at low elevation (always $<26^{\circ}$), which impacts on the $uv$-coverage and ionospheric air mass in an unfavourable way. Also, the large brightness of the background quasar PKS\,1320--446 and of Centaurus\,A's inner lobes (e.g. Fig.\,\ref{fig:fig1}) can cause serious dynamic range (DR) limitations in the entire image. The remainder of the paper is organized as follows. Section\,\ref{sect:obs} describes the GMRT observations and data reduction. In Section\,\ref{sect:results}, we present the new GMRT images and combine the GMRT data with those of the ATCA at higher frequencies with the aim of establishing spectral indices of the {\it vertex} and {\it vortex} filaments. We discuss filament pressure, ageing and particle acceleration constraints, and expound upon turbulence properties on different scales of the giant lobes in Section\,\ref{sect:interpretation}. We then test various scenarios for the origin of the {\it vertex} and {\it vortex} and show that these structures are most likely not unique among the lobe filaments and are plausibly identified with weak shocks in transonic MHD turbulence. The key findings are summarised in Section\,\ref{sect:summary}. Throughout the paper, we use J\,2000.0 coordinates, and define the energy spectral indices $\alpha$ in the sense $S_{\!\nu}\propto\nu^{-\alpha}$. | \label{sect:summary} We have presented new, high-dynamic range GMRT observations at 325 and 235\,MHz of parts of the southern giant lobe of Centaurus\,A, and have modelled the origin of the filamentary structure associated with the lobe. The key results of this paper are as follows: 1. The detection at 325 and 235\,MHz, with comparable resolution to the 1.4\,GHz ATCA images, confirms the reality of the {\it vertex} and {\it vortex} filaments associated with the southern giant lobe. The spatial extent of the {\it vertex} and {\it vortex} nearly coincides with their morphology at 1.4\,GHz, reinforcing their synchrotron origin. The {\it vertex} shows fine substructure and appears twisted. The {\it vertex} and {\it vortex} fields demonstrate surplus filamentary features, however, we find no clear connection at 325\,--235\,MHz of the filaments to the extant or extinct jet. 2. Combining the ATCA and GMRT data, and restricting the range of baselines to $0.15-2.5$\,k$\lambda$, we have inferred a spectral index $\alpha=0.81\pm0.10$ for the {\it vertex} filament and $\alpha=0.83\pm0.16$ for the {\it vortex}. This is marginally steeper than the spectral index of the general Centaurus\,A lobe plasma, and we discuss this in terms of an excess-loss scenario with particle confinement in the filaments. Our spectral fitting implies spectral ages that are difficult to reconcile with the `turbulent ages' (i.e. the longevity of the filaments stretched by the turbulent eddies) of $\sim2-3$\,Myr without invoking very high magnetic field strengths. 3. Our minimum pressure analysis for the filaments reveals $1.5\times10^{-13}$\,dyn\,cm$^{-2}$ ({\it vertex}) and $1.3\times10^{-13}$\,dyn\,cm$^{-2}$ ({\it vortex}) which is a factor $\sim3$ higher than the minimum global pressure of the lobes. Such an overpressure could be identified with weak shocks (Mach number $\mathcal{M}\sim1.7$). Synchrotron emissivity ratios result in a pressure jump of about $1.3$, compatible with expansion at the sound speed. No efficient Fermi\,I-type particle acceleration is expected for such slow expansions, and it also makes a spherical cocoon collapsing scenario with $\mathcal{M}\gg1.7$ in the giant lobes untenable. 4. Scaling down from the driving scale in the giant lobes with a presumable turbulence level of $\delta B/B_0\sim1$, we derive a turbulence level $\delta B/B_0\ga3\times10^{-3}$ at $\sim10^{-3}$\,pc. The viscous scale in the giant lobes is clearly considerably smaller than that derived from Coulomb scattering. From our calculated low value of the specific magnetic diffusivity, and therefore a large magnetic Prandtl number, we deduce that the MHD turbulence extends well below the viscous dissipation scale, with the resistive dissipation scale of order $10^{-6}$\,pc. This sets the width of the current sheet of the tearing mode. 5. We have considered several mechanisms that may generate the filaments in the southern giant lobe. We have shown that the dwarf irregular galaxy KK\,196 (AM\,1318--444) can be excluded as the origin of the {\it vertex}/{\it vortex} filaments, principally on grounds of its low relative velocity and mass, and on the morphology of the {\it vertex}/{\it vortex}. Our turbulence power spectrum modelling does not support different origin of the {\it vertex} and/or {\it vortex} from the other filaments in the lobe. The Kelvin-Helmholtz instability provoked at the lobe-intragroup interface is ruled out based on its growth time and observational constraints. The Rayleigh-Taylor and Richtmyer-Meshkov instabilities are highly unlikely to account for the {\it vertex}/{\it vortex} within the available observational constraints. Of the MHD instabilities, the tearing mode is supported by its growth time which lies conveniently within both the dynamical and spectral ages of the lobes and also within our derived turbulent ages of the {\it vertex}/{\it vortex}. The filaments are inconceivably affected by the sausage instability given the presumable presence of an axial $B$-field in the {\it vertex}/{\it vortex} which suppresses its growth. To the contrary, the kink instability {\it is} supported by a presence of such axial field, moreover, the existence of the kink instability is anticipated based on the filament radio morphology and on the growth time which is again sufficiently within the dynamical and spectral ages of the lobes and within the turbulent ages of the {\it vertex}/{\it vortex}. The radiative instabilities are ruled out based on their growth times. We lean towards the {\it vertex} and {\it vortex} filaments originating from intralobe MHD turbulence or from last stages of the activity of the pre-existing jet, or an interplay of both. There are several aspects that remain to be explored. The magnetic field direction and a possible variability of the spectral index along the filaments may be revealed by observations with the ATCA-CABB at GHz frequencies. With an instantaneous field of view of $30$\,deg$^2$ between 700 and 1800\,MHz and $20$ times higher spatial resolution in comparison to the current ATCA and GMRT images, the Australian SKA Pathfinder (ASKAP) will be the ideal facility for further investigations of the origin of the filaments, including the faint edge-like features, the {\it wisps}. In a future paper we will report on {\it XMM-Newton} observations designed to constrain the magnetic field strength of the individual filaments. Reproducing the complex morphology of the {\it vertex} will be a challenge for future MHD simulations. | 14 | 4 | 1404.2424 |
1404 | 1404.7266.txt | It has been only $\sim$15 years since the discovery of dark energy (although some may argue there were strong indications even earlier). In the short time since measurements of type Ia supernovae indicated an accelerating universe, many other techniques have now confirmed the acceleration is real. The variety of ways in which dark energy has been confirmed is one of the reasons we are so confident in the statement that most of the energy in the universe is in a form we can not see except through its gravitational influence. This review aims to summarise briefly the many varied ways we now have measured dark energy. The fact that these different techniques all indicate that the simplest model remains the best -- that dark energy contributes a constant background acceleration -- is remarkable, since each of these different types of measurements represented opportunities for this simplest model to fail. Although we currently lack a compelling theoretical explanation for this acceleration, any explanation will have to explain the wide variety of complementary observations that we review here. This is an informal presentation, following the lines of the talk I presented at the General Relativity and Gravitation (GR20) conference in Warsaw in July 2013. {\blue This astro-ph version contains bonus material, indicated by blue text, that would not fit within the published version's page limits.} | \label{intro} \vspace{-5mm} We're at an exciting point in the link between cosmological observations and fundamental physics. We've discovered that the universe is accelerating. The cause of that acceleration we give the name {\em dark energy}. However, we don't know what that dark energy actually is. Could it require alterations to the laws of gravity? Is it a fluid with negative pressure? And if it is vacuum energy, could a quantum theory of gravity naturally explain why its value is $\sim$ 54 orders of magnitude larger than the naive value quantum physics predicts?\footnote{The fabled 120 orders of magnitude that is usually quoted is apparently an exaggeration --- see \cite{martin12}, around Eq.~548. Nevertheless, this remains one of the worst ever matches between theory and observation.} Since the discovery in 1998 of the acceleration of the expansion of the universe \citep{riess98,perlmutter99}, many new and varied measurements have confirmed its existence. And despite many chances to find otherwise, every observation so far has confirmed that it is consistent with a cosmological constant -- uniform throughout space, it doesn't clump and does not dilute as the universe expands. This strange behaviour means that it could be a form of vacuum energy, of the type that is predicted to exist by quantum physics. The only problem is that quantum physics predicts a larger amount of this vacuum energy than we actually see. Whether or not that is a problem may depend on whether the successful merging of quantum physics and gravity into a quantum theory of gravity can explain away that conundrum. In any case, a decade and a half of observations have provided numerous new {\em types} of measurements, which could potentially have revealed discrepancies from the vacuum energy / cosmological constant picture of dark energy. However, in every case, the observations have remained consistent with vacuum energy -- the simplest form of dark energy possible. The next generation of experiments could potentially reveal the same thing. If so, we will be none the wiser. The real breakthrough in dark energy research at this point has to be theoretical. Even if observers do find some discrepancy with vacuum energy, it may still be that a compelling theoretical explanation is lacking. However, it is very difficult to make a theory of dark energy that differs from a cosmological constant, without violating one observation or another. The purpose of this review, is to summarise the many varied observations that now confirm dark energy, with a view to guiding theorists in the many ways that their theory has to pass observational tests if it is to be successful. It is through this communication between observation and theory that we will be able to advance our knowledge of this enigmatic feature of our universe. This is an informal review following the lines of the talk I presented at the General Relativity and Gravitation (GR20) conference in Warsaw in July 2013. I aim to fill the gap between technical papers and popular accounts. As such this is a primarily qualitative review. For more technical details I highly recommend the recent review \cite{weinberg13}. \vspace{-3mm} | The purpose of this review was to give a general qualitative review of the many varied ways in which dark energy has been measured, and thus the many ways in which theories of dark energy have to be tested before they can be validated. I find it astonishing, the range and variety of measurements that the standard ${\rm \Lambda}$CDM model has now passed. One of the difficulties in testing new theories of gravity, or models of dark energy, is that it is not always obvious what effect they will have on all the observational effects above. Strong collaboration between theorists and the teams of observers making these measurements will be crucial for theory to be robustly tested and to make progress on identifying the nature of dark energy. %\paragraph{Paragraph headings} Use paragraph headings as needed. | 14 | 4 | 1404.7266 |
1404 | 1404.7806_arXiv.txt | {We derive analytical expressions for the power spectra at the end of inflation in theories with two inflaton fields and non-canonical kinetic terms. We find that going beyond the slow--roll approximation is necessary and that the nature of the non-canonical terms have an important impact on the final power spectra at the end of inflation. We study five models numerically and find excellent agreement with our analytical results. Our results emphasise the fact that going beyond the slow--roll approximation is important in times of high-precision data coming from cosmological observations.} | Whilst inflation has enjoyed multiple successes in explaining the observed large scale structure, formed by density perturbations in the early universe, there is still much work to be done in narrowing down the specifics regarding the types of models still viable in this age of precision cosmology --- especially in light of the current data coming from Planck \cite{Planck06,Planck13} and BICEP2 \cite{BICEP2} on the properties of the Cosmic Microwave Background radiation (CMB). Early models involved only a single scalar field, the inflaton \cite{Guth81,Linde82} rolling down to it's minimum to drive inflation, but more recently multi-field models have come to the fore motivated by theoretical considerations in high energy physics \cite{Kofman87,SilkTurner,Wands96,Staro1,Shiu2011,White,Kaiser1,Kaiser2,Kallosh2013,Kaiser3,Kaiser4,Riberio}. There is no clear reason that inflation should be driven by only a single field so it is natural to study this class of models equally --- especially when they lead to a much richer and more diverse set of predictions. In addition to using multiple scalar fields, these higher energy theories suggest that the inclusion of non-standard kinetic terms is a natural progression from the standard models --- and that's what we shall look at here. Studying the evolution of perturbations (and power spectra) of single field models is a relatively simple task in that they become frozen in as the mode of interest exits the horizon. This is not, however, the case with multi-field models in which the added degree of freedom allows for perturbations in two directions --- those along the direction of the background trajectory (curvature perturbations) and those orthogonal (isocurvature perturbations) --- which are not mutually independent as inflation proceeds. Isocurvature perturbations describe the relative perturbations between the fields present and it has already been shown (see e.g. \cite{GarcWands,Starob95,Wands2}) that curvature perturbations can be sourced by isocurvature perturbations long after horizon exit, thereby adding an additional layer of complexity to finding the values of the power spectra come the end of inflation. This sourcing of perturbations is strongest when there are sharp turns in field space and we expect that the coupling between the fields will both lead to additional curvature in the background trajectory in a number of cases along with another independent source term \cite{DiMarco03}, in turn leading to additional curvature \cite{Lalak07,DiMarco05}. It is therefore important to be able to track the perturbations and their mixing throughout inflation to ascertain a faithful estimate of their final values in order to compare to observational data. A significant amount of work has already been done on this \cite{Langlois99,Bartolo01,Byrnes06,Cremonini10,Cremonini11, Hu11} both using the $\delta N$ formalism \cite{Starob85,Sasaki96,Lee05,Sugiyama12} and the transfer matrix method \cite{Lalak07,Davis12} where it has been noted that in some circumstances the $\delta N$ formalism is unsuitable and so we take a closer look at the transfer matrix method and attempt to generalize the work from \cite{DiMarco03,DiMarco05,Lalak07,Davis12} to include terms second order in slow-roll parameters in both canonical and non-canonical cases. Previous work has largely focused on higher order approximations in purely canonical cases or first order approximations in non-canonical cases so the logical next step is to bring these two situations together. We find that due to the relative sizes of some of the non-canonical slow roll parameters (calculated from the background trajectories), introduced later, this step is necessary and well motivated as non-canonical terms can dominate over their standard counterparts. In this paper we examine the effects of these non-canonical terms at second order in two distinct regimes --- the early time/horizon crossing regime along with the super-horizon evolution regime. Splitting the evolution up in this way is necessary because of the very different behaviours during these times. The early evolution is dominated by an explicit time dependence with (generally) very small slow roll paramaters. After this, we expect the explicit time dependence to vanish and the evolution to be dominated purely by the growing slow roll terms. The final results given here shall combine both of these approaches, with the results normalised consistently for ease of comparison with earlier work. The paper is organised as follows. The next section gives details of the background and the form of the models to be looked at along with an introduction to the slow roll parameters used later on. It then details the early times regime, calculating the resulting power spectra approximations before continuing on to the super-Hubble regime and finding analytic approximations there too. The calculation presented in this section follows \cite{Lalak07} closely, but going to second order in the slow-roll parameter. Section 3 introduces the numerical procedure along with the inflationary potentials we shall be looking at. The fourth section looks at the results of the numerics and compares them to the first and second order analytic approximations found earlier in a number of cases. Finally, we give our conclusions based on the results of section 4. In the appendix, the reader can find some formulae which are needed in the main text. | In this paper we have looked at the effect of non-canonical kinetic terms in the form of $e^{b(\phi)}$ where where we have set $b(\phi) = \beta\phi$ or $b(\phi) = \beta\phi^2$. The effects of such a term have important consequences for the shape of the background trajectory and hence the slow roll parameters --- of which we introduced a new parameter $\xi_2$ following on from the definition of $\xi_1$ in \cite{Lalak07}. Whilst the majority of cases studied involve only the linear non-canonical term and therefore leave $\xi_2 = 0$, the final example shows the importance of these corrections when higher powers of $\phi$ are used in the exponential --- providing the basis for further work with such conditions. We have also seen that in some cases (eg. non-canonical double inflation) it is easily justified that second order $\xi_1$ terms are necessary to track the evolution accurately as they dominate over other slow roll parameters through both the sub-horizon and super-horizon regimes. Unfortunately, this generalisation of the canonical second order approach to include these non-canonical terms does lose a certain amount of accuracy when compared to the success of the canonical approach , but these differences are best explained not by errors in the expansion itself, but rather as problems in the altered field space trajectory. For example, the product potential (figure \ref{canprodpot}) behaves well with slow turns in the trajectory when $b(\phi) = 0$ but when $b(\phi) \not= 0$ (figure \ref{noncanprodpot}) we see a much more abrupt change of direction and subsequent loss of accuracy. The inclusion of a non-canonical term alters all of the slow roll parameters through this change of trajectory such that the errors are accounted for not only by $\xi_{1,2}$ but also by both the first and second order `normal' slow roll parameters --- of which we find agreement with earlier work. We finally emphasise that whilst we do find an improvement on previous approximations through the inclusion of second order non-canonical terms it is still necessary to artificially constrain the amplitude of $b(\phi)$ in order for the approximation to work. This can be done either by setting $\phi_0$ or $\beta$ to be small --- as without doing so $\xi_{1,2}$ can become much larger than the other slow roll parameters much earlier on. | 14 | 4 | 1404.7806 |
1404 | 1404.5518_arXiv.txt | We study the axion monodromy inflation with a non-perturbatively generated sinusoidal term. The potential form is a mixture between the natural inflation and the axion monodromy inflation potentials. The sinusoidal term is subdominant in the potential, but leaves significant effects on the resultant fluctuation generated during inflation. A larger tensor-to-scalar ratio can be obtained in our model. We study two scenarios, the single inflation scenario and the double inflation scenario. In the first scenario, the axion monodromy inflation with a sufficient number of e-folds generates a larger tensor-to-scalar ratio of about 0.1-0.15 but also a tiny running of the spectral index. In the second scenario of double inflation, axion monodromy inflation is its first stage, and we assume another inflation follows. In this case, our model can realize a larger tensor-to-scalar ratio and a large negative running of the spectral index simultaneously. | Recent detection of the gravitational wave perturbation by BICEP2~\cite{Ade:2014xna} indicates its large amplitude and its tensor-to-scalar ratio of \begin{equation}\label{eq:BICEP2-1} r _T = 0.20^{+0.07}_{-0.05} \end{equation} for a lensed-$\Lambda$CDM plus tensor mode cosmological model, and \begin{equation}\label{eq:BICEP2-2} r _T = 0.16^{+0.06}_{-0.05} \end{equation} after foreground subtraction based on dust models. This implies that the energy scale of inflation is high and the inflation potential would belong to the so-called large field model, where an inflaton takes a super-Planckian field value, such as chaotic inflation~\cite{Linde:1983gd,ChaoticAfterBicep}. However, it is non-trivial to control a flat potential with a super-Planckian field value. An axion is one of the interesting candidates for inflaton fields, because it has a shift symmetry and its potential would be flat for a super-Planckian field value. In this sense, the so-called natural inflation~\cite{Freese:1990rb} is interesting, and when studied in light of the BICEP2 data~\cite{NaturalAfterBicep}. Furthermore, axion monodromy inflation \cite{Silverstein:2008sg,McAllister:2008hb,Flauger:2009ab} has been proposed as an axion inflation model within the framework of low-energy effective field theory derived from superstring theory (see also \cite{Kaloper:2008fb}).\footnote{ For a review, see \cite{Baumann:2014nda}, and also for recent works \cite{recentwork}.} While in natural inflation the potential form is a sinusoidal function, in a simple axion monodromy model the potential is a linear function of the inflaton, $V=a\phi$.\footnote{ The potential $V=a \phi^r$ with $r$ being a fractional number is also possible. In addition, such a potential can be also derived by field-theoretical strong dynamics~\cite{Harigaya:2012pg} or by non-canonical kinetic terms~\cite{HMLee}.} Axion monodromy inflation with the linear potential is compatible with the data. However, if we examine it in detail, there are a few issues. One is that the linear potential inflation predicts the scalar spectral index $n_s \sim 0.96$ as indicated by PLANCK~\cite{Ade:2013zuv} and $r_T \sim 0.08$. The predicted $r_T$ looks a bit too small compared with BICEP2 results even if we compare with Eq.~(\ref{eq:BICEP2-2}). Another is a tension between BICEP2 and PLANCK, which is a problem not only for this particular model but for most inflation models. BICEP2 reported a somewhat larger tensor-to-scalar ratio than the upper bound $r_T < 0.11$ obtained by PLANCK. As is pointed out in Ref.~\cite{Ade:2014xna}, the tension can be relaxed if the running of the scalar spectral index, $\alpha_s$, is negatively large as $\alpha_s \sim -$(0.02-0.03) \cite{Ade:2013zuv} (see also \cite{Li:2014cka}). In this paper, we study the inflation model driven by the linear potential derived from the axion monodromy inflation model, taking a correction term for non-perturbative effects into account. That is, non-perturbative effects would generate a correction term for the axion in the potential, whose form is the sinusoidal function. Such a correction was mentioned in Ref.~\cite{McAllister:2008hb}, but it has been neglected because it is subdominant in the potential. However, we point out non-negligible contributions by the correction term in derivatives of the potential.\footnote{ See also \cite{Kobayashi:2010pz}, where the same potential was used to explain WMAP seven-year data with $n_s \sim 1.03$ and $\alpha_s \sim -0.03$ without considering tensor-to-scalar ratio.} Since the slow roll parameters are expressed in terms of the derivatives of the potential, the resultant correction in the slow roll parameters is quite important in the evaluation of the inflationary observables. Thus, we study the inflation potential with the linear term and sinusoidal term. Our purpose is two-fold, and we study two scenarios for each of these. First, we point out that the sinusoidal correction term increases the predicted $r_T$ to as much as 0.1-0.15 for the number of e-folds $N=$ 50-60, which corresponds to the cosmological scale $k_* = 0.002\, {\rm Mpc}^{-1}$. This size of $r_T$ is within the range of Eq.~(\ref{eq:BICEP2-2}) as reported by BICEP2. We estimate observables $n_s$, $r_T$, and $\alpha_s$ for several parameter sets in our model. Next, we study the case where $r_T \simeq$ 0.1-0.2 and the tension between BICEP2 and PLANCK is resolved by a large negative running $\alpha_s$. The sinusoidal correction term can induce negative running by its potential derivatives; however, the size is not enough as long as we assume that both the horizon and the flatness problem are solved only by this axion monodromy inflation. On the other hand, if we regard this monodromy inflation as the first stage in the double inflation scenario~\cite{DoubleInflation} followed by another inflation, we can obtain favored values of the observables $(n_s,r_T,\alpha_s) \sim (0.96, 0.15,-0.02)$. In a previous work, this kind of possibility was studied by two of the present authors (T. K. and O. S.) in the context of the supersymmetric hybrid inflation model~\cite{Kobayashi:2014rla}.\footnote{ A large $r_T$ from double inflation was also studied in Ref.~\cite{Choi:2014aca}.} Our paper is organized as follows. In Sect. II, we explain our model explicitly. In Sect. III, we study observables derived from our model in both the single and double inflation scenarios. Section IV is devoted to conclusion and discussion. | We have studied axion monodromy inflation with a sinusoidal correction term. We find the sinusoidal correction term is important in estimating inflationary observables; in fact, $n_s$ and $r_T$ are significantly affected by the correction. We have shown that a larger tensor-to-scalar ratio compatible with the recent BICEP2 results can be obtained in both the single and double inflation scenarios. A large negative running of the spectral index can be realized in the double inflation scenario, whose first stage is driven by our monodromy inflation model with sinusoidal correction term. | 14 | 4 | 1404.5518 |
1404 | 1404.7037_arXiv.txt | { We present an analysis of the metallicity and star formation activities of H\,{\sc ii} regions in the interacting system Arp 86, based on the first scientific observation of the multi-object spectroscopy on the 2.16m Telescope at Xinglong Observatory. We find that the oxygen abundance gradient in Arp 86 is flatter than that in normal disk galaxies, which confirms that gas inflows caused by tidal forces during encounters can flatten the metallicity distributions in galaxies. The companion galaxy NGC 7752 is currently experiencing a galaxy-wide starburst with higher surface density of star formation rate than the main galaxy NGC 7753, which can be explained that the companion galaxy is more susceptible to the effects of interaction than the primary. We also find that the galaxy 2MASX J23470758+2926531 has similar abundance and star formation properties to NGC 7753, and may be a part of the Arp 86 system. | Gravitational interactions and mergers play a major role in galaxy evolution, drastically modifying both their morphology and star formation activities \citep{Barnes1992, Hopkins2010}. Detailed investigations of individual interacting galaxies can provide important information about the physics of the encounter, including the enhancement or suppression of star formation (SF), as well as hydrodynamical processes \citep{Struck2003}. The metallicity distribution and the properties of stellar populations in galaxies are important to understand the physical processes in the formation and evolution of galaxies and have been studied by many authors \citep[e.g.,][]{Wu2005b, Zhou2011}. Extragalactic H\,{\sc ii} regions represent perfect laboratories for deriving physical properties of gaseous nebulae and stars clusters across the surface of nearby galaxies \citep{Osterbrock06}. Their characteristic emission-line spectra have been extensively used to probe the stellar populations and chemical composition of local star-forming galaxies, which can provide observational tests for the mechanisms of galaxy evolution \citep{Bresolin2012, LiFabio2013}. Thanks to the multi-object spectroscopy (MOS), which offers the possibility of obtaining spectra of tens to hundreds objects simultaneously. The development of MOS instruments at ground-based telescopes provides an opportunity to derive physical properties of interacting galaxies using optical spectra of the associated ionized gas. In the current study, we present spectroscopic observations of an interacting system Arp 86 with the help of MOS, to probe the metallicity, star formation rates(SFRs) and stellar populations of its H\,{\sc ii} regions, in an attempt to study the impact of interacting on the evolution of galaxies. Arp 86 is an interacting galaxy pair resembling M51 system with a redshift of {\it z} $\sim$ 0.0162 from the NASA/IPAC Extragalactic Database (NED). The galaxy pair consists of a grand-design galaxy NGC 7753, and a small companion NGC 7752. NGC 7753 is a SAB galaxy with the radii R$_{25} \sim$ 1 arcmin (corresponding to 20 kpc), which is defined by the isophote at the brightness of 25 mag/arcsec$^2$ in the B-band. A tidal bridge connecting two galaxies is found in optical images and active star formation is lying in two galaxies and the bridge \citep{Laurikainen1993}. The infrared luminosities (8 -- 1000 $\mu$m) of Arp 86 is $10^{11.01} L_\odot$ \citep{Sanders2003}, indicating that it is a luminous infrared galaxy (LIRG) system. Radio continuum observations show a complex distribution of H{\sc i} tails and bridges due to tidal interactions \citep{Sengupta2009}. H{\sc i} maps show that the compact dwarf galaxy 2MASX J23470758+2926531 lying in the southeast of Arp 86 may also be a part of this system \citep{Sengupta2009}. The layout of this article is as follows: in Section~\ref{sec2} we introduce the selection of target star-forming regions for spectra, together with a description of the observations and data reduction procedures. In Section~\ref{sec3} we present and analyze the observational results, including dust extinction, excitation properties, metallicities, and star formation activities. The results are discussed and interpreted in Section~\ref{sec4}, and then summarized in Section~\ref{sec5}. | \label{sec4} In the previous section we mainly illustrated the properties of abundances and star formation activities in the interacting galaxy pair Arp 86. The slope of the abundance gradient in the inner disk of NGC 7753 is less than 0.1 dex $R_{25}^{-1}$ along with a much shallower slope in the outer disk and tidal bridge. H\,{\sc ii} regions in NGC 7752 have higher SFRs than those in NGC 7753, one order of magnitude higher in common. The stellar populations in NGC 7752 are in the age of $\sim$ 10 -- 100 Myr. These evidences indicate that more active star formation is ongoing in the companion galaxy than in the main galaxy. These results provide solid evidence that galaxy interactions play an important role in modifying the metallicity properties and star formation activities of galaxies. Simulations indicate that tidal forces during encounters can cause large-scale gas inflows in galaxies \citep{Barnes1996}, which can flatten the metallicity distributions \citep{Rupke2010}. \citet{Kewley2006} proposed a scenario in which galaxy interactions drive large gas inflows toward the central regions, less enriched gas is carried from the outskirts of the galaxy into the central regions, disrupting metallicity gradients, and diluting central metallicities. Consistently with these models, our results from Figure~\ref{fig5} show a very flatting abundance gradient with the slope of 0.09 $\pm$ 0.04 dex $R_{25}^{-1}$ in the inner disk of the main galaxy, which is corresponding to $\sim$ 0.005 dex kpc$^{-1}$. The slope is one order of magnitude lower than the typical values of 0.03--0.10 dex kpc$^{-1}$ in normal spiral galaxies, such as NGC 628 \citep{Gusev2013}, NGC 3621 \citep{Bresolin2012}, M33 \citep{Bresolin2011}, M101 \citep{Lin2013}. Their observational results provide similar evidences. \citet{Kewley2010} systematically studied a sample of close galaxy pairs and found that the mean gradient in their galaxy pairs is -0.25 dex $R_{25}^{-1}$ compared with a mean gradient of -0.67 dex $R_{25}^{-1}$ for the isolated spiral galaxies, and proved galaxy pairs have flatter metallicity gradients due to large tidal gas inflows in galaxy interactions and mergers. Interaction-induced star formation has also been investigated by observations and models. In many sample and case studies, ultraviolet, H$\alpha$ and infrared images show enhanced star formation activities in interacting systems \citep[e.g.,][]{Cao2007,Smith2007}. The simulations of Cox et al. (2008) found merger-driven star formation is a strong function of merger mass ratio, and the less massive companion is expected to be more susceptible to tidal forces and may have a larger enhancement of star formation. In our results, Figure~\ref{fig6} and \ref{fig7} show the same trend, where the SFRs of H\,{\sc ii} regions are one order of magnitude higher in NGC 7752 than in the main galaxy NGC 7753. Such evidences are also found in NGC 7771+NGC 7770 interacting system \citep{Alonso2012} and statistics based on Sloan Digital Sky Survey Data \citep{Woods2007}. Beside NGC 7753 and 7752, the galaxy 2MASX J23470758+2926531 may be a part of the Arp 86 system. This galaxy is visible in the GALEX UV images \citep{Smith2010}, along with many optical images. \citet{Sengupta2009} estimated the stellar mass and H\,{\sc ii} mass of this galaxy, and found they are 2.9 $\times 10^9 M_{\odot}$ and 4.5 $\times 10^8 M_{\odot}$, respectively. HI column density image shows an connection between NGC 7752 and 2MASX J23470758+2926531 \citep{Sengupta2009}. We also obtained the spectra of 2MASX J23470758+2926531, and found its redshift $z = 0.0166 \pm 0.0003$, similar to Arp 86 (z $\sim$ 0.0162). It is located at the composite region in the BPT diagram, the $\Sigma_{SFR}$ is $\sim$ 0.027 $M_{\odot}yr^{-1}kpc^{-1}$, and the oxygen abundance is similar to most of regions in NGC 7753, which prove that 2MASX J23470758+2926531 is an companion of NGC 7753. | 14 | 4 | 1404.7037 |
1404 | 1404.0617_arXiv.txt | We search for the Fe ${\rm K\alpha}$ line in spectra of Ultra Compact X-ray Binaries (UCXBs). For this purpose we have analyzed {\it XMM-Newton} observations of five confirmed UCXBs. We find that the object 2S 0918-549 -- whose optical spectrum bears tentative signatures of a C/O accretion disk -- is devoid of any emission features in the 6-7\,keV range, with an upper limit of less than 10\,eV for the equivalent width (EW) of the iron line. 4U 1916-05 -- whose optical spectrum is consistent with reflection from a He-rich accretion disk -- exhibits a bright broad iron emission line. This behavior is in agreement with the theoretical predictions presented in \cite{2013MNRAS.432.1264K}. Namely, we expect strong suppression of the Fe ${\rm K\alpha}$ emission line in spectra originating in moderately bright ($\rm LogL_x$ less than $\approx 37.5$) UCXBs with C/O or O/Ne/Mg-rich donors. On the other hand the EW of the iron line in spectra from UCXBs with He-rich donors is expected to retain its nominal value of ${\rm \approx 100\,eV}$. Our analysis also reveals a strong Fe ${\rm K\alpha}$ line in the spectrum of 4U 0614+091. This detection points towards a He-rich donor and seems to be at odds with the source's classification as C/O-rich. Nevertheless, a He-rich donor would explain the bursting activity reported for this system. Lastly, based on our theoretical predictions, we attribute the lack of a strong iron emission line -- in the two remaining UCXB sources in our sample (XTE J1807-294, 4U 0513-40) -- as an indication of a C/O or O/Ne/Mg white dwarf donor. From the upper limits of the Fe ${\rm K\alpha}$ line EW in 4U 0513-40, 2S 0918-549 and XTE J1807-294 we obtain a lower limit on the oxygen-to-iron ratio, O/Fe$\ge10\times{\rm[O/Fe]_{\odot}}$. | Low mass X-ray binaries (LMXBs) with orbital periods of less than one hour are known as ultra-compact X-ray binaries. Their short orbital periods imply orbits that are so tight that only an evolved compact donor could fit (e.g. \citealt{1984ApJ...283..232R}; \citealt*{1986ApJ...311..226N}). Therefore, they must consist of a white dwarf or a helium star that has filled its Roche lobe and is accreting onto a neutron star \citep*[e.g.][]{1993ARep...37..411T, 1995ApJS..100..233I, 1995xrbi.nasa..457V, 2003ApJ...598.1217D, 2005ApJ...624..934D}. X-ray radiation from LMXBs usually consists of a primary and a reflected component \citep[e.g.][and references therein]{2010LNP...794...17G}. Primary radiation is most likely created in a hot optically thin corona, the disk itself or -- in the case of a neutron star accretor -- in the boundary layer that forms on the surface of the star. The reflected component is produced when primary radiation is reprocessed by the optically thick Shakura - Sunyaev accretion disk and by the surface of the donor star facing the compact object. X-ray reflection spectra originating in normal LMXBs with main sequence or red giant donors are characterized by a bright iron $\rm K{\rm\alpha}$ emission line at $\approx 6.4-6.9$\,keV with an equivalent width (EW) typically of the order of $\approx100$\,eV \citep[e.g.][]{2010ApJ...720..205C}. The composition of the accreting material in UCXBs is expected to be significantly different from the solar composition accretion disks of typical LMXBs with main sequence or red giant donors. Due to the nature of their compact donor, their chemical composition is expected to be consistent with the ashes of H burning (mostly He and $\rm ^{14}N$), He burning (mostly C/O) or carbon burning (mostly O/Ne). Depending on initial parameters and the environment (e.g. being part of a globular cluster) of UCXB progenitors they will follow different evolutionary channels, resulting in a variety of donors ranging from non-degenerate He stars to C-O or O-Ne-Mg white dwarfs \citep*[e.g.][]{1986A&A...155...51S,2002ApJ...565.1107P,2002A&A...388..546Y, 2004ApJ...607L.119B}. Due to the fact that the different UCXB formation channels lead to degenerate donors of similar mass, determining the chemical composition of the disk (and therefore the donor star) in UCXBs can provide valuable insights into the evolutionary path that created each system. In principle, a straight forward determination of the chemical composition of the disk and donor star in these systems could be achieved using optical spectroscopy. A He-rich object could be identified by the presence of strong He lines in its spectrum \citep[e.g][]{2006MNRAS.370..255N}, while a C/O-rich object can be inferred by the lack of H and He lines combined with the presence of strong C and O lines \citep[e.g.][]{2004MNRAS.348L...7N, 2006A&A...450..725W}. However, due to their small sized accretion disks \citep{1994A&A...290..133V} the optical counterparts of UCXBs are quite faint, with V-band absolute magnitudes that are usually larger than $\approx$5 with distances ranging from $\approx$3-12\,kpc \citep[e.g.][]{2004MNRAS.348L...7N, 2006MNRAS.370..255N}. Therefore, ensuring definitive proof of the donor star composition -- using optical spectroscopy -- is a difficult task that can only be attempted using the latest generation of $>$8m telescopes. In the case of X-ray spectroscopy the presence of O and Ne emission features -- that appear in the spectra of reprocessed emission from the accretion disk and white dwarf surface -- \cite[e.g.][]{2010MNRAS.407L..11M} and K-edges stemming from absorbing material in the vicinity of the disk \cite[e.g.][]{2010ApJ...725.2417S} could also provide direct indication of a C/O or O/Ne-rich disk and donor star. However, due to increased interstellar absorption below 1\,keV and contamination of the reflected component by the primary emission, detection of these features with sufficient accuracy, often proves to be difficult. On the other hand, in \cite{2013MNRAS.432.1264K}, we demonstrated that the most striking and readily observable consequence of an anomalous C/O abundance involves the iron $\rm K{\rm\alpha}$ line located at 6.4\,keV. In particular, for a source of moderate luminosity (${\rm L}\rm_X\lesssim$ a few $10^{37}\rm erg\,s^{-1}$) we predicted a strong suppression of the Fe $\rm K{\rm\alpha}$ line in the case of a C/O or O/Ne/Mg WD donor. This translates to a more than an order of magnitude decrease of the EW of the line. On the other hand, in the case of a He-rich donor the iron line is expected to remain unaffected with its EW similar to that observed in LMXBs with main sequence or red giant donors. As was demonstrated in Koliopanos et al. these results are luminosity dependent. Namely, for luminosities exceeding $\rm LogL\rm_X\approx 37.5 $, we expect C, O and Ne to be fully ionized in the inner parts of the disk and thus canceling their screening effect on the iron line. In addition to spectroscopic analysis, one could indirectly infer the accretion disk and donor star composition by studying a system's bursting activity. Gradual accumulation of H and/or He on the surface of an accreting neutron star can eventually result in the ignition of the accumulated shell, producing a thermonuclear flash that is known as a type I X-ray burst (e.g. \citealt{1976ApJ...205L.127G}; \citealt{1975ApJ...195..735H} and for a detailed review \citealt{2006csxs.book..113S}). Half of the total population of known UCXBs have exhibited bursting activity, ranging from a few sporadic bursts to frequent bursting activity with a recurrence time extending from a few hours to a few weeks. Sporadic bursts could be due to trace amounts of H and He in an otherwise C/O-rich accreted material. Frequent bursting activity, on the other hand, would require copious amounts of H and/or He to refuel the bursts. Consequently, such an activity would support arguments in favor of a He-rich donor in a particular UCXB. This is illustrated by the detection of frequent burster \citep{2008ApJS..179..360G} 4U 1916-05 (discussed in this paper) which is also an optically confirmed He-rich source \citep{2006MNRAS.370..255N}. On other hand the same approach can yield conflicting results as is the case of 4U 0614+091 (also discussed in this work) whose bursting activity \citep{2010A&A...514A..65K, 2012ApJ...760..133L} seems to be inconsistent with the strong evidence in favor of a C/O-rich donor \citep{2004MNRAS.348L...7N, 2006A&A...450..725W}. In the present paper we investigate the chemical composition of the accretion disk in five UCXBs using X-ray spectroscopy. In particular we analyze {\it XMM-Newton} spectra of these sources and compare our results with the findings of Koliopanos et al. in order to put a constraint on the chemical composition of their accretion disks and donor star. We also analyze the spectra of two normal LMXBs, which we use as a control sample. In Section 2 we present the sample of UCXBs and LMXBs chosen for our analysis. We describe the details of data extraction, report on the specifics of each observation and present our data analysis where we look for the existence and strength of a potential iron $\rm K{\rm\alpha}$ line at $\approx 6.4$\,keV. The analysis is followed by discussion and conclusions in Sections 3 and 4. | We searched for the iron ${\rm K\alpha}$ in the spectra of five UCXBs with H-deficient donors. Based on the non-detection of a Fe line and the predictions of \cite{2013MNRAS.432.1264K}, we have concluded that the accretion disk material of three of the objects in our sample (2S 0918-549, XTE J1807-294 and 4U 0513-40) has an O/Fe ratio that is at least $\approx$10\,times higher than the solar value. In the context of UCXBs this suggests a C/O or O/Ne/Mg-rich donor. Furthermore, the presence of a strong Fe ${\rm K\alpha}$ line in the spectra of the remaining two systems (4U 0614+091 and 4U 1916-05) indicates a He-rich donor. In the case of 2S 0918-549 and 4U 1916-05 our findings are also supported by results obtained through optical spectroscopy. On the other hand, our suggestion of a He-rich donor in 4U 0614+091 contradicts arguments in favor of a C/O-rich donor, but is consistent with the source's regular bursting activity. | 14 | 4 | 1404.0617 |
1404 | 1404.3564_arXiv.txt | The ANAIS (Annual modulation with NaI(Tl) Scintillators) experiment aims at the confirmation of the DAMA/LIBRA signal using the same target and technique at the Canfranc Underground Laboratory (LSC). 250\,kg of ultra pure NaI(Tl) crystals will be used as target, divided into 20 modules, 12.5\,kg mass each, and coupled to two high efficiency photomultiplier tubes from Hamamatsu. The ANAIS-25 set-up at the LSC consists of two prototypes, amounting 25\,kg NaI(Tl), grown from a powder having a potassium level under the limit of our analytical techniques, and installed in a convenient shielding at the LSC. The background has been carefully analyzed and main results will be summarized in this paper, focusing on the alpha contamination identified in the prototypes and the related background contributions. Status of fulfillment of ANAIS experimental goals and prospects for the building of ANAIS-250 experiment will be also revised. | \label{sec:intro} ANAIS project aims at the study of the annual modulation signal attributed to galactic dark matter particles\,\cite{annual_modulation} using 250\,kg NaI(Tl) at the Canfranc Underground Laboratory (LSC), in Spain. The DAMA experiment, at the Laboratori Nazionali del Gran Sasso, in Italy, reported first evidence of the presence of an annual modulation in the detection rate compatible with that expected for a dark matter signal, just in the region below 6\,keVee (electron equivalent energy) with a high statistical significance\,\cite{DAMA}. This signal was further confirmed by the LIBRA experiment, using 250\,kg of more radiopure NaI(Tl) detectors\,\cite{LIBRA}. Using the same target than DAMA/LIBRA experiment makes possible for ANAIS to confirm such a result in a model independent way. To achieve this goal, ANAIS detectors should be as good (or better) as (than) those of DAMA/LIBRA in terms of energy threshold and radioactive background below 10\,keVee: energy threshold below 2\,keVee and background at 1-2\,counts/keV/kg/day. After the operation of several prototypes at the LSC\,\cite{ANAIS_prototypes, ANAISbkg, ANAIS_RICAP}, the main challenge for ANAIS is the achievement of the required low background level, being contaminations in the bulk of the crystal still dominant in the background. However, backgrounds at low, medium and high energy are quite well understood, as shown with ANAIS-0 prototype\,\cite{ANAISbkg} and some other interesting results, as very slow scintillation in NaI(Tl)\,\cite{ANAISom} or an anomalous fast event population attributable to quartz scintillation\,\cite{ANAISquartz} have been obtained. In the following, we will report on the main results derived from the ANAIS-25 prototypes concerning background level and analysis of the dominant contributions (Section\,\ref{sec:bck}), light collection efficiency and energy threshold (Section\,\ref{sec:yield}). Before, we will briefly describe the experimental setup (Section\,\ref{sec:setup}) and, finally, prospects for the building of ANAIS-250 will be revised (Section\,\ref{sec:prospects}). | 14 | 4 | 1404.3564 |
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1404 | 1404.3087_arXiv.txt | Motivated by consideration of the solar tachocline, we derive, via an asymptotic procedure, a new set of equations incorporating velocity shear and magnetic buoyancy into the Boussinesq approximation. We demonstrate, by increasing the magnetic field scale height, how these equations are linked to the magneto-Boussinesq equations of Spiegel and Weiss (1982). \begin{keywords}Boussinesq approximation, magnetic buoyancy, velocity shear, solar tachocline \end{keywords} | } Instabilities driven by magnetic buoyancy have been studied over a number of years, with particular emphasis given to their role in disrupting a strong, predominantly toroidal magnetic field in the solar interior \citep[see, for example, the review by][]{Hughes_2007}. For a variety of (essentially unrelated) reasons, it has been suggested that the bulk of the Sun's magnetic field is stored at the base of, or just below, the convection zone. From estimates of the rise times of magnetic flux tubes through the convection zone, \citet{Parker_1975} argued that it would be difficult to confine the magnetic field for times comparable with the solar cycle period unless the dynamo operated only in the `very lowest levels of the convective zone'. \citet{Golub_etal_1981} \citep[see also][]{SW_1980} proposed a similarly deep-seated layer of toroidal field, but from arguments based instead on the expulsion of magnetic fields by convective motions. Perhaps the most compelling evidence for pinning down the location of the solar toroidal field comes from the discovery, by helioseismology, of the solar tachocline, a thin region of strong radial and latitudinal velocity shear, sandwiched between the convective and radiative zones \citep{Schou_etal_1998}. Although there is little consensus on exactly how the solar dynamo operates, it is generally agreed that toroidal field is wound up from a relatively weak poloidal ingredient via strong differential rotation (the $\omega$-effect of mean field dynamo theory). Consequently, the tachocline becomes the natural location for a deep-seated, predominantly toroidal magnetic field. Given this, it is natural to seek to build upon previous studies of magnetic buoyancy instabilities by incorporating the effects of a velocity shear. Using the energy principle, \citet{TH_2004}, extending the results of \citet{Adam_1978}, obtained necessary conditions for the ideal (diffusionless) linear instability of a magnetohydrodynamic (MHD) state with aligned horizontal flow and magnetic field, each stratified arbitrarily in the vertical direction. From a different perspective, \citet{VB_2008} considered the fully nonlinear evolution of magnetic buoyancy instabilities in a magnetic layer generated through the stretching of an initially vertical magnetic field by a horizontal, depth-dependent shear flow. Instability due to magnetic buoyancy is an inherently compressible phenomenon, with the magnetic pressure playing the crucial role in reducing the local density of the gas. Thus, most studies of the instability have employed the equations of fully compressible MHD. However, just as convection of a compressible fluid can, under certain circumstances, be treated within the almost-incompressible Boussinesq approximation \citep{SV_1960}, so can magnetic buoyancy be incorporated into a similar magneto-Boussinesq approximation (Spiegel and Weiss 1982; hereinafter SW82). Such approximations afford a simplification of the governing equations and thus aid both theoretical and numerical analysis. Our aim in this paper is to incorporate the effects of a velocity shear into the magneto-Boussinesq equations, self-consistently and in such a way that the influence of the shear is comparable with that of the magnetic buoyancy instability. The equations of the Boussinesq approximation for a compressible fluid were derived in the classic paper of \citet{SV_1960}, who considered thermal convection of a layer of fluid subject to two important assumptions: the first is that the depth of the fluid layer is much smaller than the scale height of any thermodynamic quantity; the second is that motion-induced fluctuations in density, temperature and pressure do not exceed their static variation. The first assumption is a statement about the basic state, the second is an eminently reasonable supposition that can be verified \textit{a posteriori}. Under these assumptions, the governing equations simplify considerably. In particular, the fluid is treated as incompressible, with density variations neglected except in the buoyancy term in the equation of motion; furthermore, fluctuations in the pressure are small --- a reflection of the low Mach number --- and thus density variations are directly proportional to variations in temperature. For problems such as magnetoconvection, magnetic fields can be incorporated into the Boussinesq approximation in a straightforward manner \citep[see, for example,][]{PW_1982}. The field enters through the induction equation and via the Lorentz force in the momentum equation; variations in magnetic pressure are assumed to have no influence on density fluctuations. Including the effects of magnetic buoyancy is however a more subtle procedure. SW82 considered the problem of the instability of a stratified, horizontal magnetic field with scale height $H_B$ very large compared with the layer depth $d$. The crucial ordering is now one in which variations in the \textit{total} pressure (gas $+$ magnetic) are small; this has implications for all the governing equations. In the momentum equation, density fluctuations are related to variations in both the temperature and the magnetic pressure; similarly, variations in magnetic pressure enter into the energy equation. The velocity is, to leading order, incompressible. However, it becomes necessary to include the next order correction to $\bmnabla {\bm \cdot} \bmu$ in the induction equation; in standard notation this then takes the form \begin{equation} \frac{\partial \bmB}{\partial t} + \bmu {\bm \cdot} \bmnabla \bmB = \bmB {\bm \cdot} \bmnabla \bmu - \frac{w}{H_\rho} \bmB + \eta \nabla^2 \bmB, \end{equation} where $H_\rho$ is the density scale height of the basic state. The final, and extremely important feature to note is that within the magneto-Boussinesq approximation, magnetic buoyancy is relevant only for modes of a certain horizontal scale. In particular, when considering the stability of an equilibrium state with a unidirectional horizontal field, magnetic buoyancy is of significance for perturbations with a long ($\Orm (H_B)$) length scale in the direction of the imposed field. One consequence of this is that the magnetic field is not exactly solenoidal; $\bmnabla {\bm \cdot} \bmB = 0$ only to $\Orm (d/H_B)$, an approximation that is however consistent with the overall level of approximation introduced in the magneto-Boussinesq approximation. In an approach complementary to that of SW82, Corfield (1984) (hereinafter C84) re-derived the magneto-Boussinesq equations through a formal scaling analysis, expanding all variables in terms of the two small parameters of the system: $d/H$, where $H$ denotes any of the scale heights (all comparable), and $\delta \rho/\rho_0$, the ratio of fluctuations in density to a representative value. Our aim in this paper is to incorporate the effects of a shear flow into the magneto-Boussinesq approximation. As explained in Appendix~\ref{ap:noshear}, if this is done in what might be considered the obvious fashion --- namely with the shear flow of the same order as the velocity perturbations in Corfield's ordering --- then the influence of the shear has no bearing on the onset of instability. Thus, in order to consider a regime in which a shear flow may interact with the magnetic buoyancy instability, it becomes necessary to consider in some detail the magnitudes of the imposed magnetic field and the velocity shear flow, together with their gradients, as well as the horizontal scale of the perturbations. In section~\ref{sec2} we present a derivation of the scalings inherent to the magneto-Boussinesq approximation in the absence of an imposed shear flow; the derivation is along similar lines to that of \citet{Corfield_1984}, though we are more explicit in stating the underlying physical assumptions. In section~\ref{sec3} we explore the orderings of the imposed shear flow and magnetic field that are necessary in order to accommodate the effects of magnetic buoyancy and velocity shear on the same footing. Following this, section~\ref{sec4_1} contains the main result of the paper, the derivation of asymptotically consistent magneto-Boussinesq equations incorporating velocity shear; the crucial differences with the equations of C84 are discussed in section~\ref{sec4_2}. In section~\ref{sec5} we explore these differences systematically by explaining how the various scalings change with the magnitude of the magnetic field scale height, thus providing a transition between the equations of \citet{Corfield_1984} and our new set of equations. The concluding discussion is contained in section~\ref{sec6}. | } The principal result of this paper is the derivation of a new set of MHD equations governing the evolution of magnetic buoyancy instabilities in the magneto-Boussinesq approximation and in the presence of a horizontal, depth-dependent shear flow. The equations are derived via an expansion procedure in two small parameters: $\ep$, the ratio of the layer depth to the pressure scale height, and $\ept$, the ratio of the square of the Alfv\'en speed to the square of the sound speed. Section~\ref{sec2}, which follows the treatment of \citet{Corfield_1984} to a certain extent, lays the foundations for the magneto-Boussinesq orderings in general, without specific reference to the incorporation of any shear flow. Unlike \citet{Corfield_1984} however, we make no assumption about the magnetic field scale height; as a result, all the orderings are valid for $d \lesssim H_B \lesssim H_p$. Section~\ref{sec3}, with reference to Appendix~\ref{ap:noshear}, describes how the na\"{i}ve incorporation of a shear flow into the equations of \citet{SW_1982} and \citet{Corfield_1984} (i.e.\ with $H_B \sim H_p$) has no influence on the linear stability problem. In order that the shear flow assumes a non-trivial role in the magnetic buoyancy instability, two conditions must be met: that $H_U$ is $\mathrm{O}(d)$ and that $U_*^2 \sim c_A^2$. For consistency with the scalings determined in section~\ref{sec2}, it follows that $H_B$ must also be $\Orm(d)$. The various orderings derived in sections~\ref{sec2} and \ref{sec3} are applied to the full MHD governing equations in section~\ref{sec4}, yielding the leading order equations~\eqref{eq:new}. Interestingly, equations~\eqref{eq:new} also allow us to examine the effects of magnetic buoyancy for a magnetic field with an $\mathrm{O} (d)$ scale height in the absence of velocity shear, a scenario that is excluded from the equations of \citet{Corfield_1984}, as identified by \citet{Hughes_1985}. The transformation between equations~\eqref{eq:new} and those of \citet{SW_1982} and \citet{Corfield_1984} can be effected by increasing the magnetic field scale height from $\mathrm{O}(d)$ to $\mathrm{O}(H_p)$. Section~\ref{sec5} describes the resulting changes in the governing equations, identifying three different regimes, each with their own set of equations: $H_B \sim d$ (equations~\eqref{eq:new}), $H_B \sim H_p$ (\citet{SW_1982} and \citet{Corfield_1984}) and a third, intermediate regime. Finally, it is important to consider the implications of our study to the solar tachocline, and, in particular, to examine the parameter regimes in which the set of equations~\eqref{eq:new} is expected to hold. Let us first consider the magnitudes of the two small quantities in our asymptotic expansions, $\ep$ and $\ept$. The pressure scale height in the tachocline $\approx 0.08 R_\odot$ \citep{Gough_2007}. Estimates of the vertical extent of the tachocline vary a little, according to how it is defined \citep[see, for example,][]{Miesch_2005}, but lie in the range between $0.02 R_\odot$ and $0.05 R_\odot$. Thus $\ep = d/H_p$ is certainly less than unity, but is not particularly small. As for the ratio $\ept$, this is $\mathrm{O} \left( 10^3 / B_*^2 \right)$, where $B_*$ is measured in Gauss \citep{Ossendrijver_2003}. Estimates of the mean toroidal field strength in the tachocline result solely from theoretical considerations, and vary between $10^3 \Grm$ and $10^5 \Grm$, depending on the theoretical assumptions involved; this certainly makes $\ept$ small, in the range $10^{-7} \lesssim \ept \lesssim 10^{-3}$. Given that the magnitudes of $\ep$ and $\ept$ for the tachocline suggest, at least \textit{a priori}, that a magneto-Boussinesq approach is appropriate, we nonetheless need to examine whether the tachocline shear flow inferred from helioseismology is \textit{influential} in the sense of equations~\eqref{eq:HUd} and \eqref{eq:U_cA}. Equation~\eqref{eq:HUd} specifies that $H_U \sim d$; this is true of the tachocline, almost by definition. Expression~\eqref{eq:U_cA} requires that $U_*$ be comparable with the Alfv\'en speed $c_A$. Since we have a good estimate of $U_*$ from helioseismological inversions, but no direct knowledge of the magnetic field strength $B_*$, it makes more sense to look at this from the other perspective and to ask what values of $B_*$ will allow \eqref{eq:U_cA} to be satisfied. From the helioseismological results of \citet{Schou_etal_1998}, the jump in the angular velocity across the tachocline (at the equator) is of the order of 20 nHz, which translates into $U_* \approx 30 \mathrm{ms}^{-1}$. Requiring $c_A \sim U_*$ determines the characteristic magnetic field strength as $B_* \approx 10^3 \Grm$. Thus everything ties together very nicely, suggesting that equations~\eqref{eq:new} form an appropriate system for the study of magnetic buoyancy instabilities in the tachocline. \medskip \noindent \textbf{Acknowledgements} \smallskip \noindent JAB was supported by an STFC studentship; DWH and EK were supported by the STFC Consolidated Grant ST/K000853/1. | 14 | 4 | 1404.3087 |
1404 | 1404.1928_arXiv.txt | We consider the time derivatives of the period $P$ of pulsars at the Galactic Center due to variations in their orbital Doppler shifts. We show that in conjunction with a measurement of a pulsar's proper motion and its projected separation from the supermassive black hole, Sgr A*,measuring two of the three derivatives $\dot{P}$, $\ddot{P}$, or $\dddot{P}$ sets a constraint that allows for the recovery of the complete six phase space coordinates of the pulsar's orbit, as well as the enclosed mass within the orbit. Thus, one can use multiple pulsars at different distances from Sgr A* to determine the radial mass distribution of stars and stellar remnants at the Galactic center. Furthermore, we consider the effect of passing stars on the pulsar's period derivatives and show how it can be exploited to measure the characteristic stellar mass in the Galactic Center. | The recent discovery of J1745-2900, a magnetar orbiting the supermassive black hole Sgr A* at a projected separation of $0.09$ pc \citep{b1,c3,c7} stimulated much interest in its timing and astrometry. Pulsars close to Sgr A* could allow for a precise measurement of the black hole's mass and spin, in addition to a host of relativistic effects \citep{c4,c10,c11,c5,c6}. Unfortunately, the timing of the magnetar J1745-2900 is not sufficiently stable for dynamical measurements \citep{kaspi1}. Furthermore, it is located too far from Sgr A* (with a Keplerian orbital period of $\sim 500$ years) for it to be useful as a probe of strong field gravity. Calculations imply that there could be $\sim 200$ pulsars within a parsec from Sgr A* \citep{b6}, although perhaps only $\sim20$ of them being bright enough to be detected \citep{dexter}. Most of these pulsars might also be located too far from Sgr A* for testing strong field gravity. Nevertheless, one can still use pulsars at these larger distances to probe the astrophysical environment of the Galactic Center. In particular, the orbital dynamics of a pulsar is determined by the mass distribution within its orbit. Therefore, by measuring the imprint of the orbital Doppler effect on the pulsar's period, $P$, one should be able to constrain the radial mass profile of stars and stellar remnants around Sgr A*. A previous study \citep{Gould} considered this possibility, but neglected the contributions of closely passing stars. In this letter, we evaluate the limitations of this technique due to this extra source of uncertainty, and also show that one can constrain the characteristic stellar mass in this environment by measuring the third time derivative of the pulsar's period, $\dddot{P}$. This letter is organized as follows. In \S 2 we discuss the orbital contribution to the first, second, and third period derivatives $\dot{P}$, $\ddot{P}$, and $\dddot{P}$ by the mean field, and discuss how it can be used to measure the mass enclosed within the pulsar's orbit. In \S 3 we calculate the effects of passing stars on the period derivatives, and how it could be used to constrain the characteristic stellar mass in the Galactic Center. | If the pulsar's projected separation from Sgr A*, proper velocity, and line of sight distance are measured, then 5 of the 6 pulsar's phase space coordinates are known. One of the period derivative constraints represented by equations (\ref{eq:pdot}), (\ref{eq:result}), or (\ref{eq:raw3}) can then be used to derive a final constraint on the pulsar's phase space coordinates. Another constraint can be used to limit the mass enclosed within the pulsar's orbit. In this case, the line of sight velocity $v_l=v_l(M)$ depends on $M$ itself. As such, $M(\vec{r}, \vec{v})=M(\vec{r}, \vec{v}_\perp, v_l(M,\vec{r}, \vec{v}_\perp))=M(\vec{r}, \vec{v}_\perp)$. Due to this complicated dependence, an analytic solution is not feasible and the related analysis has to be done numerically. The mass distribution itself can be determined if the above measurements are performed at multiple times for a pulsar on a plunging orbit. However, unless the pulsar is located very close to Sgr A*, the orbital timescale is too long for such a study. Nevertheless, by performing this measurement on multiple pulsars, one would still be able to probe the radial mass distribution. In particular, the difference in the measured $M(r)$'s of two pulsars located at two radial distances determines the mass enclosed in the spherical shell between these radii. This can be used to constrain the distribution of low-mass stars or stellar remnants (black holes, white dwarfs, and neutron stars) that are too faint to be detected directly. An extra source of uncertainty in measuring $M(r)$ comes from the effects of passing stars. These scatter $\ddot{P}$ about the mean field value, and the contribution is large for $r$ greater than $\sim 0.03$ pc. As such, measurements should be taken close to Sgr A*, where they can constrain cumulative mass of stars and stellar remnants surrounding the black hole. Measuring $M(r)$ further away from Sgr A* will require multiple pulsars, and thus be a challenging task. Finally, we note that the scatter of $\dddot{P}$ about the mean field value due to passing stars is affected by the characteristic stelar mass, $m_*$. As such, measurements of $\dddot{P}$ of multiple pulsars at the Galactic Center will allow us to probe the charasteristic mass of stars and remnants in this extreme environment. Such measurements can also place exquisite constraints on the existence of intermediate-mass black holes in the vicinity of Sgr A*. | 14 | 4 | 1404.1928 |
1404 | 1404.4627.txt | { \\ We study gravitational interaction of Higgs boson through the unique dimension-4 operator $\,\xi H^\dag H\mathcal{R}$\,,\, with $\,H\,$ the Higgs doublet and $\,\mathcal{R}\,$ the Ricci scalar curvature. We analyze the effect of this dimensionless nonminimal coupling $\,\xi\,$ on weak gauge boson scattering in both Jordan and Einstein frames. We explicitly establish the longitudinal-Goldstone boson equivalence theorem with nonzero $\xi$ coupling in both frames, and analyze the unitarity constraints. We study the $\xi$-induced weak boson scattering cross sections at ${\cal O}(1-30)$TeV scales, and propose to probe the Higgs-gravity coupling via weak boson scattering experiments at the LHC\,(14\,TeV) and the next generation $pp$ colliders ($50-100$\,TeV). We further extend our study to Higgs inflation, and quantitatively derive the perturbative unitarity bounds via coupled channel analysis, under large field background at the inflation scale. We analyze the unitarity constraints on the parameter space in both the conventional Higgs inflation and the improved models in light of the recent BICEP2 data. } | \label{intro} \vspace*{2mm} The LHC discovery of a Higgs boson ($\sim\! 125$\,GeV) \cite{LHC2012,LHC2013} has begun a new era for particle physics and its interface with cosmology and gravitation research. The Higgs boson plays a distinctive role in the standard model (SM) of particle physics. It is the only fundamental scalar particle in the SM. It spontaneously breaks the electroweak gauge symmetry and provides the origin of inertial masses for all massive particles: weak gauge bosons, quarks, leptons and neutrinos. As measured from the current LHC experiments \cite{LHC2013}, the properties of this 125\,GeV new particle (including its signal strengths in several decay channels and its spin/parity) are still compatible with the SM predictions. However, most of its couplings (especially its Yukawa couplings and self-couplings) have not yet been tested, and possible new physics can cause deviations of these couplings from those of the SM Higgs boson, which will be probed at the upcoming LHC runs and the future $e^+e^-$ and $pp$ colliders \cite{peskin}. Furthermore, the SM is apparently incomplete for not containing the gravitational force, despite all SM particles join in gravitation. Even though the Einstein general relativity (GR) still gives the best description of gravitation, it is a notoriously nonrenormalizable field theory \cite{HV}. Hence, it is compelling to incorporate the SM and GR together as a joint low energy effective theory below the Planck scale, and explore the testable effects from this unavoidable interface. Especially, with the LHC Higgs discovery \cite{LHC2012,LHC2013}, we are strongly motivated to study gravitational interactions of the Higgs boson, because the Higgs boson generates inertial masses for all SM particles while the gravity force arises from their gravitational masses. Such an effective theory always has an ultraviolet (UV) cutoff, at or below the Planck mass. In this formulation, one can write down the most general action under all known symmetries, as a series of effective operators with increasing mass-dimensions and with proper suppressions by the UV cutoff \cite{EFT}. Thus, for the experimentally accessible energy ranges being well below the UV cutoff, the leading terms of this effective action can provide a fairly good approximation of the full theory. In fact, under the $\,U(1)_Y^{}\otimes SU(2)_L^{}\otimes SU(3)_c^{}\,$ gauge symmetries and given the three families of leptons and quarks, the SM Lagrangian is already the most general effective theory up to dimension-4 operators. On the other hand, the Einstein-Hilbert action of general relativity represents the leading terms of mass-dimension zero and two, under the generally covariant expansion, % \bge S_{\text{EH}}^{} ~=~ \Mp^2\int\!\!\di^4x\,\sqrt{-g}\,\Big(\!-\Lambda+\FR{1}{2}\mathcal{R}\Big), \ede % where $\,\Mp=(8\pi G)^{-1/2}\simeq 2.44\times 10^{18}$\,GeV gives the reduced Planck mass, $\,\Lambda$\, denotes the cosmological constant, and $\,\mathcal{R}$\, is the Ricci scalar. One can continue to write down more operators with higher mass-dimensions in this series. Up to dimension-4, we have % \bge S^{}_{\text{G}4} ~=\, \int\!\!\di^4x\,\sqrt{-g}\, \(\,c_1\mathcal{R}^2+c_2\mathcal{R}_{\mu\nu}\mathcal{R}^{\mu\nu}\,\)\,. \ede % There is another possible term $\,\mathcal{R}_{\mu\nu\rh\si}\mathcal{R}^{\mu\nu\rh\si}$\, allowed by the symmetry, but is not independent up to integration by parts. In the GR, the gravitational interactions of matter fields (including all the SM particles) are introduced in the manner of minimal coupling. In this way, the fluctuation of spacetime metric couples to matter fields through the energy-momentum tensor, % \beqa \label{eq:MC} S_{\text{MC}} \,=\, -\int\!\!\di^4x\,\sqrt{-g}\,\de g_{\mu\nu} T^{\mu\nu}_{\text{SM}} \,, \eeqa % where the energy-momentum tensor $\,T_{\text{SM}}^{\mu\nu}$\, contains the SM fields. For bosonic fields, the rule of minimal coupling is practically equivalent to making two replacements in the SM Lagrangians. One is to replace Minkowski metric by a general metric $\,\eta_{\mu\nu}\to g_{\mu\nu}$\, (together with the rescaling of integral measure $\,\di^4x\to \di^4x\,\sqrt{-g}$\,). The other is to replace the partial derivative by covariant derivative $\,\pd_\mu^{}\to\nabla_\mu^{}$,\, where $\,\nabla_\mu$\, is adapted for $g_{\mu\nu}$ with $\,\nabla_\lambda^{} g_{\mu\nu}^{}=0\,$.\, For fermionic fields, the vierbein and spin connection are introduced. With these, we could conclude that the joint action $\,S_{\text{EH}}^{}+S_{\text{G}4}^{}+S_{\text{MC}}^{}$\, provides an effective description of the SM with gravitation. But, this action is incomplete up to dimension-4 operators. There is a unique dimension-4 operator which couples the Higgs doublet $H$ to the scalar curvature $R$,\, and thus should be added to the above action, % \beqa \label{eq:NMC} S_{\text{NMC}} \,=\, \int\!\!\di^4x\sqrt{-g\,}\,\xi\mathcal{R}H^\dag H \,, \eeqa % where $\,\xi\,$ is a dimensionless coupling. This term is conventionally called nonminimal coupling term since it does not follow the rule of minimal coupling. We note that up to dimension-4 operators, the nonminimal coupling could only appear for the spin-0 field. This fact adds a unique feature to the Higgs boson in the SM. Hence, the complete Lagrangian up to dimension-4 operators and joining both the SM and GR should take the following form, % \beqa \label{Action} S ~=~ S_{\text{EH}}^{} + S_{\text{G}4}^{} + S_{\text{MC}}^{} + S_{\text{NMC}}^{} \,. \eeqa % The non-minimal coupling term $\,S_{\text{NMC}}^{}\,$ is generally covariant and respects all known symmetries of the SM. We further note that $\,\xi\to 0\,$ does not enlarge the symmetry, and a nonzero $\,\xi\,$ will still be generated by loop diagrams even if one sets $\,\xi=0\,$ classically \cite{RGxi}. Another special value is the conformal coupling $\,\xi=-1/6$,\, which makes the theory Weyl-invariant for massless scalar field. But, the SM Higgs doublet is not massless, and the Weyl symmetry (which reduces to the conformal symmetry in flat spacetime) is also not a symmetry of the SM. All these facts imply that the size of this dimensionless nonminimal coupling $\,\xi\,$ can be rather large \emph{a priori}. In fact, a large $\,\xi\,$ around the order of $\,10^4\,$ has been put in use for the Higgs inflation models \cite{bezrukov,Barvinsky:2008ia,DeSimone:2008ei,Barvinsky:2009fy,Barvinsky:2009ii,BgdDep2010,BgdDep} in which the Higgs boson is responsible for two distinctive physical processes, namely, it drives inflation at a typically very high inflation scale, and triggers the electroweak symmetry breaking at weak scale.\footnote{ Ref.\,\cite{Barvinsky:2008ia} first observed that the value of Higgs boson mass can be directly related to the CMB parameters in the Higgs inflation.} Recently, Ref.\,\cite{atkins} derived an interesting bound on $\xi$ from the LHC Higgs data, by assuming the 125\,GeV boson to be the SM Higgs boson. As will be shown in Sec.\,\ref{formal}, a large $\,\xi$\, will cause a universal suppression of the Higgs boson coupling with all other SM particles. Thus, using the measured Higgs signal strengths in 2012, Ref.\,\cite{atkins} derived an upper bound, $\,|\xi|<2.6\times 10^{15}$.\, Furthermore, in the recent study \cite{XRH}, we derived the perturbative unitarity bound on $\,\xi\,$ by analyzing the coupled-channel longitudinal weak boson scattering under flat spacetime background, and we demonstrated the longitudinal-Goldstone boson equivalence theorem\,\cite{He:1997zm} in the presence of $\,\xi\,$ coupling. In \cite{XRH}, we did calculations only in Einstein frame, where the nonminimal coupling is transformed away by redefining the metric tensor. But, we may also perform the analysis in Jordan frame, i.e., with the field variables written in the action (\ref{Action}). The physical (in)equivalence between Jordan frame and Einstein frame is a subtle issue which still lacks a full consensus (especially at the quantum level) \cite{conformal,Bezrukov:2009db,Barvinsky:2009fy,Barvinsky:2009ii,JE-new}. Then, it is desirable to perform an independent analysis within the Jordan frame, in comparison with our previous Einstein frame analysis \cite{XRH}. In this paper, we will show that the same results can be inferred from Jordan frame with a fully different set of Feynman rules (Appendix\,\ref{A:FR}). This serves as a valuable consistency check of our analysis. For the first time, we will further explicitly prove the longitudinal-Goldstone equivalence theorem with nonzero $\,\xi\,$ in Jordan frame. It provides another nontrivial consistency check on our Jordan-frame analysis. There are some discussions on the unitarity issue with the nonminimal coupling for the purpose of Higgs inflation models \cite{ext}. People usually applied power-counting arguments to get the scalar or vector boson scattering amplitudes, and estimate the allowed regime for the perturbative calculations of Higgs inflation. At the first sight, the unitarity bound is around $\,\Mp/\xi$\, for $\,\xi\gg 1\,$,\, which is lower than the typical inflation scale $\,\Mp/\sqrt{\xi}\,$.\, Later studies \cite{BgdDep2010,BgdDep} suggested that unitarity bounds vary with respect to classical background of inflaton field. Considering this background dependence, the unitarity bound is expected to be relaxed to $\,O(\Mp/\!\sqrt\xi)$\, in the inflationary era. This implies that the perturbative analysis of inflation dynamics and primordial fluctuation would be reliable. These discussions are suggestive, but are only qualitative power-counting estimates with different focus and context. In this paper, we will systematically extend our analysis to quantitatively derive the unitarity constraints for a generical Higgs inflaton background. We will consider the conventional Higgs inflation\,\cite{bezrukov} and the improved models\,\cite{B2new1,B2new2,B2new3} in light of the recent BICEP2 data \cite{BICHEP2}. This paper is organized as follows. In Sec.\,\ref{formal}, we will outline the formulation with nonminimal coupling for the Jordan and Einstein frames. In Sec.\,\ref{WBscat}, we study the longitudinal weak boson scatterings in both frames. This gives a systematical extension of our previous short study\,\cite{XRH} which was for the Einstein frame alone and at the lowest order of $\,1/\Mp^{2}\,$.\, In Sec.\,\ref{sec3.3}, we quantitatively derive the perturbative unitarity bound on the Higgs-curvature coupling $\,\xi\,$ in both the electroweak vacuum and the large field background. We further study $\xi$-dependent weak boson scattering cross sections at the scales of $\order{1-30}$TeV energies, which serve as the new probes of $\,\xi\,$ at the upcoming LHC\,(14\,TeV) and the future high energy $pp$ colliders ($50-100$\,TeV) \cite{FCC}. In Sec.\,\ref{BkgD}, we systematically extend our analysis to the Higgs inflation models in the large field background. We conclude in Sec.\,\ref{conclusion}. Finally, we present the necessary Feynman rules for both Jordan and Einstein frames in Appendix\,\ref{A:FR}. \vspace*{2mm} | \label{conclusion} \vspace*{2mm} It is striking that the gravitational force not only shapes the world at its macroscopic and cosmological scales, but will also play key role at the fundamental Planck scale. We would then ask: {\it what happens in between?} Given the LHC discovery of a 125\,GeV Higgs boson \cite{LHC2012,LHC2013}, it is strongly motivated for us to explore the Higgs gravitational interactions in connection with the electroweak symmetry breaking mechanism and the origin of inertial mass generation for all elementary particles, as well as the Higgs inflation. Combining the SM with general relativity (GR) as a joint effective theory, we note that there is a unique dimension-4 operator (\ref{eq:NMC}) for the Higgs-gravity interactions with nonminimal coupling $\,\xi\,$. This provides a generic Higgs portal to the new physics beyond SM. In this work, we systematically studied the contributions of this Higgs-gravity interaction (\ref{eq:NMC}) to weak boson scattering processes in both Jordan and Einstein frames, over the energy regions accessible by the LHC\,(14\,TeV) and the future circular $pp$ colliders ($50-100$\,TeV). We explicitly demonstrated the equivalence theorem in the presence of Higgs-gravity coupling $\,\xi\,$ in both Jordan and Einstein frames. For the $\xi$-induced leading amplitudes, we derived the full results at $\order{E^2}$,\, which are needed for studying the case of large background field in Higgs inflations. Then, we analyzed the perturbative unitarity bound on $\,\xi\,$ via coupled channel analysis in the background of the electroweak vacuum. We also verified the equivalence between the two frames for computing the scattering amplitudes and cross sections. This systematically extends our previous short study\,\cite{XRH} with analysis in the Einstein frame alone and only to the first order of $\,1/\Mp^{2}\,$.\, For applications to Higgs inflation, we further studied the weak boson scatterings and unitarity constraints for the large background field case. We quantitatively established the viable perturbative parameter space of the conventional Higgs inflation\,\cite{bezrukov} and the improved models\,\cite{B2new1,B2new2} in light of the recent BICEP2 data \cite{BICHEP2}. To be concrete, in Sec.\,\ref{formal} we presented the formulation in Jordan and Einstein frames. We derived the $\xi$-induced Higgs-gravity interactions for both frames, and summarized all the relevant Feynman rules in Appendix\,\ref{A:FR}. Then, in Sec.\,\ref{WBscat} we systematically analyzed longitudinal weak boson scattering and the corresponding Goldstone boson scattering in both frames. In each frame, we explicitly demonstrated the longitudinal-Goldstone boson equivalence theorem with nonzero Higgs-gravity coupling $\,\xi\,$.\, We further verified the equivalence between the two frames for all scattering processes. In Sec.\,\ref{sec3.3}, we performed a coupled channel analysis of weak boson scattering in the electroweak vacuum, and derived unitarity bound on $\,\xi\,$ in Fig.\,\ref{fig:4}. We further studied two intriguing scenarios, in which the UV cutoff for the SM\,+\,GR effective theory is around $\,\cut = \order{10\,\text{TeV}}\,$ and $\,\cut = \order{50\,\text{TeV}}\,$,\, respectively. Thus, the $\,\xi\,$ coupling can reach up to $\,\xi =\order{10^{15}}\,$ for $\,\cut = \order{10\,\text{TeV}}$,\, or, reach up to $\,\xi =\order{10^{14}}\,$ for $\,\cut = \order{50\,\text{TeV}}$,\, as shown in Fig.\,\ref{fig:4}(a). In Fig.\,\ref{fig:5}, we presented our predictions of the $WW$ scattering cross sections with coupling $\,\xi=\order{10^{15}}\,$,\, over the energy scale $\,E(WW)=0.2-4\,$TeV, which is accessible at the LHC\,(14\,TeV). These exhibit {\it different behaviors} from the naive SM result ($\xi =0$), and thus will be discriminated by the upcoming runs at the LHC\,(14\,TeV) with higher integrated luminosity. We further analyzed the $WW$ scattering cross sections in the energy range of $\,E(WW)=1-30\,$TeV. These will be realized at the future circular $pp$ colliders ($50-100$\,TeV) \cite{FCC}, which may have sensitivity to probe the Higgs-gravity coupling at the level of $\,\xi=\order{10^{14}}\,$,\, as shown in Fig.\,\ref{fig:6}. We suggest that the $\,\xi\,$ coupling can be further probed by invoking the cubic Higgs self-interactions [Eq.\,\eqref{DL_int_ss}] at the future high energy $pp$ colliders. In Sec.\,\ref{BkgD}, we studied the Higgs-field-background dependent weak boson scattering amplitudes, and quantitatively performed the unitarity analysis for the Higgs inflation models. We generalized the formulation of Sec.\,\ref{formal} to a generic Higgs-field background in both Jordan and Einstein frames. We derived the new Feynman rules and the scattering amplitudes accordingly. For the case of large field background, we have taken account of the full contributions at $\,\order{E^2}\,$ for the scattering amplitudes. With these, we demonstrated that the unitarity bound on the $\xi$ coupling is substantially relieved, as shown in Fig.\,\ref{fig:4}(b). Finally, we applied this analysis to the conventional Higgs inflation\,\cite{bezrukov} and the improved models\,\cite{B2new1,B2new2} in light of the recent BICEP2 observation\,\cite{BICHEP2}. We quantitatively analyzed the viable perturbative parameter space for the Higgs inflation models, as shown in Fig.\;\ref{fig:7}(a)-(c) for three sample inputs of the $\,\xi\,$ coupling. %\newpage \vspace*{5mm} \noindent {\bf Acknowledgements}\\[1.5mm] We thank John R.\ Ellis for valuable discussions during his recent visit at Tsinghua HEP Center. We thank Michael Trott and Xavier Calmet for valuable discussions on this subject. This work was supported by National NSF of China (under grants 11275101, 11135003) and National Basic Research Program (under grant 2010CB833000). %\paragraph{Acknowledgements.} % \addcontentsline{toc}{section}{Acknowledgments\,} \newpage %\begin{appendix} %\vspace*{10mm} \noindent {\bf\Large Appendix} \appendix %\vspace*{3mm} | 14 | 4 | 1404.4627 |
1404 | 1404.6952_arXiv.txt | {Constraints on stellar models can be obtained from observations of stellar populations, provided the population results from a well defined star formation history.} {We present a new tool for building synthetic colour-magnitude diagrams of coeval stellar populations. We study, from a theoretical point of view, the impact of axial rotation of stars on various observed properties of single-aged stellar populations: magnitude at the turnoff, photometric properties of evolved stars, surface velocities, surface abundances, and the impact of rotation on the age determination of clusters by an isochrone fitting. One application to the cluster NGC 663 is performed.} {Stellar models for different initial masses, metallicities, and zero-age main sequence (ZAMS) rotational velocities are used for building interpolated stellar tracks, isochrones, and synthetic clusters for various ages and metallicities. The synthetic populations account for the effects of the initial distribution of the rotational velocities on the ZAMS, the impact of the inclination angle and the effects of gravity and limb darkening, unresolved binaries and1 photometric errors. Interpolated tracks, isochrones, and synthetic clusters can be computed through a public web interface.} {For clusters with a metallicity in the range $[0.002,0.014]$ and an age between $30\,\text{Myr}$ and $1\,\text{Gyr}$, the fraction of fast rotators on the main sequence (MS) band is the largest just below the turnoff. This remains true for two different published distributions of the rotational velocities on the ZAMS. This is a natural consequence of the increase in the MS lifetime due to rotation. The fraction of fast rotators one magnitude below the turnoff also increases with the age of the cluster between $30\,\text{Myr}$ and $1\,\text{Gyr}$. The most nitrogen-rich stars are found just below the turnoff. There is an increase in the fraction of enriched stars when the metallicity decreases. We show that the use of isochrones computed from rotating stellar models with an initial rotation that is representative of the average initial rotation of the stars in clusters provides a reasonable estimate of the age, even though stars in a real cluster did not start their evolution with an identical initial rotation.} {} | Populations of coeval stars such as those found in many open clusters in the Galaxy and the Magellanic Clouds represent an excellent benchmark to sample of stars with identical initial composition and age. The morphology of the distribution of stars in the colour-magnitude diagrams provides both very interesting constraints on stellar models and a way to obtain the age of the population, although of course ages are still model dependent. Our aim in the present work is twofold. On the one hand, we present the new tool SYCLIST (for SYnthetic CLusters, Isochrones, and Stellar Tracks), which was developed to produce single-aged stellar populations built on recently published grids of stellar models \citep{Ekstrom2012a,Georgy2013a,Georgy2013b}. This tool will be improved in the future, allowing non-coeval populations to be described. It is presently partially available through a web interface\footnote{\footnotesize{\url{http://obswww.unige.ch/Recherche/evoldb/index/}.}}. On the other hand, we present applications for investigating various effects. Among them we study the impact of the dispersion in the initial rotational velocities on the age determinations through the isochrone method. We also quantify the effects of gravity and limb darkening on the photometric appearance of a cluster. To our knowledge, these two darkening effects (or brightening, depending on the inclination) are for the first time accounted for in the building of colour-magnitude diagrams (CMDs). We discuss where the fast rotators and nitrogen-rich stars are located in clusters of various ages and metallicities. A complete discussion that includes the whole parameter space (age, metallicity, velocity, and inclination distributions, presence or not of the gravity- or limb-darkening, of unresolved binaries, calibrations between effective temperature-colours and bolometric corrections, accounting for photometric noise) is beyond the scope of this paper that aims only at approaching the impact these effects and their interplay might have on synthetic stellar populations. We eventually compare the output of the present tool with the cluster NGC 663 and show that a reasonable description of observed data can be achieved. The SYCLIST code operates on the following stellar models libraries: \begin{itemize} \item the large grids of models covering most of the stellar mass domain (between $0.8$ and $120\,M_\sun$), with two different initial equatorial velocities ($V_\text{eq, ini}/V_\text{crit} = 0$ and $0.4$), and two metallicities: $Z=0.014$ \citep[solar metallicity,][]{Ekstrom2012a} and $Z=0.002$ \citep[SMC metallicity,][]{Georgy2013b}; \item the grids centred on the B-type star mass domain (between $1.7$ and $15\,M_\sun$) with nine different initial rotation rates between $\Omega_\text{ini}/\Omega_\text{crit} = 0$ and $0.95$ (where $\Omega_\text{crit} = \sqrt{\frac{GM}{R^3_\text{e, crit}}}$ and $R_\text{e, crit}$ the equatorial radius when the star rotates at the angular velocity $\Omega_\text{crit}$) at three metallicities: $Z=0.014$, $Z=0.006$ (LMC metallicity) and $Z=0.002$ \citep{Georgy2013a}; \item in addition to the two previous sets of models, the online version also includes the grid of non-rotating stellar models from \citet{Mowlavi2012a}, with a very fine mesh covering the mass domain between $0.5$ and $3.5\,M_\sun$ and $6$ metallicities between $Z=0.006$ and $Z=0.04$ . \end{itemize} Four different outputs are proposed\footnote{\footnotesize{Note that the online version of SYCLIST offers as of today only the first three outputs: Interpolated tracks and isochrones are directly computed online, and a request form for synthetic cluster computation can be sent through the same interface.}}: \begin{enumerate} \item\textit{Interpolated single stellar models:} interpolated tracks are provided for any choice of the initial mass, metallicity, and equatorial rotational velocity. The range of allowed values are determined by the choice of the library; \item\textit{Isochrones:} isochrones are computed with a given initial metallicity and rotational velocity; \item\textit{Synthetic coeval stellar populations:} synthetic clusters of single-aged stellar populations are built, offering various optional settings for the initial distributions of the velocities \citep[][Dirac]{Huang2006a,Huang2010a} and of the inclination angles (random or Dirac), for the account for the gravity and limb darkening \citep{vonZeipel1924a,EspinosaLara2011a,Claret2000a}. The effect of unresolved binaries and photometric noise can also be added. Various calibrations for the transformation of the theoretical quantities (luminosities and effective temperatures) to the observed magnitudes and colours can be used (see Sect.~\ref{Sect_CalibrationCouleur}); \item\textit{Time evolution of star count:} In this mode, the code computes the evolution of the relative numbers of various types of stars (spectral types, blue-, yellow-, and red-supergiants, Wolf-Rayet subtypes, stars in a given rotation rate range, \textit{etc}.) as a function of time. \end{enumerate} The paper is structured as follows. In Section~\ref{Sec_Code}, we describe precisely how a synthetic population of stars is built in SYCLIST. In Section~\ref{Sec_Results}, we use the code to explore specific questions regarding mainly the impact of rotation on isochrones and synthetic population. A comparison with the observed cluster NGC 663 is made in Section~\ref{Sec_NGC663}. Finally, our conclusions are presented in Section~\ref{Sec_Conclu}. | We present the SYCLIST code, a new tool for interpolating between stellar tracks, building isochrones, creating synthetic clusters, and following the evolution of stellar populations. It includes an IMF, various initial velocity and viewing angle distributions, and is able to account for the gravity- and limb-darkening. The binary fraction and a photometric noise are additional options for the outputs of the ``Synthetic cluster'' mode. In this paper we explain how these effects are implemented in the code, and study to which extent they impact the aspects of stellar tracks, isochrones, and synthetic clusters. We also study typical synthetic clusters at various ages and metallicities, and discuss their main features. We briefly present the potential use of the SYCLIST code in comparison with observed clusters. More extensive studies and comparisons will be the subject of a forthcoming paper. | 14 | 4 | 1404.6952 |
1404 | 1404.3093_arXiv.txt | It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories gives rise to a quantum corrected Raychaudhuri equation (QRE). In this article we derive the second order Friedmann equations from the QRE, and show that this also contains a couple of quantum correction terms, the first of which can be interpreted as cosmological constant (and gives a correct estimate of its observed value), while the second as a radiation term in the early universe, which gets rid of the big-bang singularity and predicts an infinite age of our universe. | 14 | 4 | 1404.3093 |
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1404 | 1404.7679_arXiv.txt | It is well known that the formal series representing the invariant manifolds (tori) near stable equilibria or stable periodic orbits in Hamiltonian systems are not convergent in general (for a review see Contopoulos 2002), except in the case of integrable systems. However, near unstable equilibria, or unstable periodic orbits, the invariant manifolds can be represented by {\it convergent} formal series (Cherry 1926, Moser 1956, 1958) (see also Bruno 1971, 1989, Giorgilli 2001, Delshams and L\'{a}zaro 2005). The motion near the unstable points takes place along such invariant manifolds. On the other hand, near these points there is chaos. Thus the question is how is it possible for convergent (analytic) series to represent chaotic motions. The structure of chaos near the unstable points is determined by the intricate forms of the stable and unstable asymptotic manifolds, which intersect in a complicated way forming the so-called homoclinic or heteroclinic tangles. So far, these structures have been studied in concrete examples mainly by numerical means (e.g. Bertlett 1978, Bartlett 1982, Bartlett 1989, Contopoulos 1990, Roeder et al. 2003, Contopoulos and Polymilis 1993, Bazzani et al. 1993, Contopoulos et al. 1994, Contopoulos et al. 1996, Rom-Kedar 1990, Evans et al. 2004, Polymilis et al. 2003). For computations related to celestial mechanics see Simo 1990, Jorba and Masdemont 1999, Perozzi and Ferraz-Mello 2010, G\'{o}mez and Barrad\'{e}s 2011 and references therein. Nevertheless, little has been done {\it analytically} to explore the convergent series expansions in order to study the chaotic structures formed by the invariant manifolds. This was due to the fact that the domain of convergence established in the original theorems of Moser is finite, and in general it is considered to be rather small. However, the question of the true size of the domain of convergence is still open. In an early calculation, Franceschini and Russo ( Franceschini and Russo 1981) computed several lobes and homoclinic points of the asymptotic manifolds in the 2D H\'{e}non mapping using a variant of the normal form series approach. In a more general context, Da Silva Ritter et al. (Da Silva Ritter et al. 1987) have shown that in the case of some simple 2D symplectic mappings analytic and with an analytic inverse over the whole plane, the domain of convergence along the asymptotic invariant manifolds extends to {\it infinity}. (As pointed out in the historical notes of Cabr\'{e} et al. (2005), this property is a direct consequence of a theorem of functional analysis going back to Poincar\'{e} (Poincar\'{e} 1890). This property allows to reproduce many non-trivial features of the homoclinic tangle using only series. On the other hand, it was up to now unknown whether a similar extension applies in the case of Hamiltonian flows as well (see Vieira and Ozorio de Almeida 1996, Ozorio de Almeida and Vieira 1997). In the present paper we make a detailed numerical study of the size of the domain of convergence of the hyperbolic normal form series both in 2D mappings and in 2D Hamiltonian systems. In particular, we perform an analytical computation of the invariant manifolds up to high truncation orders, and provide evidence regarding i) how well they can represent the true form of the invariant manifolds, and ii) what is the extent of the domain of convergence. Regarding this last question, we note, first, the well known fact that the non-convergence or convergence of the formal series is related to the appearance or non-appearance, in the series, of {\it small divisors}. In the case of systems of two degrees of freedom, near a stable periodic orbit we have in general divisors of the form $m_1\omega_1+m_2\omega_2$, with $m_1,m_2$ integer and $\omega_1,\omega_2$ real. Such divisors can become very small when $|m|=|m_1|+|m_2|$ becomes large, or zero when $\omega_1, \omega_2$ are commensurable. The latter (resonant) case requires a special treatment, which, however, presents similar non-convergence features as the non-resonant case. On the other hand, in the case of unstable periodic orbits we have two frequencies $\omega_1$ (real) and $\omega_2=-i\nu$ (imaginary). Then, it can be shown that the corresponding divisors never approach very close to zero, since they are bounded by a quantity $|m|\gamma$, where $\gamma$ is a positive constant of the order of the minimum of $|\omega_1|$ or $|\nu|$ (see Giorgilli 2001). The first proof of the convergence of the formal series was provided by Cherry (1926), while a more general proof was provided by Moser (1956, 1958) and Giorgilli (2001). The first paper of Moser (1956) refers to 2D area preserving maps. In this case, the unstable fixed points correspond to unstable periodic orbits on the surface of section of two degrees of freedom Hamiltonian systems. On the other hand, the second paper (Moser 1958) investigates N-degree of freedom Hamiltonian systems of the form $H(x,y)=H_0(x,y)+H_1(x,y)+...$, where $x\equiv(x_1,\ldots,x_N)$, $y\equiv(y_1,\ldots,y_N)$, are canonical positions and momenta, and $H_i$ are polynomials in $(x,y)$ of degree $i+2$, with a quadratic part \begin{equation}\label{hammos} H_0 = \sum_{j=1}^N i\omega_j x_j y_j \end{equation} with $\omega_1/\omega_2$ non-real, and $k_1\omega_1+k_2\omega_2 \neq \omega_j$ for all integers $k_1,k_2$ and all $j>2$. The case of unstable equilibrium in two degrees of freedom systems corresponds to $\omega_1$ real,and $\omega_2=-i\nu$ imaginary, while, for more than two degrees of freedom, the theorem applies also to complex unstable points (i.e. $\omega_1,\omega_2$ complex). Moser's theorem then establishes the existence of special solutions of the Hamiltonian equations of motion in which all variables $x_j,y_j$ can be expressed via four parameters $(q,p,\xi,\eta)$, i.e. of the form $x_j=X_j(q,p,\xi,\eta)$, $y_j=Y_j(q,p,\xi,\eta)$, such that for the variables $(q,p,\xi,\eta)$ we have the `normal form' time evolution given by \begin{equation}\label{qpxiet} q=q_0e^{i\Omega(J,c)t},~~ p=p_0e^{-i\Omega(J,c)t},~~ \xi=\xi_0e^{\Lambda(J,c)t},~~ \eta=\eta_0e^{-\Lambda(J,c)t}~~ \end{equation} with $\Omega=\omega_1+...$, $\Lambda=\nu+...$, and $J=iq_0p_0$, $c=\xi\eta$. The quantities $J,c$ represent integrals of motion of Moser's normal form, since we have $q(t)p(t)=-iJ$, $\xi(t)\eta(t)=c$ for all times $t$. In particular: i) the values $c=J=0$ correspond to the unstable equilibrium point, and ii) the values $J\neq 0, c=0$ correspond to unstable periodic orbits with a frequency equal to $\Omega(J,0)$, as well as to their {\it asymptotic orbits} lying on the invariant manifolds of the periodic orbits. Finally, iii) the values $c\neq 0$ correspond to orbits in the neighborhood of the unstable periodic orbits (or points), subject to locally hyperbolic dynamics under the Eqs.(\ref{qpxiet}). The theorem of Moser was completed in an essential way by Giorgilli (2001), who demonstrated that the special solutions of Moser can be recovered via a convergent {\it canonical} transformation of the variables $(x,y)$, such that in the new canonical variables the Hamiltonian resumes a normal form leading to the solutions (\ref{qpxiet}). In the theorem of Giorgilli, one still has no small divisors, and the proof of the convergence of the normalizing tranformation in a domain surrounding the origin follows by a proper control of the Cauchy estimates (see Giorgilli 2002 for a review) applying to the derivatives of various analytic functions appearing in the normalization canonical procedure. For a discussion of the convergence properties of the hyperbolic normal form series nonlinear flows see also Bruno (1971), Delshams and L\'{a}zaro (2005). The theorems of Moser and Giorgilli guarantee the existence of a disc of finite radius of convergence of the hyperbolic normal form series around the origin. However, the true extent as well as the true shape of the domain of convergence are not yet fully understood. Da Silva Ritter et al. (1987) demonstrated that in the case of simple conservative 2D mappings (i.e. mappings represented by analytic functions over the whole phase space) the domain of convergence of the hyperbolic normal form series goes to infinity along the axes $\xi=0$ and $\eta=0$ of the new canonical variables resulting after the mapping's normalizing transformation. Since these axes represent the stable and the unstable manifolds of the unstable point, this property permits in practice a purely analytic computation of the invariant manifolds and of all features connected with homoclinic dynamics, using only series (and not numerical integration methods). In order to verify this fact, we presently compute the hyperbolic normal form in two simple 2D symplectic mappings, namely the standard map and the H\'{e}non map. In order to estimate the radius of absolute convergence of the hyperbolic series along particular directions from the origin, we use D'Alembert's criterion. We then find that the successive radii $\rho_r$ of the D'Alembert sequence yield larger and larger values as the truncation order $r$ increases, thus providing evidence that the successive values $\rho_r$ tend to infinity as $r\rightarrow\infty$. Furthermore, we find that the rate of increase of $\rho_r$ with $r$ is different in the case of the standard map than in the case of the H\'{e}non map. Namely, we have a logarithmic dependence $\rho_r\sim log(r)$ in the former, while we find a power-law dependence $\rho_r\sim r^p$, with $p\simeq 2$, in the latter. Nevertheless, when back-transforming to the original variables, in both maps we find that the series truncated at order $r$ represent successfully the invariant manifolds up to an extent whose length scales as $\sim\log(r)$. On the other hand, in Hamiltonian systems of two degrees of freedom, some numerical calculations (see, for example, Fig.4 of Vieira and Ozorio de Almeida (1996), and Fig.2 of Bongini et al. (2001)) give the impression that the domain of convergence of Moser's normal form should extend at most up to the point where the two branches $\xi=0$ and $\eta=0$ (stable and unstable manifolds) of the invariant curve $\xi\eta=c=0$, when transformed to curves in the original canonical variables, intersect each other at a homoclinic point. According to Bongini et al. (2001) , such a point constitutes a ``singularity'' of the formal expansions that ``defines the applicability limit of the normal form dynamics''. Despite these indications, Vieira and Ozorio de Almeida (1996) have conjectured that the domain of convergence of Moser's normal form may extend long enough as to include homoclinic points. In fact, the same authors presented numerical calculations by which it was apparently possible to compute a homoclinic intersection in the H\'{e}non-Heiles 2D Hamiltonian model which possesses a (triple) hyperbolic equilibrium point. However, a careful examination of their calculations reveals that the computation was partly based on numerical propagation of the orbits and not exclusively on series. On the other hand, a purely analytic computation, based on series up to the 16th degree, failed to give a precise location of even one homoclinic point. In Ozorio de Almeida and Vieira (1997), the authors invoke an argument according to which, using repeatedly {\it analytic continuation} (see our section 4), it becomes possible to obtain the time evolution of all initial conditions at $t=0$ along the Hamiltonian flow under the form of a symplectic mapping connecting the initial conditions with the values of the canonical variables at a later time $t$. As we shall see, however, the fact that this mapping has a limited domain of analyticity introduces a crucial difference between the Hamiltonian and the simple mapping cases, thus, not allowing for the extension of the domain of convergence proposed by Ozorio de Almeida and Vieira to apply in the case of Hamiltonian flows. Our own main results in the present paper regarding the Hamiltonian case can be summarized as follows: 1) We compute the hyperbolic series around unstable periodic orbits in generic Hamiltonian systems expressed in action - angle variables, of which the polynomial Hamiltonian systems with unstable equilibria considered by Moser are a special case. In such systems, we provide strong numerical indications that the domain of convergence of the hyperbolic series is finite, and that it contains no homoclinic intersections. 2) However, we propose a new method, which materializes the main idea of the analytic continuation technique of Ozorio de Almeida and Vieira (1997), and allows to obtain a parametrization of the invariant manifolds using only series in a domain extending well beyond the limit of convergence of the original series. This, in turn, allows to compute many homoclinic intersections and the lobes formed by the invariant manifolds using only series. 3) In the case of systems of non-polynomial form that can be written in action-angle variables, the main element of our method is to use truncated Fourier series {\it not expanded in the angles} around the unstable point. In fact, we exploit the property of the Fourier series that their singularity with respect to the angles is on the imaginary axis, while all computations with the angles lying on the real axis remain convergent. 4) We show that the accuracy of computations depends (a) on the order of truncation of the series, and (b) on the number of digits used in calculating the coefficients of the series. 5) Furthermore, we define `invariant' and `quasi-invariant' curves on the surface of section corresponding to values of $c\neq 0$. For small values of $c$ they correspond to initial conditions that are mapped onto segments of the same curve up to an extent large enough to include several oscillations and lobes similar to those of the asymptotic manifolds (see detailed definitions in section 4). Thus, such curves characterize the structure of chaos in the neighborhood of the unstable periodic orbit. Also, they have self-intersections, which, as shown in Da Silva Ritter et al. (1987) can be exploited in order to compute high order periodic orbits accumulating to one or more homoclinic points. Our analytical method facilitates the computation of such orbits. However, a detailed study of such computations is deferred to a future work. The paper is organized as follows. In section 2 we present our results for the convergence of the hyperbolic normal form series and the analytic computation of invariant manifolds in 2D symplectic mappings. Section 3 presents our Hamiltonian model as well as the algorithm of computation of the hyperbolic normal form series in the Hamiltonian case. We also find analytically the characteristic curve, i.e., the position of the basic unstable periodic orbit as a function of our model's perturbation parameter $\epsilon$. Then, we study numerically the domain of convergence in the Hamiltonian model. In section 4 we introduce our extended analytical method of computation of the invariant manifolds, and demonstrate its use in the computation of the structure of the homoclinic tangle and its neighborhood. In section 5 we study the convergence properties of the hyperbolic normal form as well as the application of our extended method in a polynomial Hamiltonian system which reduces to the case considered by Moser exactly. Section 6 is a summary of our basic conclusions. | We studied the convergence properties of the hyperbolic normal form series used in the computation of the invariant manifolds of an unstable equilibrium point, or an unstable periodic orbit, in 2D mappings and in 2D generic Hamiltonian systems expressed in action-angle variables. Our main findings can be summarized as follows: 1) In 2D mappings analytic over their whole phase space, we confirmed by numerical experiments the statement of Da Silva Ritter et al. (1987) that the convergence of the normal form extends to infinity along the invariant manifolds, and to finite, but large domain, for nearby `quasi-invariant' curves. This allows in practice for the computation of many interesting features of the homoclinic tangle using only series (e.g. homoclinic points, periodic orbits of high period, high order lobes of the invariant manifolds etc.) 2) In two different 2D mappings that we studied, the rate by which the sequence of D'Alembert radii of the formal series goes to infinity is found to obey different laws. In the standard map it is found to grow logarithmically with the normalization order $r$, while in the H\'{e}non map it is quadratic in $r$. However, when back-transforming to the original variables, in both cases the length along the manifolds recovered by the truncated analytical series increases with the truncation order $r$ as $\log(r)$. Finally, if a mapping has a limited analyticity domain, then the sequence of D'Alembert radii tends to a constant, indicating that the domain of convergence in this case is finite. 3) As a first example of the Hamiltonian case, we studied a pendulum model with periodic perturbation, which cannot be reduced to a polynomial form. We find a finite domain of convergence of the hyperbolic normal form, and we provide results indicating that this domain does not reach any homoclinic point. We also give the form of the domain of convergence on the plane of the new hyperbolic canonical variables. Finally, we checked the accuracy of our computations when computing the normal form series using the usual double precision, or 80-digit precision. The latter is needed in order to control the propagation of round-offs in some cases, beyond a high normalization order. 4) Then, we proposed a new method by which one can compute extensions of the original normalizing transformations of Moser using only series. Thus we materialize the idea of analytic continuation proposed by Ozorio de Almeida and Viera (1997). However, contrary to these authors, we choose action angle variables to represent the series yielding a part of the extended transformation (namely the mappings $F^m$ in Eq.(\ref{compo})), without expanding the trigonometric functions of the angle corresponding to the hyperbolic degree of freedom in power series. In this way, it becomes possible to parameterize the invariant manifolds up to an arbitrarily large extent. We show the efficiency of the method by concrete numerical examples. 5) We emphasized the fact that the possibility to extend the normalizing transformations to a large domain allows one to study features of chaos using only series. In particular, we approximate the intricate lobes formed by the asymptotic manifolds near the unstable point, and we compute curves of the form $c=\xi'\eta'$ (mapped in the old variables), which are near the asymptotic manifolds. We call these features `the structure of chaos'. We propose to use the same approach in order to compute high order periodic orbits that accumulate around one or more homoclinic points. 6) We finally study the case of a polynomial Hamiltonian model, in which the original normal form of Moser is applicable. In this case as well we confirm the results of sections 3, and 4, namely i) we provide numerical evidence that the convergence domain of Moser's normalizing transformations does not reach any homoclinic point, and ii) that an extension using our method of section 4 allows to parameterize the manifolds over an extent long enough to include several homoclinic points. The results found so far point towards a number of applications and extensions. In particular, we emphasize two benefits from the extended transformations (\ref{compo}): i) the possibility to obtain a parametrization of the invariant manifolds over an arbitrary length, and ii) the possibility, in numerical implementations, to obtain the manifolds with uniform linear sampling density over any desired length, using higher values of the multiplicity $m$ (see Eq.(\ref{compo})) to achieve the same density for a longer length. Property (i) marks the essential difference between our new method and previous numerical methods that simply propagate forward initial conditions obtained by accurate calculations within the domain of convergence of the original method of Moser. Property (ii), on the other hand, is useful in practical computations and visualizations of asymptotic orbits, up to an arbitrarily long extent. On the other hand, the possibility to represent analytically not only the asymptotic manifolds, but also other invariant manifolds in the neighborhood of an unstable orbit poses a number of interesting theoretical questions related to the structure of chaos in such a neighborhood. In particular, it is known (Contopoulos et al. 1996) that tiny islands of stability can exist arbitrarily close to the unstable fixed point. Such islands are found both outside and inside lobes. According to the Newhouse theorem (Newhouse 1977) such islands are generated by new (irregular) periodic orbits which appear near points of tangency between the stable and unstable asymptotic manifolds. In systems with a compact phase space, such points are generated continuously, for arbitrarily high values of the non-linearity parameter (Contopoulos et al. 1994). In fact, the method of analytic computation of the invariant manifolds lends itself to the computation of such points of tangency of an arbitrarily high order. However, the curves $\xi'\eta'=c$ for $c\neq 0$ cannot represent the islands of the stable irregular periodic orbits. In the model studied in the present paper, the asymptotic invariant manifolds emanating from the periodic orbit at $\psi=-\pi$ can be formally considered as forming heteroclinic intersections with the manifolds emanating from the periodic orbit at $\psi=\pi$. However the second orbit is the same with the first one modulo $2\pi$. On the other hand, the present method can be used with little modification in order to study true heteroclinic connections between more than one periodic orbits. In fact, this is the case in the model studied by Vieira and Ozorio de Almeida (1996), which possesses a triple periodic orbit. Similar results can be found for unstable periodic orbits of any multiplicity. There are also examples (e.g. Polymilis et al. 2003) in which, after a period doubling bifurcation, the homoclinic connections between some periodic orbit evolve, by varying one parameter, to heteroclinic connections between two different unstable periodic orbits. The transition from homoclinic to heteroclinic dynamics takes place at the point of the period doubling. The study of such connections by analytical invariant manifolds can provide important information on the kinds and statistics of the recurrences, as well as the transport phenomena taking place in the heteroclinic tangle and its neighborhood.\\ \\ {\bf Acknowledgements:} This research has been supported in part by the Research Committee of the Academy of Athens (grant 200/815). | 14 | 4 | 1404.7679 |
|
1404 | 1404.5998_arXiv.txt | Forecasting models of the solar wind often rely on simple parameterizations of the magnetic field that ignore the effects of the full magnetic field geometry. In this paper, we present the results of two solar wind prediction models that consider the full magnetic field profile and include the effects of Alfv\'en waves on coronal heating and wind acceleration. The one-dimensional MHD code ZEPHYR self-consistently finds solar wind solutions without the need for empirical heating functions. Another 1D code, introduced in this paper (The Efficient Modified-Parker-Equation-Solving Tool, TEMPEST), can act as a smaller, stand-alone code for use in forecasting pipelines. TEMPEST is written in Python and will become a publicly available library of functions that is easy to adapt and expand. We discuss important relations between the magnetic field profile and properties of the solar wind that can be used to independently validate prediction models. ZEPHYR provides the foundation and calibration for TEMPEST, and ultimately we will use these models to predict observations and explain space weather created by the bulk solar wind. We are able to reproduce with both models the general anticorrelation seen in comparisons of observed wind speed at 1 AU and the flux tube expansion factor. There is significantly less spread than comparing the results of the two models than between ZEPHYR and a traditional flux tube expansion relation. We suggest that the new code, TEMPEST, will become a valuable tool in the forecasting of space weather. | The solar wind is a constant presence throughout the heliosphere, affecting cometary tails, planetary atmospheres, and the interface with the interstellar medium. Identifying the acceleration mechanism(s) that power the wind remains one of the key unsolved mysteries in the field. Theorists have proposed a variety of physical processes that may be responsible, and these processes are invoked in models that seek to explain both the heating of the solar corona and the acceleration of the solar wind. Such models are often categorized by their primary use of either magnetic reconnection and the opening of closed magnetic loops (Reconnection/Loop-Opening models, RLO) or the generation of magnetoacoustic and Alfv\'en waves and the turbulence created by them (Wave/Turbulence-Driven models, WTD). Several reviews have discussed the many suggested models and the associated controversies \citep{1993SoPh..148...43Z, 1996SSRv...75..453N, 2006SoPh..234...41K, 2009LRSP....6....3C}. \\ \indent RLO models require closed field lines, where both footpoints of magnetic flux tubes are anchored to the photosphere. Interactions between neighboring closed loops or between closed and open field lines lead to magnetic reconnection, which releases stored magnetic energy when the magnetic topology is reconfigured. Reconnection in closed field regions has been suggested to play a role in streamers \citep{1999JGR...104..521E, 2011ApJ...731..112A} and in the quiet Sun on supergranular scales \citep{1992sws..coll....1A, 1999JGR...10419765F, 2003JGRA..108.1157F, 2006ApJ...642.1173S, 2011ApJ...731L..18M, 2013ApJ...770....6Y}. However, \citet{2010ApJ...720..824C} provided evidence that the complex and continuous evolution of this so-called ``magnetic carpet'' \citep{1998ASPC..154..345T} of open and closed field lines may not provide enough energy to accelerate the outflow to match in situ measurements of wind speed. \\ \indent Alternatively, WTD models are useful for explaining heating and wind acceleration in regions of the Sun where the flux tubes are primarily open, that is, they are rooted to the photosphere by only one footpoint and reconnection is less likely to release significant amounts of energy. In this case, Alfv\'en waves and magnetoacoustic oscillations can be launched at the footpoints when the flux tube is jostled by convection at the photosphere. As the density of the solar atmosphere drops with height, the waves are partially reflected; counter-propagating waves interact and generate magnetohydrodynamic (MHD) turbulence. This turbulence generates energy at large scales, and the break-up of eddies causes an energy cascade down to smaller scales where the energy can be dissipated as heat at a range of heights. WTD models have naturally produced solar winds with properties that match observed outflows in the corona and further out in the heliosphere \citep{1986JGR....91.4111H, 1991ApJ...372L..45W, 1999ApJ...523L..93M, 2006JGRA..111.6101S, 2007ApJS..171..520C,2010ApJ...708L.116V}. This paradigm for solar wind acceleration has, however, also been challenged \citep{2010ApJ...711.1044R}, so perhaps the answer to the entire question of coronal heating is more complex than previously thought.\\ \indent One of the most striking aspects of the observations of the solar wind is the appearance of a bimodal distribution of speeds at 1 AU. The existence of separate components of the outflow has been observed since {\it Mariner 2} began collecting data in interplanetary space \citep{1962Sci...138.1095N, 1966JGR....71.4469N}. The fast wind has asymptotic wind speeds above roughly 600 km s$^{-1}$ and is characterized by low densities, low variability, and photospheric abundances. The slow wind, however, has speeds at 1 AU at or below 450 km s$^{-1}$ and is chaotic, with high densities and enhanced abundances of low-FIP elements \citep{1995SSRv...72...49G}. It has been widely accepted that fast wind streams originate from coronal holes, which are characterized by unipolarity, open magnetic field, and lower densities \citep[and references therein]{1977chhs.conf.....Z, 2009LRSP....6....3C}. The location of slow wind is more of a mystery. Slow solar wind has often been attributed to sources in the streamer belt \citep{2012JGRA..117.4104C}, but recent progress suggests that perhaps pseudostreamers or the edges of coronal holes may significantly contribute to this slower population \citep{2012ApJ...749..182W, 2011ApJ...731..112A, 2004JASTP..66.1295A}. However, a variety of acceleration mechanisms have been proposed along with these suggested slow wind sources. In this paper, we investigate many of these sources and coronal structures using a single theoretical framework, allowing us to determine if the different populations of solar wind can be explained by simply a difference in their region of origin.\\ \indent Current observations have not been able to distinguish between the many competing theoretical models, as many models have a variety of free parameters that can be adjusted to fit observations without specifying all of the physics. To compare the validity of these models at different points in the solar cycle and for different magnetic field structures on the Sun, the community needs flexible tools that predict wind properties using a limited number of input parameters that are all based on observations and fundamental physics. In this project, we study the extent of magnetic field structures that can produce solar wind that matches observations using two WTD models. In Section 2, we set up a grid of flux tube models as a parameter study of a broad range of open magnetic structures throughout the solar cycle. We present in Section 3 the analysis of this grid of models using ZEPHYR \citep{2007ApJS..171..520C}. We introduce the new code TEMPEST in Section 4 and discuss its use as a forecasting tool. In Section 5 we compare the results of ZEPHYR and TEMPEST and discuss differences in the models. Finally, in Section 6 we discuss these results and their importance in solving the coronal heating problem. | We have used WTD models to heat the corona through dissipation of heat by turbulent cascade and accelerate the wind through increased gas pressure and additional wave pressure effects. Our primary goal for this project is to improve empirical forecasting techniques for the steady-state solar wind. As we have shown, the community often relies on WSA modeling, based on a single parameter of the magnetic field expansion in open flux tubes. Even with the advances of combining MHD simulations as the WSA-ENLIL model, comparisons between predictions and observations make it clear that further improvements are still necessary. An important point to make is that extrapolations from magnetograms show that many flux tube magnetic field strengths do not all monotonically decrease, so two models with identical expansion factors could result in rather different structures. We anticipate that TEMPEST could easily be incorporated within an existing framework to couple it with a full MHD simulation above the source surface.\\ \indent The first code we discuss, ZEPHYR, has been shown to correspond well with observations of coronal holes and other magnetic structures in the corona. We investigate here the results of a grid of models that spans the entire range of observed flux tube strengths throughout several solar cycles to test the full parameter space of all possible open magnetic field profiles.\\ \indent ZEPHYR also provides us with temperature-magnetic field correlations that help to take out much of the computation time for a stand-alone code, TEMPEST, that solves the momentum conservation equation for the outflow solution of the solar wind based on a magnetic field profile. The solar physics community has come a long way since Parker's spherically symmetric, isothermal corona, but the groundwork laid by this early theory is still fully applicable.\\ \indent The special case presented by pseudostreamers is an ongoing area of our analysis. Pseudostreamers do not contribute to the heliospheric current sheet and they seem to be a source of the slow solar wind. The community does not fully understand the differences in the physical properties of the solar wind that may emanate from pseudostreamers and helmet streamers, although observational evidence suggests the slow wind is generated from these areas or the edges of coronal holes. Our results from both codes do not currently recreate the bimodal distribution of wind speeds observed at 1 AU. It is unclear whether this is due to the inclusion of many unphysical flux tube models or because the fast wind and the slow wind are generated by {\it different} physical mechanisms.\\ \indent One slightly troubling feature of the ZEPHYR and TEMPEST model results is a relative paucity of truly ``slow'' wind streams ($u \lesssim 350$ km s$^{-1}$) in comparison to the observed solar wind. However, \cite{2011JGRA..116.3106M} showed that many of the slowest wind streams at 1 AU were the result of gradual deceleration due to stream interactions between 0.1 and 1 AU. Similarly, \cite{2013ApJ...767..125C} found that ZEPHYR models of near-equatorial quiet-Sun stream lines exhibited a realistic distribution of slow speeds at 0.1 AU, but they exhibited roughly 150 km s$^{-1}$ of extra acceleration out to 1 AU when modeled in ZEPHYR without stream interactions. Clearly, taking account of the development of corotating interaction regions and other stream-stream effects is key to producing more realistic predictions at 1 AU.\\ \indent Another important avenue of future work will be to compare predictions of wind speeds from TEMPEST with in situ measurements, when the results from ZEPHYR and TEMPEST agree to a greater extent. We are already able to reproduce well-known correlations and linear fits from observations, but accurate forecasting is our goal. Other ways in which forecasting efforts can be improved that TEMPEST does not address include better lower boundary conditions on and coronal extrapolation of $\vec{B}$, moving from 1D to a higher dimensional code, and including kinetic effects of a multi-fluid model ($T_{p} \ne T_{e}$, $T_{\parallel} \ne T_{\perp}$).\\\indent Space weather is dominated by both coronal mass ejections (CMEs) and high-speed wind streams. The latter is well-modeled by the codes presented in this paper, and these high-speed streams produce a greatly increased electron flux in the Earth's magnetosphere, which can lead to satellite disruptions and power-grid failure \citep{2011A&A...526A..20V}. Understanding the Sun's effect on the heliosphere is also important for the study of other stars, especially in the ongoing search for an Earth analog. The Sun is an indespensible laboratory for understanding stellar physics due to the plethora of observations available. The modeling we have done in this project marks an important step toward full understanding of the coronal heating problem and identifying sources of solar wind acceleration. | 14 | 4 | 1404.5998 |
1404 | 1404.7486_arXiv.txt | \noindent We have obtained a deep, simultaneous observation of the bright, nearby Seyfert galaxy IC~4329A with {\it Suzaku} and {\it NuSTAR}. Through a detailed spectral analysis, we are able to robustly separate the continuum, absorption and distant reflection components in the spectrum. The absorbing column is found to be modest ($\sim6 \times 10^{21} \pcmsq$), and does not introduce any significant curvature in the Fe K band. We are able to place a strong constraint on the presence of a broadened Fe K$\alpha$ line ($E_{\rm rest}=6.46^{+0.08}_{-0.07} \keV$ with $\sigma=0.33^{+0.08}_{-0.07} \keV$ and $EW=34^{+8}_{-7} \eV$), though we are not able to constrain any of the parameters of a relativistic reflection model. These results highlight the range in broad Fe K line strengths observed in nearby, bright AGN (roughly an order of magnitude), and imply a corresponding range in the physical properties of the inner accretion disk in these sources. We have also updated our previously reported measurement of the high-energy cutoff of the hard X-ray emission using both observatories rather than just {\it NuSTAR} alone: $E_{\rm cut}=186 \pm 14 \keV$. This high-energy cutoff acts as a proxy for the temperature of the coronal electron plasma, enabling us to further separate this parameter from the plasma's optical depth and to update our results for these parameters as well. We derive $kT=50^{+6}_{-3} \keV$ with $\tau=2.34^{+0.16}_{-0.11}$ using a spherical geometry, $kT=61 \pm 1 \keV$ with $\tau=0.68 \pm 0.02$ for a slab geometry, with both having an equivalent goodness-of-fit. | \label{sec:intro} X-ray observations of active galactic nuclei (AGN) elucidate many physical processes that drive the production of high-energy photons close to a supermassive black hole (SMBH). In addition to probing the properties of the corona in radio-quiet AGN, X-ray data can constrain the nature of the inner accretion flow by measuring the morphology of the Fe K$\alpha$ line. This emission line, with a rest energy of $6.4 \keV$ for neutral iron, arises via fluorescence from the accretion disk, which is illuminated by the Compton-scattered continuum X-rays. Given the relatively high cosmic abundance of iron and its high fluorescent yield, coupled with the lack of other lines expected in that part of the spectrum, it is a reasonably ``clean'' probe of the kinematics of the accreting material. Narrow (usually unresolved by CCD detectors, i.e., $v/c \lesssim 0.005$) Fe K$\alpha$ lines have been observed in the vast majority of Seyfert galaxies \markcite{Yaqoob2004}({Yaqoob} \& {Padmanabhan} 2004). In addition to their small width, the lack of variability implies that they originate from the illumination by the primary X-ray source of reprocessing material relatively far from the black hole, likely in the outer disk or torus of Seyfert unification schemes \markcite{Antonucci1993,Urry1995}({Antonucci} 1993; {Urry} \& {Padovani} 1995). Indeed, this emission region has been spatially resolved in the Seyfert 2 AGN NGC~4945 \markcite{Marinucci2012}({Marinucci} {et~al.} 2012), and it lies at a distance from the nucleus of $30-50 \pc$ ($\sim10^8-10^9\,r_{\rm g}$ for the $10^6 \Msun$ black hole at its core, where $r_{\rm g} \equiv GM/c^2$). The near ubiquity of these features suggests that this distant material is present in almost all Seyfert AGN. In some Seyfert galaxies the Fe K line appears to be broadened (to $v/c \gtrsim 0.1$), most likely by relativistic effects; e.g., MCG--6-30-15, first observed by \markcite{Tanaka1995}{Tanaka} {et~al.} (1995), and recently also confirmed in NGC~1365 \markcite{Risaliti2013}({Risaliti} {et~al.} 2013). These sources are two of the best examples of AGN displaying a prominent red wing indicative of fluorescing material close to the innermost stable circular orbit (ISCO) in the accretion disk. A broad Fe K$\alpha$ line originating from material extending to the ISCO allows us to determine whether the black hole is rotating, and if so, to determine its spin and possibly direction as well (for recent reviews, see, e.g., \markcite{Reynolds2013}{Reynolds} 2013 and \markcite{Brenneman2013b}{Brenneman} 2013). However, such broad, relativistic emission lines are not observed in all Seyferts observed with high signal-to-noise (S/N) \markcite{Nandra2007,dlCP2010,Brenneman2012}({Nandra} {et~al.} 2007; {de La Calle P{\'e}rez} {et~al.} 2010; {Brenneman} {et~al.} 2012), possibly indicating the absence of relatively cold, Compton-thick gas close to the black hole (though the caveats to line detection detailed in \markcite{Ballantyne2010}{Ballantyne} 2010 should also be kept in mind). Regardless of the mechanism by which they are determined, any inferences regarding the structure, location, and physical conditions of the accretion disk and the corona require a precise, high S/N measurement of the broad-band X-ray spectrum from $\leq 2$ to $\geq 50 \keV$. This is necessary in order to disentangle various emission and absorption components contributing to the total observed X-ray emission, described above. A significant advance towards such measurements is provided by the deployment of the focusing hard X-ray telescopes onboard the {\it NuSTAR} observatory, the latest in the series of NASA's Small Explorer satellites. This mission is sensitive in the bandpass of $3-79 \keV$ with the updated calibration, and provides a hundredfold improvement of sensitivity in the hard X-ray band over previous instruments \markcite{Harrison2013}({Harrison} {et~al.} 2013). The use of {\it NuSTAR} in conjunction with X-ray telescopes that are more sensitive at softer energies (e.g., {\it XMM-Newton} and {\it Suzaku}) yields the highest S/N ever achieved across the $\sim0.2-79 \keV$ bandpass. Equally important in deriving the physical properties of the disk and corona is the selection of a representative, bright target. One good candidate is the southern Seyfert 1.2 galaxy IC~4329A ($z=0.0161$, \markcite{Willmer1991}{Willmer} {et~al.} 1991; $N_{\rm H}\,[{\rm gal}]=4.61 \times 10^{20} \pcmsq$, \markcite{Kalberla2005}{Kalberla} {et~al.} 2005; $M_{\rm BH}=1.20 \times 10^8 \Msun$, \markcite{dlCP2010}{de La Calle P{\'e}rez} {et~al.} 2010), which in the hard X-ray/soft $\gamma$-ray band appears similar to an average radio-quiet Seyfert (e.g., \markcite{Zdziarski1996}{Zdziarski} {et~al.} 1996). The host galaxy is an edge-on spiral in a pair with IC~4329, separated by $\sim3$ arcmin. IC~4329A was one of the first AGN observed to have a Compton reflection component in addition to its strong Fe K$\alpha$ line \markcite{Piro1990}({Piro}, {Yamauchi}, \& {Matsuoka} 1990). As with most other X-ray emitting Seyferts, it is variable, but the variability amplitude during a typical observation is modest: the root mean square fractional variability has been measured at $\leq20\%$ in the $15-150 \keV$ {\it RXTE} band \markcite{Markowitz2009}({Markowitz} 2009), and $(17 \pm 3) \%$ in the $14-195 \keV$ band with {\it Swift}/BAT \markcite{Soldi2014}({Soldi} {et~al.} 2014). The average $2 - 10 \keV$ flux historically ranges from $F_{\rm 2-10} \sim (0.1-1.8) \times 10^{-10} \ergpcmsqps$ \markcite{Beckmann2006,Verrecchia2007}({Beckmann} {et~al.} 2006; {Verrecchia} {et~al.} 2007). IC~4329A has been the subject of many X-ray observations, beginning with the analysis of its simultaneous {\it ROSAT} and {\it OSSE} spectrum \markcite{Zdziarski1994,Madejski1995}({Zdziarski} 1994; {Madejski} {et~al.} 1995). In harder X-rays, the source has also been observed by {\it BeppoSAX} \markcite{Perola2002}({Perola} {et~al.} 2002), {\it ASCA+RXTE} \markcite{Done2000}({Done}, {Madejski}, \& {{\.Z}ycki} 2000) and {\it INTEGRAL} \markcite{Molina2013}({Molina} {et~al.} 2013), which have placed rough constraints on the high-energy cutoff of the power-law (a proxy for coronal temperature) at $E_{\rm cut} \geq 180 \keV$, $E_{\rm cut}=150-390 \keV$ and $E_{\rm cut}=60-300 \keV$, respectively. Combining the non-simultaneous {\it INTEGRAL} and {\it XMM-Newton} data further constrained the cutoff energy to $E_{\rm cut}=130-203 \keV$ \markcite{Molina2009}({Molina} {et~al.} 2009), while a combination of the {\it XMM} and {\it BeppoSAX} data yielded $E_{\rm cut}=150-390 \keV$ \markcite{Gondoin2001}({Gondoin} {et~al.} 2001). A detailed examination of the {\it ASCA} and simultaneous {\it RXTE} data revealed that the continuum is indeed described well by the model used to describe the {\it ROSAT+OSSE} data (either thermal or non-thermal Comptonization plus neutral, distant reflection), and that the Fe K$\alpha$ line is moderately broadened and can be described by a Gaussian with FWHM of $\sim30,000 \kmps$ \markcite{Done2000}({Done} {et~al.} 2000). This is consistent with the conclusions of \markcite{Dadina2007}{Dadina} (2007), who noted a moderately broad Fe K$\alpha$ line of similar width and equivalent widths up to $EW \sim 180 \eV$ in {\it BeppoSAX} data, paired with measured reflection fractions up to $R \sim 1.5$. Both the {\it ASCA} and {\it ROSAT} data, as well as the {\it XMM-Newton} observations \markcite{Steenbrugge2005}({Steenbrugge} {et~al.} 2005), suggest that the soft X-ray spectrum is absorbed by a combination of neutral and partially ionized gas, with a total column of $\sim3 \times 10^{21} \pcmsq$. This is comparable to the host galaxy's ISM column density \markcite{Wilson1979}({Wilson} \& {Penston} 1979). After accounting for the reflection component, the source shows some modest spectral variability of the primary continuum, being softer at higher flux levels \markcite{Madejski2001,Miyazawa2009,Markowitz2009}({Madejski}, {Done}, \& {{\.Z}ycki} 2001; {Miyazawa}, {Haba}, \& {Kunieda} 2009; {Markowitz} 2009). Here, we report on results from our simultaneous {\it Suzaku} and {\it NuSTAR} observation of IC~4329A. We discussed our measurements of the properties of the underlying continuum in \markcite{Brenneman2014}{Brenneman} {et~al.} (2014) (hereafter referred to as paper I), and in this work we update those values and focus on constraining the reprocessing components. In \S2, we report on the {\it Suzaku} and {\it NuSTAR} observations, and in \S3 we present a brief timing analysis of the data. Our spectral analysis follows in \S4, with a discussion of the inferred accretion disk properties and their implications in \S5. | \label{sec:disc} \subsection{Summary} \label{sec:summary} In our deep observation of IC~4329A, performed simultaneously with {\it Suzaku} and {\it NuSTAR}, we are able to robustly separate the continuum, absorption and distant reflection components in the spectrum using the broad energy range of our observations. The results of our analysis can be summarized as follows: \begin{itemize} \item{IC~4329A was viewed in a flux state near its historical average, and displayed little variability on short timescales and $\sim30\%$ variability over the course of the campaign, {\bf as has been found in previous X-ray observations}.} \item{While we were able to place a strong constraint on the presence of a broadened Fe K$\alpha$ line in the data ($EW=34^{+6}_{-9} \eV$ in Model~1, the highest equivalent width seen in our modeling), we were not able to constrain any of the parameters when a relativistic line model was applied to the data. As such, it is not possible to derive any constraints on the spin of the black hole in IC~4329A using these observations.} \item{We have made the most accurate, precise measurement of the high-energy cutoff of the X-ray emission to date: $E_{\rm cut}=186 \pm 14 \keV$. This measurement improves on that made with {\it NuSTAR} alone in paper I ($E_{\rm cut}=178^{+74}_{-40} \keV$), demonstrating the necessity of obtaining high-S/N, broadband X-ray data in order to determine the properties of the corona.} \item{Using data from both {\it Suzaku} and {\it NuSTAR}, we derive $kT=50^{+6}_{-3} \keV$ and $\tau=2.34^{+0.16}_{-0.21}$ for the spherical geometry, with $kT=61 \pm 1 \keV$ and $\tau=0.68 \pm 0.02$ for the slab geometry.} \end{itemize} \subsection{Understanding the Corona} \label{sec:corona} It is important to establish the continuum level in AGN in order to determine their overall energy budget, and the high-S/N, broadband X-ray spectra we have obtained using {\it Suzaku} and {\it NuSTAR} simultaneously enable us to disentangle the continuum, absorption and reflection signatures more accurately than we are able to with either observatory alone. Our spectral and timing analyses of the simultaneous {\it Suzaku} and {\it NuSTAR} observations of IC~4329A demonstrate that changes in the continuum flux are responsible for the modest, secular changes in the overall source flux that we detect. The high-S/N, broadband spectra enable us to determine that neither the absorption nor reflection components show any significant variability over the course of our observing campaign. Though this result was hinted at in paper I, the addition of the {\it Suzaku} data to the analysis confirms the lack of absorption variability, in particular. Referencing Model~1, we note that the power-law normalization decreases by $\sim30\%$ between the high- and low-flux states during our observations (\S\ref{sec:spec_var}); similarly, the overall source flux decreases by approximately the same amount (\S\ref{sec:timing}). The variation is more pronounced at energies below $\sim10 \keV$ (Fig.~\ref{fig:high_low_diff_norefl}), in keeping with our examination of the RMS variability spectrum (Fig.~\ref{fig:fvar}). We note that the spectrum is rather hard: the cutoff power-law fit in Model~1 returns a photon index of $\Gamma=1.73 \pm 0.01$, also confirming the results from paper I. This is consistent with several recent measurements taken with {\it Chandra} and {\it XMM} (average $\Gamma=1.73$; \markcite{McKernan2004,Steenbrugge2005,Markowitz2006}{McKernan} \& {Yaqoob} 2004; {Steenbrugge} {et~al.} 2005; {Markowitz}, {Reeves}, \& {Braito} 2006), but inconsistent with the joint {\it XMM+INTEGRAL} spectral fitting performed by \markcite{Molina2009}{Molina} {et~al.} (2009) ($\Gamma=1.81 \pm 0.03$). We note, however, that the data reported by Molina \etal were not obtained simultaneously. Spectral fitting returned a significantly softer index in previous epochs as well; between 1995 and 2001, the average reported spectral slope was $\Gamma=1.91$ with a range between $\Gamma=1.83-2.0$ \markcite{Madejski1995,Cappi1996,Perola1999,Done2000,Gondoin2001}({Madejski} {et~al.} 1995; {Cappi} {et~al.} 1996; {Perola} {et~al.} 1999; {Done} {et~al.} 2000; {Gondoin} {et~al.} 2001). Caution should be used when measuring the power-law slope using only data $\leq10 \keV$, as the true slope of the continuum is best assessed over a much broader energy band extending out to higher energies where the continuum is more dominant. We also note that the quality of our data at high energies with {\it NuSTAR} now far surpasses that of the spectra obtained with {\it RXTE, BeppoSAX, CGRO} or {\it INTEGRAL}. Even so, these differences in measured power-law slope may indicate that IC~4329A undergoes significant coronal variability on $\leq$years-long timescales. It would be interesting to investigate whether the cutoff energy of the power-law shows similar variations to the spectral index, but unfortunately the constraints placed on this parameter historically are too loose to enable this test. In all of the observations prior to 2009, either the cutoff energy was fixed to the $E_{\rm cut}=270^{+167}_{-80} \keV$ result obtained by \markcite{Perola1999}{Perola} {et~al.} (1999), or did not improve on this result (e.g., $E_{\rm cut} \geq 100 \keV$, \markcite{Madejski1995}{Madejski} {et~al.} 1995; $E_{\rm cut}=270 \pm 120 \keV$, \markcite{Gondoin2001}{Gondoin} {et~al.} 2001). Our result ($E_{\rm cut}=186 \pm 14 \keV$, consistent with yet more precise than the measurement from paper I) is consistent with that obtained by \markcite{Molina2009}{Molina} {et~al.} (2009), as discussed in \S~\ref{sec:broadband}. It is also at the median point of the high-energy power-law cutoffs that have been measured in Seyfert AGN thus far with {\it NuSTAR}. Others include Ark~120 ($\geq190 \keV$, \markcite{Matt2014}{Matt} {et~al.} 2014), SWIFT~J2127.4+5654 ($108^{+11}_{-10} \keV$, \markcite{Marinucci2014}{Marinucci} {et~al.} 2014) and Mrk~335 ($\geq153 \keV$, Parker \etal, submitted). Owing to the high quality and broadband energy coverage of our data, we were able to reach beyond the phenomenological power-law representation of the continuum and consider more physical models, following our work with the {\it NuSTAR} data alone in paper I. Models~2-3 provide roughly equivalent statistical fits to the data, incorporating a {\tt compTT} model that parametrizes the temperature, optical depth and geometry of the electron plasma, as well as an {\tt xillver} model that assumes a neutral slab of material inclined at $60 \degmark$ to our line of sight and leaves the reflected flux from the disk and its iron abundance as free parameters. We also added in two Gaussian components to represent (1) a blend of the resonance, intercombination and forbidden O\,{\sc vii} emission lines, and (2) a contribution from a broad Fe K$\alpha$ line from the inner disk. The goodness-of-fit is largely insensitive to the coronal geometry assumed, though the temperatures derived from the spherical and slab geometries are inconsistent at the $>2\sigma$ level ($kT=50^{+6}_{-3} \keV$ and $kT=61 \pm 1 \keV$, respectively). The two models also produce different values for the optical depth of the corona: $\tau=2.34^{+0.16}_{-0.21}$ and $\tau=0.68 \pm 0.02$, respectively. These values differ by $>4\sigma$ (see Fig.~\ref{fig:hist}) even after the factor-of-two geometrical difference in calculating the optical depth is accounted for (see paper I), indicating that a physical change in the properties of the plasma is necessary when applying a different geometry in order to achieve a good fit. This was not the case when Models~2-3 were fit to the {\it NuSTAR} data alone in paper I. Unfortunately, the lack of both short timescale variability and significant relativistic, inner disk reflection in IC~4329A during our observing campaign prevents us from determining the distance of the corona from the accretion disk, and from being able to constrain how centrally concentrated the coronal emission is. \begin{figure}[H] \hbox{ \centering \includegraphics[width=0.35\textwidth,angle=270]{f12a.eps} \includegraphics[width=0.35\textwidth,angle=270]{f12b.eps} } \caption{{\small {\it Left:} Probability density for the {\tt compTT} electron temperature ($kT_{\rm e}$) in the spherical (black) and slab (red) geometries, as determined from our MCMC analysis. {\it Right:} The same plot, this time for the optical depth ($\tau$) of the electrons. The optical depths for the slab geometry have been multiplied by a factor of two (see paper I) to make them more directly comparable to the optical depths measured in the spherical geometry.}} \label{fig:hist} \end{figure} Though the spherical model returns a slightly better statistical fit, we conclude that the slab model is more physically believable due to the tighter match it provides between coronal temperature and power-law cutoff energy (assuming $E_{\rm cut} \sim 2-3kT$; in this case, $3kT=183 \pm 3 \keV$, which is much closer than Model~2 to being compatible with the measured power-law cutoff value in Model~1). We also note that the temperature and optical depth of the plasma are much more tightly constrained in the slab geometry. Due to an inherent modeling degeneracy between the optical depth and temperature of the electron plasma in each geometry, however, there is a small, linearly correlated range of values for these parameters which demonstrate approximately equal statistical fit quality, as can be seen in Figs.~\ref{fig:mo2_contours}a and \ref{fig:mo3_contours}a. It is thus not surprising that, as the temperature increases in the slab vs. sphere case, the optical depth decreases to compensate and produce an equivalent goodness-of-fit. Nonetheless, both parameters are constrained with the best precision and accuracy ever achieved. We also note that both sets of values for the coronal temperature and optical depth measured with the combined, simultaneous {\it Suzaku} and {\it NuSTAR} datasets deviate significantly from those obtained when fitting the {\it NuSTAR} data alone in Models~2-3 of paper I (Figs.~\ref{fig:mo2_contours}a, \ref{fig:mo3_contours}a and \ref{fig:hist}). In particular, the slab geometry in paper I returned $kT_{\rm e}=37^{+7}_{-6} \keV$ and $\tau=1.25^{+0.20}_{-0.10}$, which is inconsistent with the results for this geometry using the combined dataset at a $>3\sigma$ level. We attribute this difference to the larger spectral energy coverage of the combined dataset, which, as noted previously, allows us to definitively disentangle the signatures of the continuum, reflection and absorption in ways that {\it NuSTAR} alone cannot, since its effective area only extends down to $3 \keV$ and its spectral resolution in the Fe K band is three times worse than that of {\it Suzaku} ($450 \eV$ vs. $150 \eV$). The amount of reflection in the system and the curvature induced by the high-energy cutoff of the continuum are particularly degenerate at energies $>10 \keV$, but having the high-S/N, high spectral resolution {\it Suzaku} data in the Fe K band, especially, allows us to break this degeneracy and to independently constrain $kT_{\rm e}$ and $K_{\rm refl}$ (see Figs.~\ref{fig:mo2_contours}b and \ref{fig:mo3_contours}b). Taking these factors into account, we consider the values for the coronal temperature and optical depth measured in this work to be the definitive physical properties of the corona in IC~4329A. Their deviation from those determined through the analysis of only $>3 \keV$ data at lower spectral resolution underscore the importance of obtaining high-S/N data across a broad X-ray bandpass in order to draw conclusions about the corona from Comptonization models. As more constraints on coronal parameters are measured from a sample of AGN, it will be interesting to compare the coronal properties (e.g., $\Gamma$, $kT$, $\tau$) with the those of the black hole and inner accretion flow (e.g., $M_{\rm BH}$, $a$, $\dot{m}$). It has long been thought that more actively accreting black holes cool their coronae more efficiently (\markcite{Skipper2013}{Skipper}, {Mc Hardy}, \& {Maccarone} 2013 and references therein), but a sample of AGN with sensitive, broad-band X-ray spectra, as presented here for IC~4329A, would help to test this conjecture. \subsection{The Fe K Region} \label{sec:iron} The addition of the {\it Suzaku} data enables us to perform a detailed analysis of the Fe K region in IC~4329A, while the {\it NuSTAR} data provide an important check on the physical consistency of our models by simultaneously showing us the Compton reflection continuum $>10 \keV$. The majority of the reflection component originates in material at large distances from the black hole (e.g., the putative torus), and is well fit by a static, neutral {\tt xillver} component. Though there is evidence for a broad Fe K$\alpha$ line or a Compton shoulder due to the residuals remaining after a narrow Fe K$\alpha$ line is included, the broad line explanation is more likely since the reflection models we employ already incorporate a Compton shoulder component. That said, the Compton shoulder explanation cannot be conclusively ruled out with these data. Assuming that the residuals do correspond to a broad iron line component, modeling this emission feature with a relativistic line profile (e.g., {\tt diskline, laor} or {\tt relline}) yields no improvement in the fit and the model parameters cannot be constrained. We have successfully modeled this residual emission with a Gaussian line at $E \sim 6.4 \keV$, and can place a limit on its strength relative to the continuum of $EW=24-42 \eV$ (Model~1). Only $\sim1\%$ of the reflected emission arises from the broadened Fe K$\alpha$ feature. While obviously present and originating from well within the broad emission line region ($v_{\rm FWHM} \sim 36,000 \kmps$), this feature likely represents only a weak broad line from the inner disk. Indeed, the reflection fraction constrained via the {\tt pexrav} model in \S\ref{sec:suzaku} is also low by comparison with other bright, nearby Seyfert 1 AGN \markcite{Walton2013}({Walton} {et~al.} 2013). Such a finding is in keeping with the theoretical work of \markcite{Ballantyne2010}{Ballantyne} (2010), however, who suggested that the majority of Seyferts may have broad Fe K$\alpha$ lines with $EW \leq 100 \eV$. Our inability to constrain any of the parameters when a relativistic disk line model is applied renders it useless in constraining the spin of the black hole, however. Similarly, attempting to fit this feature with a relativistic smearing kernel convolved with an ionized disk reflection spectrum also results in no statistical improvement in fit and no parameter constraints. The feature is not apparent in the high-low flux difference spectrum of the AGN, meaning that it is not significantly variable over the course of the observations. Even if it does arise from inner disk reflection this is not surprising, given the lack of short timescale variability of the continuum. A broad Fe K line has been reported in every observation taken of IC~4329A with an X-ray observatory capable of spectrally resolving it \markcite{Piro1990,Madejski1995,Cappi1996,Perola1999,Done2000,Gondoin2001,McKernan2004,Steenbrugge2005,Markowitz2006,Dadina2007,Molina2009,Molina2013}({Piro} {et~al.} 1990; {Madejski} {et~al.} 1995; {Cappi} {et~al.} 1996; {Perola} {et~al.} 1999; {Done} {et~al.} 2000; {Gondoin} {et~al.} 2001; {McKernan} \& {Yaqoob} 2004; {Steenbrugge} {et~al.} 2005; {Markowitz} {et~al.} 2006; {Dadina} 2007; {Molina} {et~al.} 2009, 2013). Such a line was also noted in the {\it XMM-Newton} analysis of the source by \markcite{dlCP2010}{de La Calle P{\'e}rez} {et~al.} (2010), suggesting that this line, though difficult to characterize definitively, is a persistent feature of the spectrum over years-long timescales. Provided that sufficient photon counts have been obtained in the observation (i.e., $\geq200,000$ from $2-10 \keV$), broad Fe K lines are detected in $\geq40\%$ of all AGN \markcite{Guainazzi2006,Nandra2007,dlCP2010}({Guainazzi}, {Bianchi}, \& {Dov{\v c}iak} 2006; {Nandra} {et~al.} 2007; {de La Calle P{\'e}rez} {et~al.} 2010). Further, some actively accreting AGN have had broad Fe K emission lines reported in previous epochs but not currently (e.g., NGC~5548, \markcite{Brenneman2012}{Brenneman} {et~al.} 2012). Taking these points into consideration, it is perhaps not surprising to find that IC~4329A does not exhibit strong relativistic reflection signatures during our observation. Indeed, marginal detections of broad Fe K emission lines such as that found here may be the norm rather than the exception among even actively accreting AGN \markcite{Ballantyne2010}({Ballantyne} 2010). Within this framework, it is intriguing to note that the source is accreting at $L_{\rm bol}/L_{\rm Edd} \sim 0.46$ for a black hole with an estimated mass of $M_{\rm BH}=1.20 \times 10^8 \Msun$ \markcite{dlCP2010}({de La Calle P{\'e}rez} {et~al.} 2010). Given that the Keplerian velocity of the broadened Fe K$\alpha$ feature places its origin at $r \sim 70\,r_{\rm g}$ from the black hole, this suggests that the optically thick disk may not extend down to the ISCO. The disk may be truncated within this radius, or perhaps it is too highly ionized to significantly contribute to the reflection spectrum. Indeed, highly ionized disks are expected in relatively high accretion rate sources \markcite{Ballantyne2011}({Ballantyne}, {McDuffie}, \& {Rusin} 2011) such as IC~4329A. The power-law photon index of the source is also considerably harder ($\Gamma \sim 1.73$) than is typical for an actively accreting source with an inner disk extending down to its ISCO, and marks a departure of $>6\sigma$ from the AGN relation measured by \markcite{Brightman2013}{Brightman} {et~al.} (2013). According to these authors, for an Eddington ratio of $L_{\rm bol}/L_{\rm Edd}=0.46$, one should measure $\Gamma=2.16 \pm 0.07$, in contrast to the $\Gamma=1.73 \pm 0.01$ measured here for IC~4329A (however, the intrinsic scatter in this relation must be considered, as must the uncertainty in measuring the Eddington ratio in a given source). The relative weakness of the reflection features compared to similar AGN coupled with the hard power-law index of the source, particularly, lends credence to the hypothesis put forward in paper I: that we are witnessing an outflowing corona with $v_{\rm out} \sim 0.2c$, following the work of \markcite{Beloborodov1999}{Beloborodov} (1999) and \markcite{Malzac2001}{Malzac}, {Beloborodov}, \& {Poutanen} (2001). Although an ionized inner disk would certainly inhibit strong reflection features from this region, as per \markcite{Ballantyne2010}{Ballantyne} (2010), it is worth noting that the outflowing corona scenario would suppress them as well: if the main locus of coronal emission is situated at a height of $\geq50\,r_{\rm g}$ then we become insensitive to reflection from the disk within $50\,r_{\rm g}$. Also, if the corona is relativistically outflowing then aberration decreases the illumination of the inner disk, again making us less sensitive to any reflection from this region. Under any of the above conditions we would not expect to be able to constrain the spin of the black hole in IC~4329A. A deep multi-wavelength campaign involving UV spectra, particularly, in addition to the outstanding data now available in X-rays with {\it NuSTAR} and {\it Suzaku, XMM-Newton} or {\it Chandra} would be necessary in order to properly evaluate the characteristics and structure of the inner accretion disk, and to place our results on the energetics of the system in their proper context. | 14 | 4 | 1404.7486 |
1404 | 1404.2606_arXiv.txt | High levels of exozodiacal dust have been observed in the inner regions of a large fraction of main sequence stars. Given the short lifetime of the observed small dust grains, these `exozodis' are difficult to explain, especially for old ($>100$ Myr) stars. The exozodiacal dust may be observed as excess emission in the mid-infrared, or using interferometry. We hypothesise that exozodi are sustained by planetesimals scattered by planets inwards from an outer planetesimal belt, where collision timescales are long. In this work, we use N-body simulations to show that the outwards migration of a planet into a belt, driven by the scattering of planetesimals, can increase, or sustain, the rate at which planetesimals are scattered from the outer belt to the exozodi region. We hypothesise that this increase is sufficient to sustain the observed exozodi on Gyr timescales. No correlation between observations of an outer belt and an exozodi is required for this scenario to work, as the outer belt may be too faint to detect. If planetesimal driven migration does explain the observed exozodi, this work suggests that the presence of an exozodi indicates the presence of outer planets and a planetesimal belt. | \label{sec:intro} Emission from dusty material is commonly observed in the outer regions of planetary systems. \Herschel observations of solar-type stars find 20\% have excess emission associated with a debris disc \citep{Eiroa2013}. This presents an increase from the $\sim16\%$ of stars found by Spitzer \citep{trilling08}. % Spitzer detected similar excess emission, from warmer dusty material, around less than 1\% of stars at 8.5-12$\mu$m \citep{Lawler2009}. Detailed modelling of many systems find that the emission is likely to originate from multiple cold and warm components \citep[e.g.][]{Hr8799su, Churcher11}. This could be compared to our Solar System, with its dusty emission from both the Kuiper and asteroid belts, as well as zodiacal dust in the terrestrial planet region. In general cold, outer debris discs can be explained by the steady-state collisional grinding of large planetesimals \citep{DominikDecin03, Wyatt2002, wyattreview}. However, there exists a maximum level of dust that can be produced in steady-state \citep{Wyatt07hot}. Many of the warmer dusty systems exceed this limit \citep{Wyatt07hot,Absil06, bonsor_exozodi}. The observed small dust has a short lifetime against both radiative forces and collisions. The origin of the high levels of warm dust are not fully understood. It is these systems that are the focus of this work. The term exozodi is commonly used to refer to systems with high levels of warm dust in the inner regions, referring to the similarity in location of the dust with our Solar System's zodiacal cloud. There are two main techniques that can be used to probe high levels of warm dust in the inner regions of planetary system, with distinct abilities to detect dust with different properties. Warm emission has been detected in the mid-infrared, for example using Spitzer/IRS/Akari/WISE, from very bright, dusty systems. Near and mid-infrared interferometry, on the other hand, can probe closer to the star and detect lower levels of hotter dust. Together these observations build a picture of complex, diverse planetary systems in which dusty emission from the inner regions is common and in many cases has a complex structure, for example the dust may be split into various different belts \citep[e.g.][]{Lebreton2013, Su2013}. In this work, we focus on improving our understanding of any system in which high levels of exozodiacal dust are observed that cannot be explained by steady-state collisional evolution. The detection statistics resulting from the mid-infrared observations are very different to those from interferometry, mainly due to the differences in sensitivities of the two techniques and the two different populations probed. Both Spitzer and WISE found that emission from dust at 8.5-12$\mu$m \citep{Lawler2009} and $12\mu$m is rare \citep{Kennedy2013}, occuring for less than 1\% of stars (Spitzer) or less than 1 in 10,000 (WISE, specifically emission from BD+20307-like systems). Interferometry has the advantage of being able to readily distinguish emission from the star and emission external to the star. A recent survey using CHARA/FLUOR found excess emission around $18^{+9}_{-5}\%$ of a sample of 28 nearby FGK stars with ages greater than 100Myr \citep{Absil2013}. Although the constraints on the position, composition and distribution of the dusty material are poor, Bayesian analysis has found in a handful of cases that the emission most likely originates from small (less than $\mu$m) grains within 1-3AU \citep{Defrere_Vega, diFolco07,Absil06}. \cite{Ertelinprep} find a similarly high occurence rate for exozodiacal dust in H-band, using PIONIER, a visitor instrument on the VLTI. \begin{figure*} \includegraphics[width=0.9\textwidth]{mig_di.eps} \caption{A diagram (not to scale) to illustrate the scattering of planetesimals by an outer planet, that leads to an exchange of angular momentum and the outerward migration of that planet. Some of the scattered particles are ejected, whilst some are scattered into the inner planetary system, where they interact with the inner planets. This scattering leads to a flux of material into the exozodi region. } \label{fig:mig_di} \end{figure*} Such high levels of small grains cannot be explained in steady-state. One explanation that is regularly postulated is that we are fortunate enough to observe these systems during the aftermath of a single large collision \citep{Lisse2009,Lisse12}, maybe something like the Earth-Moon forming collision \citep{Jackson2012} or the aftermath of a dynamical instability similar to our Solar System's Late Heavy Bombardment \citep{Absil06, Lisse12,Wyatt07hot}. Not only do such collisions occur rarely at the later times ($>$100Myr) where exozodiacal dust is observed, but \cite{bonsor_instability} show that, whilst high levels of dust are produced in the inner regions of planetary systems following instabilities, this dust is short-lived, and therefore, it is highly improbable that we observe such dust in more than 0.1\% of systems. On the other hand, \citep{Kennedy2013} shows that stochastic collisions could explain the distribution of (high) excesses observed with WISE at $12\mu$m. Whilst it is not clear whether the same explanation holds for both the handful of sources with high levels of excess emission in the mid-IR, and the $\sim20\%$ of sources with K-band excess detected using interferometry \citep{Absil2013}, it is clearly easier to find an explanation for the former. A link with outer planetary systems has been hypothesised \citep{Absil06,resolveHD69830, bonsor_exozodi, ecc_ring}. It has been shown that the emission could be reproduced in steady-state by a population of highly eccentric ($e>0.99$) planetesimals \citep{ecc_ring}, but it is not clear how such a population could form. An alternative explanation could lie in the trapping of nano grains in the magnetic field of the star \citep{Su2013, Czechowski2010}, but this still requires detailed verification. Most of the dust ($>90\%$) observed in our Solar System's zodiacal cloud is thought to originate from the disruption of Jupiter Family Comets scattered inwards by the planets from the Kuiper belt \citep{Nesvorny10}. Steady-state scattering in exo-planetary systems is not sufficiently efficient to sustain the high levels of dust observed in exozodi \citep{bonsor_exozodi}. We propose here that the efficiency at which planetesimals are scattered inwards by planets can be increased by the migration of a planet into an outer belt. We suggest that this could explain the high levels of exozodiacal dust observed in some planetary systems, in the manner illustrated by Fig.~\ref{fig:mig_di}. In the early evolution of our Solar System, Neptune is thought to have migrated outwards, due to an exchange of angular momentum as it scattered Kuiper belt objects \citep[\eg][]{Fernandez1984,Ida2000, Levison2003,Gomes2004}. This can explain some of the observed features of the Kuiper belt, including Pluto's resonant, eccentric orbit \citep{Malhotra1993}, or the `hot classical Kuiper belt' \citep{Gomes2003}. A similar exchange of angular momentum can occur between a planet and planetesimals in an exo-planetary system \citep[\eg][]{Kirsh2009,Bromley2011, Ormel2012}. Such planetesimal driven migration can occur in either an outwards or an inwards direction, at a rate and for a timescale that depends on the properties of the disc and the planet \citep{Kirsh2009, Ormel2012}. We hypothesise that such planetesimal driven migration can sustain the scattering of planetesimals into the inner regions of a planetary system on long timescales. Such scattered planetesimals could account for the high levels of exozodiacal dust observed in some planetary systems, particularly in old ($>100$Myr) planetary systems. In this work we use N-body simulations to consider when planetesimal driven migration occurs and its effect on the planetary system, in particular the rate at which planetesimals are scattered into the inner regions. We consider that such scattered material has the potential to resupply an exozodi on long timescales. We investigate whether the rate at which material is transported inwards is sufficient to sustain the observed exozodi. We start in \S\ref{sec:simulations} by discussing our simulations. In \S\ref{sec:migration} we discuss the migration of the outer planet in our simulations and in \S\ref{sec:scattering} the manner in which this migration increases the rate at which material is scattered into the inner regions of the planetary system. In \S\ref{sec:coll} and \S\ref{sec:observations} we discuss the collision evolution and observations of the outer disc. Our conclusions are made in \S\ref{sec:discussion}. \begin{table*} \begin{tabular}{|c |c| c|} \hline {\bf Planet} & & \\ \hline Outer planet semi-major axis& $a_{pl, out}$& 15AU \\ Planet semi-major axes & $a_{pl}$ & 5,6.6,8.7,11.4,15AU\\ Planet semi-major axes$^*$ & $a_{pl}$ & 5,8.7,15AU \\ Planet masses $M_{belt}(0)=10M_\oplus$ & $M_{pl}$& 2, 5, 10, 15, 20, $30M_\oplus$ \\ Planet masses $M_{belt}(0)=100M_\oplus$ & $M_{pl}$& 50, 70, 100, 130, 165, $465M_\oplus$ \\ Planet density ($M_{pl}<0.5M_\oplus$) & $\rho$& $3.9$gcm$^{-3}$\\ Planet density ($0.5<M_{pl}<10M_\oplus$) & $\rho$& 5.5gcm$^{-3}$\\ Planet density ($11<M_{pl}<49M_\oplus$)& $\rho$ &1.6gcm$^{-3}$\\ Planet density ($50<M_{pl}<500M_\oplus$) &$\rho$&1.3gcm$^{-3}$\\ Ratio between planet periods & $\frac{a_2}{a_1}$& 1.3, 1.5,1.7\\ Inner pair of planets &\multicolumn{2}{c}{$[10M_\oplus,5M_\oplus]$, $[30M_\oplus,5M_\oplus]$, $[100M_\oplus,5M_\oplus]$, $[100M_\oplus,30M_\oplus]$, $[30M_\oplus,100M_\oplus]$}\\ & & \\ \hline {\bf Planetesimal belt} & & \\ \hline No. of particles & N & 2,500\\ Planetesimal mass & {\tt no mass} & 0 \\ Planetesimal mass & {\tt mass} & $M_{belt}(0)/N$\\ Total mass & $M_{belt}(0)$ & $10$, $100M_\oplus$ \\ Surface density & $\Sigma dr$ & $\propto r^{-1}dr$ \\ Semi-major axes & $a_{pp}$ & 15-30AU \\ Eccentricity & $e_{pp}$ & 0-0.01\\ Inclinations & $i_{pp}$ & $0-0.1'$\\ Longitude of ascending node & $\Omega_{pp}$&$0-360^\circ$\\ Longitude of pericentre & $\Lambda_{pp}$&$0-360^\circ$\\ Free anomaly &$f_{pp}$ &$0-360^\circ$\\ \hline {\bf Other parameters} & & \\ \hline Stellar Mass &$M_*$& $1M_\odot$ \\ Ejection radius& $r_{out}$& 10000AU \\ Inner radius &$r_{in}$ & 3AU \\ \hline \end{tabular} \caption{Initial conditions of our simulations} \begin{flushleft} $^*$ For planet masses higher than $M_{pl}= 40M_\oplus$ \end{flushleft} \label{tab:initialcond} \end{table*} | \label{sec:discussion} High levels of dust observed in the inner regions of planetary systems, known as exozodi, are difficult to explain, particularly in old ($>100$Myr) planetary systems. In this work we investigate whether the migration of an outer planet, driven by the scattering of planetesimals, can explain these observations. We show that in principle the outwards migration of the planet maintains a reasonably high mass flux of planetesimals scattered inwards to the inner regions of the planetary systems, as long as the planet continues to migrate outwards. We hypothesise that these planetesimals could resupply the observed exozodi. An example of this scenario, applied to the specific constraints of the Vega planetary system is illustrated in \cite{RaymondVega2014}. Tight constraints on the architecture of the planetary system, however, are required in order for this scenario to work. Firstly, we re-iterate that the constraints on how much material must be transported inwards are poor, incorporating the poor observational constraints on the mass of small dust grains, the poor theoretical constraints on the lifetime of this dust and the poorly constrained conversion of large planetesimals to small dust grains. We estimate the minimum mass flux required and show that this can be produced by planetesimals scattered inwards by planets, either if the outer planet migrates into a low surface density outer disc whilst the migration continues, or at early ($<500$Myr) times for higher surface density discs, independent of migration of the outer planet (although the efficiency of the scattering was increased in our simulations by separating the inner planets by constant ratios of their orbital periods). We show that the migration of an outer planet can be sustained on Gyr timescales, and longer in planetary systems with wide outer belts. Whether or not a planet migrates, and how fast it migrates, depends critically on the mass of the planet and the surface density of the disc. Migration stalls if the planet mass is sufficiently high that it clears the zone surrounding it of material before it has migrated across it. In order to sustain migration on long timescales, the best candidates are the slow migration of planets with masses just below the critical limit at which their migration is stalled, and in discs of lower surface density. The lower surface density of the disc also avoids problems with collisional depletion of the disc material stalling the migration. Wide belts are required if the migration is to continue for the full 10Gyr main-sequence lifetime of a sun-like star. This suggests that the `old' (several Gyr) planetary systems with detectable exozodis, in this scenario, would originally have had wide planetesimal belts, although these belts may by now have been cleared. It also suggests that if the frequency of planetary systems with narrow planetesimal belts is higher than that with wider planetesimal belts, there would be an increased probability of planetesimal driven migration producing exozodi around younger stars, in stark constrast to the lack of age dependence in the exozodi phenomenum found in the observations of \cite{Absil2013}. On the other hand, our estimations in \S\ref{sec:observations} suggest that the lack of a correlation between the presence of an exozodi and a detection of a cold, outer belt does not rule out the ability of planetesimal driven migration to supply the observed exozodi. To summarise, we have presented simulations that illustrate the manner in which the outwards migration of a planet into a planetesimal belt could increase the rate at which planetesimals are scattered inwards and thus, has the potential to produce detectable exozodis, even in old ($>$Gyrs) planetary systems. | 14 | 4 | 1404.2606 |
1404 | 1404.5817_arXiv.txt | Two-dimensional simulations of hot Jupiter upper atmospheres including the planet's magnetic field are presented. The goal is to explore magnetic effects on the layer of the atmosphere that is ionized and heated by stellar EUV radiation, and the imprint of these effects on the Ly$\alpha$ transmission spectrum. The simulations are axisymmetric, isothermal, and include both rotation and azimuth-averaged stellar tides. Mass density is converted to atomic hydrogen density through the assumption of ionization equilibrium. The three-zone structure -- polar dead zone, mid-latitude wind zone, and equatorial dead zone -- found in previous analytic calculations is confirmed. For a magnetic field comparable to that of Jupiter, the equatorial dead zone, which is confined by the magnetic field and corotates with the planet, contributes at least half of the transit signal. For even stronger fields, the gas escaping in the mid-latitude wind zone is found to have a smaller contribution to the transit depth than the equatorial dead zone. Transmission spectra computed from the simulations are compared to HST STIS and ACS data for HD 209458b and HD 189733b, and the range of model parameters consistent with the data is found. The central result of this paper is that the transit depth increases strongly with magnetic field strength when the hydrogen ionization layer is magnetically dominated, for dipole magnetic field $B_0 \ga 10\ {\rm G}$. Hence transit depth is sensitive to magnetic field strength, in addition to standard quantities such as the ratio of thermal to gravitational binding energies. Another effect of the magnetic field is that the planet loses angular momentum orders of magnitude faster than in the non-magnetic case, because the magnetic field greatly increases the lever arm for wind braking of the planet's rotation. Spin-down timescales for magnetized models of HD 209458b that agree with the observed transit depth can be as short as $\simeq 30\ {\rm Myr}$, much shorter than the age of the system. | Hot Jupiters are gas giants orbiting close to their parent stars. The large stellar EUV flux heats and ionizes the upper atmosphere of these planets, increasing the thermal energy to a value approaching the gravitational binding energy, leading to a region weakly bound to the planet. The resulting large gas scale heights and atmospheric escape form an extended upper atmosphere around the planet, which may be probed by transmission spectroscopy using strong atomic resonance lines. The existence of an extended upper atmosphere has been established through a variety of observations. Spectroscopic UV observations of HD 209458b (\citealt{Henry 2000}) indicate a $\sim 10\%$ decrease in flux during transit at $\sim 100\ \rm km\ s^{-1}$ from the center of the hydrogen Ly$\alpha$ line. This transit depth has been attributed to an atmosphere of neutral H extending to a radius $\simeq 2.4 R_p$, where $R_p$ is the radius of the broadband photosphere of the planet (see \citealt{Vidal 2008}). As this radius is comparable to the Roche lobe radius, \citet{Vidal 2004} suggested that the planet is losing mass through Roche lobe overflow. Additional observations of HD 209458b at transit have indicated absorption in other resonance lines, including NaI \citep{Charbonneau 2002, Sing 2008}, OI \citep{Vidal 2004}, CII \citep{Vidal 2004, France 2011}, and SiIII \citep{Linsky 2010, France 2011}. Follow-up observations and re-analysis of HST-ACS data, in comparison with HST-STIS low and medium-resolution spectra, confirmed the reduction of Ly$\alpha$ flux \citep{Ehrenreich 2008}. Transmission spectra of the hot Jupiter HD 189733b have also revealed absorption due to HI (in both Ly$\alpha$ and H$\alpha$; \citealt{Lecavelier 2010} and \citealt{2012ApJ...751...86J}) and NaI \citep{Redfield2008, Snellen 2008}. HST-COS observations by \citet{Linsky 2010} have indicated absorption at up to $\pm50$ km s$^{-1}$ from line center in CII and SiIII that may be indicative of high velocity absorbers in the upper atmosphere (although these observations probe deeper layers than those probed by the HI observations). Multi-epoch spectra have also revealed significant changes in the Ly$\alpha$ transit depth, which are correlated with flares in ionizing radiation from the host star detected with HST and SWIFT \citep{Lecavelier 2012}. This paper will focus on the Ly$\alpha$ absorption observed in the upper atmospheres of HD 209458b and HD 189733b. One interpretation of this absorption invokes hydrogen with thermal velocity $\sim 10\ \rm km\ s^{-1}$ with such a large column density that the damping wings of Ly$\alpha$ become optically thick (e.g. Yelle 2004). Alternatively, a much smaller column is required if hydrogen atoms at thermal velocities $\sim 100\ \rm km\ s^{-1}$, created by charge exchange with stellar wind protons \citep{2008Natur.451..970H, 2010ApJ...709..670E, Tremblin 2012}, produce a sufficiently broad line profile. This paper considers the former scenario in which the transit depth is due to a layer of thermal hydrogen in the planet's atmosphere. A number of studies have already explored the properties of strongly irradiated exoplanet atmospheres, and the possibility of thermally-driven hydrodynamic outflow \citep{Yelle 2004, Yelle 2006, 2005ApJ...621.1049T, Garcia 2007, Murray-Clay 2009, Ehrenreich 2011} and/or Roche Lobe overflow \citep{2003ApJ...588..509G, 2010Natur.463.1054L, 2010ApJ...721..923L, Ehrenreich 2011}. The present study stands apart from the previous ones by including, through detailed magnetohydrodynamic (MHD) simulations, the effect of the planetary magnetic field. It is a follow-up of Trammell et al. (2011), which considered the magnetic effects semi-analytically. \citet[][hereafter, Paper I]{Trammell 2011} showed that the addition of the planetary magnetic field leads to the formation of an equatorial ``dead-zone" (DZ) --- a static region where the wind ram pressure is insufficient to overwhelm magnetic stresses and open the field lines into an outflow. This effect is well known in the classical MHD stellar wind theory (e.g. Mestel 1968). Paper I found a second static region near the poles where the wind can be shut off by the increased gravitational potential barrier from the stellar tide. In the strong tide limit, a wind-zone (i.e., the outflow region; WZ) is then expected to exist only at intermediate latitudes. A goal of the present paper is to verify this analytically-obtained three-zone structure with detailed numerical simulations. Another conclusion from Paper I was that observations of Ly$\alpha$ absorption at the 5-10\% level for HD 209458b may be detecting neutral H which is collisionally coupled to ionized gas confined to the equatorial DZ by the planet's magnetic field. The bulk of the absorbing gas observed at transit thus may not be escaping, but rather is in the static equatorial dead zone. This qualitative result differs from the basic assumption in the hydrodynamic escape and Roche Lobe overflow models, that the transit observations are probing gas in the act of escaping from the planet. A limitation of the analytic models in Paper I is that they ignore magnetic forces, which means that the poloidal magnetic geometry was assumed rather than computed self-consistently. Another limitation is that the fluid was assumed to corotate with the planet everywhere, including the wind zone, where the corotation is expected to break down at large distances. The treatment in this paper overcomes these limitations by performing MHD simulations, which compute the magnetic field structure and fluid rotation self-consistently. This allows a more accurate calculation of the mass and angular momentum loss rates, as well as the density and velocity profiles required to compute transmission spectra. The plan of the paper is as follows. Section \ref{zeus.sec} describes the simulation setup and model parameters, and Section \ref{sims.sec} presents the simulation results. Section \ref{transit.sec} describes the method for computing model Ly$\alpha$ spectra. The frequency-dependent and frequency-integrated transit depths for a range of simulation parameters are compared with observations of HD 209458b and HD 189733b. Findings are summarized in Section \ref{summary.sec}. The Appendix contains a discussion of numerical effects at the shear layer separating the dead and wind zones. | 14 | 4 | 1404.5817 |
|
1404 | 1404.3957_arXiv.txt | { NGC7538 IRS1 is claimed to be a high-mass young stellar object (YSO) with $30~M_{\odot}$, surrounded by a rotating Keplerian-disk, probed by a linear distribution of methanol masers. The YSO is also powering a strong compact H II region or ionized wind, and is driving at least one molecular outflow. The axes orientations of the different structures (ionized gas, outflow, and disk) are however misaligned with each other, which led to different competing models proposed to explain individual structures. We investigate the 3D kinematics and dynamics of circumstellar gas with very high linear resolution, from tens to 1500 AU, with the ultimate goal of building a comprehensive dynamical model for what is considered the best high-mass accretion disk candidate around an O-type young star in the northern hemisphere. We use high-angular resolution observations of 6.7~GHz \meth\ masers with the EVN, \nh3\ inversion lines with the JVLA B-Array, and radio continuum with the VLA A-Array. In particular, we employed four different observing epochs of EVN data at 6.7 GHz, spanning almost eight years, which enabled us to measure, besides line-of-sight (l.o.s.) velocities and positions (as done in previous works), also l.o.s. accelerations and proper motions of \meth\ masers. In addition, we imaged highly-excited \nh3\ inversion lines, from (6,6) to (13,13), which enabled us to probe the hottest molecular gas very close to the exciting source(s). We confirm previous results that five 6.7~GHz maser clusters (labeled from "A" to "E") are distributed over a region extended N--S across \ $\approx$1500~AU, and are associated with three components of the radio continuum emission. We propose that these maser clusters identify three individual high-mass YSOs in \NGC1, named IRS1a (associated with clusters "B" and "C"), IRS1b (associated with cluster "A"), and IRS1c (associated with cluster "E"). We find that the 6.7~GHz masers distribute along a line with a regular variation of \Vlsr\ with position along the major axis of the distribution of maser cluster~"A" and the combined clusters~"B"+"C". A similar \Vlsr\ gradient (although shallower) is also detected in the \nh3\ inversion lines. Interestingly, the variation of \Vlsr\ with projected position is not linear but quadratic for both maser clusters. We measure proper motions for 33 maser features, which have an average amplitude ($4.8\pm0.6$~\kms) similar to the variation in \Vlsr\ across the maser cluster, and are approximately parallel to the clusters' elongation axes. By studying the time variation of the maser spectrum, we derive also l.o.s. accelerations for 30 features, with typical amplitude of \ $\sim10^{-3}-10^{-2}$~\kmsy. We model the masers in both clusters~"A" and "B"+"C" in terms of an edge-on disk in centrifugal equilibrium. Based on our modeling, masers of clusters~"B"+"C" may trace a quasi-Keplerian $\sim$1~M$_{\sun}$, thin disk, orbiting around a high-mass YSO, IRS1a, of up to $\approx$25~M$_{\sun}$. This YSO dominates the bolometric luminosity of the region. The disk traced by the masers of cluster~"A" is both massive ($\lesssim$16~M$_{\sun}$ inside a radius of $\approx$500~AU) and thick (opening angle $\approx$ 45\degree), and the mass of the central YSO, IRS1b, is constrained to be at most a few M$_{\sun}$. Towards cluster~"E", \nh3\ and 6.7~GHz masers trace more quiescent dynamics than for the other clusters. The presence of a radio continuum peak suggests that the YSO associated with the cluster~"E", IRS1c, may be an ionizing, massive YSO as well. We present compelling evidence that \NGC1\ is not forming just one single high-mass YSO, but consists of a multiple system of high-mass YSOs, which are surrounded by accretion disks, and are probably driving individual outflows. This new model naturally explains all the different orientations and disk/outflow structures proposed for the region in previous models. } | The formation of massive stars (O-B type) by the same accretion processes believed to form low-mass stars appears problematic, because the intense radiation pressure from the star luminosity and the thermal pressure from the \HII\ region around the young stellar objects (YSOs) may be sufficient to reverse the accretion flow and prevent matter from reaching the star \citep{Zin07}. The "standard" theory predicts that this occurs for stars having masses in excess of 8~M$_{\sun}$, leading to the paradoxical conclusion that stars above this limit should not exist \citep{Pal93}. Recent theories have demonstrated that the radiation pressure problem can be solved if accretion occurs through a circumstellar disk \citep[e.g.,][]{Kui10, Kui11}, thus explaining the formation of stars up to 140~M$_{\sun}$. In a quite different scenario, \citet{Bon98} proposed that O-type stars may form through the merger of low-mass objects. Despite the theoretical evidence, while a handful of disk candidates in B-type ($M_{\star} < 20$~M$_{\sun}$) protostars has been reported in the literature in recent years \citep[][and references therein]{Ces06}, there has been no clear evidence for accretion disks around more massive O-type stars so far. The few rotating molecular structures detected around O-type stars (on scales $>$10000~AU) have been interpreted as gravitationally-unstable, transient bodies, infalling and accreting either to a central cluster of low-mass protostars \citep{Sol05,Bel11} or to a single massive protostar \citep{San03,Beu08}. Since O-type stars form at large distances (a few kpc) and deeply embedded inside dense massive cores (likely containing protoclusters), both confusion/crowding and poor resolution in previous studies have precluded to discriminate between different star-formation scenarios and, ultimately, to establish whether the globally rotating and infalling material in the cloud actually accretes onto individual massive protostars. This would require to resolve the structure and dynamics of accreting gas at small radii ($\lesssim$1000~AU) from massive YSOs but this has been challenging so far (present millimeter interferometers have typical resolutions of order of 1\arcsec, corresponding to 1000 AU at 1 kpc). Therefore, observational signatures of rotating disks around O-type forming stars are essential to progress in our understanding of the mass-accretion process and to constrain theoretical models of high-mass star formation (HMSF). In this context, one excellent diagnostic tool of gas kinematics within 10--1000~AU from YSOs is provided by multi-epoch very long baseline interferometric (VLBI) observations of interstellar masers \citep{God06a,God06b,God11a,Mat10,Mos07,Mos11a,Mos13,San10a,San10b,Tor03,Tor11}. Among different molecular masers, \meth\ is particularly interesting, because it is exclusively associated with HMSF and provides an excellent probe of accretion. Recently, \citet{God11a} reported a convincing signature of infall of a circumstellar molecular envelope with a radius of only 300~AU around a B-type forming star in AFGL~5142, by using multi-epoch VLBI observations of \meth\ masers spanning six years. Measurements of the 3D velocity field of the circumstellar gas has provided the most direct and least unbiased measurement (yet obtained) of infall of a molecular envelope onto an intermediate- to high-mass protostar. Other interesting examples of 3D kinematics with methanol masers are reported in \citet{San10a,San10b} and \citet{Mos11a,Mos13}. In order to characterize the accretion process in an O-type YSO, in this paper we study one of the best high-mass accretion disk candidates in the northern hemisphere, \NGC1. This region is relatively nearby (2.7 kpc; \citealt{Mos09}), very luminous ($\sim$10$^5$~L$_{\sun}$; e.g., \citealt{Aka05}), it contains an \HII\ region \citep[e.g.,][]{Wyn74}, and it has been suggested to be powered by an O6/7 star of about 30~M$_{\sun}$. Very Large Array (VLA) continuum observations revealed a double-peaked structure in the ionized gas within 0\farcs2 from the central core and a more extended ($\sim$1\arcsec) emission elongated N--S \citep[e.g.,][]{Gau95}. Radio recombination lines observed at cm- and mm-wavelengths show extremely broad line widths, suggestive of expanding motions of the ionized gas \citep{Gau95,Ket08}. A multi-wavelength study of the radio continuum showed that the free-free emission from IRS1 is dominated by an ionized jet, rather than a hyper-compact HII region \citep{Sand09}. Recently, a number of interferometric studies conducted with increasing angular resolution, at 1.3~mm with the SMA (3\arcsec\ beamsize, \citealt{Qiu11}), at 1.3~and~3.4~mm with the SMA and CARMA (0\farcs7 beamsize, \citealt{Zhu13}), and at 0.8~mm with the PdBI (0\farcs2 beamsize, \citealt{Beu13}), detected several typical hot-core species, showing inverse P-Cygni profiles, probing inward motion of the dense gas on scales $\gtrsim$1000~AU with a mass infall rate \ $\dot{M}\sim$10$^{-3}$~M$_{\sun}$~yr$^{-1}$. These radio centimeter and millimeter observations also identified several outflows emanating from \NGC1, along N--S \citep{Gau95,Sand09}, NW--SE \citep{Qiu11}, and NE--SW \citep{Beu13}. The simultaneous presence of jets/outflows and a strong accretion flow toward IRS\,1, led some authors to postulate the presence of an accretion disk surrounding IRS\,1. \citet{Min98} observed a linear distribution of 6.7 and 12.2 GHz \meth\ masers with a position angle (PA) of about 112\degree \ and \citet{Pes04} proposed an edge-on Keplerian disk model to explain positions and l.o.s. velocities of maser spots. A mid-infrared (IR) study however questioned the edge-on disk model traced by the \meth\ masers, suggesting that the radio continuum emission (elongated N--S) traces an ionized wind emanating from the surface of a disk with \ PA of $\sim$30\degree\ perpendicular to the NW--SE CO-bipolar outflow \citep{DeBui05}. In an attempt to explain the different orientation of the elongated structures observed in the \meth\ masers and in the near-IR emission, \citet{Krau06} proposed that the edge-on disk is driving a precessing jet. \citet{Sur11} however pointed out that, in addition to the linear \meth\ maser cluster proposed to trace the edge-on Keplerian disk, there are additional maser clusters in the region within 1\arcsec, and they proposed an alternative scenario where all the observed \meth\ maser clusters should mark the interface between the infalling envelope and a large-scale torus, having a rotation axis with the same PA (30\degree) \ of the elongated near-IR emission observed by \citet{DeBui05}. While the individual competing models explain some properties of the system, either the ordered structure of one maser cluster \citep[e.g.,][]{Pes04}, or the global spatial distribution of all clusters \citep[e.g.,][]{Sur11}, or the complex pattern of molecular outflows emerging from IRS\,1 \citep{Krau06}, they fail to provide a clear picture of accretion/outflow in terms of a simple disk/jet system, as expected in the context of a canonical picture of star formation. Likewise, despite the plethora of interferometric studies on the region at (sub)mm-wavelengths (with angular resolutions in the range \ 0\farcs2--2\arcsec), no clear evidence of a rotating disk has been found and only a confusing picture for the outflows has been drawn so far. In this paper, we overcome the shortcomings of previous works by analyzing a multi-epoch dataset of 6.7~GHz CH$_3$OH maser observations and complementing the maser data with new interferometric images of highly-excited inversion lines of \nh3, from (6,6) to (13,13). This approach has a two-fold advantage. First, the multi-epoch dataset (spanning almost eight years), enables us to measure proper motions and l.o.s. accelerations of \meth\ masers, besides positions and l.o.s. velocities (as done in previous works). Second, highly-excited inversion lines of \nh3\ at cm-wavelengths, enable us to probe the hottest gas close the YSO(s) in an optically-thin regime and at the highest angular resolutions achievable with connected-element interferometers (previous works were conducted at mm-wavelengths and/or with poorer angular resolutions). A detailed analysis of the \nh3\ data will be presented in a forthcoming paper (Goddi et al. in prep.). The main goal of this paper is to investigate the 3D dynamics of the circumstellar molecular gas at the small scales (10--500~AU) probed by the masers and relate it to the large-scale motions (500--2000~AU) probed by the complementary interferometric thermal \nh3\ data. We describe observations and data reduction in Sect.~\ref{obs} and our observational results in Sect.~\ref{results}. In Sect.~\ref{vlsr_regu}, we examine the ordered velocity structures measured with the \meth\ masers and thermal \nh3\ lines. We present a dynamical model to explain our measurements in Sect.~\ref{mas_kin}, followed by a discussion on the nature of star formation in \NGC1\ in Sect.~\ref{phy_sen}. Some implications of our model and a comparison with previous models are illustrated in Sect.~\ref{discu}. Finally, we summarize our main findings in Sect.~\ref{summary}. | \label{discu} \subsection{General Implications of the Model for \NGC1} In previous section, we described the main properties of the individual YSOs and their surrounding disks, as derived from our \meth\ and \nh3\ measurements as well as our edge-on disk model. We discuss here general implications of this model. We start discussing the structure, geometry, and velocity field of the circumstellar gas associated with individual YSOs with respect to the natal molecular clump. Looking at Fig.~\ref{nh3_pvI_mas}, three regions at different \Vlsr\ can be identified in the \nh3\ absorption: \ 1)~the most redshifted (weak) absorption to the SE of the maser elongation of cluster~"A"; \ 2)~the (strong) absorption near the systemic velocity ($-$59.4~\kms) towards the centre of the maser clusters~"B"+"C"; \ 3)~absorption in between the two maser clusters or YSOs IRS1a and IRS1b, where the gas \Vlsr\ steadily increases, going from the centre of the clusters~"B"+"C" towards the cluster~"A". One should distinguish here between gas motion {\it between} the two YSOs and {\it around} a given YSO. Owing to limited angular resolution, close to the cluster~"A" the two contributions to the gas motion are not resolved and the direction of the \Vlsr\ gradient bends from close to N--S (as it is at the middle point between the two clusters) to SW--NE. Blending of the two different motions accounts also for the orientation of the \Vlsr\ gradient visible in the \nh3\ first-moment maps (see Figure~\ref{nh3_mom1}), which is directed NE--SW at PA = 30\degree -- 40\degree. Taking into account the bias introduced by the blending of the two motions, Fig.~\ref{nh3_pvI_mas} then indicates that the \Vlsr\ gradient in the gas {\it between} the two YSOs IRS1a and IRS1b is directed close to N--S and extends from \ $\approx$ $-$59~\kms (at the centre of the clusters~"B"+"C") to \ $\approx$ $-$56~\kms (close to the cluster~"A"). This finding suggests that the observed \Vlsr\ gradient between the two maser clusters could reflect original gas motions inside the molecular core out of which the YSOs IRS1a and IRS1b have formed. Since we model the maser clusters~"A" and "B"+"C" as two disks close to edge-on, separated by less than 500~AU, we could ask which are the chances to observe two nearby edge-on disks oriented at different PA in the plane of the sky. A possible explanation could be maser excitation effects. In fact, an edge-on geometry implies large column densities of masing molecules which in turn enable to strongly amplify the maser emission. In principle, there could be many YSOs in the region but only those with edge-on disks would be traced by the methanol masers. In practice, we think that this is not the case. In fact, the small separation between IRS1a and IRS1b (i.e., $<$500~AU) would imply a Jeans length for the collapsing and fragmenting core of at most a few hundreds of AU. Even assuming an average density as high as \ $n_{\rm H_2}$ = 10$^9$~cm$^{-3}$ (i.e., the peak value measured towards IRS1a by \citealt{Beu13}), the mass of individual fragments would correspond to only a few hundredths of solar mass. We conclude therefore that the presence of other undetected massive YSOs in the region, besides the ones identified by the methanol maser clusters, is unrealistic. An alternative and more plausible explanation could be a physical mechanism producing an edge-on alignment. \citet{Sur11} measured the linear polarized emission of all \meth\,masers in the region, finding that the magnetic field is aligned close (within 20\degr) to the plane of the sky and preferentially oriented perpendicularly to the elongation axes of clusters "A", "B", and "C", that is perpendicular to the disks around IRS1a and IRS1b (see their Table~3). This finding agrees with predictions of star formation models which include magnetic fields \citep[e.g., ][]{Ban07,Sei11}. In these models, the collapsing core flattens preferentially along a direction perpendicular to that of the magnetic field lines. These predictions are consistent with the general result of a polarimetric survey of \meth\,masers towards high-mass star forming regions \citep{Sur13} and suggest that the magnetic field may be dynamically important in the mass-accretion and mass-loss regulating the formation of high-mass YSOs. In this framework, an edge-on geometry for protostellar disks could be favoured if the magnetic field in the natal core (before collapse) were orientated near the plane of the sky. Although this qualitative argument explains the edge-on geometry of the two disks around IRS1a and IRS1b, it does not explain their different PA in the sky. One could now ask whether the disks around IRS1a and IRS1b are stable or transient structures. The Toomre stability parameter for disks, $Q$, is given by the expression \ $ Q = (2 \, \Omega \, \Delta V) / (\sqrt{8 \ln2} \, \pi \, G \, \Sigma) $, with \ $\Omega$ \ the angular velocity, $\Sigma$ \ the surface density, and \ $ \Delta V$ \ the FWHM linewidth. For the maser cluster~"A", the disk model requires that at \ $R = R_0 = 550$~AU, $\Omega = \beta = 0.025$~\kmo, with the disk/envelope mass equal to \ $M_0 = 16$~M$_{\sun}$ (see Equation~\ref{fit_clA}). Using these parameters, we derive \ $Q_{clA} = 0.18 \, \left[\frac{\Delta V}{{\rm km \, s}^{-1}}\right] $. The condition for instability,\ $Q_{clA} \le 1$, is then satisfied if \ $\Delta V \le $5.6~\kms. From our \nh3\ lines, we measure FWHM linewidths of 7--10 \kms, where however the two YSOs IRS1a and IRS1b, with a velocity separation of 3 \kms\ (see Sect.~\ref{mas_kin}), are blended together. We then expect \ $Q_{clA} \le 1 $, that is the massive disk/envelope around IRS1b is probably not gravitationally stable and could break up into fragments. For IRS1a, if a large fraction of the \ 25~M$_{\sun}$ \ inside a radius \ $R_0$ = 740~AU (see Equation~\ref{fit_clBC}) actually constitutes the YSO mass, then the disk surface density should be about one order of magnitude lower than for the disk/envelope around IRS1b. Since the value of \ $\Omega = 0.02$~\kmo\ is comparable, the condition for instability for IRS1a would require \ $\Delta V \le $1~\kms. The measured values of FWHM linewidths are definitively larger than this threshold, indicating that the disk surrounding the high-mass YSO IRS1a is actually gravitationally stable. In the rest of this section, we will discuss excitation effects and implications on the physical structure of the observed disks. Excitation models predict that the 6.7~GHz \meth\ masers, radiatively pumped by IR radiation, are strongly inverted over an extended range of gas density, 10$^4$~cm$^{-3}$ $\le n_{\rm H_2} \le$ 10$^{9}$~cm$^{-3}$, and kinetic temperature, 25~K $\le T_K \le$ 250~K \citep{Cra05}. The IR radiation can be produced by warm dust nearby the methanol masing molecules, with an allowed range of dust temperature for efficient maser pumping \ 100~K $\le T_d \le$ 300~K. Following the discussion in Sect.~\ref{phy_sen}, the gas temperature towards the 6.7~GHz maser clusters in \NGC1\ should vary from the lowest value in IRS1c to the highest value (250~K) in IRS1a. Therefore, the gas temperature measured and/or expected towards each maser cluster is within the range predicted by the model of \citet{Cra05} for strong maser action. The value of gas density \ $n_{\rm H_2} \sim$10$^{9}$~cm$^{-3}$ \ towards IRS1a derived from the SMA observations by \citet{Beu13}, is close to the upper end of the maser excitation range, but still consistent with the models of \citet{Cra05}. A more quantitative comparison between the physical conditions deduced from our kinematical model and those required for maser excitation can be done for IRS1b and the cluster~"A". Looking at the spatial distribution of the maser features onto the edge-on disk (see Fig.~\ref{disk_pl}, left panel), one can see that the maser emission abruptly decreases in intensity and vanishes at radii between \ 500 and 300~AU. As indicated by \ Equation.~\ref{nh2_a}, at radii smaller than \ $R_0 = 550$~AU \ the local gas density rapidly increases to values \ $n_{\rm H_2}$ > 10$^9$~cm$^{-3}$, and the masers are probably thermally quenched, in line with the model predictions of \citet{Cra05}. The edge-on disk model for cluster~"A" predicts a maximum radius of 6.7~GHz maser emission of \ $\approx$2500~AU, which can also be explained in terms of the maser excitation model of \citet{Cra05} if the IR radiation flux at this radius falls below the threshold for efficient maser pumping. Assuming that the dust absorbs the stellar photons and re-emits them at IR wavelengths like a black-body, one derives an inverse square-root dependence for the dust temperature on the distance from the star. If $T_d \approx$300~K (i.e., the maximum value expected for efficient pumping) at the closest maser radii of \ $\approx$300~AU, at the largest maser radius of \ $\approx$2500~AU \ $T_d \approx$100~K, that is the value indicated by \citet{Cra05} as the lower limit for efficient excitation of the 6.7~GHz masers. From \ Equation~\ref{nh2_a} it is also clear that the opening angle \ $\alpha$ \ of the disk around IRS1b has to be large enough ($\alpha$ $\approx$ 45\degree) to ensure that the gas density does not exceed the threshold for the thermal quenching even at \ $R \ge R_0$. Such a geometry reminds the profiles of the rotationally flattened, circumstellar envelopes observed towards low-mass YSOs at millimeter wavelengths \citep{Koe95} and in the near-IR \citep{Cot01}. If high-mass star formation proceeds as a scaled-up version of the low-mass case, rotationally flattened, thick disks/envelopes could characterize the earliest protostellar phase, when only a minor fraction of the available circumstellar material has been accreted onto the protostar. Finally, it is worth discussing more thoroughly the distribution of the 6.7~GHz masers around IRS1a and IRS1b as predicted by the edge-on disk model (see Fig.~\ref{disk_pl}). We note two main differences between the two maser distributions: 1)~the maser pattern in the IRS1b disk is more elongated along the l.o.s and more compact in the perpendicular direction than the one in IRS1a; \ 2)~approaching the line-of-sight to the star, the maser intensity increases in the IRS1b disk and decreases in the IRS1a disk. The analysis of \citet[][see Table~3]{Sur11} shows that most of the 6.7~GHz masers in \NGC1\ are unsaturated, so that their intensity depends linearly on the background radiation. Therefore, a l.o.s. elongated maser pattern can naturally result if masers amplify a compact continuum source (like a hypercompact \HII\ region or an ionized jet) around the star, in such a fashion that only the l.o.s. intercepting sufficiently strong continuum background radiation would result in maser emission. Regarding point 1), since IRS1a is more massive and evolved than IRS1b, it should have a more developed and extended continuum, which naturally explains the observation of the 6.7~GHz features at larger projected separation from the star (up to \ $\approx$400~AU compared with \ $\approx$200~AU for IRS1b). Regarding point~2), the opposite trend observed in IRS1a and IRS1b can be explained with slightly different disk geometries for the two YSOs. For a perfectly edge-on disk, as in the case of IRS1b, any l.o.s. offset from the star will intercept less column density than the l.o.s. along the star. The increasing maser intensity approaching the l.o.s. to IRS1b can then result from longer velocity-coherent paths, since, for a pure rotation pattern, velocities at all radii have equally null projection along the l.o.s. to the centre of rotation. If the disk is however not perfectly edge-on, as it is probably the case for IRS1a (see discussion in Sect.~\ref{mas_kin_qua}), this argument does not hold anymore. In this case one key element to consider is instead the role played by circumstellar dusty disks in shielding the masing molecules against the disruptive action of the UV stellar radiation. The dissociation of methanol molecules follows the temperature distribution, which, for an hydrostatic Keplerian disk, depends on both the radial distance on the disk plane and the vertical height above/below the mid-plane. In the following, we show that any l.o.s. offset from the star provides better shielding enabling the methanol molecules to more easily survive. Let us consider a point above the disk midplane, which we assume (for simplicity) to lie on the plane containing the disk major axis and the l.o.s.. Indicating with \ $i_d$ \ the angle between the disk plane and the l.o.s., with \ $s$ \ and \ $z$ \ the offset from the star along the major axis and the distance along the l.o.s. to the the major axis, respectively, the height \ $H$ \ from the disk mid-plane of the selected point is given by \ $ H = z \sin(i_d) $. The projection of the point onto the disk mid-plane is at a radial distance \ $R$ \ from the star given by \ $ R = \sqrt{ z^2 \cos^2(i_d) + s^2 }=\sqrt{ H^2 / \tan^2(i_d) + s^2 }$. This expression shows that at a given height \ $H$, the l.o.s. to the star ($s=0$) intersects the disk atmosphere at a radial distance from the star {\em smaller} than that of the l.o.s. offset by \ $s$ \ along the major axis. Similarly, it is possible to show that at a given radial distance $R$, the l.o.s. to the star ($s=0$) intersects the disk atmosphere at a height from the disk plane {\em larger} than that of the l.o.s. offset by \ $s$ \ along the major axis. Consequently, l.o.s. with smaller and smaller offset \ $s$ \ from the star cross {\em increasingly warmer} portions of the disk atmosphere, where methanol molecules can be more easily dissociated and maser emission reduced. As a result, (strong) maser emission can be observed only along l.o.s. sufficiently offset from the star to intersect better shielded disk positions. This interpretation can readily account for the 6.7~GHz maser emission fading away towards the l.o.s. to IRS1a, and indirectly proves the reliability of the position of IRS1a derived by our model. The opposite trend observed in IRS1b can be used to conclude that its disk has to be very close to edge-on. Since here we propose kinematical models, we do not attempt to explain the physical nature of the ordered maser patterns, which would require a full analysis of the physical and kinematical conditions of the gas, coupled with a consistent treatment of the radiative transport in the methanol maser line. \subsection{Comparison with Previous Models} For completeness, here we discuss briefly some of the alternative models previously proposed to explain NGC7538 IRS1. As mentioned in the Introduction, \citet{Pes04} modelled the linear distribution of 6.7 and 12.2 GHz \meth\ masers of cluster "A" as an edge-on Keplerian disk, rotating around a 30 \ms \,protostar. While the geometrical properties of this modeled disk are qualitatively compatible with the model described in Sect.~\ref{mas_kin} (e.g., PA and radius), that model unlike ours does not set constraints on the mass/density distribution in the disk and the central mass, which is given in input to the model (assuming that the YSO exciting the maser cluster "A" accounts for the region's bolometric luminosity). Another limitation is the assumption of Keplerian rotation, despite an evident bend in the position-velocity diagram, which can be naturally explained if the rotation velocity increases with the radius. Our model includes as constraints l.o.s. accelerations and proper motions (besides l.o.s. velocities and positions), and allows us to constrain the mass/density distribution in the disk and the central mass, as well as to establish the radial profile of the rotation velocity. An alternative model to the edge-on disk model was proposed by \citet{DeBui05}, based on a mid-IR study. They find that the circumstellar dust associated with IRS1 is extended both northwest-southeast (on scales $\sim4000$ AU, PA$\sim-45$\degree) and northeast-southwest (on small scales $\sim400$ AU, PA$\sim30$\degree). Since the large-scale mid-IR emission is extended along a position angle similar to that of the CO outflow, they suggest that it is coming from dust heated on the walls of the outflow cavities near the star, as opposed to trace a circumstellar disk. They also propose that the small-scale elongation seen in the mid-IR, nearly perpendicular to the axis of the CO outflow (and the linearly distributed methanol masers), is a circumstellar disk. While this "outflow" model explains the main properties of the mid-IR emission, individual maser features in cluster "A" would be either clumps in the cavity or recent ejecta from the outflow, but both options are inconsistent with our measurements of velocities and accelerations of \meth\ masers (see arguments at the end of Sect.~\ref{mas_kin_qua} ). In an attempt to explain the different orientations of the elongated structures of cluster "A" of \meth\ masers and of the near/mid-IR emission as well as the CO outflow axis, \citet{Krau06} proposed that the edge-on disk modeled by \citet{Pes04} is driving a precessing jet. This model requires as the most plausible explanation, the presence of a relatively tight binary (with an orbital separation of tens of AU and an orbital period of tens of years). While we cannot exclude it, there is no evidence of a tight binary in \NGC1, and we believe that the presence of multiple outflows from individual YSOs provides a more natural explanation. Aiming for a more complete picture, \citet{Sur11} also tried to incorporate the presence of methanol clusters B, C, D, and E (besides A) in a "torus" model alternative to the edge-on Keplerian disk model for feature A. Evidence for a large torus (of several thousands of AU) is provided by the measurements of velocity gradients in molecular lines approximately perpendicular to the large-scale CO bipolar outflow \citep{Kla09,Qiu11,Beu13} They proposed that all the observed \meth\ maser clusters should mark the interface between an infalling envelope and this large-scale torus, oriented perpendicularly to the elongated mid-IR emission observed by \citet{DeBui05}. This scenario has the merit of incorporating all maser clusters (and not just cluster "A" as in previous models), but it does not explain the changing of the position angle of the outflow based on radio continuum imaging \citep[e.g., ][]{Cam84}. Nevertheless, this simplified and qualitative model where all the observed maser clusters are associated with one large-scale torus of several thousands of AU, does not exclude the presence of smaller accretion disks, like the ones probed individually by clusters "A" and "B"+"C" in our edge-on disk model. | 14 | 4 | 1404.3957 |
1404 | 1404.3485_arXiv.txt | During the structure formation, charged and neutral chemical species may have separated from each other at the gravitational contraction in primordial magnetic field (PMF). A gradient in the PMF in a direction perpendicular to the field direction leads to the Lorentz force on the charged species. Resultantly, an ambipolar diffusion occurs, and charged species can move differently from neutral species, which collapses gravitationally during the structure formation. We assume a gravitational contraction of neutral matter in a spherically symmetric structure, and calculate fluid motions of charged and neutral species. It is shown that the charged fluid, i.e., proton, electron and $^7$Li$^+$, can significantly decouple from the neutral fluid depending on the field amplitude. The charged species can, therefore, escape from the gravitational collapse. We take the structure mass, the epoch of the gravitational collapse, and the comoving Lorenz force as parameters. We then identify a parameter region for an effective chemical separation. This type of chemical separation can reduce the abundance ratio of Li/H in early structures because of inefficient contraction of $^7$Li$^+$ ion. Therefore, it may explain Li abundances of Galactic metal-poor stars which are smaller than the prediction in standard big bang nucleosynthesis model. Amplitudes of the PMFs are controlled by a magneto-hydrodynamic turbulence. The upper limit on the field amplitude derived from the turbulence effect is close to the value required for the chemical separation. | \label{sec1} In the standard cosmology, abundances of light elements, i.e., hydrogen, helium, lithium, and very small amounts of other nuclides, evolve during big bang nucleosynthesis (BBN) at the redshift of $z\sim 10^9$ \citep{Fields:2011zzb}. Lithium abundance predicted in standard BBN (SBBN) model \citep*{Coc:2011az,Coc:2013eea}, however, disagrees with that determined by spectroscopic observations of metal-poor stars (MPSs) ~\citep{Melendez:2004ni,Asplund:2005yt}. The observational number ratio of lithium and hydrogen is $^7$Li/H$=(1-2) \times 10^{-10}$~\citep*{Spite:1982dd,Ryan:2000zz,Melendez:2004ni,Asplund:2005yt,bon2007,Shi:2006zz,Aoki:2009ce,Hernandez:2009gn,Sbordone:2010zi,Monaco:2010mm,Monaco:2011sd,Mucciarelli:2011ts}. It is 2--4 times lower than the prediction in SBBN model with the baryon-to-photon ratio from the observation of the cosmic microwave background radiation by Wilkinson Microwave Anisotropy Probe (WMAP)~\citep{Spergel:2003cb,Spergel:2006hy,Larson:2010gs,Hinshaw:2012aka}. The formations of atom and molecules proceed in the redshift range of $z\la 10^4$ \citep{Saslaw1967,Peebles1968,Lepp1984,Dalgarno1987,Galli:1998dh,Vonlanthen:2009ns}. Since lithium has a low ionization potential, it remains ionized when the recombination of hydrogen occurs \citep{Dalgarno1987}. The relic abundance of Li$^+$ is, therefore, high \citep{Galli:1998dh}. A recent study \citep{Vonlanthen:2009ns} shows that abundances of Li and Li$^+$ are almost equal at $z=10$. Magnetic fields exist in various astronomical objects, such as Sun, Galaxy, galactic cluster (see \citep{Grasso:2000wj} for a review). Magnetic field have possibly existed in the early universe. The origin of the magnetic fields is, however, not determined yet. Magnetic fields can be generated through electric currents induced by a velocity difference of electrons and ions \citep{Biermann1950,Browne1968ApL}. Such an electric current is produced in a rotating gas system because of different viscous resistances of electrons and ions \citep{Browne1968ApL}. This current creates poloidal magnetic field. Similarly, the drift current can be produced from gravitation working on electrons and ions, and it can generate a magnetic field \citep{Browne1968ApL,Browne1982,Browne1985}. It has been noted \citep{Harrison1969}, however, that these batteries \citep{Biermann1950,Browne1968ApL} can not generate a large magnetic field since the time-scale of field generation is much larger than the age of the universe \citep{Spitzer1948,Hoyle1960,Harrison1969}. The primordial magnetic field (PMF) can be generated at a couple of epochs in the early universe, i.e., the inflation, electroweak and quark-hadron transitions, and reionization \citep[see][and references therein]{Grasso:2000wj,Widrow:2002ud,Widrow:2011hs}. The PMF generation, however, most probably occurs around the cosmological recombination epoch \citep*{Harrison1970,Matarrese:2004kq,Takahashi:2005nd,ichiki2006,Ichiki:2007hu,Takahashi:2007ds,fen2011,Maeda:2011uq}. In the evolution of primordial density perturbation, the magnetic field can be perturbatively generated at second order through the vorticity \citep{Matarrese:2004kq} and the anisotropic stress of photon \citep{Takahashi:2005nd,ichiki2006}. These generation processes can be calculated rather precisely with use of the cosmological perturbation theory. Recent calculation \citep{fen2011} shows that the comoving amplitude of generated field on cluster scales, i.e., 1 Mpc, is about $3\times 10^{-29}$ G at redshift $z=0$. Effects of PMFs on Galaxy formation have been studied \citep{Rees1972,Wasserman1978,Coles1992}. Effects on Galactic angular momentum and Galactic magnetic fields have been also investigated utilizing magneto-hydrodynamic (MHD) equations \citep{Wasserman1978,Coles1992}. It was found that a magnetic field can trigger a large density fluctuation with an overdensity of $\delta=1$. Such a large fluctuation is produced in a structure with a scale $L_B$ if the comoving field amplitude measured in the present intergalactic medium (IGM) is as large as $B_0(L_B)\sim 10^{-9}(L_B/1~{\rm Mpc})$ G \citep{Wasserman1978,Coles1992}. It has been suggested that an inhomogeneous magnetic field causes a streaming velocity of baryon relative to dark matter, and resultantly an infall of baryon in potential wells of dark matter may be inhibited. Cosmological structure formation is thus affected by the inhomogeneous field \citep{Coles1992}. In this paper, we study a chemical separation of charged and neutral species triggered by a PMF during the structure formation. Neutral chemical species collapse gravitationally during the structure formation. Motions of charged species can, however, decouple from that of neutral species by PMF, and an ambipolar diffusion occurs. If the PMF has a gradient in a direction perpendicular to the field direction in the early universe, an electric current of charged species necessarily exists in the direction perpendicular to both of the field lines and the gradient direction. The Lorentz force working on the charged species then causes a velocity difference between charged and neutral species in the direction of the field gradient. This velocity difference enables an ambipolar diffusion. Therefore, it is possible that $^7$Li$^+$ ions did not collapsed, while neutral $^7$Li atoms gravitationally collapsed into structures. We suggest that the ambipolar diffusion provides a possible explanation of the small Li abundance in MPSs. The situation of the $^7$Li$^+$ depletion due to PMFs and structure collapse studied in this paper is analogous to that of the charged grain depletion in the star-forming magnetic molecular clouds (MCs). The chemical separation by an ambipolar diffusion has been studied for the case of the gravitational collapse in dusty interstellar MCs \citep[e.g.][]{cio1994,cio1996}. In the MCs, the abundance of charged dust grains which is a component of their plasma is reduced since the magnetic field retards the infall of the grains while the neutral particles collapse to form a protostellar core \citep{cio1994}. The depletion of the grain abundance by the magnetic field is a very important phenomenon since information on the star formation mechanism can in principle be obtained from the ratio of observed abundances of grains in the core and the envelope of MC \citep{cio1996}. The organization of this paper is as follows. In Sec.~\ref{sec2} we describe the model of chemical separation during a gravitational collapse of a structure. In Sec.~\ref{sec3} we introduce physical quantities used in this study, and typical numerical values relevant to the structure formation. In Sec.~\ref{sec4} we show results of calculations of the chemical separation caused by the magnetic field. In Sec.~\ref{sec5} we comment on the magnetic field amplitude. In Sec.~\ref{sec6} we comment on a possible generation of a magnetic field gradient during the gravitational collapse. In Sec.~\ref{sec7} we identify a parameter region required for a successful chemical separation. In Sec.~\ref{sec8} we briefly mention a later epoch of the structure formation and possible reactions neglected in this study. We suggest that the chemical separation of the $^7$Li$^{+}$ ion can reduce the abundance ratio $^7$Li/H in the early structure. Another theoretical constraint on the magnetic field amplitude is also described. In Sec.~\ref{sec9} we summarize this study. In Appendix \ref{app2} we show drift velocities of protons and electrons in a structure, equations for ions and electrons which should be satisfied in equilibrium states, and typical values of variables required for an efficient chemical separation. In Appendix \ref{app3} we show supplemental results for the calculations of the chemical separation. In this paper, the Boltzmann's constant ($k_{\rm B}$) and the light speed ($c$) are normalized to be unity. | \label{sec8} \subsection{Later epoch of the structure formation}\label{sec8_2} We comment on a possibility of chemical separation in a later epoch of structure formation. Depending on the virialization temperature of the collapsing structure, the ionization degree after the virialization can be smaller than that during the gravitational collapse because of the high density. The baryon density in the late epoch is, on the other hand, much larger than that during the collapse. Then, the larger friction force must be balanced by the Lorentz force originating from a larger magnetic field. For a fixed structure mass, the gravitation term [the first term in RHS of Eq. (\ref{eqa1})] roughly scales as $\propto \rho_{\rm b}^{5/3} \propto (1+\delta)^{5/3}$ [Eq. (\ref{eqa4})]. On the other hand, the Lorentz force term (the second term) scales as $\propto B^2/L_B \propto (1+\delta)^{5/3}$ if we roughly assume adiabatic contractions of charged species and magnetic domains in the early epoch of structure formation. Therefore, it is expected that if an ambipolar diffusion does not occur in the early structure formation epoch, it does not also in a later epoch as long as a magnetic field generation does not operate during the structure formation. \subsection{Chemical reactions}\label{sec8_1} Lithium atoms can be ionized by a ultraviolet (UV) photon as \begin{equation} {\rm Li}+\gamma\rightarrow {\rm Li}^+ +e^-. \label{eq28} \end{equation} They can be ionized also through a collision with an H$^+$ ion, which is generated by UV photons or cosmic rays: \begin{equation} {\rm Li}+{\rm H}^+ \rightarrow {\rm Li}^+ +{\rm H}. \label{eq29} \end{equation} The ionization potential of Li is $I($Li$)=5.39$ eV which corresponds to the temperature $T=2I($Li$)/3\sim 4\times 10^4$~K. Some proportion of Li atoms can be also easily ionized by external UV sources or a gas heating at the virialization of structures. The Li$^+$ ions produced secondarily in this way can then be trapped by magnetic field, and possibly be left out of forming structures. Such a contribution to a resulting lithium abundance in the collapsed structure, however, operates after the gravitational collapse considered in this paper. They are then neglected here. \subsection{Li abundance of MPS}\label{sec8_3} Astronomical observations indicate primordial abundances of D \citep{Pettini:2012ph}, $^3$He \citep*{Bania2002}, and $^4$He \citep*{Izotov:2010ca,Aver:2010wq} consistent with those predicted in SBBN model. Primordial $^7$Li abundance is inferred from spectroscopic observations of metal-poor halo stars. We adopt log($^7$Li/H)$=-12+(2.199\pm 0.086)$ determined with a 3D nonlocal thermal equilibrium model~\citep{Sbordone:2010zi}. This estimation corresponds to the $2\sigma$ range of \begin{equation} 1.06\times 10^{-10} < ({\rm ^7Li/H})^{\rm MPS} < 2.35\times 10^{-10}. \label{eq27} \end{equation} This Li abundance level is $\sim 3$--$4$ times smaller than the SBBN prediction \citep{Coc:2011az,Coc:2013eea}, and the dispersion of observed Li abundance is small. Since the observed $^7$Li abundance is not so different from the SBBN prediction, it is naturally expected that SBBN model successfully describes the outline of primordial light element synthesis. The Li abundances in MPSs can be affected by several physical processes operating after the BBN epoch. The abundance ratio of Li and H in MPSs is then expressed as \begin{equation} ({\rm Li/H})^{\rm MPS}=({\rm Li/H})^{\rm SBBN}~F^{\rm dep}, \label{eq26} \end{equation} where (Li/H)$^{\rm SBBN}$ is the abundance ratio in SBBN model, and $F^{\rm dep}$ is the depletion factor associated with 1) modified BBN models including exotic long-lived particles or changed expansion rate, 2) the structure formation as considered in this paper, 3) the virialization of the structure, 4) the formation of observed MPSs, and 5) the stellar processes in surfaces of MPSs occurring from the star formation until today. Generally, cosmological processes change elemental abundances universally, while astrophysical processes do locally depending on physical environments of respective stars. It is, therefore, difficult to explain the discrepancy in $^7$Li abundance with astrophysical processes which result in large dispersions in the abundance. The depletion factor from the chemical separation during the structure formation can be described by \begin{eqnarray} F^{\rm dep}&\equiv&\frac{[(n_{^7{\rm Li}}+n_{^7{\rm Li}^+})/(n_{{\rm H}}+n_{{\rm H}^+})]_{\rm str}}{[(n_{^7{\rm Li}}+n_{^7{\rm Li}^+})/(n_{\rm H}+n_{{\rm H}^+})]_{\rm uni}} \nonumber\\ &\approx & \frac{\chi_{^7{\rm Li},{\rm uni}} + \chi_{{\rm Li}^+,{\rm str}}}{\left( \chi_{^7{\rm Li}}+\chi_{^7{\rm Li}^+} \right)_{\rm uni}}, \label{eq79} \end{eqnarray} where quantities with subscripts, `uni' and `str', are values of the homogeneous early universe after the cosmological recombination, and those of the collapsed structure in the late universe, respectively. In the second line, it was assumed that the primordial ionization degree of hydrogen is negligibly small, i.e., $\chi_{{\rm H}^+} \ll 1$, and that values of the number ratio $\chi_{^7{\rm Li}}$ are equal in the homogeneous early universe and the structure. We suppose the initial abundance ratio of $^7$Li$^+$/$^7$Li $\sim 1$ as suggested from a chemical history of homogeneous early universe \citep{Vonlanthen:2009ns}. The chemical separation via the ambipolar diffusion can only dilute the charged $^7$Li$^+$. The depletion factor is, therefore, 1/2 at minimum when the primordial $^7$Li$^+$ is completely expelled from the structure. This factor would be smaller if the initial $^7$Li$^+$ abundance in the gravitational structure formation is larger for some reason. For example, even a small intensity of ionizing photon of $^7$Li would quickly transform $^7$Li to $^7$Li$^+$ without absorption by neutral hydrogen (Sec. \ref{sec8_1}). On the other hand, the depletion factor would be larger if the chemical separation is less efficient. The Li abundance of MPSs may not be explained by the chemical separation only. In that case, we need another depletion mechanism. As an example, a rotationally induced mixing model \citep{Pinsonneault:1998nf,Pinsonneault:2001ub} for MPSs is chosen here since dispersions as well as depletion factors are predicted theoretically only in this model among stellar depletion models. Since the predicted depletion factor is proportional to the dispersion factor, the depletion factor is constrained from observed dispersions. Pinsonneault et al. estimated the depletion factor: `0.13 dex, with a 95 \% range extending from 0.0 to 0.5 dex' \citep{Pinsonneault:2001ub}. This model explains a part of the Li abundance discrepancy although the complete solution by this mechanism only seems almost impossible. The Li abundances in MPSs may, therefore, be explained by the combination of the ambipolar diffusion during the structure formation and the rotationally induced mixing in stars. Stellar Li abundances in metal-poor globular clusters (GCs) have also been measured. For example, GC M4 was studied using high-resolution spectra with GIRAFFE at Very Large Telescope. The Li abundance in turn-off stars is then found to be log($^7$Li/H)$=-12+(2.30\pm 0.02 +0.10)$ \citep{Mucciarelli:2010gz}. All Li abundances measured so far are summarized in Fig. 3 of \citet{Mucciarelli:2010gz}, and they are consistent with abundances in metal-poor halo stars at present. If the ambipolar diffusion studied in this paper caused the small Li abundances of MPSs, however, reduction factors of MPSs can reflect respective histories of parent structure of MPSs. In a modern model calculation for GC formation, the Galaxy formation results from a continuous process of merging and accretion which is realized in a hierarchical structure formation scenario \citep{Kravtsov:2003sm}. In the model, GCs form at densest regions of filaments in a large-scale structure. \subsection{Other constraint on PMF}\label{sec8_4} Theoretical and observational constraints on the cosmic magnetic field have been summarized in \citet{Durrer:2013pga}. The magnetic field strength in the interesting parameter region found in this study (Sec. \ref{sec7}) looks somewhat higher than the theoretical upper limit from the effect of dissipation of magnetic field through the processing by MHD turbulence. The propagation length of Alfv\'en wave is given by $\lambda_B\sim v_A t$, where $v_A$ is the Alfv\'en speed. This length scale corresponds to ``the size of largest processed eddies'' \citep{Durrer:2013pga} by MHD turbulence. The Alfv\'en speed during the matter dominated epoch of the homogeneous universe is given by $v_{\rm A}=B/\sqrt[]{\mathstrut 4 \pi \rho_{\rm b}}$ with $\rho_{\rm b}\propto (1+z)^3$ the baryon density [Eq. (\ref{eq32})]. Note that the density used in the Alfv\'en speed is that of fluid with a frozen-in magnetic field. The density is then given by the total density if the fluid is fully ionized or if the neutral fluid is effectively coupled to the charged fluid through the collision so that the magnetic field can be considered frozen also into the neutral fluid. The physical states considered in this paper are ones in which the matter is only weakly ionized and the coupling of the charged and neutral fluids is effective. Although the ambipolar diffusion reduces the magnetic pressure gradient until the Lorentz force becomes comparable to the gravitation [cf. Eq. (\ref{grav_Lorentz_ratio})], the coupling is effective after then. Therefore, the total fluid has a frozen-in magnetic field and its density is used in the Alfv\'en speed. The distance is then given by \begin{eqnarray} \lambda_B &\sim& \left[\frac{B_0}{\left(4\pi \rho_{\rm b0}\right)^{1/2}} (1+z)^{1/2} \right] \left[\frac{2}{3H_0 \Omega_{\rm m}^{1/2} (1+z)^{3/2}}\right] \nonumber\\ &=& \frac{2^{3/2} }{3^{3/2}} \frac{B_0}{m_{\rm Pl} H_0^2 \Omega_{\rm b}^{1/2} \Omega_{\rm m}^{1/2} (1+z)}, \end{eqnarray} where $m_{\rm Pl}$ is the Planck mass. Consequently, the comoving propagation length $\lambda_{B0}=\lambda_B(1+z)$ is constant. Since the magnetic fields on scales shorter than $\lambda_{B0}(B_0)$ decay, there is a maximum amplitude of magnetic field which escapes from this decay for a given $\lambda_{B0}$. From the above equation, an upper limit on the $B_0$ value is derived as \begin{eqnarray} B_{0} &\la& 1.3 \times 10^{-10}~{\rm G} \left(\frac{h}{0.700}\right)^2 \left(\frac{\Omega_{\rm b}}{0.0463}\right)^{1/2} \left(\frac{\Omega_{\rm m}}{0.279}\right)^{1/2} \left(\frac{\lambda_{B0}}{10~{\rm kpc}}\right). \label{eq66} \end{eqnarray} This upper limit is lower than the field value required for the chemical separation [Eqs. (\ref{eqa7}) and (\ref{eq67})] (by a factor of $\sim$ two for $\lambda_{B0}=10$ kpc). However, Eq (\ref{eq66}) is just a rough estimate, and realistic limits should be derived in precise calculations in future. It is interesting that the upper limit caused by the MHD processing in the early universe is near to the interesting field strength. It indicates that relatively large magnetic field in the early universe may have been reduced by the MHD effect to the level which is most appropriate for the chemical separation causing the lithium problem. During the gravitational collapse of structures, the Alfv\'en speed increases as $\propto (1+\delta)^{1/6}$ if the dissipation of magnetic field is not operative. The dissipation scale in collapsed structures which are decoupled from the cosmic expansion is then given by \begin{equation} \lambda_B^{\rm str}(z) \sim \frac{2^{3/2} }{3^{3/2}} \frac{B_0(1+z)^{1/2} (1+\delta)^{1/6}}{m_{\rm Pl} H_0^2 \Omega_{\rm b}^{1/2} \Omega_{\rm m}^{1/2} (1+z)^{3/2}}. \end{equation} The contraction increases the dissipation scale slightly. The MHD effect then becomes significant in a large density environment. Therefore, after the collapse, the magnetic field strength can be decreased further. | 14 | 4 | 1404.3485 |
1404 | 1404.2483_arXiv.txt | In this review, the methodology of large eddy simulations (LES) is introduced and applications in astrophysics are discussed. As theoretical framework, the scale decomposition of the dynamical equations for neutral fluids by means of spatial filtering is explained. For cosmological applications, the filtered equations in comoving coordinates are also presented. To obtain a closed set of equations that can be evolved in LES, several subgrid scale models for the interactions between numerically resolved and unresolved scales are discussed, in particular the subgrid scale turbulence energy equation model. It is then shown how model coefficients can be calculated, either by dynamical procedures or, a priori, from high-resolution data. For astrophysical applications, adaptive mesh refinement is often indispensable. It is shown that the subgrid scale turbulence energy model allows for a particularly elegant and physically well motivated way of preserving momentum and energy conservation in AMR simulations. Moreover, the notion of shear-improved models for inhomogeneous and non-stationary turbulence is introduced. Finally, applications of LES to turbulent combustion in thermonuclear supernovae, star formation and feedback in galaxies, and cosmological structure formation are reviewed. | \label{sec:intro} Turbulent flows with high Reynolds numbers are often encountered in computational astrophysics. Examples are the solar wind, stellar convection zones, star-forming clouds, and probably the gas in galaxy clusters. This review concentrates on computational methods that treat turbulence in the limit of high Reynolds numbers by explicitly solving the compressible Euler equations for the large-scale dynamics of the flow, while incorporating small-scale effects such as viscous dissipation into a subgrid-scale model. Since the non-linear turbulent interactions between different scales are at least partially resolved, this type of simulation is called large eddy simulation (LES). The relative importance of non-linear interactions and viscous damping is specified by the Reynolds number. It is determined by the characteristic velocity $V$ of the flow, its integral length scale $L$, and the microscopic viscosity $\nu$: \begin{equation} \label{eq:Re} \Reyn = \frac{VL}{\nu} \end{equation} The flow becomes turbulent if the non-linear interactions are much stronger than viscous damping. Generally, this happens if $\Reyn$ reaches values greater than a few $10^3$, but $\Reyn$ can become much greater than that. For instance, an estimate for the turbulent convection zone of the Sun is $\Reyn\sim 10^{14}$ \cite{Canuto94}. In principle, we can also define a scale-dependent Reynolds number $\Reyn(\ell) = v'(\ell)\ell/\nu$, where $v'(\ell)$ is the typical magnitude of velocity fluctuations on the length scale $\ell$. The length sale of strong viscous damping is then given by $\Reyn(\ell_{\rm K})\sim 1$. For incompressible turbulence, substitution of the Kolmogorov-Obukhov scaling law $v'(\ell)\sim(\epsilon\ell)^{1/3}$ yields \cite{Frisch} \[ \frac{\epsilon^{1/3}\ell_{\rm K}^{4/3}}{\nu}\sim 1\,. \] Since the mean dissipation rate $\epsilon\sim V^3/L$, it follows that \begin{equation} \frac{L}{\ell_{\rm K}}\sim\Reyn^{3/4}. \end{equation} The problem of high \Reyn\ is thus a problem of largely different length scales or, equivalently, a high number of degrees of freedom. In a numerical simulation of turbulence, the range of length scales is limited by the grid scale $\Delta$, which is simply the linear size of the grid cells. Only if $\Delta\lesssim\ell_{\rm K}$, turbulence can be fully resolved by a so-called \emph{direct numerical simulation} (DNS). However, DNS become infeasible for very large \Reyn\ because the total amount of floating point operations (FLOPs) increases with $(L/\Delta)^4\gtrsim (L/\ell_{\rm K})^4\sim \Reyn^{\,3}$. The scaling may differ for highly compressible turbulence, but the basic problem remains the same. For a DNS of solar convection over one dynamical time scale, it would be necessary to perform very roughly $10^{42}$ FLOP, which would take far longer than the current age of the Universe on the fastest existing computer. In practice, however, it is neither feasible nor useful to account for all degrees of freedom in a simulation of high-\Reyn\ turbulence. To reproduce statistical properties, a much coarser sampling of the degrees of freedom can be quite sufficient. This is why LES encompass only the energy-containing scales and structures dominated by non-linear interactions, which are part of the turbulent cascade down to a cutoff scale much greater than the microscopic dissipation scale. The cutoff scale is given by grid scale $\Delta$. The defining criterion for LES is thus $L\gg\Delta\gg \ell_{\rm K}$ or, equivalently, \[ \Reyn\gg\Reyn(\Delta)\gg 1\,. \] Here, $\Reyn(\Delta)\sim v'(\Delta)\Delta/\nu$ is the Reynolds number of subgrid-scale turbulence. The product $v'(\Delta)\Delta$ can be interpreted as turbulent viscosity of the numerically unresolved eddies of size $\ell\lesssim \Delta$. The effective Reynolds number of the numerically computed flow is therefore given by \begin{equation} \label{eq:Re_eff} \Reyn_{\rm eff} = \frac{\Reyn}{\Reyn(\Delta)}\sim \frac{VL}{v'(\Delta)\Delta}\sim \left(\frac{L}{\Delta}\right)^{4/3}\,. \end{equation} This means that LES reduces the number of degrees of freedom by replacing the microscopic viscosity $\nu$ by a turbulent viscosity of the order $v'(\Delta)\Delta\gg \nu$. As a result, the purely non-linear turbulent dynamics of the ``large eddies" is separated from microscopic dissipation.\epubtkFootnote{ For many applications, particularly in astrophysics, the definition used here is appropriate. In a broader sense, LES may include the case where microscopic dissipation is partially resolved. DNS can then be considered as limiting case of LES for $\Reyn(\Delta)\sim 1$. } The biggest challenge when implementing this concept is to find an appropriate model for the coupling between the small- and large-scale dynamics. A mathematical framework for LES is based on the notion of a filter, which separates large-scale ($\ell\gtrsim\Delta$) from small-scale ($\ell\lesssim\Delta$) fluctuations. Filters can be used to decompose the equations of fluid dynamics into equations for smoothed variables, which have a very similar mathematical structure as the unfiltered equations, and equations for second-order moments of the fluctuations. The latter are interpreted as subgrid-scale variables. In Section~\ref{sec:separation}, we will carry out the decomposition of the compressible Navier-Stokes equation by applying the filter formalism of Germano \cite{Germano92}. This formalism comprises the so-called Reynolds-averaged Navier-Stokes (RANS) equations as limiting case if the filter length is comparable to the integral length scale of the flow. Simulations based on the RANS equations work with low $\Reyn_{\rm eff}$, while LES have high $\Reyn_{\rm eff}$. In principle, second-order moments can be expressed in terms of higher-order moments. Since this would entail an infinite hierarchy of moments, the set of variables is limited by introducing closures. Usually, one attempts to find closures for the second-order moments by expressing them in terms of the filtered variables. This is what is called a subgrid-scale (SGS) model.\epubtkFootnote{In astrophysics, the term subgrid-scale model may comprise models that capture sub-resolution physics other than turbulence. A typical example are star-formation models in galaxy simulations. } For example, a complete second-order closure model for turbulent convection is formulated in \cite{Canuto94}. Much simpler, yet often employed is the one-equation model for the SGS turbulence energy $K$, i.~e., the local kinetic energy of numerically unresolved turbulent eddies. For this reason, it is sometimes called the $K$-equation model. Closures for the transport and source terms in the SGS turbulence energy equation are presented in some detail in Section~\ref{sec:subgrid}, followed by a discussion of how the closure coefficients can be determined (Section~\ref{sec:closure}). Of particular importance is the prediction of the local turbulent viscosity, which is is given by $\Delta\sqrt{K}$ times a dimension-less coefficient. The turbulent viscosity is required to calculate the turbulent stresses, which enter the equations for the filtered variables analogous to the viscous stresses in the unfiltered Navier-Stokes equations (see Section~\ref{sec:turb_stress}). Filtering the dynamical equations is usually considered to be equivalent to numerical discretization. The filter length can then be identified with the grid scale $\Delta$. Since the numerical truncation errors of stable finite difference or finite volume schemes are more or less diffusion-like terms, they produce a numerical viscosity that effectively reduces the Reynolds number to a value comparable to equation~(\ref{eq:Re_eff}). It is actually a common assumption that numerical viscosity approximates the turbulent viscosity on the grid scale. This leads to the notion of an \emph{implicit} large eddy simulation (ILES) \cite{Garnier}, which is widely used for simulating turbulent flows in astrophysics. Numerous numerical studies demonstrated that ILES is a very robust method, which reliably predicts scaling laws of compressible turbulence at sufficiently high resolution \cite{SyPort00,KritNor07,BenzBif08,SchmFeder08,FederRom10,KritWag13}. This is a consequence of the independence of inertial-range scaling from the dissipation mechanism, be it microscopic, turbulent or numerical viscosity, provided that the dynamical range of the simulation is large enough. In simulations of statistically stationary isotropic turbulence, however, the inertial subrange is very narrow for computationally feasible resolutions because the bottleneck effect distorts the spectrum over a large range of high wave numbers below the Nyquist wavenumber \cite{Falko94,DobHaug03,SchmHille06}. It appears that LES with an explicit SGS model, such as the $K$-equation model, can reduce the bottleneck effect to some degree and reproduce scalings from ILES or DNS at lower resolution \cite{HauBrand06,WoodPort06,Schm09b}. However, more systematic studies covering the parameters space of forced compressible turbulence are necessary to confirm this effect. There are, of course, alternative methods of scale separation and a large variety of SGS models (for a comprehensive overview, see the monographs \cite{Sagaut,Garnier}). An example are the Camassa-Holm equations, which follow from the incompressible Navier-Stokes equations by decomposing the trajectories of fluid elements into mean and fluctuating parts in the Lagrangian framework \cite{ChenFoi98}. Since the filtered component of the velocity is defined by an inverse Helmholtz operator of the form $(1-\alpha^2\nabla^2)^{-1}$, which is explicitly applied to determine the turbulent stresses in the filtered velocity equation, the resulting model is called Lagrangian-averaged Navier-Stokes $\alpha$-model (LANS-$\alpha$). Depending on the choice of $\alpha$, the variables computed in LES based on LANS-$\alpha$ are typically smoothed over length scales somewhat larger than the grid resolution. In other words, this type of simulation partially resolves the sub-filter scales, which improves the controllability of the model. While there is no handle on the competition between the SGS model and numerical truncation errors on the grid scale in convectional LES, LANS-$\alpha$ can, in principle, alleviate this problem by adjusting the balance between truncation and model errors \cite{GraHolm07}. Although the idea is very elegant, the numerical studies discussed in \cite{GraHolm07,GraHolm08} show that the applicability of LANS-$\alpha$ and similar models is limited, particularly for very high $\Reyn$. Moreover, the generalization to compressible turbulence is not straightforward. Models such as LANS-$\alpha$ are not further covered by this review, but they might be an option for magnetohydrodynamical LES \cite{GraMin09}. Currently, LES are mainly applied to complex astrophysical systems. In simulations of cosmological structure formation, which are discussed in Section~\ref{sec:clusters}, the length scales on which turbulence is driven by gravity are varying. Although adaptive mesh refinement is applied to track down collapsing structures, it is difficult to to resolve a wide range of length scales between the smallest driving scale and the the grid scale at the highest refinement level. In this situation, SGS effects can become fairly large. However, the variable grid scale complicates the scale separation in AMR simulations because energy has to be transferred between the resolved and SGS energy variables if a region is refined or de-refined. Section~\ref{sec:consrv} describes how to combine LES and AMR. This method, for which the acronym FEARLESS (Fluid mEchanics for Adaptively Refined Large Eddy SimulationS) was coined in \cite{MaierIap09}, has been applied to galaxy clusters, the intergalactic medium, and primordial atomic cooling halos. The results from these simulations indicate that the contribution of the numerically unresolved turbulent pressure to the support against gravity is non-negligible and the turbulent viscosity tends to stabilize disk-like structures around collapsed gas clouds. Moreover, the SGS model provides indicators of turbulence production and dissipation and allows for the computation of the turbulent velocity dispersion. A difficulty is that turbulence production by cosmological structure formation is highly inhomogeneous. This entails the problem that the SGS model should dynamically adapt to conditions ranging from laminar flow to developed turbulence. Inhomogeneous and non-stationary turbulence can be treated by dynamical procedures for the calculation of closure coefficients or shear-improved SGS models, which decompose the numerically resolved flow into mean and fluctuating components. These techniques are outlined in Sections~\ref{sec:dyn_proc} and~\ref{sec:kalman}. Furthermore, SGS models offer unique possibilities for modeling physical processes that are influenced by turbulence. An example is turbulent deflagration, where the turbulent diffusivity predicted by the SGS model dominates the effective flame propagation speed in underresolved numerical simulations. Turbulent deflagration plays a role at least in the initial phase of thermonuclear explosions of white dwarfs (see Section~\ref{sec:SN_Ia}), which is one of the scenarios that are thought to produce type Ia supernovae. A recent application along similar lines are LES of isolated disk galaxies, where the SGS turbulence energy is a crucial parameter for calculating the star formation rate and the feedback due to supernova blast wave (see Section~\ref{sec:galaxy}). Since the impact of feedback processes on the formation of galaxies and their evolution leaves many questions unanswered, galaxies are a particularly promising field of application. While great progress has been made for compressible hydrodynamics, magnetohydrodynamical LES are still in their infancy. Several SGS models have been proposed in the context of terrestrial plasma physics \cite{MuellCar02a,MuellCar02b,HauBrand06,CherKar07,GraMin09,SonOber12}, but their applicability to astrophysical plasmas is unclear. Astrophysical MHD turbulence, particularly in the interstellar medium, extends to the supersonic and super-Alfv\'{e}nic regimes. Moreover, plasmas become collisionless for high temperatures and low densities. A typical example is the solar corona. It is also likely to be the case in the intracluster medium. Since the fluid-dynamical description is not applicable in this case, kinetic methods have to be employed. Nevertheless, MHD-LES could provide a reasonable approximation on length scales that are sufficiently large compared to the characteristic scales of kinetic processes. In any case, SGS models for MHD turbulence will be a very challenging problem because of the local anisotropy of turbulent fluctuations, the potentially strong back-reaction from smaller to larger scales, and complicated dissipative processes such as turbulent reconnection \cite{BrandSub05,Buech07,ZweiYa09}. In this area, extensive fundamental studies will be necessary. \newpage | 14 | 4 | 1404.2483 |
|
1404 | 1404.0954_arXiv.txt | In this paper we present a detailed analysis of a sample of eight Am stars, four of them are in the {\it Kepler} field of view. We derive fundamental parameters for all observed stars, effective temperature, gravity, rotational and radial velocities, and chemical abundances by spectral synthesis method. Further, to place these stars in the HR diagram, we computed their luminosity. Two objects among our sample, namely HD\,114839 and HD\,179458 do not present the typical characteristic of Am stars, while for the others six we confirm their nature. The behavior of lithium abundance as a function of the temperature with respect the normal A-type stars has been also investigated, we do not find any difference between metallic and normal A stars. All the pulsating Am stars present in our sample (five out of eight) lies in the $\delta$~Sct instability strip, close to the red edge. | Among main sequence, A-type stars show a large variety of chemical peculiarities. They are driven by several physical processes, such as diffusion and/or magnetic field, just to quote some of them. All these processes have the same factor in common, i. e. the very stable radiative atmosphere which is the principal condition needed for peculiarities to arise. The metallic or Am stars are those whose Ca{\sc ii} K-line types appear too early for their hydrogen line types, and metallic-lines types appear too late, such that the spectral types inferred from the Ca{\sc ii} K- and metal-lines differ by five or more spectral subclasses. The marginal Am stars are those whose difference between Ca{\sc ii} K- and metal-lines is less than five subclasses. The commonly used classification for this class of objects include three spectral types prefixed with {\it k}, {\it h}, and {\it m}, corresponding to the K-line, hydrogen-lines and metallic lines, respectively. The typical abundances pattern show underabundances of C, N, O, Ca, and Sc and overabundances of the Fe-peak elements, Y, Ba and of the rare earths elements \citep{adelman97,fossati07}. The presence of magnetic field has also been investigated but with null result by \citet{fossati07}. The abundance of lithium in Am stars compared to that observed in normal A-type stars, has been discussed in the literature since the work of \citet{burkhart91}. They found that in general Li abundance in Am stars is close to the cosmic value or even lower in some case. \citet{richer00} developed models of the structure and evolution of Am stars in order to reproduce the observed chemical pattern of 28 elements. The most important improvement of these models has been the introduction of turbulence as the hydrodynamical process competing with atomic diffusion, in such a way that the resulting mixing reduces the large abundance anomalies predicted by previous models, leading to abundances which closely resemble those observed in Am stars. Another open question in the framework of Am stars concerns the pulsations in these objects. For many years it was thought that Am stars did not pulsate, in accordance with the expectation that diffusion depletes helium from the driving zone. Recently, intensive ground-based \citep[SuperWASP survey]{smalley11} and space-based \citep[{\it Kepler} mission]{balona11} observations have shown that many Am/Fm stars do pulsate. \citet{smalley11}, for example, found that about 169, 30 and 28 Am stars out of a total of 1600 show $\delta$~Sct, $\gamma$~Dor or Hybrid pulsations \citep[see][for a definition of these classes]{griga2010}. These authors found also that the positions in the Hertzsprung-Russel (HR) diagram of Am stars pulsating as $\delta$~Sct are confined between the red and blue radial fundamental edges, in agreement with \citet{balona11} and \citet{catanzaro12}. In this study we continue a programme devoted to determining photospheric abundance pattern in Am stars by means of high resolution spectra. Three Am stars have already been analyzed by us, namely: HD\,178327 (KIC\,11445913) and HD\,183489 (KIC\,11402951) in \citet{balona11}, and HD\,71297 in \citet{catanzaro13}, for which fundamental astrophysical quantities, such as effective temperatures, gravities and metallicities have been derived. The addition of these three stars does not alter the homogeneity of our sample, since all of them have been observed with the same instrumentation and the spectra were reduced and analyzed with the same procedure that we will describe in Sect.~\ref{obs}. Such kind of studies are crucial in order {\it i)} to put constraints on the processes occurring at the base of the convection zone in non-magnetic stars and {\it ii)} to try to define the locus on the HR diagram occupied by pulsating Am stars. With these goals in mind, we present a complete analysis of other eight stars previously classified as Am stars. Four of them belong to the sample observed by the {\it Kepler} satellite \citep{balona11} and other four are Am stars discovered to be pulsating from ground-based observations. For our purposes high-resolution spectroscopy is the best tool principally for two reasons, {\it i)} the blanketing due to the chemical peculiarities in the atmospheres of Am stars alters photometric colors and then fundamental stellar parameters based on them may not be accurate \citep[see][and Sect.~\ref{comparison} for details]{catanzaro12} and {\it ii)} the abnormal abundances coupled with rotational velocity result in a severe line blending which makes difficult the separation of the individual lines. Both problems could be overcome only by matching synthetic and observed spectra. For the confirmed Am stars we will compare the observed abundance with the predictions of the models and we will place them on the HR diagram by evaluating their luminosities. \begin{table*} \centering \caption{Results obtained from the spectroscopic analysis of the sample of Am stars presented in this work. The different columns show: (1) identification; (2) effective temperatures; (3) gravity ($\log g$); (4) microturbolent velocity ($\xi$); (5) rotational velocity (v\,$\sin i$), (6) Heliocentric Julian Day of observation; (7) radial velocity (V$_{rad}$); (8) indication of binarity (Y=binary; N=not binary; U=data insufficient to reach a conclusion); (9) indication of belonging to the Am star class (Y=Am; N=not Am); (10) indication of presence of pulsation \citep[Y=pulsating; N=not pulsating; after][and references therein]{balona11}. } \begin{tabular}{cccccccccc} \hline \hline \noalign{\medskip} HD~~ & T$_{\rm eff}$~~~~~~& $\log g$ & $\xi$ &v $\sin i$ ~~ & HJD & V$_{rad}$~~~~ & Binary & Am& Pulsating\\ & (K) ~~~~~& & (km s$^{-1}$)~ & (km s$^{-1}$)~~~& (2450000.+) & (km s$^{-1}$) & & & \\ (1) & (2) & (3) & (4) &(5) &(6) &(7) &(8) &(9) &(10) \\ \noalign{\medskip} \hline \noalign{\smallskip} 104513 & 7200\,$\pm$\,200 & 3.6\,$\pm$\,0.1 & 2.6\,$\pm$\,0.2 &72\,$\pm$\,7 & 5614.5119 & $-$3.12\,$\pm$\,1.71 & Y & Y & Y \\ 113878 & 6900\,$\pm$\,200 & 3.4\,$\pm$\,0.1 & 2.6\,$\pm$\,0.2 &65\,$\pm$\,6 & 5615.6761 & $-$2.78\,$\pm$\,1.53 & Y & Y & Y \\ 114839 & 7200\,$\pm$\,200 & 3.8\,$\pm$\,0.1 & 2.5\,$\pm$\,0.2 &65\,$\pm$\,7 & 5615.6388 & $-$2.87\,$\pm$\,1.72 & U & N & Y \\ 118660 & 7200\,$\pm$\,200 & 3.9\,$\pm$\,0.1 & 2.4\,$\pm$\,0.2 &100\,$\pm$\,10 & 5615.6490 & $-$1.70\,$\pm$\,0.25 & N & Y & Y \\ 176843 & 7600\,$\pm$\,150 & 3.8\,$\pm$\,0.1 & 2.7\,$\pm$\,0.2 &27\,$\pm$\,3 & 5696.6652 & $-$26.42\,$\pm$\,0.56 & -- & Y & Y \\ 179458 & 8400\,$\pm$\,200 & 4.1\,$\pm$\,0.1 & 2.7\,$\pm$\,0.3 &75\,$\pm$\,7 & 5697.6103 & $-$15.37\,$\pm$\,0.57 & -- & N & N \\ 187254 & 8000\,$\pm$\,150 & 4.1\,$\pm$\,0.1 & 2.5\,$\pm$\,0.2 &15\,$\pm$\,2 & 5697.6471 & $-$39.68\,$\pm$\,1.08 & Y & Y & N \\ 190165 & 7400\,$\pm$\,150 & 4.1\,$\pm$\,0.1 & 2.3\,$\pm$\,0.2 &58\,$\pm$\,6 & 5696.7086 & $-$7.45\,$\pm$\,0.45 & U & Y & N \\ \noalign{\smallskip} \hline \end{tabular} \label{param} \end{table*} | In this work we presented a spectroscopic analysis of a sample of 8 stars classified in literature as to belong to the class of the metallic Am stars. The analysis is based on high resolution spectra obtained at the {\it Telescopio Nazionale Galileo} with the SARG spectrograph. For each spectra we obtained fundamental parameters such as effective temperatures, gravities, rotational and radial velocities, and we performed a detailed computation of the chemical pattern, as well. To overcome the problem arising from blending of spectral lines, we applyed the synthesis method by using SYNTHE \citep{kur81} and ATLAS9 \citep{kur93} codes. The typical errors was about 200~K for T$_{\rm eff}$, 0.1~dex for $\log g$, and a few km~s$^{-1}$ for the v $\sin i$. The values of T$_{\rm eff}$ and $\log g$ derived here have been used to determine the luminosity of the stars and to place them on the HR diagram. According to our analysis, we ruled out two stars from the group of the Am stars, namely: HD\,114839 and HD\,179458. The reasons are different, HD\,114839 showed abundances almost solar in conten, while HD\,179458 has a chemical pattern far from the solar one, but nevertheless its peculiarity is not the one typical for Am stars. All the observed stars lie in the $\delta$\,Sct instability strip next to the red edge, in agreement with \citet{smalley11} and \citet{catanzaro12}. In the scenario described by the diffusion models developed by \citet{richer00}, stars in the range of temperature and age compatible with those of our sample should have underabundances of about 0.1 to 0.3 dex for elements such as C, N, O, Na, Mg, K, and Ca, normal abundance for Si and S, while Al, Ti, Cr, Mn, Fe, and Ni resulted overabundant of about 0.1 to 0.8 dex. For what that concern lithium, \citet{richer00} models predict anomalies of $\approx$\,$-$0.2 dex with respect the cosmic value. For our stars, in general we obtained abundances almost 0.2 dex over the cosmic value, a result in agreement with the abundances found in the Am star HD\,27411 \citep{catanzaro12} and in the Praesepe cluster \citep{fossati07}. In conclusion we measured more lithium than that predict by theory. Recently, \citet{vick10}, in the context of the project to explore various macroscopic processes which compete with atomic diffusion in Am/Fm stars, computed a grid of models in which mass-loss has been used instead of turbulence. Those models predict at the side of Li dip, where our objects lie, a smaller anomaly but still not sufficient to explain our observations. As the authors suggested, it is likely that more than one mechanism compete to diffusion, i. e. mass-loss in combination with turbulence, but at the moment is not possible to conclude about one of this possibility. In any case, our detailed abundance analysis can help theorist in setting more constraints in their diffusion models. | 14 | 4 | 1404.0954 |
1404 | 1404.0023_arXiv.txt | We present 279 galaxy cluster candidates at $z > 1.3$ selected from the 94 deg$^{2}$ {\it Spitzer} South Pole Telescope Deep Field (SSDF) survey. We use a simple % algorithm to select candidate high-redshift clusters of galaxies based on {\it Spitzer}/IRAC mid-infrared data combined with shallow all-sky optical data. We identify distant cluster candidates in SSDF adopting an overdensity threshold that results in a high purity (80\%) cluster sample based on tests in the {\it Spitzer} Deep, Wide-Field Survey of the Bo\"otes field. Our simple algorithm detects all three $1.4 < z \leq 1.75$ X-ray detected clusters in the Bo{\"o}tes field. % The uniqueness of the SSDF survey resides not just in its area, one of the largest contiguous extragalactic fields observed with {\it Spitzer}, but also in its deep, multi-wavelength coverage by the South Pole Telescope (SPT), % {\it Herschel}/SPIRE and {\it XMM-Newton}. % This rich dataset will allow direct or stacked measurements of Sunyaev-Zel'dovich effect decrements or X-ray masses for many of the SSDF clusters presented here, and enable systematic study of the most distant clusters on an unprecedented scale. We measure the angular correlation function of our sample and find that these candidates show strong clustering. Employing the COSMOS/UltraVista photometric catalog in order to infer the redshift distribution of our cluster selection, we find that these clusters have a comoving number density $n_c = (0.7^{+6.3}_{-0.6}) \times 10^{-7} h^{3} \mathrm{Mpc}^{-3}$% and a spatial clustering correlation scale length $r_0 = (32 \pm 7) h^{-1} \rm{Mpc}$% . Assuming our sample is comprised of dark matter halos above a characteristic minimum mass, $M_{{\rm min}}$, we derive that at $z=1.5$ these clusters reside in halos larger than $M_{{\rm min}} = 1.5^{+0.9}_{-0.7} \times 10^{14} h^{-1} M_{\odot}$ % . We find the mean mass of our cluster sample to be equal to $M_{{\rm mean}} = 1.9^{+1.0}_{-0.8} \times 10^{14} h^{-1} M_{\odot}$, thus our sample contains the progenitors of present-day massive galaxy clusters. | Emerging from the cosmic web, galaxy clusters are the most massive gravitationally bound structures in the universe. Thought to have begun their assembly at $z > 2$, clusters provide insights into the growth of large-scale structure as well as the physics that drives galaxy evolution. Understanding how and when the most massive galaxies assemble their stellar mass, stop forming stars, and acquire their observed morphologies remain outstanding questions. The redshift range $1.4 < z < 2$ is a key epoch in this respect: elliptical galaxies start to become the dominant population in cluster cores, and star formation in spiral galaxies is being quenched \citep[e.g.,][]{Blakeslee06, Rosati09, Mei09, Overzier09, Rettura10, Rettura11, Raichoor11, Strazzullo10, Stanford12, Snyder12, Zeimann12, Mei12, Nantais13}. Interestingly, some field galaxy studies find that the star formation rate (SFR)-density relation reverses at $z=1$ relative to $z=0$ \citep{Cooper07, Elbaz07}, such that star formation no longer decreases with increasing galaxy density at $z=1$. However some other studies disagree with this result \citep{Patel09, Muzzin12, Scoville13} and conclude the reversal must happen at $z>1$ as they find the local density correlations to be already in place by $z = 1$. There is also observational evidence for a progressive increase in the amount of star formation that occurs in galaxy cluster cores at $z \gtrsim 1.4$ \citep[e.g.,][]{Hilton09, Hayashi10, Tran10, Fassbender11, Tadaki12, Brodwin13, Alberts14}. This suggests that significant star formation is occurring in high-density environments at early epochs. Therefore, increasing evidence points to clusters at $1.5 < z < 2$ as being the ideal laboratories to study cluster formation and to catch in the act transformations in their stellar populations. Until recently, however, this redshift range was essentially unreachable with available instrumentation, % with clusters at these redshifts exceedingly challenging to identify from either ground-based optical/near-infrared (NIR) imaging or from X-ray surveys. Mid-infrared (MIR) imaging with {\it Spitzer} has changed the landscape. % Previous {\it Spitzer} wide-area surveys have proven effective at identifying samples of galaxy clusters down to low masses at $1 \lesssim z < 2$ \citep[e.g., SDWFS, SWIRE, CARLA][]{Eisenhardt08, Papovich08, Wilson09, Demarco10, Galametz10, Stanford12, Zeimann12, Brodwin13, Galametz13, Muzzin13, Wylezalek13} where current X-ray observations are restricted to only the most massive systems. X-ray follow-up has verified several of these MIR-selected clusters, implying masses of a few $10^{14} M_{\odot}$ \citep{Papovich10, Brodwin11, Muzzin13}. To date, however, only a few clusters have been confirmed at $z > 1.5$, in part due to a lack of sufficiently large {\it Spitzer} surveys. With the {\it Spitzer}-South Pole Telescope Deep Field survey \citep[SSDF;][]{Ashby13}, we aim to discover hundreds of cluster candidates at these redshifts. The uniqueness of the SSDF survey resides not just in its area, 94 deg$^2$, one of the largest contiguous extragalactic fields surveyed with {\it Spitzer}, but also in its coverage by deep observations for the Sunyaev-Zel'dovich (SZ) effect by the South Pole Telescope (SPT), with even deeper observations being taken with the new SPT camera, SPTpol \citep{George12}. Approximately one fourth of the SSDF field also has deep X-ray observations from the {\it XMM-Newton} XXL Survey \citep{Pierre11}. This rich multi-wavelength dataset will allow us to determine cluster masses for many of the SSDF clusters at $1 .5< z < 2$, enabling systematic study of the cluster population at an important cosmic epoch. The structure of this paper is as follows. The description of our datasets comprise \S 2. In \S 3 we describe the method we employ to identify distant galaxy clusters, and we estimate our sample purity based on analysis of the Bo{\"o}tes field. In \S 4 we study the clustering of our sample, deriving the characteristic minimum mass, $M_{\rm min}$, of the dark matter halos in which our clusters reside. Section 5 summarizes the conclusions of our study. Throughout, we assume a $\Omega_{\Lambda} = 0.73$, $\Omega_{m} = 0.27$ and $H_{0} = 71\ \rm{km} \rm{s}^{-1} \rm{Mpc}^{-1}$ cosmology \citep{Spergel03}, and use magnitudes in the AB system. | We have identified a large sample of massive high-redshift galaxy cluster candidates of galaxies at $z>1.3$ over the 94 deg$^2$ {\it Spitzer} survey of the SPTpol field. Our algorithm identifies the most significant overdensities of galaxies based upon their IRAC color ($[3.6]-[4.5]>-0.1$), their $4.5 \mu$m magnitude ($[4.5]>19.5$) and requiring non-detection in the shallow SuperCOSMOS $I$-band data ($I > 20.45$). We identify 279 distant cluster candidates using a $X_{f} \geq 5.2$ detection significance, for which we estimate a $\sim 80\%$ purity by running our algorithm on comparable-depth observations of the {\it Spitzer} surveys of the Bo{\"o}tes field \citep{Eisenhardt04, Ashby09}, which has been the target of extensive ground- and space-based spectroscopic and photometric campaigns over the past decade. We find that the SSDF cluster sample shows strong clustering. From the angular correlation analysis, we find our sample has a comoving number density $n_c = (0.7^{+6.3}_{-0.6}) \times 10^{-7} h^{3} \mathrm{Mpc}^{-3}$% and a spatial clustering correlation scale length $r_0 = (32 \pm 7) h^{-1} \rm{Mpc}$% . These values are consistent with previous observational studies and match expectations based on $\Lambda$CDM high-resolution simulations. The high-redshift cluster sample presented here has a mean mass $M_{{\rm mean}} = 1.9^{+1.0}_{-0.8} \times 10^{14} h^{-1} M_{\odot}$. Assuming these clusters grow according to predictions of $\Lambda$CDM \citep[e.g.,][]{Fakhouri10}, they will evolve into massive clusters ($> 5 \times 10^{14} h^{-1} M_{\odot}$) at $z=0.2$. \smallskip This study showcases the impact that large {\it Warm Spitzer} surveys can have on the identification of large samples of massive clusters of galaxies at very high redshifts in the upcoming years. In particular, this sample has been selected in an area where deep observations for the SZ effect with the SPTpol camera are underway and part of this field has also {\it XMM-Newton} deep X-ray observations from the XXL Survey. These ancillary data will allow us to determine cluster masses for our sample, enabling systematic study of the cluster population in a crucial epoch for their assembly. | 14 | 4 | 1404.0023 |
1404 | 1404.7525_arXiv.txt | The concordance model of cosmology, \LCDM, provides a satisfactory description of the evolution of the universe and the growth of large scale structure. Despite considerable effort, this model does not at present provide a satisfactory description of small scale structure and the dynamics of bound objects like individual galaxies. In contrast, MOND provides a unique and predictively successful description of galaxy dynamics, but is mute on the subject of cosmology. Here I briefly review these contradictory world views, emphasizing the wealth of distinct, interlocking lines of evidence that went into the development of \LCDM\ while highlighting the practical impossibility that it can provide a satisfactory explanation of the observed MOND phenomenology in galaxy dynamics. I also briefly review the baryon budget in groups and clusters of galaxies where neither paradigm provides an entirely satisfactory description of the data. Relatively little effort has been devoted to the formation of structure in MOND; I review some of what has been done. While it is impossible to predict the power spectrum of the microwave background temperature fluctuations in the absence of a complete relativistic theory, the amplitude ratio of the first to second peak was correctly predicted a priori. However, the simple model which makes this predictions does not explain the observed amplitude of the third and subsequent peaks. MOND anticipates that structure forms more quickly than in \LCDM. This motivated the prediction that reionization would happen earlier in MOND than originally expected in \LCDM, as subsequently observed. This also provides a natural explanation for massive, early clusters of galaxies and large, empty voids. However, it is far from obvious that the mass spectrum of galaxy clusters or the power spectrum of galaxies can be explained in MOND, two things that \LCDM\ does well. Critical outstanding issues are the development of an acceptable relativistic parent theory for MOND, and the reality of the non-baryonic dark matter of \LCDM. Do suitable dark matter particles exist, or are they a modern \ae ther? \PACS{04.50.Kd,95.35.+d,96.10.+i,98.52.Nr,98.65.Cw} | There is copious evidence for mass discrepancies in the universe \cite{sandersbook}. The usual dynamical laws --- specifically, Newton's law of gravity and Einstein's generalization thereof --- fail when applied to the visible mass in galaxies, clusters of galaxies, and the universe as a whole. These are well tested, fundamental theories, so the observed discrepancies are usually attributed to unseen mass. The evidence for dark matter remains entirely astronomical in nature. The existence of dark matter is an inference based on the reasonable assumption that General Relativity suffices to describe the dynamics of the universe and its contents. The same evidence calls this assumption into question. \subsection{What's in a name? The Missing Mass problem or the Acceleration Discrepancy?} The need for dark matter is often referred to as the `missing mass problem.' This terminology prejudices the answer. More appropriately, we might call it the mass discrepancy problem: there is either missing mass, or a discrepancy in the equations that lead to its inference \cite{milgrom83}. It has also been suggested \cite{bekensteinreview} that the proper terminology should be the acceleration discrepancy, as the problem manifests at a nearly universal acceleration scale \cite{LivRev}. Though General Relativity is well tested in a variety of precise ways, the only data that test it on the scales of galaxies are the data that show the discrepancy. If we drop the assumption that General Relativity applies in regimes where it is otherwise untested, much of the evidence for dark matter becomes rather ambiguous. Indeed, the data can often be interpreted as well in terms of a modification of dynamics as dark matter \cite{MdB98a,MdB98b}. Some data favor one interpretation and some the other, and which we choose is dictated entirely by how we weigh disparate lines of evidence. \subsection{Philosophical Aspects} The current situation is reminiscent of that described by Kuhn \cite{kuhn}. Proponents of competing para\-digms have different ideas about the importance of solving different scientific problems, and about the standards that a solution should satisfy. The vocabulary and methods of the paradigms differ to the point where they can become mutually incomprehensible. The concordance cosmology is about the geometry and expansion history of the universe. The language is that of metrics and power spectra. From this perspective, galaxies are small things that serve best as tracers of the large scale structure that extends across the immeasurable vastness of the universe. In contrast, MOND \cite{milgrom83} is about the dynamics of objects in the low acceleration regime. The language is that of gravitational potentials and orbital mechanics. From this perspective, the dynamics of individual galaxies are connected to their observed shapes with minute precision. The contradictory concepts of dark matter and modified gravity have been developed into paradigms that enjoy successes and suffer problems in different arenas. Presumably one must subsume the other, but it is far from obvious how this can be achieved short of a hybrid solution \cite{sandersbosons,blanchet,Blanchetnatural,angussterile}, which some might find aesthetically distasteful. To illustrate the situation, I briefly state the impossibility of each alternative from the perspective of the other. | There are at present two dialectically opposed explanations for the observed mass discrepancies in the universe. In the concordance cosmology, \LCDM, the universe is filled with non-baryonic, dynamically cold dark matter. In MOND, the mass discrepancy is ascribed instead to a change in the force law at a critical acceleration scale $a_{\dagger} \approx 10^{-10}\;\mathrm{m}\,\mathrm{s}^{-2}$. I have reviewed some of the data pertinent to each paradigm. Where one makes clear predictions, the other tends to be mute. This makes comparison of the two fraught. The conclusion one comes to depends on how one chooses to weigh the various lines of evidence. There are serious challenges for both ideas. The acceleration scale $a_{\dagger}$ is clearly written in the dynamical data. This is not natural to the scale free nature of CDM, so one important issue is whether plausible \LCDM\ models can be constructed to accommodate this fact. Here `plausible' is key. There are many moving parts in galaxy formation models. There is no doubt that they have sufficient flexibility to fit any given set of data. Since such models can do an enormous variety of things, yet the data for individual galaxies do the one specific and unique thing predicted by MOND, fine-tuning galaxy formation models inevitably violates Occam's razor \cite{myrutgers,MdB98a}. The looming challenge for MOND is to find a satisfactory relativistic theory that reproduces all the successes of General Relativity as well as MOND in the appropriate limits. This is no small task. At present, there are many theories under consideration. Whether any are satisfactory is too soon to judge. However, it seems to me that \textit{if} MOND is true, then we are missing something conceptual at a fundamental level. Perhaps this is related to Mach's Principle and the origin of inertial mass, but this is simply speculation. Finally, a fundamental question is whether non-baryonic CDM actually exists. \textit{If} the concordance cosmology is correct, it must. Contrawise, the non-existence of CDM falsifies the concordance cosmology. The situation is somewhat reminiscent of that of \ae ther in the nineteenth century. Given what we know of cosmology today, non-baryonic dark matter must exist. But does it? We know there must be new physics, but of what kind? The existence of the \ae ther was at least falsifiable. It is not obvious that CDM meets this standard, and we teeter on the brink of the definition of science. The existence of CDM is confirmable: a clear laboratory detection of appropriate WIMPs would suffice. However, the existence of dark matter is not falsifiable \cite[though see][]{MdB98a,kroupafalsify,KPM12}. If we fail to find WIMPs, maybe it is axions. If not axions, we are free to invent another form of dark matter --- and another, and another, and so on, \textit{ad infinitum}. CDM was invented for very good reasons. But if this hypothesis happens to be wrong, how do we tell? | 14 | 4 | 1404.7525 |
1404 | 1404.7149_arXiv.txt | No, within a broad class of scenarios. Gravitational-wave (GW) astronomy will open a new window on compact objects such as neutron stars and black holes (BHs). It is often stated that large signal-to-noise detections of ringdown or inspiral waveforms can provide estimates of the masses and spins of compact objects to within fractions of a percent, as well as tests of General Relativity. These expectations usually neglect the realistic astrophysical environments in which compact objects live. With the advent of GW astronomy, environmental effects on the GW signal will eventually have to be \emph{quantified}. Here we present a wide survey of the corrections due to these effects in two situations of great interest for GW astronomy: the BH ringdown emission and the inspiral of two compact objects (especially BH binaries). We mainly focus on future space-based detectors such as eLISA, but many of our results are also valid for ground-based detectors such as aLIGO, aVirgo and KAGRA. We take into account various effects such as: electric charges, magnetic fields, cosmological evolution, possible deviations from General Relativity, firewalls, and the effects related to various forms of matter such as accretion disks and dark matter halos. Our analysis predicts the existence of resonances dictated by the external mass distribution, which dominate the very late-time behavior of merger/ringdown waveforms. The mode structure can drastically differ from the vacuum case, yet the BH response to external perturbations is unchanged at the time scales relevant for detectors. This is because although the vacuum Schwarzschild resonances are no longer quasinormal modes of the system, they still dominate the response at intermediate times. Our results strongly suggest that both parametrized and ringdown searches should use at least two-mode templates. Our analysis of compact binaries shows that environmental effects are typically negligible for most eLISA sources, with the exception of very few special extreme mass ratio inspirals. We show in particular that accretion and hydrodynamic drag generically dominate over self-force effects for geometrically thin disks, whereas they can be safely neglected for geometrically thick disk environments, which are the most relevant for eLISA. Finally, we discuss how our ignorance of the matter surrounding compact objects implies intrinsic limits on the ability to constrain strong-field deviations from General Relativity. | Unlike large-distance corrections --~where cosmological observations are in clear conflict with theoretical expectations~-- the motivation to modify GR in the strong-curvature regime is inspired by conceptual arguments. These arguments rely in one way or another on the conflict of the classical equations of GR with quantum mechanics and lead to the obvious conclusion that the ultimate theory of quantum gravity will differ from GR where curvature effects are important. In this paradigm, curvature effects become important close to singularities -- but these seem to be hidden from us by horizons, as all evidence indicates. The very existence of horizons also sets an upper limit on the energy scale involved, so that putative quantum effects at the Planck scale are negligible for astrophysical BHs. Therefore, it appears that any problem that might potentially affect the strong-gravity dynamics of astrophysical objects can be understood \emph{within} GR rather than by extending it. Nonetheless, paradigms such as this have been challenged time and again in physics. Current experiments can probe gravitational potentials which are roughly six orders of magnitude weaker than those experienced near a massive BH and they can probe only curvatures which are thirteen orders of magnitude smaller than those experienced near and within compact objects~\cite{Psaltis:2008gka}. Extrapolating Einstein's theory to those unexplored regions introduces dangerous bias in our understanding of the strong gravitational interaction~\footnote{As a comparison, the gravitational potential on Earth's surface, where Newtonian gravity proved to be extremely successful, is only 4 orders of magnitude smaller than its corresponding value on the Sun surface where relativistic effects are relevant, as shown by the classical tests of GR. Likewise, even a very successful theory as quantum electrodynamics cannot be extrapolated from atomic to nuclear energy scales, the latter being 6 orders of magnitude larger and well described by strong interactions.}. GW astronomy promises to test GR in the strong-curvature, highly-dynamical regimes which are completely unexplored to date (cf. e.g. Ref.~\cite{Yunes:2013dva}). While waiting for experiments to guide the theoretical efforts, the study of beyond-GR effects on the GW signal faces the problem that each theory is associated with different corrections and that a case-by-case analysis seems to be required. Deviations from GR (as well as matter effects) in spinning geometries were considered in the so-called ``bumpy-BH'' formalism~\cite{0264-9381-9-11-013,Collins:2004ex,Vigeland:2009pr,Vigeland:2011ji} and in other approaches~\cite{Glampedakis:2005cf,Johannsen:2011dh}, although none of them is free from limitations. A different promising approach is the so-called parametrized post-Einstein (ppE) expansion, which attempts to model modified gravitational waveforms directly, in a way that can potentially accommodate most of the corrections to the GR signal~\cite{Yunes:2009ke,Yunes:2013dva}. Here we use and extend some of the salient features of these available approaches. In order to parametrize generic corrections to the background metric, we adopt an approach similar to the bumpy-BH case: taking advantage of the assumption of spherical symmetry, we parametrize possible deviations from GR directly at the level of the metric by considering weak-field deformations around the most general static and spherically symmetric geometry. With respect to the bumpy-BH formalism, this approach has the merit to be generic (we do not assume Einstein's equations nor any particular symmetry other than the spherical one) and sufficiently simple to provide direct order-of-magnitude estimates. On the other hand, to parametrize corrections to the GW fluxes, in some sections of Part~\ref{part:testsGR} we use the ppE framework. An alternative theory of gravity would modify the GR signal essentially in three ways: \textit{i)} by altering the background solutions, i.e. by deforming the geometry of compact objects; \textit{ii)} by modifying the GW emission, for example introducing monopolar and dipolar radiation, changing the coupling with sources and possibly suppressing some radiation (as in the case of massive fields~\cite{Cardoso:2011xi,Alsing:2011er}); \textit{iii)} by modifying the physical properties of the GWs once they are emitted, e.g. the dispersion relation, the polarization and the way they interact with matter and with the detector. In this section we mostly focus on the ``conservative'' effects of \textit{i)}, which in many situations are the dominant correction. ``Dissipative'' effects related to \textit{ii)} and \textit{iii)} are discussed in Part~\ref{part:testsGR}. We consider a general static, spherically symmetric spacetime: \begin{equation} ds^2=-A(r)dt^2+\frac{1}{B(r)}dr^2+r^2\left(d\theta^2+\sin^2\theta\,d\phi^2\right)\,, \label{ansatz} \end{equation} which we treat as a small deformation of the Schwarzschild geometry. Accordingly, we expand the metric coefficients as \begin{eqnarray} A(r)&=&\left(1-\frac{r_+}{r}\right)\left[1+\sum_{i=1}^{N_\alpha} \alpha_i \frac{M^i}{r^i}\right]\,,\label{PRA1}\\ B(r)&=&\left(1-\frac{r_+}{r}\right)\left[1+\sum_{i=1}^{N_\beta} \beta_i \frac{M^i}{r^i}\right]^{-1}\,,\label{PRA2} \end{eqnarray} where $r_{+}$ is the horizon's radius, and we assume that $\alpha_i$ and $\beta_i$ are small dimensionless parameters. In writing the expansions above, we have required regularity of the metric (which implies $A(r_+)=B(r_+)=0$ at the horizon) and asymptotic flatness. The asymptotic behavior of the metric reads \begin{eqnarray} A(r)&=&1-\frac{r_+-M\alpha_1}{r}+\frac{M^2\alpha_2-M r_+ \alpha_1}{r^2}+{\cal O}(1/r^3)\,, \label{Asympt}\\ B(r)^{-1}&=&1+\frac{r_++M\beta_1}{r}+{\cal O}(1/r^2)\,.\label{Bsympt} \end{eqnarray} By comparing this with the parametrized post-Newtonian (PPN) expansion of the metric~\cite{Will:2005va}, \begin{eqnarray} A(r)&=&1-\frac{2M}{r}+2(\beta-\gamma)\frac{M^2}{r^2}+{\cal O}(1/r^3)\,,\\ B(r)^{-1}&=&1+2\gamma\frac{M}{r}+{\cal O}(1/r^2)\,, \end{eqnarray} we can identify \begin{equation} r_+=2M+M\alpha_1\,,\qquad \beta_1=2(\gamma-1)-\alpha_1\,,\qquad \alpha_2=2(\beta-\gamma)+\alpha_1(2+\alpha_1)\,.\label{PPNconditions0} \end{equation} The PPN parameters are very well constrained by observations~\cite{Will:2005va} and their measured value is close to unity, $\delta\gamma\equiv\gamma-1\sim10^{-5}$ and $\delta\beta\equiv\beta-1\sim 10^{-3}$. In the following we consider $\delta\gamma,\delta\beta\ll1$ and work to first order in all these perturbative quantities.\footnote{Note however that the PPN constraints are derived assuming the central object is a star. Since we are mainly interested in BHs, we make the extra assumption that the asymptotic behaviors~\eqref{Asympt}--\eqref{Bsympt} are the same for a BH geometry and a star. This might not be the case in some modified gravity, for example in theories which allow for some Vainshtein-like mechanism~\cite{Babichev:2013usa}, but is the case, for instance, in scalar-tensor theories, \AE-theory and Ho\v rava gravity. Also, note that the assumption $\delta\gamma,\delta\beta\ll1$ is \textit{weaker} than requiring that Birkhoff theorem be satisfied in modified gravity.} Equation~\eqref{PPNconditions0} can be written as \begin{equation} r_+=2M+M\alpha_1\,,\qquad \beta_1=2\delta\gamma-\alpha_1\,,\qquad \alpha_2=2(\delta\beta-\delta\gamma)+\alpha_1(2+\alpha_1)\,.\label{PPNconditions} \end{equation} This model has $N_\alpha+N_\beta$ parameters, in addition to the mass $M$. The parameters $\delta\gamma$ and $\delta\beta$ are already strongly constrained, but we keep them undetermined to explore the potential of GW measurements to provide stronger constraints than those currently in place. The remaining parameters are currently unconstrained in a PN sense. It is worth stressing that $\alpha_1$ is also unconstrained. This parameter is related to a shift of the event horizon for a given mass (i.e. to a deformation of the BH area formula) and it was neglected in previous analyses (e.g. in Ref.~\cite{Johannsen:2011dh} and in subsequent studies, cf. Ref.~\cite{Joao} for a discussion) although it is the dominant term in a weak-field expansion. Note that the parametrization~\eqref{PRA1}--\eqref{PRA2} is substantially different from a PN expansion, because it includes strong-gravity effects such as the presence of an event horizon. The metric above is effectively a weak-field expansion around the Schwarzschild geometry and, as such, it is not unique. Furthermore, a priori there is no guarantee that the expansion~\eqref{PRA1}--\eqref{PRA2} converges for small values of $N_\alpha$ and $N_\beta$ in the strong-field regime. In other words, there is no reason why any strong-field observable derived from such a deformed metric should depend more strongly on the lowest order coefficients. We will show, however, that only the first coefficients of the $\alpha_i$ and $\beta_i$ series do indeed give relevant contributions to GW observables, even at the strongest curvatures that can be probed with GW astronomy. Naively, this is due to the fact that geodesic motion has an upper cutoff in frequency given by the innermost stable circular orbit (ISCO) $r\sim 6M$, whereas the ringdown emission is governed by the light ring at $r\sim 3M$. Both the ISCO and the light ring radii are larger than the central mass $M$, so higher powers of $M/r$ are suppressed. As a result, Eqs.~\eqref{PRA1}--\eqref{PRA2} provide a very efficient parametrization, at least in the static case, where $M/r\lesssim 1/2$ outside the horizon. \clearpage \newpage \part{Ringdown}\label{part:ringdown} | \label{sec:conclusions} The advent of GW astronomy demands for a careful quantification of the impact of realistic astrophysical environments on the GW signal. Our results strongly suggest that GW astronomy can become a {\it precision} discipline: given an appropriate and sensitive detector, astrophysical environmental effects are small and do not prevent a precise mapping of the compact-object content of the visible universe. Moreover, if adequately modeled, GWs might be used in the most optimistic scenarios to study matter configurations around compact objects as is routinely done in the electromagnetic band. We have presented a survey of several environmental effects in two situations of great interest for GW astronomy: the ringdown emission of massive BHs and the two-body inspiral of compact objects. We have studied the GW signal associated to the presence of electric charges, magnetic fields, cosmological evolution, matter disks and halos and finally the effects of possible deviations from GR. Our analysis revealed novel effects related to the ringdown modes in the presence of environmental effects. The QNM spectrum of nonisolated BHs can be drastically different from that of isolated BHs, yet the BH response to external perturbations is unchanged at the relevant time scales for ringdown. This result is interesting on its own and would deserve an independent study. In particular, it would be interesting to see if such resonances can be excited during an extreme-mass ratio inspiral around BH surrounded by matter, thus providing a clean GW signature of matter configurations around compact objects. Toy models suggest this will happen at low frequencies when the inspiralling object is far away from the BH. Head-on collisions could also excite these modes which would then presumably show up at very late-times competing with Price's power-law tails. More realistic models are clearly necessary to understand the full implications of these results. A curiosity with possible observational effects is that matter {\it close} to the event horizon also gives rise to such modified modes and response. This might have important implications for the so-called ``firewall'' proposal~\cite{Almheiri:2012rt}: the analysis in Sec.~\ref{sec:firewall} shows that any localized field with mass $\delta M\gtrsim 10^{-4}M$ close to the horizon of a massive BH would affect the ringdown frequencies to detectable levels. Investigating the implications of this effect for the gravitational waveforms in realistic scenarios is an interesting extension of our analysis. Self-force in BH spacetimes has been shown to be directly connected to the QNMs structure~\cite{Casals:2009zh,Casals:2013mpa}. In view of the sometimes dramatic change in the QNM spectrum of nonisolated BHs, an open question is whether self-force outside ``dirty'' BHs also shows the same exquisite dependence on the environment configuration and distribution. We note that the ringdown spectrum in the presence of matter at large distance shares many features with the spectrum of light massive fields around BHs (cf. Ref.~\cite{Cardoso:2013krh} for a review). In this case, the field is localized at $\sim1/\mu$, where $\mu$ is the mass of the field. It is known that also in this case the late-time behavior is drastically modified and a novel family of modes emerges which does {\it not} reduce to GR when the mass goes to zero. Overall, our results confirm the generic claim that environmental effects can be safely neglected for detection. However, in some situations such effects become important for parameter estimation and for searches of new physics. Environmental effects can in some cases be comparable to first- and second-order self-force corrections and can put intrinsic limits on our ability to test modified theories of gravity. We have provided order-of-magnitude estimates of these limits that are largely model- and theory-independent. Clearly, a precise analysis might in principle disentangle environmental effects from self-force and beyond-GR corrections but, given our ignorance of matter configurations around compact objects, a precise modeling of the dirtiness signal would be mandatory to perform such an analysis. In general the corrections to the ringdown signal are smaller than those affecting the inspiral waveforms. This is expected because the latter can accumulate during the last stages of the inspiral. In addition, our analysis selects some ``smoking guns'' of dirtiness in the ringdown signal: isospectrality breaking, monopole and dipole radiation, novel families of modes, resonant effects in the GW flux and changes of the late-time GW signal. The main limitation of our study is the fact that we neglected spin effects. Compact objects are usually spinning and angular momentum plays a crucial role in the GW signal. Spin modifies the multipolar structure of the background geometries as well as the geodesic motion and the GW emission. We have considered only static configurations and our approach has the merit of being very general within this strong assumption. Including spin effects for compact objects in a model- and theory-independent framework is a remarkable open problem which goes beyond the scope of this work. Because spin effects are typically dominant over environmental effects, one does not expect any degeneracy problem. Furthermore, most of the effects we discuss are not directly related to the spin, so that we expect our analysis can capture the correct order of magnitude also in the case of spinning objects. One important exception to the above are near-extremal BHs. In this case the light-ring and the ISCO are located close to the event horizon, thus probing regions of stronger gravitational field with respect to the static case. We have shown that a parametrization of deformed Schwarzschild geometries in powers of $M/r$ [cf. Eqs.~\eqref{PRA1}--\eqref{PRA2}] provides a very efficient expansion, because higher-order corrections are suppressed even in the strong-field limit. We have shown this for nonspinning objects and our conclusions would likely remain valid in the slow-rotation limit. However the same is not true in the case of near-extremal objects, for which both ringdown and inspiral can probe the strong-curvature region $M/r\sim1$, where an expansion similar to~\eqref{PRA1}--\eqref{PRA2} would likely not converge. This suggests that strong-gravity effects are amplified in the near-extremal case, making highly-spinning compact objects the most promising astrophysical probes of strong gravity. Another possible extension of this work would be to consider the impact of environmental effects on the eccentricity of compact-object binaries (see Refs.~\cite{Barausse:2007dy,gair} for some results for the eccentricity evolution under the effect of dynamical friction and accretion). | 14 | 4 | 1404.7149 |
1404 | 1404.1073_arXiv.txt | {The magnetic activity of planet-hosting stars is an important factor for estimating the atmospheric stability of close-in exoplanets and the age of their host stars. It has long been speculated that close-in exoplanets can influence the stellar activity level. However, testing for tidal or magnetic interaction effects in samples of planet-hosting stars is difficult because stellar activity hinders exoplanet detection, so that stellar samples with detected exoplanets show a bias toward low activity for small exoplanets.} {We aim to test whether exoplanets in close orbits influence the stellar rotation and magnetic activity of their host stars.} {We developed a novel approach to test for systematic activity-enhancements in planet-hosting stars. We use wide (several 100 AU) binary systems in which one of the stellar components is known to have an exoplanet, while the second stellar component does not have a detected planet and therefore acts as a negative control. We use the stellar coronal X-ray emission as an observational proxy for magnetic activity and analyze observations performed with Chandra and XMM-Newton.} {We find that in two systems for which strong tidal interaction can be expected the planet-hosting primary displays a much higher magnetic activity level than the planet-free secondary. In three systems for which weaker tidal interaction can be expected the activity levels of the two stellar components agree with each other.} {Our observations indicate that the presence of Hot Jupiters may inhibit the spin-down of host stars with thick outer convective layers. Possible causes for this effect include a transfer of angular momentum from the planetary orbit to the stellar rotation through tidal interaction, or differences during the early evolution of the system, where the host star may decouple from the protoplanetary disk early because of a gap opened by the forming Hot Jupiter.} | Stellar magnetic activity is a phenomenon that shapes the environment of exoplanets. Magnetically induced processes such as stellar flares, high-energy emission, and coronal mass ejections can have profound effects on the atmospheres of close-in exoplanets, causing the heating of high-altitude layers and atmospheric evaporation \citep{Vidal-Madjar2003, Murray-Clay2009, Lammer2003, Khodachenko2012}. It is well known that the activity of cool stars decreases over time; because rotation is the driver of activity, the magnetic braking caused by the stellar wind causes all activity processes to weaken over timescales of gigayears. Some processes can preserve high activity levels over long timescales, such as tidal locking in close binaries, which sustains fast stellar rotation and therefore activity. It has been speculated that similar effects, albeit on a weaker scale, may occur for stars with Hot Jupiters \citep{Cuntz2000, Lanza2008}. Observational studies have been performed on individual systems \citep{Shkolnik2005, Shkolnik2008, PoppenhaegerLenz2011, Pillitteri2011, Miller2012} as well as on larger samples of planet-hosting stars \citep{Kashyap2008, Poppenhaeger2010, Shkolnik2013}, finding weak correlations of stellar activity with the presence of Hot Jupiters. Indications for higher $v\sin i$ values have also been reported \citep{Pont2009tidal} for systems with Hot Jupiters compared with systems hosting smaller or more distant planets, yielding first indications of a tidal influence of exoplanets on their host stars. This was solidified in a detailed study by \cite{Husnoo2012}, who found indications for excess rotation of several hot Jupiter host stars. However, unambiguous signatures of a planet-induced enhanced activity level are difficult to identify, because planet-detection methods favor magnetically inactive stars. Active stars usually only allow for the detection of planets with strong RV signatures or deep and frequent transits (i.e.\ Hot Jupiters). This bias induces spurious trends in the population of stars with detected planets \citep{Poppenhaeger2011}. We have developed an observational approach to test for planetary influences on the stellar activity level without most of the common biases induced by planet detection. We have selected a small sample of planet-hosting stars that have a known stellar companion; the stellar companions are not known to have planets themselves. Companionship of the two stellar components has been established through common proper motion or common radial velocity; the two stars can therefore be assumed to have the same age. The distance between these stellar components is large enough so that no influence on the activity level can be expected. For close (<0.1 AU) or medium-distance (<10 AU) binaries, such an influence has been observed and traced back to tidal locking or, in the case of moderate distances, to differences in the circumstellar disk evolution \citep{Meibom2007, Morgan2012}. Our systems, however, have binary distances of $>100$ AU, for which such trends are absent. We list our sample of five such systems in Table~\ref{systems}. In these systems, the stellar companions without a known planet act as a negative control group to the planet-hosting stars whose activity level may have been influenced by their planets. \begin{table*} \renewcommand{\tabcolsep}{0.07cm} \begin{footnotesize} \begin{tabular}{l c c c c c c c c c c c c c c } \hline \hline Star & spec.\ type & B-V & ang.\ sep.\ & dist. & $P^{\ast}_{rot}$ & $M_P$ & $P_{orb}$ & $a_{sem}$ &$\log R^\prime_{HK}$ & $\log L_X$ & apparent age & $J_{\ast}$ & $J_{orb}$ & $h_{tide}/h_{scale}$\\ & & & (arcsec) & (pc) & (d) & ($M_{Jup}$)& (d) & (AU) & & (erg\,s$^{-1}$)& & (kg m$^2$ d$^{-1}$) & (kg m$^2$ d$^{-1}$)& \\ \hline \object{HD\,189733}\,A & K0V &0.93 & 11.2'' & 19.3 & 12 & 1.14 & 2.22 & 0.031 &-4.501 & 28.2 & 1-2 Gyr & 9.3e46&1.3e47 &0.008\\ HD\,189733\,B & M4V & & 11.2'' & 19.3 & & & & & & 26.7 & $\geq$ 5 Gyr & & &\\ \object{CoRoT-2}\,A & G7V &0.854 & 4'' & 270 & 4.5 & 3.31 & 1.74 & 0.028 &-4.331 & 29.2 & 0.1-0.3 Gyr &4.3e47 &4.0e47 &0.072\\ CoRoT-2\,B & K9V & & 4'' & 270 & & & & & & 27.0 & $\geq$ 5 Gyr & & &\\ \object{$\tau$ Boo}\,A & F7V &0.52 & 2.5'' & 15.0 & 3.3 & 8.14 & 3.31 & 0.048 &-4.70 & 28.8 & 1-2 Gyr &2.0e48 &1.5e48 & 0.047\\ $\tau$ Boo\,B & M & & 2.5'' & 15.0 & & & & & & 27.65 & 1-3 Gyr & & &\\ \object{$\upsilon$ And}\,A& F8IV-V &0.53 & 52'' & 13.5 & 9.5 & 0.62 & 4.62 & 0.059 &-5.04 & 27.7 & $\geq$ 5 Gyr &6.4e47 &1.4e47 &0.002\\ $\upsilon$ And\,B&M4V & & 52'' & 13.5 & & & & & & 26.45 & $\geq$ 5 Gyr & & &\\ \object{55\,Cnc}\,A & G8V &0.87 & 81'' & 13 & 43 & 0.026 & 0.74 & 0.015 &-5.04 & 27.07 & $\geq$ 5 Gyr &4.6e46 &2.3e45 &0.005\\ 55\,Cnc\,B & M3-4V & & 81'' & 13 & & & & & & 26.22 & $\geq$ 5 Gyr & & &\\ \hline\hline \end{tabular} \end{footnotesize} \caption{Wide binary systems consisting of two main-sequence cool stars with at least one exoplanet for which X-ray data has been collected. The closest exoplanet is given in case of multiple exoplanets per system. } \label{systems} \end{table*} | \begin{enumerate} \item We presented X-ray luminosities of the individual stellar components in five wide binary-star systems in which one of the stars is known to host an exoplanet. \item We showed that for two of the systems -- those for which one expects the strongest tidal interaction between planet and host star -- the X-ray emission of the planet-hosting primary is stronger than expected from the secondary, assuming a common stellar age. These host stars are also over-rotating in comparison with the activity level of the secondary. \item We interpret this as an indication that a tidal influence of Hot Jupiters on host stars with thick outer convection zones can occur, which either inhibits the typical spin-down of such stars, or has had an influence on the initial rotation of the stars when they arrive on the main sequence through changes in the star-disk coupling at young ages of the system. We are conducting observations of a larger sample of such systems to substantiate these initial findings. \end{enumerate} | 14 | 4 | 1404.1073 |
1404 | 1404.6523_arXiv.txt | Robust gauge conditions are critically important to the stability and accuracy of numerical relativity (NR) simulations involving compact objects. Most of the NR community use the highly robust---though decade-old---moving-puncture (MP) gauge conditions for such simulations. It has been argued that in binary black hole (BBH) evolutions adopting this gauge, noise generated near adaptive-mesh-refinement (AMR) boundaries does not converge away cleanly with increasing resolution, severely limiting gravitational waveform accuracy at computationally feasible resolutions. We link this noise to a sharp (short-wavelength), initial outgoing gauge wave crossing into progressively lower resolution AMR grids, and present improvements to the standard MP gauge conditions that focus on stretching, smoothing, and more rapidly settling this outgoing wave. Our best gauge choice greatly reduces gravitational waveform noise during inspiral, yielding less fluctuation in convergence order and $\sim 40\%$ lower waveform phase and amplitude errors at typical resolutions. Noise in other physical quantities of interest is also reduced, and constraint violations drop by more than an order of magnitude. We expect these improvements will carry over to simulations of all types of compact binary systems, as well as other $N$+1 formulations of gravity for which MP-like gauge conditions can be chosen. | With the first direct observations of incident gravitational waves (GWs) expected in only a few years, an exciting new window on the Universe is about to be opened. But our interpretation of these observations will be limited by our understanding of how information about the GW sources is encoded within the waves themselves. The parameter space of likely sources is large, and compact binary systems consisting of two black holes (BHs), two neutron stars, and one of each are likely to be the most promising sources. However, filling this parameter space with the corresponding theoretical gravitational waveforms through merger---when GWs are strongest and many binary parameters are most distinguishable---will require a large number of computationally expensive numerical relativity (NR) simulations. At the heart of the computational challenge lies an arguably even greater theoretical one, which seeks to find an optimal approach for solving Einstein's equations on the computer. These approaches generally decompose the intrinsically four-dimensional set of Einstein's field equations into time-evolution and constraint equations---similar to Maxwell's equations \cite{Baumgarte_2010}. Once the data on the initial 3D spatial hypersurface are specified, the time-evolution equations are repeatedly evaluated, gradually building the four-dimensional spacetime one 3D hypersurface at a time. Einstein's equations guarantee the freedom to choose coordinates in the 4D spacetime, and these are specified via a set of gauge evolution equations. Devising robust gauge conditions, particularly when black holes inhabit the spacetime, has been a problem at the forefront of NR for decades. In fact, discovery of gauge conditions leading to stable evolutions in the presence of moving black holes played a large role in the 2005 numerical relativity revolution, culminating in the first successful binary black hole (BBH) inspiral and merger calculations~\cite{Pretorius:2005gq,Campanelli:2005dd,Baker:2005vv}. The most widely adopted formulation for compact binary evolutions is the highly robust ``BSSN/moving puncture'' (hereafter BSSN/MP) formulation \cite{Campanelli:2005dd,Baker:2005vv}, which combines the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) 3+1 decomposition of Einstein's equations \cite{Nakamura:1987zz,Shibata:1995we,Baumgarte:1998te} with the ``moving puncture'' (MP) gauge conditions that implement the {\tt 1+log}/$\Gamma$-freezing gauge evolution equations \cite{Alcubierre:2002kk,vanMeter:2006vi}. It has been about a decade since BSSN/MP was first developed, and it remains in use by much of the NR community, largely unmodified. This is a testament to the robustness of the MP gauge choice, as well as the difficulties associated with devising stable techniques for evolving spacetimes containing BHs. The BSSN/MP equations are typically solved on the computer with high-order finite-difference approaches on adaptive-mesh refinement (AMR) numerical grids \cite{Zlochower:2005bj,Baker:2006yw,Bruegmann:2006at,Campanelli:2007ew,Herrmann:2007ac,Sperhake:2006cy,Etienne:2007jg,Pollney:2007,Pollney:2009yz}. Such grids are essential for computational efficiency, as the simulation domain must be hundreds to thousands of times larger than the initial binary separation to causally disconnect the outer boundary from the physical domain of interest for the duration of the simulation. This effectively prevents errors linked to the enforcement of approximate outer boundary conditions from propagating inward and lowering the convergence order of our gravitational waveforms. In addition, very high resolution must be used in the strongly curved spacetime near the BHs, while resolution requirements are much lower far from the binary, where GWs with wavelengths of order $10M$ must be accurately propagated ($M$ is the total ADM mass of the system). Thus, AMR grids in MP calculations typically resolve the strong-field region best, with progressively lower resolutions away from this region to the outer boundary. Typical gridspacings at the outer boundary can be $\sim 1000$ times larger than in the strong-field region. The BSSN/MP+AMR paradigm has been most thoroughly tested in the context of BBH evolutions, and a large number of theoretical BBH GWs have been produced with this paradigm that widely sample parameter space (e.g., \cite{Lousto:2013wta,Pekowsky:2013ska,Hinder:2013oqa}). However, when the BSSN/MP+AMR paradigm is pushed to very high accuracies or to difficult regions of BBH parameter space, it has been found (e.g., \cite{Zlochower:2012fk}) to yield inconsistent gravitational waveform convergence with increasing resolution, making error estimates difficult, and effectively limiting waveform accuracy. In \cite{Zlochower:2012fk} it was hypothesized that these convergence issues might be linked to noise from high-frequency waves generated at grid refinement boundaries. This is a compelling hypothesis, especially in light of Fig.~\ref{Intro_Ham_constraint_bumps}, which shows regularly-spaced spikes in L2 norm Hamiltonian constraint violations on a logarithmic time scale. Interestingly, the onset of each spike in this BBH evolution is timed almost perfectly to grid refinement crossings of a wave that starts from the strong-field region at the onset of the calculation and propagates outward {\it superluminally at speed $\sqrt{2}c$} (vertical lines). This propagation speed is a smoking gun, as linearized analyses \cite{Alcubierre:2002iq} indicate only one propagation mode with that speed in the standard BSSN/MP formulation. This mode primarily involves the lapse and is governed by the lapse evolution gauge condition. The connection between spikes in Hamiltonian constraint violations and the initial outgoing lapse wave has been noted previously~\cite{Baker:2006yw}. \begin{figure} \includegraphics[angle=270,width=0.45\textwidth]{Ham_constraint__step0_with_AMR_bdries.eps} \caption{L2 norm of Hamiltonian constraint violation $||\mathcal{H}(t)||$ outside black hole horizons (Eq.~\ref{L2_Ham}), versus time (solid red curve), for ``standard'' BSSN/MP+AMR BBH calculation. Dashed blue vertical lines denote the times at which an outgoing wave traveling at $\sqrt{2}c$---starting from the origin at the onset of the calculation---encounters a grid refinement boundary.} \label{Intro_Ham_constraint_bumps} \end{figure} Expanding on this idea, we note that all BSSN evolution equations are coupled to the lapse and its derivatives, so noise from reflections in this {\it gauge} quantity can be easily converted into noise in {\it physical} modes (e.g., noise in GWs) and even constraint violations. Further, differencing errors from the part of the wave that is transmitted into the coarser grid are converted into constraint violations and errors in non-gauge waves as well. We expect improved resolution would mitigate this problem, but even a factor of two increase---the typical range in most BSSN/MP convergence studies---would enable evolution of a sharp (short-wavelength) feature through only one additional coarser level before it succumbs to dissipation through under-resolution. Additionally, it is likely that zero- or low-speed modes in Hamiltonian constraint violations (see, e.g., \cite{Gundlach:2004jp}) may exacerbate any errors generated as the initial sharp lapse wave propagates into a coarse grid. Since sharp features in the initial outgoing lapse wave are likely responsible for spikes in Hamiltonian constraint violations, as well as noise and other errors in physical quantities, we can conceive of at least two strategies for mitigating this effect: (1) adjusting the initial conditions to minimize gauge dynamics, in a similar vein to~\cite{Hannam:PRD80:2009}, or (2) modifying the standard MP lapse evolution equation so that the initial sharp outgoing lapse wave is stretched and smoothed as it propagates outward from the binary. We chose the latter strategy. Strikingly, we find our stretching and smoothing modifications to the lapse evolution equation are sufficient to reduce constraint violations by {\it more than an order of magnitude}, confirming our hypothesis, {\it except near the beginning of our calculations}, where early-time spikes in constraint violations remain. We remove these stubborn spikes by initially reducing the timestep on the BSSN field equations by a factor of $\sim 10^3$, while the gauge evolution equations are evolved according to the original time coordinate. This time reparameterization technique increases the gauge wave speeds to about 30 times the coordinate speed of light, allowing the gauge evolution to very quickly relax near $t=0$ in response to the physical fields. As the gauge fields relax, evolution of the BSSN field variables is slowly accelerated so that their timestep matches that of the MP gauge evolution, after about $10M$ of evolution in the un-reparameterized time coordinate. We show this time reparameterization is, on an analytic level, equivalent to a time-dependent rescaling of the lapse and shift, leaving the BSSN field equations unmodified in the reparameterized time coordinate. When combined, these gauge improvements significantly reduce constraint violations {\it from the onset of the calculation through BBH merger}. For example, the L2 norm Hamiltonian constraint violation outside the BHs is reduced on average by a factor of 20 at $t>0$ at lowest resolution. Hamiltonian constraint violations converge at a much higher order in the presence of our improved gauge conditions, so this factor increases to $\sim 50$ at the highest resolutions attempted. Turning to gravitational waveforms, we find that in the ``standard'' BSSN/MP+AMR paradigm, noise appears to dominate GW power at wave periods $\sim 10M$, and this spike in power does not diminish with increasing resolution. Meanwhile, our ``best'' gauge choice appears to drop this noise-generated GW power spike by about an order of magnitude, and its power spectrum at short wave periods {\it does} drop with increasing resolution. In conjunction with this removal of waveform noise---and perhaps most significantly---we find that gravitational waveform convergence is far cleaner when using the new techniques, enabling more reliable Richardson extrapolations and possibly paving the way to higher accuracies than the standard BSSN/MP+AMR paradigm might allow. In fact, our ``best'' gauge choice reduces Richardson-extrapolation-based error estimates of GW phase and amplitude error during inspiral by about 40--50\%. However, we observe in these waveforms that only the phase error is reduced significantly at merger. Our gauge improvements are presented exclusively in the challenging context of an 11-orbit, equal-mass BBH calculation in which one BH is nonspinning and the other possesses a spin of dimensionless magnitude 0.3, aligned with the orbital angular momentum. Despite our focus on a single physical scenario, we expect these new techniques will improve the accuracy and reliability of simulations couple the MP+AMR paradigm to BSSN and other $N$+1 NR formulations (e.g., \cite{Bona:2003fj,Gundlach:2005eh,Bernuzzi:2009ex,Zilhao:2011}), not only for BBH and single-BH evolutions, but also for binary systems with matter, such as neutron star--neutron star and black hole--neutron star binaries. Finally, we anticipate that careful reparameterization of the time coordinate when the gauge and physical quantities change most significantly---both at the beginning of evolutions {\it and during merger}---may help stabilize compact binary simulations, making it easier to cover difficult regions of parameter space. The rest of the paper is organized as follows. Section~\ref{Basic_Equations} summarizes our basic equations and gauge improvements, Sec.~\ref{Num_Algs_Techs} outlines numerical algorithms and techniques, Sec.~\ref{Results} details results from these improved gauge conditions, and Sec.~\ref{Conclusions} summarizes both our conclusions and plans for future improvements. | \label{Conclusions} It has been found that the standard BSSN/MP+AMR paradigm yields inconsistent convergence in gravitational waveforms in BBH evolutions. Without consistent convergence, it may be impossible to produce reliable error estimates for these waveforms, particularly when very high accuracies are needed. It has been hypothesized \cite{Zlochower:2012fk} that this inconsistent convergence may be related to short-wavelength waves being reflected from grid-refinement boundaries, producing high-frequency noise and constraint violations. We present a set of improvements to the moving-puncture gauge conditions that, with {\it negligible} increase in computational expense, greatly reduce noise and improve convergence properties of gravitational waveforms from BBH inspiral and mergers. These improvements are presented in the context of an NRAR \cite{Hinder:2013oqa} BBH calculation that evolves a low-eccentricity BBH system $\approx 11$ orbits to merger, where one BH has an initial dimensionless spin of $0.3$ aligned with the orbital angular momentum, and the other is nonspinning. Evolutions are performed at up to four resolutions with a variety of gauge choices, starting with the ``standard'' moving puncture gauge choice and adding improvements one by one until our ``best'' gauge choice is reached. Our gauge improvements in part stem from the observation that regularly-spaced spikes in Hamiltonian constraint violations are timed precisely to the grid-refinement boundary crossings of an early outgoing wave traveling at coordinate speed $\sqrt{2}$. Based on linear analyses \cite{Alcubierre:2002iq}, we know of only one propagation mode with that speed in the standard BSSN/MP formulation, which primarily involves the lapse and is governed by the lapse evolution gauge condition. The initial outgoing lapse wave pulse possesses sharp features, which are problematic because, as \cite{Zlochower:2012fk} points out, high-frequency waves crossing into a coarser AMR grid will be partially reflected at the boundary, generating noise. Now the lapse {\it and its derivatives} are strongly coupled to the gravitational field evolution equations, so noise generated by this sharp outgoing lapse pulse crossing refinement boundaries can be easily converted to noise in gravitational field variables (such as GWs) and constraint-violating modes (cf. \cite{Etienne:2011re}). Guided by this, we focus our efforts primarily on modifications to the lapse evolution equation, aimed at stretching and smoothing the initial outgoing lapse wave pulse. We stretch the lapse wave by monotonically increasing its speed as it propagates outward so that the front of the lapse pulse propagates slightly faster than the back. We smooth the lapse wave by adding both parabolic and stronger-than-usual Kreiss-Oliger dissipation terms. The most significant improvements spawn from the stretching of the initial lapse pulse. Despite the stretching of the initial lapse pulse, early-time spikes in the constraint violations are not reduced. We are able to significantly tamp down these spikes via a time reparameterization that greatly accelerates the initial evolution of the lapse and shift relative to the BSSN gravitational field evolution variables. Effectively, this modification makes lapse waves propagate at speeds up to $\sim 30$ times the coordinate speed of light initially, enabling the lapse to respond much more quickly to the rapidly-settling gravitational fields in the strong-field region during the early evolution. % Our ``best'' gauge condition (BestGauge) reduces Hamiltonian and momentum constraint violations by factors of $\sim 20$ and $\sim 13$, respectively. In addition, with this same gauge choice, noise in the dominant gravitational-wave mode---$\psi^4_{2,2}(t)$---is reduced by nearly an order of magnitude, particularly at peak noise frequencies. Such numerical noise can be far more problematic in sub-dominant [i.e., $(l,m)\neq$(2,2)] modes, at times completely obscuring the signal. As an example, with OldGauge, the $(l,m)$=(4,4) mode is noise-dominated throughout much of the inspiral, but with the new gauge improvements, this mode is much cleaner and more amenable to analysis. We observe improvements, generally of a lesser degree, in other sub-dominant modes as well. Finally, we observe a significant reduction in ADM mass and angular momentum noise at large radius, particularly during inspiral and merger. Regardless of gauge choice, we observe a large amount of noise in ADM angular momentum just after merger, corresponding to a spike in momentum constraint at about this time. We are uncertain of the cause for this noise/spike, but suspect they may be due to either rapid coordinate and spacetime evolution associated with BH merger, or possibly high-frequency {\it physical} waves propagating outward into less-refined numerical grids. This warrants further investigation, as the former hypothesis can be tested through a late-time time reparameterization and the latter through grid structure adjustments. In addition to analyses of how constraint violations and noise are affected by our new gauge choices, we perform a suite of constraint-violation, irreducible-mass, and waveform ($\psi^4_{2,2}$) convergence tests with a set of three gauge choices, starting from the ``standard'' moving-puncture gauge choice (OldGauge) to our ``best'' gauge choice (BestGauge). Using the ``standard'' moving-puncture gauge choice (OldGauge), the L2 norm of Hamiltonian constraint violations converges to zero at between first and second order with increasing resolution. If this L2 norm integral excludes the wavezone region far from the binary, convergence order increases to between fifth and sixth order, indicating that subconvergence is related to effects far from the binary, on distant, low-resolution grids. Meanwhile, with our improved gauge choices, we observe between fifth- and sixth-order convergence in this diagnostic {\it even when the integral extends to the outer boundary}. Though momentum constraint violations at a given resolution are significantly reduced with our new gauge choices, we do not observe an improvement in the convergence to zero of momentum constraint violations. This may be due to the fact that even in our ``best'' gauge choice, some high-frequency noise remains in our BBH calculations. Based on our waveform convergence analyses, we find that $\psi^4_{2,2}(t)$ data at \{mr,hr,hhr\} resolutions yield approximate fifth-order convergence, though large fluctuations around fifth order are observed in the OldGauge case. These fluctuations are significantly reduced when improved gauge conditions are adopted, particularly in the BestGauge case. With such consistent fifth-order convergence observed in the highest three resolutions in our best gauge choice (BestGauge), we then analyze the difference between two Richardson-extrapolated realizations of phase and normalized amplitude. One realization uses data at ``hr'' and ``hhr'' resolutions and the other ``mr'' and ``hr'' resolutions. Any nonzero difference between these Richardson-extrapolated realizations of phase and normalized amplitude can be attributed to fluctuations in assumed convergence order $n$ from $n=5$ (which appears to be related to noise) or to error from higher-order terms (cf. Eqs.~\ref{convergence} and~\ref{convergence_exact}). Since these differences in Richardson-extrapolated values are directly related to errors, we use them as our error estimates for the amplitude and phase (though it may be an unconventional choice; cf. \cite{Hinder:2013oqa}). Comparing the ``standard'' moving-puncture gauge choice to our ``best'' gauge, we find significant (factor of $\sim$ 2) reductions in both amplitude and phase errors during inspiral. At the end of the inspiral, when the frequency of the $\psi^4_{2,2}$ is $M\omega=0.2$, we observe roughly a factor of two reduction in phase errors in the BestGauge case but no significant improvement in amplitude errors, as these are dominated near merger by small offsets in the time of merger at different resolutions. We then perform a GW noise analysis, comparing OldGauge and BestGauge results at different resolutions (see Fig.~\ref{Fig:Psi4_waveform_noise_convergence}). In the OldGauge case, the largest spike in GW power directly related to numerical GW noise, at wave periods $P\approx 10M$ (Fig.~\ref{Fig:Psi4_noise_reduction}), does not drop with increasing resolution. Further, we find that the noise-dominated power in this OldGauge spike is about 1\% of the physical GW power maximum at $P=0.5P_\text{orb}$ throughout much of the early inspiral. GW power at wave periods associated with noise in OldGauge runs is reduced by nearly an order of magnitude in the BestGauge runs, and unlike OldGauge, the power at these wave periods appears to drop monotonically with resolution, suggesting that noise in BestGauge converges away more cleanly. Given the excellent amplitude- and phase-convergence properties observed in the BestGauge case, we believe this GW power spectrum analysis strongly indicates that poor convergence in the ``standard'' moving-puncture gauge conditions may indeed be related to poorly-convergent GW noise generated by the initial sharp outgoing lapse pulse. Future work will examine remaining uncertainties in these evolutions, including the nearly simultaneous large spike in momentum constraint violations and large noise in the ADM angular momentum surface integral at the end of our evolutions. Though we have found that our gauge improvements greatly reduce noise in many quantities apparently generated by the sharp initial outgoing lapse pulse, we have not completely eliminated the noise, and it is unknown how much more phase and amplitude errors can be driven downward with the current improvements. Without doubt, higher resolutions and higher-order evolutions will be helpful in determining this. Though these new gauge conditions and techniques have been presented in the context of moving-puncture BBH evolutions only, we fully expect them to be beneficial in a wide variety of NR contexts, including compact binary systems with matter or even BBH evolutions using other $N$+1 NR formulations. With the era of gravitational-wave astronomy now upon us, we hope this work will spur others to join the search for gauge conditions and methods optimal for generating high-quality gravitational waveforms within the MP+AMR context, as each improvement will accelerate our community toward its goals in this exciting time. | 14 | 4 | 1404.6523 |
1404 | 1404.7419_arXiv.txt | {The actual realization of the electroweak symmetry breaking in the context of a natural extension of the Standard Model (SM) and the nature of Dark Matter (DM) are two of the most compelling questions in high-energy particle physics. Composite Higgs models may provide a unified picture in which both the Higgs boson and the DM particle arise as pseudo Nambu-Goldstone bosons of a spontaneously broken global symmetry at a scale $f \sim$ TeV. In this paper we analyze a general class of these models based on the coset $SO(6)/SO(5)$. Assuming the existence of light and weakly coupled spin-1 and spin-1/2 resonances which mix linearly with the elementary SM particles, we are able to compute the effective potential of the theory by means of some generalized Weinberg sum rules. The properties of the Higgs boson, DM, top quark and the above resonances are thus calculable and tightly connected. We perform a wide phenomenological analysis, considering both collider physics at the LHC and astrophysical observables. We find that these models are tightly constrained by present experimental data, which are able to completely exclude the most natural setup with $f \simeq 800$ GeV. Upon increasing the value of $f$, an allowed region appears. In particular for $f\simeq 1.1$ TeV we find a concrete realization that predicts $m_{\rm DM}\simeq 200$ GeV for the DM mass. This DM candidate lies close to the present sensitivity of direct detection experiments and will be ruled out -- or discovered -- in the near future. } | After a quest lasting nearly half a century, the discovery of the Higgs boson \cite{Higgs,Higgs2,Higgs3} was supposed to shed light on the mechanism triggering the electroweak symmetry breaking (EWSB) \cite{Aad:2012tfa,Chatrchyan:2012ufa}. However -- as it often happens -- new discoveries prompt further and deeper questions. A light Higgs boson is unnatural in the Standard Model (SM), unless its mass is shielded from large quantum corrections. This longstanding issue of the SM is elegantly solved if the Higgs boson is protected by a new symmetry, and the most popular realization of this idea is the introduction of supersymmetry \cite{Djouadi:2005gi,Djouadi:2005gj}. Moreover, some supersymmetric extensions of the SM predict the existence of a stable particle, often identified with the lightest neutralino, that can play the role of Dark Matter (DM) in the Universe \cite{Jungman:1995df}. The lack of signals of new physics first at the LEP and now at the LHC, however, has pushed these models towards a corner of their natural validity \cite{Arvanitaki:2013yja,Gherghetta:2014xea}. Composite Higgs models \cite{Kaplan:1983fs,Georgi:1984af,Kaplan:1983sm,Dugan:1984hq,Contino:2003ve,Agashe:2004rs} offer an alternative solution to supersymmetry based on the possibility that the Higgs boson arises as the pseudo Nambu-Goldstone boson (pNGB) of a spontaneously broken global symmetry of a new, unspecified, strongly coupled sector at the TeV scale. The minimal, phenomenologically viable, realization of this idea relies on the breaking pattern $SO(5)\to SO(4)$. Despite their undeniable theoretical complexity, Composite Higgs models provide robust and falsifiable predictions like deviations of the Higgs couplings and the presence of light (sub-TeV) top partners as a consequence of the measured value of the Higgs mass \cite{Matsedonskyi:2012ym,Redi:2012ha,Marzocca:2012zn,Pomarol:2012qf}. In ref.~\cite{Frigerio:2012uc} it has been shown that a Composite Higgs model based on the breaking pattern $SO(6)\to SO(5)$ predicts also the existence of an extra pNGB, singlet under the SM gauge group, that features all the prerogatives needed to be a realistic DM candidate. In this theoretical setup both DM and collider phenomenology are therefore tightly linked. In this paper we realize concretely this connection making use of the \textit{Minimal Higgs Potential} hypothesis proposed in ref.~\cite{Marzocca:2012zn}. The key point is that the assumptions underlying this hypothesis allow to write explicitly the effective potential that involves both the Higgs and the DM particle. This effective potential, in turn, provides the possibility to compute observable quantities that can be either matched with observations -- as with top and Higgs masses -- or compared with the experimental bounds -- as with DM properties and the mass of the top partners. Equipped by this result, we will be able to subject the model to a careful analysis exploring both collider phenomenology and astrophysical implications. The structure of this paper is as follows. In section~\ref{sec:TheoreticalOverview} we present our Composite DM model. In section~\ref{Sec:Potential} we analyze the effective potential, while sections~\ref{sec:phenoLHC} and \ref{sec:PhenoAstro} are devoted to the phenomenological analysis of the model. We present our result in section~\ref{sec:results}. Finally, we conclude in section~\ref{sec:conclusions}. In the appendices, we provide further details about the theoretical structure of the model. In appendix~\ref{App:parametrizations}, we study different parametrization of the $SO(6)/SO(5)$ coset. In appendix~\ref{App:EffectivePotential}, we describe in detail the effective potential analyzed in section~\ref{Sec:Potential}. | \label{sec:conclusions} In this paper we have analyzed the Composite DM model proposed in ref.~\cite{Frigerio:2012uc}. The model assumes the existence of a composite sector described by some new fundamental strongly-coupled theory and characterized by a global symmetry $SO(6)$ spontaneously broken to the subgroup $SO(5)$ by a condensate of the strong dynamics, at a scale $f$. The NGBs arising from this breaking are the Higgs doublet $H$ and a real, gauge singlet, pseudo-scalar $\eta$. The former contains the physical Higgs boson $h$ while the latter plays the role of DM. The global $SO(6)$ symmetry is also explicitly broken by the linear mixing between the composite states and the elementary SM particles. These terms induce, at one-loop, an effective potential for $h$ and $\eta$ which is assumed to be dominated by the contributions of SM fields, spin-1/2 top partners and composite spin-1 resonances (i.e. the \textit{Minimal Higgs Potential} hypothesis proposed in ref.~\cite{Marzocca:2012zn}) and made calculable by imposing generalized Weinberg sum rules. From a phenomenological viewpoint, the most important consequence of this theoretical construction is that the Higgs boson, the DM particle, the top quark and the composite resonances are inextricably linked by the effective potential. This fact allowed us to study the constraints imposed on the model considering both DM and collider searches. Combining the results from direct and indirect detection of DM, invisible Higgs decay width and direct searches of top partners and vector resonances at the LHC, we were able to show that the model can reproduce the observed value of relic density only if $\xi =0.05$ (or lower), corresponding to the value $f\simeq 1.1$ TeV. As far as the DM mass and the Higgs portal coupling are concerned, for $\xi =0.05$ our phenomenological analysis predicts $m_{\eta}\simeq 200$ GeV and $\lambda \simeq 6 \times 10^{-2}$. Most importantly, we have shown that this prediction lies well within the reach of future DM direct detection experiments. We argue that the model presented in this paper, therefore, will be definitely ruled out -- or discovered -- in the near future. | 14 | 4 | 1404.7419 |
1404 | 1404.5907_arXiv.txt | \label{sec:conclusions} Lucky imaging with low light level CCDs, after 10 years of development by the Cambridge lucky imaging group, is maturing into an effective and widely applicable technique. It is starting to achieve wider recognition as a low cost high resolution imaging technique, and shows promise for delivering sub 50 milliarcsecond resolution from the ground when coupled with adaptive optics. A combination of continued software development and development of dedicated hardware should also see lucky imaging becoming more accessible and applicable to non-specialised astronomers in the near future. | 14 | 4 | 1404.5907 |
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1404 | 1404.7243_arXiv.txt | {In the magneto-centrifugal mechanism for jet formation, accreting neutron stars are assumed to produce relativistic jets only if their surface magnetic field is weak enough ($B\sim10^8$~G). However, the most common manifestation of neutron stars are pulsars, whose magnetic field distribution peaks at $B\sim10^{12}$~G. If the neutron star magnetic field has at least this strength at birth, it must decay considerably before jets can be launched in binary systems.} {We study the magnetic field evolution of a neutron star that accretes matter from the wind of a high-mass stellar companion so that we can constrain the accretion rate and the impurities in the crust, which are necessary conditions for jet formation. } {We solved the induction equation for the diffusion and convection of the neutron star magnetic field confined to the crust, assuming spherical accretion in a simpliflied one-dimensional treatment. We incorporated state-of-the-art microphysics, including consistent thermal evolution profiles, and assumed two different neutron star cooling scenarios based on the superfluidity conditions at the core.} {We find that in this scenario, magnetic field decay at long timescales is governed mainly by the accretion rate, while the impurity content and thermal evolution of the neutron star play a secondary role. For accretion rates \mbox{$\dot{M}\gtrsim 10^{-10}$~M$_{\odot}$~yr$^{-1}$}, surface magnetic fields can decay up to four orders of magnitude in $\sim$10$^7$~yr, which is the timescale imposed by the evolution of the high-mass stellar companion in these systems. Based on these results, we discuss the possibility of transient jet-launching in strong wind-accreting high-mass binary systems like supergiant fast X-ray transients.} {} | A new class of short X-ray transients was discovered by {\it INTEGRAL} observations of the Galactic plane. The so-called supergiant fast X-ray transients (SFXTs) are presumably composed of a compact object (a neutron star --NS-- or a black hole) and an OB supergiant. These binaries show short flares that last from a few hours to days, reaching $L_{\rm X}\sim 10^{36}-10^{37}$~erg~s$^{-1}$ and returning to quiescent levels of $L_{\rm X}\sim 10^{32}$~erg~s$^{-1}$ \citep{sguera2005,negueruela2006}. They are more frequently in an intermediate state in which $L_{\rm X}\sim10^{33}-10^{34}$~erg~s$^{-1}$, because of residual accretion onto the compact object \citep{sidoli2008}. At present, the SFXTs class has ten members, identified through the association of the transient X-ray source with blue supergiant companions. In addition, there are several candidates without confirmed optical/IR counterparts \citep[see e.g.,][for a recent review]{sidoli2011}. In at least four SFXTs, the discovery of X-ray pulsations that reach from 4.7 to 228~s confirms the presence of a NS. Orbital periods have also been measured; they range from 3.3 to 165 days. Three models have been proposed for the fast-flaring mechanism \citep[see the review by][]{sidoli2009}: (i) spherically symmetric clumpy winds, where the X-ray flares are produced when a dense clump is accreted by the compact object \citep{intzand2005,walterzurita2007,negueruela2008,ducci2009}; (ii) anisotropic winds, where the flare occurs when the compact object crosses a slow and dense equatorial wind component, which increases the accretion process \citep{sidoli2007a}; (iii) gated mechanisms, where accretion is inhibited by a centrifugal or magnetic barrier \citep{grebenevsunyaev2007,bozzo2008}, which requires an NS with a strong magnetic field ($B \sim 10^{14}-10^{15}$~G) and a slow spin period ($P_{\rm s} \sim 10^3$~s). However, magnetar activity in SFXTs has not been detected yet. An estimate of a low magnetic field ($B \sim 10^{11}$~G) has been obtained through a cyclotron line in the spectrum of SFXT IGR J18483--0311, for an electron origin. However, a magnetar cannot be discarded if this cyclotron line is caused by protons, for which $B \sim 5\times 10^{14}$~G. Four unidentified $\gamma$-ray transient sources, AGL J2022+3622, 3EG J1837--0423, 3EG J1122--5946, and AGL J1734--3310, are spatially correlated with three SFXTs (or candidates): IGR J20188+3647, AX J1841.0--0536, IGR J11215--5952 \citep{sguera2009}, and one intermediate SFXT: IGR J17354--3255 \citep{sguera2011}. These possible associations raise the possibility that SFXT might also produce radiation at energies above 100 MeV. Recently, \citet{sgueraromero2009} developed a model for the $\gamma$-ray emission from SFXT AX J1841.0--0536 based on the hypothesis that the high-energy radiation is originated from the cooling of relativistic particles accelerated in a collimated outflow from the NS. Although jets have been confirmed in some NSs that belong to low-mass X-ray binaries (LMXBs), in high-mass X-ray binaries (HMXBs) that host an NS no jet has been detected so far, although currently a possible jet origin is discussed for HMXB \mbox{LS I +61 303} for its $\gamma$-ray emission \citep{romero2007}. The magneto-centrifugal mechanism for jet formation in accreting NSs requires the accreted material to drag magnetic field lines near to the surface of the compact object. The fluid pressure in this region must be higher than that exerted by the NS magnetic field. If this is the case, the field should not be greater than $B\sim10^8$~G \citep{massikauf2008}. For LMXBs with old NSs ($\gtrsim$10$^9$~yr), the magnetic field has enough time to decay several orders of magnitude from a typical value $\sim$10$^{12}$~G of the initial field to the required field for jet launching. On the other hand, the timescales are quite short for HMXBs, since the donor star has a short lifetime as well ($\sim$10$^7$~yr). However, this type of stars presents strong and highly inhomogeneous winds \citep{runacres2005,owocki2006, negueruela2010} that enhance the accretion process onto the NS and might trigger an accelerated magnetic field decay at the NS surface by advecting the currents originating the magnetic field to the interior of the star in a burial process \citep[see the pioneering work from][]{bisno1974}. Moreover, impurities in the crust due to accretion might amplify its resistivity. In this work we explore necessary conditions for an NS that belongs to an HMXB system to undergo a surface magnetic field decay from an initial field of the order of $B \sim 10^{12}$~G to a final value of $B\lesssim10^8$~G, which could allow for jet formation in the system. We used a one-dimensional spherical accreting NS model, including state-of-the-art mycrophysics, electrical conductivity, and thermal evolution profiles, considering qualitatively different scenarios in terms of accretion rates, superfluidity in the NS core, and impurity content in the NS crust, for which we numerically solved the induction equation for the magnetic field evolution with appropriate initial and boundary conditions on a timescale of $10^7$~yr. With this first approach to the problem, we aim to put initial constraints in preparation for deeper investigations that use a more realistic model for the magnetic field evolution \citep[see][]{pons2012}. The structure of this paper is as follows: in Sect.~2 we present the accreted NS crust model, the thermal profiles, and the model adopted for the magnetic field evolution according to the induction equation and transport properties in the NS crust. In Sect.~3 we show our numerical results, and in Sect.~4 we discuss them in the context of the SFXTs. Finally, we summarize our conclusions in Sect.~5. | In the past decade, the number of known HMXBs has grown enormously, mainly because of the surveys of the Galactic Plane carried out by the {\it INTEGRAL} satellite. In particular, several systems consisting of a compact object (a black hole or a neutron star) and a high-mass supergiant star (of O or B spectral type) have been detected. These stars have strong winds \citep[with mass losses of the order of $10^{-6}$~M$_{\odot}$~yr$^{-1}$ and velocities $v_w \sim 1000-2000$~km~s$^{-1}$,][]{vink2000}, hence X-ray emission is produced by the accretion of the wind by the compact object. Some HMXBs show transient flaring activity in X-rays, with high dynamic ranges (3--5 orders of magnitude) and short timescales (from a few hours to days) \citep{sguera2005,negueruela2006}. The distance obtained from their optical/IR counterparts implies typical X-ray luminosities $L_{\rm X}\sim10^{36}$~erg~s$^{-1}$ in outburst and $L_{\rm X}\sim 10^{32}$~erg~s$^{-1}$ in quiescence. Most of the time, however, the sources are in an intermediate state of $L_{\rm X}\sim10^{33}-10^{34}$~erg~s$^{-1}$, the product of residual accretion onto the compact object \citep{sidoli2008}. In some of these systems outburts are regular and coincident with the orbital period of the binary system, but in most cases no period has been found and a random behaviour prevails. To explain this phenomenology, \citet{intzand2005} proposed that the transient X-ray flaring is produced by the accretion of clumps originating from a highly structured wind from the supergiant companion \citep[see e.g.,][]{runacres2005,owocki2006}. This idea was explored by \citet{walterzurita2007} and later by \citet{negueruela2008}, leading to a thorough clumpy wind model developed by \citet{ducci2009}. To explain the periodic outbursts from IGR J11215--5952, \citet{sidoli2007a} proposed that the regular flaring activity might be generated when the compact object crosses a slow and dense disk-like wind component, twice per orbital period, which proposition was based on an accretion scenario. Another model proposed by \citet{grebenevsunyaev2007} suggested that high-energy transient emission might be produced in these systems by the interaction of the stellar wind with the magnetosphere of the NS, in a so-called gated mechanism. \citet{bozzo2008} showed that this is possible for a magnetic field of the NS of the order of $B\sim10^{14}-10^{15}$~G, as in the so-called magnetars. A cyclotron emission line at $3.3$~keV in the SFXT IGR J18483--0311 allowed infering a magnetic field $B\sim10^{11}$~G, assuming an electron origin. Nevertheless, a magnetar cannot be ruled out if the line is caused by protons, for which $B\sim5\times10^{14}$~G \citep{sguera2010}. Three SFXTs (and one candidate) are spatially correlated with unidentified transient $\gamma$-ray sources detected by {\it EGRET} and/or {\it AGILE} satellites, as mentioned in the introduction. They are IGR J20188+3647/AGL J2022+3622, AX J1841.0--0536/3EG J1837--0423, IGR J11215--5952/3EG J1122-5946 \citep{sguera2009}, and IGR J17354--3255/AGL J1734--3310 \citep{sguera2011}. No {\it Fermi} source has been found to our knowledge, but this is not surprising because of the transient character of the phenomena and the survey-mode operation of the instrument\footnote{The source-detection step of the latest {\it Fermi} catalogue \citep{nolan2012} was only applied to the data from the full 24-month time interval of the data set. No search for transient sources that may have been bright for only a small fraction of the 2-year interval was systematically implemented so far. The {\it a priori} probability of detection of moderate transient sources with very short duty-cycles, such as those that might be associated with SFXTs, is very low.}. If the $\gamma$-ray emission is real, the spatial association opens the possibility of a common origin of the emission at different wavelengths. We briefly discuss these sources individually below. \subsubsection*{AX J1841.0--0536} AX J1841.0--0536 is a transient X-ray pulsar ($P_{\rm s}=4.7$~s) detected by the {\it ASCA} satellite in 1994 and 1999 \citep{bamba2001}, while displaying X-ray flares of a factor of $\sim$10 on timescales of $\sim$1 hour. A {\it Chandra} observation allowed determining its coordinates with precision \citep{halperngotthelf2004}. This enabled \cite{halpern2004} to find an optical/IR counterpart of the system, which is a supergiant star of spectral type B1 Ib \citep{nespoli2008}. The source was also detected during an outburst by {\it INTEGRAL} and {\it Swift}, and finally confirmed as a member of the SFXT class after the deep study of \cite{romano2011}. In the third {\it EGRET} catalogue, 3EG J1837--0423 is a transitory point source, and although the spatial correlation with AX J1841.0--0536 is ambiguous, the absence of another hard X-ray source in the region suggests a physical relation between them \citep{sgueraromero2009}. \subsubsection*{IGR J11215--5952} This source was discovered with {\it INTEGRAL} by \citet{lubinski2005}. It is associated with a B0.7 supergiant counterpart at a distance of 8 kpc \citep{negueruela2007}. Pulsed emission of $P_{\rm s} = 187$~s \citep{swank2007} showed that the compact object in this SFXT is an NS. Moreover, this is the first periodic member of the class, showing regular outbursts every $\sim$165~days according to \cite{romano2009}, with typical X-ray luminosities of $L_{\rm X} \sim 5 \times 10^{36}$~erg~s$^{-1}$, and long quiescent states of $L_{\rm X} \sim 10^{33}$~erg~s$^{-1}$. The unidentified {\it EGRET} source EGR J1122--5946 is well spatially correlated with SFXT IGR J11215--5952 \citep{sguera2009}. In addition, the absence of other counterparts in the soft $\gamma$ band suggests the possibility of a physical association between them. However, {\it EGRET} observations do not allow to confirm whether the source is constant or transient. \subsubsection*{IGR J20188+3647} In 2004, {\it INTEGRAL} discovered the transient X-ray source IGR J20188+3647. Its X-ray flaring properties, with timescales of $\sim$1 hour, resemble those of SFXTs, and hence it is considered as an SFXT candidate \citep{sguera2006b}. An unidentified $\gamma$-ray source, named AGL J2022+3622, was observed by {\it AGILE} \citep{chen2007} in the same region. It is a variable source in the MeV band, seen active for approximately only one day. IGR J20188+3647 is the only hard X-ray source inside the positional error circle of this {\it AGILE} source \citep{sguera2009}. \subsubsection*{IGR J17354--3255} IGR J17354--3255 is a hard X-ray transient discovered by {\it INTEGRAL} \citep{kuulkers2006,kuulkers2007}. With an orbital period of 8.4~days \citep{dai2011}, the source presents flares with X-ray luminosities $L_{\rm X} \gtrsim 10^{36}$~erg~s$^{-1}$ with a dynamic range $\gtrsim$20, typical of intermediate SFXTs \citep{sguera2011,bozzo2012}. Recently, \citet{coleiro2013} found the near-IR counterpart of the system, an 09Iab supergiant, thus confirming its SFXT classification. This {\it INTEGRAL} source is the only hard X-ray source unambiguously located inside the error circle of the unidentified source AGL J1734--3310 \citep{sguera2011,sguera2013}, which is a transient MeV/GeV source detected in outburst by the {\it AGILE} satellite \citep{bulgarelli2009}. Here, the possible association is based not only on the spatial correlation, but also on the temporal behaviour of the two sources at different wavelengths. However, based on observations performed in the soft X-ray band by the {\it Swift}/XRT, \cite{ducci2013} suggest that IGR J17354-3255 is an almost persistent HMXB. The authors argued against the SFXT nature of this source, proposing an eclipse origin for its variability. It is important to remark that the only observational evidence available at present to support a possible physical association of these sources is a certain spatial, and sometimes temporal, correlation. It is clear that long-time observations both in $\gamma$ and X-ray bands are necessary to establish a physical connection among these sources. As was argued by \citet{sgueraromero2009}, a promising approach to explaining the production of relativistic particles capable of generating a transient $\gamma$-ray source, under the particular conditions imposed by the SFXTs, is the formation of a transient jet powered by a magnetic tower. Such an outflow could carry away a considerable fraction of the accreting material \citep{kato2007}. In the magneto-centrifugal model of jet formation, the ejection of matter is only possible if the material of the inner part of the accretion disk can reach distances of $\sim$40 gravitational radii \citep{kato2004}. Thus, the Alfv\'en radius, $R_{\rm A}$, cannot be much larger than the NS radius, $R_{\rm NS}$, implying that the magnetic field of the NS must be weak enough to allow the matter penetration. In this sense, a simple basic condition for jet formation in accreting NSs was obtained by \citet{massikauf2008}, who showed that the magnetic field at the surface of the NS must be $B\lesssim10^8$~G. Although jet emission in accreting NSs was already observed in some LMXBs \citep[e.g. Cir X-1,][]{fender1998}, this phenomenon was not detected in HMXBs yet (but see the discussion about \mbox{LS I +61 303}, \citet{romero2007}, for which jet models have been proposed, \citet{boschramon2006}). Our numerical results suggest that if a significant fraction of the strong wind emitted by the donor star can be accreted by the NS, a magnetic field evolution from a typical $B=10^{12}$~G surface field to $B\la 10^8$~G might be possible on timescales $t \sim 10^7$~yr, allowing for jet formation. In Figure \ref{plot1} we summarize the timescale for magnetic field decay from a typical initial pulsar-strength, $B=10^{12}$~G to $B\la$10$^8$~G, which is necessary for jet formation, as a function of the impurity content in the crust, $Q$, and the accretion rate, $\dot{M}$, for LM and HM models (considering no neutron superfluidity in the core, {\it no SF}). In the plot, it can be observed that if $\dot{M} < 6 \times 10^{-11}$~M$_{\odot}$~yr$^{-1}$, the magnetic field cannot decrease four orders of magnitude in $t < 2 \times 10^7$~yr. In contrast, if $\dot{M} > 1.7 \times 10^{-10}$~M$_{\odot}$~yr$^{-1}$ , the magnetic field may decay by more than four orders of magnitude at the surface for $Q>0.65$ in the HM model, while in the LM model, such a decay might be possible for all the explored values of the impurity content. In both models, for $0.6 \la Q \la 1.2$, a decrease of four orders of magnitude might be possible for a much wider range of $\dot{M}$. \begin{figure} \centering \includegraphics[height=8.8cm,angle=-90, trim=0 0 0 0,clip]{GAR2013_contour.eps} \caption{Timescale, $t$, for magnetic field decay from $10^{12}$~G to $\sim$10$^{8}$~G, as a function of the impurity content, $Q$, and the accretion rate, $\dot{M}_{-10}$, in units of $10^{-10}$~M$_{\odot}$~yr$^{-1}$, for both LM and HM models, in the {\it no SF} case.} \label{plot1} \end{figure} In our approach to the problem we assumed important constraining hypotheses that we discuss now. First, the magnetic field has a fixed geometry: a dipolar configuration. We have neglected higher-order terms that cannot evolve. However, the local reorganization of the field has been found to have important effects on a short timescale and for strongly magnetized sources like magnetars for which $B\sim 10^{14}$~G \citep{pons2009, pons2012}. Although including higher-order terms in the field description is more realistic, the long-term evolution would be dominated by the global geometry of the field and the ohmic diffusion and convection caused by the accreted material. Second, the accretion process was assumed to be spherical and with constant mass rate, neglecting any redirection of the material through the magnetic field poles and any stellar wind dynamics over $\sim$10$^7$~yr. For fields $B \sim 10^8 - 10^{12}$~G and typical wind accretion rates, the magnetic energy density outside the star is much higher than the energy density of the accreting matter, and thus matter will flow onto the star's surface in narrow channels. A more realistic scenario should include a two-dimensional treatment for which the material is accumulated at the magnetic polar caps with a local accretion rate as the relevant parameter that varies according to the evolution of the companion star. Although the modification of the results shown here under a two-dimensional columnar accretion model are difficult to predict, qualitatively speaking, the burying of the magnetic field that dominates the evolution at the surface should also take place, and thus the net effect found in the one-dimensional spherical model might play an important role in a columnar accretion scenario as well \citep[see, for instance,][]{payne2004,payne2007,lovelace2005}. The results shown in this work will certainly motivate future studies in this direction, and for these we mention that such theoretical efforts are most likely not in correspondence with other uncertainties of the problem, such as the observationally inferred accretion rates and the stellar dynamics themselves. Another approximation we adopted was that the crust is isothermal and its evolution does not consider possible heat deposition due to the accretion process. Nevertheless, in the long-term evolution the results might be more affected by the crust composition; therefore we have considered a modified accreted equation of state for the thermal profiles, as in \citet{aguilera2008}. Finally, the impurity content has been set as a constant parameter through the outer crust, and with no relation with the intensity of the accretion process (total accreted mass and/or accretion period) because no quantitative relation between them has been found so far; recent studies of quiescent thermal emission of LMXBs indicate that values of $Q\sim 1$ are required to adjust data for two sources whose accretion rates are in the range $1-5 \times 10^{-10}$~M$_{\odot}$~yr$^{-1}$ \citep{turlioneaguilera2013}. | 14 | 4 | 1404.7243 |
1404 | 1404.2185_arXiv.txt | { Cosmic structures determine how light propagates through the Universe and consequently must be taken into account in the interpretation of observations. In the standard cosmological model at the largest scales, such structures are either ignored or treated as small perturbations to an isotropic and homogeneous Universe. This isotropic and homogeneous model is commonly assumed to emerge from some averaging process at the largest scales. We assume that there exists an averaging procedure that preserves the causal structure of space-time. Based on that assumption, we study the effects of averaging the geometry of space-time and derive an averaged version of the null geodesic equation of motion. For the averaged geometry we then assume a flat Friedmann-Lema\^{i}tre (FL) model and find that light propagation in this averaged FL model is not given by null geodesics of that model, but rather by a modified light propagation equation that contains an effective Hubble expansion rate, which differs from the Hubble rate of the averaged space-time.} \begin{document} | The standard model of modern cosmology describes large-scale structures as perturbations of an isotropic and homogeneous Universe, the Friedmann-Lema\^{i}tre (FL) model. Measurements of the cosmic microwave background (CMB) and many other observations confirm that the standard model is a good description of the Universe. Despite of its success, the FL model is only a large-scale approximation to highly nonlinear structures at small scales. Consequently, one can ask how to justify this high degree of symmetry at the largest scales and how to connect the smallest scales to the largest ones. Eventually, we must not ignore the effects of local inhomogeneities from which an averaged space-time with certain symmetries seems to emerge. By \textit{local} we refer to scales on which gravitationally bound structures exist, i.e.~from $\sim 100$ Mpc down to the Planck scale. Above the $100$ Mpc, the Universe appears to be statistically homogeneous and isotropic, but on smaller scales, unlike the FL model, it is inhomogeneous. For testing large-scale homogeneity, several tests have been applied to the data from the Sloan Digital Sky Survey \cite{Hogg} and the WiggleZ Dark Energy Survey \cite{Blake}. In both cases a transition to homogeneity at scales of about $100$ Mpc is found. In this work, we are specifically interested on the effects of the local inhomogeneities at and below the $100$ Mpc scale on the propagation of light. The averaging problem was introduced in general relativity by Shirkov and Fisher in 1963 \cite{Fisher}. They proposed a space-time averaging procedure, but it was not covariant such that a tensor did not remain to be a tensor after applying averaging. The issue was not very well known until 1984 when Ellis gave a description of the concept of \textit{backreaction} from small to large structures \cite{Ellis}. The question was further considered by Futamase \cite{65,66} who studied the gravitational correlation by employing the metric perturbations and by Zotov and Stoeger \cite{129}, whose procedure was equivalent to the one by Shirkov and Fisher, hence not covariant. Two breakthroughs in the study of the averaging problem and backreaction were achieved by Zalaletdinov \cite{1992,1993} in a covariant and exact way and by Buchert \cite{19,buchert}, who restricted the problem to scalar quantities only. A connection to dark energy has been proposed in \cite{Schwarz 2002}, \cite{rasanen}, \cite{Wiltshire111}, \cite{Wiltshire222}, and \cite{kolb}, who attempted to explain dark energy by means of a backreaction of small scale structures on the large scale evolution of the Universe, while many others like \cite{wald111} and \cite{wald222} were completely against that idea. The question is still open. So far nobody could present a proof that would exclude this idea and nobody could prove that the backreaction effects are large enough to explain dark energy. However, it seems to be generally accepted that backreaction effects cannot be neglected if one is interested in precision cosmology. The idea has been later on discussed in \cite{baz Coley, Kolb2010, R2006, schwarz1, schwarz2, Clarkson2} and many others. The aim of this paper is to investigate the effects of averaging on light propagation in the Universe, or how to derive the equation of motion of light in an averaged description of the Universe from the null geodesic equation in the inhomogeneous universe. Therefore we ask if some effects can be seen in observations in the lumpy universe. For example how do averaged inhomogeneities affect the redshift of photons. The motion of photons in an averaged geometry has already been studied in \cite{coley2} and in a more precise way in \cite{R2008, R2009}. Yet in a different approach using a gauge invariant formalism, the averaged geometry on the past null cone has been introduced \cite{veneziano1, veneziano2}. This allows to average the luminosity-redshift relation \cite{veneziano3, veneziano4, veneziano5}. The study of light propagation in inhomogeneous Swiss cheese models by simulating Hubble diagrams has been probed recently in \cite{Fleury1, Fleury2, Fleury3}. Here we follow a new approach. We make the plausible assumption that an averaging procedure that respects the causal structure of space-time exists. Based on this and a second assumption specified in Sec.~3, we derive an effective equation for light propagation in an averaged Universe. The central finding of our work is that photons in an averaged Universe follow a FL geodesic equation of motion, but with the Hubble rate replaced by an effective Hubble rate that does not coincide with the Hubble rate that one would infer from the averaging of the space-time itself. In contrast to many previous studies, this result is not based on a perturbative approach and does not make use of a toy model. The work is organized as follows. In the next section we introduce the concept of a covariant averaging of a tensor and briefly discuss what has been achieved in the works by Zalaletdinov and Buchert. It is essential for our work that a covariant procedure to average a space-time metric exists. As we show below, it is irrelevant for our purpose how this is defined in detail. In the third section we derive our central result --- an effective equation for the propagation of light in an averaged space-time and in section four we evaluate that equation for a Universe that can be described by a FL model after averaging. The last two sections contain a discussion and a conclusion. | In this work, we have considered the propagation of light rays in an averaged space-time. Our central result is a modification of the equation of null geodesic motion, see (\ref{eq:modiT}). This new equation of motion is a fully covariant vector equation for the wave-vector $k^\mu$. Rays describing the propagation of light in an averaged space-time are generated by this wave vector, which is null w.r.t.~the averaged space-time. In order to prove those points we assume that the averaged space-time (pseudo-)metric is a tensor and that it respects the causal structure of the microscopic space-time. That such averaging procedures exist has been shown by Zalaletdinov \cite{Zalal 2008}. As we consider a fixed light ray (source and observer are fixed events on the manifold) we think that it is justified not to average the wave vector and its derivative, but to just average the metric and its derivatives. We then apply this light propagation equation (recall, it is not the geodesic equation of the averaged space-time) to a cosmological model. We assume that the averaged metric is a flat, spatially isotropic and homogeneous (as suggested by the success of the standard model of cosmology). We have shown that the relation between photon frequency and affine parameter is modified. This modification can be expressed as an effective Hubble rate, as shown in (\ref{eq:effective}). Our result is in perfect agreement with previous non-perturbative investigations \cite{R2012} and with the results of the study of toy models, like the Swiss cheese model \cite{Fleury3}. Also perturbative studies are in line with our findings \cite{veneziano5}. So far we restricted our attention to the study of a single light ray. The next logical step is to study the equation of geodesic deviation in order to ask if an analogous modification occurs, which would allow us to find a modification to the luminosity and angular diameter distances. In this context it will be interesting to ask if it is true that a microscopic Weyl focussing leads to an effective Ricci focusing after averaging. We thus have shown that the Hubble rate associated with the averaged space-time metric does not necessarily coincide with the effective Hubble rate that should be considered for photon propagation. A quantitative study of the order of magnitude of the effect is beyond the scope of this work. The most important result of this work is that the averaging effects on light propagation can be absorbed into an effective Hubble rate. This might be one of the more fundamental reasons for the great success of the Friedmann-Lema\^itre models. | 14 | 4 | 1404.2185 |
1404 | 1404.6559_arXiv.txt | In dense astrophysical plasmas, neutron capture populates highly excited nuclear states close to the neutron threshold. The impact of additional low-energy nuclear excitations via coupling to the atomic shell on the ability of the so-formed compound nucleus to retain the captured neutron is investigated. We focus on the mechanism of nuclear excitation by electron capture in plasmas characterized by electron fluxes typical for the slow neutron capture process of stellar nucleosynthesis. The small effect of this further excitation on the neutron capture and gamma decay sequence relevant for nucleosynthesis is quantified and compared to the corresponding effect of an additional low-energy photoexcitation step. | At the interface between nuclear and atomic physics, a special role is played by nuclear processes that directly involve atomic electrons. For instance, it is well known that the population and lifetime of nuclear excited states can be affected by the electronic shells in the processes of nuclear electron capture (EC) and internal conversion (IC). Counterintuitive examples where more electrons available for IC or EC do not necessarily lead to a shorter nuclear excited state lifetime have been experimentally observed, for instance in $^{57}_{26}\mathrm{Fe}$ where decay measurements of the 14.4~keV M\"ossbauer level in one- and two-electron ions have shown that the nuclear lifetime is about $20\%$ shorter in H-like $\mathrm{Fe}^{25+}$ ions than in He-like $\mathrm{Fe}^{24+}$ ions or in the neutral atom \cite{Philips}. Similarly, experimental results have been obtained for EC rates in H-, He-like and neutral $^{140}_{59}\mathrm{Pr}$, where the nuclear lifetime of the one-electron $\mathrm{Pr}^{58+}$ ion is shorter than the ones of the corresponding two- or many-electron cases \cite{Yuri}. The inverse processes of IC and EC, namely, nuclear excitation by electron capture (NEEC) and bound $\beta$ decay, respectively, require the presence of vacancies in the atomic shell. NEEC in highly charged ions followed by x-ray emission has been shown to prolong by two orders of magnitude the lifetime of excited states in actinides \cite{Pa08}. More spectacularly, the opening of the new bound $\beta$ decay channel in highly charged ions influences the half life of unstable levels in nuclei \cite{Takahashi1983,Takahashi2} and via this mechanism the ground state $^{187}_{75}\mathrm{Re}$ lifetime decreases by more than nine orders of magnitude from 42~Gyr for the neutral atom to 32.9 yr for bare ions as a consequence of new bound $\beta$ decay branches to the ground and excited states of the $^{187}_{76}\mathrm{Os}$ daughter \cite{Bosch2,bound_beta_clock}. The case of $^{187}_{75}\mathrm{Re}$ is particularly interesting in astrophysical context, since it concerns the accuracy of the $^{187}\mathrm{Re}-^{187}\mathrm{Os}$ cosmochronometer \cite{bound_beta_clock}. The behavior of nuclei in highly charged ions is thus of potential interests in nuclear astrophysics and studies of nuclear decay properties. So far, the role of NEEC was never a subject of sustained investigation in nuclear astrophysics. In the resonant process of NEEC, a free electron with matching kinetic energy recombines into a highly charged ion with the simultaneous excitation of the nucleus, as it is schematically shown in Fig.~\ref{fig1}. As nuclear excitation mechanism, NEEC becomes increasingly efficient with rising electron density and degree of ionization. These conditions are predominant in dense astrophysical plasmas in the interior of stars and supernovae. In the context of isomer depletion, NEEC and its sibling nuclear excitation by electron transition (NEET) populating low-lying nuclear excited states under dense plasma conditions have been investigated \cite{Gosselin04, Gosselin07, Gosselin10, Morel2010,Gunst2014}, predicting an enhancement of the isomer state decay up to several orders of magnitude. As resonant electron recombination channel, NEEC favors free electrons with low kinetic energy. Fast electrons are less likely to recombine such that the amount of energy that can be transferred to the nucleus is limited; when starting from the ground state, typically only nuclear excitation to low-lying excited states occurs. In nucleosynthesis models, the sometimes significant excitation of such levels due to the interaction with the hot thermal photon bath is accounted for by assuming thermally equilibrated nuclei \cite{s_process_review}. This procedure does not address explicitly the particular transition mechanisms, and all the information on the thermal population of low excited states is captured in the stellar enhancement factor (SEF) \cite{bao:neutron, Rauscher2000}. \begin{figure}[!h] \vspace{-0.2cm} \centering \scalebox{0.5}{\includegraphics{fig1.pdf}} \caption{\label{fig1} (color online). Schematic illustration of NEEC. If the atomic and nuclear transition energies match, an electron can recombine into an ion (depicted in the left panel by the bare $K$ and $L$ atomic shells) with the simultaneous excitation of the nucleus (right panel) from the ground state $\mathrm{G}$ to the excited state $\mathrm{E}$.} \end{figure} In this work we investigate a different scenario, in which NEEC occurs not from the nuclear ground state or metastable states in its vicinity, but instead from highly excited states close to the neutron threshold. An intrinsic assumption of neutron capture nucleosynthesis models is that the formed compound nucleus decays practically instantaneously from an initial state with $E\simeq S_n+kT$, where $S_n$ denotes the neutron separation energy, to a thermal distribution of low-lying nuclear levels \cite{B2FH,s_process_review}. Only recently it was argued in Refs.~\cite{Bernstein,Bernstein2} that the neutron capture may be followed by the absorption of a low-energy photon (less than $1\,\mathrm{MeV}$) prior to statistical $\gamma$-ray emission. This effect was found to be temperature dependent and to dominate over the direct $\gamma$ decay above a certain temperature typical for rapid neutron capture nucleosynthesis (r-process). Since the decay branching ratio of the compound state is highly sensitive to its energy, even excitation by a small energy amount would lead to an effective reduction of the neutron separation energy as a function of the environment temperature and density and would eventually shift the nucleosynthesis path towards the valley of stability. The purpose of the present work is to find out whether such an effect can also be expected when considering NEEC as excitation mechanism instead of photoabsorption. Resonant electron recombination mechanisms like NEEC are believed to be the dominating form of recombination in hot astrophysical plasmas \cite{Massey1942}, where high degrees of ionization and high electron densities prevail. Additionally, theoretical values show that excitation of the nucleus by coupling to the atomic shell can be more efficient than photoabsorption for nuclear transitions of low energy \cite{Pa07,PaJMO}. An estimate of the possible impact of NEEC occurring on compound nuclei formed by the capture of a slow neutron would be a useful counterpart of the results on r-process in Refs.~\cite{Bernstein,Bernstein2}. We therefore investigate possible changes via the additional nuclear excitation on the neutron capture and $\gamma$ decay sequence relevant for s-process nucleosynthesis. The NEEC formalism developed in Ref. \cite{Pa06} for nuclear transitions close to the ground state is adapted to describe excitation starting from the compound state. For nuclear excitation energies on the order of several $\mathrm{MeV}$, nuclear states are rather described by level densities than discrete spectra. The nuclear matrix elements in the NEEC transition rates, for transitions between discrete levels given by the reduced nuclear transition probabilities, are here estimated with the help of a nuclear level density parametrization obtained from the photon strength function of the giant dipole resonance~\cite{Greiner}. Furthermore, we extend the theoretical NEEC treatment to take into account the relevant temperature domain of both neutron and electron fluxes as well as the role of multiple neutron resonances of the neutron capture spectrum. The impact of NEEC is quantified by defining a stellar mitigation factor as the counterpart of SEF taking into account the additional excitation of the compound nucleus. Our results for the numerical examples $^{187}\mathrm{Os}$ and $^{193}\mathrm{Ir}$ show that for typical s-process nucleosynthesis conditions, the effect of coupling highly excited nuclei to the atomic shell is small, with SMF values on the order of $10^{-9}$ raising to $10^{-4}$ only for a plasma temperature of $T\simeq 1.2\cdot 10^9$ K. A comparison with the results in Ref. \cite{Bernstein} shows that such higher plasma temperatures as typical for r-process nucleosynthesis equally not favor the coupling to the atomic shells, but rather photoabsorption. The paper is organized as follows. In Sec.~\ref{scheme} we present the model used to include the additional excitation of the compound nucleus in astrophysical scenarios. This is followed by an outline of the NEEC rate calculations in dense plasmas considering multiple neutron resonances. Our numerical results are presented in Sec.~\ref{results}. The paper concludes with a Summary in Sec.~\ref{conclusion}. | } We have investigated the impact of a further low-energy excitation step via NEEC or PA on the decay channels of a compound nucleus formed by neutron capture in astrophysical s-process sites. To this end we have introduced and calculated the SMF as a highly excited nucleus-counterpart of the well-known SEF. Our results show that from the two considered processes, only PA can potentially switch the role of $\gamma$-decay and neutron reemission decay channels for the compound nucleus, provided that high plasma temperatures on the order of $k_BT=100$ keV are available. This is rather the parameter regime of the r-process nucleosynthesis. Due to its decreasing cross sections for high-energy electrons, NEEC starting from the compound nucleus is not competitive with the main decay channels $\gamma$ decay and neutron reemission and does not have a significant effect on the decay branching ratio relevant for nucleosynthesis. This holds true both at the lower temperatures dominating the s-process sites as well as the higher temperatures typical for the r-process. We conclude that the role of the coupling of the nucleus to the atomic shells in dense astrophysical plasmas is restricted to low-lying levels in the vicinity of the ground state or of specific isomeric states. | 14 | 4 | 1404.6559 |
1404 | 1404.6135_arXiv.txt | {The search for planets orbiting metal-poor stars is of uttermost importance for our understanding of the planet formation models. However, no dedicated searches have been conducted so far for very low mass planets orbiting such objects. Only a few cases of low mass planets orbiting metal-poor stars are thus known. Amongst these, HD\,41248 is a metal-poor, solar-type star on which a resonant pair of super-Earth like planets has been announced. This detection was based on 62 radial velocity measurements obtained with the HARPS spectrograph (public data).} {In the present paper we present a new planet search program that is using the HARPS spectrograph to search for Neptunes and Super-Earths orbiting a sample of metal-poor FGK dwarfs. We then present a detailed analysis of an additional 162 radial velocity measurements of HD\,41248, obtained within this program, with the goal of confirming the existence of the proposed planetary system.} {We analyzed the precise radial velocities, obtained with the HARPS spectrograph, together with several stellar activity diagnostics and line profile indicators. } {A careful analysis shows no evidence for the planetary system previously announced. One of the signals, with a period of $\sim$25\,days, is shown to be related to the rotational period of the star, and is clearly seen in some of the activity proxies. The remaining signal (P$\sim$18\,days) could not be convincingly retrieved in the new data set. } {We discuss possible causes for the complex (evolving) signals observed in the data of HD\,41248, proposing that they may be explained by the appearance and disappearance of active regions on the surface of a star with strong differential rotation, or by a combination of the sparse data sampling and active region evolution. } | \label{sec:intro} Precise spectroscopic studies of stars with {giant planets} show that their frequency is a strong function of the stellar metallicity. It is easier to find such a planet around a metal-rich star than around a metal-poor object \citep[][]{Gonzalez-1998,Santos-2001,Santos-2004b,Reid-2002,Fischer-2005,Sousa-2011}. Several studies on solar neighborhood stars have shown that at least 25\% of stars with [Fe/H] above $+$0.3\,dex (twice the solar value) have an orbiting giant planet. This frequency decreases to about 5\% for solar metallicity stars. This observational result is usually interpreted as due to a higher probability of forming a giant planet core before the dissipation of the proto-planetary disk in a metal rich environment \citep[e.g.][]{Mordasini-2009a}. A number of questions are still open, however, whose answer may have strong implications for planet formation models, especially in the metal-poor regime. In the context of one of the HARPS surveys, a search for giant planets around a sample of $\sim$100 metal-poor stars was conducted. Three new giant planet candidates were discovered, and a fourth interesting candidate was announced \citep[][]{Santos-2007,Santos-2011}. As expected, the results seem to confirm that metal-poor stars have a lower frequency of short-period giants \citep[see also][]{Sozzetti-2009}, and when these are found, they tend to have longer period orbits \citep[][]{Adibekyan-2013}. Curiously, however, the results also suggest that the frequency of giant planets orbiting metal-poor stars may be higher than previously thought, at least for values of [Fe/H]$>-$0.7 \citep[][]{Mortier-2012}. Present numbers also indicate that the frequency of giant planets as a function of stellar metallicity may not be described by a simple power-law \citep[as previously suggested for the metal-rich regime --][]{Johnson-2010}, and may be flat for metallicities below $-$0.1\,dex \citep[e.g.][]{Udry-2007,Mortier-2013a}. A tentative lower limit of the stellar metallicity ($\sim$$-$0.7\,dex) below which no giant planets can be formed was also found \citep[e.g.][]{Mortier-2013a}. In brief, the giant planet formation efficiency in the metal-poor regime is still a matter of lively debate. Since the metallicity is one of the most important ingredients controlling planet formation \citep[][]{Ida-2004b,Mordasini-2009a}, the answer to these issues is mandatory if we want to fully access the process of planet formation and evolution. Additional information about the frequency of other types of planets (Neptune and super-Earth like) as a function of stellar metallicity is key in this discussion. In fact, contrarily to what one might expect, the known correlation between the presence of planets and the stellar metallicity that exists for stars hosting {giant planets} does not seem to exist for stars hosting their lower mass planetary counterparts \citep[][]{Udry-2006,Sousa-2008}. Recent results have shown that stars with Neptune-mass planets have a rather flat metallicity distribution. Moreover, considering systems with only hot Neptunes (without any other Jupiter mass analog), though the number is still small, the metallicity distribution becomes slightly metal-poor \citep[e.g.][]{Mayor-2011,Sousa-2011,Buchhave-2012}. These observational facts are supported by theoretical work \citep[][]{Ida-2004b,Mordasini-2009a}, showing that {planets in the Neptune-mass regime should be common around stars with a wide range of metallicities}, while giant planets should be more common only around metal-rich stars. This can be interpreted as due to the fact that high metallicity proto-planetary disks are able to form rocky/icy cores fast enough so that gas runaway accretion will lead to the formation of a giant planet before disk dissipation occurs. In turn, lower metallicity disks will imply longer planet formation timescales, leading to a lower fraction of giant planets: cores don't grow fast enough to accrete gas in large quantities before disk dissipation and thus remain ``Neptune" or ``Super-Earth" like. However, given the still relatively small number of discovered low mass planets, and the reduced number of metal-poor stars surveyed {(no specific survey for low mass planets orbiting metal-poor stars has been carried out)}, it is still not possible to conclude on the frequency of low mass planets as a function of stellar metallicity. In this paper we present a new project that makes use of precise HARPS radial velocities to search for Neptunes and Super-Earth planets orbiting a sample of metal-poor stars. The goals of the program and the sample are presented. We then turn our attention to the case of \object{HD\,41248}, a metal-poor G dwarf from our sample that was recently announced to have a pair of resonant Super-Earths or Neptunes \citep[][]{Jenkins-2013}. Using the set with more than 200 precise radial velocities measurements together with different stellar activity diagnostics, we explore the existence of the planets announced by \citet[][]{Jenkins-2013}. The results of this analysis are presented and discussed. | \label{sec:conclusions} In a recent paper, \citet[][]{Jenkins-2013} reported the existence of a system of two low-mass planets orbiting HD\,41248 in almost circular orbits of periods $\sim$18 and 25\,days. In this paper we analyzed this system after adding almost 160 new radial velocity points obtained with the HARPS spectrograph. The results of this analysis do not allow us to confirm the planetary origin of the signals observed in the RV data of HD\,41248 as previously suggested by \citet[][]{Jenkins-2013}. The observed 25-day period signal is almost exactly reproduced in the stellar activity index $\log{R'_{HK}}$ as well as in the FWHM of the HARPS CCF. This signal has a complex structure and varying amplitude with time, making it difficult to model with present day tools. This fact renders the analysis of the putative 18-day periodicity difficult. However, although we cannot fully discard the existence of a stable, periodic signal at 18\,days as expected from the presence of a planet, the different tests that we conducted show that the current data (both the RV and activity/line profile indicators) does not support its existence. In brief, the 25-day period signal detected by \citet[][]{Jenkins-2013} is best explained as induced by stellar activity phenomena. Our analysis also suggests that the 18-day signal may have a similar origin. We assume here that at a period of 25-days, a Neptune like planet will not be able to induce strong tidal or magnetic interactions with the star, which could result in an activity signature with a period similar to the orbital period of the planet \citep[][]{Saar-2001,Shkolnik-2003}\footnote{Or possibly half the orbital period in case of tidal interaction.}. We note that cases have been found where the orbital period seems to coincide, within the uncertainties, with the rotational period of the host star \citep[][]{Santos-2003b}. If this is the case for HD\,41248, the low amplitude of the signals and the complexity of the data will make it very difficult to confirm. The complexity of the signals observed and the estimate for the rotational period of the star ($\sim$20\,days -- Table\,\ref{tab:parameters}) leads us to propose that the observed 18\,day and 25\,day signals may be caused by at least two different active regions/longitudes in a star presenting a strong differential rotation pattern. In this scenario, the 18 and 25\,day period signals would imply a differential rotation with an amplitude of about 25\%. The Sun itself rotates, at the equator, with a rotational period of 26\,days, while at the poles the value increases to $\sim$35\,days. Higher levels of differential rotation have been found in earlier type stars \citep[][]{Barnes-2005,Reiners-2006,Ammler-2012,Reinhold-2013}\footnote{\citet[][]{Gastine-2014} suggest that the cooler stars may even present antisolar differential rotation, where the poles rotate faster than the equator.}. A difference in rotational period of 25\% in the surface of HD\,41248 seems thus perfectly plausible. This scenario would explain the existence of a growing 25-day period signal, caused by a growing active region that kept its phase all over the period of our measurements, as well as the disappearance of the 18-day period signal, if caused by an active region that disappeared (or became much weaker) and was positioned at a lower stellar latitude. It would also provide a simple explanation for the forest of peaks observed in data set\,\#2, if we assume that other active regions may have appeared and disappeared at other latitudes. One alternative scenario to explain the observed complex pattern is related with the fact that the data presented above present a very complex structure. It is clear from the plots that the activity patterns we are observing in this star present signatures of having evolved over the timespan (more than 10 years) of our measurements. An interesting hint may come, however, from the study of \citet[][]{Lanza-2003} where the authors analyzed the rotational period of the sun using the Total Solar Irradiance (TSI) observed during the maximum of the eleven-year cycle. In the Sun, large spot groups have typical lifetimes of 10-15 days, while the rotational period is close to 25\,days. The fact that the timescales for spot evolution are shorter than the rotational period, together with the appearance and disappearance of new spot groups in different rotational phases, renders the derivation of rotational periods (from the data) a complex issue. As a result, \citet[][]{Lanza-2003} have found that, during the 1999-2001 period when the Sun was close to solar maximum, it was impossible to properly retrieve the rotational period of the Sun using the TSI data, as the analysis yielded values from 24 up to 31\,days. Given the complex pattern of data presented in the present paper for HD\,41248, together with the uneven sampling, the presence of signals at 18 and 25 days may simply reflect a difficulty in fitting the data properly (at least using ``simple'' Keplerian functions). The present paper presents a good example of how difficult the analysis of radial velocity data can be when searching for very low-mass planets that induce low-amplitude signals, close to the measurement precision. The results also point very clearly the importance of following a star for a sufficiently long period of time until one can confidently secure the characterization of the whole system, including the effects of stellar activity. In this particular case, a proper sampling of the data (as in set\,\#3) was fundamental to disentangle the sources of the radial velocity signals. This study also shows that Bayesian analysis are not immune from false-positive detections, especially in the presence of stellar activity which might not be approximated by a series of Keplerian functions. The present case also demonstrates how important it is to make use of methodologies and tools to model and understand the signals produced by stellar activity. A complete characterization of the data may imply the development of more detailed physical models of stellar activity and its impact on radial velocity measurements \citep[e.g.][]{Boisse-2012}, as well as of more sensitive diagnostic methods \citep[e.g.][]{Figueira-2013}. Without that it will be very difficult to fully analyze these systems with any statistical/fitting procedure. The amplitudes of the RV signals imposed by stellar activity are, even in the case of a relatively inactive star such as HD\,41248, often of the same order of magnitude as the expected signals due to a low mass planet. Alternatively, complementary spectroscopic measurements using other wavelengths (e.g. near-IR) may be useful to disentangle real planets from activity induced signals \citep[e.g.][]{Huelamo-2008,Prato-2008,Figueira-2010b}. A new generation of near-IR spectrographs is presently being developed \citep[e.g. CARMENES and Spirou --][]{Quirrenbach-2014,Delfosse-2013}, opening great perspectives in this domain. | 14 | 4 | 1404.6135 |
1404 | 1404.4792.txt | LISA Pathfinder (LPF), the precursor mission to a gravitational wave observatory of the European Space Agency, will measure the degree to which two test-masses can be put into free-fall, aiming to demonstrate a suppression of disturbance forces corresponding to a residual relative acceleration with a power spectral density (PSD) below ${\left(30\,\rm{fm/s^2/\sqrt{Hz}}\right)}^2$ around $1\,\rm{mHz}$. In LPF data analysis, the disturbance forces are obtained as the difference between the acceleration data and a linear combination of other measured data series. In many circumstances, the coefficients for this linear combination are obtained by fitting these data series to the acceleration, and the disturbance forces appear then as the data series of the residuals of the fit. Thus the background noise or, more precisely, its PSD, whose knowledge is needed to build up the likelihood function in ordinary maximum likelihood fitting, is here unknown, and its estimate constitutes instead one of the goals of the fit. In this paper we present a fitting method that does not require the knowledge of the PSD of the background noise. The method is based on the analytical marginalisation of the posterior parameter probability density with respect to the background noise PSD, and returns an estimate both for the fitting parameters and for the PSD. We show that both these estimates are unbiased, and that, when using averaged Welch's periodograms for the residuals, the estimate of the PSD is consistent, as its error tends to zero with the inverse square root of the number of averaged periodograms. Additionally, we find that the method is equivalent to some implementations of iteratively re-weighted least-squares fitting. We have tested the method both on simulated data of known PSD, and on data from several experiments performed with the LISA Pathfinder end-to-end mission simulator. | Introduction } LISA Pathfinder (LPF) \cite{LPF} is the precursor mission to a gravitational wave (GW) observatory of the European Space Agency (ESA). Its primary goal is that of assessing if a set of reference test-masses (TMs) can be put into free motion, with residual accelerations, relative to the local inertial frame, having a power spectral density (PSD) less than ${\left(30\,\rm{fm/s^2/\sqrt{Hz}}\right)}^2$, at frequencies between 1 and 30~mHz. This goal is pursued by measuring the relative acceleration of two TMs, separated by a nominal distance of 38 cm, along the line -- whose direction we call x -- joining their centres of mass (Fig. \ref{lpf}). The relative motion between the TMs, $x_{12}$, is measured by means of a laser interferometer, the output of which $s_{12}=x_{12}+n_{12}$ is affected by a readout noise $n_{12}$ with less than $\left(6\,\rm{pm/\sqrt{\mathrm{Hz}}}\right)^2$ PSD at mHz frequencies. The \emph{relative} acceleration $a$ is then calculated by numerically performing the second time derivative \cite{deriv} of the interferometer output $s_{12}$: \begin{equation} \label{2deriv} a=\frac{d^2 s_{12}}{dt^2}=\frac{d^2 x_{12}}{dt^2}+\frac{d^2 n_{12}}{dt^2}\equiv \frac{d^2 x_{12}}{dt^2}+a_r \end{equation} where we have implicitly defined the readout acceleration noise $a_r$. The TMs are not both free-falling along x. One TM, the inertial reference, is indeed following a pure geodesic orbit, but both the satellite, and the other TM, that we call TM2, are forced, by some force control loop, to stay nominally at fixed positions relative to the reference TM. The satellite is actuated by a set of $\mu N$ thrusters within a feedback loop driven by the signal from a dedicated interferometer, which measures the relative displacement $x_{1}$ between the satellite and the reference TM. The second TM is instead subject to a weak electrostatic force commanded by a feedback loop driven by the main interferometer signal $s_{12}$. \begin{figure}[h] \begin{center} \includegraphics[width=0.48\textwidth]{LPF.pdf} \end{center} \caption{Schematic of LPF. The figure shows the reference TM, TM2, and the two laser interferometers --represented by their respective laser beam paths-- that measure $x_{1}$ and $x_{12}$ respectively. The $x$-axis, shown in the figure, is parallel to the line joining the centres of mass of the two TMs. The $z$-axis, normal to the figure, points toward the Sun. Also shown are the electrodes used to apply the forces to TM2, necessary to keep it at nominally fixed distance from the reference TM. Similarly, the picture shows a pair of $\mu N$-thrusters that are used to force the satellite to stay at a nominally fixed position relative to the reference TM. Not shown in the figure are the electrodes and the $\mu N$-thrusters used to control TM and satellite along degrees of freedom other than $x$. } \label{lpf} \end{figure} The relative motion of the satellite and the TMs, along degrees of freedom other than x, is also measured, either by laser interferometers or by capacitive sensing, and controlled by a combination of electrostatic forces and torques on the TMs, and of $\mu N$-thrusters-generated forces and torques acting on the satellite. In standard operations, control loops keep the relative motion small enough that the system is expected to behave linearly, obeying a set of linear dynamical equations \cite{Congedo}. For instance, the equation for $a$ is: \begin{equation} \label{dynamics} \begin{split} &a=\sum_{j} R_{j}\divideontimes \frac{d^{2}s_{j}}{dt^{2}} -\sum_{j} \omega_{j}^{2} \divideontimes s_{j}+\sum_{j} A_{j}\divideontimes g_{j}^{c}+\\ &+g+a_{r}. \end{split} \end{equation} The symbol $\divideontimes$ indicates time convolution. $R_{j}$ in Eq. \ref{dynamics} is a linear operator that represents the unwanted pickup, by the differential interferometer, of generalised coordinates other than $x_{12}$, like for instance $x_1$. These coordinates are measured by the signals $s_j$, just as $s_{12}$ measures the coordinate $x_{12}$. Ideally $R_{j}$ should be zero, but imperfections and misalignments make it non-zero. In principle $R_{j}$ acts on coordinates, not on signals. Substituting coordinates with signals, produces an extra term, as signals are always affected by some readout noise. We absorb this term into the overall readout noise $a_r$. The readout noise, because of the second time derivation, raises, in power, with the frequency $f$ as $\sim f^4$, and is expected to dominate the data above some 30 mHz, thus setting LPF's measurement bandwidth. The generalised differential forces \emph{per unit mass}, appearing on the right-hand side of Eq. \ref{dynamics} are split into three contributions: \begin{itemize} \item{The linear operator $\omega_{j}^{2}$ converts the relative motion of the TMs and the satellite, along any of the degrees of freedom, into a differential force along x. For really free-falling TMs, $\omega_{j}^{2}$ should be zero. However static force gradients within the satellite makes the diagonal coefficients non-zero, while various kind of imperfections and misalignments contribute to non-diagonal terms.} \item{The forces commanded by the control loops $g_{j}^{c}$, that are converted into true forces by the linear ``calibration'' operator $A_{j}$. $A_{j}$ should be just 1 when j corresponds to the electrostatic force commanded along $x$ on TM2, and zero for any other value of $j$, but deviates from that because of imperfect calibration, delays and signal cross-talk.} \item{The random forces $g$ stemming from all remaining disturbances, and whose measurement is the primary target of LPF.} \end{itemize} Measuring $R_{j}$ and $A_{j}$ is one of the tasks of our analysis. Furthermore, as the coupling of the TMs to the satellite is expected to be present also in a GW observatory like eLISA \cite{Vitale}, one of the goals of LPF is to give a measurement of $\omega_{j}^{2}$ to be compared with the prediction of the physical model of the system. \emph{The most important goal for LPF though, is that of measuring the PSD of $g$, the parasitic forces that act on TMs and push them away from their geodesic trajectories.} Eq. \ref{dynamics} suggests a natural way of achieving both these goals. Indeed both the $s_{j}$'s and the $g_{j}^{c}$'s are known, as the first have been measured, and the second have been commanded by the control loops. Thus a fit of the $s_{j}$'s and the $g_{j}^{c}$'s to $a$, returns $R_{j}$, $\omega_{j}^{2}$, and $A_{j}$, as best fit parameters, but also allows the estimation of the PSD of $g$ from the fit residuals, that is from the difference between the acceleration data series and the fitting model. In reality we need to perform such fits on the data from two different kinds of experiment. When the target is that of measuring, with comparatively high precision, the values of $R_{j}$, $\omega_{j}^{2}$ and $A_{j}$ (see Eq. \ref{dynamics}), we perform dedicated calibration campaigns, where some proper guidance signals are injected into the appropriate control loops, so that the $s_{j}$'s and the $g_{j}^{c}$'s undergo large variations. This way $R_{j}$, $\omega_{j}^{2}$ and $A_{j}$ can be measured with large Signal-to-Noise Ratio (SNR). When the target is instead a higher accuracy measurement of the PSD of the ultimate background acceleration noise, we do not apply any guidance signal, but just record acceleration noise data. These data are then fit to the $s_{j}$'s and the $g_{j}^{c}$'s, with the aim of separating $g $ from the effect of the other force terms in the right hand side of Eq. \ref{dynamics}. Indeed $g $ becomes now the residual of the fit, that is, the difference between the acceleration data and the best fit model. Actually, also other time series, like thermometer or magnetometer data, may be fitted to the acceleration data to detect and separate specific disturbance sources. It is worth stressing that, the $s_{j}$'s and the $g_{j}^{c}$'s cannot be turned off at any time so that an independent measurement of $g$ cannot be performed. A similar situation would also hold for a GW detector like eLISA, where large signals are expected to dominate the data at all times so that an independent measurement of the background noise cannot be performed. To perform these fits we could not use a standard least squares method, and we had to develop a different fitting method. Indeed, to perform a least squares fit on data with coloured background noise, as is certainly the case for LPF, one needs an {\it a priori} knowledge of the background noise PSD, either to set up a whitening filter, if the fit is performed in the time domain, or, for the more common case of a fit in the frequency domain, to assign the statistical weights to each fit residual. However, in our case, the PSD is not known {\it a priori} and is actually one of the targeted outputs of the fit. We have then developed a fitting method that works without an {\it a priori} knowledge of the background noise PSD. The method returns, besides the value of the fitting parameters, also an estimate for the background noise PSD. To achieve a comparatively high precision PSD estimation, the method preserves the ability of averaging over independent data stretches, like with the standard Welch's averaged periodogram technique \cite{Welch}. We use this method in the framework of Bayesian estimation. However, we show in the paper that it can also be extended to the standard ``frequentist'' fitting approach. Over the last few years, different authors, in the framework of GW detection and Bayesian parameter estimation, have addressed the problem of fitting without a complete \emph{a priori} knowledge of the noise PSD \cite{littenberg, Rover2007, Rover}. The emphasis of these studies was mostly on minimising the bias that such a lack of knowledge may induce in the estimated signal parameters. This is a different target than the one we are discussing here, where the estimation of the noise is the main goal of the measurement, but the essence of the problem is the same. Two main approaches have been followed in these studies: \begin{enumerate} \item{Within the first approach \cite{Cornish, littenberg}, the value of the noise PSD $S_k\equiv S\left(f_k \right)$, at each discrete frequency $f_k\equiv k/N T $, with N the length of the data series and T the sampling time, is assumed to be described by some relatively smooth function of frequency, also depending on a vector of some adjustable parameters $\vec{\eta}$, $S_k=S\left(f_k,\vec{\eta}\right)$. The likelihood of the fit residuals becomes then a function both of signal parameters and of $\vec{\eta}$. Appropriate prior probability densities -- often some broad Gaussian or uniform densities -- are then chosen for both the signal parameters and $\vec{\eta}$. Finally the posterior likelihood for all parameters is numerically derived by the Markov Chain Monte Carlo (MCMC) technique. Once the global likelihood has been derived, the marginal likelihood of the signal parameters alone, can be derived by numerically marginalizing over the $\vec{\eta}$.} \item{In the second approach \cite{Rover2007, Rover} the values of the PSD \emph{at each discrete frequency} $S_k$, are considered as independent parameters of the likelihood, each one distributed with a prior in the form of a scaled inverse $\chi^2$ density, a family of distributions describing the statistics of the reciprocal of the square of Gaussian variables, that depend on two characteristic parameters \cite{Rover, GelmanBook}. This way the posterior density of both the signal parameters and of the $S_k$, becomes an analytical function of the observed residuals and of the prior parameters. Once the values for these prior parameters have been chosen for each frequency, and the authors discuss possible criteria for this choice, the likelihood can be calculated numerically by MCMC.} \end{enumerate} Our approach is close to the one in point 2 above with the following main differences and/or extensions: \begin{enumerate} \item{We adopt, for the $S_k$, a family of priors that are uniform, either in the logarithm or in some small power of $S_k$, over a wide, but finite range of values. These priors give a realistic representation of our knowledge on the residual noise of the system (see sect. \ref{Fitting}). The infinite range counterpart of these uniform priors can be obtained from the scaled inverse $\chi^2$ family for particular values of the prior parameters.} \item{With this assumption we are able to extend the method to the very important case where the time domain data are partitioned into (overlapping) stretches, so that the standard Welch's averaged, and windowed, periodogram of the residuals can be used for the fit \cite{Welch}. We show that, by using this approach,} \begin{enumerate} \item{The posterior likelihood can be \emph{analytically} marginalized over the $S_k$'s so that the marginalized likelihood of signal parameters, which takes a very simple form, can be easily calculated numerically by MCMC, or numerically maximised within a standard fitting approach.} \item{ $S_k$ can then be estimated analytically, and this estimate is shown to be consistent, itÕs error tending to zero as the inverse square root of the number of averaged periodograms.} \item{The above estimate shows a slight bias that depends on the specific prior adopted, but this bias tends to zero linearly with the inverse of the number of averaged periodograms.} \end{enumerate} \end{enumerate} The paper presents such a method and is organised as follows. In Sec. \ref{sec:2} we describe the method. In Sec. \ref{test} we give a test of the method with synthetic data of known PSD, and we present a few examples of its application to the reduction of data from LPF end-to-end mission simulator. Finally, in Sec. \ref{disc} we briefly discuss the results and the possibility of extending the method to signal extraction for the data of GW detectors. | 14 | 4 | 1404.4792 |
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1404 | 1404.6251_arXiv.txt | The baryon cycle of galaxies is a dynamic process involving the intake, consumption and ejection of vast quantities of gas. In contrast, the conventional picture of satellite galaxies has them methodically turning a large gas reservoir into stars until this reservoir is forcibly removed due to external ram pressure. This picture needs revision. Our modern understanding of the baryon cycle suggests that in some regimes the simple interruption of the fresh gas supply may quench satellite galaxies long before stripping events occur, a process we call overconsumption. We compile measurements from the literature of observed satellite quenching times at a range of redshifts to determine if satellites are principally quenched through orbit-based gas stripping events -- either direct stripping of the disk (ram pressure stripping) or the extended gas halo (strangulation) -- or from internally-driven star formation outflows via overconsumption. The observed timescales show significant deviation from the evolution expected for gas stripping mechanisms and suggest that either ram pressure stripping is much more efficient at high redshift, or that secular outflows quench satellites before orbit-based stripping occurs. Given the strong redshift evolution of star formation rates, at high redshift (z $>$ 1.5) even moderate outflow rates will lead to extremely short quenching times with the expectation that such satellites will be quenched almost immediately following the cessation of cosmological inflow, regardless of stripping events. Observations of high redshift satellites give an indirect but sensitive measure of the outflow rate with current measurements suggesting that outflows are no larger than 2.5 times the star formation rate for galaxies with a stellar mass of 10$^{10.5}\ $\Msun. | The conventional picture of the interaction between galaxies and their environments is based on the idea that galaxies enter dense environments with a reservoir of gas. The removal of this reservoir, either from the stellar disk (ram pressure stripping), or the galaxy's halo (strangulation), leads to a decline in the star formation rate. This view is out of date with our understanding of the dynamic baryon cycle in galaxies. Cosmological simulations, as well as semi-analytic models, show that galaxies grow as a result of gas infall from surrounding filaments. At least at high redshift, rapid star formation is fed by a supply of fresh, infalling gas which dominates over the consumption of any reservoir \citep[eg.,][]{papovich_2011_short}. Taking this into account leads to a significant update to our picture of how galaxies interact with their environment. If this scenario is correct, simply removing the supply of fresh material will have a dramatic effect on the properties of satellite galaxies, without the need for gas stripping processes. In this Letter, we use a compilation of observed satellite star formation timescales at a range of redshifts, to examine the mechanisms which quench satellites and the insights this gives to the baryon cycle of all galaxies. In recent years, many authors have combined direct observations of satellite quenched fractions with cosmological infall rates of galaxies to estimate the time it takes a satellite to quench; the so-called ``quenching time'' \citep[eg.,][]{mcgee_11_short, delucia_infall, wetzel_timescale}. This is interpreted as the length of time after ``accretion'', where accretion is loosely associated with the time a galaxy is within the virialized region of some larger structure, until the galaxy is completely quenched. At low redshift, this timescale is long (several Gyrs) \citep{wetzel_timescale}, leading to the suggestion that gentle stripping of the gas reservoir is the mechanism responsible. However, such a picture naturally leads to most satellite galaxies having relatively paltry star formation rates as their gas is dwindled away. In direct contrast, observational studies of satellites have been hampered by the lack of such `smoking guns' of galaxy transformation. Indeed, many recent studies have shown that those satellites which are forming stars are doing so at a rate indistinguishable from central galaxies of similar mass \citep[eg.][]{peng10, mcgee_11_short, wetzel, muzzin_gclass}. To parametrize this behaviour, \citet{wetzel_timescale} introduced the notion of a `delay time' -- that is, the length of time after infall for which a satellite galaxy appears to track the star formation rate of an analogous central galaxy\footnote{The existence of this delay time is still a matter of some debate as several authors have found that star forming galaxies have lower specific star formation rates in satellites than in centrals \citep[eg.][]{patel_2009, vulcani_2010, Haines_2013}. However, some of this discrepancy results from the definition of star forming galaxies, where authors who have more inclusive definitions find the discrepancy. Nonetheless, the existence of a tail of low star formation rate galaxies does not affect the overall observation that most satellites are forming stars at normal rates for a significant time.}. In context of a rapid baryon cycle, the length of this delay time holds clues for our understanding of galaxy formation as it is expected that the fresh gas supply is also cut off near infall. Dark matter simulations show that the accretion of mass into a subhalo stops when it reaches 1.8 R$_{\mathrm{vir}}$ (as defined in \citep{Bryan_norman_98}) of a larger halo \citep{behroozi_accretion}. This limits the reservoir of gas which can be used for future star formation of the satellite, even in the absence of stripping. The final relevant timescale of satellite quenching is a `fading time'. This is equal to the quenching time minus the delay time, and is interpreted physically as the time it takes a satellite to be quenched once its star formation rate deviates from that of an analogous, central galaxy. This phase is short ($<$ 1 Gyr) and is reflected in the relative lack of `green' or intermediate star forming galaxies. In this letter, we compile measurements of the quenching and delay times of satellites at a range of redshifts to determine if `orbit-based' or `outflow-based' models dominate the quenching. Further, we can directly put limits on the outflow rates allowed by such delay times. We finish by exploring the difficulty of achieving long delay times in standard models of galaxy formation. In this letter, we adopt a \LCDM cosmology with the parameters: $\Omega_{\rm m} = 0.27$, $\Omega_{\Lambda}=0.73$ and $h=H_0/(100 \kmsmpc)=0.70$. All stellar masses assume a \citet{chabrier_imf} initial mass function. | We have compiled measurements of the quenching and delay times of satellite galaxies as a function of redshift from the literature. We have used these measurements, in combination with a simple model for the baryon cycle in galaxies, to arrive at the following conclusions: \begin{itemize} \item While our compilation of measurements may be subject to systematic effects, the evolution of quenching timescales is consistent with the scaling expected if the quenching was driven not by `orbit-based' stripping events like ram pressure stripping or strangulation but rather by secular outflows in light of a halt of cosmological accretion (overconsumption). Alternatively, it may be that `orbit-based' stripping is significantly more effective at high redshift than a dynamical scaling would suggest. \item The delay time of satellite galaxies places an upper limit on the rate of outflow driven gas, or the mass-loading, which from current data is $\eta$ = 2.5 in \Mstel\ = 10$^{10.5}$\Msun\ galaxies. Further measurements at higher redshift and lower masses will put even tighter constraints on the outflow rate. \item The delay time requires an uninterrupted rate of cooling gas from the gas reservoir. This presents a challenge to typical models of cooling gas for which the cooling rate is strongly dependent on the density of the reservoir, and thus declines quickly as the reservoir drains. \item We predict that at z$>$1.5 satellite galaxies are quenched through secular outflow processes instead of external stripping events. Future observations of such galaxies will put constraints on the outflow rates of all star forming galaxies and probe this unique quenching mechanism. \end{itemize} | 14 | 4 | 1404.6251 |
1404 | 1404.4976.txt | { The observed baryon asymmetry, as well as potentially an asymmetry in the dark matter sector, can be produced through dissipative particle production during inflation. A distinctive feature of this mechanism is the generation of matter isocurvature perturbations that are fully (anti-)correlated with the dominant adiabatic curvature perturbations. We show that chaotic warm inflation models yield anti-correlated isocurvature modes that may partially or even completely screen the contribution of primordial gravity waves to the CMB temperature power spectrum. The tensor-to-scalar ratio inferred from the latter may thus be parametrically smaller than the one deduced from B-mode polarization maps, which is particularly relevant in the light of the recently announced results of the BICEP2 experiment. } | The BICEP2 experiment \cite{Ade:2014xna} has recently reported evidence for a large tensor-to-scalar ratio $r=0.16^{+0.06}_{-0.05}$ (or $r=0.20^{+0.07}_{-0.05}$ without foreground dust subtraction) from the observation of B-mode polarization in the cosmic microwave background (CMB) at degree angular scales. While this is good news for the inflationary paradigm \cite{Guth, Albrecht, Linde}, which predicts a primordial tensor component in the CMB spectrum, BICEP2's value seems to be in tension with the constraint on the tensor-to-scalar ratio reported by the Planck collaboration last year \cite{Ade:2013uln}. The Planck collaboration has, in particular, placed an upper bound $r < 0.11$ (95\% CL), assuming that primordial scalar curvature perturbations are described solely by an adiabatic component with a simple power-law spectrum, i.e.~no running of the spectral index. On the one hand, Planck has also confirmed a significant deficit of power on large angular scales with respect to their best-fit $\Lambda$CDM model, with a primordial spectrum characterized by a constant red-tilted spectral index, so that any additional contributions like gravity waves are naturally rather constrained. On the other hand, any modification of the primordial spectrum that tends to reduce the power on large scales will help relaxing the above constraint on $r$. Several possibilities were already mentioned by the Planck collaboration, and they have been further explored in view of the BICEP2 result, for example a negative running of the scalar spectral index \cite{Czerny:2014qqa,McDonald:2014kia}; sterile neutrinos as extra relativistic degrees of freedom \cite{Giusarma:2014zza, Zhang:2014dxk,Dvorkin:2014lea}; a blue-tilted tensor spectrum \cite{bluetensor1, bluetensor2}; or isocurvature perturbations \cite{Kawasaki:2014lqa,Kawasaki:2014fwa}. In particular the tension in the bound on the tensor-to-scalar ratio $r$ between Planck and BICEP2 can be resolved by introducing isocurvature perturbations that are anti-correlated with the main adiabatic component. When the cosmological baryon asymmetry is produced through dissipative particle production during inflation, a mechanism known as {\it warm baryogenesis} \cite{BasteroGil:2011cx}, super-horizon fluctuations of the inflaton field become imprinted in the resulting baryon-to-entropy ratio. This then generates baryon isocurvature fluctuations that are either fully correlated or anti-correlated with the main adiabatic curvature perturbations generated during inflation (whereas for other post-inflationary baryogenesis scenarios these will be uncorrelated, see e.g.~\cite{otherbaryo1, otherbaryo2, otherbaryo3}). However, in deriving the bounds on the tensor-to-scalar ratio $r$ from CMB temperature anisotropies, the Planck collaboration has assumed that primordial scalar curvature perturbations are described uniquely by an adiabatic component. The effects of any other component such as baryon isocurvature modes are then necessarily absorbed into an effective tensor-to-scalar ratio, $r_{eff}$, which is smaller than the true tensor contribution if the additional components are anti-correlated with the dominant adiabatic modes. This effective screening goes along the lines proposed in \cite{Kawasaki:2014lqa}, where it was shown that anti-correlated cold dark matter (CDM) isocurvature perturbations could completely cancel the tensor contribution to the temperature power spectrum. In this work, we show that in chaotic models of warm baryogenesis an either partial or even full screening is naturally present and may reconcile the BICEP2 detection of B-mode polarization with the upper bound on the tensor-to-scalar ratio placed by Planck. A partial screening would, in particular, be interesting if there is future evidence for a non-zero tensor-to-scalar ratio in the temperature power spectrum that is somewhat smaller than the value inferred from the polarization data. This screening can, in fact, be effective for a wide range of values for the tensor-to-scalar ratio and is not inherent to the large value obtained by the BICEP2 collaboration, which is presently under scrutiny. CDM isocurvature modes have been considered in several contexts, such as axion or curvaton models \cite{Lyth:2002my, Byrnes:2014xua, Ashoorioon:2009wa, Ashoorioon:2014jja}. Being more suppressed, the baryonic contribution has received relatively less attention in the literature, but since the corresponding isocurvature perturbation is $S_b=\delta \eta_s/\eta_s$, where $\eta_s$ is the baryon-to-entropy ratio, their presence is necessarily connected to the mechanism generating a cosmological baryon asymmetry. Hence, identifying such a contribution in the CMB power spectrum may provide crucial information about baryogenesis. Dissipation may also produce an asymmetry in the CDM sector, provided that CDM particles are characterized by a global charge that is not conserved in the relevant dissipative processes. In this work, we thus consider the more general {\it warm mattergenesis} scenario, where isocurvature modes can be generated in both the baryon and CDM fluids. We show, in particular, that the spectrum of these perturbations is entirely determined by the underlying inflationary model and particle interactions, yielding concrete predictions that may be further tested in the near future. The tension between BICEP2 and Planck naturally leads one to question whether the simplest inflationary models can really describe the observable universe, with only a single dynamical scalar field driving accelerated expansion in an almost perfect vacuum. A particular assumption underlying these simple models is that interactions between the inflaton field and other degrees of freedom have a negligible effect during the accelerating phase, only becoming relevant after the inflaton field has exited the slow-roll regime and the Hubble rate has decreased sufficiently. However, this is not necessarily the case in general, and inflation may in fact occur in a dissipative regime, as is actually the case for most dynamical systems in Nature. Dissipation is a natural consequence of interactions between the inflaton and other fields and may have a plethora of interesting effects. By dissipating its energy, the inflaton will roll more slowly down its potential, alleviating the need for very flat potentials. At the same time, the dissipated energy will necessarily source other fluids, counteracting the diluting effect of the quasi-exponential expansion and thus sustaining a non-vacuum state during inflation. Although this may be an arbitrary state, most discussions in the literature consider the case where the particles produced by dissipation thermalize within a Hubble time, leading to a near-equilibrium configuration characterized by a slowly-evolving temperature $T$. This idea is thus generically known as {\it warm inflation} \cite{Berera:1995wh, Berera:1995ie, Berera:2008ar}, as opposed to the supercooled regime of the conventional non-dissipative models. Warm inflation has several interesting features besides slowing down the inflaton's motion. Although sub-leading during the slow-roll phase, the relative abundance of the radiation bath may slowly increase, eventually taking over the inflaton's vacuum energy at the end of inflation. This yields a smooth exit into the standard Big Bang cosmology, with no need for a separate reheating period since the universe never actually supercooled. It is also a well-known result that dissipation induces fluctuations in a system, the inflaton being no exception, and as a result the presence of dissipative effects necessarily changes the spectrum of primordial density perturbations. By looking for signatures of dissipative effects in the CMB, one may thus hope to learn something about the interactions between the inflaton and other degrees of freedom, for which there is little hope with a separate reheating period occurring 50-60 e-folds after the relevant CMB scales left the Hubble horizon during inflation. A finite temperature during inflation has also been recently argued as a means to stabilize the Higgs field during inflation \cite{Espinosa:2007qp, Fairbairn:2014zia}, in particular since the high inflationary scale suggested by the BICEP2 results would render the electroweak vacuum unstable. The combination of thermal and dissipative effects may also lead to several other processes during inflation, including the production of baryons and dark matter as originally proposed in \cite{BasteroGil:2011cx}, which is the main focus of this work. Dissipation naturally produces particles in an out-of-equilibrium fashion, so that if baryon number (or an analogous dark matter number), as well as $C$ and $CP$, are not conserved in the interactions between the inflaton and other fields, all the conditions established by Sakharov \cite{Sakharov:1967dj} for the asymmetric production of baryons and anti-baryons are satisfied. We discuss below how this mechanism is concretely realized within the best understood quantum field theory framework for warm inflation, where one of the most significant consequences is the fact that the resulting baryon/CDM asymmetry depends on the inflaton field value. Hence, the very same inflaton fluctuations that generate adiabatic curvature perturbations will also generate super-horizon perturbations in the baryon/CDM-to-entropy ratio, i.e.~isocurvature modes as anticipated above. In this work we focus on the relation between matter isocurvature modes and the resulting effective tensor-to-scalar ratio in models which can produce a large value of $r$, i.e.~chaotic models with a power-law potential. In \cite{Bartrum:2013fia} it was shown that a quartic chaotic potential can be reconciled with Planck when dissipative effects are taken into account, and the interactions can maintain a thermal distribution of inflaton particles. We will now show that, if the observed baryon asymmetry is produced during inflation, observational predictions can be consistent with both BICEP2 and Planck, in the sense of having a detection of tensors on large scales screened by the isocurvature contribution in the analyses realized by Planck so far. In fact, for values of $r$ somewhat below the current BICEP2 range, which for warm chaotic models correspond to larger temperatures, this screening can render gravity waves unobservable in the CMB temperature power spectrum. We will show, moreover, that tensor screening can be effective for matter isocurvature perturbations within the bounds placed by Planck \cite{Ade:2013uln}. This article is organized as follows. In section II we revise the basic mechanism and dynamics of warm inflation and the associated predictions for the primordial perturbation spectrum. We study both the quartic and quadratic warm inflation models and compare their observational predictions. In section III we explore the effect of isocurvature modes in screening the tensor-to-scalar ratio for these models. We summarize and discuss our main conclusions in section IV. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | There have been several proposals in the literature to explain the BICEP-Planck discrepancy, essentially by including other parameters in the model describing the temperature power spectrum. The BICEP2 collaboration was in fact the first to propose the inclusion of a significant running of the scalar spectral index \cite{Ade:2014xna}, which seems however difficult to find within conventional inflationary models. Other interesting proposals include for example novel light species such as sterile neutrinos \cite{Zhang:2014dxk}. However, the inclusion of isocurvature modes in the context of warm baryogenesis or mattergenesis is, in our opinion, particularly attractive, since it may provide a unique observational window into the generation of baryonic and/or cold dark matter with very distinct observational signatures. Our results for chaotic models suggest that a large tensor-to-scalar ratio could be accommodated by the current Planck results due to the presence of matter isocurvature modes associated with an asymmetric dissipation of the inflaton's energy density into baryonic or CDM species. Typically the latter give a too large screening of the tensor-to-scalar ratio in the temperature power spectrum and are already in tension with the current Planck bounds in a few cases, with baryonic perturbations yielding the most promising avenue. Nevertheless, CDM isocurvature modes may yield a parametrically smaller screening if an asymmetry is produced in only a sub-sector of the dark matter species. The CMB temperature power spectrum does not distinguish between baryonic and CDM perturbations, but it is possible that 21 cm line observations could break this degeneracy in the near future \cite{Kawasaki:2011ze}, thus helping to determine which type of asymmetries could be produced during inflation. The analysis performed in this work shows that isocurvature modes from warm baryogenesis/mattergenesis could yield a significant effective contribution to the spectrum of CMB temperature anisotropies. Naturally, the next step should be to include these components explicitly in the analysis of the temperature data. A study along these lines has recently been performed in \cite{Kawasaki:2014fwa}, combining the BICEP2 and Planck data, and which reinforces the preference for the inclusion of anti-correlated matter isocurvature modes that was already observed in last year's Planck analysis \cite{Ade:2013uln}. A preliminary comparison shows that the predictions of warm baryogenesis/mattergenesis for the quartic model with nearly-thermal inflaton fluctuations are in good agreement with this analysis, although the authors of \cite{Kawasaki:2014fwa} have yet to consider the effects of astrophysical foreground subtraction in the BICEP2 data. We point out that, to the best of our knowledge, warm baryogenesis/mattergenesis is the only model where a full (anti-)correlation between adiabatic and isocurvature modes is naturally generated. We are experiencing exciting times for research in inflationary dynamics, with the results of the BICEP2 experiment leading the way to really test the inflationary hypothesis. The BICEP2 results point towards the inclusion of additional ingredients in the simplest single-field inflation models, but the claim for the observation of primordial gravity waves with a large amplitude will remain uncertain until other experiments are able to confirm this result and exclude other possible sources of astrophysical B-mode polarization \cite{Liu:2014mpa}. Warm inflation provides a complete change of paradigm with respect to conventional supercooled scenarios, introducing significant modifications to the dynamics of inflation and its observational predictions, as well as the role of the inflaton in addressing other cosmological problems. As in the supercooled framework, observational predictions in warm inflation depend on the particular inflationary potential considered. As we have illustrated in this work, even chaotic models could yield a range of values for the tensor-to-scalar ratio, from very small to above the level claimed by BICEP2, depending essentially on the ambient temperature at horizon-crossing. In fact, if the observed tensor-to-scalar ratio turns out to be below 0.1, the warm quartic model will be amongst the most compelling. Other potentials such as in SUSY hybrid inflation, where the waterfall fields mediate dissipative effects, typically yield a small tensor-to-scalar ratio, and for example the predictions for the spectral index are in much better agreement with the Planck data than in the corresponding supercooled regime \cite{Bastero-Gil:2013owa}. We would thus like to emphasize that, although particularly relevant to address the present tension between the Planck and BICEP results, baryon and CDM isocurvature modes may have a significant effect independently of the true gravity wave abundance produced during inflation. Only time and further scrutiny will tell if the tensor-to-scalar ratio is really as large as BICEP2 suggests, but it is clear that individual observables cannot break the degeneracy between supercooled and warm inflation scenarios. However, the existence of additional effects such as isocurvature perturbations or a potentially observable primordial non-gaussianity, as well as consistency relations between these different observables \cite{Bartrum:2013oka}, yield a promising avenue to accurately determine the paradigm that best describes the inflationary universe. Moreover, we note that interactions between the inflaton and other fields are always required in a complete inflationary model, since a `graceful exit' into the standard Big Bang evolution must always be attained after inflation. Whether inflation occurs in a supercooled or warm regime depends parametrically on the couplings and field multiplicities involved, which determine whether a radiation bath can be sustained all through inflation or if it can only be (re-)created at the end of the slow-roll evolution. If, on the one hand, warm inflation may seem to require more parameters to describe the slow-roll dynamics and associated observables, these are in fact only relegated to describing a separate reheating period in supercooled scenarios. On the other hand, as we have discussed in this work, this opens up the possibility for new physical processes to occur during inflation, with additional observables and distinctive features that provide us with a unique opportunity to probe the full particle physics description behind the inflationary universe. The emerging picture after the recent results of Planck and then BICEP2 shows that warm inflation can be consistent with the data for the simplest and most robust monomial potentials, in particular the quartic potential. The warm inflation models analyzed in this article arise from full first principles quantum field theory calculations \cite{BasteroGil:2010pb, BasteroGil:2012cm} and much of what has been applied here was developed over the past several years alongside the cosmological applications to warm inflation. More recently, studies focused primarily on reheating have emerged, which have relevance to warm inflation, thermalization \cite{Mukaida:2012qn, Mukaida:2012bz, Drewes:2013iaa, Enqvist:2013qba, Harigaya:2013vwa} and dissipation \cite{Mukaida:2012qn, Mukaida:2012bz, Mukaida:2014yia}. Moreover, the same fluctuation-dissipation dynamics relevant for warm inflation has applicability for reheating \cite{BasteroGil:2010pb}, curvaton dynamics and other early universe scenarios \cite{Bastero-Gil:2014jsa}. There is a growing understanding of the dynamics of warm inflation and further developments will eventually allow for an embedding of warm inflation into concrete particle physics models of the early universe. This will ultimately provide a full dynamical description of not only inflation but also other cosmological problems, such as baryogenesis or dark matter, with overlaps between these areas, as we have demonstrated in this work. | 14 | 4 | 1404.4976 |
1404 | 1404.2472_arXiv.txt | Gravitinos are generically produced by inflaton decays, which place tight constraints on inflation models as well as supersymmetry breaking scale. We revisit the gravitino production from decays of the inflaton and the supersymmetry breaking field, based on a chaotic inflation model suggested by the recent BICEP2 result. We study cosmological constraints on thermally and non-thermally produced gravitinos for a wide range of the gravitino mass, and show that there are only three allowed regions of the gravitino mass: $m_{3/2}\lesssim 16$\,eV, $m_{3/2}\simeq 10$--$1000$\,TeV and $m_{3/2} \gtrsim 10^{13}$\,GeV. | Recently the BICEP2 collaboration reported a detection of the primordial B-mode polarization of the cosmic microwave background (CMB)~\cite{Ade:2014xna}, which, if confirmed, would provide the strong case for inflation~\cite{Guth:1980zm,Linde:1981mu}. The BICEP2 result can be explained by a large tensor-to-scalar ratio, $r=0.20^{+0.07}_{-0.05}$. Taken at face value, it implies large-field inflation models, where the inflaton field excursion exceeds the Planck scale~\cite{Lyth:1996im}. Among various large-field inflation models, by far the simplest one is the quadratic chaotic inflation model~\cite{Linde:1983gd} given by \begin{equation} V(\varphi) = \frac{1}{2}m^2\varphi^2, \label{quad} \end{equation} where $\varphi$ is the inflaton, and the inflaton mass is fixed to be $m \simeq 2\times 10^{13}$\,GeV by the the observed curvature perturbations. The energy density of the Universe during inflation is close to the GUT scale, and therefore, it is conceivable that the inflation model (\ref{quad}) is realized in the framework of supergravity or string theory. The chaotic inflation model in supergravity was proposed in Ref.~\cite{Kawasaki:2000yn,Kawasaki:2000ws}, where an approximate shift symmetry on the inflaton was introduced to have good control over inflaton field values greater than the Planck scale.\footnote{ There are various large-field inflation models in the supergravity and superstring theory~\cite{Freese:1990ni,Murayama:1992ua,Dimopoulos:2005ac,Kallosh:2007ig,Silverstein:2008sg,McAllister:2008hb,Kaloper:2008fb,Takahashi:2010ky, Nakayama:2010kt,Kallosh:2010ug,Nakayama:2010sk,Kallosh:2010xz,Harigaya:2012pg,Croon:2013ana,Nakayama:2013jka, Nakayama:2013nya,Cicoli:2014sva,Czerny:2014wza,Czerny:2014xja,Nakayama:2014koa,Harigaya:2014sua,Harigaya:2014qza}. } In order to lead to the standard big bang cosmology after inflation, the inflaton must transfer its energy to the standard model (SM) particles, i.e., reheating of the Universe. In supergravity, the inflaton generically decays through various Planck-suppressed interactions, unless the inflaton is charged under unbroken symmetry. Specifically, the inflaton decays into top quarks and Higgs, gluon pairs, right-handed neutrinos, etc., even without introducing ad hoc couplings with the visible sector~\cite{Endo:2006qk,Endo:2007ih,Endo:2006nj}. Some unwanted relics, however, are also produced at the same time. One of such unwanted relics is the gravitino. In fact, it is known that gravitinos are generically produced by decays of the inflaton~\cite{Kawasaki:2006gs,Asaka:2006bv,Endo:2007ih, Endo:2007sz} and the moduli~\cite{Endo:2006zj,Dine:2006ii,Endo:2006tf}, and the solutions to the gravitino overproduction problem were studied in Refs.~\cite{Endo:2006xg,Endo:2007cu,Nakayama:2012hy}. The amount of gravitinos produced by the inflaton decay depends on the properties of the inflaton and the supersymmetry (SUSY) breaking field. The gravitino production rate is enhanced for a heavier inflaton with a larger coefficient of the linear term in the K\"ahler potential. In many inflation models, the latter approximately coincides with the vacuum expectation value (VEV) of the inflaton or waterfall fields after inflation. The gravitino overproduction problem becomes acute especially if the SUSY breaking field, $z$, is a purely singlet, i.e., the so called Polonyi field, as in the gravity mediation~\cite{Dine:2006ii,Endo:2006tf,Kawasaki:2006gs}. In this case the inflaton decay produces too many gravitinos, and as a result, various inflation models are tightly constrained or excluded for a wide range of the gravitino mass~\cite{Kawasaki:2006gs,Asaka:2006bv,Endo:2007ih,Endo:2007sz}. Moreover, the Polonyi field itself causes a serious cosmological problem~\cite{Coughlan:1983ci}; the coherent oscillations of the Polonyi field easily dominate the energy density of the Universe, and typically decay into the SM particles during and after the big-bang nucleosynthesis (BBN), altering the light element abundances in contradiction with observations, and they also produce too many lightest SUSY particles (LSPs). It is possible to consider dynamical SUSY breaking scenarios in which $z$ is charged under some symmetry and is stabilized with a heavy SUSY breaking mass~\cite{Banks:1993en,Coughlan:1983ci,Nakayama:2012hy,Evans:2013nka}. Then, the Polonyi problem becomes significantly relaxed since the Polonyi field can be stabilized at the enhanced symmetry point during inflation, suppressing the initial oscillation amplitude. Also, the inflaton decay rate into gravitinos and the Polonyi fields can be suppressed~\cite{Nakayama:2012hy}. In this letter we revisit the gravitino overproduction problem in the chaotic inflation in light of the recent BICEP2 data, for a wide range of the gravitino mass. In particular we take account of various sources for the gravitino production; thermal production as well as non-thermal one from decays of the inflaton and the Polonyi field. We will show that there are only three allowed regions of the gravitino mass, $m_{3/2}\lesssim 16$\,eV, $m_{3/2}\simeq 10$--$1000$\,TeV and $m_{3/2} \gtrsim 10^{13}$\,GeV. | In this paper we revisited the gravitino overproduction problem in the chaotic inflationary Universe scenario, in light of recent BICEP2 result. Taking account of the non-thermal gravitino production from the direct inflaton decay as well as thermal production, and also the effect of Polonyi coherent oscillation, we have shown that there are only three allowed regions of the gravitino mass: $m_{3/2}\lesssim 16$\,eV, $m_{3/2}\simeq 10$--$1000$\,TeV and $m_{3/2} \gtrsim 10^{13}$\,GeV. It is interesting that, except for the trivial limits of ultra light and ultra heavy gravitino, the gravitino mass of $\sim 100$\,TeV appeared from these considerations, which fits the pure gravity mediation scenario. Interestingly, the inflaton decays into the visible sector even without introducing ad hoc couplings, because there is generically a linear term of the inflaton in the K\"ahler potential. Therefore the inflaton generically decays into all the fields that appear in the superpotential, and the reheating temperature is naturally as high as $\sim 10^{9}$\,GeV so that thermal leptogenesis successfully works. The non-thermal leptogenesis is also possible, if the right-handed neutrino mass is close to the inflaton mass~\cite{Endo:2006nj}. The large tensor-to-scalar ratio observed by BICEP2 indicates a detectable level of stochastic gravitational wave background of the primordial origin around the frequency of $\sim 1$\,Hz, which can be detected by future space-based gravitational wave detectors. In particular, the observation of the shape of the gravitational wave spectrum enables us to determine the reheating temperature, if it is around $\sim 10^9$\,GeV~\cite{Seto:2003kc,Nakayama:2008wy}. | 14 | 4 | 1404.2472 |
1404 | 1404.2191_arXiv.txt | We investigate the radial dependence of the spectral break separating the inertial from the dissipation range in power density spectra of interplanetary magnetic field fluctuations, between $0.42$ and $5.3$ AU, during radial alignments between MESSENGER and WIND for the inner heliosphere and between WIND and ULYSSES for the outer heliosphere. We found that the spectral break moves to higher and higher frequencies as the heliocentric distance decreases. The radial dependence of the corresponding wavenumber is of the kind $\kappa_b\sim R^{-1.08}$ in good agreement with that of the wavenumber derived from the linear resonance condition for proton cyclotron damping. These results support conclusions from previous studies which suggest that a cyclotron-resonant dissipation mechanism must participate into the spectral cascade together with other possible kinetic noncyclotron-resonant mechanisms.\\ | \footnotetext[1]{Both Authors contributed equally to this work} Solar wind fluctuations show a typical Kolmogorov inertial range % extending over several frequency decades. This range is bounded, at low frequency, by a knee separating the $k^{-5/3}$ from the $k^{-1}$ scaling, typical of the large scale energy containing eddies. The origin of this $k^{-1}$ scaling is still obscure in spite of the fact that many attempts have been made in order to explain the physical mechanism governing this behavior \citep{matthaeus1986, dmitruk2007, verdini2012}. This frequency break moves to ever larger scales as the wind expands \citep{brunocarbone2013}. This has been interpreted as evidence that non-linear processes are at work governing the evolution of solar wind fluctuations \citep{tumarsch1992}. The radial dependence of this break shows a power law of the order of $R^{-1.5}$ \citep{brunocarbone2013} for fast ecliptic wind and $R^{-1.1}$ for fast polar wind \citep{horbury1996} % suggesting that the turbulence evolution in the polar wind is slower than in the ecliptic, as expected \citep{bruno1992, grappin1991}. Not far from the local cyclotron frequency, there is another spectral break \citep[see review by][]{alexandrova2013} which marks the beginning of the region where kinetic effects must be considered \citep{leamon1998}. Within this region, for about one decade, the spectral index steepens towards values roughly comprised between $-3$ and $-4$ \citep{leamon1998}. At these scales (see reviews by \citet{gary1993} and \citet{marsch2006}) a perpendicular proton temperature remarkably higher that the parallel one and a temperature radial dependence much slower that the expected $R^{-4/3}$ for adiabatic expansion suggest that protons are continuously heated during the wind expansion \citep{marsch2012}. One possible source of proton heating is represented by some form of dissipation, at proton kinetic scale, of the energy transferred along the inertial range. This would change the scaling exponent. There are different relevant lengths which can be associated with this phenomenon, depending on the particular dissipation mechanism we consider. Since the solar wind plasma is essentially non-collisional, waves must play a major role in the observed heating experienced by the ions. Plasma waves like the ion-cyclotron, ion-acoustic and whistler, high-frequency extensions of the Alfv\'{e}n, slow and fast magnetoacoustic waves, play a role similar to collisions in ordinary fluids. The characteristic scales which could correspond to the observed spectral break are the proton inertial length $\lambda_i=c/\omega_{p}$ and the proton Larmor radius $\lambda_L= v_{th}/\Omega_{p}$, expressed in $cgs$ units. $\omega_{p}=(4\pi n q^2/m_p)^{1/2}$ and $\Omega_{p}=q B/(m_p c)$ are the plasma and cyclotron frequencies, respectively, where $q$ is the proton electric charge, $n$ the proton number density, $B$ the local magnetic field intensity, $m_p$ the proton rest mass and $c$ the speed of light. Since $c/\omega_{p}=v_A/\Omega_{p}$, the proton inertial length can also be expressed as $\lambda_i=v_A/\Omega_{p}$, where $v_A=B/(4\pi n m_p)^{1/2}$ is the Alfv\'{e}n speed. The role of $\lambda_i$ becomes relevant for 2-D turbulence dissipation which, through turbulence reconnection process, tends to generate current sheets along the magnetic field and strong field fluctuations in the transverse direction. \citet{dmitruk2004} showed that these magnetic structures, of the order of proton inertial length, strongly energize protons in the transverse direction due to the induced electric field experienced by the particles moving at the plasma MHD velocity. The same $\lambda_i$ can be associated to another process which is able to steepen the spectrum without involving dissipation: the Hall effect. This effect becomes relevant at kinetic scales, shorter than the ion inertial length and at time scales shorter than the proton cyclotron period \citep{galtier2006, smith2006, galtier2007}. It operates modifying the nonlinear interactions between different eddies and generating a turbulent cascade of energy beyond the proton inertial scale, as shown by \citet{alexandrova2008}. Moreover, for typical values of solar wind plasma $\beta$, as soon as $k_\parallel$ of Alfv\'{e}n cyclotron waves approaches scales comparable with the proton inertial length $\lambda_i$, cyclotron resonance and damping is quickly activated \citep{gary2004}. On the other hand, $\lambda_L$ is invoked for damping kinetic Alfv\'{e}n waves propagating at large angles with respect to the local mean field \citep{howes2008, leamon1998, leamon1999}. Then, \citet{leamon1998b} postulated a balancing between cyclotron-resonant and noncyclotron-resonant dissipation effects able to transfer energy cascading from the MHD range of scales into the dissipation range. The cyclotron-resonant part of this mechanism was able to account for the left-handed magnetic helicity signature often found in the dissipation range \citep{he2011}. However, \citet{markovskii2008} concluded that none of the available models was able to reproduce the exact location of the break observed at 1 AU by ACE and suggested that the position of the spectral break is determined by a combination of the scale of the turbulent fluctuations and their amplitude at that scale. \begin{deluxetable}{p{2,5cm}cccccccccc} \tabletypesize{\scriptsize} \tablecaption{Summary of data intervals used in this analysis\label{tabone}} \tablehead{ Interval&s/c& R(AU)&B(nT)&n(cm$^{-3}$)&V$_{\mbox{\tiny{sw}}}$(\rm{km/s})& T(K)&IR&DR& f$_{\mbox{\tiny{b}}}$(Hz)&$\theta_{\mbox{\tiny{BR}}}[^\circ]$ } \startdata 2011, 100.87-101.03&MESS&0.42&21.53&(22.58)&(586)&(670581)&-1.58&-2.90&$0.848\pm0.008$&11.8\\ 2010, 182.04-182.65&MESS&0.56&6.28&(6.25)&(604)&(218382)&-1.58&-3.72&$0.534\pm0.003$&24.7\\ 2010, 182.83-183.95&WIND&0.99&3.89&1.96&604&140390&-1.65&-3.26&$0.331\pm0.002$&46.3\\ 2011, 102.65-102.78&WIND&0.99&5.93&3.98&586&327533&-1.64&-3.17&$0.387\pm0.003$&20.7\\ 2007, 239.12-240.24&WIND&0.99&4.81&2.58&632&242000&-1.69&-3.45&$0.409\pm0.002$&38.7\\ 2007, 241.77-243.29&ULYSS&1.4&2.14&1.25&560&107162&-1.76&-3.58&$0.192\pm0.001$&27.0\\ 2000, 192.96-193.34&ULYSS&3.2&0.737&0.216&732&74060&-1.74&-2.59&$0.096\pm0.003$&49.0\\ 1992, 235.92-236.30&ULYSS&5.3&0.412&0.087&766&48322&-1.68&-2.59&$0.065\pm0.005$&52.2\\ \enddata \end{deluxetable} \citet{sahraoui2009} reported the first evidence of the cascade of turbulence below the proton gyroscale $\lambda_L$ and its dissipation at the electron gyroscale via collisionless electron Landau damping showing that turbulence made of highly oblique Kinetic Alfv\'{e}n Waves could account for the observations. \citet{alexandrova2009} clearly distinguished the different role of the different spatial kinetic plasma scales and showed that the electron Larmor radius represents the dissipation scale of magnetic turbulence in the solar wind but could not exclude that at the ion and electron cyclotron frequencies there might be some dissipation by cyclotron damping. \citet{chen2012} found the same steep spectral index (about -2.75) for magnetic and density fluctuations between ion and electron scales. This spectral index, steeper than expected for strong turbulence dispersive cascade which predicts -7/3 \citep{biskamp1996}, as for pure whistler or KAW cascade, is consistent with damping of some of the turbulent energy at these scales or with increased intermittency, since both density and magnetic fluctuations become organized in highly intermittent, two-dimensional structures (\citet{boldyrev2012}, \citet{alexandrova2013}). \citet{alexandrova2012} found that the high frequency steepening of the spectra, when the magnetic field is sampled at large angles, was nicely fitted by $E(k_\perp)=A k_\perp^{-8/3}exp(-k_\perp \rho_e)$, being $k_\perp$ and $\rho_e$ the perpendicular wavenumber component and the electron Larmor radius, respectively and, the amplitude of the spectrum $A$ was the only free parameter of this model. Their results were compatible with the Landau damping of magnetic fluctuations at electron scales. \citet{bourouaine2012} analyzed magnetic field spectra between $0.3$ and $0.9$ AU and, assuming a dominant two-dimensional nature of the turbulent fluctuations, found a better agreement between the spatial scale corresponding to $f_b$ and the proton inertial scale $\lambda_i$ rather than the proton gyroradius scale $\lambda_L$. However, \citet{bourouaine2012} remarked that while $\lambda_i$ and $\lambda_L$ varied with distance as expected, $f_b$ remained almost constant, varying only between $0.2$ and $0.4$ Hz. These findings were in agreement with previous results obtained by \citet{perri2010} who analyzed the radial evolution of $f_b$. These authors took several time intervals from ULYSSES observations during fast wind and magnetic field observations from MESSENGER when the s/c was at 0.3 and 0.5 AU but they could not determine the solar wind conditions during the intervals they analyzed because of the lack of plasma observations. Since the largest variations of the solar wind parameters happen to be within the inner heliosphere, a special care is required when selecting time intervals at different heliocentric distances in order to analyze, as far as possible, the same type of wind, either fast or slow \citep{brunocarbone2013}. Conscious about this caveat, we analyzed again the radial dependence of $f_b$ trying to select, whenever possible, s/c alignments during fast wind in order to observe the same plasma at different heliocentric distances. | We investigated the radial dependence of the spectral break between fluid and kinetic scales in the power density spectra of interplanetary magnetic field fluctuations, between $0.42$ and $5.3$ AU, during radial alignments between MESSENGER and WIND for the inner heliosphere and between WIND and ULYSSES for the outer heliosphere. We found, for the first time in literature, a well established radial dependence of the high frequency spectral break of the kind $f_b\sim R^{-1.09}$. This radial trend is quite slower than the one observed for the spectral break separating the $f^{-1}$ from the $f^{-5/3}$ frequency regions which goes like $f_b\sim R^{-1.5}$ \citep{brunocarbone2013}. This supports the fact that the turbulent character of the fast wind increases during the wind expansion since the effective Reynolds number can be estimated, adopting the classical hydrodynamics relationship, by the square of the ratio of the scales associated with these two spectral breaks \citep{batchelor1953}. The radial dependence of the wavenumber associated with the frequency break $\kappa_b\sim R^{-1.08}$ is very similar to the one shown by the wavenumbers corresponding to the proton inertial length $\lambda_i$ and the proton Larmor radius $\lambda_L$. However, the best agreement is found for the wavenumber $\kappa_r$ corresponding to the resonance condition for parallel propagating Alfv\'{e}n waves. This correspondence held also when we took into account the effect of the finite angle between the local magnetic field, along which the resonant waves are propagating, and the radial direction which corresponds to the sampling direction. These results support the suggestions given by \citet{leamon1998b}, according to whom a cyclotron-resonant dissipation mechanism must participate in the spectral cascade together with other possible kinetic noncyclotron-resonant mechanisms. The large radial extent, the selection of only fast wind, the choice to exploit radial alignments between different s/c and the use of much higher data sampling make this analysis different from all the previous ones that appeared in literature and allowed us to demonstrate the radial dependence of the inertial range's high frequency break. | 14 | 4 | 1404.2191 |
1404 | 1404.0688_arXiv.txt | As a continuation of the previous investigations of the symmetric and strongly non-symmetric ion-atom absorption processes in the far UV region within the models of the quiet Sun photosphere, these processes are studied here within a model of the sunspot. Here we mean the absorption processes in the H$(1s)$+H$^{+}$ and H$(1s)+X^{+}$ collisions and the processes of the photo-dissociation of the H$_{2}^{+}$ and H$X^{+}$ molecular ions, where $X$ is one of the metal atoms: $X=$Na, Ca, Mg, Si and Al. Obtained results show that the influence of the considered ion-atom absorption processes on the opacity of sunspots in the considered spectral region (110 nm $\lesssim \lambda \lesssim$ 230 nm) is not less and in some parts even larger than the influence of the referent electron-atom processes. In such a way, it is shown that the considered ion-atom absorption processes should be included \emph{ab initio} in the corresponding models of sunspots of solar-type and near solar-type stars. Apart of that, the spectral characteristics of the considered non-symmetric ion-atom absorption processes (including here the case $X$ = Li), which can be used in some further applications, have been determined and presented within this work. | In the previous investigations the significant influence of the relevant ion-atom absorption processes on the solar photosphere opacity was already demonstrated. So, in \citet{mih86, mih93, mih94} and \cite{mih07a}) have been studied such symmetric ion-atom processes, as the molecular ion H$_{2}^{+}$ photo-dissociation \begin{equation} \label{eq:sim1} \varepsilon_{\lambda} + \text{H}_{2}^{+} \longrightarrow \text{H} + \text{H}^{+}, \end{equation} and the absorption charge exchange in (H$^{+}$ + H)-collisions \begin{equation} \label{eq:sim2} \varepsilon_{\lambda} + \text{H}^{+} + \text{H} \longrightarrow \text{H} + \text{H}^{+}, \end{equation} where H=H(1s), H$_{2}^{+}$ is the hydrogen molecular ion in the ground electronic state, and $\varepsilon_{\lambda}$ - the energy of a photon with the wavelength $\lambda$. The significance of these processes was established within the solar photosphere models from \citet{ver81} and \citet{mal86} in the optical, and from \citet{ver81} in far UV and EUV regions of $\lambda$. Later, the symmetric processes (\ref{eq:sim1}) - (\ref{eq:sim2}) were included \emph{ab initio} in one of the new solar photosphere models \citep{fon09}. Then, in \citet{mih13} was undertaken the investigation of some non-symmetric ion-atom absorption processes, namely the photo-dissociation and photo-association of the the molecular ions \begin{equation} \label{eq:nonsim1} \varepsilon_{\lambda} + \text{H}X^{+} \longrightarrow \text{H}^{+} + X, \end{equation} \begin{equation} \label{eq:nonsim3} \varepsilon_{\lambda} + \text{H} + X^{+} \longrightarrow (X\text{H}^{+})^{*}, \end{equation} and the absorption charge-exchange in the ion-atom collisions \begin{equation} \label{eq:nonsim2} \varepsilon_{\lambda}+ \text{H} + X^{+} \longrightarrow \text{H}^{+} + X, \end{equation} where $X$ is the ground state atom of one of metals, relevant for the used solar photosphere model, whose ionization potential $I_{X}$ is smaller than the hydrogen atom ionization potential $I_{\text{H}}$, $X^{+}$ - the corresponding atomic ion in its ground state, H$X^{+}$ and ($X\text{H}^{+})^{*}$ - the molecular ion in the electronic states which are adiabatically correlated (at the infinite internuclear distance) with the states of the ion-atom systems H + $X^{+}$ and H$^{+}$ + $X$ respectively. These processes were examined within the same solar photosphere model as in \citet{mih07a}, i.e. the model C from \citet{ver81}, with $X$ = Mg, Si and Al. Also, in accordance with the composition of the solar atmosphere, the processes of the type (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}), but with atom He(1s$^{2}$) and ion H$^{+}$ instead H and $X^{+}$, were included in the consideration. However, it was established that in the case of this atmosphere (for the difference of some helium reach stellar atmospheres considered in \citet{ign14}) such processes can be practically neglected. Since the ion-atom systems with the mentioned $X$ are strongly non-symmetric, the examined processes generate the quasi-molecular absorption bands in the neighborhoods of $\lambda$ which correspond to the energies $\Delta_{\text{H};X} \equiv I_{\text{H}}-I_{X}$. According to the values of $\Delta_{\text{H};X}$ with the mentioned X these absorption bands lie in the part of the far UV region. We should note here that the photo-dissociation of the molecular ion HSi$^{+}$ was considered first time from the astrophysical aspect (interstellar clouds and the atmospheres of red giant stars) in \citet{sta97}. In \citet{mih13} was shown that, in the case of the quiet Sun, ion-atom processes (\ref{eq:sim1}) - (\ref{eq:sim2}) and (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}) together become seriously concurrent to some other relevant absorbtion processes in far UV and EUV regions within the whole solar photosphere. This result is especially important, since among all possible ion-atom non-symmetric processes only those of them, for which the needed data about the corresponding molecular ions were known, were taken into account. Because of that, it was natural to conclude that the non-symmetric processes (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}) should be also included \emph{ab initio} in the corresponding solar photosphere models. One can see that the previous investigations of the ion-atom absorption processes were performed only in the case of the quiet Sun. However, it is well known how significant role for the solar atmosphere the sunspots play, and certainly it was interesting to see what is the situation with these processes in such objects. Because of that, this investigation, whose some preliminary results were referred recently on a corresponding astrophysical conference \citet{sre13}, was undertaken. All considerations were within the sunspot model M from \citet{mal86}. Such choice was caused by the fact that only this model, among other models mentioned in the literature (see e.g. \citet{fon06}), provided all data needed for the calculations of the absorption coefficients which characterize the considered absorption processes. Certainly, the ion-atom absorption processes of the type (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}) were included in the considerations. However, here we take into account also additional processes of the molecular ion photo-dissociation and photo-association \begin{equation} \label{eq:sat1} \varepsilon_{\lambda} + \text{H}X^{+} \longrightarrow \text{H} + X^{+*}, \end{equation} \begin{equation} \label{eq:sat3} \varepsilon_{\lambda} + \text{H} + X^{+} \longrightarrow \text{H}X^{+*}, \end{equation} where $X^{+*}$ is the ion in excited state with the excitation energy $E_{exc}(X^{+*}) \lesssim \Delta_{\text{H};X}$ and H$X^{+*}$ - the molecular ion in the electronic state adiabatically correlated with the state of the H + $X^{+*}$ system, as well as the corresponding collisional excitation \begin{equation} \label{eq:sat2} \varepsilon_{\lambda}+ \text{H} + X^{+} \longrightarrow \text{H} +X^{+*}, \end{equation} which realizes over creation of the quasimolecular complex (H + $X^{+})^{*}$ in the excited electronic state adiabatically correlated with the state of the same system H + $X^{+*}$ as in the process (\ref{eq:sat3}). Depending of the values of $E_{exc}(X^{+*})$ the absorption bands generated by the processes (\ref{eq:sat1}) - (\ref{eq:sat2}) can lie not only in far UV region of $\lambda$, but also in near UV and visible regions. The reason for the consideration of these processes is the fact that the absorption bands generated by some of them overlap with the bands generated by the processes (\ref{eq:sim1}) - (\ref{eq:sim2}) and (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}). If the radiative transition $X^{+} \rightarrow X^{+*}$ is allowed by the dipole selection rules the corresponding absorption band can be treated, as in the case of the similar phenomena caused by atom-atom collisions (\citet{vez98,ske02}), i.e. as the satellite of the ion spectral line connected with the mentioned transition. The basic task of this investigation is to estimate the significance of the symmetric and non-symmetric ion-atom absorption processes in the case of the sunspot with respect to the processes of the negative hydrogen ion H$^{-}$ photo-detachment and inverse "bremsstrahlung" in ($e$ + H)-collisions, namely \begin{equation} \label{eq:eat1} \varepsilon_{\lambda} + \text{H}^{-} \longrightarrow \text{H} + e', \end{equation} \begin{equation} \label{eq:eat2} \varepsilon_{\lambda} + e + \text{H} \longrightarrow \text{H} + e', \end{equation} where $e$ and $e'$ denote the free electron in initial and final channel, which, similarly to the previous papers, are treated here as the referent processes. It is connected with the concept of this paper which stays the same as in all previous papers. Namely, the aim of these papers (see e.g. \citet{mih93,mih07a,mih13}) was to pay attention on the considered ion-atom radiative processes as the factors of the influence on the opacity of the solar atmosphere. For that purpose it was needed (and enough in the same time) to show that the efficiency of these processes in the considered spectral region is close to the efficiency of some known radiative processes whose significance for the solar atmosphere is accepted in literature. It is clear that in the case of this atmosphere just the electron-atom processes (\ref{eq:eat1}) and (\ref{eq:eat2}) can be taken as the referent ones. Because of that in these previous papers many other radiative processes have not been considered, including here the certainly very important processes of the metal atom photo-ionization, which were already discussed in the literature in connection with the quiet Sun atmosphere in \citet{fon11}. We mean the processes \begin{equation} \label{eq:phion} \varepsilon_{\lambda} + (X)_{g}^{*} \longrightarrow X^{+} + e', \end{equation} where $(X)_{g}^{*}$ denotes the given metal atom in the ground state, i.e. $X$, or in any possible (under the considered conditions) excited state, i.e. $X^{*}$. However, within the sunspot we have a significantly smaller temperature than in the quiet Sun photosphere (see figure about model) and consequently it is possible to expect there more larger efficiency of these photo-ionization processes, so that the position of the mentioned electron-atom processes as the referent ones is not so clear. Because of that the processes of the metal atom photo-ionization were taken into account from the beginning of this investigation (some of them were considered already in \citet{sre13}). \begin{figure*} \centering \includegraphics[height=0.34\textwidth]{Copy_of_Shema_sim.eps} \includegraphics[height=0.34\textwidth]{shema_nsim.eps} \caption{\textit{Left panel \bf{a}:}: The bound-free (bf) and free-free (ff) transitions in the case of the symmetric ion-atom processes (\ref{eq:sim1})- (\ref{eq:sim2}). \textit{Right panel \bf{b}:} The bound-free (bf), free-free (ff) and free-bound (fb) transitions in the case of the non-symmetric ion-atom processes: $\longrightarrow$ - Eqs. (\ref{eq:nonsim1})- (\ref{eq:nonsim2}), $-->$ Eqs. (\ref{eq:sat1})-(\ref{eq:sat2}).} \label{fig:schem} \end{figure*} In accordance with above mentioned the following absorption processes are included in the consideration in this work:\\ - the symmetric ion-atom processes (\ref{eq:sim1}) - (\ref{eq:sim2});\\ - the non-symmetric processes (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}) with $X$ = Na, Ca, Mg, Si and Al, for which the needed data about the corresponding molecular ions H$X^{+}$ are known;\\ - the non-symmetric processes (\ref{eq:sat1}) - (\ref{eq:sat2}) with $X^{+*}$ = Ca$^+(3p^{6}3d)$, Ca$^+(3p^{6}4p)$, Ca$^+(3p^{6}5s)$, Ca$^+(3p^{6}4d)$, Ca$^+(3p^{6}5p)$ and Al$^+(2p^{6}3s3p)$,\\ - the electron-atom processes (\ref{eq:eat1}) and (\ref{eq:eat2});\\ - the photo-ionization processes (\ref{eq:phion}) with all metal atoms relevant for the used sunspots model, i.e. including the case $X$ = Fe.\\ Let us note that as in \citet{sre13} only such non-symmetric processes are taken into account here for which all needed data about the corresponding molecular ions are known from the literature. It is well known that inside sunspot is needed to take into account the presence of its magnetic field. In connection with this we have to note that according to the existing data (see e.g. \citet{pen11}) this field is always not larger than 4000 Gs. This is very important for us since it can be shown that in our further considerations the presence of such magnetic field can be completely neglected and all needed calculations can be performed as in the case of the quiet Sun. \begin{figure*} \centering \includegraphics[height=0.34\textwidth]{Abund_Metals2_kopi.eps} \includegraphics[height=0.34\textwidth]{Maltby_ref_VS_Maltby_mod_M.eps} \caption{\textit{Left panel \bf{a}:}: The hydrogen and metal ion densities $N_{\textrm{H}^+}$ and $N_{X^+}$ for the sunspot umbral model M from \citet{mal86}. \textit{Right panel \bf{b}:} The local temperature $T$ and the densities $N(e)$ and $N(\text{H})$ of the free electrons and hydrogen atoms for the sunspot model M and referent model of the quiet Sun atmosphere from \citet{mal86}.} \label{fig:Abund} \end{figure*} The aims of this work request determination of the corresponding spectral absorption coefficients for all mentioned ion-atom processes, as well as for the concurrent absorption processes (\ref{eq:eat1}) - (\ref{eq:eat2}) and (\ref{eq:phion}), as functions of $\lambda$ and the height $h$ above the referent solar atmosphere layer. In this context the processes (\ref{eq:sim1}) - (\ref{eq:sim2}), (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}) and (\ref{eq:sat1}) - (\ref{eq:sat2}) are treated as the processes from the groups "1", "2" and "3" respectively, which is denotes by the corresponding index: $j$ = 1, 2 or 3. Let us note that here the spectral characteristics of the non-symmetric processes of the type (\ref{eq:nonsim1}) - (\ref{eq:nonsim3}), but with $X$ = Li, are also determined in rather wide regions of the temperatures and wavelengths. Namely, such processes could be of interest for lithium rich stellar atmospheres ("Li stars", \citet{hac97, sha01, sha03}) as an additional canal for the creation of the neutral lithium atoms. All relevant matter is distributed below in five Sections and two Appendices. So, the expressions of the considered absorbtion processes are given in the Sections 2 and 3, together with the needed comments about the methods of their determination. The Section 4 contains the needed comments about used calculation methods. The results of the calculations of the spectral coefficients and other quantities, which characterize the relative efficiencies of the considered processes, are presented (with the corresponding discussions) in the Section 4, and in the last Section 5 are given some conclusions and are indicated directions of the further investigations. Then, the potential curves and dipole matrix elements of the molecular ions H$X^{+}$ with $X$ = Na and Li, which are determined within this work, are given in Appendix A. Finally, some of the spectral characteristics of the processes (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}) and (\ref{eq:sat1}) - (\ref{eq:sat2}), which can be used in some other applications, are presented in Appendix B. | From the presented material it follows that the considered symmetric and non-symmetric ion-atom absorption processes influence on the opacity of sunspots in the considered spectral region (110 nm $\lesssim \lambda \lesssim$ 230 nm) not less and in some parts even larger than the referent electron-atom processes. The presented results show that further investigations of the non-symmetric ion-atom absorption processes promise that their efficiency could be increased considerably. Namely, the processes (\ref{eq:nonsim1}) - (\ref{eq:nonsim2}) with $X=$ Fe were not considered here because of the absence of the data about the needed characteristics of the corresponding molecular ion. However the Fe component, according to Fig. \ref{fig:Abund}, gives the significant contribution to the electron density. Also, some of the possible processes of the (satellite) type (\ref{eq:sat1}) - (\ref{eq:sat2}) could be very efficient. It means that the inclusion in the consideration of all possible relevant non-symmetric ion-atom absorption processes would surely increase their total efficiency. Because of that, we take such inclusion as the task for the investigations in the nearest future. For this purpose, here are presented the spectral characteristics of the considered ion-atom absorption processes which can be used in some further applications. Finally, the presented results show that in far UV region the significance of the considered ion-atom absorption processes is sufficiently large that they should be included \emph{ab initio} in the corresponding models of the sunspots. Apart of that, obtained results could be useful also in the case of different solar like atmospheres. | 14 | 4 | 1404.0688 |
1404 | 1404.0641_arXiv.txt | \noindent A ‘habitable zone’ of a star is defined as a range of orbits within which a rocky planet can support liquid water on its surface. The most intriguing question driving the search for habitable planets is whether they host life. But is the age of the planet important for its habitability? If we define habitability as the ability of a planet to beget life, then probably it is not. After all, life on Earth has developed within only ~800 Myr after its formation --- the carbon isotope change detected in the oldest rocks indicates the existence of already active life at least 3.8 Gyr ago. If, however, we define habitability as our ability to detect life on the surface of exoplanets, then age becomes a crucial parameter. Only after life had evolved sufficiently complex to change its environment on a planetary scale, can we detect it remotely through its imprint on the atmosphere --- the so-called biosignatures, out of which the photosynthetic oxygen is the most prominent indicator of developed (complex) life as we know it. Thus, photosynthesis is a powerful biogenic engine that is known to have changed our planet’s global atmospheric properties. The importance of planetary age for the detectability of life as we know it follows from the fact that this primary process, photosynthesis, is endothermic with an activation energy higher than temperatures in habitable zones, and is sensitive to the particular thermal conditions of the planet. Therefore, the onset of photosynthesis on planets in habitable zones may take much longer time than the planetary age. The knowledge of the age of a planet is necessary for developing a strategy to search for exoplanets carrying complex (developed) life --- many confirmed potentially habitable planets are too young (orbiting Population I stars) and may not have had enough time to develop and/or sustain detectable life. In the last decade, many planets orbiting old (9--13 Gyr) metal-poor Population II stars have been discovered. Such planets had had enough time to develop necessary chains of chemical reactions and may carry detectable life if located in a habitable zone. These old planets should be primary targets in search for the extraterrestrial life. | \label{sec:1} Habitability may be quantitatively defined as a measure of the ability of a planet to develop and sustain life \citep{schu}; its maximum is set as 1 for a planet where life as we know it has formed, thus it is 1 for the Earth. The requirement for a planet to be called habitable (or potentially habitable)\footnote{Both definitions {\it habitable} and {\it potentially habitable} are used in the literature, meaning essentially the same, but see Sec.~4 for our discussion on the definition.} is that the planet is located within the host's HZ and has terrestrial characteristics: rocky, with a mass range of 0.1--10 Earth masses and a radius range of $0.5\sim$ 2 Earth radii\footnote{The latest simulations have shown that after $\sim$1.7 Earth radii the planets are of increasingly lower density, indicating that they are less rocky and more like mini-Neptunes, placing the Earth's twin limit on the radius (for ex. Buchhave et al. 2014), though uncertainties remain, see, e.g. Torres et al. (2015)}. A habitable zone (HZ) is conservatively defined as a region where a planet can support liquid water on the surface (Huang 1959). The concept of an HZ is, however, a constantly evolving one, and many different variations of it have been since suggested (see, for example, an excellent review by Lammer et al. (2009) and references therein, and Heller \& Armstrong (2014a) as a more recent one). Biogenic elements (such as C, H, N, O, P and S) have also been considered as necessary complementary factors for habitability \citep{3c}, but their presence is implied by the existence of water as they are produced in the same stars \citep{wo,jp}. We would like to stress here that throughout the paper, when we talk about detecting life on exoplanets, we still mean life as we know it, the presence of which we are able to establish through predictable changes in planetary atmospheres. Even on Earth, there is a possibility of a different kind of life not based on a usual triad -- DNA--protein--lipid, see, for example, discussion on a ``shadow" biosphere by Davies et al. (2009). But just as on Earth we are not able to find it (yet) as we do not know `where or what to look for', we may not be able to distinguish these different kinds of life from the natural environments of exoplanets. Hence, when we talk about biosignatures, we mean only biosignatures that our kind of life produces --- oxygen, ozone, nitrous oxide, etc (e.g. Seager et al. 2012). A planet may host life as we know it (in other words, be not just {\it habitable} but {\it inhabited}), but we will still not detect it unless it has evolved sufficiently to change its environment on a planetary scale, for instance, through the production of an oxygen atmosphere by photosynthetic organisms. Photosynthesis is currently the only geologically documented biogenic process (see e.g. Lyons and Reinhard, 2011; Fomina and Biel, 2014 and references therein) that can provide sufficient energy to modify the global planetary (or atmospheric) properties. The large free energy release per electron transfer and stability of the oxygen molecule due to its strong bonding ensures that an oxygen-rich atmosphere provides the largest feasible energy source for compex life (e.g. Catling et al. 2005). Therefore, by analogy with the Earth, we presume the presence of an oxygen atmosphere as necessary for a planet to host a complex life. Such life would have modified the global planetary (or atmospheric) properties to be noticed from space, and from very far away; after all, the closest potentially habitable planet is at about 12 light years ($\tau$ Ceti) and we cannot go there to verify. Even Mars might still be inhabited by a primitive subsurface biota which are undetectable without a local and detailed examination. It may also be possible for life to evolve in a manner that we have not anticipated, which, even if it changes the environment globally, would not be detectable simply because we are not looking for those particular changes. For example, aphotic life can exist in the subsurface oceans of Europa or Enceladus, but such life would be currently impossible for us to detect {\it ex situ}. Biological methanogenesis was suggested as a rival to the photosynthesis process in changing the global environment and capable of enriching the exo-atmospheres with biogenic methane (Schindler \& Kasting 2000; Kharecha et al. 2005). Kharecha et al. (2005) has shown that the rate of biogenic methanogenesis in the atmosphere of an Archaen Earth could have been high enough to enrich the atmosphere with high concentration of biogenic methane. However, planets with reduced mantles might enrich their atmospheres by methane abiotically (e.g., Etiope \& Lollar 2013), and thus methane alone cannot guarantee habitability. From this point of view, methanogenic products are a less certain biosignature of Earth-like life than oxygen (Seager et al. 2012). Accounting for a competitive interrelation between metabolic and abiotic origins of methane, a more conservative understanding suggests that only the simultaneous presence of methane along with other biogases is a reliable indication of life (e.g., Selsis et al. 2002; Kaltenegger et al. 2007; Kiang et al. 2007; Kasting et al. 2014). It could also be that the planet never de- velops oxygenic photosynthetic life. In such cases, other biomarkers have been suggested; for example, dimethyl disulphide and CH3Cl may be detected in infrared (IR) in the planetary atmospheres of low-ultraviolet (UV) output stars (Domagal-Goldman et al. 2011). Carter (1983) has pointed out that the timescale for the evolution of intelligence on the Earth ($\sim 5$ Gyr) is comparable to the main sequence lifetime of the Sun ($\sim 10$ Gyr). Lin et al. (2014) suggested that intelligent life on expolanets can be detected through the pollution it inflicts on the atmosphere. However, intelligent life, once evolved, is no longer in need of a very precisely defined biosphere --- we can already create our own biospheric habitats on planets that are lifeless in our definition of habitability, for ex. Moon or Mars, though we are intelligent for only a 0.0000026\% of the time life exists on Earth: 100 years out of 3.6 Gyr. Therefore, intelligent life may not be so easily detectable, especially if they had longer time to evolve. However, to answer the most important question of ``are we alone", we do not necessarily need to find intelligent life. Even detection of a primitive life will have a profound impact on our civilization. Therefore, we need to concentrate on the period in the planet’s history when the emerged life had already influenced the atmosphere of the planet in a way that we can possibly recognize. We discuss here the importance of the age of the planet in the evaluation of whether that HZ planet contains life and whether that life is detectable. We examine the plausibility of a discovery of a habitable planet with detectable biota among the close (within 600 pc) neighbours of the Sun. We argue that variations in their albedos, orbits, diameters and other crucial parameters make the formation of a significant oxygen atmosphere take longer that the current planetary age and thus, life can be detectable on only half of the confirmed PHPs with a known age. | \begin{itemize} \item{} Age of a planet is an essential attribute of habitability along with such other factors as liquid water (or an equivalent solvent), rocky mantle, appropriate temperature, extended atmosphere, and so forth. The knowledge of the age of a ``habitable'' planet is an important factor in developing a strategy to search for complex (developed) life; \item{} Nearly half of the confirmed PHPs are young (with ages less than $\sim 3.5$ Gyr) and may not have had enough time for evolution of sufficiently complex life capable of changing its environment on a planetary scale; \item{} Planets do exist around old Pop~II stars, and recently discovered EMP stars (belonging presumably to an intermediate Pop~II.5) are good candidates for direct detection of orbiting planets in the IR and sub-mm wavelengths. Though currently only very few such potentially habitable planets are known, old giant planets may have habitable worlds in the form of orbiting moons; \item{} IR and sub-mm observations of terrestrial planets orbiting low-mass old stars is a promising way to trace biogenetic evolution on exoplanets in the solar neighbourhood. \end{itemize} | 14 | 4 | 1404.0641 |
1404 | 1404.7127_arXiv.txt | Natural (axionic) inflation~\cite{Freese:1990rb} can accommodate sizeable primordial tensor modes but suffers from the necessity of trans-Planckian variations of the inflaton field. This problem can be solved via the mechanism of aligned axions ~\cite{Kim:2004rp}, where the aligned axion spirals down in the potential of other axions. We elaborate on the mechanism in view of the recently reported observations of the BICEP2 collaboration~\cite{{Ade:2014xna}}. | Natural inflation~\cite{Freese:1990rb,Adams:1992bn} is one of the best motivated scenarios to describe the inflationary expansion in the early universe. The flatness of the potential is protected by a (shift) symmetry modelled after the QCD axion~\cite{Peccei:1977hh}, although at different mass scales. The axion exhibits a shift symmetry that is perturbatively exact, but potentially broken by non-perturbative (instantonic) effects. In its simplest form~\cite{Freese:1990rb} natural (axionic) inflation is derived from the potential \begin{equation} \label{equa:natural} V (\phi) = \Lambda^{4} \left[1 - \cos \left(\frac{\phi}{f}\right)\right], \end{equation} where $f$ is the axion decay constant and $\Lambda$ is the overall scale of the potential. This is a periodic potential with period $0 \leq \phi \leq 2 \pi f$. If inflation occurs for field values $\phi \ll f$ this coincides with chaotic inflation~\cite{Linde:1983gd} in its quadratic form $V (\phi) \approx m^{2} \phi^{2}$. Axions are well motivated also in the framework of string theory and its various antisymmetric tensor fields. Their specific properties as pseudoscalar fields allow a wide spectrum of potential applications in particle physics and cosmology (see for instance~\cite{Chatzistavrakidis:2012bb}). With the recent observation of the BICEP2 experiment~\cite{Ade:2014xna}, axionic inflation returned to the focus of the discussion~\cite{Freese:2014nla}, as it allows sizeable tensor modes up to a value of $ r \approx 0.18$. The results of BICEP2 point to a value of $r = 0.2^{+0.07}_{-0.05}$ (after dust reduction to $r=0.16^{+0.06}_{-0.05}$), a much higher value than expected compared to the results obtained by the Planck satellite~\cite{Ade:2013uln}. More observations are needed to determine the precise value for $r$. Up to now the results seem to be compatible with the prediction of axionic inflation. One general aspect of inflationary models with large tensor modes is the appearance of trans-Planckian values of the inflaton field known as the Lyth bound~\cite{Lyth:1996im,Lyth:2014yya}. For example, the model of quadratic inflation $(V (\phi) = \frac{1}{2} m^{2} \phi^{2})$ with sufficient number of e-folds requires the displacement $\triangle \phi \approx 15 M_{\text{Pl}}$, where $M_{\text{Pl}} = 2.4 \cdot 10^{18} \ \text{GeV}$. We thus have to worry whether our low energy effective description based on classical gravity is still valid under these circumstances. Quantum gravitational effects might destroy the properties of the inflationary potential. This is a generic problem of all models with ``large" tensor modes and we have to find arguments to assure the flatness of the potential even at trans-Planckian values of the field. In absence of a complete theory of quantum gravity this is a severe problem. Axionic inflation has an ingredient that helps in this direction: its shift symmetry might be respected by such effects. This is supported by string theoretic arguments through the appearance of (discrete) gauge symmetries that survive in the ultra-violet completion~\cite{Lebedev:2007hv,Kappl:2008ie,Nilles:2008gq,BerasaluceGonzalez:2011wy,Kim:2014dba}. In that sense, axionic inflation appears as the most attractive scenario to avoid the problems of trans-Planckian field values, although these questions have to be analysed on a case by case basis.\footnote{Discrete symmetries in string constructions have been discussed for example in refs.~\cite{Kobayashi:2006wq,Choi:2009jt,BerasaluceGonzalez:2011wy,Nilles:2012cy,Ibanez:2012wg,BerasaluceGonzalez:2012vb,BerasaluceGonzalez:2012zn,Anastasopoulos:2012zu,Honecker:2013hda,Marchesano:2013ega,Kim:2013bla,Berasaluce-Gonzalez:2013bba,Nilles:2014owa}.} So let us concentrate on axionic inflation. Unfortunately we still have to face some problems. In the potential (\ref{equa:natural}), trans-Planckian values of the inflation field $\triangle \phi \geq M_{\text{Pl}}$ require $2 \pi f \geq M_{\text{Pl}}$. In fact, in the region of high tensor modes $r \geq 0.1$ we obtain $f \geq M_{\text{Pl}}$ and this poses a severe problem. Within the framework of string theory we expect $f $ to be at most as large as the string scale $M_{\text{String}} \leq M_{\text{Pl}}$~\cite{Choi:1985je,Banks:2003sx,Svrcek:2006yi}.\footnote{Because of the rather high value of the observed tensor modes we expect large values for the potential $ V^{1/4}~\sim~2\cdot~10^{16}~{\rm GeV}$ and a rather high value $M_{\text{String}}\geq V^{1/4}$ of the string scale as well.} Values of $M_{\text{String}}$ and $f$ larger than $M_{\text{Pl}}$ would lead us to the uncontrollable regime of strongly interacting string theory where a meaningful discussion of the flatness of a potential will be impossible. A simple picture of axionic inflation with a single axion and potential (\ref{equa:natural}) is therefore problematic. As we have discussed earlier, string theory might provide various axion candidates, we would have the option to consider models with various axions, and this is what we want to explore in this paper. We shall follow the suggestion of ref.~\cite{Kim:2004rp} of axionic inflation with aligned axions: one axion spiralling down in the valley of a second one (see Figure~\ref{fig:spiral} and its copy on the title page). This mechanism encodes all the nice features of schemes later called ``axion monodromy''~\cite{Silverstein:2008sg,McAllister:2008hb} in a somewhat different set-up (see also~\cite{Pajer:2013fsa} for an overview on axion inflation). The alternative suggestion of many non-interacting axions, N-flation~\cite{Dimopoulos:2005ac} differs significantly from the mechanism described here. In addition it requires a really large number of axion fields~\cite{Kim:2006ys} that might be problematic in an explicit realisation. We shall comment on these mechanisms later in this paper (Section~\ref{sec:discussion}). | \label{sec:discussion} We have seen that the mechanism of aligned axions solves the problem of ``trans-Planckian" field values and thus completes the scenario of natural (axionic) inflation~\cite{Kim:2004rp}. It is characterised by a new parameter $\alpha$ that measures the amount of alignment ($\alpha=0$ corresponds to full alignment). A precise measurement of the tensor mode ratio $r$ would allow us to determine (within this scheme) a narrow range for the value of $\alpha$ (see Figure~\ref{fig:nsrplane}). Natural inflation is limited to $r\leq 0.18$ and for these values of $r,$ $\alpha$ has to be small. Values of $r\sim 0.1$ would correspond to $\alpha/\hat{f}\approx 0.2$, a rather light alignment. Therefore we are confident that such values can be achieved in explicit models without a strongly fine-tuned value of $\alpha$. Before we enter the details of potential model building let us comment on some alternative suggestions for the solution of the trans-Planckian problem. One of them is so-called N-flation~\cite{Dimopoulos:2005ac}, motivated by the mechanism of assisted inflation~\cite{Liddle:1998jc}. It should not be confused with the alignment mechanism discussed in this paper as it suggests the existence of $N$ {\it non-interactive} axions. With such a setup one can construct an effective axion scale $f_{\rm eff}\sim \sqrt{N} f_i$ (with individual scales $f_i$). In a realistic setting this mechanism requires many axions ${\mathcal O}(10^3)$ (see for instance~\cite{Kim:2006ys,Cicoli:2014sva,Baumann:2014nda}). The existence of many fields leads to a renormalisation of the Planck scale proportional to $\sqrt N$ as well and it is not clear whether $f_{\rm eff}$ could keep up with the ``increase" of the Planck-mass. Other suggestions for a solution of the trans-Planckian problem use mechanism very similar to the alignment mechanism of KNP~\cite{Kim:2004rp}. They are based on axionic fields in specific brane backgrounds motivated from string theory~\cite{Grimm:2007hs,Silverstein:2008sg,McAllister:2008hb,Hebecker:2014eua,Palti:2014kza,Marchesano:2014mla,Higaki:2014pja,Tye:2014tja} and in F-theory~\cite{Blumenhagen:2014gta,Grimm:2014vva}. These brane backgrounds (as e.g. NS5-branes) break the axionic symmetries explicitly and provide a slope for the axion to slide down. With this breakdown of the axionic symmetry one might worry whether the original shift symmetry still protects trans-Planckian displacements. The effect of brane-backreactions might be too strong for the mechanism to survive~\cite{Conlon:2011qp,Baumann:2014nda}. The original shift symmetry might thus not suffice to guarantee the flat potential needed for inflation. More work needs to be done to see whether these scenarios really solve the trans-Planckian problem (see~\cite{Germani:2010hd,Harigaya:2014eta} for alternative approaches). A scheme known as ``Dante's Inferno"~\cite{Berg:2009tg} considers a two-axion scheme as in~\cite{Kim:2004rp} and adds a background brane to tilt the potential. As this brane might lead to uncontrollable backreactions as well, it might also be counterproductive to a solution of the trans-Planckian problem. Of course, we do not yet have an explicit incorporation of the aligned axion scenario in string theory, but we think it is worthwhile to invest some work in this direction. In the original approach~\cite{Kim:2004rp} one was considering the axions from the NS-NS two form $B_2$ in the heterotic string with a breakdown of the shift symmetry through gauge instantons. There it was rather difficult to obtain a small value of $\alpha$. As is known by now, the NS-NS axions might also lead to a so-called $\eta$-problem through moduli mixing in the K\"ahler potential (see for instance~\cite{Baumann:2014nda}). At this point it seems that the $C$-axions for instance from the R-R two form $C_2$ might be better suited for our purpose. There are various effects that break the shift symmetries in a controllable way, that might allow for realistic values of the alignment parameter $\alpha$ without specific fine-tuning. In any case, let us first wait for a more precise measurement of the value of $r$ that determines the required value of $\alpha$. \subsection*{Note added} During our work on the alignment mechanism we became aware of other work that might be relevant in this direction. In~\cite{Choi:2014rja}, the authors discuss extensions of the KNP-mechanism with more than two axions, which can help to ameliorate the potential fine-tuning in $\alpha.$ In~\cite{Kallosh:2014vja}, the embedding of natural inflation in supergravity is discussed based on earlier work in the framework of supergravity shift symmetries (see for instance~\cite{Gaillard:1995az,Kawasaki:2000ws,BlancoPillado:2004ns,BlancoPillado:2006he}). \subsection*{Acknowledgements} This work was supported by the SFB-Transregio TR33 ``The Dark Universe" (Deutsche Forschungsgemeinschaft). | 14 | 4 | 1404.7127 |
1404 | 1404.0531_arXiv.txt | I review the history and development of Modified Newtonian Dynamics (MOND) beginning with the phenomenological basis as it existed in the early 1980s. I consider Milgrom's papers of 1983 introducing the idea and its consequences for galaxies and galaxy groups, as well as the initial reactions, both negative and positive. The early criticisms were primarily on matters of principle, such as the absence of conservation laws and perceived cosmological problems; an important step in addressing these issues was the development of the Lagrangian-based non-relativistic theory of Bekenstein and Milgrom. This theory led to the development of a tentative relativistic theory that formed the basis for later multi-field theories of gravity. On an empirical level the predictive success of the idea with respect to the phenomenology of galaxies presents considerable challenges for cold dark matter. For MOND the essential challenge remains the absence of a generally accepted theoretical underpinning of the idea and, thus, cosmological predictions. I briefly review recent progress in this direction. Finally I discuss the role and sociology of unconventional ideas in astronomy in the presence of a strongly entrenched standard paradigm. \PACS{01.65.+g, 95.35.+d, 98.62.-g, 98.80.-k} | In the context of the present cosmological paradigm, $\Lambda$CDM, there are two major constituents of the Universe for which the only evidence is astronomical. There is dark energy, perhaps represented by a cosmological constant in Einstein's equations. This medium, comprising 70\% of the energy density of the Universe, causes the observed present accelerated expansion evidenced by supernovae in distant galaxies and makes up the energy difference necessary for closure of the Universe. And then there is cold dark matter -- hypothetical particles, beyond the standard model of particle physics, comprising 25\% of the Universe and interacting with baryonic matter (the remaining 5\%) primarily through the force of gravity. Because it is cold (i.e., non-relativistic at the time it decouples from the photons and other relativistic particles in the early universe) this medium promotes the early formation of structure on all scales via gravitational collapse and explains the discrepancy between the directly observed baryonic matter (stars and gas) and the traditional dynamical mass of bound gravitational systems such as galaxies and clusters of galaxies. Here the cosmological paradigm impinges upon the dynamics of these well-observed local systems and should, in principle, be testable. And here it fails. The evidence supporting the standard cosmological paradigm is said to be so overwhelming that there is little room for doubt. This is in spite of the fact that the most well-motivated dark matter particles -- supersymmetric partners -- should be detectable in terrestrial experiments via the rare scattering of atomic nuclei. In fact such events have never been seen in spite of considerable effort and expense invested in particle dark matter search experiments. But efforts continue because $\Lambda$CDM has become something of an official religion -- a doctrine outside of which there is no salvation, beyond which there is only damnation. Yet there is a leading heresy that has attracted a relatively small but growing number of adherents: modified Newtonian dynamics, MOND, which, as will be argued here, is epistemologically ``more correct" than CDM. Viewed simply, MOND is an algorithm that, with one additional fundamental parameter having units of acceleration, allows calculation of the distribution of the effective gravitational force in astronomical objects from the observed distribution of baryonic matter -- and it works remarkably well. This is evidenced primarily by use of the MOND algorithm in the determination of rotation curves of disk galaxies where the agreement with observed rotation curves is often precise, even in details. The existence of such an algorithm is problematic for CDM because this is not something that dissipationless dark matter on the scale of galaxies can naturally do; it would seem require a coupling between dark matter and baryonic matter which is totally at odds with the perceived properties of CDM. Moreover, MOND subsumes the Tully-Fisher law, the observed near-perfect correlation between the baryonic mass of galaxies and the asymptotic constant rotation velocity, as a aspect of fundamental physics -- a Kepler's law for galaxies. This correlation appears unnatural in the context of dark matter because the asymptotic rotation velocity is a property of the dark matter halo that extends far beyond the relatively puny concentration of baryons in the center. In the context of dark matter it is explained as resulting from aspects of galaxy formation. But it remains difficult to understand how such a precise correlation can emerge from a process that must be inherently quite random, with each galaxy having its own unique history of formation, merging, feedback and dynamical evolution. The success of the MOND algorithm has deeper implications as a modification either of gravity (general relativity) or of the way in which particles respond to an applied force at low accelerations (inertia). The idea will not be generally accepted until these implications are understood in the context of a more general theory, but the phenomenological success should, in itself, be sufficient to raise serious doubts about existence of cold dark matter and thus the prevailing cosmological paradigm. Here my purpose to discuss MOND from a historical perspective, beginning with the phenomenological roots and philosophical basis as outlined in the original papers of Milgrom some thirty years ago \cite{milg83a,milg83b,milg83c}. I will describe the predictive successes of the idea and the initial and ongoing criticisms. I will outline the suggested physical bases of MOND while emphasizing that there is not yet a generally accepted physical theory and, therefore, cosmology. I will be brief because many of these points will be discussed in detail in the various articles in this compendium, but I will conclude with a discussion of the criteria that distinguish crazy from sensible ideas in astronomy and of the dangers to the creative process in science presented by the unquestioning acceptance of a standard dogma. | As a field, astronomy is replete with unconventional characters who propose and become obsessed with bizarre theories (often after a distinguished career as a conventional scientist). One example is provided by Victor Ambartsumian, a well-known Armenian astrophysicist who, in the mid-1950s, began speculating about the role of galactic nuclei in the formation and evolution of galaxies \cite{ambart}. He suggested that small galaxies are born complete from larger galaxies -- emerging from the nucleus like Athene springing full grown from the head of Zeus. Clusters of galaxies are not gravitationally bound systems but recently born galaxies expanding away from the large parent galaxy in the center; given a few billion years, the whole configuration will dissipate into intergalactic space -- thus solving the mass discrepancy problem in clusters. Although there were international meetings in which the idea was discussed, most astronomers did not take Ambartsumian's proposal seriously. It was just too ``crazy". [It interesting to note, however, that Ambartsumian's suggestion that the nuclei of galaxies have a dominant effect on the evolution and morphology of galaxies has re-emerged recently in a different guise with a different vocabulary -- ``feedback" in which activity of the central massive black hole limits the growth of the visible object.] Every astronomer is aware of other examples, particularly in cosmology, and given the abundance such bizarre proposals, it is an effect that we should be wary of. So in the context of the present discussion the question arises: does MOND fall into the category of crazy ideas? From the strong emotions that the mere mention of the word evokes at times, it would certainly seem as though some distinguished scientists think so. But here, I will argue that, while MOND is unconventional and inconsistent with the current cosmological paradigm, it is by no means in the category of crazy ideas. And we should recall that many constructs of modern physics, such as quarks, were at an early stage considered crazy and condemned quite viciously by renown scientists. [George Zweig, one of the creators of the concept of quarks wrote: ``The reaction of the theoretical physics community was generally not benign .... When the physics department of a leading university was considering an appointment for me, their senior theorist, one of the most respected spokesmen for all of theoretical physics, blocked the appointment at a faculty meeting by passionately arguing that the model was the work of a charlatan." (quoted by Harold Frisch \cite{frisch}).] Robert Ehrlich, in his book {\it Nine Crazy Ideas in Science} \cite{robehr} has listed several questions to be answered in order to tell if a crazy idea just might be true? I paraphrase these here as a list of criteria for an idea to be taken seriously. 1. {\it The new hypothesis should make some contact with familiar physics. Well established physical principles or some reasonable extension of those principles should be respected.} It is not, for example, easy to make such a connection for the idea of non-cosmological redshifts of quasars. But we have seen that MOND makes plausible modifications of current physical law in a regime where this law has never been tested and, certainly in its Lagrangian form, does embody cherished principles. 2. {\it The proposer of the idea should be a knowledgeable and respected scientist, although he/she may come from outside that particular field.} The world is full of gifted amateurs who imagine that they have found the key to a particular problem (or the theory of everything), but almost never are they near the truth. Again MOND and its creator, along with the several respectable scientist who have contributed to its development, meet this condition. 3. {\it The proposer should not be overly attached to the idea.} I would not rank this condition so highly because, actually, it is difficult not to become attached to an idea that one believes is correct and not to feel somewhat defensive when the idea is ignored by a majority of the relevant community. More relevant is for the proposer not to be dismissive of observations or data that does not support the idea. I believe that the supporters of MOND in general have not tried to sweep anything under the rug, although perhaps they have been overly dismissive of cosmological observations that are now quite precise. 4. {\it Statistics should be applied in an honest way.} The use of {\it a posteriori} statistics with respect to non-cosmological redshifts is an example of misapplied statistical arguments, but this is not so relevant to the problem of the mass discrepancy in astronomical objects. Of course, scaling relations such as Tully-Fisher are statistical in nature, but the most stringent and relevant selection criteria have been applied to data such as that plotted in Figure 4; for example it is the asymptotically constant value of the rotation velocity, beyond the visible disk, that is plotted rather than the width of a global line profile. 5. {\it The proposer should have no agenda going beyond the science of the issue.} This is more relevant to fields with political or economic impact, such as the reality (or not) of global warming; it does not apply here. 6. {\it The theory should not have many free parameters.} MOND has exactly one new fixed free parameter -- $a_0$ the critical acceleration which has, coincidentally, a cosmologically interesting value. 7. {\it The idea should be backed up by references to other independent work.} Here again, the tests of MOND are generally based on data -- kinematic and photometric -- taken by independent, objective observers with no personal stake in the theory. In fact, they are most often negative about the idea. 8. {\it The idea should not try to explain too much or too little.} Most of us have received emails from amateurs who attempt to explain dark matter, quasars, the Big Bang, solar neutrinos and the frequency of earthquakes with one grand theory. Such theories cannot actually calculate anything or make definite predictions. On the other hand, if the theory is too narrowly focussed on, for example dwarf spheroidal galaxies, then it lacks the generality appropriate to a physical theory but could more properly be described as a model. MOND, I would say, strikes the right balance in addressing the mass discrepancy in astronomical systems, although its implications would certainly be more general. 9. {\it The supporters should be open about their data and methods.} With respect to MOND, nothing is hidden. The data, photometric and kinematic, are published by others and generally available. The methods are simple, clear and reproducible by anyone. 10. {\it The theory should provide the simplest explanation of the phenomena.} There should not be too many epicycles necessary to save the phenomena. MOND comes out very well indeed under this criterion. It has never been modified with new constructs or parameters in order to explain those phenomena which it addresses, even though observations have become more precise and the data have improved considerably. The dark matter hypothesis, on the other hand, has required numerous tweaks and adjustments to explain the well-known discrepancies -- the cusp-core problem, the missing satellites, the galaxy mass function. To this list I would add two more points: {\it First of all, it is significant if the idea is falsifiable.} Are there observations that can disprove the theory in question? For MOND this is certainly the case; if, for example, the algorithm predicted less matter in clusters than is actually observed, this would be a certain falsification. For galaxy rotation curves, if a number of these required mass-to-light ratios that were negative, then this would be a falsification. {\it Secondly, it is significant if the number of proponents increases with time, especially if the new converts are younger scientists.} It does not bode well for a theory if its principal supporters comprise a declining group of embittered old men. This is not the case for MOND, where the number of advocates, especially younger scientists, has doubled or tripled over the past 10 years. So MOND meets most, if not all, of Ehrlich's (and my) criteria for an idea to be taken seriously. Why then has it languished for more than 30 years outside of the mainstream? After all, quarks became an accepted concept within a few years of being proposed. This is not due to some grand conspiracy. There was, however, from the first appearance of MOND an alternative and dominant paradigm that claims to account for the same phenomena. There are strong social factors that maintain support of the prevailing paradigm: an overriding tendency for scientists to work within the established framework and to select data that reinforce rather than challenge it (an effect that is supported by competition for academic positions and grants); and significantly, in this case, there is the general reluctance of most astronomers to tamper with historically established laws of nature -- in part a reaction against the plethora of crazy ideas in astronomy. But beyond this there is a tendency for astronomers to regard cosmology as the queen of sciences -- a reductionist undercurrent that gives cosmology priority over mere galaxy phenomenology. Data such as the pattern of anisotropies in the CMB are very well-fit by the standard cosmological model, albeit with a somewhat strange combination of six parameters. Given the precision of the fit, then the theory must be correct, even in its implications for galaxies. This makes most cosmologists dismissive of galaxy phenomenology and its wealth of regularities. These are problems that will be understood in the context of more detailed computations of the baryonic processes in galaxy formation and evolution -- problems for the future. But viewed strictly as a epistemological issue -- without prioritizing classes of data -- the CMB anisotropies are defined by a single curve, the angular power spectrum, which can be fit by a six parameter model. But there are at least 100 well observed galaxy rotation curves which, when combined with population synthesis models of the stellar populations of galaxies and thus color related mass-to-light ratios, can be fit by a theory having one fixed universal parameter. For MOND, the absence of a more basic theoretical underpinning of the idea remains the essential weakness. This means that cosmological calculations and predictions must be deferred. Ideally, one would like to have a theoretical determination of the function $\mu$ that interpolates between the Newtonian and MONDian regime -- at least for the phenomenon of rotation curves. The near coincidence of the acceleration parameter $a_0$ with $cH_0$ must be significant but there is not yet a convincing explanation. Does $a_0$ vary with cosmic time, as $cH_0$? Or is it an aspect of a fixed cosmological constant $\Lambda$? (In some theories, such as the Einstein-Aether version, $\Lambda$ would appear to have a scale on the order of ${a_0}^2$.) Is MOND more properly a modification of gravity or of inertia? In general relativity these are two sides of the same coin, but is that equivalence broken at low accelerations? I have argued that the success of MOND on the scale of galaxies strongly challenges the concept of a dissipationless dark fluid that clusters on these scales. But are there other problems with the standard cosmology -- problems that manifest themselves on cosmological scales and times? It is certainly impressive that, more or less, the same set of parameters emerge from different observations: the CMB anisotropies, the recent expansion history as traced by distant supernovae, the power spectrum of matter fluctuations. But rather than the precision with which the parameters of a model Universe are determined, it is the peculiar composition and the remarkable coincidences embodied by the concordance model that call for deeper insight. These motivations for questioning a paradigm are not unprecedented; such worries led to the inflationary paradigm that has had profound impact on cosmological thinking over the past 30 years. A more practical difficulty is the absence of an independent detection of dark matter particles. In the context of $\Lambda CDM$ they should be abundant locally -- they cluster in the Milky Way. Where are they? Because the properties of hypothetical particles are limited only by the human imagination, the concept of dark matter is fundamentally not falsifiable, but at some point continued non-detection must become a worry. This is an issue that is at least as problematic for dark matter as the absence of a cosmology is for MOND. Without independent detection the concept of cold dark matter clustering on galaxy scales remains hypothetical, and the standard cosmological paradigm, upon which it is based, is a pipe dream. All of this illustrates the dangers to the creative process in science presented by dogma too widely and too deeply accepted. In the context of the standard paradigm most work on galaxies -- for example semi-analytic galaxy formation models -- is built around patching up the standard model to make it work rather than challenging it. Indeed, it is difficult to imagine that a fundamental challenge could emerge from techniques characterized by numerous adjustable parameters or effects newly added as needed. MOND presents a different, and more traditional, sort of science in which definite predictions are made and verified -- or not. This is why the idea remains and gains support. I thank Moti Milgrom and Stacy McGaugh for helpful comments on the manuscript. | 14 | 4 | 1404.0531 |
1404 | 1404.1910_arXiv.txt | \label{Intro} The standard $\Lambda$CDM (cosmological constant + cold dark matter) model of Big Bang cosmology fits the observational data very well, and has been remarkably successful in describing the real Universe \cite{PlanckXXVI}. This model successfully describes the evolution of the Universe from the matter-dominated phase to the recent dark energy dominated and accelerated expansion phase in general relativity. It deserves mention that the cosmological constant $\Lambda$ is the simplest candidate of dark energy, which has constant energy density throughout the cosmic evolution \cite{8,paddy05,paddy05b,varun06}. And it suffers from theoretical problems such as fine tuning and cosmic coincidence \cite{10}. Also, it faces persistent challenges from observations on small scales known as ``small scale controversies", for instance, the observations related to innermost regions of dark matter halos and the Milky Way dwarf galaxy satellites show the inconsistency with CDM paradigm \cite{vega11,weinberg13}. On the other hand, the nature of CDM itself is elusive, and there have been different approaches to understand its nature \cite{Rind14,Heik14,Kile13}. Thus, the $\Lambda$CDM model is plagued with number of problems despite its great success in describing the Universe. Further, the late $\Lambda$CDM Universe expands forever with the de Sitter phase. However, we can not be sure about such a future of the real Universe because the observational data do not exclude the possibility of the domination of exotic dark energy stuff, which may lead to Big Rip end of the Universe \cite{PlanckXXVI,caldwell03,mel03,car03,Bennett13}. This motivates us to search/construct the viable alternative models of the Universe, in particular the ones which offer a future of the Universe different from the de Sitter one, and fit the observational data matching the success of the $\Lambda$CDM model \cite{odi10,odi12a,odi12b,odi12c,odintsov13}. The Chevallier-Polarski-Linder (CPL) parametrization of equation of state (EoS) parameter of dark energy was first introduced in \cite{Chevallier01}, and reads as $w_{\rm de}=w_0+w_1(1-a/a_0)$, where $w_0$ and $w_1$ are constants, and $a$ is cosmic scale factor with $a_0$ being its present value. One may note that the CPL parameterization carries first two terms of Taylor expansion of $w_{\rm de}$ in terms of $a$ about $a_0$, and hence it is naturally motivated, and approximates $w_{\rm de}$ very well especially in the vicinity of present epoch of the Universe, where $a\simeq a_0$. That is why, it has been frequently constrained with observational data in order to study the nature of dynamic dark energy (see \cite{PlanckXXVI} for recent constraints from Planck). However, the CPL parametrization only in terms of scale factor or redshift has been tested with the observational data in bulk of the literature. In recent studies, Akarsu et al. \cite{ozgur12,ozgur14a} investigated a cosmological model based on CPL parametrization of deceleration parameter ($q$) in terms of cosmic time $t$, and observed interesting future evolution of the Universe where it ends in Big Rip. In this model, the authors discussed the Big Rip behavior of the Universe considering the effective cosmic fluid but did not explore the dark energy source responsible for the Big Rip end of the Universe. It is worth noting that CPL parametrization of deceleration parameter in $t$ leads to CPL parametrization in $t$ for the EoS parameter ($w$) of the effective cosmic fluid in general relativity in the framework of spatially flat Roberson-Walker (RW) spacetime via the relation $q=-\frac{\ddot{a}a}{\dot{a}^2}=\frac{1+3w}{2}$, where an over dot denotes derivative with respect to time $t$. In this study, we shall begin with the CPL parametrization in $t$ for the EoS parameter of the effective cosmic fluid as we are mainly interested to explore the dynamics of the Universe, and in particular the behavior of dynamical dark energy that leads to Big Rip end of the Universe. The work is organized as follows. In Section \ref{sec2}, we give the background equations and the model. In Section \ref{sec3}, we test the success of the model with the latest observational data in contrast with the $\Lambda$CDM model. In Section \ref{sec4}, we explore the nature of dark energy responsible for the Big Rip end of the Universe in the model. We give concluding remarks in Section \ref{sec5}. | \label{sec5} The BR model describes the Universe from the matter-dominated phase to the recent dark energy dominated phase in line with the $\Lambda$CDM model but offers a Big Rip end of the Universe contrary to the everlasting de Sitter expansion of the Universe in the $\Lambda$CDM model. It fits the observational data from the $H(z)$ and SN Ia compilations matching the success of the $\Lambda$CDM model. The analysis further reveals that both the models describe almost identical evolution of the Universe from the onset of acceleration till the present epoch, in particular. In future, the $\Lambda$CDM model evolves to the de Sitter phase with constant vacuum energy density. On the other hand, the dark energy in the BR model is dynamical in nature. Interestingly, it mimics the cosmological constant behavior in the vicinity of present epoch, and exhibits phantom behavior in future. Due to the dominance of this dark energy, the Universe has finite life time in the BR model and it ends in Big Rip. Usually, solutions of the Einstein's field equations in general relativity are found and analyzed for different epochs, that is, for inflationary phase ($p_{\rm eff}\simeq -\rho_{\rm eff}$), radiation-dominated phase ($p_{\rm eff}\simeq\rho_{\rm eff}/3$) and matter-dominated phase ($p_{\rm eff}\simeq 0$). However, considering equation of state (EoS) parameter ($w_{\rm eff}=p_{\rm eff}/\rho_{\rm eff}$) for the effective fluid, unified solutions for these epochs are also presented by some authors in the literature. For instance, Israelit and Rosen \cite{14,15} considered a phenomenological form of the effective EoS parameter, and described the evolution of the Universe from pre-matter period to the radiation-dominated phase, and then radiation to matter-dominated period. Similarly, a phenomenological form of effective EoS parameter was suggested by Carvalho \cite{16} to describe a unified evolution of the Universe from the inflationary phase to the radiation-dominated phase. However, the BR model investigated in this paper is based on the naturally motivated CPL parametrization for EoS parameter of the effective cosmic fluid. We would like to emphasize that the CPL parametrization is originated from the Taylor expansion of the EoS parameter. So it does not strictly belong to the class of phenomenological parameterizations of the EoS parameter. In fact, it is a precise measure of the real EoS parameter upto the first order terms in $t$. As a final note for the prospective readers we would like to mention that the BR model does very well for describing the evolution of the Universe at low redshifts, and describes the Big Rip future of the Universe as intended in this study. However, it does well at higher redshifts too as we observed from the CMB shift parameter analysis. Probably, one more term is required in the Taylor approximation of $w_{\rm eff}(t)$ for much better performance of BR model at higher redshifts. But it will bring in an additional parameter to the model, and may introduce difficulty in analytical solution of the model. Also, the model generated by considering one extra term may not describe a Universe exhibiting the Big Rip feature essentially. Nevertheless, this idea deserves attention for further investigation. Next, it may be worthwhile to investigate a possible generalization of the BR model by considering a coupling between dark matter and dark energy (see \cite{Amen04}). It would be interesting to know whether (and how) the results of this paper might change in the presence of a direct coupling between the dark matter and dark energy components of the cosmic fluid. \subsection* | 14 | 4 | 1404.1910 |
|
1404 | 1404.6537_arXiv.txt | { A new analysis of extended data records collected with the Lunar Laser Ranging (LLR) technique performed with improved tidal models was not able to resolve the issue of the anomalous rate $\dot e$ of the eccentricity $e$ of the orbit of the Moon, which is still in place with a magnitude of $\dot e=(5\pm 2)\times 10^{-12}$ yr$^{-1}$. Some possible cosmological explanations are offered in terms of the post-Newtonian effects of the cosmological expansion, and of the slow temporal variation of the relative acceleration rate $\ddot{S} S^{-1}$ of the cosmic scale factor $S$. None of them is successful since their predicted secular rates of the lunar eccentricity are too small by several orders of magnitude. } \keyword{Experimental studies of gravity; Experimental tests of gravitational theories; Modified theories of gravity; Ephemerides, almanacs, and calendars} \PACS{04.80.-y; 04.80.Cc; 04.50.Kd; 95.10.Km} \begin{document} | \lb{Introduzione} In 2009, Williams and Boggs \citep{WilliamsBoggs2009} reported an anomalous secular rate of the eccentricity $e$ of the orbit of the Moon \eqi\dot e = (9\pm 3)\times 10^{-12}\ {\rm yr^{-1}}.\lb{rate} \eqf They fit the dynamical models of the DE421 ephemerides \citep{DE421} to a record of ranges collected with the Lunar Laser Ranging (LLR) technique from March 1970 to November 2008. The effect of \rfr{rate} is anomalous in the sense that it is in excess with respect to the eccentricity rate predicted with the tidal models of the DE421 ephemerides. Anderson and Nieto \citep{2010IAUS..261..189A} included \rfr{rate} in the current astrometric anomalies in the Solar System. Some more or less sound attempts to find an explanation of \rfr{rate} in terms of either standard and non-standard gravitational physics have been performed so far \citep{2011MNRAS.415.1266I, 2011AJ....142...68I, 2013PhyEs..26...82Z, 2013AdSpR..52.1297A, 2013PhyEs..26..567A}. Recently, Williams et al. \citep{WilliamsetalPS2014} extended their analysis of the LLR data from March 1970 to April 2013 by using the new DE430 ephemerides \citep{2014IPNPR.196C...1F} with improved tidal models. As a result, the anomalous eccentricity rate of the lunar orbit, although reduced with respect to \rfr{rate}, did not disappear, amounting now to \eqi \dot e = (5\pm 2)\times 10^{-12}\ {\rm yr^{-1}}\lb{rate2}.\eqf The rate of \rfr{rate2} exhibited a low correlation with other solved-for estimated parameters \citep{WilliamsetalPS2014}. In this Letter, we propose to look for further possible physical mechanisms able to explain the lingering anomalous lunar eccentricity rate. | \lb{conclusioni} As a result of the latest LLR data analysis performed with improved tidal models, it turned out that the anomalous eccentricity rate of the lunar orbit is still lingering; it amounts to $\dot e = (5\pm 2)\times 10^{-12}$ yr$^{-1}$. The LLR analysts seem convinced that, sooner or later, a better understanding of the intricate geophysical processes of tidal origin taking place in the interiors of our planet and of its satellite will be able to fully accommodate the selenian orbital anomaly. As such, they will continue to look for conventional causes for the anomalous eccentricity rate of the Moon. Nonetheless, as a complementary approach, the search for causes residing outside the Earth and the Moon themselves is worth of being pursued. If unsuccessful, it could also indirectly strengthen the relevance of the efforts towards an explanation in terms of standard geophysics. In this respect, in this Letter it has been shown that neither the cosmological expansion at the first post-Newtonian level nor the slow temporal variation of the relative acceleration rate of the cosmic scale factor are able to explain the anomalous lunar eccentricity increase because they induce long-term rates of change of the Moon's eccentricity too small by several orders of magnitude. Such a further negative result adds to the previous series of failed attempts to find sound non-tidal explanations appeared in the literature so far. | 14 | 4 | 1404.6537 |
1404 | 1404.0582_arXiv.txt | Stimulated by the recent discovery of the 1 yr recurrence period nova M31N 2008-12a, we examined the shortest recurrence periods of hydrogen shell flashes on mass-accreting white dwarfs (WDs). We discuss the mechanism that yields a finite minimum recurrence period for a given WD mass. Calculating the unstable flashes for various WD masses and mass accretion rates, we identified a shortest recurrence period of about two months for a non-rotating 1.38 $M_\sun$ WD with a mass accretion rate of $3.6 \times 10^{-7}~M_\odot$~yr$^{-1}$. A 1 yr recurrence period is realized for very massive ($\gtrsim 1.3~ M_\odot$) WDs with very high accretion rates ($\gtrsim1.5 \times 10^{-7}M_\odot$~yr$^{-1}$). We revised our stability limit of hydrogen shell burning, which will be useful for binary evolution calculations toward Type Ia supernovae. | \label{sec_introduction} The recent discovery of the recurrent nova M31N 2008-12a has attracted attention to novae with short recurrence periods \citep{dar14, hen14, tan14}. M31N 2008-12a showed the shortest recorded recurrence period of 1 yr, a very rapid turn-on of the stable supersoft X-ray source (SSS) phase, and a high effective temperature ($\sim 100$ eV) in the SSS phase, all of which indicate a very massive white dwarf (WD). Such massive WDs in recurrent novae are considered to be one of the candidates for Type Ia supernova (SN~Ia) progenitors \citep{hku99, hkn99, hac01kb, hkn10, han04, li97, kat12review, pag14}. SNe Ia play very important roles in astrophysics as standard candles for measuring cosmological distances and as the main producers of iron group elements in the chemical evolution of galaxies. However, their immediate progenitors just before SN Ia explosions are still unclear. Thus, studies of novae with very short recurrence periods are essential to identify immediate progenitors of SNe~Ia. Many theoretical works on hydrogen shell flashes have been published. In general, short recurrence periods are obtained for very massive WDs with high mass accretion rates. When the mass accretion rate exceeds a certain value, nuclear burning is stable, and no shell flashes occur \citep{sie75, sie80, sio79, ibe82, nom07, wol13}. The border between stable and unstable mass accretion rates is known as the stability line, i.e., $\dot M_{\rm stable}$, in the diagram of accretion rate vs. WD mass. For a given WD mass, the shortest recurrence period is obtained near the stability line. However, it is not well known whether this minimum recurrence period approaches a finite value or zero. \citet{wol13} recently obtained numerically the recurrence periods near the stability line for various WD masses and showed that the minimum recurrence period is finite. However, the theoretical reason for the finite value is still unclear. Moreover, the stability line obtained by \citet{wol13} using a time evolution calculation differs slightly from that obtained using a linear stability analysis \citep{sie75, sie80, nom07}. Because the stability line is important in binary evolution calculations toward SNe~Ia, we examine the stability line of shell flashes and clarify why there is a finite minimum value of the recurrence period. In the next section, we explain the reason for the finite minimum values of the nova recurrence period. In Section \ref{sec_evolution}, we present calculations of shell flashes on very massive WDs and numerically obtain the minimum recurrence periods for various WD masses. We also present a recalculated stability line, which could be useful for calculations of binary evolution. In Section \ref{sec_discussion}, we discuss some numerical calculations that resulted in shell flashes for mass accretion rates above the stability line. Finally, we summarize our results in Section \ref{conclusions}. \begin{figure} \epsscale{1.2} \plotone{f1.eps} \caption{ Schematic $M_{\rm env}-\log T_{\rm c}$ diagram for one cycle of nova outbursts on a $1.38~M_\sun$ WD with a given mass accretion rate $\dot M$. Here, $T_{\rm c}$ is the temperature at the bottom of the hydrogen-rich envelope, and $M_{\rm env}$ is the envelope mass. We plot three mass accretion rates: above the stability line, i.e., $\dot M > \dot M_{\rm stable}$ (thin solid line); somewhat below the stability line, i.e., $\dot M < \dot M_{\rm stable}$ (thick solid line); and much below the stability line, i.e., $\dot M \ll \dot M_{\rm stable}$ (dotted line). For the thick solid line, the WD starts accreting around point A and the envelope mass increases. When it reaches turning point B, a shell flash begins. Thus, the ignition mass is defined as $M_{\rm ig}= M_{\rm env}({\rm B})$. Then the envelope expands and reaches point C. After an optical maximum at point C, the envelope mass decreases owing to wind mass loss and nuclear burning. The optically thick wind stops at point D. Hydrogen burning ends at point E, and the envelope quickly cools toward point A. In this S-shaped sequence ABEDC, the lower branch (blue line from A to B) represents a degenerate envelope, and the middle branch (red line from B to E) represents an unstable envelope for nuclear burning. The upper branch (black line from E to C) represents an extended envelope after optical maximum, where nuclear burning is stable. For the lower mass accretion rate (dotted line), the degenerate branch is cooler owing to the smaller gravitational energy release; hence, the ignition mass is larger. For the higher mass accretion rate, the ignition mass is smaller. We found that the width of this limit cycle, $\Delta = M_{\rm env}({\rm B}) - M_{\rm env}({\rm E})$, does not vanish even for very high mass accretion rates above the stability line (thin solid line). This is the reason for the minimum recurrence period of $t_{\rm rec}^{\rm min}= \Delta / \dot M_{\rm stable}$. See text for details. \label{flash}} \end{figure} | \label{conclusions} The main results are summarized as follows. \noindent 1. We proposed a physical mechanism that leads to a finite minimum recurrence period of novae. \noindent 2. We calculated the ignition masses for various WD masses and mass accretion rates. We determined that the shortest recurrence period of novae is about two months for a non-rotating $1.38~M_\sun$ WD with a mass accretion rate of $3.6 \times 10^{-7}~M_\sun$~yr$^{-1}$. \noindent 3. A 1 yr recurrence period of a nova is possible only for very massive WDs ($M_{\rm WD} \gtrsim 1.3~ M_\sun$) and very high mass accretion rates, e.g., $\dot M =3.3 \times 10^{-7}~M_\sun$~yr$^{-1}$ for a $1.31~M_\sun$ WD, $2.4 \times 10^{-7}~M_\sun$~yr$^{-1}$ for a $1.35~M_\sun$ WD, and $1.5 \times 10^{-7}~M_\sun$~yr$^{-1}$ for a $1.38~M_\sun$ WD. \noindent 4. We revised our stability limit of hydrogen shell burning \citep{nom07}, which is useful for binary evolution calculations toward SNe Ia. | 14 | 4 | 1404.0582 |
1404 | 1404.2587_arXiv.txt | We present {\sl XMM-Newton} and {\sl Chandra} observations of two low-metallicity cometary blue compact dwarf (BCD) galaxies, Mrk 59 and Mrk~71. The first BCD, Mrk 59, contains two ultraluminous X-ray (ULX) sources, IXO 72 and IXO 73, both associated with bright massive stars and H {\sc ii} complexes, as well as one fainter extended source associated with a massive H {\sc ii} complex at the head of the cometary structure. The low-metallicity of Mrk 59 appears to be responsible for the presence of the two ULXs. IXO 72 has varied little over the last 10 yr, while IXO 73 has demonstrated a variability factor of $\sim$4 over the same period. The second BCD, Mrk 71, contains two faint X-ray point sources and two faint extended sources. One point source is likely a background AGN, while the other appears to be coincident with a very luminous star and a compact H {\sc ii} region at the ``head'' of the cometary structure. The two faint extended sources are also associated with massive H {\sc ii} complexes. Although both BCDs have the same metallicity, the three sources in Mrk 71 have X-ray luminosities $\sim$1--2 orders of magnitude fainter than those in Mrk 59. The age of the starburst may play a role. | With a heavy element abundance ranging from 3\% to 50\% that of the Sun, blue compact dwarf (BCD) galaxies are the least chemically evolved gas-rich star-forming galaxies known in the local universe \citep{T08}. They thus constitute the best laboratories for studying physical processes which occurred at high redshifts, when the gas was very metal-deficient. BCDs are undergoing intense bursts of star formation, giving birth to thousands of O stars in a very compact starburst region. Because of the presence of these many massive short-lived stars, BCDs are expected to emit in the X-ray. This X-ray emission can come from compact sources such as high-mass X-ray binaries (HMXBs) and/or hot O and Wolf-Rayet stars, or from diffuse sources such as the hot plasma associated with supernova (SN) remnants. Stellar winds and SNe inject energy and momentum into the cold ambient interstellar medium (ISM), producing large amounts of hot gas. The starburst activity that injects hot X-ray-emitting gas into the ISM lasts about 10$^7$ yr. This starburst phase is then followed by a long ($>$ 1--2 Gyr) quiescent period of passive photometric evolution, before the occurrence of the next burst. Depending on the energy injection rate into the ISM and the geometry and robustness of the cold gaseous ambient medium, expansion of the hot ISM on scales comparable to the galactic scale length can result in a funneling of hot gaseous mass into the cold gaseous halo. Because of the relatively low potential well of BCDs, mass loss can occur \citep{DH94}. Extensive mass loss can then lead to an expansion of the galaxy's size and to a morphological evolution of the dwarf galaxy \citep{YA87}. We present in this paper an X-ray study of two BCDs, Mrk 59$\equiv$I Zw 49 and Mrk 71$\equiv$NGC 2363. These are of particular interest because they are the prototypes of a particular class of BCDs, dubbed ``cometary'' galaxies by \citet{LT85} in their BCD morphological classification scheme. Cometary BCDs are characterized by a high surface brightness star-forming region (the comet's ``head'') at one end of an elongated low surface brightness stellar body (the comet's ``tail''), suggestive of a flattened dwarf irregular galaxy seen nearly edge-on. In the case of Mrk 59, the irregular galaxy is called NGC 4861, and in the case of Mrk 71, NGC 2366. In the following, we will be using the names of Mrk 59 and Mrk 71 to designate {\it both} the high surface brightness star-forming region and the low surface brightness elongated stellar body. The bright star-forming region is at the end of a long chain of fainter and smaller H~{\sc ii} regions embedded in the lower surface brightness stellar body of the cometary BCD. This chain of H~{\sc ii} regions is suggestive of self-propagating star formation which stopped at the edge of the galaxy. By studying cometary BCDs, we can examine how star formation ignites and propagates in low-mass gas-rich stellar systems. Because the brightest H~{\sc ii} region at the end of the chain is youngest and those along the chain are progressively older with increasing distance from the edge \citep{N00}, we can study the time evolution of H~{\sc ii} regions, and in particular the time dependence of their X-ray properties. Of the 2 BCDs, only Mrk 59 has been observed before in the X-ray range. Using {\sl Einstein}, \citet{F92} detected it as a strong X-ray source with an X-ray luminosity of $\sim$10$^{40}$ erg s$^{-1}$. Subsequently, \citet{P98} found from {\sl ROSAT} HRI observations of Mrk 59 that the X-ray emission splits into two sources separated by $\sim$35\arcsec. The southern one appears to coincide with the high surface brightness starburst region at the end of the stellar body, while the more luminous (by a factor of $\sim$2.5) northern one is in the low surface brightness main body, and did not appear to be associated with any evident H~{\sc ii} region. The two BCDs have also been studied extensively at other wavelength ranges. Abundance determinations give oxygen abundances 12 + log O/H of 8.0 and 7.9 for Mrk 59 and Mrk 71, respectively \citep{N00}, corresponding to 1/5 and 1/6 of the Sun's metallicity, if the solar calibration (12 + log O/H)$_\odot$ = 8.7 of \citet{A09} is adopted. \citet{N00} have derived O abundances for two other emission knots along the elongated body of Mrk 59 and found them to be the same as that of the bright knot, within the errors. The small scatter in metallicity along the major axis of Mrk 59 ($\sim$0.2 dex) suggests that the mixing of elements in the ionized gas has been efficient on a spatial scale of several kiloparsecs. As for Mrk 71, \citet{R96} found that the O abundance in several other H~{\sc ii} regions in the main body varies between 8.1 and 8.3, slightly higher than in the brightest H~{\sc ii} region. \citet{T02} have used the {\sl Far~Ultraviolet~Spectroscopic~Explorer} ({\sl FUSE}) to study the abundances in the neutral ISM of Mrk 59 from UV absorption lines. They found that the heavy element abundance in the neutral gas of Mrk 59 is about a factor of 10 less than that of the ionized gas, or about 1/50 of the solar abundance. Although it has a very low metallicity, the neutral gas of Mrk 59 is not pristine and must have been enriched by previous generations of stars. Using photometric and spectroscopic observations, \citet{N00} found that the age of the oldest stars in the low surface brightness component probably does not exceed $\sim$ 4 Gyr in Mrk 59 and $\sim$ 3 Gyr in Mrk71. This age is smaller than the typical age (5 Gyr or greater) of the underlying stellar population in BCDs of other types. Cometary galaxies thus appear to be relatively young galaxies. \citet {TI05} have used {\sl HST} $V$ and $I$ images to perform a color-magnitude diagram (CMD) analysis of the stellar populations in Mrk 71. The CMD reveals not only young stellar populations such as blue main sequence stars (age $\la$ 30 Myr), but also an intermediate-age population of blue and red supergiants (20 Myr $\la$ age $\la$ 100 Myr), and an older evolved stellar population of asymptotic giant branch (AGB) stars (age $\ga$100 Myr) and red giant stars (age $\ga$ 1 Gyr). This suggests that, in addition to the present burst with age $\la$ 100 Myr, star formation in Mrk 71 has started some 3 Gyr ago, consistent with the photometric age estimate of \citet{N00}. Near-infrared molecular hydrogen emission has been detected in both Mrk 59 \citep{I09} and Mrk 71 \citep{I11}. \citet{THL04} have studied the H {\sc i} distribution and kinematics of the two BCDs. The VLA maps show multiple H {\sc i} peaks scattered over the disk. The latter shows regular rotational kinematics, with a linear rise followed by a flattening of the rotation curve. In this paper, we will adopt a distance of 10.7~Mpc for Mrk 59 \citep{THL04}. As for Mrk 71, we will use the Cepheid-derived distance of 3.44~Mpc \citep{T95}, placing it in the M81 group. At those distances, 1\arcsec\ corresponds to a linear size of 52 pc in Mrk 59 and of 17 pc in Mrk 71. The Galactic column densities for Mrk~59 and Mrk~71 are $N_{\rm H}=1.2\times10^{20}$~cm$^{-2}$ and $N_{\rm H}=4.0\times10^{20}$~cm$^{-2}$, respectively, although based on the H {\sc i} maps of \citet{THL04}, the internal neutral hydrogen column densities in Mrk~59 and Mrk~71 could be as large as $N_{\rm H}=3\times10^{21}$~cm$^{-2}$. | We have investigated the X-ray emission of the two cometary Blue Compact Dwarf (BCD) galaxies Mrk 59 and Mrk 71, based on {\sl XMM} and {\sl Chandra} observations. Our main findings are the following: 1. Mrk 59 contains two very bright X-ray point sources, IXO 72 and IXO 73, with 0.5 -- 10 keV luminosities of (1.8--2.1)$\times$10$^{39}$ and (2.4-8.9)$\times$10$^{39}$ erg s$^{-1}$, respectively. The cometary ``head'' H {\sc ii} complex is also faintly detected, its diffuse emission constituting a few percent of the total X-ray emission from the galaxy. Both IXO 72 and IXO 73 possess optical counterparts, IXO 72's counterpart being potentially identified as an individual luminous, massive star while IXO 73's counterpart is a bright stellar object located in an slightly resolved compact H {\sc ii} region. The above identifications suggest that both IXO 72 and IXO 73 are single objects, thus qualifying them as legitimate ultraluminous X-ray (ULX) sources. The 0.5 -- 10 keV X-ray flux of IXO 72 has remained approximately constant over the past 10 yr, while that of IXO 73 has varied by a factor of $\approx$4 over the same period. The X-ray spectra of both sources are typical of ULXs. Such high X-ray luminosities may be related to the low metallicity of Mrk 59 (0.2 solar). 2. Mrk 71 contains four faint X-ray sources. The brightest one is spatially coincident with a background spiral galaxy. The second brightest one is coincident with a very compact H {\sc ii} region and a bright star; if associated with Mrk~71, this star is extremely luminous and among the brightest stars known. The other two faint X-ray sources are associated with large H {\sc ii} complexes. All three sources are 1--2 orders of magnitude fainter the Mrk 59 X-ray sources. As Mrk 71 has the same metallicity as as Mrk 59, metallicity cannot be the only factor in determining X-ray luminosities. The age of the starburst may play a role. | 14 | 4 | 1404.2587 |
1404 | 1404.0899_arXiv.txt | We present results from a homogeneous analysis of the broadband $0.3-10\kev$ CCD resolution as well as of soft X-ray high-resolution grating spectra of a hard X-ray flux-limited sample of 26 Seyfert galaxies observed with {\it XMM-Newton}. Our goal is to characterise warm absorbers (WAs) along the line-of-sight to the active nucleus. We significantly detect WAs in $65\%$ of the sample sources. {\color{black} Our results are consistent with WAs being present in at least half of the Seyfert galaxies in the nearby Universe, in agreement with previous estimates .} {\color{black} We find a gap in the distribution of the ionisation parameter in the range $0.5<\log\xi<1.5$ which we interpret as a thermally unstable region for WA clouds. This may indicate that the warm absorber flow is probably constituted by a clumpy distribution of discrete clouds rather than a continuous medium. The distribution of the WA column densities for the sources with broad Fe K$\alpha$ lines are similar to those sources which do not have broadened emission lines. Therefore the detected broad Fe K$\alpha$ emission lines are bonafide and not artifacts of ionised absorption in the soft X-rays.} The WA parameters show no correlation among themselves, with the exception of the ionisation parameter versus column density. The shallow slope of the $\log\xi$ versus $\log v_{\rm out}$ linear regression ($0.12\pm 0.03$) is inconsistent with the scaling laws predicted by radiation or magneto-hydrodynamic-driven winds. Our results suggest also that WA and Ultra Fast Outflows (UFOs) do not represent extreme manifestation of the same astrophysical system. | The X-ray and $\gamma$-ray emission of an active galaxy mostly originate from the innermost regions of the central engine, known as the Active Galactic Nuclei (AGN). It is commonly believed that the AGN is powered by accretion of plasma onto a super-massive black hole. The $0.1-10 \kev$ X-ray emission spectrum of radio quiet (RQ) AGN can be well approximated by a power-law with a photon index in the range of $1.6\le \Gamma\le2.4$, suggesting Comptonisation as the main underlying physical process \citep{1991ApJ...380L..51H,1994ApJ...434..570T}. Superposed on this continuum, several spectral components have been discovered along the history of X-ray astronomy. Most of these are believed to be due to reprocessing by an optically thick and geometrically thin accretion disk \citep{george-fabian}. Spectral distortions, most notably observed in the profile of emission lines such as the iron K${\alpha}$, suggest that the bulk of the X-ray emission comes from a region just a few gravitational radii from the black hole's event horizon \citep[for e.g., see the review by][for a different interpretative scenario]{2009A&ARv..17...47T}. Extrapolating this non-thermal component to energies lower than $\sim$1~keV unveils a ``soft X-ray excess". The physical origin of this component has so far proven elusive \citep[see e.g.,][]{2004MNRAS.349L...7G,2004A&A...422...85P,2006MNRAS.365.1067C, 2005A&A...432...15P,2006MNRAS.371...81S,2007ApJ...671.1284D}. { Redwards of the soft X-rays lie the unobservable region of the AGN spectra. The energy range of $13.6-100\ev$ is obscured from us due to the Galactic extinction. Below $13.6\ev$ the big blue bump (BBB) is the most important and dominant spectral feature. It typically spans the energy range from $\rm1\mu m$-$\rm 3nm$ or $\rm \log(\nu/Hz)\sim 14.5-17$ and is a major contributor to the AGN bolometric luminosity \citep{2013MNRAS.431..210C,2007MNRAS.381.1235V,1994ApJS...95....1E,1989ApJ...347...29S}. The most commonly accepted origin of the BBB is the multi-colored blackbody emission from a geometrically thin and optically thick accretion disk \citep{1973A&A....24..337S}.} The $0.1-10\kev$ spectra of many AGN are affected by obscuration by partially ionised material along our line of sight and intrinsic to the source, first detected by \cite{1984ApJ...281...90H} using {\it Einstein} data. Such X-ray absorbing clouds have been named warm absorbers (WA). These warm absorbers imprint their signatures on the X-ray spectrum as narrow absorption lines and edges, from elements at a wide range of ionisation stages \citep[see e.g.,][]{2000A&A...354L..83K, 2000ApJ...535L..17K,2005A&A...431..111B}. The high resolution grating X-ray spectra from the \xmm{} and \chandra{} observatories have profoundly improved our understanding of these discrete absorption and emission features. Absorption lines and photo-absorption edges are sensitive diagnostics of the ionisation structure and kinematics of the gas. The measured blue-shift of the absorption lines with respect to the systemic velocity implies that these absorbers are outflowing with moderate velocities in the range of $\sim 100-1000 \kms$. In some AGNs, high velocity ($\sim \rm 0.1c$) outflows have also been detected \citep[e.g.,][]{2003ApJ...593L..65R,2004A&A...413..921D,2005ApJ...618L..87D,2007ApJ...670..978B}. The resulting mass outflow rate can be a substantial fraction of the accretion rate required to power the AGN. Thus, warm absorbers can be dynamically important and the knowledge of their state, location, geometry and dynamics would help in understanding the central engines of AGN \citep{1995AAS...186.4501M}. \subsection{Previous studies of warm-absorbed AGN samples} \label{sect_previousstudies} Spectroscopic measurements of AGN with the X-ray CCD detectors onboard ASCA allowed the first systematic studies of sizable samples of warm absorbed AGN. \cite{1997MNRAS.286..513R} presented a study of X-ray spectral properties along with warm absorber properties for a sample of 24 type 1 AGN, using the medium resolution \asca{} data. Almost half of the objects in this sample show K-shell absorption edges of \ion{O}{VII} and \ion{O}{VIII}, and were interpreted as signatures of warm absorbers. Reynolds found a trend for less ionised absorption to be present in more luminous objects. A similar fraction of warm absorbed sources was found in a sample of 18 Seyfert~1--1.5 galaxies observed by ASCA \citep{1998ApJS..114...73G}, as well as in a sample of $\simeq$40 Palomar-Green Quasi Stellar objects (QSOs) observed by the XMM-Newton EPIC CCD cameras \citep{2005A&A...432...15P}. \cite{2005A&A...431..111B} compiled the results of previous studies of a number of Seyfert galaxies observed with the RGS (Reflection Grating Spectrometer) onboard {\it XMM-Newton}. They suggested that warm absorbers in nearby Seyfert galaxies and QSOs originate in outflows from the dusty torus. The kinetic luminosity of these outflows accounts for well under $1\%$ of the bolometric luminosities of AGN. The authors showed that the amount of matter processed through an AGN outflow system, averaged over the lifetime of the AGN, is probably large enough to have a significant influence on the evolution of the host galaxy. \cite{2007MNRAS.379.1359M} analysed a sample of 15 type 1 sources using the high resolution Chandra grating data. Ten out of the 15 sources show signatures due to intrinsic absorption from H- or He-like Oxygen, with nine out of the ten sources requiring multiple ionisation components. The ionisation parameter of the warm absorbing gas spanned almost four orders of magnitude ($\xi\sim 10^{0-4}\xiunit$), and the column density 3 orders of magnitude ($\nh\sim 10^{20-23}\cmsqi$). These authors found an apparent gap in the distribution of outflow velocities between $300-500\kms$, whose origin was unclear. \cite{2012ApJ...745..107W} studied a sample of 48 Seyfert 1-1.5 galaxies in the X-rays and hard X-rays using the {\it Suzaku} and {\it XMM-Newton} telescopes. The sources were detected in the hard X-rays using the {\it Swift} Burst alert telescope (BAT) in the $14-195\kev$ band. They detected significantly \ion{O}{VII} and \ion{O}{VIII} edges in $52\%$ of their sample. The ionised column densities of sources with \ion{O}{VII} and \ion{O}{VIII} detections cluster in a narrow range around $\rm \nh \sim 10^{21} \cmsqi$, while sources without strong detection have column densities an order of magnitude lower. Taking into account the inhomogeneous coverage of their sample in the soft X-ray band, they conclude that up to $80\%$ of nearby AGN could host warm absorbers. \cite{2010A&A...521A..57T} (hereafter T10) have carried out an extensive sample study of ultra fast outflows (UFOs), which are highly ionised outflowing clouds of gas with velocities a fraction ($\sim 0.1-0.3$) of the speed of light. Their signatures in the spectra are in the form of narrow absorption lines in the energy range $\sim 6-9 \kev$. The authors conclude that these outflowing clouds are present in about $\sim 35\%$ of Seyfert galaxies in the nearby universe. \cite{2013MNRAS.430.1102T} (hereafter T13) carried out a detailed comparison between the UFOs and the WAs and conclude that possibly both the types of ionised outflows belong to a single extended stratified ouflow. They also suggest that the UFOs may be launched from the innermost parts of the accretion disk. \subsection{Motivation of our study} Our study aims at characterising the properties of warm absorbing gas in a well defined, flux-limited sample of nearby AGN. At variance with most of the studies discussed in Sect.~\ref{sect_previousstudies}, we apply a homogeneous data reduction and analysis procedure on all the sources in our sample, use simultaneous UV and X-ray measurements to obtain the Spectral Energy Distribution (SED) of each object, employ state-of-the-art photoionisation codes to model the spectra of the warm absorbing gas, and fit simultaneously CCD spectra in the broad 0.3--10~keV energy band and high-resolution grating spectra in the 0.4--2~keV energy band to achieve a self-consistent astrophysical description of the spectra. We made use of data obtained with the XMM-Newton satellite \citep{2001A&A...365L...1J}. For each source we could combine the large collecting area of the XMM-Newton optics, the high quantum efficiency of the EPIC-pn \citep{2001A&A...365L..18S}, the high resolution RGS \citep{2001A&A...365L...7D} detectors, and the simultaneous optical photometry obtained with the Optical Monitor \citep{2001A&A...365L..36M}. This broadband coverage allowed us to self-consistently calculate the SED of each object at the same time as the warm absorber was studied. The WAX-AGN ({\it warm absorbers in X-ray AGN}, WAX hereafter) project aims at addressing the following important questions: \begin{enumerate} \item How fundamental are ionised outflows in AGN? \item What are the distribution of warm absorber properties (column density, ionisation parameter, outflow velocity, launching radius) in the parent population of nearby Seyfert galaxies ? \item What is the outflow acceleration mechanism? \item Do ionised outflows play an important role on the host galaxy chemical history and evolution? \end{enumerate} \noindent The first two questions are specifically addressed in this paper. The paper is organised as follows: Section~\ref{sect_sample} deals with the sample selection. Section~\ref{sect_data} describes the data reprocessing and spectral extraction which involves the data from all the three types of instruments aboard {\it XMM-Newton}. Sections~\ref{sect_epic}, \ref{subsec-CLOUDY} and ~\ref{section:RGS-analysis} describe the spectral analysis. Sections.~\ref{sect_results} and~\ref{sect_discussion} discusses the results, which is followed by summary and conclusion. | In this paper we analyse for the first time a hard X-ray flux-limited sample of nearby Seyfert galaxies, using broad-band EPIC-pn and high resolution RGS X-ray data. The primary goals of our study are: a) to estimate the incident rate of ionised outflows in nearby, X-ray bright Seyfert galaxies; b) To constrain their acceleration mechanism; and c) their relation with high-velocity UFOs. The main conclusions of the paper are: \begin{itemize} \item WA do not appear ubiquitously in our sample. {\color{black} The detection fraction of WA in the WAX parent population is constrained between $65-90\%$. However we could put a strict lower limit on the detection fraction $\sim 50\%$ which indicates that at least half of all the Seyfert galaxies in the nearby Universe exhibits warm ionised outflows.} \item {\color{black}We find a gap in the distribution of the ionisation parameter in the range $0.5<\log\xi<1.5$ which we interpret as a thermally unstable region for WA clouds. This may point towards discrete and clumpy configuration of WA clouds as against a continuous medium.} \item WA parameters ($\xi$, $\nh$ and $v_{\rm out}$) do not show any significant correlation between themselves except for $\log\xi$, $\log\nh$. They also do not correlate with any of the X-ray broad band continuum parameters. \item Our results are inconsistent with the correlation between the outflow velocity and the ionisation parameter predicted either by Compton-scattering driven (King 2003, $\xi \propto v_{\rm out}^{0.5}$) or MHD driven (Fuzukawa et al. 2010, $\xi \propto v_{\rm out}$) winds. The linear regression between $\log\xi$ and $\log v_{\rm out}$ on the whole sample is $0.12\pm 0.03$. A similar discrepancy occurs if the independent components of each individual source are separately considered. \item The presence of WA are not related to the presence of relativistic Fe K$\alpha$ features as we find sources without WA but with a broad Fe K$\alpha$ line. The detection of the broad line features in the X-rays are not influenced by the WA modeling. \item The UFOs and the WA may not be the same physical system. The correlations among gas observables obtained in our paper do not extend to the UFO regime. However, given the poor statistical quality of UFO data points, the linear regression line in the UFO parameter space encompasses the WA data points as well. \end{itemize} \begin{table*} {\footnotesize \centering \caption{WAX source basic properties.} \label{basic-info} \begin{tabular}{llllllllllll} \hline\hline No. & Object& Seyfert & V & Redshift & Lum dist & $\rm M_{BH}$ & $\rm N_H^{Gal}$ & \\ & name & type& mag & & (Mpc) & $\rm log(M/ M_{\odot})$ & $\times 10^{20} \cmsqi$ & \\ \hline \\ 1.& NGC4593 & 1 & 11.67 & 0.009 & 42.0 & 6.77 & 1.9 \\ \\ 2.& MRK 704 & 1.2 & 15.38 & 0.029 & 127.2 & 7.62 & 2.9 \\ \\ 3.& ESO511-G030 & 1 & 13.30 & 0.022& 97.0 & 8.4 & 4.69 \\ \\ 4.& NGC 7213 & 1.5 & 11.01 & 0.0058 & 21.2 & 8.3 & 1.06 \\ \\ 5.& AKN 564 & LINER & 14.55 & 0.024 & 98.6 & 6.7 & 5.34 \\ \\ 6.& MRK 110 & 1 & 15.6 & 0.035 & 151 & 7.4 & 1.30 \\ \\ 7.& ESO198-G024 & 1 & 15.36 & 0.045 & 192 & 8.1 & 2.93 \\ \\ 8.& Fairall-9 & 1 & 13.5 & 0.047 & 199 & 8.6 & 3.16 \\ \\ 19.& UGC 3973 & 1.5 & 13.9 & 0.022 & 94.4 & 8.1 & 5.27 \\ \\ 10.& NGC 4051 & 1.5 & 10.83 & 0.002 & 12.7 & 6.3 & 1.32 & \\ \\ 11.& MCG-2-58-22 & 1.5 & 14.6 & 0.046 & 194 & 7.36 & 2.91 \\ \\ 12.& NGC 7469 & 1.2 & 13.0 & 0.016 & 62.7 & 7.1 & 4.45\\ \\ 13.& MRK 766 & 1.5 & 13.7 & 0.0129& 57.7 & 7.5 & 1.71 \\ \\ 14.& MRK 590 & 1.2 & 13.85 & 0.026 & 107 & 8.6 & 2.65 \\ \\ 15.& IRAS05078+1626 & 1.5 & 15.6&0.017& 74.3 & 7.86 & 2.20 \\ \\ 16.& NGC3227 & 1.5 & 11.1 & 0.003 & 20.4 & 7.4 & 2.15 \\ \\ 17.& MR2251-178 & 1 & 14.36& 0.063& 271 & 8.5 & 2.42 \\ \\ 18.& MRK 279 & 1.5 & 14.57& 0.030 & 129 & 7.5 & 1.52 \\ \\ 19.& ARK 120 & 1 & 15.3& 0.032 & 138 & 8.4 & 9.78 \\ \\ 20.& MCG+8-11-11& BLSY & 15 & 0.02 &85.8 & 8.48 & 1.84 \\ \\ 21.& MCG-6-30-15 & 1.5 & 13.7& 0.007 &35.8 & 7.0 & 3.92 \\ \\ 22.& MRK 509 & 1.2 & 3.0 & 0.034 & 141 & 8.3 & 4.25 \\ \\ 23.& NGC 3516 & 1.5 & 12.5 & 0.008 & 37.5 & 7.7 & 3.45 \\ \\ 24.& NGC 5548 & 1.5 & 13.3 & 0.017 &74.5 & 8.1 & 1.55 \\ \\ 25.& NGC 3783 & 1 & 12.64 &0.009 & 44.7 & 7.8 & 9.91 \\ \\ 26.& IC 4329A & 1.2 & 14.0 & 0.016 & 70.6 & 8.2 & 4.61 \\ \\ \hline \hline \end{tabular} \\ \footnotetext{1} { The blackhole masses are obtained from \cite{2010A&A...524A..50D} and \cite{2012ApJ...745..107W}. The Redshift, V band magnitude, Luminosity distance, Seyfert classification are obtained from NED. The $\rm N_H^{Gal}$ are obtained from HEASARC.}\\ {The source identification numbers listed in column one are uniformly used in all places throughout this paper.}\\ } \end{table*} \begin{table*} {\footnotesize \centering \caption[abc]{XMM-Newton observations of WAX sources.} \label{obs-info} \begin{tabular}{llllllllllll} \hline\hline No. & Object&Obs & Date & Total & RA & Dec \\ & name &id & of obs& exposure& (Degrees)& (Degrees) \\ & & & (DD-MM-YY) & (Ks) & \\ & & & & \\ \hline \\ 1.& NGC4593 & 0109970101 & 02-07-2000 & 28 & 189.914&$-5.344$ \\ \\ 2.& MRK 704 & 0502091601 & 03-05-2008 & 98 & 139.608 &16.305 \\ \\ 3.& ESO511-G030 & 0502090201 & 05-08-2007 & 112 & 214.843 & --26.644\\ \\ 4.& NGC 7213 & 0605800301 & 11-11-2009 & 132 & 332.317 & --47.166 \\ \\ 5.& AKN 564 & 0206400101 & 05-01-2005 & 101 & 340.663 & 29.725 \\ \\ 6.& MRK 110 &0502090201 & 15-11-2004 & 47 & 141.303& 52.286 \\ \\ 7.& ESO198-G024 & 0305370101 & 04-02-2006 & 122 & 39.581& --52.192 \\ \\ 8.& Fairall-9 & 0605800401 & 09-12-2009 & 130 & 20.940 & --58.805 \\ \\ 9.& UGC 3973 & 0502091001 & 26-04-2008 & 89 & 115.636 & 49.809 \\ \\ 10.& NGC 4051 &0109141401 & 16-05-2001 & 122 & 180.790 & 44.531 \\ \\ 11.& MCG-2-58-22 & 0109130701 & 01-12-2002 & 20 &346.181 & --8.685 \\ \\ 12.& NGC 7469 & 0112170101 & 30-11-2000 & 18 & 345.815 & 8.874 \\ \\ 13.& MRK 766 & 0109141301 & 20-05-2001 & 130 & 184.610 & 29.812 \\ \\ 14.& MRK 590 & 0201020201 & 04-07-2004 & 112 & 33.639 & --0.766 \\ \\ 15.& IRAS05078+1626 & 0502090501 & 21-08-2007 & 61 & 77.689 & 16.498 \\ \\ 16.& NGC3227 & 0400270101 & 03-12-2006 & 107 & 155.877 & 19.865 \\ \\ 17.& MR2251-178 & 0012940101 & 18-05-2002 & 65 & 343.524 & --17.581 \\ \\ 18.& MRK 279 & 0302480401 & 15-11-2005 & 60 & 208.264 & 69.308 \\ \\ 19.& ARK 120 & 0147190101 & 24-08-2003 & 112 & 79.047 & --0.149 \\ \\ 20.& MCG+8-11-1 & 0201930201 & 09-04-2004 & 38 & 88.723 &46.439 \\ \\ 21.& MCG-6-30-15& 0029740701 & 08-02-2001 & 130 & 203.973 & --34.295 \\ \\ 22.& MRK 509 & 0306090201 & 19-10-2005 & 86 & 311.040 &--10.723 \\ \\ 23.& NGC 3516 & 0107460701 & 09-11-2001 & 130 &166.697 & 72.568 \\ \\ 24.& NGC 5548 & 0089960301 & 09-07-2001 & 96 & 214.498 & 25.136 \\ \\ 25.& NGC 3783 & 0112210501 & 19-12-2001 & 138 & 174.757 & --37.738 \\ \\ 26.& IC 4329A & 0147440101 & 06-08-2003 & 136 & 207.330 & --30.309 \\ \\ \hline \hline \end{tabular} \\ \footnotetext{1}{Obtained from Heasarc and XSA}. \footnotetext{2}{}. } \end{table*} \begin{table*} {\footnotesize \centering \caption{The Optical Monitor data and relevant parameters. The fourth column is the observed flux in the optical-UV bands, simultaneously observed with the X-ray data, using the OM camera. The sixth column lists the extinction corrected flux.\label{OM}} \begin{tabular}{llllllllllll} \hline\hline No. & Object & Filter$^1$ & Flux observed & $\rm ^{2}A_{\lambda}$ & Corrected flux & $\rm ^{3}kT_{diskbb}$ & \\ & name & used & { $10^{-15}$ $\funit\AA^{-1}$} & Galactic & { $10^{-15}$ $\funit\AA^{-1}$} & $(\ev)$\\ & & & & extinction & & \\ \hline 1. & NGC4593 & UVW2 & 9.99 & 0.191 & 11.91 & 26.42 \\ \\ 2. & MRK 704 & UVW1 & 7.3 & 0.150 & 8.3 & 16.20 \\ \\ 3. & ESO511-G030 & UVW2 & 14.58 & $0.533$ & 23.8 & 10.34 \\ \\ 4. & NGC 7213 & UVW1 & 6.5 & 0.079 & 6.99 & 10.95 \\ \\ 5. & AKN 564 & UVW1 & 7.06 & 0.312 & 9.4 & 27.51\\ \\ 6. & MRK 110 & UVW2 & 25 & 0.100 & 27.4 & 18.38 \\ \\ 7. & ESO198-G024 & UVM2 & 5.06 & 0.270 & 6.49 & 12.3 \\ \\ 8. & Fairall-9 & UVW1 & 17.74 & 0.141 & 20.20 & 9.21 \\ \\ 9. & UGC 3973 & UVW2 & 9.9 & 0.549 & 16.4 & 12.29\\ \\ 10. & NGC 4051 & UVW2 & 15.2 & 0.101 & 16.6 & 34.63 \\ \\ 11. & MCG-2-58-22 & UVW1 & 6.3 & 0.218 & 7.7 & 18.81 \\ \\ 12. & NGC 7469 & UVW2 & 33.5 & 0.535 & 54.8 & 21.85\\ \\ 13. & MRK 766 & UVW2 & 0.132 & 0.152 & { 0.151} & 17.36 \\ \\ 14. & MRK 590 & UVW2 & 1.56 & 0.290 & { 2.03 } & 9.21 \\ \\ 15. & IRAS05078+1626 & UVW2 & 0.32 & 2.36 &{ 2.7} & 14.11 \\ \\ 16. & NGC3227 & UVW1 & 9.0 & 0.118 & 10.0 & 18.38 \\ \\ 17. & MR2251-178 & UVW2 & 8.05 & 0.303 & 10.6 & 9.76\\ \\ 18.& MRK 279 & UVW2 & 24.32 & 0.123 & 26 & 17.36 \\ \\ 19.& ARK 120 & UVW2 & 35.8 & 0.996 & 89.6 & 10.34 \\ \\ 20.& MCG+8-11-11 & UVW1 & 8.02 & 1.136 & 22.8 & 9.87 \\ \\ 21.& MCG-6-30-15 & U Band & 0.38 & 0.267 & { 0.478 } & 23.15 \\ \\ 22.& MRK 509 & UVW2 & 38 & 0.446 & 57.3 & 10.95 \\ \\ 23.& NGC 3516 & UVW2 & 19.1 & 0.329 & 25.8 & 15.47 \\ \\ 24.& NGC 5548 & U BAND & 13.1 & 0.088 &14.2 & 12.29 \\ \\ 25.& NGC 3783 & UVW2 & 26.15 & 0.925 & 61.3 & 14.60 \\ \\ 26.& IC 4329A & UVW1 & 1.38 & 0.459 & { 2.1} & 11.60 \\ \\ \hline \hline \end{tabular} \\ {$^1$ U Band- $\rm 3440 \AA$, UVW1- $\rm 2910 \AA$, UVM2- $\rm 2310\AA$, UVW2- $\rm 2120 \AA$.}\\ {$^2$ $\rm A_{\lambda}$ is the Galactic extinction correction magnitude.}\\ {$^3$ $\rm kT_e$ is the blackbody temperature of the accretion disk emission as calculated in Section \ref{real-cont}}\\ } \end{table*} \begin{table*} {\footnotesize \centering \caption{The $2-10 \kev$ EPIC-pn continuum parameters. \label{2-10}} \begin{tabular}{l l l l llllllllll} \hline\hline No. &Source & $\Gamma$ &Fe K & Fe K & Fe K & $\frac{\chi^2}{\rm dof}$\\ & & &norm & Line centroid energy ($\kev$) & Line width $\sigma$($\ev$)& \\ & & & ($10^{-5}$)& \\ \hline\\ \\ 1. &NGC4593 & $1.76_{-0.02}^{+0.03}$ & $4.16_{-0.90}^{+1.10}$ & $6.38_{-0.01}^{+0.03}$& $\le 48$ & $\frac{178}{188}$\\ \\ 2.& MRK 704 & $1.76_{-0.02}^{+0.03}$ & $1.91_{-0.20}^{+0.31}$ & $6.39_{-0.05}^{+0.10}$ & $137_{-47}^{+50}$ & $\frac{173}{197}$\\ \\ 3.&ESO511~G030 &$1.78_{-0.01}^{+0.02}$ & $1.9_{-0.3}^{+0.2}$ & $6.33_{-0.05}^{+0.06}$& $360_{-90}^{+110} $ &$\frac{293}{200}$\\ \\ 4.& NGC 7213 & $1.69_{-0.01}^{+0.02}$ & $1.59_{-0.41}^{+0.41}$ & $6.39_{-0.02}^{+0.01}$& $ \le 60$ & $\frac{243}{193}$\\ & & & $1.62_{-0.5}^{+0.6}$ & $6.80_{-0.07}^{+0.08}$ & $ 210_{-80}^{+90}$ \\ \\ 5. &AKN564 & $2.47_{-0.02}^{+0.02}$ & $8.0_{-2.0}^{+2.0}$ & $6.93_{-0.05}^{+0.03}$& $\le 20$ & $\frac{214}{199}$\\ \\ 6.&MRK110 & $1.75_{-0.01}^{+0.02}$ & $2.13_{-0.6}^{+0.5}$ & $6.23_{-0.04}^{+0.04}$& $100_{-30}^{+80} $ &$\frac{238}{197}$\\ \\ 7.& ESO198-G24 & $1.67_{-0.02}^{+0.02}$ & $1.5_{-0.3}^{+0.4}$ & $6.42_{-0.03}^{+0.04}$& $130_{-50}^{+50}$ & $\frac{229}{199}$\\ & & & $4.07_{-1.61}^{+1.71}$ & $7.08_{-0.03}^{+0.05}$ & $ \le 10$ \\ \\ 8.& Fairall 9& $1.68_{-0.01}^{+0.01}$ & $14.0\pm 1.0$ & $6.42_{-0.01}^{+0.02}$& $120_{-20}^{+30}$ & $\frac{473}{314}$\\ & & & $3.15_{-0.8}^{+0.6}$ & $7.05_{-0.06}^{+0.02}$ & $ 10$ \\ \\ 9.&UGC3973 & $1.04_{-0.02}^{+0.03}$ & $3.39_{-0.4}^{+0.6}$ & $6.37_{-0.02}^{+0.01}$& $110_{-30}^{+40} $ &$\frac{277}{187}$\\ \\ 10. &NGC4051 & $1.88_{-0.02}^{+0.04}$ & $1.53_{-0.15}^{+0.15}$ &$6.37_{-0.01}^{+0.03}$ & $\le 20$ &$\frac{219}{194}$ \\ & & & $4.5_{-0.51}^{+0.81}$ &$6.62_{-0.60}^{+0.21}$& $85$ & \\ \\ 11.& MCG-2-58-22 & $1.70_{-0.04}^{+0.03}$ & $5.5_{-3.0}^{+3.0}$ & $6.41_{-0.21}^{+0.17}$& $300_{-17}^{+21} $ &$\frac{177}{165}$\\ \\ 12.& NGC7469 & $1.87_{-0.02}^{+0.02}$ & $2.9_{-0.3}^{+0.5}$ & $6.41_{-0.01}^{+0.01}$& $ 60 \pm 20$ & $\frac{260}{200}$\\ & & & $1.12_{-0.41}^{+0.31}$ & $7.00_{-0.01}^{+0.02}$ & $\le 20$ \\ \\ 13.&MRK766 & $2.066_{-0.02}^{+0.03}$ & $4.53_{-1.21}^{+1.31}$ & $6.53_{-0.11}^{+0.07}$& $380_{-100}^{+150}$ & $\frac{255}{199}$\\ \\ 14. &MRK590 & $1.59_{-0.05}^{+0.04}$ & $1.14_{-0.41}^{+0.41}$ & $6.41_{-0.04}^{+0.05}$& $270_{-40}^{+50} $ &$\frac{151}{172}$\\ \\ 15.& IRAS050278 & $1.53_{-0.01}^{+0.01}$ & $3.45_{-0.65}^{+0.55}$ & $6.39_{-0.02}^{+0.03}$& $ 100_{-40}^{+50}$ &$\frac{201}{199}$\\ \\ 16. &NGC3227 & $1.52_{-0.01}^{+0.01}$ & $3.9_{-0.4}^{+0.6}$ & $6.41_{-0.01}^{+0.02}$& $ 60\pm 20$ &$\frac{254}{202}$\\ \\ 17.& MR2251-178& $1.41_{-0.01}^{+0.03}$ & $1.25_{-0.50}^{+0.50}$ & $6.38_{-0.02}^{+0.04}$& $\le 128 $ &$\frac{186}{197}$\\ \\ 18.& MRK279 & $1.80_{-0.01}^{+0.02}$& $3.0_{-0.41}^{+0.31}$ & $6.43_{-0.02}^{+0.01}$ & $70 \pm 20$ & $\frac{250}{200}$\\ & & & $0.73_{-0.21}^{+0.21}$ & $6.99_{-0.03}^{+0.06}$ & $\le 20$ \\ \\ 19.& ARK 120 & $1.95_{-0.02}^{+0.03}$ & $4.7_{-0.9}^{+1.2}$ & $6.39_{-0.03}^{+0.03}$& $150_{-50}^{+50}$ & $\frac{339}{199}$\\ & & & $90_{-10}^{+20}$ & $7_{-0.5}^{+0.01}$ & $ 1000$ && . \\ \\ \hline \hline \end{tabular} \\ } \end{table*} \begin{table*} \centering {\bf Table \ref{2-10} continued} \begin{center} \begin{tabular}{llllllllllllll} \hline No. &Source & $\Gamma$ &Fe K & Fe K & Fe K & $\cd$\\ & & &norm & Line centroid energy ($\kev$) & Line width $\sigma$($\ev$)& \\ & & & ($10^{-5}$)& \\ \hline\\ \\ 20.& MCG+8-11-11& $1.64_{-0.01}^{+0.01}$ & $5.5_{-0.7}^{+0.6}$ & $6.40_{-0.01}^{+0.02}$& $70_{-30}^{+20} $ &$\frac{199}{196}$\\ \\ 21.&MCG-6-30-15 & $1.85_{-0.01}^{+0.01}$ & $7.6_{-0.8}^{+1.2}$ & $6.02_{-0.05}^{+0.08}$& $470$ & $\frac{538}{200}$\\ & & & $1.32_{-0.51}^{+0.31}$ & $6.39_{-0.05}^{+0.04}$ & $\le 20$ \\ \\ 22. &MRK509 & $1.83_{-0.01}^{+0.01}$ & $3.3_{-0.5}^{+0.45}$ & $6.39_{-0.01}^{+0.04}$& $\le 20$ & $\frac{378}{199}$\\ & & & $0.89_{-0.10}^{+0.15}$ & $7.10_{-0.01}^{+0.03}$ & $\le 20$ \\ \\ 23.& NGC 3516 & $0.94_{-0.02}^{+0.02}$ &$0.89_{-0.1}^{+0.2}$ & $6.84_{-0.05}^{+0.03}$ & $ <100$ & $\frac{930}{197}$ \\ \\ 24.& NGC5548 & $1.63_{-0.01}^{+0.03}$ & $3.2_{-0.6}^{+0.6}$ & $6.39_{-0.03}^{+0.03}$& $90_{-40}^{+50} $ &$\frac{187}{201}$\\ \\ 25.&NGC3783 & $1.47_{-0.01}^{+0.01}$ & $7.3_{-0.41}^{+0.31}$ & $6.38_{-0.01}^{+0.01}$& $53 \pm 10$ & $\frac{1071}{314}$\\ & & & $1.56_{-0.22}^{+0.22}$ & $7.02_{-0.01}^{+0.03}$ & $\le 20$ \\ \\ 26.& IC4329A & $1.63_{-0.01}^{+0.02}$ & $5.3_{-0.4}^{+0.8}$ & $6.40_{-0.02}^{+0.01}$& $ \le 50$ & $\frac{276}{200}$\\ & & & $9.2_{-1.6}^{+0.8}$ & $6.52_{-0.07}^{+0.07}$ & $ 450 \pm 70$ \\ \\ \hline \hline \end{tabular} \\ \end{center} \end{table*} \begin{table*} {\footnotesize \centering \caption{The $0.3-10 \kev$ best fit parameters obtained using the EPIC-pn data.} \begin{tabular}{l l l l llllllllll} \hline\hline \label{EPIC-pn} No. &Source & EPIC-pn & $^1$zwabs &$\Gamma$ &Fe K & Fe K & $^3\rm kT_{BB}$ & $^4\rm kT_{BB}$& $^5$Reflection & $\cd$\\ & & counts & ($\nh$) & ¢roid energy& $^2$Eqw & & & (R) & \\ & &($10^5$) & ($10^{20}\cmsqi$) & & ($\kev$) & ($\ev$) &($\ev)$ & ($\ev$) \\ \hline\\ \\ 1. &NGC4593 & $2.74$& ---&$1.74_{-0.08}^{+0.07}$ & --- & --- & $86_{-1}^{+4}$ & $268_{-20}^{+30}$ & $0.44^{+0.21}_{-0.31}$ & $\frac{231}{241}$ \\ \\ 2.& MRK 704 & $5.54$ & --- & $1.86_{-0.03}^{+0.03}$& $6.39\pm 0.07$ & $ 79\pm 12.4$ & $89_{-5}^{+5}$ & $251\pm 20$ & $0.39\pm 0.21 $& $\frac{226}{244}$ \\ \\ 3.&ESO511G030 & $10$ & --- & $2.10 \pm 0.02$ & $--$ & & $53_{-3}^{+2}$ & $ 111_{-15}^{+13}$&$2.25_{-0.22}^{+0.32}$ & $\frac{268}{254}$ \\ \\ 4.& NGC 7213 & $5.06$ & --- & $1.69\pm 0.03$ & $6.80_{-0.08}^{+0.07}$ & $ 113\pm 42.3$ & $62_{-8}^{+8}$ & $177_{-8}^{+9}$ & $0.34_{-0.22}^{+0.12}$ &$\frac{284}{242}$ \\ \\ 5. &AKN564 & $27.1$ & $<0.4$ &$2.49 \pm 0.02$ & $6.93\pm 0.04$ & $64\pm16$ & $66\pm 2$ & $149\pm 5$ & $0.15_{-0.13}^{+0.08}$& $\frac{317}{244}$ \\ \\ 6.&MRK110 & $7.0$ & --- & $1.92\pm 0.03$ & $6.23\pm 0.04$ & $70\pm 16.4$ &$ 62\pm 5$ & $140\pm 8$ & $1.07_{-0.31}^{+0.32}$ &$\frac{317}{253}$ \\ \\ 7.& ESO198-G24 & $4.05$ & --- & $1.79\pm 0.02$ & ---& ---& $149_{-5}^{+7}$& --- & ${1.13\pm 0.21}$ & $\frac{265}{252}$ \\ \\ 8.& Fairall 9 & $10$ & --- & $1.92\pm 0.04$ & $6.42\pm 0.02$ & $138\pm10$ & $74_{-3}^{+3}$ &$164\pm 9$ & $4_{+1}^{-3}$& $\frac{311}{255}$ \\ & & & & & $6.97_{-0.06}^{+0.02}$ & $48\pm 9.1$ \\ \\ 9.&UGC3973 &$1.11$ &--- & $1.15\pm 0.04$ & ---& & $102\pm 5$ & $225\pm 10$ & $0.4_{-0.4}^{+0.3}$ &$\frac{290}{236}$ \\ \\ 10. &NGC4051& 18 & ---& $2.35_{-0.01}^{+0.04}$ & $---$ & & $101_{-3}^{+3}$ &---& $\sim 5$ & $\frac{315}{250}$ \\ \\ 11.& MCG-2-58-22& $1.0$& --- & $1.76_{-0.04}^{ +0.04}$& $6.41\pm0.22$ & $ 40\pm24$ & $111_{-6}^{+7}$ & --- & $<0.46$ & $\frac{254}{225}$\\ \\ 12.& NGC7469 & $12$ & --- & $1.99_{-0.07}^{+0.07}$ &$6.97\pm 0.02$ & $33\pm8.8$ & $94_{-4}^{+1}$ & $234_{-19}^{+10}$ & $1.17_{-0.41}^{+0.42}$ & $\frac{324}{255}$ \\ \\ 13.&MRK766 & $18.9$ & ---&$ 2.08_{-0.01}^{+0.02}$ & $6.58\pm0.07$ & $166\pm 47.6$& $71_{-4}^{+3}$ & $257_{-6}^{+6}$ & $<0.2$ & $\frac{305}{244}$ \\ \\ 14. &MRK590 & $0.9$ & ---&$1.76_{-0.03}^{+0.03}$ & --- & --- & $13_{-1}^{+1}$ & --- & $1.65_{-0.52}^{+0.52}$ & $\frac{231}{231}$ \\ \\ 15.& IRAS050278 & $2.5$ & $21.9_{-0.8}^{+0.7}$ & $1.77\pm 0.02$ & $6.39\pm0.02$ & $64\pm 10.2$ & $67 \pm 5$ & ---&$4.5\pm1.2$ & $\frac{246}{254}$\\ & +1626 & \\ \\ 16. & NGC3227 & $11.5$& $10.0_{-0.9}^{+1}$ & $1.57_{-0.07}^{+0.03}$ & --- & & $55_{-2}^{+2}$ & --- & $<0.08$ & $\frac{360}{248}$ \\ \\ 17.& MR2251-178 & $2.5$ & --- & $1.43_{-0.03}^{+0.02}$ & $6.37\pm0.03$ & $34\pm13.6$ & --- & --- & $<0.1$ & $\frac{295}{245}$ \\ \\ 18.& MRK279 & $26$ & --- & $1.93\pm 0.02$ & $6.5\pm0.02$ & $42\pm4.2$ & $84 \pm 1$ & $222_{-7}^{+6}$& $3_{-0.9}^{+1.5}$ & $\frac{276}{256}$ \\ & & & & & $6.95\pm 0.02$ & $15 \pm5.1$ & \\ \\ 19.& ARK 120 & $17$ & --- & $ 1.97_{-0.03}^{+0.02}$ & ---& & $102\pm 2$ & $240\pm 4$ & $0.75_{-0.11}^{+0.22}$& $\frac{314}{253}$ \\ \\ \hline \hline \end{tabular} \\ } {\begin{flushleft} $^{1}${The intrinsic neutral absorption by the host galaxy}\\ $^2$The equivalent width of the Fe K emission line.\\ $^{3\, \&\, 4}$ The best fit blackbody temperatures.\\ $^5$ The Neutral reflection coefficient as defined in section \ref{sect_epic}.\\ \end{flushleft} } \end{table*} \begin{table*} \centering {\bf Table \ref{EPIC-pn} continued} \begin{center} \begin{tabular}{llllllllllllll} \hline No. &Source & EPIC-pn & $^1$zwabs &$\Gamma$ &Fe K & Fe K & $^3\rm kT_{BB}$ & $^4\rm kT_{BB}$& $^5$Reflection & $\cd$\\ & & counts & ($\nh$) & ¢roid energy& $^2$Eqw & & & (R) & \\ & &($10^5$) & ($10^{20}\cmsqi$) & & ($\kev$) & ($\ev$) &($\ev)$ & ($\ev$) \\ \hline\\ \\ 20.& MCG+8-11-11 & $2.91$ & $18.0_{-1.0}^{+0.7}$ & $1.68\pm 0.03$ & $6.99\pm 0.009$ & $32\pm 3$& $268_{-16}^{+19}$ &---& $<0.64$ & $\frac{240}{249}$ \\ \\ 21.&MCG-6-30-15& $ 17.9$& $2.2\pm 2.1$ &$2.0\pm 0.02$ & $7.05\pm 0.05$ & $30\pm6.8$ & $89\pm 2$& $277_{-11}^{+9}$ & $<5$ & $\frac{365}{237}$ \\ & & & & & & \\ \\ 22. &MRK509 & $15.2$& ---& $ 2.13_{-0.02}^{+0.03}$ & --- & & $79_{-2}^{+2}$& $161_{-7}^{+9}$ & $2.3_{-0.3}^{+0.5}$ & $\frac{342}{253}$\\ \\ 23.& NGC 3516 & & --- & $1.00_{-0.06}^{+0.07}$& $6.4\pm 0.005$& $185\pm 10$ & $46\pm 12$ & --- & $<0.1$& $\frac{302}{247}$ \\ & & & & & \\ \\ 24.& NGC5548 & $11.6$ & --- & $1.65\pm 0.02$ & --- & --- & $87_{-1}^{+2}$ & $313_{-7}^{+16}$ & $<0.03$& $\frac{261}{245}$ \\ \\ 25.&NGC3783 & $20$& --& $1.80 \pm 0.04$ & --- & & $102_{-1}^{+3}$ & --- & $1.0_{-0.2}^{+0.3}$ & $\frac{433}{242}$ \\ & & & & & $6.3\pm 0.02$ & $27\pm3.6$ & \\ & & & & & $6.98\pm 0.03$ & $20\pm 4$ \\ \\ 26.& IC4329A & $23.3$ &$38_{-1}^{+1}$ & $ 1.80\pm 0.04$ & $6.87\pm 0.02$ & $32\pm4.8$ & $46_{-1}^{+4}$ & $286\pm 10$ & $1.67_{-0.12}^{+0.05}$ & $\frac{298}{247}$ \\ &&&&& & \\ \\ \hline \hline \end{tabular} \\ \end{center} {\begin{flushleft} $^{1}${The intrinsic neutral absorption by the host galaxy}\\ $^2$The equivalent width of the Fe K emission line.\\ $^{3\, \&\, 4}$ The best fit blackbody temperatures.\\ $^5$ The Neutral reflection coefficient as defined in section \ref{sect_epic}.\\ \end{flushleft} } \end{table*} \begin{table*} {\footnotesize \centering \caption{The WA and narrow warm emission (WE) line parameters from combined fit of the EPIC-pn and the RGS data.} \label{RGS-table} \begin{tabular}{l l l l llllll} \hline\hline No.& Source & RGS & WE line & WE line & WA & WA-$\rm log(\nh)$&WA-velocity & $\Delta C$\\ & & Counts & centroid Energy & norm & $\rm log(\xi/\xiunit)$ & & & \\ & & ($10^3$) & ($\kev$) & ($10^{-4})$ & & & $\kms$ \\\hline \\ 1.& NGC4593 & $8.714$ & $0.652\pm 0.01$ & $8.64_{-1.74}^{+1.22}$ & $2.37_{0.10}^{+0.82}$ & $20.93_{-0.11}^{+0.21}$ & $-510_{-30}^{+180}$ & -23 \\ & & & & & $3.24_{-0.10}^{+0.11}$ & $21.55^{+0.03}_{-0.09}$ & $300_{-300}^{+300}$ & -42 \\ \\ 2. & MRK 704 & $ 28.39 $ &$0.569\pm 0.003$ & $1.6_{-0.11}^{+0.05}$ & $ 0.25_{-0.51}^{+0.41}$ & $20.3_{-0.12}^{+0.81}$ & $-1500_{-300}^{+240}$ & -55\\ & & & & & $ 2.31_{-0.15}^{+0.15}$ & $21.34_{-0.11}^{+0.11}$ & $-660_{-30}^{+30}$ & -45\\ & & & & &$3.13_{-0.51}^{+0.41}$ & $21.33_{-0.11}^{+0.12}$ & $ -3540_{-90}^{+150}$ & -53 \\ \\ 3.&ESO511~G030 & $ 62.45$ &$0.547\pm 0.002$ & $0.39_{-0.13}^{+0.17}$ & {$ \ge 3.9$} & { $<20$} &--- & --- \\ & & &$0.560\pm 0.002$ & $0.63_{-2.0}^{+2.4}$ & \\ & & &$0.572\pm 0.003$ & $0.87_{-0.27}^{+0.13}$ & \\ \\ 4.& NGC 7213 & $30.91$ & --- & --- & { $<-0.75$} & { $ <20$} & --- & --- \\ \\ 5.& AKN 564 & $161$ &$0.468\pm 0.001$ &$<0.41$ & $-0.20_{-0.12}^{+0.21}$ & $20.31_{-0.21}^{+0.21}$ &$ -690_{-90}^{+150}$ & -163\\ & & &$0.556\pm 0.001$ & $2.05_{-0.40}^{+0.40}$ & \\ & & &$0.672\pm 0.003$ & $1.4_{-0.1}^{+0.3}$ & \\ \\ 6.& MRK 110 & $40.6$ & $0.558\pm 0.004$ & $3.73_{-0.61}^{+0.12}$ &{$>3.5$} & {$<20.2$} & --- & --- \\ \\ 7.& ESO198-G24 & $27$ & $0.523\pm 0.003$ & 0 & { $1.2< \log\xi <1.93 $} & { $<20$} & --- & --- \\ \\ 8.& Fairall 9& $41$ & $0.945_{-0.03}^{+0.028}$ & $3.07_{-1.31}^{+1.22}$ &{ $-1< \log\xi <4 $} & { $18.8< \log\nh <22.7 $} & --- & --- \\ \\ 9.&UGC3973 & $7.44$& $0.579\pm 0.002$ & $1.7_{-0.21}^{+0.21}$ & $2.04_{-0.23}^{+0.57}$ & $21.29_{-0.06}^{+0.14}$ & $<-2400$ & -93\\ & & & \\ \\ 10.& NGC 4051 & $111.3$& $0.561_{-0.002}^{+0.001}$ & $1.49\pm0.33$ & $ 0.28_{-0.12}^{+0.12}$ &$20.43_{-0.21}^{+0.04}$ & $-600_{-30}^{+30}$ & -161 \\ & & & $0.597_{-0.001}^{+0.001}$ & $1.04_{-0.04}^{+0.5}$ & $2.87_{-0.21}^{+0.12} $ & $22.39_{-0.22}^{+0.22} $ & $-688_{-30}^{+30}$ & -458\\ \\ 11.& MCG-2-58-22 & $ 7.40$& --- & --- &{ $-1< \log\xi <4 $} & { $18.8< \log\nh <22.7 $} & ---&--- \\ \\ 12.& NGC 7469 & $ 78.69$ & $0.538\pm 0.2$ & $ 0.45_{-0.36}^{+0.21}$ & $2.8_{-0.1}^{+0.2}$ & $20.96_{-0.15}^{+0.21}$& $-1590_{-90}^{+90}$ & -117\\ & & &$0.554 \pm 0.0001$ & $0.33_{-0.11}^{+0.32}$ \\ & & &$0.672 \pm 0.003$ & $ 0.3_{-0.11}^{+0.12}$ \\ \\ 13.& MRK 766 & $120$ & $0.538_{-0.002}^{+0.006}$ & $ 10\pm 0.2$ & $1.35_{-0.21}^{+0.22}$ & $20.53_{-0.05}^{+0.05}$ & $ -810_{-60}^{+60}$ & -256\\ & & &$0.655\pm 0.001$ & $13.8_{-0.5}^{+0.6}$ & $-0.94_{-0.12}^{+0.15}$ & $20.46_{-0.08}^{+0.07} $ &$-1020_{-30}^{+90}$ & -22 \\ & & & $0.847\pm 0.003$ & $0.44_{-0.07}^{+0.10}$ & $-0.70_{-0.22}^{+0.15}$ & $20.6_{-0.2}^{+0.2} $ & $0_{-120}^{+150} $ & -120 \\ & & &$0.965\pm 0.001$ & $1.5_{-0.2}^{+0.1}$ \\ \\ 14.& MRK 590 & $ 18.8$ & $0.556\pm 0.0001$ & $<0.12$ & { $-1< \log\xi <4 $} & { $18.8< \log\nh <22.7 $} & --- & --- \\ \\ 15.& IRAS050278& $10.8$ & $0.534\pm 0.0007$ & $2.8_{-1.8}^{+1.7}$ & $-0.47_{-0.21}^{+0.21}$ & $21.16_{-0.15}^{+0.12}$ & $-900_{-30}^{+600}$ &-17 \\ & & & $0.561\pm 0.004$ & $4.2_{-1.0}^{+1.3}$ & $2.18_{-1.01}^{+0.52} $ & $20.66_{-0.31}^{+0.22}$ & $300_{-300}^{+30}$ & -18\\ \\ 16.& NGC 3227 & $41.8$ &$0.564\pm 0.001$ & $3.1_{-0.5}^{+0.6}$ & $ 0.04_{-0.08}^{+0.08}$ & $20.45_{-0.07}^{+0.09}$ & $ <-1290$ & -240\\ & & & $0.584\pm 0.001$ & $ 0.51\pm 0.05$ & $ 2.97_{-0.08}^{+0.12}$ & $21.50_{-0.08}^{+0.11}$ & $ <-2460$ & -32\\ & & &$0.670\pm 0.003$ & $1.8_{-0.2}^{+0.1}$& $2.24_{-0.07}^{+0.07} $ & $21.08_{-0.22}^{+0.22}$ & $<-1377$ & -161\\ \\ 17.& MR2251-178 & $17.29$ &$0.564\pm 0.001$ & $3.02_{-0.5}^{+1}$ & $1.60_{-0.02}^{+0.03}$ & $20.96_{-0.03}^{+0.41}$ & $ -3150_{-30}^{+60}$ & -12\\ & & & & & $2.92_{-0.12}^{+0.51} $ & $21.70_{-0.05}^{+0.21}$ & $-3090_{-1200}^{+210} $ & -185 \\ \\ 18.& MRK 279 & $ 55.3$ &--- & --- &{ $ \ge 3.9$} & { $ <20.0 $} & ---& --- \\ \\ 19.& ARK 120 & $123$ & $0.554\pm 0.001$ & $2.33_{-0.41}^{+0.42}$ & { $ \ge 3.5$} & { $<20.0 $} & --- & --- \\ \hline \hline \end{tabular} \\ } \end{table*} \begin{table*} \centering {\bf Table 6 continued} \begin{center} \begin{tabular}{llllllllllllll} \hline No.& Source & RGS & WE line & WE line & WA & WA-$\rm log(\nh)$&WA-velocity & $\Delta C$\\ & & Counts & centroid Energy & norm & $\rm log(\xi/\xiunit)$ & & & \\ & & ($10^3$) & ($\kev$) & ($10^{-4})$ & & & $\kms$ \\\hline \\ 20.& MCG-8+11+11& $18.7$ &$0.547\pm 0.002$ & $7.9_{-0.6}^{+0.6}$ & $ 3.18_{-0.12}^{+0.12}$ & $21.17_{-0.21}^{+0.22}$ & $-2340_{-30000}^{+900}$& -23 \\ & & &$0.729\pm 0.001$ & $0.19\pm 0.03$ & \\ \\ 21.& MCG-6-30-15& $ 132.1$ &$0.593_{-0.002}^{+0.001}$ & $13.0\pm 2.0$ & $-0.36_{0.05}^{+0.05}$ & $20.55_{-0.15}^{+0.15}$ & $ -870_{-30}^{+150}$ & -116 \\ & & &$0.654\pm 0.001$ & $2.31\pm 0.2$ & $1.25_{-0.15}^{+0.15}$ & $ 20.82\pm 0.03$ & $-450_{-30}^{+90}$ & -187\\ & & &$0.677\pm 0.002$ & $2.4_{-0.25}^{+0.4}$ & $2.53_{-0.05}^{+0.03}$ & $ 21.17\pm 0.05$ & $-2370_{-60}^{+60}$ & -162\\ \\ 22.& MRK 509 & $98$ &$0.562\pm 0.001$ & $2.6\pm 0.2$ & $3.24_{-0.21}^{+0.05}$ & $20.8_{-0.14}^{+0.15}$ & $-6500_{-120}^{+150}$ & -181 \\ & & & $0.598\pm 0.001$ & $0.23\pm 0.08$\\ \\ 23.& NGC 3516 & $16.69$& $0.556\pm 0.001$ & $0.41\pm 0.01$ & $2.69_{-0.14}^{+0.12}$ & $21.37_{-0.05}^{+0.12}$ &$-2280_{-90}^{+252}$ & -230\\ & & &$0.572\pm 0.002$ & $0.39\pm 0.01$ \\ & & &$0.884$ & $<0.04$ \\ \\ 24.& NGC 5548 & $ 89.2$&$0.562\pm 0.0001$ & $1.1\pm 0.2$ & $2.92_{-0.07}^{+0.03}$ & $21.53_{-0.05}^{+0.11}$ & $-3609_{-270}^{+180} $ &-347 \\ & & &$0.664\pm 0.002$& $1.6_{-0.3}^{+0.2}$ & $1.86_{-0.05}^{+0.08} $ & $ 21.13_{-0.07}^{+0.07}$ & $-1236_{-30}^{+42}$ &-836 \\ & & &$0.769\pm 0.001$ & $<0.05$\\ \\ 25.& NGC 3783 & $65.2$ &$0.566\pm 0.001$ & $6.2\pm 1.2$ & $ 1.55_{-0.15}^{+0.15}$ & $21.69_{-0.02}^{+0.03}$ & $-1650_{-60}^{+90}$ & $>1000$\\ & & & $0.824\pm 0.001$ & $0.6\pm 0.02$ & $ 2.91_{-0.02}^{+0.02}$ & $22.18_{-0.08}^{+0.10}$ & $-1635_{-60}^{+120}$ & $>1000$\\ \\ 26.& IC4329A & $ 92.5$&$0.528\pm 0.003$ & $2.5\pm 0.8$ & $-0.58_{-0.11}^{+0.22}$ & $20.96_{-0.31}^{+0.21}$ & $ -1020_{-120}^{+150}$ & -51\\ & & &$0.649\pm 0.005$ & $0.17\pm 0.05$ & $1.87_{-0.21}^{+0.22}$ & $20.54_{-0.08}^{+0.05}$ &$-660_{-120}^{+120}$ & -46\\ & & & & & $ 3.33_{-0.03}^{+0.07}$ & $21.27_{-0.32}^{+0.22}$ & $-990_{-30}^{+120}$ & -235\\ \\ \hline \hline \end{tabular} \\ \end{center} \end{table*} \begin{table*} {\footnotesize \centering \caption{The diskline parameters for the detected broad Fe K$\alpha$ emission lines. \label{diskline}} \begin{tabular}{l l l l llllll} \hline\hline Source & Profile & Line centroid & Eqw &$^1$Betor10 &$^1$ Index & Inclination \\ & (model)& ($\kev$) & $\ev$ & (diskline) & (Laor) & $\theta^{\circ}$ \\\hline \\ ESO~511-G030 & Laor &$6.86_{-0.32}^{+0.11}$ &$294\pm31$ &--- & $6.86_{-1.21}^{+1.22}$ & $59_{-10}^{+10}$\\ \\ UGC~3973 & Diskline & $6.5_{-0.2}^{+0.2}$ &$434\pm43$ & $-3.97_{-0.51}^{+0.71}$ &--- & $19_{-6}^{+6}$ \\ \\ NGC~4051 & Laor &$7_{-0.20}^{+0.01}$ & $461\pm52$ & --- & $7.6\pm 0.3$ & $<41$ \\ \\ NGC~3227 & Diskline &$6.60_{-0.11}^{+0.05}$ & $80\pm 11 $ & $-1.36_{-0.22}^{+0.32}$ & --- & $<5$ \\ \\ ARK~120 & Diskline &$6.9_{-0.10}^{+0.06}$ &$92\pm 10$ & $-3.8^{+0.4}_{-0.4}$ &--- & $<50$\\ \\ MCG-6-30-15 & Diskline & $6.43_{-0.1}^{+0.1}$ & $123 \pm 20$ & $-2.44^{+0.23}_{-0.3}$ &--- & $<10$\\ \\ MRK~509 & Laor &$6.63_{-0.05}^{+0.05}$ &$310 \pm 25$ & --- &$4.53\pm0.32$ & $48_{-20}^{+1}$ \\ \\ NGC~3516 &Laor & $6.4_{-0.1}^{+0.1}$ &$1560\pm 86$ &--- &$4.2_{-0.2}^{+0.2}$ & $50_{-5}^{+2}$\\ \\ NGC~3783 & Laor &$6.4_{-0.1}^{+0.1}$ &$110 \pm 12$ & --- & $3.07_{-0.22}^{+0.21}$& $<11$ \\ \\ IC~4329A & Diskline &$6.30_{-0.05}^{+0.15}$ &$125 \pm 24$ & $-2.19_{-0.21}^{+0.22}$ & --- & $30_{-5}^{+10}$ \\ \\ \hline \hline \end{tabular} \\ } $^1$ The emissivity profiles for the broad emission lines. \end{table*} \begin{table*} {\footnotesize \centering \caption{The fluxes and luminosities of the sources obtained from the broad band spectral analysis.}. \label{Luminosity} \begin{tabular}{l l l l llllll} \hline\hline No.& Source & $\rm F_{2\kev} $ & $\alpha_{OX}$ & $ \rm L_{0.3-10\kev}$&$^1\rm L_{ion}$ & $\rm L_{ion}/L_{Edd}$ & \\ \\ & & $(10^{-12})\funit\, \kev^{-1}$ & & $ \lunit$ & $\lunit$ & \\ \hline\\ \\ 1&NGC4593 & $11.5\pm0.01$ & $0.989\pm 0.01$ & $4.34_{-0.06}^{+0.06}\times 10^{42}$ & $1.37\times 10^{44}$ & $0.180$ \\ \\ 2&MRK704 & $2.94\pm 0.02$ & $1.64 \pm 0.05$ &$4.66_{-0.04}^{+0.04}\times 10^{43}$ & $2.18\times 10^{44}$ & $0.040$\\ \\ 3&ESO511-G030 & $5.55\pm 0.04$ & $1.22\pm 0.01$ &$5.08_{-0.02}^{+0.03}\times 10^{43}$ & $1.23\times 10^{44}$ & $0.003$ \\ \\ 4&NGC7213 & $61.5 \pm0.11$ & $0.726\pm 0.007 $&$1.14_{-0.005}^{+0.005}\times 10^{42}$ & $5.74\times 10^{42}$ & $ 0.0002$\\ \\ 5&AKN564 & $7.6\pm 0.03$ & $1.126\pm 0.011$ &$1.12_{-0.03}^{+0.03}\times 10^{44}$ & $7.92\times 10^{44}$ & $1.21^{\rm 2}$\\ \\ 6&MRK110 & $7.65\pm 0.08$ & $1.196\pm 0.011$ &$1.66_{-0.03}^{+0.03}\times 10^{44}$ & $2.37\times 10^{45}$ & $ 0.72$\\ \\ 7&ESO198-G24 & $2.61\pm 0.03$ & $1.166\pm 0.013$ &$8.21_{-0.04}^{+0.04}\times 10^{43}$ & $4.21\times 10^{44}$ & $0.025$\\ \\ 8&Fairall 9 & $69.5\pm 0.1$ & $0.883\pm 0.01$ &$2.53_{-0.009}^{+0.009}\times 10^{44}$ & $5.68\times 10^{45}$ & $0.109$ \\ \\ 9&UGC 3973 & $1.18\pm 0.08$ & $1.424\pm 0.012$ &$1.43_{-0.02}^{+0.02}\times 10^{43}$& $2.368\times 10^{44}$ & $0.0144$\\ \\ 10& NGC 4051 & $7.55\pm 0.02$ & $1.115\pm 0.011$ &$1.31_{-0.005}^{+0.005}\times 10^{42}$ & $2.20\times 10^{43}$ & $0.085$\\ \\ 11&MCG-2-58-22 & $7.6\pm 0.02$ &$1.09 \pm 0.009$ &$2.43_{-0.008}^{+0.008}\times 10^{44}$ & $1.13\times 10^{45}$ & $0.381$\\ \\ 12 &NGC 7469 & $8.75\pm 0.33$ & $0.91\pm 0.009$ &$3.499_{-0.01}^{+0.02}\times 10^{43}$& $1.06\times 10^{45}$ & $0.649$ \\ \\ 13&MRK766 & $7.9\pm 0.04$ &$0.32\pm 0.002$ &$2.80_{-0.007}^{+0.007}\times 10^{43}$ & $4.96\times 10^{43}$ & $0.012$\\ \\ 14&MRK 590 & $1.52\pm0.1$ &$1.03\pm 0.009$ &$1.54_{-0.04}^{+0.04}\times 10^{43}$ & $4.15\times 10^{43}$ & $0.0008$\\ \\ 15&IRAS05078 & $5.925\pm 0.03$ & $0.853\pm 0.008$ &$3.03_{-0.03}^{+0.03}\times 10^{43}$ & $7.46\times 10^{43}$ & $0.008$\\ \\ 16&NGC 3227 & $7.64\pm 0.03$ & $1.13\pm 0.011 $ &$3.23_{-0.01}^{+0.01}\times 10^{42}$ & $1.915\times 10^{43}$ & $0.005$\\ \\ 17&MR2251-178 & $4.15\pm 0.04$ & $1.14\pm 0.011$ &$2.65_{-0.01}^{+0.01}\times 10^{44}$ & $1.40\times 10^{45}$ & $0.034$\\ \\ 18&MRK 279 & $7.5\pm 0.03$ & $1.192\pm 0.012$ &$1.15_{-0.006}^{+0.006}\times 10^{44}$ & $1.54\times 10^{45}$ & $0.37$ \\ \\ 19&ARK 120 & $11.85\pm 0.13$ & $1.322\pm 0.011$ &$2.14_{-0.002}^{+0.002}\times 10^{44}$ & $3.489\times 10^{45}$ & $0.107$ \\ \\ 20&MCG+8-11-11 & $10.9\pm 0.04$ & $1.213\pm 0.010$ &$6.63_{-0.008}^{+0.008}\times 10^{43}$ & $3.23\times 10^{44}$ & $0.008$\\ \\ 21&MCG-6-30-15 & $14.05\pm 0.04$ & $0.44\pm 0.005$& $1.739_{-0.03}^{+0.03}\times 10^{43}$ & $1.411\times 10^{43}$ & $0.011$\\ \\ 22&MRK 509 & $10.42\pm 0.03$ & $1.27 \pm 0.011$&$2.06_{-0.007}^{+0.007}\times 10^{44}$ & $2.42\times 10^{45}$ & $0.093$ \\ \\ 23&NGC 3516 & $1.75\pm 0.02$ & $1.54 \pm 0.013$ &$3.32_{-0.06}^{+0.06}\times 10^{42}$ & $2.97\times 10^{43}$ & $0.004$\\ \\ 24&NGC 5548 & $9.74\pm 0.02$ & $1.30\pm 0.02$ &$4.87_{-0.002}^{+0.002}\times 10^{43}$ & $2.10\times 10^{44}$ & $0.013$\\ \\ 25&NGC 3783 & $14.685\pm 0.12$ & $1.22\pm 0.012$ &$2.74_{-0.05}^{+0.05}\times 10^{43}$ & $3.45\times 10^{44}$ & $0.042$ \\ \\ 26&IC 4329A & $25.5\pm 0.03$ & $0.673\pm 0.007$ &$1.837_{-0.005}^{+0.005}\times 10^{44}$ & $1.88\times 10^{45}$ & $0.091$ \\ \\ \hline \hline \end{tabular} \\ } \begin{flushleft} $^1$ The ionising luminosity is calculated over the energy range of $13.6 \ev-30 \kev$.\\ $^{ 2}${This super Eddington rate for AKN~564 has also been seen by other authors like \cite{2012ApJ...753...75C, 2012ApJ...745..107W}} \end{flushleft} \end{table*} \begin{table*} {\footnotesize \centering \caption{The Spearman rank correlations for WA parameters. The first quantity in the bracket is the Spearman correlation coefficient while the second term is the correlation probability.\label{corr}} \begin{tabular}{llllllllllll} \hline\hline Quantity & WA-$\log\xi$& WA-$\log\nh$ & WA-velocity \\ \hline \\ WA-$\log\xi$ & 1 & (0.64,{\bf $>99.99\%$}) & (0.33,$94\%$) \\ \\ WA-$\log\nh$ & (0.64,{\bf $>99.99\%$}) & 1 & (0.36,{\bf $96\%$}) \\ \\ WA-velocity & (0.33,{\bf $94\%$}) & (0.36,{\bf $96\%$}) & 1 \\ \\ \hline \hline \end{tabular} \\ } \end{table*} \begin{table*} {\footnotesize \centering \caption{The linear regression analysis for warm absorber parameters ($y=a\,x+b$). \label{Table:lin-reg}} \begin{tabular}{llllllllllll} \hline\hline $x$ & $y$ & $a$ & \hspace{1cm}Dev$(a)$ & \hspace{1cm} $b$ & \hspace{1cm} Dev$(b)$ & \hspace{1cm}$R_S$ &\hspace{1cm} $P_{null}$\\ \hline \\ $\log\xi$ &$\log\nh$ & $0.31$ &\hspace{1cm} $0.06$ & \hspace{1cm}$20.46$ & \hspace{1cm}$0.11$ & \hspace{1cm}$0.64$ & \hspace{1cm} $>99\%$\\ \\ $\log\xi$ & $\log v_{out}$ & $0.12$ &\hspace{1cm} $0.03$ & \hspace{1cm}$2.97$ & \hspace{1cm}$0.05$ & \hspace{1cm}$0.33$ & \hspace{1cm} $>93\%$ \\ \\ $\log\nh$ & $\log v_{out}$ & $0.8$ &\hspace{1cm} $0.7$ & \hspace{1cm}$-13$ & \hspace{1cm}$18$ & \hspace{1cm}$0.36$ & \hspace{1cm} $>96\%$ \\ \\ \hline \hline \end{tabular} \\ \footnotetext{1}{ $R_S$ stands for the Spearman rank correlation coefficient.} } \end{table*} \begin{table*} {\footnotesize \centering \caption{The Spearman rank correlations for chosen subsets of WA parameters and the continuum parameters. The first quantity in the bracket is the Spearman correlation coefficient while the second term is the correlation probability. See section \ref{subsec:corr-analysis} for details. \label{Tab:corr-high-and-low}} \begin{tabular}{llllllllllll} \hline\hline Quantity & MBH & $\rm L_{Xray}$ &$\rm L_{ion}$ & $\Gamma$ & $\alpha_{OX}$ \\ \hline \\ WA-highest$\log\xi$ & (0.05,0.84) & (0.40,0.11) & (0.23,0.37) & (0.04,0.87) & (-0.01,0.97) \\ \\ WA-lowest$\log\xi$ & (-0.34,0.174) & (-0.35,0.15) & (-0.48,0.05) &(0.10,0.68) & (0.11,0.66) \\ \\ WA-highest$\log\nh$ & (0.10,0.68) & (0.40,0.10) & (0.43,0.08) &(0.16,0.53) & (0.018,0.94) & \\ \\ WA-lowest$\log\nh$ & (-0.03,0.89) & (-0.19,0.45) & (-0.32,0.19) &(0.09,0.71) & (-0.11,0.65) & \\ \\ WA-highest-velocity & (0.25,0.33) & (0.23,0.36) & (0.16,0.53) &(-0.14,0.56) & (0.14,0.58) \\ \\ WA-lowest-velocity & (0.29,0.25) & (0.036,0.88) & (-0.08,0.75) &(-0.29,0.24) & (-0.04,0.87) \\ \\ \hline \hline \end{tabular} \\ } \end{table*} \begin{figure*} \centering \hbox{ \includegraphics[width=7cm,angle=0]{histograms_30June13/MBH-histogram.ps} \includegraphics[width=7cm,angle=0]{histograms_30June13/redshift-histogram.ps} } \caption{Left: The distribution of black hole mass (left panel) and redshift (right panel) for the WAX sample.} \label{sample_2} \end{figure*} \begin{figure*} \centering \hbox{ \includegraphics[width=5.5cm,angle=0]{histograms_30June13/Alphaox-histogram.ps} \includegraphics[width=5.5cm,angle=0]{histograms_30June13/Gamma-histograms.ps} \includegraphics[width=5.5cm,angle=0]{histograms_30June13/L_Xray.ps} } \caption{From left to right: The distributions of $\alpha_{OX}$, power-law photon index $\Gamma$, and the $0.3-10\kev$ X-ray unabsorbed luminosity for the WAX sample. } \label{sample_1} \end{figure*} \clearpage \begin{figure} \centering \hbox{ \includegraphics[width=8cm,angle=0]{RGS-counts-vs-WA-plots_25July13/RGS-SNR-WA-sources-distribution.ps} \includegraphics[width=8cm,angle=0]{RGS-counts-vs-WA-plots_25July13/SNR-num-of-WA.ps} } \caption{Left: Histogram of the number of sources as a function of net 0.4--2~keV RGS counts. The blue histogram is for sources with confirmed WA detections while the red histogram is for sources with no WA detections; Right: Number of detected WA components as a function of RGS1 net counts}\label{fig:SNR-RGS} \end{figure} \begin{figure*} \centering \hbox{ \includegraphics[width=8cm,angle=0]{histograms_30June13/NH.ps} \includegraphics[width=8cm,angle=0]{histograms_30June13/Xi.ps} } \caption{Left: The distribution of column density for detected WA components shown in green. The upper limit on the column densities for sources without detectable WA are shown in blue. Right:The distribution of the ionisation parameter for warm absorbers with the same color coding as on the {\it left}.} \label{xi-NH-distribution} \end{figure*} \clearpage \begin{figure*} \centering \hbox{ \includegraphics[width=8cm,angle=0]{correlation-plots_Aug13/logxi-logv-with-Tombesi-UFO-datapoints-WAX-lin-reg-extrapol.ps} \includegraphics[width=8cm,angle=0]{correlation-plots_Aug13/Xi-NH-lin-reg-showing-UFOs-NOT-same-distribution.ps} } \caption{{\tt Left:} Correlation between ionisation parameter and outflow velocity of the WAs in the WAX sample (large dots) and the UFO (small dots). The shaded regions correspond to the root mean square (RMS) deviation of the data points from the best fit linear regression line (solid line). The UFOs do not lie in the defined band. {\tt Right:} the same for the ionisation parameter versus the column density. The dotted line is the best fit linear regression line for the UFOs obtained by T13.} \label{fig:linear-reg-xi-V} \end{figure*} \begin{figure*} \centering { \includegraphics[width=10cm,angle=90]{correlation-plots_Aug13/Matteo_wa_vs_disk.ps} } \caption{ Distribution of the column density of the detected WA components. The top panel is for the sources which have relativistic Fe K$\alpha$ emission lines while the bottom panel is for sources without such a detection. The shaded areas correspond to upper limits.} \label{Fe-line-NH-distrib} \end{figure*} \begin{figure*} \centering { \includegraphics[width=10cm,angle=0]{warm-emission-lines/WE-OVII.ps} } \caption{Distribution of the O VII emission line centroid energies. The resonant line of the O VII He-like triplet emission has a rest frame energy of $0.574\kev$ while the forbidden line has a rest frame energy of $0.561\kev$. We detect more forbidden line emission in the WAX sample compared to resonant lines. This implies a photo-ionisation origin of the emission lines from distant clouds.} \label{OVII} \end{figure*} \clearpage \appendix | 14 | 4 | 1404.0899 |
1404 | 1404.5158_arXiv.txt | {We present new low-resolution (R$\sim$800) optical spectra of 22 Galactic planetary nebulae (PNe) with {\it Spitzer} spectra. These data are combined with recent optical spectroscopic data available in the literature to construct representative samples of compact (and presumably young) Galactic disc and bulge PNe with {\it Spitzer} spectra. Attending to the nature of the dust features - C-rich, O-rich, and both C- and O-rich dust features (or double chemistry) - seen in their {\it Spitzer} spectra, the Galactic disc and bulge PNe are classified according to four major dust types (oxygen chemistry or OC, carbon chemistry or CC, double chemistry or DC, featureless or F) and subtypes (amorphous and crystalline, and aliphatic and aromatic), and their Galactic distributions are presented. Nebular gas abundances of He, N, O, Ne, S, Cl, and Ar, as well as plasma parameters (e.g.\ N$_e$, T$_e$) are homogeneously derived by using the classical empirical method. We study the median chemical abundances and nebular properties in Galactic disc and bulge PNe depending on their {\it Spitzer} dust types and subtypes. The differences and similarities between PNe in the Galactic disc and bulge are reported. In particular, the median abundances for the major {\it Spitzer} dust types CC and OC are representative of the dominant dust subtype (which are different in both Galactic environments), while these values in DC PNe are representative of the two DC subtypes. A comparison of the derived median abundance patterns with AGB nucleosynthesis predictions mainly show that i) DC PNe, both with amorphous and crystalline silicates, display high-metallicity (solar/supra-solar) and the highest He abundances and N/O abundance ratios, suggesting relatively massive ($\sim$3--5 M$_{\odot}$) hot bottom burning AGB stars as progenitors; ii) PNe with O-rich and C-rich unevolved dust (amorphous and aliphatic) seem to evolve from subsolar metallicity (z$\sim$0.008) and lower mass ($<$3 M$_{\odot}$) AGB stars; iii) a few O-rich PNe and a significant fraction of C-rich PNe with more evolved dust (crystalline and aromatic, respectively) display chemical abundances similar to DC PNe, suggesting that they are related objects. A comparison of the derived nebular properties with predictions from models combining the theoretical central star evolution with a simple nebular model is also presented. Finally, a possible link between the {\it Spitzer} dust properties, chemical abundances, and evolutionary status is discussed.} | Planetary nebulae (PNe) are a short evolutionary phase in the life of low- and intermediate-mass stars (0.8 $\leq$ M $\leq$ 8 M$_{\odot}$) occurring after they leave the ssymptotic giant branch (AGB) and before ending their lives as white dwarfs \citep[e.g.][]{Iben1995}. However, many details of the physical processes leading to the creation of the nebula and its subsequent evolution remain unclear. Still, a better knowledge of the PN phase is necessary for understanding not only the final fate of stars like our Sun, but also the formation and the chemical evolution of the Milky Way and other galaxies. At the tip of the AGB phase, stars experience a strong superwind that efficiently enriches the surrounding interstellar medium with huge amounts of gas and dust from the outer layers of the star \citep[e.g.][]{Herwig2005}. When the strong mass loss stops, they leave the AGB, and the future central star rapidly evolves towards hotter effective temperatures in the Hertzsprung--Russell diagram. Thus, when the ionization of the ejected gas takes place, a new PN emerges. Owing to their emission-line nature, PNe can be easily observed at very large distances, and the chemical composition of the gas and other properties can be derived. Some of the abundances (e.g.\ the Ar/H and Cl/H ratios) may remain practically unchanged in these objects, reflecting the primordial composition of the interstellar matter where their central stars were born. But there are other abundance ratios (e.g.\ N/O or C/O) that are strongly modified during the life of low- and intermediate-mass stars. The products of the hydrogen burning and shell helium burning are brought to the stars' outer layers in dredge-up episodes (the third dredge-up, TDU) taking place during the thermally pulsing phase on the AGB, converting originally O-rich stars into C-rich ones. In addition, the stellar surface can be enriched in products of the so-called hot bottom burning \citep[HBB, e.g.][]{SackmannBoothroyd1992,Mazzitelli1999} process for the more massive (M$>$3-4 M$_{\odot}$) AGB stars \citep[e.g.][]{GH06,GH07,GH09}, preventing formation of C-rich stars. At solar metallicity, low-mass ($\sim$1.5$-$3-4 M$_{\odot}$) stars are expected to be C-rich (C/O$>$1) at the end of the AGB phase, while more massive HBB stars may remain O-rich (C/O$<$1) during the full AGB evolution.\footnote{Very low-mass (e.g. $\leq$1.5 M$_{\odot}$) and solar metallicity AGB stars are expected to be O-rich due to a rather inefficient TDU.} It has been believed for a long time that post-AGB objects belong to only one of the two chemical branches mentioned above: either those characterized by an O-rich chemistry or those surrounded by C-rich material. PNe with rare Wolf--Rayet type central stars \citep[e.g.][]{GornyTylenda2000} were the first and the only ones in the Galactic disc to simultaneously show the presence of both carbon-based (e.g.\ polycyclic aromatic hydrocarbons; PAHs) and oxygen-based dust (e.g.\ crystalline silicates) - \cite{Waters1998a}. However, a sample of Galactic bulge PNe (GBPNe) observed with {\it Spitzer/IRS} has been analysed, and a majority of them show such dual-dust chemistry \citep{Gutenkunst2008,PereaCalderon2009}; the dual-dust chemistry phenomenon is clearly not restricted to objects with Wolf--Rayet (WR) central stars. More recently, \cite{GuzmanRamirez2011} have proposed a scenario that may explain the simultaneous presence of PAHs and crystalline silicates in circumstellar disc-like structures around the central stars of GBPNe, but this scenario does not address the crucial question of why such a phenomenon is obserwed in Galactic disc PNe only in PNe with [WR] central stars. Apparently, in the Galactic bulge only a small fraction of PNe do not share that phenomenon and only have oxygen-based dust. The reason for the apparent difference between Galactic disc and bulge PNe remains unknown and is studied in this paper. Various characteristics of GBPNe with peculiar {\it Spitzer} IR spectra were analysed by \cite{Gorny2010}, who found that PNe characterized by carbon-based dust (i.e.\ PAHs) and simultaneously oxygen-based dust (in the form of both crystalline and amorphous silicates) - the so-called DC$_{a+cr}$-type PNe in this paper - have unusual chemical compositions of the nebular gas. Oxygen seems to be under-abundant relative to hydrogen and nitrogen (see the location of DC$_{a+cr}$-type PNe in their figure 11) but not to other elements. This cannot be explained in the standard picture of the AGB chemical evolution for objects with the typical Milky Way metallicity. On the other hand, PNe surrounded by only oxygen-rich dust (both in amorphous and crystalline forms) - the so-called OC$_{a+cr}$-type PNe in this paper - have very low abundances of nitrogen (see their figure 11). The latter could be explained if these OC$_{a+cr}$-type PNe do not come from single stars but from binary systems because the presence of a companion may change the final abundances of the nebula \citep[e.g.][]{DeMarco2009}. Very recently, a large and complete sample ($\sim$150) of compact Galactic disc PNe have been analysed through {\it Spitzer/IRS} spectroscopy by \cite{Stanghellini2012}. These authors find many PNe with peculiar dust characteristics (the DC$_{a+cr}$- and OC$_{a+cr}$-type PNe described above) similar to those previously found in the Galactic bulge \citep{Gorny2010}. In particular, 28\% (42 PNe) and 30\% (45 PNe) of the sample turned out to be among the DC$_{a+cr}$- and OC$_{a+cr}$-type PNe, respectively. Owing to sensitivity limits of the \textit{Infrared Space Observatory} (\textit{ISO}), most of the disc PNe with IR spectra have [WR] central stars probably because they are bright sources. It is a paradox of the high sensitivity of the {\it Spitzer} IRS instrument that, in contrast, only the optically fainter Galactic disc PNe could be observed \citep{Stanghellini2012}. As a result, proper optical spectra are not available yet for most of them. New optical spectroscopic observations are needed to form a proper reference sample of Galactic disc PNe and overcome selection effect problems. We want to alleviate this problem with the present paper by forming balanced samples of the Galactic disc and Galactic bulge PNe for a more extensive investigation. In this paper, we present new low-resolution spectroscopy of 22 Galactic PNe with {\it Spitzer} spectra. These spectroscopic data are combined with recent data to construct representative samples of the Galactic disc and bulge PNe. Various nebular gas abundances of the Galactic disc and bulge PNe are studied depending on their dust properties (i.e.\ {\it Spitzer} dust types/subtypes). PNe in environments with different metallicity and chemical history such, as the Galactic disc and bulge, are also compared. Our new low-resolution spectroscopic observations, the nebular chemical abundance analysis, and the optical data available in the literature are described in Section 2. We give an overview of the {\it Spitzer} dust types/subtypes and the Galactic distribution of our final samples of the Galactic disc and bulge PNe in Section 3, while in Section 4 we report the derived chemical abundances versus the {\it Spitzer} dust types and subtypes. Section 5 presents the nebular properties of the PNe with different {\it Spitzer} dust types and subtypes. Our results are discussed in Section 6, while a final summary of our work is given in Section 7. | We have combined new low-resolution (R$\sim$800) optical spectra with recent data in order to construct representative samples of Galactic disc and bulge PNe (mostly compact and presumably young) with {\it Spitzer} spectra. Depending on the nature of the dust features - C-rich, O-rich, and both C- and O-rich dust features (or double chemistry) - seen in their {\it Spitzer} spectra, the Galactic disc and bulge PNe are classified into four major dust types (oxygen chemistry or OC, carbon chemistry or CC, double chemistry or DC, featureless or F) and subtypes (amorphous and crystalline, and aliphatic and aromatic) and their Galactic distributions are presented. Nebular gas abundances of He, N, O, Ne, S, Cl, and Ar, as well as plasma parameters, were derived in a homogeneous way by using the classical empirical method. We studied the median chemical abundances in the Galactic disc and bulge PNe depending on their {\it Spitzer} dust types and subtypes and compared them with the homogeneous dataset of AGB nucleosynthesis predictions by Karakas (2010). Also, we analysed the nebular properties among the several types and subtypes of PNe and discussed a possible link between the {\it Spitzer} dust properties, chemical abundances, and evolutionary status. The main results of our work can be summarized as follows. \begin{enumerate} \item{The several {\it Spitzer} dust types and subtypes of PNe (with the exception of F PNe) are distributed differently between the Galactic disc and bulge regions. In particular, DC PNe are less common in the Galactic disc than OC and CC PNe but clearly dominate the Galactic bulge region, which otherwise show an almost complete lack of CC PNe. Both OC and DC PNe with amorphous silicates (OC$_{am}$ and DC$_{am+cr}$) are more uncommon in the Galactic bulge than in the disc, while the opposite is seen for OC and DC PNe with crystalline silicates (OC$_{cr}$ and DC$_{cr}$). CC PNe with aliphatic features (CC$_{al}$) completely dominate in the Galactic disc. DC PNe in the Galactic disc are mainly located towards the Galactic centre with no significant difference between the DC$_{am+cr}$ and DC$_{cr}$ subtypes. OC PNe with amorphous silicates (OC$_{am}$) and featureless (F) PNe are located further away from the Galactic plane than the other types/subtypes of PNe.} \item{The median abundance pattern (mainly N/H, He/H, Ar/H, and N/O) of DC PNe is statistically different from that of OC PNe in both Galactic environments with DC PNe and OC PNe in the Galactic disc and bulge sharing almost the same abundance pattern. CC disc PNe (lacking in the bulge region) display an abundance pattern that is quite similar to that of the OC disc PNe, with the exception of S, which is found to be significantly more depleted in the CC objects. Our dissection of the {\it Spitzer} dust subtypes vs.\ the nebular gas abundances shows that i) the DC subtypes (DC$_{cr}$ and DC$_{am+cr}$) are indistinguishable, and they show an abundance pattern identical to the major DC type; ii) the OC subtypes with amorphous silicates (OC$_{am}$ and OC$_{am+cr}$) are chemically very similar, dominating the abundance pattern observed in the major OC type, while the less numerous OC$_{cr}$ PNe are more metal rich; iii) the CC subtypes with aliphatic dust features (CC$_{al}$ and CC$_{ar+al}$) display similar abundances, dominating the chemical pattern observed in the major CC type, while CC$_{ar}$ PNe, being more metal-rich, are also scarcer; iv) a few OC$_{cr}$ and about half ($\sim$50\%) of CC$_{ar}$ PNe display nebular gas abundances that are almost identical to those seen in DC PNe, suggesting that they are related objects.} \item{The several {\it Spitzer} dust types and subtypes correspond to different populations of PNe (with different average progenitor masses and metallicities) in both Galactic environments. We note that although the progenitor masses that we infer from comparisons with the AGB nucleosynthesis predictions may be rather uncertain, our finding of different average progenitor masses and metallicities among the several {\it Spitzer} dust types/subtypes is assured. In summary: {\bf i)} DC PNe both with amorphous and crystalline silicates (DC$_{am+cr}$ and DC$_{cr}$) are high metallicity (solar/supra-solar) sources evolving from relatively massive $\sim$3--5 M$_{\odot}$ AGB stars experiencing HBB. They show the highest median He abundances and N/O abundance ratios, which are consistent with solar metallicity (z$\sim$0.02) $\sim$5 M$_{\odot}$ HBB AGB stars. However, other possible evolutionary channels cannot be discarded now. In addition, it is still not clear that \DCamcr\ PNe could evolve towards the \DCcr\ stage. Curiously, there are a few DC PNe in the bulge with some indications of the O-N cycle activation, which are not present in the disc. {\bf ii)} OC PNe with amorphous silicates (OC$_{am}$) are low-metallicity sources with median He abundances and N/O abundance ratios that agree well with predictions of low-metallicity (z$\sim$0.008) and very low-mass ($\sim$1 M$_{\odot}$) AGB stars. OC PNe with both amorphous and crystalline silicates (OC$_{am+cr}$) are chemically similar to the OC$_{am}$ ones, but we have found tentative hints (i.e.\ in the S$_{H\beta}$ vs.\ S$_V$ diagram and S$_{H\beta}$ distributions), suggesting that OC$_{am+cr}$ PNe could be more massive than OC$_{am}$ PNe. The bulk of OC PNe with only crystalline silicates (OC$_{cr}$) are higher metallicity (nearly solar) objects with their median He abundances and N/O abundance ratios consistent with solar metallicity (z$\sim$0.02) $\sim$1--1.5 M$_{\odot}$ AGB stars. {\bf iii)} CC PNe with aliphatic features (CC$_{al}$ and CC$_{ar+al}$) (mostly located in the Galactic disc) are low-metallicity (z$\sim$0.008) objects that probably evolve from relatively low-mass (1.9 $\leq$ M $<$ 3 M$_{\odot}$) AGB stars. The best fit to the observed abundances is given by the models for the low-metallicity (z$\sim$0.008) $\sim$1.9 M$_{\odot}$ AGB star.} \item{In both Galactic regions (bulge and disc), most of the PNe dust classes analysed here show a similar intermediate level of ionization, probably reflecting that our PNe samples are dominated by relatively young PNe. The only exceptions are the featureless F-type PNe that represent more advanced evolutionary stages. There is an apparent dichotomy of DC PNe in the S$_{H\beta}$ vs.\ S$_V$ diagram that could suggest an additional high-metallicity evolutionary channel for these objects; e.g.\ less massive (1 $<$ M $<$ 3 M$_{\odot}$) with some kind of extra mixing. Also, there is tentative evidence that OC$_{am+cr}$ PNe could be slightly more massive than the OC$_{am}$ ones. This evidence, however, comes from comparisons with simple theoretical tracks that may not be representative of the several types of PNe with {\it Spitzer} spectra. More interesting is that OC and CC with unevolved dust (OC$_{am}$ and CC$_{al}$ PNe, respectively) seem to originate in progenitor masses in a narrow mass range, in agreement with the nucleosynthesis predictions.} \end{enumerate} In short, our most remarkable result is that DC PNe, both with amorphous and crystalline silicates, display high-metallicity (solar/supra-solar) and the highest He abundances and N/O ratios, indicating that they likely evolve from relatively massive ($\sim$3--5 M$_{\odot}$) HBB AGB stars; however, PNe with O-rich and C-rich unevolved dust (amorphous and aliphatic) evolve from subsolar metallicity (z$\sim$0.008) and lower mass ($<$3 M$_{\odot}$) AGB stars. Although we have obtained very interesting results by studying more balanced samples of the Galactic disc and bulge PNe, more optical spectroscopic observations would be desirable. In particular, the available data for some {\it Spitzer} OC (OC$_{cr}$ and OC$_{am+cr}$) and CC (CC$_{ar}$ and CC$_{ar+al}$) dust subtypes are still very scarce, so more chemical abundances would be useful to discard or confirm any possible evolutionary link among the several {\it Spitzer} dust subtypes. More theoretical efforts (e.g.\ a detailed study of AGB evolution and nucleosynthesis at supra-solar metallicity) are also encouraged. | 14 | 4 | 1404.5158 |
1404 | 1404.0709.txt | Transitional disks are protoplanetary disks characterized by reduced near- and mid-infrared emission, with respect to full disks. This characteristic spectral energy distribution indicates the presence of an optically thin inner cavity within the dust disk believed to mark the disappearance of the primordial massive disk. We present new \emph{Herschel Space Observatory} PACS spectra of [O{\sc i}] 63.18 $\mu$m for 21 transitional disks. Our survey complements the larger \emph{Herschel} GASPS program \citep[``Gas in Protoplanetary Systems,''][]{dent13} by quadrupling the number of transitional disks observed with PACS in this wavelength. [O{\sc i}] 63.18 $\mu$m traces material in the outer regions of the disk, beyond the inner cavity of most transitional disks. We find that transitional disks have [O{\sc i}] 63.18 $\mu$m line luminosities $\sim2$ times fainter than their full disk counterparts. We self consistently determine various stellar properties (e.g. bolometric luminosity, FUV excess, etc.) and disk properties (e.g. disk dust mass, etc.) that could influence the [O{\sc i}] 63.18 $\mu$m line luminosity, and we find no correlations that can explain the lower [O{\sc i}] 63.18 $\mu$m line luminosities in transitional disks. Using a grid of thermo-chemical protoplanetary disk models, we conclude that either transitional disks are less flared than full disks, or they possess lower gas-to-dust ratios due to a depletion of gas mass. This result suggests that transitional disks are more evolved than their full disk counterparts, possibly even at large radii. | Protoplanetary disks (gas-rich dust disks around young stars) provide the raw building-blocks for solar systems. While significant progress has been made in understanding the relevant evolutionary timescales of protoplanetary disks, little is known about the physical mechanisms driving the eventual dispersal of dust and gas about these young systems \citep[for review, see:][]{pascuccitachibana10}. The goal of this paper is to gain insight into these dispersal processes by investigating a special type of protoplanetary disk that is thought to be in the process of losing its primordial dust disk: the transitional disks. Transitional disks, like their full protoplanetary disk cousins, are often identified by their spectral energy distributions (SEDs). While there is significant variation in the SEDs of young star systems, transitional disks appear as a distinct subgroup of protoplanetary disks: their SEDs show reduced near- and mid-infrared emission, with respect to full disks \citep{strom89}. This characteristic SED points to the presence of an optically thin inner cavity, extending from the star out to 1 $\sim$ 20 AU. The excavation of this cavity is believed to mark the early stages of the dispersal of the primordial, massive dust disk -- whose continuous dust disk extended as close as a few stellar radii to the central star \citep[e.g.,][]{calvet02, espaillat07}. The existence of inner cavities has been directly confirmed for a few transitional disks via sensitive, high-resolution millimeter observations which detect reduced (or absent) dust emission from the inner disk, as a result of a deficit of millimeter size grains \citep[e.g.,][]{andrews09, brown09}. While transitional disks may posess dust cavities, it is known that, in most cases, these dust cavities are not devoid of gas. Transitional disks are still actively accreting \citep[e.g.,][]{n07}, and various optical emission lines (e.g. CO lines, [O{\sc i}] 6300 \AA $\,$ and 5577 \AA, etc.) indicate the presence of gas within the dust cavity region - though it may be depleted \citep[e.g. TW Hya,][]{gorti11}. There are three leading hypotheses for the driving mechanism behind the formation of cavities in transitional disks: \citep[for review, see:][]{espaillatPPIV}: \begin{itemize} \item \emph{Dust coagulation.} As disks evolve submicron-sized dust grains coagulate into larger aggregates which have little emission at infrared wavelengths and thus reduce the disk opacity. These larger aggregates would eventually coalesce into planetesimals and planetary embryos. Since dynamical timescales increase with increasing radial distance from the central star, grain growth occurs inside-out and leads to the development of an expanding optically thin inner cavity, although the total mass of this inner disk region is not necessarily lower \citep[e.g.,][]{dullemonddominik2005}. \item \emph{Photoevaporation.} High-energy photons from the central star can drive photoevaporative winds, particularly from the outer regions of the protoplanetary disk (beyond $\sim$few AU). As the viscous accretion rate drops below the photoevaporation mass loss rate, a gap opens in the disk and the inner disk viscously accretes onto the star -- resulting in an inner cavity \citep[e.g.][]{alexander14}. Direct irradiation of the cavity wall is expected to rapidly disperse the outer disk \citep{alexander06}. Photoevaporative winds have been detected for select protoplanetary disks via blueshifted ($\sim$few km/s) [Ne {\sc ii}] 12.81 $\mu$m lines, which traces unbound winds within the inner $\lesssim$ 10's of AU \citep{pascucci09}. \item \emph{Dynamical clearing by giant planets.} Dynamical interactions between the disk and an embedded giant planet (with masses roughly equal to that of Jupiter) can open gaps within the disk \citep[e.g.,][]{lubow99}. Gas from the inner disk (within the planet's orbit) can continue to accrete onto the central star, while most of the gas from the outer disk (beyond the planet's orbit) accretes onto the planet, and only a small amount of gas flows past the planet into the inner disk. In addition to the physical gap created by the planet, pressure gradients setup at the outer edge of the gap can act as a dust filter - allowing only grains below a critical size to reach the inner disk, and perhaps forming an optically thin inner cavity \citep{rice06}. \end{itemize} While these different mechanisms can produce qualitatively similar SEDs, they predict distinctive differences in the distribution of disk gas. Furthermore, these different processes can, and probably do, operate simultaneously. In this paper, we use \emph{Herschel Space Observatory} far-infrared data to examine whether full disks and transitional disks are different in their outer disk regions, beyond 10's of AU. We use the [O{\sc i}] 63.18 $\mu$m emission line and the nearby 63 $\mu$m continuum emission to trace the gas and dust components respectively, beyond 10$\sim$100 AU \citep[e.g.][]{aresu12}. In addition, we use ancillary data to characterize our sample at different wavelengths. In \emph{Section 2}, we provide a short description of our sample, the \emph{Herschel}/PACS observations and data reduction, and the ancillary stellar and disk properties used to characterize our sample. In \emph{Section 3}, we summarize our [O{\sc i}] 63.18 $\mu$m line 63 $\mu$m continuum results. Most notably, we find that transitional disks possess [O{\sc i}] 63.18 $\mu$m line luminosities a factor of 2$\sim$3 lower than full disks, despite having similar 63 $\mu$m continuum luminosities { -- a trend previously identified by \citet{howard}, though expanded in this work with quadruple the number of transitional disks.} In \emph{Section 4}, we rule out various observable stellar and disk properties (e.g. FUV and X-ray luminosity) as the potential cause for this [O{\sc i}] 63.18 $\mu$m line luminosity difference between full disks and transitional disks. In \emph{Section 5} we use the results of the DENT grid \citep[a grid of 300,000 thermo-chemical protoplanetary disk models, by][]{woitke10}, to examine other possible causes for the [O{\sc i}] 63.18 $\mu$m line luminosity difference. We conclude that the lower [O{\sc i}] 63.18 $\mu$m line luminosity of transitional disks could be due to transitional disks either being less flared, or by having lower gas-to-dust ratios. In \emph{Section 6}, we discuss the implications of this result for disk evolution models, and potential followup observations. | %% We have shown that transitional disks have statistically lower [O{\sc i}] 63.18 $\mu$m line luminosities compared to full disks (by a factor of a few), but similar 63 $\mu$m continuum luminosities. We have ruled out stellar flux (\emph{Section 4.1}), FUV excess luminosity (\emph{Section 4.2}), X-ray luminosity (\emph{Section 4.3}), and and dust mass (\emph{Section 4.4}) as causes of this difference in [O{\sc i}] 63.18 $\mu$m line luminosities. We hypothesize two possible scenarios to explain the lower [O{\sc i}] 63.18 $\mu$m line luminosities in transitional disks: either transitional disks are less flared (\emph{Section 5.1}), or transitional disks are depleted in gas (and thus have lower gas-to-dust ratios), either by a global loss of gas (\emph{Section 5.2}), or solely within the central cavity (\emph{Section 4.4}). Both of these scenarios point to transitional disks being more evolved than full disks. \subsection{Implications for Disk Evolution Models} Photoevaporation may be a natural mechanism by which the disk gas-to-dust mass ratio is reduced with time. High-energy stellar photons heat the disk and drive a photoevaporative wind which primarily removes the gas component from the disk surface. Amongst our sample of transitional disks, CS Cha, TW Hya, T Cha, RXJ1615.3-3255 and YLW8 have been observed with {\it VLT/VISIR} and present [Ne~II] emission lines blueshifted by several km/s, implying on-going photoevaporation \citep{pascucci09, sacco12}. GM Aur has been observed with \emph{Gemini/TEXES}, but with insufficient S/N to precisely determine the line centroid \citep{najita09}. While photoevaporation has been detected from these objects, the rate at which gas is lost via this mechanism is still unknown. If [Ne {\sc ii}] is tracing the very thin EUV irradiated region, the mass loss rate is negligible ($\sim 10^{-10} M_{\sun}/yr$); while, if [Ne~{\sc ii}] is tracing the deeper X-ray irradiated layer, the mass loss rate may be significant ($\sim 10^{-8} M_{\sun}/yr$). In the latter case, if we assume that full disks start with a mass of $\sim 22 \, M_{Jupiter}$ (the mean value derived from millimeter data; see \emph{Section 2.3.3}), they could loose half of their gas mass in just 1\,Myr via photoevaporation. Planet-disk interactions may also provide a mechanism for reducing the gas-to-dust ratio in protoplanetary disks \citep[e.g.][]{espaillat13}. \citet{rice06} showed that pressure gradients at the outer edge of a gap cleared by a giant planet can act as dust filters. In such a scenario, small dust grains and gas flow across the gap and are either lost to the planet or the inner disk (and eventually the host star), while large dust grains remain trapped in the outer disk. This has the effect of removing gas from the outer disk while retaining most of the mm- and cm-size dust, and thus decreasing the gas-to-dust ratio of the outer disk. However, the leak of small, micron-size dust particles into the inner disk still necessitates some additional mechanism, such as dust coagulation, to explain the dust cavities in transitional disks \citep{zhu12}. Additionally, dust filtration alone is not a realistic mechanism for a decreasing the gas-to-dust ratio by 0.5 dex, as suggested by our work. As gas leaves the outer disk and flows into the gap formed by the planet, it will either be accreted onto the planet, or completely cross the gap into the inner disk, where it can then accrete onto the central star. \citet{lubow06} showed that when mass flows across into these gaps formed by giant planets, $\sim 90 \%$ of the mass will be accreted onto the planet. Thus, for dust filtration to be the driver of a low gas-to-dust ratio in the outer disk, it is at the expense of putting a large majority of the outer disks's gas mass directly into planets. If we assume full disks start with a gas mass of $\sim 22 \, M_{Jupiter}$ (the mean value derived from millimeter data; see \emph{Section 2.3.3}), $\sim 7 \, M_{Jupiter}$ of gas would need to be lost to planet formation to result in a decrease in the gas-to-dust of 0.5 dex. If instead, we assume that a full protoplanetary disk can be characterized by a minimum mass solar nebula \citep[MMSN,][]{weidenschilling77, kuchner04}, then it would be necessary for the disk to lose even more mass: upwards of $\ga 20 \, M_{Jupiter}$\footnotemark[10]\footnotetext[10]{The total disk mass is calculated by integrating the surface mass density from the inner edge of the protoplanetary disk ($\sim 0.07$ AU) to the outer edge (conservatively, $\sim40$ AU). Using the MMSN described by \citet{kuchner04} ($\Sigma = 4225 \; g/cm^{2} \; (a / 1 \, AU)^{-1.78}$) results in a total disk mass of 24 $M_{Jupiter}$. Using the classical MMSN described by \citet{weidenschilling77} ($\Sigma = 4200 \; g/cm^{2} \; (a / 1 \, AU)^{-1.5}$) results in a total disk mass of 38 $M_{Jupiter}$. A loss of 0.5 dex of the disk mass for these two models correspond to $17$ and $26$ $M_{Jupiter}$, respectively. Using more liberal estimates of the outer edge of the protoplanetary disk \citep[e.g. 270 AU;][]{chianggoldreich97} results in even larger masses.}. These simple calculations also assume that all of the dust in the outer disk is somehow protected, perhaps due to a planet-induced pressure bump. If the loss of dust across the gap is large, these mass estimates would only be lower limits. If all of this mass is lost to forming planets, this would suggest the formation of a large number of giant planets at large semimajor axes ($\gtrsim 10$ AU), which does not seem to agree with the current (though still debated) statistics of giant exoplanets \citep{nielsen13, fressin13, biller13}. Lastly, while large, Jovian-mass planets can clear gaps and cause global depletions in the gas surface density of disks, they only deplete the surface density of the disk by a factor of a few \citep[e.g. Fig. 3 of ][]{lubow06}. As discussed in \citet{bruderer13} (and in \emph{Section 4.4}) our observed factor of 2 line flux difference between transitional disks and full disks would require a drop in the surface density by a factor of $\gtrsim100$. \subsection{Potential Followup Observations} Direct measurement of the gas-to-dust ratio in full disks and transitional disks would break our observed degeneracy between gas-to-dust ratio and disk flaring. While the dust mass of protoplanetary disks can be estimated with millimeter observations \citep[e.g.][]{mohanty}, the total gas mass of protoplanetary disks is difficult to directly measure. Combining our observations of the [O{\sc i}] 63.18 $\mu$m line with low J CO rotational lines, has been suggested as a possible way to directly measure total disk gas mass. While this method has been implemented for select, well studied disks \citep[e.g. TW Hya,][]{thi10}, its reliability is still under discussion \citep{gorti09, bergin12}. Both low J CO and [O{\sc i}] lines are optically thick, which make them both primarily sensitive to temperature - and only weakly dependent on disk mass. Alternatively, observations of isotopologues may provide direct estimates for disk mass. Isotopologues (such as $^{13}$C) are minor components within the disk and can be optically thin and directly trace disk mass (modulo the assumed abundances of the relative species). With the significant ($\sim10$x) increase in sensitivity allowed by ALMA, detecting emission from minor disk components out to nearby star-forming regions (e.g. Taurus-Auriga) is now possible. %The most direct way to measure the flaring of protoplanetary disks (and the disk scale height) is to directly image near edge-on disks in scattered light. Unfortunately, there is a significant lack of spatially resolvable, edge-on disks. This, combined with the inherent rarity of transitional disks would make a statistical comparison of scale heights between full and transitional disks impractical. For select disks, it may be possible to directly measure the relative vertical distribution of dust (via mm-emission) and gas (via gas emission lines, such as CO and its isotopologues) with high spatial and spectral resolution observations with ALMA \citep{rosenfeld13}. Detailed SED modeling covering the mid-infrared, far-infrared, and millimeter wavelengths may be able to break the degeneracy between disk gas mass and disk scale height. Flared disks intercept more stellar radiation at larger semimajor axes than flatter disks. Emission from these warm, outer disk, surface layers dominate the SED beyond $\sim$20 $\mu$m \citep{chianggoldreich97}. It is difficult to directly measure the flaring of \emph{gas} in protoplanetary disks. For select nearby and edge-on disks, it may be possible to directly measure the relative vertical distribution of dust (via mm-emission) and gas (via gas emission lines, such as CO and its isotopologues) with high spatial and spectral resolution observations with ALMA \citep{rosenfeld13}. Detailed SED modeling covering the mid-infrared, far-infrared, and millimeter wavelengths may be able to break the degeneracy between disk gas mass and disk scale height. Flared disks intercept more stellar radiation at larger semimajor axes than flatter disks. Emission from these warm, outer disk, surface layers dominate the SED beyond $\sim$20 $\mu$m \citep{chianggoldreich97}. | 14 | 4 | 1404.0709 |
1404 | 1404.2913_arXiv.txt | The quasilinear premise is a hypothesis for the modeling of plasma turbulence in which the turbulent fluctuations are represented by a superposition of randomly-phased linear wave modes, and energy is transferred among these wave modes via nonlinear interactions. We define specifically what constitutes the quasilinear premise, and present a range of theoretical arguments in support of the relevance of linear wave properties even in a strongly turbulent plasma. We review evidence both in support of and in conflict with the quasilinear premise from numerical simulations and measurements of plasma turbulence in the solar wind. Although the question of the validity of the quasilinear premise remains to be settled, we suggest that the evidence largely supports the value of the quasilinear premise in modeling plasma turbulence and that its usefulness may also be judged by the insights gained from such an approach, with the ultimate goal to develop the capability to predict the evolution of any turbulent plasma system, including the spectrum of turbulent fluctuations, their dissipation, and the resulting plasma heating. | The presence of turbulence impacts the evolution of a wide variety of plasma environments, from galaxy clusters to accretion disks around compact objects, to the solar corona and solar wind, and to the laboratory plasmas of the magnetic confinement fusion program. Establishing a thorough understanding of plasma turbulence is a grand challenge that has the potential to impact this wide range of research frontiers in plasma physics, space physics, and astrophysics. Ultimately, such efforts are aimed at developing the capability to predict the evolution of any turbulent plasma system. The \emph{quasilinear premise} \citep{Klein:2012} is a hypothesis for the modeling of plasma turbulence with the potential to lead to a quantitative, predictive theory of plasma turbulence. The quasilinear premise states simply that \emph{some} characteristics of the turbulent fluctuations in a magnetized plasma may be usefully modeled by a superposition of randomly-phased, linear wave modes. The nonlinear interactions inherent to the turbulent dynamics may be considered to transfer energy among these linear wave modes---therefore, the model is quasilinear. This premise is hotly debated at present, with significant questions raised by the heliospheric physics community about the validity of using the theory of linear plasma waves to analyze and interpret the turbulent fluctuations measured in the solar wind plasma. On one hand, a large body of work on plasma turbulence either explicitly or implicitly assumes the relevance of some linear plasma wave properties.\footnote{A small sample of these studies includes \citet{Coleman:1968,Belcher:1971,Tu:1984,Matthaeus:1990, Tu:1994,Verma:1995,Leamon:1998b,Quataert:1998, Stawicki:2001,Bale:2005,Markovskii:2006,Hamilton:2008, Howes:2008b,Sahraoui:2009,Schekochihin:2009,Chandran:2010a,Chen:2010, Podesta:2010a,Saito:2010,Rudakov:2012}. } On the other hand, the nonlinearity inherent in turbulent interactions raises obvious questions about the relevance of linear theory. In this paper, we define precisely the concepts encapsulated by the quasilinear premise and identify the limitations of such an approach. We outline the theoretical arguments that justify the application of linear plasma wave theory to the study of plasma turbulence, and review supporting and conflicting evidence from theory, simulation, and observation. | \label{sec:conc} The quasilinear premise is a hypothesis for the modeling of plasma turbulence in which the turbulent fluctuations are represented by a superposition of randomly-phased linear wave modes, and energy is transferred among these wave modes via nonlinear interactions. Although a large body of work on plasma turbulence either explicitly or implicitly assumes the relevance of some linear plasma wave properties, the nonlinearity inherent in turbulent interactions raises obvious questions about the relevance of linear theory. This papers attempts to present a broad range of theoretical, numerical, and observational evidence in the attempt to evaluate the validity of the quasilinear premise. After defining the quasilinear premise precisely, we highlight the the aspects of turbulence that can and cannot be described by such an approach: turbulent fluctuation properties such as the eigenfunction, frequency, and collisionless damping rate as well as second-order statistics such as the energy spectra or magnetic helicity of the turbulence can be described by a model of turbulence based on the quasilinear premise; third-order and higher order statistics, such as intermittency and coherent structures, such as current sheets, cannot be investigated using such an approach. We present a wide range of theoretical arguments in support of the relevance of linear wave properties even in a strongly turbulent plasma, motivated by the mathematical properties of the nonlinear equation of evolution for an incompressible MHD plasma. We present an analogy with the case of a critically damped simple harmonic oscillator, and suggest that it is neither necessary nor expected that one should see evidence of a linear dispersion relation ($\omega$ vs.~$k$) in measurements of turbulence. In addition, we present argument that linear collisionless damping may persist even in the strongly turbulent regime and the resulting plasma heating certainly can be spatially non-uniform, despite frequent claims to the contrary. We review evidence in support of the quasilinear premise from numerical simulations, including results supporting the applicability of linear eigenfunctions and linear collisionless damping rates in the turbulent plasma. Frequency diagnostics of plasma turbulence simulations have yielded contradictory findings, but simulations employing all three dimensions in space appear to largely find the frequency of the turbulent dynamics consistent with the linear wave frequencies. Given that the idea of critical balance in strong plasma turbulence is essentially a quasilinear concept, evidence in support of critical balance indirectly supports the quasilinear premise. Simulations again yield contradictory results, but the line dividing these conflicting results appear to coincide with the method used to determine the direction of the magnetic field: studies using a \emph{local} mean magnetic field are consistent with the predictions of critical balance, while studies employing a global magnetic field are not. Finally, we discuss observational evidence from turbulence in the solar wind that supports the quasilinear premise, including multi-spacecraft k-filtering analyses that find plasma-frame frequencies of the turbulent fluctuations consistent with \Alfven and kinetic \Alfven waves. Measurements of the the magnetic energy spectrum as a function of the angle of the solar wind flow with respect to the magnetic field also find support for critical balance found when the magnetic field direction is determined locally. The question of the validity of the quasilinear premise---that linear wave properties are relevant to strong plasma turbulence---clearly remains to be settled. On balance, however, we argue here that the bulk of the evidence appears to support it as a valuable means of modeling turbulence. The utility of the quasilinear premise for the study of plasma turbulence, however, may also be judged \emph{a posteriori} by the insights gained from such an approach, and we review a number of studies, including those using the novel \emph{synthetic spacecraft data method}, that have succeeded in more strongly constraining the fundamental nature of plasma turbulence. The ultimate goal of turbulence models based on the quasilinear premise is to develop the capability to predict the evolution of any turbulent plasma system, including the spectrum of turbulent fluctuations, their dissipation, and the resulting plasma heating. | 14 | 4 | 1404.2913 |
1404 | 1404.3725_arXiv.txt | We use cosmological N-body simulations to investigate whether measurements of the moments of large-scale structure can yield constraints on primordial non-Gaussianity. We measure the variance, skewness, and kurtosis of the evolved density field from simulations with Gaussian and three different non-Gaussian initial conditions: a local model with $\fnl=100$, an equilateral model with $\fnl=-400$, and an orthogonal model with $\fnl=-400$. We show that the moments of the dark matter density field differ significantly between Gaussian and non-Gaussian models. We also make the measurements on mock galaxy catalogs that contain galaxies with clustering properties similar to those of luminous red galaxies (LRGs). We find that, in the case of skewness and kurtosis, galaxy bias reduces the detectability of non-Gaussianity, though we can still clearly discriminate between different models in our simulation volume. However, in the case of the variance, galaxy bias greatly amplifies the detectability of non-Gaussianity. In all cases we find that redshift distortions do not significantly affect the detectability. When we restrict our measurements to volumes equivalent to the Sloan Digital Sky Survey II (SDSS-II) or Baryon Oscillation Spectroscopic Survey (BOSS) samples, the probability of detecting a departure from the Gaussian model is high by using measurements of the variance, but very low by using only skewness and kurtosis measurements. For example, if our local non-Gaussian model were the true model in the universe, a variance measurement in the BOSS survey would have a $\sim$95\% chance of detecting this non-Gaussiantity at the $2\sigma$ level, whereas a skewness measurement would only have at best a $\sim$25\% chance of doing so. We estimate that in order to detect an amount of non-Gaussianity that is consistent with recent CMB constraints using skewness or kurtosis, we would need a galaxy survey that is much larger than any planned future survey. Skewness and kurtosis measurements are thus never likely to yield useful constraints on primordial non-Gaussianity. On the other hand, future surveys should be large enough to place meaningful constraints using measurements of the galaxy variance. | \label{s:introduction} Inflation is the most promising paradigm for the early universe \citep{Guth:1981}. The standard inflationary paradigm predicts nearly Gaussian and scale invariant primordial density fluctuations, which are consistent with the observations of the Cosmic Microwave Background (CMB) and Large-Scale Structure (LSS) in the last few decades. However, even the simplest inflation model predicts some small deviation from Gaussianity \citep{Falk:1993, Gangui:1994, Maldacena:2003, Bartolo:2004}. Within the standard inflationary paradigm, there are currently many viable inflationary models, but it is difficult to discriminate between them. While most of the popular inflation models predict slight deviations from Gaussian fluctuations, different models predict different amounts and flavors of non-Gaussianity, which makes it a very powerful tool for constraining inflationary models (e.g., see \citealt{Chen:2010} for a review). Detecting primordial non-Gaussianity is thus an important goal of modern cosmology and it has recently garnered much attention. The primordial density fluctuations are both the direct cause of CMB anisotropy, and the seeds of large scale structure (LSS) formation. Deviations from primordial Gaussianity can thus leave signals on both the CMB and LSS. To date, observations of the CMB have been playing the central role in constraining the amplitudes of various types of primordial non-Gaussianity, with tight constraints coming from both WMAP \citep{Bennett:2013} and, most recently, Planck \citep[][ paper XXIV]{PlanckCollaboration:2013}. However, ongoing and future high quality redshift surveys raise hope for detecting non-Gaussianity in LSS. The Sloan Digital Sky Survey (SDSS; \citealt{York:2000}) has provided redshifts of over 100,000 luminous red galaxies (LRGs) in a large volume \citep{Eisenstein:2001}, and the ongoing Baryon Oscillation Spectroscopic Survey (BOSS; \citealt{Dawson:2013}), which is part of the SDSS-III project \citep{Eisenstein:2011}, is mapping 1.5 million luminous galaxies to redshift $z \sim 0.7$. Future redshift surveys like eBOSS, DESI, and Euclid will map even larger volumes. These surveys provide great opportunities of constraining primordial non-Gaussianity with large-scale structure. There are several avenues for constraining primordial non-Gaussianity with galaxy surveys, including the galaxy power spectrum, higher order correlations of the density field, e.g., the bispectrum, and statistics of rare peaks, i.e., the abundance of massive clusters. There have been many studies attempting to detect non-Gaussianity using the galaxy power spectrum \cite[e.g., ][]{Slosar:2008,Afshordi:2008,Ross:2013,Giannantonio:2013}. The galaxy bispectrum is much more difficult to measure and there has only been one attempt to use it for the purpose of constraining non-gaussianity \citep{Scoccimarro:2004}. However, it provides a highly sensitive probe of non-Gaussianity and is likely to yield the best constraints from LSS with future surveys \citep{Sefusatti:2007, Sefusatti:2009, Baldauf:2011, Scoccimarro:2012} A much simpler set of statistics for quantifying departures from Gaussianity are the higher order moments of the density field, of which the most frequently used are the third order normalized moment \emph{skewness} and fourth order normalized moment \emph{kurtosis}. Though gravitational evolution contributes most of the signal in these moments in the present day density field, small departures from Gaussianity in the primordial density field may still cause slightly different skewness and kurtosis today, which may be detectable in sufficiently large galaxy redshift surveys. The evolution of skewness, and kurtosis for Gaussian initial conditions has been studied both analytically and numerically in many published works \citep{Peebles:1980, Fry:1985, Coles:1991, Juszkiewicz:1992, Weinberg:1992, Bouchet:1992, Lahav:1993, Luo:1993, Coles:1993, Juszkiewicz:1993, Lucchin:1994, Frieman:1994, Bernardeau:1994, Hui:1999, Bernardeau:2002}. For arbitrary non-Gaussian initial conditions, \cite{Fry:1994} computed the evolution of skewness in second-order perturbation theory, and \cite{Chodorowski:1996} computed the kurtosis case. Observationally, skewness and kurtosis have been measured for many galaxy redshift surveys \citep{Bernardeau:2002}, such as QDOT \citep{Saunders:1991}, 1.2Jy IRAS \citep{Bouchet:1992, Bouchet:1993, Kim:1998}, CfA-SRSS \citep{Gaztanaga:1992}, 1.9Jy IRAS \citep{Fry:1994a}, PPS \citep{Ghigna:1996}, SRSS2 \citep{Benoist:1999}, PSCz \citep{Szapudi:2000p}, Durham/UKST \citep{Hoyle:2000}, Stromlo/APM \citep{Hoyle:2000}, 2dFGRS \citep{Croton:2004}, VVDS \citep{Marinoni:2005}, and SDSS \citep{Szapudi:2002, Ross:2008, P'apai:2010}. So far all results are consistent with Gaussian initial conditions, but these surveys have not had sufficient volume to detect plausible amounts of primordial non-Gaussianity. With much larger redshift surveys coming out in the next decade, we think this is a good time to revisit this question. Though the skewness and kurtosis contain less information than their corresponding non-zero separation correlations, the 3 and 4-point correlation functions (and their Fourier transforms, the bispectrum and trispectrum), they are conceptually simpler and much easier to measure. In this paper, we use N-body simulations to investigate the detectability of inflationary-motivated primordial non-Gaussianity from skewness and kurtosis measurements of the present day galaxy distribution. We also investigate the second order moment of the density field, \emph{variance}, which contains similar information to the power spectrum. In \S\ref{s:theory}, we review the background theory and some related definitions. In \S\ref{s:data} we present the details of our simulations, which include both Gaussian and non-Gaussian initial conditions, and we describe how we measure the density field moments from these simulations. We show our results in \S\ref{s:results}, including measurements on both dark matter particles and mock galaxy catalogs constructed to model the distribution of SDSS LRGs. We also make measurements on subsets of the simulations that have volumes equivalent to the SDSS-II and BOSS surveys, and we calculate the likelihood of detecting departures from the Gaussian model with variance, skewness or kurtosis measurements from these surveys. We present our conclusions and some discussion in \S\ref{s:discussion}. | \label{s:discussion} In this paper, we have measured the variance $\Psi_2$, skewness parameter $S_3$, and kurtosis parameter $S_4$ on N-body simulations that are seeded with local ($\fnl=100$), equilateral ($\fnl=-400$), and orthogonal ($\fnl=-400$) non-Gaussian initial conditions, as well as with Gaussian initial conditions. We have made measurements on the evolved dark matter density field and on two different sets of mock galaxy catalogs that were designed to simulate two different luminosity samples. Finally, we have investigated the detectability of non-Gaussianity for different galaxy survey volumes. Our main conclusions are as follows. \begin{itemize} \item Simulations seeded with Gaussian and different non-Gaussian initial conditions show different variance, skewness, and kurtosis in the evolved density field. The differences are clear in both the dark matter distribution and mock galaxy catalogs. \item Galaxy bias, for the LRG-type galaxies that we consider, significantly reduces the detectability of primordial non-Gaussianity using skewness and kurtosis measurements, but dramatically increases the detectability using measurements of the variance. Since different non-Gaussian models provide different scale-dependent bias corrections, the deviation of non-Gaussian models from the Gaussian case depends on the amount of bias and the scale, as well as the nature of the non-Gaussian model. \item Redshift distortions shift the variance, skewness, and kurtosis in the same way for Gaussian and non-Gaussian initial conditions. As a result, they do not affect the detectability of primordial non-Gaussianity. \item Skewness and kurtosis measurements made in current galaxy survey volumes will not have sufficient signal-to-noise to detect primordial non-Gaussianity. The likelihood of finding $2\sigma$ evidence for $\fnl$ by making a skewness measurement in a volume equivalent to the BOSS survey is less than $\sim 25$\% for the galaxy samples and scales and $\fnl$ values we consider. Kurtosis measurements provide even worse constraining power. Measurements of the galaxy variance however, have a high probability of detecting our $\fnl$ values in a volume equivalent to BOSS. \item The unnormalized higher order moments $\Psi_3$ and $\Psi_4$ provide more constraining power than their normalized versions $S_3$ and $S_4$. However, these moments do not perform as well as the variance, and they are expected to be more covariant with $\Psi_2$. \item Using simple arguments to scale our results to more realistic $\fnl$ values (for example, $\fnl=6$ for the local model and $\fnl=-75$ for the equilateral model), we find that skewness and kurtosis measurements will likely never have sufficient signal-to-noise to detect non-Gaussianity of inflationary type, since the required survey volumes exceed those of the largest planned future surveys. Measurements of the galaxy variance, however, should be able to probe interesting values of $\fnl$ for some non-Gaussian models in a survey like Euclid. \end{itemize} These results are not surprising because the skewness and kurtosis only contain reduced information about the density field. They are not nearly as sensitive as the bispectrum and trispectrum when used as a probe of primordial non-Gaussianity. On the other hand, the variance contains very similar information to the power spectrum, which many studies have shown will be able to provide competitive constraints on non-Gaussianity \citep[e.g.,][]{Giannantonio:2012}. Measurements of the skewness and kurtosis from larger future redshift surveys, such as eBOSS, DESI, and Euclid will have much larger signal-to-noise and will provide tighter constraints on non-Gaussian models. However, as we discussed above, these constraints will not be competitive with already existing constraints from Planck. Only the bispectrum and trispectrum have sufficient constraining power to have a chance at detecting primordial non-Gaussianity. Their higher constraining power results from the shape dependence of these correlators that is lost when integrating it out with spherical top-hat filters to get the skewness and kurtosis parameters. To take advantage of such dependencies, however, nontrivial effects due to bias and redshift-space distortions must be fully accounted for. We hope to report on this soon. | 14 | 4 | 1404.3725 |
1404 | 1404.1450_arXiv.txt | We discuss the physics resulting from the supersymmetric Higgs-lepton inflation model and the recent CMB B-mode observation by the BICEP2 experiment. The tensor-to-scalar ratio $r=0.20^{+0.07}_{-0.05}$ of the primordial fluctuations indicated by the CMB B-mode polarization is consistent with the prediction of this inflationary model for natural parameter values. A salient feature of the model is that it predicts the seesaw mass scale $M$ from the amplitude of the tensor mode fluctuations. It is found that the 68\% (95\%) confidence level (CL) constraints from the BICEP2 experiment give 927 GeV $< M <$ 1.62 TeV (751 GeV $< M <$ 2.37 TeV) for 50 e-foldings and 391 GeV $< M <$ 795 GeV (355 GeV $< M <$ 1.10 TeV) for 60 e-foldings. In the type I seesaw case, the right-handed neutrinos in this mass range are elusive in collider experiments due to the small mixing angle. In the type III seesaw, in contrast, the heavy leptons will be within the reach of future experiments. We point out that a significant portion of the parameter region corresponding to the 68\% CL of the BICEP2 experiment will be covered by the Large Hadron Collider experiments at 14 TeV. | \label{sec:introduction} The discovery of the cosmic microwave background (CMB) B-mode polarization by the BICEP2 experiment \cite{Ade:2014xna} is truly remarkable as the existence of the tensor mode in the primordial fluctuations provides a direct evidence for inflation in the early Universe\footnote{ The BICEP2 experiment uses 150 GHz single wavelength bolometers. In order to conclude that the gravitational waves causing the polarization are undeniably of inflationary origin, the results need to be confirmed also at other wavelengths.}. It has a significant impact on inflation model building. In the past decade models producing small tensor mode fluctuations were considered favourable since, for example, the Planck data in 2013 \cite{Ade:2013uln} constrained the tensor-to-scalar ratio $r < 0.11$ at 95\% confidence level (CL). The models of inflation producing such small $r$ include the Higgs inflation model \cite{CervantesCota:1995tz,Bezrukov:2007ep}, supersymmetric Higgs inflation-type models \cite{Einhorn:2009bh,Ferrara:2010yw,Ferrara:2010in,Arai:2011nq,Arai:2013vaa}, the hill-top inflation model \cite{Boubekeur:2005zm}, and the $R^2$ inflation model \cite{Starobinsky:1980te}. Among these, the Higgs inflation model is a particularly simple and concrete particle physics realization of inflation that also provides predictions in low-energy particle physics. These models are in tension with the finding of the BICEP2 experiment. See Refs. \cite{Okada:2014lxa,Bezrukov:2014bra,Hamada:2014iga} for the updated status of various models. In the present paper we point out that the prediction of the inflationary scenario which we call the Higgs-lepton inflation (HLI) \cite{Arai:2011aa,Arai:2012em} fits extremely well with the new data for natural choice of parameters. The HLI scenario is realized in the supersymmetric seesaw model, which is the simplest extension of the minimal supersymmetric Standard Model (MSSM) to include the right-handed neutrinos. The model incorporates the type I \cite{seesaw} or type III seesaw mechanism \cite{Foot:1988aq} by which the small nonzero neutrino masses that are evidenced by the neutrino oscillations are naturally explained. It also includes possibility for generating baryon asymmetry through leptogenesis or the Affleck-Dine mechanism. As a feature of the model, HLI directly associates the spectrum of the CMB with the mass scale of the right-handed neutrinos. We will see that the new data from the BICEP2 experiments constrains this mass scale to be between a few hundred GeV and a few TeV. These constraints are potentially useful since the right-handed (s)neutrinos may also be searched in colliders. | 14 | 4 | 1404.1450 |
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1404 | 1404.4872_arXiv.txt | Using the MOSFIRE near-infrared multi-slit spectrograph on the Keck 1 Telescope, we have secured high signal-to-noise ratio absorption line spectra for six massive galaxies with redshift $2 < z < 2.5$. Five of these galaxies lie on the red sequence and show signatures of passive stellar populations in their rest-frame optical spectra. By fitting broadened spectral templates we have determined stellar velocity dispersions and, with broad-band HST and Spitzer photometry and imaging, stellar masses and effective radii. Using this enlarged sample of galaxies we confirm earlier suggestions that quiescent galaxies at $z>2$ have small sizes and large velocity dispersions compared to local galaxies of similar stellar mass. The dynamical masses are in very good agreement with stellar masses ($\log \Mstar/\Mdyn = -0.02 \pm 0.03$), although the average stellar-to-dynamical mass ratio is larger than that found at lower redshift ($-0.23 \pm 0.05$). By assuming evolution at fixed velocity dispersion, not only do we confirm a surprisingly rapid rate of size growth but we also consider the necessary evolutionary track on the mass-size plane and find a slope $\alpha = \mathrm{d} \log \R / \mathrm{d} \log \Mstar \gtrsim 2$ inconsistent with most numerical simulations of minor mergers. Both results suggest an additional mechanism may be required to explain the size growth of early galaxies. | \label{sec:intro} The assembly history of nearby quiescent and morphologically early-type galaxies remains an important issue in extragalactic astronomy. Of particular interest is the fate of the population of compact red galaxies at redshift $z \sim 2$ \citep{daddi05, trujillo06, vandokkum06} which has been the subject of much observational effort. To match the properties of local galaxies, the growth in size must be significantly larger than the growth in mass. Although initial progress relied on photometric data, providing measures of both compact sizes and stellar masses of large samples beyond redshift $z \sim 1$ \citep[e.g.,][]{damjanov09, bezanson11, bezanson12}, key advances have become possible with spectroscopic samples. Spectroscopic data address the relative growth of the dynamical and stellar masses \citep{belli14lris}, as well as mean luminosity-weighted ages \citep{newman14}. As stellar velocity dispersions should remain stable through merger episodes, spectroscopic observations can link high-redshift progenitors with their local descendants. This is particularly important in considering progenitor bias, i.e., the continued arrival of recently-quenched larger galaxies \citep[e.g.,][]{carollo13}. Via the first comprehensive spectroscopic sample at $z>1$, we quantified the size and mass growth rates of individual galaxies demonstrating significant growth \citep{belli14lris} at a rate consistent with minor mergers observed from independent imaging studies \citep{newman12}. Attention now focuses on understanding the population of massive compact sources at $z > 2$. Deep imaging with the Wide Field Camera 3 (WFC3/IR) onboard \emph{Hubble Space Telescope} (\HST) has determined the growth rate is particularly rapid over the brief interval corresponding to $1.5<z<2.5$ \citep{newman12}. However, only limited spectroscopy is available as absorption line work is difficult in the near-infrared \citep[e.g.,][]{kriek06}. Until recently the relevant instruments (e.g. X-Shooter on the Very Large Telescope) were single-object long slit facilities. Despite heroic efforts, few stellar velocity dispersions are available beyond $z\simeq2$ \citep{vandokkum09, toft12, vandesande13}. The MOSFIRE multi-slit near-infrared spectrograph on Keck 1 \citep{mclean12} provides the first opportunity to systematically explore quiescent galaxies beyond $z \sim 2$. Here we present absorption line spectroscopy for a reasonable sample of compact massive galaxies at $2 < z < 2.5$. Our goal is to derive stellar velocity dispersions and dynamical masses, testing the rapid size growth rate inferred photometrically, as well as to examine this growth in the context of numerical simulations of galaxy merging. \begin{figure*}[tbp] \centering \includegraphics[width=\textwidth]{mosfig_spectra_err} \caption{\HST\ images and MOSFIRE spectra for a sample of six galaxies with detected absorption lines. For each object, the ID and spectroscopic redshift are indicated; the 4 arcsec cutout shows the F160W image with a 10 kpc ruler; the observed spectrum (inverse-variance smoothed, black line), its uncertainty (divided by 3, light blue), and the best-fit model (red line) are plotted. Absorption and emission features are marked by gray dotted lines. For 4732, only ground-based data are available, and the cutout is from the UltraVISTA H-band imaging \citep{mccracken12}.} \label{fig:spectra} \end{figure*} Throughout we use AB magnitudes and assume a $\Lambda$CDM cosmology with $\Omega_M$=0.3, $\Omega_{\Lambda}$=0.7 and $H_0$= 70 km s$^{-1}$ Mpc$^{-1}$. | We use our new dynamical measurements, together with those from lower-redshift observations, to constrain the evolution of the size and structure of quiescent galaxies. Figure \ref{fig:cube}a shows the mass-size relation for similarly-selected $UVJ$-quiescent galaxies over $0 < z < 2.5$. We show the local population from the Sloan Digital Sky Survey \citep[SDSS DR7,][grayscale map]{abazajian09}, a sample at $1 < z < 1.6$ from \citet[][small orange points]{belli14lris}, and the other two quiescent galaxies at $z>2$ for which velocity dispersion measurements have been published (\citealt[][purple]{vandokkum09}, and \citealt[][blue]{vandesande13}; see also \citealt{toft12}). Our MOSFIRE sample is shown in red. Clearly, the mass-size relation evolves with redshift. At fixed stellar mass, galaxies at $z \sim 1.3$ are about 0.25 dex smaller than the local population. At $z>2$, the logarithmic offset from the local sample nearly doubles, implying evolution accelerates at earlier cosmic times. These findings confirm the results of previous photometric studies, as shown by the agreement of our points with the mass-size relation at $z\sim 2.2$ from \citet[][red line]{newman12}. Object 5517, the brightest galaxy (BCG) of a protocluster, is an exception, suggesting that such systems have large sizes already at $z\sim2$, in agreement with other studies at $z\lesssim1.8$ \citep{papovich12, stanford12, newman14}. The main advance of this paper is that we can now explore the dynamical properties of galaxies at $z > 2$. Figure \ref{fig:cube}b shows high-redshift galaxies have significantly larger velocity dispersions than lower redshift objects of similar stellar mass. Most of our MOSFIRE objects have similar dispersions, $\sigmae \approx 300$ km s $^{-1}$, with the exception of 4126 (shown as an open symbol). This galaxy is the only post-starburst object in our sample, and presents an elongated morphology and low \Sersic\ index, $n=1.4$, typical of disk-like galaxies. Velocity dispersions enable us to calculate dynamical masses, via $\Mdyn = 5 \sigmae^2 \R / G$. Figure \ref{fig:cube}c compares the dynamical and stellar masses, again contrasting the trend with samples drawn from the literature. While the $z\sim1.3$ sample closely follows the local distribution, $z>2$ galaxies tend to have higher stellar-to-dynamical mass ratios. This difference was first suggested by \citet{toft12} and \citet{vandesande13}, but as our MOSFIRE sample doubles the number of dynamical masses with $z>2$, it is now more significant, particularly as our velocity dispersions are more accurate. We calculate the average mass ratio for all the $z>2$ quiescent galaxies, excluding the BCG, and we find $\log \Mstar/\Mdyn = -0.02 \pm 0.03$ and an average stellar mass of $10^{11.3} \Msun$. Although our sample is modest, this is a remarkably tight agreement. Considering the most massive galaxies of the $1<z<1.6$ sample, we find $\log \Mstar/\Mdyn = -0.23 \pm 0.05$ and an average mass of $10^{11.1} \Msun$. This significant evolution could arise if $z>2$ quiescent galaxies have a reduced dark matter fraction, a heavier stellar IMF or different structure compared to their lower-redshift counterparts. We now use our dynamical masses to infer the rate of size growth for high-redshift quiescent galaxies. Following \citet{belli14lris}, we assume that we can link progenitor and descendant galaxies by selecting populations at \emph{fixed velocity dispersion}. This follows the results of numerical simulations that show that velocity dispersion is minimally affected during merger events \citep[e.g.][]{hopkins09scalingrel,oser12}, and the observed unchanging velocity dispersion function \citep{bezanson12}. For each of our $z>2$ objects, we therefore select SDSS galaxies with similar velocity dispersions (within 0.05 dex). We calculate the median size of the local subsample and assume that our high redshift object will grow in size until it reaches that value. We repeat this procedure for lower-redshifts samples and show the inferred growth rates in the left panel of Figure \ref{fig:fixedsigma}. Typical $z>2$ galaxies\footnote{The BCG and the \citet{vandokkum09} galaxy are omitted because in the local universe there are no objects with such high velocity dispersions. Additionally both have the most uncertain dispersions.} are noticeably smaller than those at $z\sim1.3$, despite the small interval in cosmic time between the two samples. Our results are qualitatively in agreement with the size growth at \emph{fixed number density} derived by \citet[][violet line]{vandokkum10}. Interestingly, the growth of individual galaxies is not dissimilar to that of the total population derived from the evolution of the mass-size relation \citep[][red line]{newman12}. Although minor merging is likely responsible for the size evolution of quiescent galaxies at $z<1.5$, such a rapid growth at $z\sim2$ is hard to reconcile with the observed merger rate (\citealt{newman12}; see also \citealt{cimatti12}). In the right panel of Figure \ref{fig:fixedsigma} we show the mass-size relation for galaxies with $\log \sigmae > 2.40$ at all redshifts. This velocity dispersion bin includes all the $z>2$ galaxies except the post-starburst object 4126. The local population forms a clear sequence whereas objects at intermediate redshifts show a mild offset towards smaller sizes (and masses). However, the $z>2$ galaxies populate a distinct region of the mass-size plane with almost no overlap with lower redshift samples; almost all have radii 0.3 dex below the local sample. The inescapable conclusion is that quiescent galaxies at $z>2$ must undergo a dramatic and rapid size growth. A powerful method to constrain the physical processes responsible for this size growth is to measure the slope $\alpha = \mathrm{d} \log \R / \mathrm{d} \log \Mstar $ of the evolutionary tracks on the mass-size plane and compare it with theoretical predictions. Simple virial arguments \citep{naab09, bezanson09} give $\alpha = 1$ for identical mergers and $\alpha = 2$ for the limiting case of mergers with infinitely diffuse satellites. More realistic numerical simulations, which include the effect of dark matter, gas, and a distribution of orbits, indicate that minor mergers are less efficient than the theoretical limit, and yield values in the range $1.4 < \alpha < 1.8$ \citep{hopkins09scalingrel, nipoti12, oser12, posti14}. The simulations of \citet{hilz13}, in which massive dark matter halos enhance the efficiency of minor merging up to $\alpha=2.4$, are the only exception. However, the large dark matter fraction at the center of these simulated galaxies disagrees with the observed stellar-to-dynamical mass ratios at both low and high redshift. Assuming evolution at fixed velocity dispersion, we measure $\alpha$ by considering the tracks that high-redshift points must follow in order to match the local distribution. Using this technique, the $z\sim1.3$ sample yields $\alpha = 1.4 \pm 0.2$ \citep{belli14lris}. Merging can therefore readily explain the size growth over $0 < z < 1.5$, a conclusion supported by direct imaging \citep{newman12}. However, at $z>2$ the growth is clearly much more rapid. It is not possible to derive a robust measurement of the slope $\alpha$ for two reasons: firstly, our $z>2$ sample is not velocity dispersion complete; secondly, one of our basic assumptions might not hold, since the velocity dispersion function has not been probed beyond $z\sim1.5$. As the number density of quiescent galaxies declines steeply at this redshift, a strong progenitor bias is expected. Despite these limitations, we can still derive an important lower limit on $\alpha$, by assuming that the average high-redshift galaxy (shown in black, excluding the BCG) will evolve into one of the most massive objects at $z\sim0$. Using this method, for all the $z>2$ quiescent galaxies excluding the BCG we derive a lower limit of $\alpha \gtrsim 2$, shown as a dashed line in the figure. In summary, our spectroscopic data allows us to conclude that both the absolute rate of size growth {\it and} the inferred motion in the mass-size plane are independently inconsistent with minor mergers being the principal physical process governing the evolution of quiescent galaxies at $z\sim2$. \\ We thank Chuck Steidel, Ian McLean and their team for their work in producing the remarkable MOSFIRE instrument. We thank Guillermo Barro for useful discussions. The authors acknowledge the very significant cultural role that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. | 14 | 4 | 1404.4872 |
1404 | 1404.4569_arXiv.txt | In light of recent successes in measuring baryon acoustic oscillations (BAO) in quasar absorption using the \lymana\ (\lya) transition, I explore the possibility of using the 1548\AA\ transition of triply ionized carbon (\CIV) as a tracer. While the \Lya\ forest is a more sensitive tracer of intergalactic gas, it is limited by the fact that it can only be measured in the optical window at redshifts $z > 2$. Quasars are challenging to identify and observe at these high redshifts, but the \CIV\ forest can be probed down to redshifts $z\approx1.3$, taking full advantage of the peak in the redshift distribution of quasars that can be targeted with high efficiency. I explore the strength of the \CIV\ absorption signal and show that the absorbing population on the red side of the \Lya\ emission line is dominated by \CIV\ (and so will dominate over the potential BAO signal of other metals). As a consequence, I argue that forthcoming surveys may have a sufficient increase in quasar number density to offset the lower sensitivity of the \CIV\ forest and provide competitive precision using both the \CIV\ autocorrelation and the \CIV-quasar cross correlation at $\langle z \rangle \approx 1.6$. | Baryon acoustic oscillations (BAO) are imprinted on large-scale structures and provide a probe of cosmic expansion through their use as a standard ruler (\citealt{2013PhR...530...87W} and references therein). Since the intergalactic medium is thought to represent the overwhelming majority of baryons at $z>1$ (\citealt{2009RvMP...81.1405M} and references therein), absorbers tracing these baryons are a probe of the characteristic BAO scale. Recent results have demonstrated this by using the autocorrelation of \lya\ forest absorbers along the line of sight to distant quasars \citep{2013A&A...552A..96B,2013JCAP...04..026S, 2014arXiv1404.1801D}. They measure the BAO scale with a uncertainty of 2\% at $\langle z \rangle=2.3$ and are particularly effective at constraining the Hubble parameter. This has been supplemented by the cross-correlation between \Lya\ forest absorption and quasars at the same redshift \citep{2014JCAP...05..027F}, which is more effective as a probe of the angular diameter distance. Together they have proven to be a powerful cosmological probe \citep{2014arXiv1404.1801D}. The BAO peak has been observed at $z \le 0.6$ using the galaxy-galaxy correlation function (e..g. \citealt{2011MNRAS.415.2892B,2014MNRAS.439...83A}), but a gap exists at intermediate redshifts. This will be filled by the extended Baryon Oscillation Spectroscopic Survey (eBOSS) through surveys of luminous red galaxies, emission line galaxies and quasars. An additional, and effectively free probe, is possible at $1.3<z<3.5$. \Lya\ forest based studies are not possible at $z<2$ as \Lya\ leaves the optical band, but metal forests with longer transition wavelengths allow the possibility of tracing structure at lower-redshifts. Triply ionized carbon (\CIV) provides a useful doublet \CIVa\ ($\lambda 1548$\AA) and \CIVb\ ($\lambda 1551$\AA) as it is an effective tracer of metal enriched gas over a wide range of densities (e.g. {\citealt{2003ApJ...596..768S}), has high oscillator strength, and a suitable rest-frame wavelength. In this Letter, I shall explore the potential for using the \CIV\ forest to measure the BAO scale and so provide a new probe of the expansion of the universe. This work is set out as follows: in Section~\ref{data}, the data set used will be described, in Section~\ref{strength}, the strength of the \CIV\ signal is explored, Section~\ref{metalpop} describes tests of the metal population, Section~\ref{survey} presents a potential survey, and Section~\ref{challenges} explores some observational challenges. | I have explored the potential for using the \CIV\ forest down to redshift $z=1.3$ as a new probe of baryon acoustic oscillations, and an alternative to the \Lya\ forest. The need for turning to this weaker probe of intergalactic structure is driven by the fact that \lya\ absorption drops out of the optical window at $z\approx 2$, and the relative ease with which quasars below $z\approx2$ can be surveyed. Two bands redward of the quasar \Lya\ emission line were investigated between \Lya\ and \CIV\ in emission, split by the \SiIV\ emission line. Using BOSS DR9 quasar spectra, the metal power, metal populations, and strength of the \CIV\ absorption signal in relation to \Lya\ absorption were tested. I find that \CIV\ absorption dominates these bands, and represents 80\% of absorption. Furthermore, the signal associated with the \CIV\ forest at low redshift is a factor of 4--25 weaker that that associated with the \Lya\ forest at high redshift, but with greater bias, and a dynamic range suited to probing higher density regions. The upcoming eBOSS survey will provide five times the effective number density of quasars available for a $z<2$ \CIV\ forest survey compared to the BOSS \Lya\ forest survey. Therefore it may provide broadly comparable accuracy of around 2\% in the BAO scale. In combination with the eBOSS quasars redshift distribution, the \CIV- quasar cross-correlation may provide uncertainty as low as 1\%. Forthcoming quasar surveys as part of Dark Energy Spectroscopic Instrument (DESI) and WHT Enhanced Area Velocity Explorer (WEAVE) also have the potential to provide improved constraints. | 14 | 4 | 1404.4569 |
1404 | 1404.3663_arXiv.txt | \label{sec1} The Bicep2 collaboration has recently reported the detection of a B mode polarization that has been attributed to the presence of gravitational waves of inflationary origin \cite{BICEP2,BICEP1} (see also \cite{SPTpol} for the detection of the B mode coming from lensing). The tensor fluctuations of the geometry are able to generate a B mode polarization in the Cosmic Microwave Background (CMB in what follows) provided the typical wavelengths of the relic gravitational waves were larger than the Hubble radius after matter radiation equality but before decoupling, i.e. at the moment when the initial conditions of the polarization anisotropies are set. In principe the B mode polarization maybe the result of a more mundane process well known in the treatment of cold plasmas, namely the Faraday effect. According to the Faraday effect the polarization plane of the incoming radiation is rotated because of the presence of a magnetic field in a medium with finite density of charge carriers. The latter requirement is met by the predecoupling plasma that is globally neutral but intrinsically charged since the electrons and the ions have a common concentration that is ${\mathcal O}(10^{-10})$ the concentration of the photons at the corresponding epoch. The only further assumption to get a B mode polarization is therefore the presence of a magnetic field that will be assumed to be stochastic not to conflict with the assumed isotropy of the background geometry. The Faraday effect of the CMB polarization was analyzed almost two decades ago and, to some extent, even before (see \cite{far1} and references therein). These suggestions and have been subsequently discussed in a number of different articles (see \cite{far2} and references therein). There are, in principle, other sources of B mode polarization due to the magnetic fields but they are smaller than the contribution of the Faraday effect. The first task of the present paper will therefore be to establish if the observed B mode polarization can be ascribed to the Faraday effect. The answer to the question will be, in short, that the observed B mode polarization cannot be attributed predominantly to a Faraday rotated E mode polarization since the magnetized temperature autocorrelations would be too distorted. In the second and more technical part of the paper the attention will then be focussed on the interference of the Faraday effect with the B mode produced by the tensor mode of the geometry. The aim will be to derive a set of scaling rules that could be directly applied to the E mode and B mode power spectra. The Faraday rotation will be described terms of a stationary, quasi-Markovian and random process \cite{stochde1}. It will be shown that the evolution of the brightness perturbations obeys a set of stochastic differential equations that can be solved using the cumulant expansion \cite{stochde2,stochde3}, pioneered in similar contexts by Van Kampen. The stochastic approach to the Faraday effect has been exploited in astrophysics where the source of linear polarization is provided by the properties synchrotron emission \cite{SYNC1,SYNC2,SYNC3}. It has been recently suggested \cite{RC1} that a consistent stochastic description can be successfully achieved in the case of the Cosmic Microwave Background (CMB in what follows) where the linear polarization is primarily provided by the adiabatic initial conditions of the Einstein-Boltzmann hierarchy \cite{WMAP9}. The B mode induced by the stochastic Faraday effect thanks to the presence of the linear polarization of the CMB can be expressed, according to the results of \cite{RC1} as: \begin{equation} C_{\ell}^{(EE)} = e^{- \omega_{F} }\, \cosh{\omega_{F}} \,\overline{C}_{\ell}^{(EE)}, \qquad C_{\ell}^{(BB)} = e^{- \omega_{F} }\, \sinh{\omega_{F}} \,\overline{C}_{\ell}^{(EE)}, \label{INT1} \end{equation} where $\overline{C}_{\ell}^{(EE)}$ denotes the autocorrelation of the E mode polarization obtained in the absence of stochastic Faraday term and $\omega_{F}$ is given by: \begin{equation} \omega_{F} = 4 \int_{\tau_{r}}^{\tau} \, d\tau_{1} \, \int_{\tau_{r}}^{\tau} \, d\tau_{2} \langle X_{F}(\tau_{1}) \, X_{F}(\tau_{2}) \rangle. \label{INT2} \end{equation} In Eq. (\ref{INT2}) $X_{F}(\tau)$ denotes the Faraday rotation rate and the stochastic process has been assumed, for sake of simplicity, homogeneous in space. The derivation of Eq. (\ref{INT1}) does not demand $\omega_{F}\ll 1$ and shows that the stochastic Faraday rate affects not only the B mode polarization but, to some extent, also the E mode itself. Equations (\ref{INT1}) and (\ref{INT2}) have been derived in \cite{RC1} by assuming that the sole sources of linear polarization were the scalar fluctuations of the geometry. It was anticipated in \cite{RC1} that the results could be extended to the case where the initial source of polarization is not only provided by the scalar modes but also by the tensor modes that appear in one of the minimal extensions of the so-called $\Lambda$CDM paradigm, where $\Lambda$ stands for the dark energy component and CDM for the cold dark matter contribution. While this analysis was in progress there have been claims of detection of a primordial B mode polarization by the Bicep2 collaboration \cite{BICEP2} (see also \cite{BICEP1}) complementing the results of the B mode from lensing \cite{SPTpol}. Although these data are in tension with other data sets for various reasons, it seems timely to present a derivation of the analog of Eq. (\ref{INT1}) when the sources of polarization is not only provided by the standard adiabatic mode but also by the tensor fluctuations of the geometry. The main result of the present analysis can be summarized by writing the analog of Eq. (\ref{INT1}) in this extended set-up where the E modes and the B mode power spectra of the tensors are included: \begin{eqnarray} C_{\ell}^{(EE)} &=& e^{-\omega_{F}} \cosh{\omega_{F}} \, \biggl( \overline{C}_{\ell}^{(EE)} + {\mathcal C}_{\ell}^{(EE)} \biggr) + e^{- \omega_{F}}\, \sinh{\omega_{F}}\, {\mathcal C}_{\ell}^{(BB)}, \nonumber\\ {\mathcal C}_{\ell}^{(BB)} &=& e^{-\omega_{F}} \sinh{\omega_{F}} \biggl( \overline{C}_{\ell}^{(EE)} + {\mathcal C}_{\ell}^{(EE)} \biggr) + e^{-\omega_{F}} \, \cosh{\omega_{F}} \, {\mathcal C}_{\ell}^{(BB)}; \label{INT3} \end{eqnarray} as in Eq. (\ref{INT1}) $\overline{C}_{\ell}^{(EE)}$ denotes the E mode power spectrum coming from the scalar modes of the geometry while ${\mathcal C}_{\ell}^{(BB)}$ and ${\mathcal C}_{\ell}^{(EE)}$ (both in calligraphic style) denote, respectively, the polarization observables induced by the tensor modes of the geometry. Following the standard terminology, the B-mode autocorrelations are denoted by BB. With similar logic, we talk about the TT, TE and EE angular power spectra denoting, respectively, the autocorrelations of the temperature, the autocorrelations of the E mode and their mutual cross correlations. It is appropriate to recall that the tensor modes of the geometry not only produce BB correlations but also EE and TT power spectra (see e.g. \cite{apprais}). Comparing Eqs. (\ref{INT2}) and (\ref{INT3}) in the limit $\omega_{F} \to 0$ we can appreciate that the B mode polarization disappears from Eq. (\ref{INT2}) while it persists in Eq. (\ref{INT3}) and it is solely given by the tensor B mode. According to Eqs. (\ref{INT2}) and (\ref{INT3}) both the E mode and the B mode polarization are frequency dependent since $\omega_{F}$ is proportional to the square of the rate and, ultimately, to the fourth power of the comoving wavelength. The stochastic approach to the Faraday rate represents an ideal framework for deriving a set of scaling laws only involving the measured polarization power spectra. The present findings support the consistency of the whole description and are suitable for a discussion of the Faraday effect when the predominant source of the B mode polarization is provided by relic gravitons with wavelengths comparable with the current Hubble radius. The present paper is organized as follows. In section \ref{sec2} we shall examine, in the light of the Bicep2 findings, the Faraday interpretation of the B mode polarization. In section \ref{sec3} we shall corroborate the analysis with a numerical discussion. In section \ref{sec4} we shall describe the phenomenon of stochastic Faraday mixing. The polarization observables and their scaling properties will be deduced in section \ref{sec5} while the concluding remarks will be collected in section \ref{sec6}. To avoid digressions some relevant technical aspects of the discussions have been collected in the appendices \ref{APPA}, \ref{APPB} and \ref{APPC}. \renewcommand{\theequation}{2.\arabic{equation}} \setcounter{equation}{0} | \label{sec6} This paper investigated the Faraday effect of the CMB as a different and more mundane source of the B mode polarization detected by Bicep2. In the first part of the paper we discussed a maximalist alternative to the tensor B mode where the whole Bicep2 data are explained by a Faraday rotated E mode polarization. In the second part of the paper we discussed the possibility where the tensor B mode interferes with the Faraday rotated E mode polarization. It has been shown both analytically and numerically that the Faraday rotation alone cannot explain the Bicep2 data. If this happens other CMB observables will be excessively distorted. The first estimate can be obtained by maximizing the E mode autocorrelation and by computing the induced B mode polarization. In this case we see that, given the Bicep2 frequency (i.e. $150$ GHz), the Bicep2 normalization can only be reproduced when the magnetic field is ${\mathcal O}(15)$ nG. This value of the magnetic field is too large since it would induce unobserved distortions in the temperature autocorrelations. Indeed much lower magnetic fields (i.e. ${\mathcal O}(1.5)$ nG ) already produce excessive distortions on the TT correlations if the magnetic power spectrum is nearly scale-invariant (i.e. $n_{B} \to 1$). An independent test, in this respect, is provided by the frequency scaling of the signal which can be separately discussed. Other signals of B mode polarization can be induced directly by the tensor and vector modes of the geometry induced by the magnetic fields. It is however well established that these signals are much smaller than the Faraday effect for two reasons. First the magnetized adiabatic mode of scalar origin dominates at the level of the initial conditions and at the level of the TT correlation: the vector and tensor modes of magnetic origin are comparatively smaller. Second the B mode signals induced by the vectors and the tensors are quadratic in the magnetic power spectrum while the Faraday B mode is linear in the magnetic power spectrum. The realistic situation is therefore the one where there are two physically plausible sources of B mode polarization: the first is given by the tensor modes of the geometry, i.e. relic gravitons with present wavelengths comparable with the Hubble radius; the second is given the Faraday rotated E mode polarization. The second part of the present paper dealt with the possibility that two effects can interfere. The B mode polarization of tensor origin is virtually frequency independent. Conversely the Faraday rotated E mode polarization does depend on the frequency. Elaborating on a recent suggestion the Faraday effect has been treated as a random, stationary and quasi-Markovian process. The stochastic treatment of this phenomenon bears some analogy with the case of synchrotron emission and the obtained results encompass and complement previous analyses where the formation of the Faraday effect has been customarily presented as a purely deterministic process in time. Within this approach a set of scaling laws only involving observable power spectra can be derived. These scaling laws, once applied to observational data at different frequencies, can be used to disentangle the Faraday induced B mode polarization from the tensor B mode. | 14 | 4 | 1404.3663 |
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1404 | 1404.0383_arXiv.txt | The central engine of short gamma-ray bursts (sGRBs) is hidden from direct view, operating at a scale much smaller than that probed by the emitted radiation. Thus we must infer its origin not only with respect to the formation of the {\it trigger} - the actual astrophysical configuration that is capable of powering a sGRB - but also from the consequences that follow from the various evolutionary pathways that may be involved in producing it. Considering binary neutron star mergers we critically evaluate, analytically and through numerical simulations, whether the neutrino-driven wind produced by the newly formed hyper-massive neutron star can allow the collimated relativistic outflow that follows its collapse to actually produce a sGRB or not. Upon comparison with the observed sGRB duration distribution, we find that collapse cannot be significantly delayed ($\leq 100$~ms) before the outflow is choked, thus limiting the possibility that long-lived hyper-massive remnants can account for these events. In the case of successful breakthrough of the jet through the neutrino-driven wind, the energy stored in the cocoon could contribute to the precursor and extended emission observed in sGRBs. \keywords {hydrodynamics --- relativistic processes --- gamma-ray burst: general --- stars: winds, outflows --- stars: neutron} | The most popular model for short gamma-ray bursts (sGRBs) invokes the coalescence of binary neutron stars and the subsequent production of a beamed, relativistic outflow \citep{eichler89, paczynski91, narayan92, meszaros92}. The launching of a relativistic jet requires material with sufficient free energy to escape the gravitational field of the central object as well as a mechanism for imparting some directionality to the outflow \citep{mochkovitch93, rosswog03, aloy05, rezzolla11,palenzuela2013}. A potential death trap for such relativistic outflows is the amount of entrained baryonic mass from the surrounding environment \citep[see e.g.][and references therein]{lee07}. In neutron star binaries the elevated post-merger neutrino fluxes are capable of ablating matter from the surface of the remnant at a rate \begin{equation} \dot{M}_{\rm w}\approx 5 \times 10^{-4}\left({L_\nu \over 10^{52}\;{\rm erg/s}}\right)^{5/3}\;M_\odot/{\rm s} \label{eq:wind} \end{equation} \citep{qian96, rosswog02, dessart09}. Thus the rest mass flux arising from the neutrino-driven wind bounds the bulk Lorentz factor of the jet to \begin{equation} \Gamma_\nu \approx 10 \left({L_{\rm jet}\over 10^{52}\;{\rm erg/s}}\right)\left({\dot{M}_{\rm w} \over 5 \times 10^{-4}\;M_\odot/{\rm s}}\right)^{-1} \label{eq:bpop} \end{equation} and hence the successful launch of a highly relativistic jet might have to wait until the collapse of the merger remnant and the ensuing formation of the black hole plus debris disk system. The fate of the post-merger, hyper-massive neutron star is, however, uncertain, and is contingent on the mass limit for support of a hot, differentially rotating configuration \citep[e.g.][]{baumgarte2000,duez2006,giacomazzo13,hotokezaka13a}. The threshold for collapse can be calculated roughly as $M_{\rm thres}=1.35 M_{\rm cold}$ \citep{shibata06}, where $M_{\rm cold}$ is the corresponding value for a cold, non-rotating configuration. In agreement with the mass determination in PSR J0348+0432 \citep[$M_{\rm cold} \gtrsim 2 M_\odot$;][]{demorest10}, a total mass greater than $\approx 2.7 M_\odot$ is required for prompt collapse to a black hole. When $M_{\rm cold} < M < M_{\rm thres}$, various mechanisms could act to dissipate and/or transport energy and angular momentum, possibly inducing collapse after a delay which could range from tens of milliseconds to a few seconds \citep[for a recent review see][]{faber12}. During this period, a baryon loaded wind is continuously ejected for a time $t_{\rm w}$, which precedes jet formation \citep{lehner12}. As a result, a dense wind remains to hamper the advance of the jet, whose injection lifetime, $t_{\rm j}$, is determined by the viscous time scale of the neutrino-cooled disk \citep{lee2004,lee2005a,Setiawan2004,metzger2008,lee2009}. In this {\it Letter}, we study with the use of hydrodynamical simulations how the expansion of the relativistic jet is modified by the previously ejected wind and investigate the conditions necessary for successful sGRB production in binary neutron star mergers. There are three sections. Section~\ref{ana} gives an account of the properties that determine the advancement of the jet in the wind and its possible successful emergence. Section~\ref{num} describes the results of the numerical calculations. Finally, Section~\ref{dis} gives a compendium of the types of observational signatures expected for jets propagating through neutrino-driven winds of different mass loading and durations together with a model proposal for generating sGRBs with precursor and extended emission. | \label{dis} The rate of neutrino-driven mass loss (equation \ref{eq:wind}) emanating from the merger remnant, as argued in Sections~\ref{ana} and \ref{num}, has significant repercussions on the appearance of a relativistic jet propagating through it. But the requirements for successful break-through are most sensitive to the duration of the neutrino-driven wind phase ($t_{\rm w}$), which in turn depends on the stability of the resulting hot, differentially rotating post-merger configuration. If collapse to a black hole and the ensuing jet production is significantly delayed (i.e. $t_{\rm w} > 0.1$ s), the majority of jets will not be able to break free from the wind during the typical duration of a sGRB. On the contrary, if collapse occurs more promptly (i.e. $t_{\rm w} \ll 0.1$ s), the successful break-through of the jet would take place swiftly enough to allow for the production of a typical sGRB. The observed duration distribution of sGRBs can thus be used to constrain the longevity of the post-merger remnant, which is currently under debate. In systems where a stable remnant is formed \citep[the magnetar model; e.g.][]{metzger2008ex}, jet formation can not be notably delayed ($\leq 100$ ms) from the onset of the neutrino-driven wind. Otherwise, a choked jet would result without exception. This is because in stable (hyper-massive) neutron stars, the neutrino-driven wind is expected to continue for at least a diffusion timescale, which is commensurate with the duration of the longest lasting sGRB. Effective sGRB production under such circumstances would not only be afflicted by baryon contamination (equation~\ref{eq:bpop}) and wind confinement (equation~\ref{eq:lumreq}) but also by the time delay between the onset of neutrino-driven mass ablation and jet formation. Whatever one's view of the relative merits of the magnetar and the black hole plus debris disk models in producing ultra-relativistic outflows, it is clear that the presence of a long lived, dense wind, a common feature in the magnetar model, severely hinders the successful production of a sGRB. The shocks responsible for producing the $\gamma$-rays must surface after the jet has broken free from the neutrino-driven wind. For a large subset of compact merger progenitors, with the exception of black hole neutron star mergers, a hyper-massive remnant will be formed. A neutrino-driven wind will thus persist to obstruct the progress of the jet. The cocoon would be able to collimate the jet provided that $\tilde{L} < \theta_{\rm j}^{-4/3}$ \citep{bromberg11}. In the simplest case considered here of a wind whose properties do not vary over its lifetime, the jet's head velocity is constant and the cocoon is unable to compensate for the jet's expansion (Figures~\ref{fig:time} and~\ref{fig:lum}). Collimation is seen to increase with decreasing $k$ for $k \leq 2$ where $\rho_{\rm w} \propto r^{-k}$. While writing this paper we became aware of a recent preprint \citep{nagakura2014}, in which the interaction of a jet with the previously dynamically ejected material (which is independent of the neutrino-driven wind we consider here) in a binary merger \citep{hotokezaka13b} is used to argue as an effective mechanism for the collimation of a sGRB jet. The energy supplied by the jet exceeds that imparted to the swept-up wind material by a factor $\beta_{\rm h}/\beta_{\rm j} < 1$. The excess energy must then not gather near the working surface but be deposited within a cocoon surrounding the jet (Figures~\ref{fig:time} and \ref{fig:lum}). Unless there is violent mixing of baryons from the wind, the build-up of energy to baryon-rest-mass in the cocoon will be given approximately by $\approx \Gamma_{\rm h}$. As soon as the jet reaches the edge of the wind, $r_{\rm w}$, the cocoon material would itself be able to break-out and expand through the wind along the direction of least resistance, which is likely to be along the jet's axis. Beyond $r_{\rm w}$, the external pressure drops steeply, and the cocoon material will expand freely with $\Gamma_{\rm c} \propto r/r_{\rm w}$ \citep{ramirez-ruiz2002}. If its unhampered transverse expansion starts just outside $r_{\rm w}$, where the Lorentz factor of the cocoon material is only a few, then it will spread over a wide angle. In the case of a successful break-through of the relativistic jet, the outflowing cocoon could result in potentially interesting and observable phenomenon \citep{ramirez-ruiz2002, thompson2007, morsony2007}. The relativistic material that accumulated in the cocoon could have an energy comparable to that of the jet when $t_{\rm j} \gtrsim t_{\rm j,b}$. Not only would a typical sGRB be detectable, followed by a standard afterglow, but also there could be additional emission before and after the main event when the cocoon material becomes transparent and when it decelerates. While the main afterglow radiation will be produced by the slowing down of the jet as in the usual case, prompt X-ray emission at early stages could be caused by the deceleration of the cocoon blast wave, which is expected to be less energetic. This could resemble the so called {\it extended emission} in sGRBs \citep{norris2006}, in particular if it is slowly varying. There could also be precursor signatures \citep{ramirez-ruiz2001,troja2010} which are not associated with internal dissipation in the jet, but with the dynamics of the cocoon fireball. The $\gamma$-ray signal emerging from the cocoon fireball as it becomes transparent will most likely appear as a transient signal before the beginning of the main burst \citep{ramirez-ruiz2002, suzuki2013}, where the observed variability time scale would be related to the typical size of the shocked plasma region containing the photon field: $\Delta \approx r_{\rm w}$ for $r/\Gamma_{\rm c}^2 <\Delta$. The detection of these prompt signatures would be a test of the neutron star binary merger model and the precise measurement of the time delay between emissions may help constrain the duration and properties of the neutrino driven wind phase. If we were to venture a general classification scheme for GRBs, on the hypothesis that the central engine involves a black hole formed in double neutron star mergers, we would obviously expect the disk and black hole mass \citep{lee2005b,oechslin2006,giacomazzoetal13}, the angular momentum of the black hole and the orientation relative to our line of sight to be essential parameters. It is then necessary, within such a model, to identify sGRBs with merging systems for which black hole formation occurs promptly ($\leq 100$ ms) as any moderate delay at the hyper-massive neutron star stage would result in a choked jet. | 14 | 4 | 1404.0383 |
1404 | 1404.2723_arXiv.txt | We propose methods for extracting limits on the strength of $\mathcal{P}$-odd interactions of pseudoscalar and pseudovector cosmic fields with electrons, protons and neutrons. Candidates for such fields are dark matter (including axions) and dark energy, as well as several more exotic sources described by standard-model extensions. Calculations of parity nonconserving amplitudes and atomic electric dipole moments induced by these fields are performed for H, Li, Na, K, Rb, Cs, Ba$^+$, Tl, Dy, Fr, and Ra$^+$. From these calculations and existing measurements in Dy, Cs and Tl, we constrain the interaction strengths of the parity-violating static pseudovector cosmic field to be $7\times10^{-15}$ GeV with an electron, and $3\times10^{-8}$ GeV with a proton. | 14 | 4 | 1404.2723 |
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1404 | 1404.5335_arXiv.txt | We conduct a statistical analysis of a combined sample of direct imaging data, totalling nearly 250 stars. The stars cover a wide range of ages and spectral types, and include five detections ($\kappa$ And b, two $\sim$60 M$_{\rm J}$ brown dwarf companions in the Pleiades, PZ Tel B, and CD$-$35 2722B). For some analyses we add a currently unpublished set of SEEDS observations, including the detections GJ 504b and GJ 758B. We conduct a uniform, Bayesian analysis of all stellar ages using both membership in a kinematic moving group and activity/rotation age indicators. We then present a new statistical method for computing the likelihood of a substellar distribution function. By performing most of the integrals analytically, we achieve an enormous speedup over brute-force Monte Carlo. We use this method to place upper limits on the maximum semimajor axis of the distribution function derived from radial-velocity planets, finding model-dependent values of $\sim$30--100 AU. Finally, we model the entire substellar sample, from massive brown dwarfs to a theoretically motivated cutoff at $\sim$5 M$_{\rm Jup}$, with a single power law distribution. We find that $p(M, a) \propto M^{-0.65\pm0.60} a^{-0.85\pm0.39}$ (1$\sigma$ errors) provides an adequate fit to our data, with 1.0--3.1\% (68\% confidence) of stars hosting 5--70 $M_{\rm Jup}$ companions between 10 and 100 AU. This suggests that many of the directly imaged exoplanets known, including most (if not all) of the low-mass companions in our sample, formed by fragmentation in a cloud or disk, and represent the low-mass tail of the brown dwarfs. | \label{sec:intro} Since the first exoplanet around a main-sequence star was discovered in 1995 \citep{Mayor+Queloz_1995}, large radial velocity \citep[e.g.][]{Cumming+Butler+Marcy+etal_2008, Bonfils+Delfosse+Udry+etal_2013} and transit surveys \citep{Bakos+Noyes+Kovacs+etal_2004, Pollacco+Skillen+CollierCameron+etal_2006, Batalha+Rowe+Bryson+etal_2013} have found many hundreds of worlds. Previous models of planet formation, extending back decades \citep[e.g.][]{Kuiper_1951, Hayashi_1981}, were based heavily on the Solar system. New discoveries have enabled a much fuller characterization of exoplanets within $\sim$3 AU of their host stars, around both main sequence \citep{Cumming+Butler+Marcy+etal_2008} and evolved \citep{Johnson+Fischer+Marcy+etal_2007} systems. These distributions hold clues to the formation and subsequent dynamical evolution of planetary systems. While constraints on the mass function of planets have only recently been determined, the initial mass function (IMF) of stars has been studied for many decades \citep{Salpeter_1955}, and is now well-constrained. The stellar IMF has also recently been extended to brown dwarfs \citep{Kroupa_2001, Reid+Gizis+Hawley_2002, Chabrier_2003}, objects below the minimum mass ($\sim$80 M$_{\rm J}$) necessary to sustain hydrogen fusion, but above the minimum mass for deuterium burning ($\sim$13 M$_{\rm J}$). Large samples of substellar objects are difficult to assemble, both because brown dwarfs have a limited supply of internal energy, and because the IMF turns over near the hydrogen-burning boundary. Brown dwarfs are also uncommon as close companions to main-sequence stars, a phenomenon known as the ``brown dwarf desert'' \citep{Marcy+Butler_2000, Grether+Lineweaver_2006}. The companion mass function (CMF) rises from this ``desert'' both towards higher, stellar masses, and towards lower, planetary masses. The companion mass function, well-established at small separations from radial velocity surveys \citep{Cumming+Butler+Marcy+etal_2008}, is much less clear at tens of AU. The conditions in a protoplanetary disk are very different far from the host star and may not support the formation mechanism responsible for the radial-velocity (RV) distribution \citep{Dodson-Robinson+Veras+Ford+etal_2009}, though such a conclusion is far from certain \citep{Lambrechts+Johansen_2012, Kenyon+Bromley_2009}. Companions near or below the deuterium-burning limit might form like stars in gravitational collapse or fragmentation \citep{Boss_1997, Vorobyov_2013}, by core-accretion in-situ \citep{Pollack+Hubickyj+Bodenheimer_1996, Alibert+Mordasini+Benz+etal_2005}, or they might form in a location more conducive to planet formation and subsequently migrate or be scattered to their observed orbits. The distribution function of such objects could provide important clues to their formation mechanism, and connect them to either more massive brown dwarfs or to the planet populations observed at smaller separations. As a result, these massive exoplanets are being heavily targeted using large telescopes with adaptive optics. The sensitivity to exoplanets with direct imaging has been rapidly improving, and recent discoveries have begun to fill the parameter space of substellar objects at separations of tens of AU. Companions near or below the deuterium burning limit have been discovered around the M-dwarfs 2MASS J01225093-2439505 \citep{Bowler+Liu+Shkolnik+etal_2013}, 2MASS J01033563-5515561AB \citep{Delorme+Gagne+Girard+etal_2013}, and ROXs 42B \citep{Currie+Daemgen+Debes+etal_2014}, the G-dwarf GJ 504 \citep{Kuzuhara+Tamura+Kudo+etal_2013}, the A stars HR 8799 \citep{Marois+Macintosh+Barman+etal_2008, Marois+Zuckerman+Konopacky+etal_2010}, $\beta$ Pictoris \citep{Lagrange+Gratadour+Chauvin+etal_2009}, and HD 95086 \citep{Rameau+Chauvin+Lagrange+etal_2013}, and the late B star $\kappa$ And \citep{Carson+Thalmann+Janson+etal_2013}. These detections were made possible by recent technological advances in adaptive optics and the use of differential imaging techniques. In addition, recent work to identify nearby members of young moving groups \citep[MGs, e.g.][]{Torres+Quast+Melo+etal_2008, Zuckerman+Rhee+Song+etal_2011, Schlieder+Lepine+Simon_2012a, Shkolnik+Anglada+Liu+etal_2012, Malo+Doyon+Lafreniere+etal_2013, Moor+Szabo+Kiss+etal_2013, Rodriguez+Zuckerman+Kastner+etal_2013, Gagne+Lafreniere+Doyon+etal_2014} and stars that harbor debris disks \citep{Rieke+Su+Stansberry+etal_2005, Chen+Sargent+Bohac+etal_2006, Plavchan+Werner+Chen+etal_2009, Moor+Pascucci+Kospal+etal_2011, Eiroa+Marshall+Mora+etal_2011} has provided excellent targets for direct imaging searches. The stellar age is particularly important, because substellar objects are unable to sustain hydrogen fusion in their cores, and quickly fade beneath the sensitivity limits of the best observing facilities on the ground and in space. Over the last decade, numerous direct imaging surveys around nearby young stars have begun to constrain the distribution and frequency of substellar companions. These have mostly used non-detections to place upper limits on the planet fraction within a range of masses and semimajor axes, or upper limits beyond which the distribution function measured by radial velocity surveys cannot extend. \cite{Lafreniere+Doyon+Marois+etal_2007} used the Gemini Deep Planet Survey (GDPS) to place upper limits of $\sim$10\% on the fraction of stars with 0.5--13 M$_{\rm J}$ companions in the range from 50 to 250 AU, assuming an RV-like mass distribution. \cite{Nielsen+Close_2010} used a sample of 118 targets, dominated by the GDPS, to find that the RV distribution of \cite{Cumming+Butler+Marcy+etal_2008} cannot be extrapolated past $a_{\rm max}$ from $\sim$65--200 AU depending on the substellar cooling model and on the correlation between planet frequency and stellar mass. \cite{Chauvin+Lagrange+Bonavita+etal_2010} imaged 88 stars, around which they detected three substellar companions, including an $\sim$8-M$_{\rm J}$ companion to the brown dwarf 2M1207 and a $\sim$13 M$_{\rm J}$ companion to AB Pic. More recently, \cite{Vigan+Patience+Marois+etal_2012} placed a lower limit to the planet ($<$13-M$_{\rm J}$) frequency around A stars of 6\% based on the International Deep Planet Survey and the detections around HR 8799 and $\beta$ Pictoris. \cite{Biller+Liu+Wahhaj+etal_2013} placed a similar model-dependent upper limit of 6\%--18\% for companions from 1--20 M$_{\rm J}$ between 10 and 150 AU around later-type stars. \cite{Chauvin+Vigan+Bonnefoy+etal_2014} observed 86 stars without detecting substellar companions, placing an upper limit of 10\% on 5--10 $M_{\rm Jup}$ objects 50--500 AU from young solar-type stars. However, the distribution function for these companions remains uncertain, and statistical analyses often artificially truncate it at or near the deuterium burning threshold. In this work, we provide a new framework for determining the distribution function of substellar companions to stars, and apply this framework to the published sub-sample of the Subaru SEEDS survey, combined with the publicly available GDPS \citep{Lafreniere+Doyon+Marois+etal_2007} and NICI MG sample \citep{Biller+Liu+Wahhaj+etal_2013}. In Section \ref{sec:distributions}, we discuss what is currently known about the stellar and substellar mass distributions. In Section \ref{sec:data}, we present our combined data set, and in Section \ref{sec:bayes_ages}, we summarize our method for deriving their age probability distributions; in Section \ref{sec:cooling_models}, we discuss our choice of substellar cooling models. We present our statistical framework and method for determining constraints on the substellar distribution function in Section \ref{sec:framework}, with additional details, derivations, and fitting functions in the Appendix. Section \ref{sec:results} presents and discusses our results, including our limits on an extrapolated RV-like distribution function, and the ability of a single distribution to include most or all wide-separation substellar objects. We conclude with Section \ref{sec:conclusions}. | 14 | 4 | 1404.5335 |
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1404 | 1404.3598.txt | Since the B-mode polarization of the cosmic microwave background (CMB) was detected by the BICEP2 experiment and an unexpectedly large tensor-to-scalar ratio, $r=0.20^{+0.07}_{-0.05}$, was found, the base standard cosmology should at least be extended to the 7-parameter $\Lambda$CDM+$r$ model. In this paper, we consider the extensions to this base $\Lambda$CDM+$r$ model by including additional base parameters relevant to neutrinos and/or other neutrino-like relativistic components. Four neutrino cosmological models are considered, i.e., the $\Lambda$CDM+$r$+$\sum m_\nu$, $\Lambda$CDM+$r$+$N_{\rm eff}$, $\Lambda$CDM+$r$+$\sum m_\nu$+$N_{\rm eff}$, and $\Lambda$CDM+$r$+$N_{\rm eff}$+$m_{\nu,{\rm sterile}}^{\rm eff}$ models. We combine the current data, including the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, the cosmic shear data, and the BICEP2 polarization data, to constrain these neutrino cosmological models. We focus on the constraints on the parameters $\sum m_\nu$, $N_{\rm eff}$, and $m_{\nu,{\rm sterile}}^{\rm eff}$. We also discuss whether the tension on $r$ between Planck and BICEP2 can be relieved in these neutrino cosmological models. | \label{sec:intro} %The primordial gravitational waves (PGWs) were recently discovered by the BICEP2 experiment Recently, the BICEP2 (Background Imaging of Cosmic Extragalactic Polarization) Collaboration reported the detection of the B-mode polarization of the cosmic microwave background (CMB), which implies that the primordial gravitational waves (PGWs) are likely to have been detected~\cite{bicep2}. If confirmed by upcoming experiments, the BICEP2's result will greatly impact on the fundamental physics. The tensor-to-scalar ratio derived by the observed B-mode power spectrum is unexpectedly large, $r=0.20^{+0.07}_{-0.05}$, with $r=0$ disfavored at the 7.0$\sigma$ level~\cite{bicep2}. This result is in tension with the upper limit $r<0.11$ (95\% CL) deduced from the measurements of temperature power spectrum by the Planck Collaboration (Planck+WP+highL, where WP refers to the WMAP 9-year polarization data and highL refers to the temperature data from ACT and SPT)~\cite{planck}. One simple way of relieving this tension is to allow for a negative running of the scalar spectral index of order $10^{-2}$, which challenges the design of the inflation models since the usual slow-roll inflation models predict a negligible running (of order $10^{-4}$). To reduce the tension, more possibilities should be explored. One interesting suggestion is to consider additional sterile neutrino species in the universe~\cite{zx14,WHu14}. Since the tensor-to-scalar ratio $r$ is found to be around 0.2, the standard cosmology should at least be extended to $\Lambda$CDM+$r$ model (now this is the base model with seven parameters). Thus, the model with sterile neutrino is naturally called $\Lambda$CDM+$r$+$\nu_s$ model, in which two additional parameters, $N_{\rm eff}$ and $m_{\nu,{\rm sterile}}^{\rm eff}$, are included. It is shown that in the $\Lambda$CDM+$r$+$\nu_s$ model the tension between Planck and BICEP2 can be greatly relieved at the expense of the increase of $n_s$~\cite{zx14,WHu14}. Moreover, actually, by including a sterile neutrino species in the universe, not only the tension between Planck and BICEP2 is relieved, but also the other tensions between Planck and other astrophysical observations, such as the $H_0$ direct measurement, the cluster counts, and the galaxy shear measurement, can all be significantly reduced.\footnote{In fact, even before the release of the Planck temperature data, the effects of neutrino mass and additional neutrino species in relieving the tension between CMB+BAO and other observations, such as $H_0$ and cluster counts, were discussed~\cite{SPT,Burenin2013}. Then, after the Planck data release, the result was further confirmed; see, e.g., Refs.~\cite{tsz,snu1,snu2,snu3,Gariazzo:2013gua}. } Thus, the model with sterile neutrino seems to be an economical choice for the cosmology today. Furthermore, by combining the Planck+WP with the baryon acoustic oscillations (BAO), $H_0$, Sunyaev-Zeldovich (SZ) cluster counts, CMB lensing, galaxy shear, and BICEP2 data, it is found that in the $\Lambda$CDM+$r$+$\nu_s$ model %$n_s=0.999^{+0.012}_{-0.011}$, $r=0.21^{+0.04}_{-0.05}$, $N_{\rm eff}=3.961^{+0.318}_{-0.325}$ %and $m_{\nu,{\rm sterile}}^{\rm eff}=0.511^{+0.120}_{-0.133}$ eV~\cite{zx14}. %In other words, the existing cosmological data prefer $\Delta N_{\rm eff}>0$ at the 2.7$\sigma$ level and a nonzero mass of sterile neutrino at the 3.9$\sigma$ level~\cite{zx14}. (See also Ref.~\cite{WHu14} for a similar analysis.) Other proposals to address the large B modes include, e.g., foregrounds or some uncounted temperature-polarization leakage~\cite{Liu:2014mpa}, non-standard inflation models or more general early-universe scenarios~\cite{Harigaya:2014qza,Nakayama:2014koa,Brandenberger:2014faa, Contaldi:2014zua,Miranda:2014wga,Gerbino:2014eqa,McDonald:2014kia,Hazra:2014a,Hazra:2014b}, large-field excursions~\cite{Kehagias:2014wza,Lyth:2014yya}, primordial magnetic fields~\cite{Bonvin:2014xia}, topological defects~\cite{Lizarraga:2014eaa,Moss:2014cra}, spatial variation of $r$~\cite{Chluba:2014uba}, and so on. Obviously, the forthcoming new data from, e.g., Planck and Keck array are expected to improve the foreground model and provide more tight constraints on the B modes, resolving the current tension problem. In this paper, we will consider neutrinos and extra relativistic components within the base $\Lambda$CDM+$r$ model. We will use the current data to constrain the models with neutrinos. The models we consider in this paper include: (i) the active neutrinos with additional parameter $\sum m_{\nu}$, (ii) the extra relativistic components with additional parameter $N_{\rm eff}$, (iii) the active neutrinos along with the extra relativistic components with additional parameters $\sum m_{\nu}$ and $N_{\rm eff}$, and (iv) the massive sterile neutrino with additional parameters $N_{\rm eff}$ and $m_{\nu,{\rm sterile}}^{\rm eff}$. The observational data we use in this paper are from Planck+WP+BAO, $H_0$ direct measurement, Planck SZ cluster counts, Planck CMB lensing, cosmic shear measurement, and BICEP2. This work will provide a detailed cosmological analysis on the models with neutrinos under the consideration of the BICEP2 data. The paper is organized as follows. In Sec.~\ref{sec:cosmol}, we briefly describe the cosmological models with neutrinos and the observational data. In Sec.~\ref{sec:result}, we present the fit results and discuss these results in detail. Conclusion is given in Sec.~\ref{sec:concl}. | \label{sec:concl} After the detection of the PGWs by the BICEP2 experiment, the base standard cosmology should at least be extended to the 7-parameter $\Lambda$CDM+$r$ model. In this paper, we consider the extensions to this base $\Lambda$CDM+$r$ model by including additional base parameters relevant to neutrinos and/or other neutrino-like relativistic components. Four neutrino cosmological models are considered, i.e., the $\Lambda$CDM+$r$+$\sum m_\nu$, $\Lambda$CDM+$r$+$N_{\rm eff}$, $\Lambda$CDM+$r$+$\sum m_\nu$+$N_{\rm eff}$, and $\Lambda$CDM+$r$+$N_{\rm eff}$+$m_{\nu,{\rm sterile}}^{\rm eff}$ models. We use the current observational data to constrain these models. The cosmological data used in this paper include: Planck+WP, BAO, $H_0$, Planck SZ cluster, Planck CMB lensing, cosmic shear, and BICEP2 data. The main results of this paper are shown in Figs.~\ref{fig1}--\ref{fig4} and Tables~\ref{tab1}--\ref{tab4}. Here, we summarize the findings from our analysis. \begin{itemize} \item The $\Lambda$CDM+$r$+$\sum m_\nu$ model. With the Planck+WP+BAO data, we find a limit on the active neutrino mass, $\sum m_\nu<0.28~{\rm eV}$ (95\% CL). Including the $H_0$+SZ+Lensing data leads to a strikingly tight constraint: $\sum m_\nu=0.28\pm 0.07~{\rm eV}$, preferring a nonzero mass of active neutrinos at about the 4$\sigma$ level. Further adding the BICEP2 data does not improve the constraint on the mass. We also find that this model cannot alleviate the tension on $r$ between Planck and BICEP2. \item The $\Lambda$CDM+$r$+$N_{\rm eff}$ model. Using only the Planck+WP+BAO data gives $N_{\rm eff}=3.52^{+0.31}_{-0.32}$, and further adding the $H_0$+SZ+Lensing data gives $N_{\rm eff}=2.97^{+0.20}_{-0.22}$, and combination of all data (including BICEP2) leads to $N_{\rm eff}=3.07\pm0.20$. These results are consistent with the standard value of 3.046. We also find that this model cannot effectively alleviate the tension on $r$ between Planck and BICEP2. \item The $\Lambda$CDM+$r$+$\sum m_\nu$+$N_{\rm eff}$ model. With the Planck+WP+BAO data, we obtain $\sum m_\nu< 0.50$ eV (95\% CL) and $N_{\rm eff} = 3.69^{+0.33}_{-0.40}$, so in this case only an upper limit on the total mass of active neutrinos can be given, but the weak preference for $N_{\rm eff}>3.046$ at about the 1.6$\sigma$ level is shown. Combining with the $H_0$+SZ+Lensing data can lead to tight constraints, $\sum m_\nu=0.58^{+0.14}_{-0.15}$ eV and $N_{\rm eff} = 4.04^{+0.35}_{-0.34}$, giving the evidence for nonzero mass of active neutrinos and $\Delta N_{\rm eff}>0$ at the 3.9$\sigma$ and 2.9$\sigma$, respectively. Further adding the BICEP2 data can improve the results to $\sum m_\nu=0.63^{+0.13}_{-0.16}$ eV and $N_{\rm eff} = 4.20\pm 0.32$, favoring $\sum m_\nu>0$ and $\Delta N_{\rm eff}>0$ at the 4.0$\sigma$ and 3.6$\sigma$ levels, respectively. We also show that this model is very helpful in relieving the tension between Planck and BICEP2. The increase of $r$ is at the cost of the increase of $n_s$, and consequently the exact scale-invariant spectrum cannot be excluded. \item The $\Lambda$CDM+$r$+$N_{\rm eff}$+$m_{\nu,{\rm sterile}}^{\rm eff}$ model. With the Planck+WP+BAO data, we obtain $m_{\nu,{\rm sterile}}^{\rm eff}< 0.51$ eV (95\% CL) and $N_{\rm eff} =3.72^{+0.32}_{-0.40}$, thus in this case only an upper limit on the sterile neutrino mass can be derived and the preference for $\Delta N_{\rm eff}>0$ at the 1.7$\sigma$ level is shown. Further including the $H_0$+SZ+Lensing data significantly improves the constraints, $m_{\nu,{\rm sterile}}^{\rm eff}=0.48^{+0.11}_{-0.13}$ eV and $N_{\rm eff} = 3.75^{+0.34}_{-0.37}$, favoring a nonzero mass of sterile neutrino and $\Delta N_{\rm eff}>0$ at the 3.6$\sigma$ and 1.9$\sigma$ levels, respectively. Finally, further adding the BICEP2 data improves the constraints to $m_{\nu,{\rm sterile}}^{\rm eff}=0.51^{+0.12}_{-0.13}$ eV and $N_{\rm eff} = 3.95\pm0.33$, showing the evidence of nonzero sterile neutrino mass and $\Delta N_{\rm eff}>0$ at the 3.9$\sigma$ and 2.7$\sigma$ levels, respectively. It is shown that this model is very helpful in relieving the tension between Planck and BICEP2, and the expense of the increase of $r$ is the increase of $n_s$, thus the exact scale-invariant spectrum cannot be excluded in this case, either. The fitting results indicate a fully thermalized sterile neutrino with sub-eV mass, in tension with the short-baseline neutrino oscillation experiments that prefer the mass of sterile neutrino at around 1 eV. The implication of this tension for cosmology deserves further investigation. \end{itemize} %\appendix % | 14 | 4 | 1404.3598 |
1404 | 1404.4808_arXiv.txt | { Approximately half of the Universe's baryons are in a form that has been hard to detect directly. However, the missing component can be traced through the cross-correlation of the thermal Sunyaev-Zeldovich (tSZ) effect with weak gravitational lensing. We build a model for this correlation and use it to constrain the extended baryon component, employing data from the Canada France Hawaii Lensing Survey and the {\it Planck\/} satellite. The measured correlation function is consistent with an isothermal $\beta$-model for the halo gas pressure profile, and the 1- and 2-halo terms are both detected at the 4$\sigma$ level. In addition, we measure the hydrostatic mass bias $(1-b)=0.79^{+0.07}_{-0.10}$, which is consistent with numerical simulation results and the constraints from X-ray observations. The effective temperature of the gas is found to be in the range ($7\times10^{5}$--$3 \times10^{8}$)\,K, with approximately $50\%$ of the baryons appearing to lie beyond the virial radius of the halos, consistent with current expectations for the warm-hot intergalactic medium.} \arxivnumber{1404.4808} | The general processes driving structure formation, from the sizes of galaxies to the largest scales observable, are reasonably well understood, though many details are still unclear. Knowledge of the distribution of baryonic and dark matter in galaxies, groups, and clusters of galaxies is essential for understanding how they form and evolve, including complex processes such as down-sizing and star-formation quenching \citep{benson2010,tinker2013}. However, stellar mass accounts for only ${\sim}\,10\%$ of all the baryons in the Universe; the other $90\%$ resides in a diffuse component, a large fraction of which is thought to reside in low mass halos~\cite{Fukugita04}. A complete picture of structure formation requires a full census of baryons in the Universe. Baryons are more dissipative than dark matter, and hence naturally populate the centres of halos, but feedback processes play a fundamental role in recycling baryons back to a diffuse form. Thus, accounting for the extended baryon distribution is necessary to understand the physical processes governing structure formation, including star formation and feedback. Historically, the diffuse component is observed via its X-ray emission or through the thermal Sunyaev-Zeldovich effect (tSZ, i.e., inverse Compton scattering \cite{SZ1972}), but the sensitivity of current instruments limits such observations to the most massive, densest, and hottest gas environments. To date, only about half of the known baryon component has been directly observed at redshifts less than $z \simeq 2$ \cite{Fukugita04,Bregman07}; the remaining baryons are thought to be too cold to be detected with X-rays or the SZ effect, and too warm to be detected in the UV. Numerical simulations suggest that the ``missing'' baryons might be in a warm, low-density plasma (${\sim}\,10^{5}$--$10^{7}\,$K) correlated with large structures and filaments \cite{Cen06}. One possible way of observing these baryons is by cross-correlating with another cosmic field. Gravitational lensing by large-scale structure provides an unbiased tracer of the matter distribution that can be used for this purpose. \citet{Waerbeke14} found a significant correlation between the Canada France Hawaii Lensing Survey (CFHTLenS) mass map and tSZ maps obtained from {\it Planck\/} satellite data. % This signal was consistent with warm baryonic gas tracing large-scale structure, with an amplitude $\bar{n}_{\rm e} T_{\rm e} b_{\rm gas} \simeq 0.201 {\,\rm keV\, m^{-3}}$ at redshift $z=0$. This suggests that if the bias $b_{\rm gas}\simeq 6$ and $\bar{n}_{\rm e}=0.25 {\, \rm m^{-3}}$ (the cosmic baryon abundance), then it is in line with the missing baryons being at $T_{\rm e}\simeq10^{6}\,$K. The model adopted for the warm gas in Ref.~\cite{Waerbeke14} was simplistic and did not capture some of the essential physical properties. It assumed: (i) that the temperature and density of the gas are independent of the underlying halo mass and redshift; and (ii) that the bias of gas pressure relative to dark matter follows $b_{\rm gas} \propto a$, where $a$ is the cosmic scale factor, independent of halo mass and redshift. Moreover the formalism used could not account for gas lying outside single halos, thus it was incapable of tracking the ``missing baryons'' that are thought to reside outside the cluster virial radius. Here we attempt to provide a realistic description of the baryon distribution within the framework of the ``halo model''~\cite{Cooray02}. By interpreting the cross-correlation between tSZ and lensing we investigate the consequences for the warm baryonic component. Except for Fig.~\ref{fig:wmap-planck}, we use best-fit cosmological parameters obtained from the {\it Planck\/} satellite~\cite{Planck16} throughout the paper, i.e., \{$\Omega_{\rm m}$, $\Omega_{\rm b}$, $\Omega_{\Lambda}$, $\sigma_{8}$, $n_{\rm s}$, $h$\} = \{0.3175, 0.0490, 0.6825, 0.834, 0.9624, 0.6711\}. | Our halo model for the lensing--tSZ cross-correlation signal $\xi^{\kappa y}$ has enabled us to investigate the baryon distribution at cluster scales and to explore the possible identification of the missing baryons in the warm-hot intergalactic medium (WHIM). The observed cross-correlation function from the CFHTLenS mass map and the {\it Planck\/} tSZ map is particularly effective at tracing baryons over a wide range of clustering scales. In the context of the universal pressure profile, we find that their predicted $\xi^{\kappa-y}(\theta)$ function is higher than the observational data at small angular scales; the added hydrostatic mass bias $(1-b)\simeq 0.8$ can reconcile the tension to some extent, but on large angular scales it predicts lower power than seen observationally. By employing a likelihood function to fit the $(1-b)$, we find its value to be $(1-b)=0.79^{+0.07}_{-0.1}$ (at $95\%$ CL), which is consistent with previous values found values in numerical simulations~\cite{Shaw10,Rasia12,Nagai07,Piffaretti08,Meneghetti10}, as well as some observational constraints~\cite{Hoekstra15,Israel14,Planck2015-24}. In the context of the isothermal $\beta$ profile, the 1- and 2-halo terms are each detected at ${\sim}\,4\sigma$, while the total signal is detected at ${\sim}\,6\sigma$. We find evidence that baryons are distributed beyond the virial radius, with a temperature in the range of ($10^{5}$--$10^{7}$)\,K, consistent with the hypothesis that this signal arises from the missing baryons. We further separate the model signal into different radial profile and mass bins, and find that about half of the integrated signal arises from gas outside the virial radius of the dark matter halos, and that 40\% arises from low-mass halos. Our study is an example of a general class of large-scale cross-correlations that are now becoming feasible, thanks to the availability of deep multi-waveband surveys over large fractions of the sky. Correlation of tSZ maps with galaxies \cite{PlanckI11}, with CMB lensing \cite{Hill14} and with X-rays \cite{Hajian13}, plus the use of correlations with the kinetic SZ effect \cite{Hand12,Li2014}, allow for a multi-faceted study of the role of baryon physics in structure formation. Further improvements in the quality of the data will require more sophisticated models than we have presented here, perhaps involving direct comparison of diagnostics of the WHIM with hydrodynamical simulations. Our results show that such cross-correlation studies have the potential to trace the ``missing baryons'' and to account for the cosmic baryon distribution with high precision. | 14 | 4 | 1404.4808 |
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