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1403 | 1403.5792_arXiv.txt | {Supermassive black holes reside in cores of galaxies, where they are often surrounded by a~nuclear cluster and a~clumpy torus of gas and dust. Mutual interactions can set some stars on a~plunging trajectory towards the black hole.}{We model the pericentre passage of a~dust-enshrouded star during which the dusty envelope becomes stretched by tidal forces and is affected by the interaction with the surrounding medium. In particular, we explore under which conditions these encounters can lead to periods of enhanced accretion activity.}{We discuss different scenarios for such a dusty source. To this end, we employed a modification of the \texttt{Swift} integration package. Elements of the cloud were modelled as numerical particles that represent the dust component that interacts with the optically thin gaseous environment.}{We determine the fraction of the total mass of the dust component that is diverted from the original path during the passages through the pericentre at $\simeq10^3$ Schwarzschild radii and find that the main part of the dust ($\gtrsim90\%$ of its mass) is significantly affected upon the first crossing. The fraction of mass captured at the second passage generally decreases to very low values.}{As an example, we show predictions for the dusty source evolution assuming the current orbital parameters of the G2 cloud (also known as Dusty S-Cluster Object, DSO) in our Galactic centre. Encounter of a core-less cloud with a supermassive black hole is, most likely, a non-repeating event: the cloud is destroyed. However, in the case of a dust-enshrouded star, part of the envelope survives the pericentre passage. We discuss an offset of $\lesssim0.3$ arcsec between the centre of mass of the diverted part and the star along the eccentric orbit. Finally, we examine an interesting possibility of a binary star embedded within a~common wind envelope that becomes dispersed at the pericentre passage.} | Most galaxies host supermassive black holes (SMBH; $10^6M_{\odot}\lesssim M_{\bullet} \lesssim 10^9M_{\odot}$) in their cores, where these accrete gas and dust in the form of an accretion flow from their immediate neighbourhood \citep{1999agnc.book.....K,2012bhae.book.....M}. The example nearest to us is the compact radio source Sgr~A*, which contains a black hole of mass $M_{\bullet}=4.4\times10^6M_{\odot}$ at distance $8.2$~kpc in the centre of the Milky Way \citep{2005bhcm.book.....E,2007gsbh.book.....M,2010RvMP...82.3121G}. The character of accretion and the corresponding accretion rate vary greatly over different galaxy types. It appears that the availability of mass supply and the accretion mode that is established in the course of evolution of the system are the main agents that determine the power output and the spectral energy distribution of supermassive black holes \citep{2002apa..book.....F}. In several ways, the Galactic centre can serve as a paradigm for low-luminosity nuclei. Active galactic nuclei (AGN) and quasars host radiatively efficient types of disc accretion (i.e., the standard scheme of geometrically thin accretion discs, or slim discs; \citeauthor{1973A&A....24..337S} \citeyear{1973A&A....24..337S}; \citeauthor{1988ApJ...332..646A} \citeyear{1988ApJ...332..646A}) with accretion rates reaching and even exceeding the Eddington limit of $\dot{M}_{\rm{}Edd}\simeq L_{\rm{}Edd}/(0.1c^2)$, where \begin{equation} L_{\rm{}Edd}=\frac{4\pi GM_{\bullet}m_{\rm p}c}{\sigma_{\rm{}T}}\simeq1.3\times10^{44}\;\frac{M_\bullet}{10^6M_\odot}\quad[{\rm erg/s}], \label{ledd} \end{equation} with $m_{\rm{}p}$ proton mass, $\sigma_{\rm{}T}$ Thomson cross-section. Low-luminosity nuclei exhibit significantly lower accretion rates, $\dot{M}_{\bullet}\ll \dot{M}_{\rm{}Edd}$ \citep{2013PoS}. This can be explained as a combination of a diminishing supply of material falling onto the black hole and the radiatively inefficient mode of accretion at certain stages. In this context, the present state of the Galactic centre represents an extreme example of an inactive nucleus: $\dot{M_\bullet}\simeq10^{-8}M_{\odot}$ per year, which can be understood in terms of advection-dominated flow \citep{2008NewAR..51..733N}.\footnote{For the supermassive black hole of Sgr~A* in the Galactic centre, the quiescent bolometric luminosity is $L_{\rm{}bol}=\eta\dot{M}_{\bullet}c^2\simeq10^{36}$ erg~s$^{-1}$. This corresponds to the dimensionless efficiency parameter for the conversion of accreted mass into radiation of about $\eta\simeq10^{-3}$, although it can be as low as $10^{-5}$ at the present stage of the source. The accretion outflow of Sgr A* is radiatively inefficient compared with predictions from the standard accretion disc theory, where $\eta\simeq 0.06$--$0.42$ is the predicted range.} The temperature of the accreted material grows in the course of its infall in the gravitational field of the central black hole because the potential energy is converted into heat and is only partially released in the form of emerging radiation \citep[e.g.][]{2002apa..book.....F,1999agnc.book.....K}. While at the distance of several tens to hundreds Schwarzschild radii ($r_{\rm{}s}\equiv 2GM_{\bullet}/c^2\dot{=}2.95\times10^5\,M_{\bullet}/M_{\odot}$\,cm) the medium consists of ionised gas of the accretion disc and hot, diluted corona, farther out the temperature drops below the critical value for dust sublimation, $T_{\rm{}sub}\simeq 1.5\times10^3$~K \citep{1987ApJ...320..537B,2005dusd.book.....K}. Therefore, at larger distances a clumpy torus can persist with a fraction of its mass in the form of dust \citep{1988ApJ...329..702K,2010A&A...523A..27H}. An equilibrium can be reached through processes of dust sublimation (by strong irradiation from the central source and stars of the nuclear cluster), in competition with the replenishment of dust by stellar winds and the infall of clouds from the outer regions, where the circumnuclear torus is present \citep{1993ARA&A..31..473A,1995PASP..107..803U}. The co-evolution of gas and dust phases within clouds falling onto a supermassive black hole is relevant for our understanding of mass transport in the innermost regions of galactic nuclei. Recently, an infrared-excess source named G2/DSO has been discovered \citep{2012Natur.481...51G} and subsequently detected in L- and K-bands \citep{2013ApJ...763...78G, 2013ApJ...773L..13P, 2013arXiv1311.2753E}. It may indeed be a manifestation of a common mechanism of material transport in low-luminosity nuclei. We analyse the scenario of an infrared-excess, dusty stellar source. As indicated in \citet{2014ApJ...783...31S}, the cloud component of the source is optically thin and diluted and not thick and dense. Therefore, it is valid to assume that the cloud component is mainly constituted by the gaseous wind driven by the radiation pressure of central star and the dust that is located and formed in such a wind. This is the reason that in the following analysis we assume the dust to be in contact only with stellar wind and the ambient atmosphere around Sgr A* through which G2/DSO travels. The adopted scenario is not necessarily only connected to this single event. It may be applied to other observed infrared-excess stellar sources that have been shown to move through the gaseous medium near the Galactic centre (e.g., \citeauthor{2005A&A...443..163M}, \citeyear{2005A&A...443..163M}, \citeauthor{2010A&A...521A..13M}, \citeyear{2010A&A...521A..13M}). Moreover, it may be relevant for modelling the environment in other low-luminosity active galactic nuclei. In this paper we adopt a simplified (toy) model: dust grains are treated as numerical particles under the influence of gravity of SMBH ($M=M_\bullet$) and the embedded star ($M=M_\star$), or the components of a binary ($M_\star^{(1)}$, $M_\star^{(2)}$), and the effect of an outflowing wind of gas. We focus on dust-enshrouded stars with different distributions of dust bound to the central star, and we explore the amount of material that is lost from the cloud to the black hole. Effects arise from the ambient pressure of a central wind, the wind pressure from the star, and a bow-shock forming at the interface of winds. The star moves at transonic speed near the pericentre. In this way we address the question whether and how dust particles embedded in the wind envelope are affected by close passages near the SMBH. For most model parameters, most of the dusty material is stripped from the envelope already on the first transit. For low accretion rates, the dust component can survive down to quite small radii, especially in regions shielded by obscuration. Furthermore, if the Field criterion \citep{1965ApJ...142..531F,2012MNRAS.424..728B} is fulfilled for the thermal stability of a two-temperature medium, the dust may co-exist with the hot medium at the same radius. The dust component by itself would be unimportant, but it contributes significantly to the radiation in NIR and tracing it helps to understand the observed emission. Similar treatment of dust dynamics is often employed in other astrophysical systems (mainly protoplanetary discs and stellar atmospheres, see e.g., \citeauthor{2011ApJ...734L..26V}, \citeyear{2011ApJ...734L..26V}). We model the encounters over a broad span of parameters. To present specific examples we use orbital parameters relevant for the Galactic centre G2/DSO infrared source \citep{2013ApJ...774...44G}, and we also attempt to distinguish among different outcomes of the passages through the pericentre \citep{2013A&A...551A..18E,2013ApJ...773L..13P}. \begin{figure*}[tbh] \centering \includegraphics[width=0.32\textwidth]{illustration_nostar.eps} \includegraphics[width=0.32\textwidth]{illustration_star.eps} \includegraphics[width=0.32\textwidth]{illustration_binary.eps} \caption{Three variants of the model setup for which the predictions are qualitatively different especially at the post-pericentre phase. The model ingredients include the central supermassive black hole (black circle), an infalling cloud made of gas and dust (red), an embedded star (yellow), and a hot diluted flow (blue). We consider the pericentre at about $10^3$ Schwarzschild radii, so that the star is not expected to be tidally disrupted. However, the gaseous/dusty envelope is affected significantly. \textit{Left panel:} a core-less cloud on an eccentric trajectory, interacting with the diluted ambient medium near the SMBH. \textit{Middle panel:} the cloud enshrouds an embedded star. A radial wind of the outflowing gaseous atmosphere occurs and a bow-shock forms ahead of the stellar body. \textit{Right panel:} binary system enclosed by a common envelope that becomes largely dispersed at the first pericentre passage. At the same time, the three-body interaction with the central SMBH causes the binary components to separate from the nominal trajectory.} \label{illustration} \end{figure*} Furthermore, we point out to the possibility that the stellar core may actually consist of two components of a binary star. This idea is suggested by models of the origin of S-stars in the Galactic centre as a product of three-body interaction during the pericentre passage of a binary star on a highly eccentric trajectory \citep{2003ApJ...592..935G,2007ApJ...656..709P}. Although the presence of a stellar core and its putative binary nature within the G2 cloud are on a purely hypothetical level, this scenario can connect, in a natural way, two apparently different aspects: the high eccentricity of the plunging trajectory, and the origin of the population of stars near the supermassive black hole. If there is indeed a star enshrouded by a dusty atmosphere, it was proposed that high eccentricity can be achieved by the Kozai mechanism \citep{2005A&A...433..405S} or by resonant relaxation \citep{2006ApJ...645.1152H}. The geometrical setup and the main ingredients of our model are illustrated in figure~\ref{illustration}. Three different flavours of the basic scenario were considered: a core-less cloud infalling onto the SMBH, a star embedded within the dusty envelope, and an embedded binary that becomes disrupted near the SMBH. We focus on the latter two scenarios. Our simplified approach is complementary to purely hydrodynamical situations that neglect the dust component \citep{2012ApJ...759..132A,2012ApJ...750...58B,2013ApJ...776...13B,2014ApJ...783...31S}, which is consistent with an optically thick, dense medium where the dust is dragged along with the gas. However, for optically thin atmospheres, dust dynamics needs to be treated separately. In the following analysis, we do not treat Br$\gamma$ production or the radiation processes in the bow-shock region \citep{2013MNRAS.433.2165S}. We do see, however, that the dusty envelope is stretched by the gravitational and drag forces (depending on the initial distribution of particles in phase space and the parameters of the wind outflow), which leads to the gradual offset between the dust component and the stellar core. We note that observationally any difference between the cloud location in L-band with respect to the location of K (Br$\gamma$) in the orbit is most likely due to uncertainties in the determination of the orbital positions; it may be heavily affected by different systematics in the two bands. The paper is organized as follows: in sect. \ref{sec1} we set up the model and describe the numerical procedure to explore the mutual interaction between the star and its environment. We discuss the dependence of the dust temperature on the distance and the luminosity of the central source. Then we consider the effect of the star enshrouded by an initially spherical dusty envelope and a remnant disc. In sect. \ref{sec2}, we present the results of the simulations including the wind blowing from the centre and the effect of the bow-shock region. We compare the difference between a disc-like Keplerian distribution and a Gaussian distribution of particles in the phase space. Finally, we determine the fraction of dust mass affected at subsequent encounters, and we show the offset that develops gradually between the centre of mass of the cloud and the nominal position of the star in the orbit. In sect. \ref{discussion} we summarize and discuss our results, and we conclude in sect. \ref{conclusions}. | \label{conclusions} We modelled the fate of an infalling star with an extended envelope near the SMBH. The complex medium was treated in terms of numerical particles with their mass and size as parameters, interacting with the ambient environment. The mass of dust particles is typically large enough so that the gravitational influence on the grains needs to be taken into account close to the SMBH and the mass-losing star. We assumed an orbit pericentre of the order of $10^3r_{\rm{s}}$, so that the star itself was not tidally disrupted. However, the surrounding cloud was affected very significantly (core-less clouds are influenced even more, and they are basically destroyed on the first encounter with the black hole). We noticed a significant mass-loss from the cloud at the first pericentre passage in all considered cases ($\gtrsim 90\%$). During the second passage the mass loss fluctuates. In other words, if the star is enshrouded in a dusty shell before the first pericentre passage, it becomes stripped of most of the envelope, unless the material is continuously replenished. If a binary star is embedded within the envelope, there is a chance that the two components separate during the pericentre passage, revealing the nature of the cloud core. During the pericentre passage, the centre of mass of the cloud separates from the stellar core inside the cloud, but then it returns to the star as the unbound particles are destroyed by sublimation or become accreted onto the black hole. The presence of the bow shock around a star somewhat diminishes the amount of captured particles (Table \ref{tab_captured_mass}), and a greater fraction of the cloud can survive to the following pericentre passage. On the other hand, the presence of a binary tends to dissolve the cloud more efficiently at the moment of close encounter with the SMBH. The characteristics of motion across the bow shock depend strongly on parameters, mainly the mass-loss rate and the stellar-wind velocity, so the predictions are uncertain and the outcome of the simulations vary. In addition, there are still uncertainties in the density and temperature profiles of the flow near the Galactic centre. However, the comparison of our simulations with post-pericentre observations can help to set better constraints. | 14 | 3 | 1403.5792 |
1403 | 1403.5271_arXiv.txt | We demonstrate that for a cosmic variance limited experiment, CMB $E$ polarization {\it alone} places stronger constraints on cosmological parameters than CMB temperature. For example, we show that \EE\ can constrain parameters better than \TT\ by up to a factor $2.8$ when a multipole range of $\ell=30-2500$ is considered. We expose the physical effects at play behind this remarkable result and study how it depends on the multipole range included in the analysis. In most relevant cases, \TE\ or \EE\ surpass the \TT\ based cosmological constraints. This result is important as the small scale astrophysical foregrounds are expected to have a much reduced impact on polarization, thus opening the possibility of building cleaner and more stringent constraints of the \LCDM\ model. This is relevant specially for proposed future CMB satellite missions, such as \textit{CORE} or \textit{PRISM}, that are designed to be cosmic variance limited in polarization till very large multipoles. We perform the same analysis for a Planck-like experiment, and conclude that even in this case \TE\ alone should determine the constraint on $\Omega_ch^2$ \emph{better} than \TT by $\sim 15\%$ , while determining $\Omega_bh^2$, $n_s$ and $\theta$ with comparable accuracy. Finally, we explore a few classical extensions of the \LCDM\ model and show again that CMB polarization alone provides more stringent constraints than CMB temperature in case of a cosmic variance limited experiment. | \label{intro} The results from the Planck satellite have recently confirmed that the cosmic microwave background (CMB) anisotropies are a powerful probe of cosmology \cite{planckcosmo}. While these first cosmological results were based on Planck temperature data alone, interesting improvements are expected with the next release of data, when CMB polarization will be included in the analysis. CMB polarization is often described in the literature as a unique source of information for reionization studies \cite{zaldarriaga97,mortonson08}, thanks to the large-scale signature that reionization is expected to leave in the polarization power spectra, and for inflation studies, as primordial gravitational waves are expected to produce B-mode CMB polarization \cite{seljak97,zaldarriagaspergel97,baumann09,bock09,kenney98,bicep} and because polarization provides a cleaner probe of initial conditions \cite{spergel97,mortonson09,huspergel,durrer01,peiris03}. Furthermore, it is in general recognised that adding the information coming from polarization can improve the constraints on cosmological parameters and can help breaking some degeneracies \cite{seljak97,rocha03,colombo09,tegmark00,eisenstein99,bucher01,wu14,galli}. In this paper, we argue that the CMB $E$ polarization data is much more than a mere improvement over the temperature anisotropies measurement. We demonstrate that either the temperature-polarization cross-correlation \TE\ or the \EE\ polarization power spectra can provide tighter constraints on cosmological parameters than the temperature power spectrum \TT, in the case of a Cosmic Variance Limited experiment (hereafter \CVL). The constraining power of \EE\ had already been noticed in \cite{rocha03}. Here we show, for the first time, that \TE\ as well is more constraining than the \TT\ power spectrum, and explicit the physical reasons behind this conclusion. We find that the \EE\ power spectrum can constrain the parameters (including the optical depth $\tau$) by up to a factor $2.8$ better than \TT\ in the case of a \CVL\ experiment probing up to multipoles $\ell=2500$, even when excising the large scales polarized signature of reionization ($\ell<30$). Overall, the constraining power of the \EE\ power spectrum is found to be mildly dependent on the availability of small scales ($\ell>2000$) and dramatically on the large scales ($30<\ell<130$). The \TE\ based constraints are also found to be tighter than the \TT\ based ones. In the case of a more realistic Planck-like experiment, we demonstrate that the \TE\ power spectrum provides comparable constraints to the \TT\ one, and a better one for the dark matter physical density $\Omega_{c}h^2$ by about $15\%$. Finally, we show that even for classical extentions of the \LCDM\ models, the polarized based constraints are at least equivalent and often better than the temperature based one, for a \CVL\ experiment. Our results open the possibility of improving the robustness of the CMB based cosmological constraints. In fact, an important limitation of the \TT\ based cosmological constraints both from Planck \cite{2013arXiv1303.5075P} and from ground based experiments \cite{Dunkley:2013vt,Reichardt:2011il} is the presence of astrophysical foregrounds, particularly at small scales where the CMB temperature anisotropies are dominated by the contribution from unresolved radio and infrared galaxies. Polarization, however, is expected to suffer less from this contamination \cite{seiffert07,tucci04}. Using the exceptional constraining power of the polarized CMB observations, one should thus be able to build cross-checks of the temperature results and improve the temperature foreground models at small scales. In Section \ref{sec:fisher}, we first describe the Fisher Matrix formalism that will be used to calculate forecasts on cosmological parameters. Then, in Section \ref{sec:CVL} we present the main results on \LCDM\ parameters for a \CVL\ experiment. In particular, we show how the constraints depend on the maximum or minimum multipole included in the analysis, and describe the physics at play in this setting. Section \ref{sec:planck} reproduces the analysis for a Planck-like experiment. The sensitivity of the constraints to prior knowledge of the reionization optical depth $\tau$ is discussed in Section \ref{sec:tau}, and we show how the large scales ($\ell<30$) contribute to the determination of $\tau$. Finally, Section \ref{sec:exten} allows us to generalize our conclusions to classical \LCDM\ model extensions. | \label{sec:conclusions} We have forecasted the power to constrain cosmological parameters from the \TT, \EE\ or \TE\ CMB power spectra taken separately. We find that for a cosmic variance limited experiment, \EE\ is the best at constraining all cosmological parameters in a $\Lambda$CDM model compared to \TE\ and \TT\ alone. This fact holds true when different amount of information about cosmic reionization is included in the analysis, e.g. whether the polarized power spectra are cut at $\lmin=2$ or $\lmin=30$, or whether a prior on the reionization optical depth $\tau$ is included in the analysis. We find that most of the degeneracy breaking power of the \EE\ power spectrum comes from $\ell$ ranges between $100-200$, a region where we expect the galactic dust contamination to be harder to clean. We have also shown for the first time the constraining power of the temperature-polarization cross-correlation power spectrum \TE, finding that for a \CVL\ experiment it would also constrain parameters more efficiently than \TT\ alone. The advantage of \TE\ over \EE\ however, is that the constraints are less affected when $\ell\lesssim 200$ are excluded from the analysis, making it less sensitive to large-scale foreground modelling. We have also shown that \EE\ is the best at constraining $\tau$, compared to \TE\ or \TT, either from the large scale polarization reionization bump, or from the degeneracy breaking effect of lensing at small scales. We find that observing the polarization bump provides constraints that are a factor $\sim 3$ stronger than the ones obtainable by the effect of lensing. These findings are particularly interesting for future proposed CMB missions such as \textit{CORE} \cite{core} or \textit{PRISM} \cite{prism}, as such experiments are designed to be cosmic variance limited both in temperature and in polarization in wide multipole ranges. We also forecast constraints for a Planck-like satellite experiment. In spite of the much higher noise of polarization, we find that \TE\ determines the dark matter density $\Omega_ch^2$ by $15\%$ better than \TT, and the other parameters at a similar level of precision. This result has never been forecasted before, and opens the possibility to verify the Planck results from \TT\ with those from \TE. The advantage of this procedure is that the two spectra are expected to have different dependencies on systematics and foregrounds. We emphasize here that our forecasts do not include marginalization over foreground parameters. However, the level of foreground contamination at small scales in polarization is expected to be lower than the one in temperature, so we expect that our broad conclusions about the superiority of polarization should not depend on this factor. | 14 | 3 | 1403.5271 |
1403 | 1403.5265_arXiv.txt | We report on the discovery of a relation between the number of star formation (SF) peaks per unit time, $\nu_{\rm peak}$, and the size of the temporal smoothing window function, $\Delta t$, used to define the peaks: $\nu_{\rm peak}\propto\Delta t^{1-\phi}$ ($\phi\sim 1.618$). This relation holds over the range of $\Delta t=10$ to $1000$Myr that can be reliably computed, using a large sample of galaxies obtained from a state-of-the-art cosmological hydrodynamic simulation. This means that the temporal distribution of SF peaks in galaxies as a population is fractal with a Hausdorff fractal dimension equal to $\phi-1$. This finding reveals, for the first time, that the superficially chaotic process of galaxy formation is underlined by a temporal self-organization up to at least one gigayear. It is tempting to suggest that, given the known existence of spatial fractals (such as the power-law two-point function of galaxies), there is a joint spatio-temporal self-organization in galaxy formation. From an observational perspective, it will be urgent to devise diagnostics to probe SF histories of galaxies with good temporal resolution to facilitate a test of this prediction. If confirmed, it would provide unambiguous evidence for a new picture of galaxy formation that is interaction driven, cooperative and coherent in and between time and space. Unravelling its origin may hold the key to understanding galaxy formation. | \label{sec: intro} Galaxy formation involves a large set of physical processes - cosmological expansion, gravity, hydrodynamics, atomic physics and feedback from star formation, stellar evolution and black hole growth - and spans large dynamic ranges in time (at least $0.1$Myr to $10$Gyr) and space (at least $1$pc to $100$Mpc). Some of the most interesting results on galaxy formation are thus obtained using large-scale simulations, providing fundamental insights on a variety of different aspects \citep[e.g.,][]{1988Frenk, 1994Cen, 1998Gnedin, 1999Klypin, 1999Moore, 1999Cen, 2002Wechsler, 2002Abel, 2002Bromm, 2005Springel, 2005Keres, 2006Hopkins, 2006Croton, 2006Naab, 2007Bournaud, 2008Diemand, 2009Dekel, 2010Schaye}. The spatial distributions of galaxies have been extensively studied observationally, primarily at low redshift. Among the most striking is the nature's ability to maintain a powerlaw galaxy-galay two-point correlation function over a significant range ($\sim 0.1-10h^{-1}$Mpc) \citep[e.g.,][]{1977Groth}, although there is evidence of a slight inflection at $\sim 1-2h^{-1}$Mpc in recent analysis \citep[e.g.,][]{2004Zehavi}. This spatial regularity is not inherited from the linear power spectrum but must be a result of cooperation between nonlinear evolution and galaxy formation. In self-gravitating systems, such as galaxies, the temporal and spatial structures may be related. This may be seen by two examples. First, for an isolated (non-dissipative) spherical system, the collapse time of each shell (assuming no shell crossings) is uniquely determined by the interior mass and specific energy of the shell that in turn is determined by the density structures. Second, during the growth of a typical galaxy, in addition to direct acquisition of stars via mergers and accretion (along with dark matter), significant spatial interactions may induce significant star formation activities hence leave temporal imprints in its star formation history. Taking these indications together suggests that one should benefit by tackling the problem of galaxy formation combining the spatial and temporal information. Here, as a step in that direction, we perform a novel analysis, utilizing the ab initio LAOZI adaptive mesh refinement cosmological hydrodynamic simulation, to understand the statistical properties of star formation episodes in galaxies. | \label{sec: conclusions} This paper is the third in the series ``On the Origin of the Hubble Sequence". Utilizing {\it ab initio} {\color{red}\bf L}arge-scale {\color{red}\bf A}daptive-mesh-refinement {\color{red}\bf O}mniscient {\color{red}\bf Z}oom-{\color{red}\bf I}n cosmological hydrodynamic simulations ({\color{red}\bf LAOZI Simulations}) of the standard cold dark matter model, we undertake a unique study of the statistical properties of star formation episodes in galaxies. We find a relation between the number of star formation (SF) peaks per unit time, $\nu_{\rm peak}$, and the size of the temporal smoothing window function, $\Delta t$, used to define the peaks: $\nu_{\rm peak}\propto\Delta t^{1-\phi}$ ($\phi\sim 1.618$), valid over the range of $\Delta t=0.01-1$Gyr. It is expected that the findings do not significantly depend on precise cosmological parameters, since the responsible processes are mostly in the nonlinear regime, although it remains to be seen if the relation extends to below 10Myr, where non-gravitational processes, including feedback processes, may introduce time scales of their own. The implication is profound: galaxy formation is temporally fractal and displays a self-organization up to at least one gigayear, with a \citet[][]{1919Hausdorff} dimension equal to $\phi-1$. % We attribute this temporal self-organization, tentatively, to interactions between galaxies that presumably trigger star formation peaks and are organized temporally in a way that is yet to be quantitatively understood. Qualitatively, the found results may be explained as follows. One could envision that galaxies are normally (at least at high redshift) embedded in a gas reservoir, which is the potential fuel of star formation. When there is a trigger, some of this gas is driven inward to fuel star formation. The triggers are likely due to significant interactions between galaxies, such as major and minor mergers or close fly-bys of significant galaxies, or some torquing events, or some hydrodynamic events. The triggers may be democratically distributed temporally in the sense that at a given time baseline a large trigger is not usually preceded or followed by another large trigger, but rather by small triggers. One might even argue that in some rare cases, even if a large trigger does follow a preceding large one, a significant ``drawdown" of gas by the preceding SF peak may cause the second SF peak to be less powerful that it otherwise would. Such compensated behavior could give rise to the temporal structures seen. Were the triggers distributed randomly, then ${\phi}$ would be $2$. Should the triggers be completely correlated (i.e., a delta function in time), then ${\phi}$ would be $1$. Since the triggering of SF peaks by galaxy interactions implies spatial correlations of galaxies, and given that galaxies are known to exhibit spatial fractals, such as the power-law galaxy two-point correlation function \citep[e.g.,][]{1980Peebles}, our results are strongly indicative that galaxy formation may be governed by a fundamental joint spatio-temporal self-organization. Understanding the origin of this self-organization may hold a key to understanding galaxy formation. Observational diagnostics to probe SF histories of galaxies with competitively good temporal resolution from a few Myr to Gyr, especially those that are applicable to a sufficient sample of galaxies, are highly wanted, in order to test the predictions made here. In addition, with the development of this new line of inquiry, more accurate observational characterizations of galaxy clustering at high redshift at the peak of star formation will be useful. In spite of the apparent coincidence, it would be premature to emphatically relate $\phi$ to the golden ratio. % Nonetheless, the ubiquitous manifestations of the golden ratio in nature suggest that further investigations with higher statistical accuracies may be warranted. Could the galaxy formation be golden after all? \vskip 1cm I would like to thank Claire Lackner for providing the SQL based merger tree construction software. The analysis program yt \citep[][]{2011Turk} is used to perform some of the analysis. Computing resources were in part provided by the NASA High- End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. This work is supported in part by grant NASA NNX11AI23G. | 14 | 3 | 1403.5265 |
1403 | 1403.2390_arXiv.txt | We present $4.5\ \mu$m luminosity functions for galaxies identified in 178 candidate galaxy clusters at $1.3 < z < 3.2$. The clusters were identified as {\it Spitzer}/IRAC color-selected overdensities in the Clusters Around Radio-Loud AGN (CARLA) project, which imaged 421 powerful radio-loud AGN at $z > 1.3$. The luminosity functions are derived for different redshift and richness bins, and the IRAC imaging reaches depths of $m^{*} + 2$, allowing us to measure the faint end slopes of the luminosity functions. We find that $\alpha = -1$ describes the luminosity function very well in all redshifts bins and does not evolve significantly. This provides evidence that the rate at which the low mass galaxy population grows through star formation, gets quenched and is replenished by in-falling field galaxies does not have a major net effect on the shape of the luminosity function. Our measurements for $m^{*}$ are consistent with passive evolution models and high formation redshifts ($z_{f} \sim 3$). We find a slight trend towards fainter $m^{*}$ for the richest clusters, implying that the most massive clusters in our sample could contain older stellar populations, yet another example of cosmic downsizing. Modelling shows that a contribution of a star-forming population of up to 40 \% cannot be ruled out. This value, found from our targeted survey, is significantly lower than the values found for slightly lower redshift, $z \sim 1$, clusters found in wide-field surveys. The results are consistent with cosmic downsizing, as the clusters studied here were all found in the vicinity of radio-loud AGNs -- which have proven to be preferentially located in massive dark matter halos in the richest environments at high redshift -- and may therefore be older and more evolved systems than the general protocluster population. | Many attempts have been made to measure the formation epoch of galaxy clusters, generally finding high formation redshifts, $z_f \sim 2 - 4$. Studies focusing on galaxy colors provide insight into when stellar populations formed \citep[e.g.,][]{Stanford_1998, Holden_2004, Eisenhardt_2008}, while the assembly of galaxies and their evolution can be measured by analysing the fundamental plane or galaxy luminosity functions \citep[e.g.,][]{Van_Dokkum_2003, Mancone_2010}. As a few examples, \citet{Eisenhardt_2008} infer stellar formation redshifts of $z_f > 4$ for cluster galaxies by comparing their $I-[3.6]$ colors to passive galaxy evolution models. Studying the color and the scatter of the main sequence, \citet{Mei_2006} infer a mean luminosity-weighted formation redshift of $z_f > 2.8$ for cluster ellipticals in two high-redshift clusters in the Lynx supercluster. Earlier formation epochs are inferred for galaxies closer to the cores, with early-type galaxies within 1 arcmin of the cluster centers having $z_f > 3.7$. \citet{Kurk_2009}, who also look at the position of the red sequence in color-magnitude diagrams and compare them to theoretical predictions, infer $z_f \sim 3$ for a protocluster at $z = 1.6$. By comparing the fundamental plane of a Lynx cluster at $z=1.27$ to the fundamental plane of the nearby Coma cluster, \citet{Van_Dokkum_2003} infer a stellar formation redshift of $z_f = 2.6$ for the distant cluster, with passive evolution thereafter. Studying the mid-infrared (mid-IR) luminosity function at high redshifts ($1 < z <3$) probes rest-frame near-infrared (near-IR) emission ($J,H,K$), which is a good proxy for stellar mass for all but the youngest starbursting galaxies \citep{Muzzin_2008, Ilbert_2010}. Such studies have shown that the bulk of the stellar mass in clusters is already in place by $z \sim 1.3$ \citep[e.g.,][]{Lin_2006, Muzzin_2008, Mancone_2010} and that $\alpha$, the faint end slope of the galaxy luminosity function, does not evolve significantly with redshift \citep[e.g.,][]{Propris_1998, Muzzin_2007, Strazzullo_2010, Mancone_2012}. It seems that processes that might lead to a substantial increase in mass such as mergers and star formation, and processes that would strip mass away from the cluster such as galaxy-galaxy interactions, or galaxy harassment, either balance each other or do not to play an important role in cluster evolution. On the other hand, there is evidence for considerable stochastic star formation in clusters at $z > 1.3$. For a sample of 16 spectroscopically confirmed galaxy clusters at $1 < z < 1.5$ selected from the IRAC Shallow Cluster Survey \citep[ISCS;][]{Eisenhardt_2008}, \citet{Brodwin_2013} show that star formation is occurring at all radii and increases towards the core of the cluster for clusters at $z > 1.4$. These clusters were identified as 3-D overdensities in the Bo\"{o}tes Survey \citep{Stanford_2005, Elston_2006, Eisenhardt_2008} using a photometric redshift probability distribution and wavelet analysis \citep{Brodwin_2006}. \citet{Brodwin_2013} observe a rapid truncation of star formation between $z \sim 1.5$ and $z \sim 1$, by which time the cores of the clusters become mostly quiescent. Investigating the color and scatter of the red sequence galaxies, \citet{Snyder_2012} conclude that at $z \sim 1.5$ significant star formation is occurring and that at this redshift the red sequence in the centers of clusters was rapidly growing. In a related analysis also using the Bo\"otes cluster sample, \citet{Mancone_2010} measured the evolution of the mid-IR luminosity function for a sample of galaxy clusters spanning $0.3 < z < 2$. By measuring the luminosity function and the evolution of $m^*$ compared to theoretical passive evolution models, \citet{Mancone_2010} found $z_f \sim 2.4$ for the low redshift ($z < 1.3$) portion of their cluster sample. At higher redshift ($1.3 < z < 1.8$) a significant deviation from the passive models was measured which could most likely be explained by ongoing mass assembly at those redshifts. However, the highest redshift bins suffered from small sample sizes. This paper aims to continue and complement these previous results and extend the luminosity function analysis to higher redshift. We study the evolution of the luminosity function of almost 200 galaxy cluster candidates at $1.3 < z < 3.2$ discovered through the Clusters Around Radio Loud AGN, or CARLA, project \citep{Wylezalek_2013}. The clusters were found in the fields of radio-loud active galactic nuclei (RLAGN), including both typical unobscured (e.g., type-1) radio-loud quasars (RLQs), and obscured (e.g., type-2) radio-loud AGN, also referred to as radio galaxies (RGs). Significant research stretching back many decades show that RLAGN belong to the most massive galaxies in the universe \citep{Lilly_1984, Rocca_2004, Seymour_2007, Targett_2012} and are preferentially located in rich environments up to the highest redshifts \citep[e.g.,][]{Minkowski_1960, Stern_2003, Kurk_2004, Galametz_2012, Venemans_2007, Hutchings_2009, Hatch_2011, Matsuda_2011, Mayo_2012, Husband_2013, Ramos_2013, Wylezalek_2013}. As described in \citet{Wylezalek_2013}, the selection of candidate cluster members in the vicinity of the CARLA targets is based purely on the mid-IR colors of galaxies around a luminous RLAGN with a spectroscopic redshift. The selection is thus independent of galaxy age, morphology, or the presence of a red sequence; we discuss the selection in more detail in \S~6. This sample allows us to perform a statistical study of the mid-IR luminosity functions of a large sample of very high-redshift galaxy clusters, achieving statistics never before achieved at these early epochs. The paper is structured as follows: \S2 describes the observations and the cluster sample used in this work, \S3 describes the fitting procedure and estimation of the uncertainties while the results are presented in \S4. In \S5 we explain the robustness tests carried out and discuss our measurements in \S6. Section~7 summarises the work. Throughout the paper we assume $H_{0}$ = 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\rm{m}}$ = 0.3, $\Omega_{\Lambda}$ = 0.7. All magnitudes and colors are expressed in the AB photometric system unless stated otherwise. | \subsection{Alternatives to pure passive Evolution Models} The above results suggest an early formation epoch for galaxy clusters that are passively evolving and an early build-up of the low-mass galaxy population. These measurements, however, seem to be at odds with results investigating lower redshift clusters. \citet{Thomas_2010} shows that the age distribution in high-density environments is bimodal with a strong peak at old ages and a secondary peak comprised of young, $\sim 2.5$ Gyr old galaxies. This secondary peak contains about $\sim 10$\% of the objects. Similarly, \citet{Nelan_2005} derives a mean age of low-mass objects of low redshift galaxy clusters to be about 4 Gyrs in low-redshift clusters. Although their observation suggests a decline of star-forming galaxies and a trend of downsized galaxy formation, low mass galaxies are still assembling until relatively recent times. Measurements of the star-formation activity for higher redshift cluster galaxies also provide evidence for continuous star-formation activity, albeit evolving more rapidly than the star-formation activity in field galaxies \citep[e.g.]{Alberts_2014}. We therefore investigate the extent to which our results can be explained by a sum of various stellar populations to estimate the maximum fraction of a star-forming cluster population that is still consistent with the data. We divide the cluster population into two stellar populations, a simple stellar population (SSP) with a delta-burst of star formation at high redshift and a composite stellar population (CSP) with a continuous, only slowly decaying star-formation rate of the form $\propto exp(-t/\tau)$ and large $\tau$. The details of the three different model sets we derive are as follows: \begin{itemize} \item Model 1: Sum of SSP with $z_f = 3$ and CSP with $z_f = 3$ and $\tau = 10$ Gyr with ratios (SSP:CSP) ranging between 90:10 and 0:100\footnote{a ratio (SSP:CSP) of (100:0) is equivalent with a passive evolution model and is already discussed above} by mass. \item Model 2: Sum of SSP with $z_f = 3$ and CSP with $z_f = 3$ and $\tau = 1$ Gyr with ratios (SSP:CSP) ranging between 90:10 and 0:100 by mass. \item Model 3: Sum of SSP with $z_f = 5$ and CSP with $z_f = 3$ and $\tau = 10$ Gyr with ratios (SSP:CSP) ranging between 90:10 and 0:100 by mass. \end{itemize} A prolonged mass assembly means that at high redshift the observed $4.5\ \mu$m magnitude of galaxies is fainter because the stellar population is still forming. Therefore, accounting for mass assembly, i.e. allowing for star-forming population to contribute to the observed $m^{*}$, causes $m^{*}$ to become fainter at high redshift depending on the contribution of this star-forming population. In Figure \ref{models} we show these models in the context of our results. They allow us to set an upper limit on the star-forming fraction, $P$, in our candidate cluster sample. Model 1, which allows for a significant star formation that is only very slowly decaying with cosmic time, shows that at all redshifts the mass fraction of the star-forming population cannot be larger than 40\% (with one outlying exception of up to 60\% at $z \sim 1.7$). In Model 2 the star formation rate (SFR) of the CSP decays faster and the contribution of the SSP becomes dominant much earlier than in Model 1. It therefore predicts $m^{*}$ to be brighter at high redshifts and resemble the prediction of the passive evolution model. Consequently, our empirical results are in agreement with large contributions of up to 90\% of the CSP in Model 2, with the CSP starting to passively evolve $\sim 2.3$ Gyrs earlier (at $z \sim 1.7$) than in Model 1 (at $z \sim 0.9$). Model 3 shows the evolution of a mixed population with a delta burst of star formation at $z_{f} = 5$ (SSP) and a long burst of star formation at $z_f = 3$ (CSP with $\tau = 10$ Gyrs). The SSP with $z_f = 5$ is fainter in IRAC2 at $1.5 < z < 3$ than a SSP with $z_f = 3$, so that an additional starburst at $z=3$ leads to an even fainter $m^{*}$ at $1 < z < 3$ for Model 3. Model 3 does not reproduce the results of the LF analysis and therefore this scenario can be ruled out by the data. This shows that the results for the evolution of $m^{*}$ obtained in this analysis -- although consistent with passive evolution models -- also allow for a limited contribution of a star-forming population in galaxy clusters. Our models show that this contribution is small (up to 40 \% by mass, but probably on average around $\sim 20$ \%) for a population with a high and slowly decaying star-formation rate, or that this contribution is large (up to 80\%) for a population with a fast decaying SFR and an evolution that resembles passive evolution $\sim 2.3$ Gyrs earlier. For a sample of 10 rich clusters at $0.86 < z < 1.34$ \citet{vanderburg_2013} compares the contributions of quiescent and star-forming populations to the total mass function. We integrate the published mass functions for the quiescent and star-forming population \citep{vanderburg_2013} over galaxy masses with $10^{10.1} < M_*/M_{\sun} < 10^{11.5}$. We find a mass fraction of the quiescent population of $\sim 80$\% compared to the total stellar mass of the clusters . This is also in agreement with the upper limit for the fraction of the star-forming population derived for CARLA clusters in the lowest redshift bin. As CARLA clusters at $z \sim 3$ will not necessarily be the progenitors of CARLA clusters at $z \sim 1.5$, we unfortunately cannot constrain the evolution of the maximum fraction of a star-forming population and cannot make conclusions about the quenching timescales and processes. \begin{figure} \centering \includegraphics[scale = 0.43]{model_35sig.eps} \includegraphics[trim = 0 0 0 2 cm, clip = true, scale = 0.43]{model_35_2sig.eps} \includegraphics[scale = 0.43]{model_35sig_3.eps} \caption{Model predictions for the evolution of $m^*$ for a superposition of a passive and star-forming galaxy population. The passive, simple stellar population (SSP) formed stars in a delta burst at $z_f$ and evolved passively thereafter while the star-forming, composite stellar population (CSP) shows an exponentially decaying SFR with an $e$-folding timescale $\tau$. We show models with differing mass ratios of the SSP and CSP. Comparing the models with our measurements for $m^{*}$ allows to set an upper limit on the contribution of the CSP. \textit{Top panel: Model 1:} SSP with $z_f = 3$, CSP with $z_f = 3$ and $\tau = 10$ Gyrs \textit{Middle panel: Model 2:} SSP with $z_f = 3$, CSP with $z_f = 3$ and $\tau = 1$ Gyr \textit{Bottom panel: Model 3:} SSP with $z_f = 5$, CSP with $z_f = 3$ and $\tau = 10$ Gyrs } \label{models} \end{figure} \subsection{Biases of the CARLA cluster sample} Our analysis shows that the evolution of the CARLA clusters seems to be significantly different from the cluster sample analysed by \citet{Mancone_2010}. Using \textit{Spitzer} $24\ \mu$m imaging for the same cluster sample, \citet{Brodwin_2013} analysed the obscured star formation as a function of redshift, stellar mass and clustercentric radius. They find that the transition period between the era where cluster galaxies are significantly quenched relative to the field and the era where the SFR is similar to that of field galaxies occurs at $z \sim 1.4$. Combining these measurements with other independent results on that sample \citep{Snyder_2012, Martini_2013, Alberts_2014}, the authors conclude that major mergers contribute significantly to the observed star formation history and that merger-fueled AGN feedback may be responsible for the rapid truncation between $z = 1.5$ and $z = 1$. While the ISCS clusters studied in \citet{Mancone_2010} and \citet{Brodwin_2013} were selected from a field survey as 3-D overdensities using a photometric redshift wavelet analysis, the clusters studied here are found in the vicinity of RLAGN. With RLAGN belonging to the most massive galaxies in the universe \citep[$ m \sim 10^{11.5}$ M$_{\sun}$; ][]{Seymour_2007, Breuck_2010}, these clusters could reside in the largest dark matter halos, deepest potential wells and densest environments. Indeed, \citet{Mandelbaum_2009} derives halo masses for 5700 radio-loud AGN from the Data Release 4 of the Sloan Digital Sky Survey and finds the halo masses of these radio-loud AGN to be about twice as massive as those of control galaxies of the same stellar mass. Previous work \citep[e.g.][]{Best_2005}has shown that more massive black holes seem to trigger radio jets more easily, but as this boost in halo mass is independent of radio luminosity, the authors conclude that the larger-scale environment of the RLAGN must play a crucial role for the RLAGN phenomenon. Similarly, albeit at higher redshift, Hatch et al., in prep. finds that the environments of CARLA RLAGN are significantly denser than similarly massive quiescent galaxies. They detect a weak positive correlation between the black-hole mass and the environmental density on Mpc-scales, suggesting that even at high redshift the growth of the black hole is also linked to collapse of the surrounding cluster. This peculiar interplay between radio jet triggering, stellar mass, black hole and halo mass of the RLAGN and the larger-scale environment suggest that (proto-)clusters and the large-scale environments of RLAGN are distinct from clusters found in field surveys. If mergers are significantly contributing to the transition of clusters from unquenched to quenched systems, as suggested in \citet{Brodwin_2013}, this transition redshift will be dependent on cluster halo mass. If the environments and dark matter halos around radio-loud AGN are indeed more massive this would explain the conflict of our results with those from \citet{Mancone_2010}. CARLA clusters have probably undergone this transition period much earlier than the ISCS clusters. At $1.4 < z <1.8$ where the star-forming fraction of ISCS clusters analysed by \citet{Mancone_2010} still seems to be very high ($\sim 80$\%), this contribution is already much smaller in CARLA clusters. As mentioned earlier, our measurements allow us to derive upper limits on the contribution of a star-forming population but do not allow for a definite constraint on the transition redshift. | 14 | 3 | 1403.2390 |
1403 | 1403.0676_arXiv.txt | In this paper I introduce a precise constraint on primordial magnetogenesis, for a generic class of single-field inflationary model followed by small field excursion below the Planck scale. I also establish a connection between the magnetic field at the present epoch and primordial gravity waves ($r$) via non-vanishing CP asymmetry parameter ($\epsilon_{\bf CP}$), which triggers the leptogenesis scenario. Finally, I explore various hidden cosmophenomenological features of theoretical CMB B-mode polarization spectra, which can be treated as a significant probe to put further stringent constraint on low and high scale small field inflationary models after releasing the Planck B-mode polarization data. | 14 | 3 | 1403.0676 |
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1403 | 1403.5053_arXiv.txt | We analyze a scenario in which the lightest heavy neutrino $N_1$ is a dark matter candidate and the second-heaviest neutrino $N_2$ decays producing lepton number. If $N_1$ were in thermal equilibrium, its energy density today would be much larger than that of the observed dark matter, so we consider energy injection by the decay of $N_2$. In this paper, we show the parameters of this scenario that give the correct abundances of dark matter and baryonic matter and also induce the observed neutrino masses. This model can explain a possible sterile neutrino dark matter signal of $M_1$=7 keV in the x-ray observation of x-ray multi-mirror mission. | There are at least three phenomena that cannot be explained within the standard model of particle physics (SM). They are neutrino masses, dark matter (DM), and baryon asymmetry of the Universe (BAU). In the SM, particles acquire masses by the Higgs mechanism, but neutrinos are assumed not to couple to the Higgs particle so they remain massless. By introducing right-handed neutrinos, neutrinos can couple to the Higgs particle, and acquire Dirac masses. Right-handed neutrinos are singlets under the SM gauge group $SU(2)_L\times U(1)_Y$, so they can also have Majorana masses without breaking the symmetry of the SM. If these Majorana masses are much larger than the Dirac masses, mass eigenstates are separated into two groups. One of them is active, light neutrinos mainly composed of left-handed neutrinos, and the other is sterile, heavy neutrinos almost coinciding with right-handed neutrinos. This is called the seesaw mechanism \cite{Minkowski:1977sc,Yanagida:1979as,gell1979r}, and we use this mechanism in this paper. Two other phenomena beyond the SM can be found in the Universe. In the observable range of the Universe, no primordial antimatter has been found. To explain the asymmetry of matter and antimatter, we need $CP$ violation \cite{Sakharov:1967dj}. By observation of the anisotropy of cosmic microwave background \cite{Ade:2013ktc}, the ratio of baryon density to critical density today is $\Omega_b h^2= 0.02214\pm 0.00024$(68\% limit), which can be converted into the baryon number to entropy ratio $Y_B\simeq 0.86\times 10^{-10}$. In the SM, $CP$ is violated by Yukawa couplings between the quarks and Higgs particle, but it is too small to explain this asymmetry. If there are right-handed neutrinos, $CP$ can also be broken by the couplings between the neutrinos and Higgs particle. A heavy neutrino, which is Majorana particle, it can decay into either lepton or antilepton by Yukawa interaction. The difference between these decay rates results in nonzero lepton number (called leptogenesis \cite{Fukugita:1986hr}), and it is transferred to a baryon number by electroweak processes (sphaleron processes \cite{Kuzmin:1985mm}). Another problem the Universe offers us is dark matter. Dark matter does not interact with electromagnetic forces and is stable, or its lifetime is longer than the age of the Universe. In the SM, such a particle is not included, and even massive left-handed neutrinos are too light to explain all dark matter. Many candidates of dark matter have been proposed, and sterile neutrino is one of them. Sterile neutrinos, of course, do not participate in electromagnetic nor strong interactions. If their mass is roughly of order keV, they can live longer than the Universe, so they can be dark matter (see Refs. \cite{Kusenko:2009up,Merle:2013gea} for reviews). There are several ways to produce sterile neutrino dark matter $N_1$. The simplest production mechanism is to use the mixing of sterile and active neutrinos, proposed Dodelson and Widrow (DW mechanism, \cite{Dodelson:1993je}). This model, however, is disfavored by observations of x-rays and Lyman alpha forest \cite{Asaka:2006nq}. Another way is resonant production, or the Shi-Fuller mechanism \cite{Shi:1998km}. If there were relatively large lepton number (at least $Y_L\gtrsim 8\times10^{-6} $), light neutrinos can be efficiently converted to sterile neutrinos. In this case, some mechanism is needed to make this lepton number much larger than the baryon number after the freeze-out of sphalerons. In the neutrino minimal standard model ($\nu$MSM), which is an extension of the SM with right-handed neutrinos with masses smaller than the electroweak scale\cite{Asaka:2005an,Asaka:2005pn}, this lepton asymmetry is produced by the decay of sterile neutrinos $N_2,\; N_3$ with masses $\gtrsim 100$MeV. In this model, their masses need to be highly degenerate, roughly $(M_3-M_2)/M_2\lesssim 10^{-3}$ to produce BAU \cite{Laine:2008pg,Canetti:2012kh}. % Other production mechanisms need more extensions of the SM, such as decays of scalar fields \cite{Petraki:2007gq,Merle:2013wta} or new gauge interactions. We consider the last case in this paper. The Majorana mass term of the right-handed neutrinos appears as the result of a gauge symmetry breaking, and its scale is much higher than the electroweak scale. This naturally happens if grand unification exists at high energy. In this paper, we suppose the lightest sterile neutrino $N_1$ constitutes all dark matter and the second-lightest one $N_2$ causes leptogenesis, and they were in thermal equilibrium by a gauge interaction of right-handed neutrinos \cite{Bezrukov:2009th}. There are many advantages in this case. We need not assume an initial abundance of $N_1$ and $N_2$. Their abundance is completely determined by statistical mechanics without uncertainty. The lepton number is efficiently produced, because there is no cancelation of lepton asymmetry which happens if $N_2$ is produced by Yukawa interaction. The temperature of $N_1$ is colder compared to the DW mechanism case, so constraint from Lyman alpha forest is weakened. The drawback of thermal relic $N_1$ is its overproduction. This problem can be solved by the decay of an out-of-equilibrium particle. Such a decay gives energy into the thermal bath, and the temperature of the thermal bath drops slowly compared to that of the decoupled particle $N_1$. The energy ratio of $N_1$ today becomes smaller, so the problem of overproduction can be solved. Cases of low-scale new gauge interaction were considered in Refs. \cite{Bezrukov:2009th,Nemevsek:2012cd}. % We consider a case that the dark matter $N_1$ was diluted by the entropy production during the leptogenesis. This idea was proposed in Ref. \cite{Bezrukov:2012as}. They estimated the orders of $M_2, M_3$ and scale of gauge interaction of right-handed neutrinos. We refine their analysis, considering seesaw mechanism and various constraints on parameters more seriously. We explicitly show the parameters which can explain observed neutrino masses, the BAU, and dark matter abundance. As a result, we found that a Majorana mass term of left-handed neutrinos $M_L$ is essential for masses of active neutrinos $m_\nu$, since the two eigenvalues of the difference $X_\nu\equiv m_\nu-M_L$ need to be very small, $X_1\lesssim 10^{-10}{\rm eV},\;X_2\lesssim 10^{-5}$eV. The third eigenvalue is much larger, $X_3\gtrsim O(0.1)$eV, in order to produce the BAU. If there is no fine-tuning, $M_2\gtrsim O(10^{8})$GeV and the scale of gauge interaction of right-handed neutrinos is $G_{FR}^{-1/2}\gtrsim 10^{12}$GeV. Recently, an unidentified line at 3.5keV in x-ray spectra was found \cite{Bulbul:2014sua,Boyarsky:2014jta}. There are many works to explain this anomaly (see, for example, Refs. \cite{Frandsen:2014lfa,Abazajian:2014gza} If this photon was emitted by dark matter, our model can explain it by decay of $N_1$, with $M_1$=7keV and $X_2+X_3|R_{31}|^2\sim 1\times 10^{-7}$eV ($R_{31}$ is a parameter of Yukawa coupling). We use the left-right symmetric model \cite{Mohapatra:1974hk} as an example, but if $N_1$ and $N_2$ can be in thermal equilibrium, any other model is possible. Our discussion does not involve the detail of the new gauge interaction that we will introduce. Note that the idea of diluting dark matter by leptogenesis can be applied to other particles that freeze out before the decay of the heavy neutrino. This paper is organized as follows. In Secs. \ref{numass}-\ref{BAU}, we describe how right-handed neutrinos can explain three beyond the SM phenomena described above. In Sec. \ref{COP}, we summarize constraints on parameters from various observations and our thermal history scenario. In Sec. \ref{Ana} we show parameters that satisfy all conditions obtained in previous sections, and compare the result with observations. \label{sec:intro} | \label{sec:conc} We considered a model in which heavy neutrinos $N_1$ and $N_2$ are in thermal equilibrium due to a new gauge interaction at the temperature $T\gtrsim 10^{10}$ GeV. In this case, dark matter $N_1$ is overproduced, so we supposed $N_1$ was diluted by out-of-equilibrium decay of $N_2$. This decay also produces the observed matter-antimatter asymmetry. Because of the condition from entropy production, and an oscillation constraint of $N_1$, the two eigenvalues of $X_\nu\equiv m_\nu-M_L$ have to be much smaller than the observed mass differences. This means $M_L$ is needed in our scenario. We determined the possible range of eigenvalues of $X_\nu$, masses of right-handed neutrinos $M_I$, and parameter of Yukawa couplings $R$, which can simultaneously explain three beyond-the-SM phenomena: neutrino masses, the BAU, and dark matter. In this model, a wider range of dark matter mass $M_1$ is allowed than in the DW mechanism and the $\nu$MSM. Our model can explain the recent anomaly in x-ray observation by taking $M_1\simeq 7 {\rm keV},\; X_2+X_3|R_{31}|^2\sim1\times 10^{-7}\rm eV$. In the near future, the ASTRO-H mission will clarify whether this signal is from a dark matter decay or not.% | 14 | 3 | 1403.5053 |
1403 | 1403.0730_arXiv.txt | {}{We investigate the free magnetic energy and relative magnetic helicity budgets of solar quiet regions.} {Using a novel non-linear force-free method requiring single solar vector magnetograms we calculate the instantaneous free magnetic energy and relative magnetic helicity budgets in 55 quiet-Sun vector magnetograms.} {As in a previous work on active regions, we construct here for the first time the (free) energy-(relative) helicity diagram of quiet-Sun regions. We find that quiet-Sun regions have no dominant sense of helicity and show monotonic correlations a) between free magnetic energy/relative helicity and magnetic network area and, consequently, b) between free magnetic energy and helicity. Free magnetic energy budgets of quiet-Sun regions represent a rather continuous extension of respective active-region budgets towards lower values, but the corresponding helicity transition is discontinuous due to the incoherence of the helicity sense contrary to active regions. We further estimate the instantaneous free magnetic-energy and relative magnetic-helicity budgets of the entire quiet Sun, as well as the respective budgets over an entire solar cycle.} {Derived instantaneous free magnetic energy budgets and, to a lesser extent, relative magnetic helicity budgets over the entire quiet Sun are comparable to the respective budgets of a sizeable active region, while total budgets within a solar cycle are found higher than previously reported. Free-energy budgets are comparable to the energy needed to power fine-scale structures residing at the network, such as mottles and spicules.} | Free magnetic energy corresponds to the excess energy of any magnetic region from its ``ground'', current-free (potential) energy state, while magnetic helicity quantifies the stress and distortion of the magnetic field lines compared to their potential-energy state. Free magnetic energy builds up mainly through continuous flux emergence on the solar surface and other processes such as coronal interactions \citep[e.g. ``fly-bys'',][]{gals00} or photospheric twisting \citep[e.g.][]{pari09}. Magnetic helicity either emerges from the solar interior via helical magnetic flux tubes or is being generated by solar differential rotation and peculiar photospheric motions. In solar active regions (ARs) considerable, localized magnetic flux emergence of the order of 10$^{22}$ Mx \citep{schr:harv} builds up strong opposite-polarity regions that are sometimes separated by intense, highly sheared polarity inversion lines (PILs), hence deviating substantially from a potential-field configuration. ARs tend to store large amounts of both free magnetic energy and magnetic helicity. Free magnetic energy is released, via magnetic reconnection events, in solar flares and/or coronal mass ejections (CMEs). Helicity, however, cannot be efficiently removed by magnetic reconnection \citep{berg84}, and if not transferred to larger scales via existing magnetic connections, it can only be expelled in the form of CMEs \citep{low94, devo:00}. The role of both free magnetic energy and helicity in ARs has been recently investigated by \citet{geo12a} and \citet{tzio12,tzio13}. On the other hand, quiet-Sun regions are dominated by the flow pattern of large convective cells called supergranules that range in diameter from 10\,000 km to 50\,000 km, with an average diameter between 13\,000 and 18\,000 km \citep{hage:97}. High-resolution magnetograms show continuous emergence of new bipolar elements inside the cell interiors, called the internetwork (IN), that are swept by the supergranular flow towards the boundaries of supergranular cells where opposite polarity fluxes cancel, whereas like-polarity fluxes merge \citep{wang96,schr97}. By this process hierarchic flux concentrations are formed at the intersection of supergranular cells. These magnetic flux concentrations, which are characterized by magnetic fluxes of the order of 10$^{18}$-10$^{19}$ Mx and typical diameters of 1\,000-10\,000 km \citep{parn:01}, constitute the so called {\em magnetic network}. Free magnetic energy, released in the network mainly by reconnection can fuel the dynamics of several small-scale structures, such as mottles/spicules, residing there and governed by the dynamics and physics of the network magnetic field \citep[see the review by][for further details]{tsir:12}. Free magnetic energy release from non-potential magnetic configurations in the quiet Sun has also been reported to result in small-scale structures, such as bright points \citep{zhao09}, blinkers \citep{wood99} and quiet-Sun corona nanoflares \citep{meyer13}. There are no reports in the literature concerning the accumulation and expulsion of relative magnetic helicity in the magnetic network and quiet-Sun regions in general and this mechanism's role in quiet-Sun dynamics; only \citet{zhao09} have investigated current helicity budgets in network bright points. However, there exist reports \citep{jess09,curd11,depo12} arguing for torsional oscillations in fine structures, such as explosive events and spicules, thus suggesting the existence of twisting motions that could lead to expulsion or transfer of helicity to larger scales in the solar atmosphere. Until recently, no robust method existed to calculate the instantaneous free magnetic energy and relative magnetic helicity budgets of a solar region. Existing methods were based either on integration in time of an energy/helicity injection rate \citep{berfie84} or evaluation of classical formulas \citep[hereafter {\em volume calculations},][]{finn85, berg99} using a three-dimensional magnetic field derived from extrapolations. However, energy/helicity injection rates depend on the determination of the photospheric velocity field, which involves significant uncertainties \citep[e.g.,][]{wels07}. On the other hand, volume calculations depend on model-dependent nonlinear force-free (NLFF) field extrapolations that also carry several uncertainties and ambiguities \citep[e.g.,][ and references therein]{schr06,metc08}. Recently, \citet{geo12a} proposed a novel NLFF method to calculate the instantaneous magnetic free energy and relative helicity budgets from a single (photospheric or chromospheric) vector magnetogram. The method was used for calculating the free magnetic energy and relative helicity budgets in solar ARs \citep{geo12a,tzio13} and for deriving the energy-helicity diagram of solar ARs \citep{tzio12}. The latter shows a nearly monotonic dependence between the two quantities. The aim of this paper, is to a) derive the instantaneous budgets of free magnetic energy and relative magnetic helicity in quiet-Sun regions using the aforementioned NLFF method, b) construct the corresponding energy-helicity diagram and compare it with the respective diagram for ARs, and c) calculate available budgets of free energy and helicity over an entire solar cycle and associate them with the energetics and dynamics of fine-scale quiet-Sun structures. Section~\ref{obsmeth} briefly describes and discusses the observations and the methodology, Sect.~\ref{res} presents the results, while Sect.~\ref{conc} discusses the results and summarizes our findings. | \label{conc} We have applied the recently proposed NLFF field method by \citet{geo12a} to calculate the instantaneous free magnetic energy and relative magnetic helicity budgets of quiet Sun regions from single photospheric vector magnetograms. On a sample of 55 such magnetograms we find, (1) a nearly monotonic relation between free-magnetic-energy/relative-helicity and magnetic network area (Fig.~\ref{hmecarea}) as well as total area (Fig.~\ref{areas}), and as a consequence (2) a nearly monotonic relation between the free magnetic energy and the relative magnetic helicity in quiet Sun regions (Fig.~\ref{ehdiag}). Derived energy/helicity budgets are much lower than respective budgets of ARs reported by \citet{tzio12}. Free magnetic energy budgets of quiet-Sun regions represent a rather continuous extension of respective AR budgets towards lower values (Fig.~\ref{ehdiag}). On the other hand, the corresponding helicity transition is discontinuous due to the lack of a dominant sense of relative magnetic helicity in quiet-Sun regions contrary to ARs \citep{tzio12,tzio13}. However, globally quiet-Sun regions show instantaneous budgets of free energy and, to a lesser extent, relative helicity that are comparable to those of a sizable AR. Furthermore, they do not show any hemispheric helicity preference, contrary to previous reports \citep[e.g.][]{geo09}, but this could well be a selection effect, since most of the analyzed quiet Sun areas cover parts of both north and south hemispheres. The aforementioned derived monotonic relations between the instantaneous budgets of energy/helicity and magnetic network area can be used to infer the respective budgets for an entire solar cycle. For such a derivation the respective helicity/energy injection rates have to be evaluated. Since magnetic flux concentrations used for the calculation of the instantaneous budgets are concentrated in supergranular boundaries (magnetic network) it can be assumed that the instantaneous budgets of energy/helicity replenish within the lifetime of supergranules, which is of the order of 1.8$\pm$0.9 d \citep[see][and references therein]{rieu10}. However, such an assumption, although valid for the free magnetic energy which is always dissipated through resistive processes, such as reconnection, is not always valid for helicity. The latter, if not bodily removed, is roughly conserved during reconnection and can only be transferred to nearby regions via existing large-scale magnetic connections. Assuming that a) both quantities dissipate/replenish within the aforementioned supergranular lifetime, and b) a sinusoidal variation of the network area between 10\% and 25\% within a solar cycle \citep[see Fig.3 in][]{cacc98} we can derive the total quiet-Sun budgets for free magnetic energy and helicity in a solar cycle. The derived values for different network thresholds are presented in Table~\ref{table3}. The derived helicity budgets of $\sim$10$^{45}$ Mx$^2$ are two orders of magnitude higher than the value of $\sim$10$^{43}$ Mx$^2$ reported by \citet{wels03} and an order of magnitude higher than the value of $\sim$1.5 $\times$ 10$^{44}$ Mx$^2$ reported by \citet{geo09}. However, we must stress the high uncertainties attached to our solar-cycle helicity derivation which mostly stem from the weakness of the used linear fit (Fig.~\ref{hmecarea}) as expressed by the low values of the its goodness $r$. Moreover, the estimates of \citet{wels03} and \citet{geo09} rely on typical photospheric flow velocities and the respective helicity injection rates. These have been found to underestimate the respective integrated budgets \citep{tzio13}. This work presents the first inference of the quiet-Sun free-energy budget over an entire solar cycle. However, we do know that energy in the magnetic network is dissipated, mostly through reconnection, in fine-scale structures residing at the supergranular boundaries, such as mottles and spicules \citep{tsir:12}. \cite{tsir04} have reported a value of at least 1.2 $\times$ 10$^5$ erg~cm$^{-2}$~s$^{-1}$ for the energy flux from mottles, while \citet{moor11} reported a value of 7 $\times$ 10$^5$ erg~cm$^{-2}$~s$^{-1}$ from spicules by including co-generated Alv\'{e}n waves. Assuming again a sinusoidal variation of the network area between 10\% and 25\% within a solar cycle we can integrate the aforementioned values to derive respective energies within a solar cycle of 2 $\times$ 10$^{35}$ erg and 1.2 $\times$ 10$^{36}$ erg. These values are of the same order of magnitude as the derived values of free magnetic energy $\sim$10$^{36}$ erg (see Table~\ref{table3}). Hence, there seems to be enough free energy in the quiet Sun within a solar cycle to power fine-scale structures. \cite{tsir04} have argued that considerable amounts of energy are also needed for heating the chromosphere. We should, however, note that, as discussed in \cite{geo12a}, the derived free magnetic energy is a lower limit and hence there could be even larger amount of free magnetic energy available in quiet Sun regions. Unfortunately, there exist no estimations of helicity in fine-scale structures, such as mottles and spicules, however such structures often show a helical behaviour \citep{jess09,curd11,depo12,tsir:12}. Whether this behaviour is a manifestation of episodes of helicity removal and how this process actually takes place is still unknown. There exist, however, simulations of larger-scale solar polar jets \citep{pari09}, observed in polar coronal holes, that investigate the reconnection-driven dynamics and the energy and helicity evolution. Future magneto-hydrodynamic (MHD) simulations of fine-scale structures, combined with high resolution observations of the chromosphere, could probably shed light on the processes of heliospheric helicity expulsion - if any - from quiet-Sun regions. | 14 | 3 | 1403.0730 |
1403 | 1403.5924_arXiv.txt | We exploit wide-field \lya\ imaging with Subaru to probe the environment around TN~J1338--1942, a powerful radio galaxy with a $>100\, \rm kpc$ \lya\ halo at $z=4.11$. We used a sample of \lya\ emitters (LAEs) down to $\log(L_{\rm Ly\alpha} [\ergs])\sim 42.8$ to measure the galaxy density around \tnj1338, compared to a control sample from a blank field taken with the same instrument. We found that \tnj1338\ resides in a region with a peak overdensity of $\delta_{\rm LAE}=2.8\pm 0.5$ on scales of $8\, h^{-1}\rm Mpc$ (on the sky) and $112\, h^{-1}\rm Mpc$ (line of sight) in comoving coordinates. Adjacent to this overdensity, we found a strong underdensity where virtually no LAEs are detected. We used a semi-analytical model of LAEs derived from the Millennium Simulation to compare our results with theoretical predictions. While the theoretical density distribution is consistent with the blank field, overdense regions such as that around \tnj1338\ are very rare, with a number density of $6.4\times 10^{-8}\rm Mpc^{-3}$ (comoving), corresponding to the densest $< 0.4$ percentile at $z\simeq 4.1$. We also found that the \lya\ luminosity function in the \tnj1338\ field differs from that in the blank field: the number of bright LAEs ($\log(L_{\rm Ly\alpha}[\ergs]) \ga 43.3$) is enhanced, while the number of fainter LAEs is relatively suppressed. These results suggest that some powerful radio galaxies associated with \lya\ nebulae reside in extreme overdensities on $\sim 3$--$6\, \rm Mpc$ scales, where star-formation and AGN activity may be enhanced via frequent galaxy mergers or high rates of gas accretion from the surroundings. | 14 | 3 | 1403.5924 |
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1403 | 1403.6116_arXiv.txt | We present Magellan/MIKE and Keck/HIRES high-resolution spectra of six red giant stars in the dwarf galaxy Segue\,1. Including one additional Segue\,1 star observed by \citeauthor{norris10_seg}, high-resolution spectra have now been obtained for every red giant in Segue\,1. Remarkably, three of these seven stars have metallicities below $\mbox{[Fe/H]} = -3.5$, suggesting that Segue\,1 is the least chemically evolved galaxy known. We confirm previous medium-resolution analyses demonstrating that Segue\,1 stars span a metallicity range of more than 2\,dex, from $\mbox{[Fe/H]} = -1.4$ to $\mbox{[Fe/H]} = -3.8$. All of the Segue\,1 stars are $\alpha$-enhanced, with $\mbox{[$\alpha$/Fe]}\sim 0.5$. High $\alpha$-element abundances are typical for metal-poor stars, but in every previously studied galaxy [$\alpha$/Fe] declines for more metal-rich stars, which is typically interpreted as iron enrichment from supernova Ia. The absence of this signature in Segue\,1 indicates that it was enriched exclusively by massive stars. Other light element abundance ratios in Segue\,1, including carbon-enhancement in the three most metal-poor stars, closely resemble those of metal-poor halo stars. Finally, we classify the most metal-rich star as a CH star given its large overabundances of carbon and s-process elements. The other six stars show remarkably low neutron-capture element abundances of $\mbox{[Sr/H]} < -4.9$ and $\mbox{[Ba/H]} < -4.2$, which are comparable to the lowest levels ever detected in halo stars. This suggests minimal neutron-capture enrichment, perhaps limited to a single r-process or weak s-process synthesizing event. Altogether, the chemical abundances of Segue\,1 indicate no substantial chemical evolution, supporting the idea that it may be a surviving first galaxy that experienced only one burst of star formation. | The early phases of the chemical evolution of the Universe can be reconstructed through the study of metal-poor stars. Given their low metallicity, these stars are assumed to have formed in the early Universe. Since then, these long-lived stars have locked up information on the properties of their birth gas clouds and the local chemical and physical conditions in their atmospheres that can be extracted through spectroscopic analysis. Metal-poor stars in the halo of the Milky Way have thus been used for decades to unravel the chemical enrichment history of the Galaxy (e.g., \citealt{McWilliametal, ARAA, psss}). In this way the Galaxy has been found to be chemically diverse, with multiple populations and components, and to contain a variety of substructure. These signatures clearly show how closely the chemical evolution of a galaxy is connected to its assembly history. But it is difficult to cleanly uncover the various astrophysical processes that have been involved in element nucleosynthesis and star formation in the Milky Way over billions of years. Dwarf galaxies, however, being smaller systems with presumably simpler formation histories, provide the means to study chemical enrichment in a more straightforward way. At the same time, comparison of their population of metal-poor stars with those in the Milky Way provides insight into the assembly of the Galactic halo. In the last decade, the Sloan Digital Sky Survey (SDSS) transformed our picture of the Milky Way's satellite galaxy population. The wide sky coverage and sufficiently deep photometry revealed dwarf galaxies with total luminosities ranging from 300 to $10^5~L_{\sun}$ \citep[e.g.,][]{willman05,zucker06,belokurov07,martin08}. These new galaxies were found not only to be unprecedentedly faint but also unprecedentedly dominated by dark matter \citep{sg07}. Nonetheless, they form a continuous sequence of stellar mass with the classical dwarf spheroidal galaxies in terms of star formation history \citep{brown12}, structural properties \citep{okamoto12}, and metal content \citep{kirby08,kirby11b}. A significant challenge to study individual stars in these dwarf galaxies in great detail is the difficulty in achieving the spectral data quality required for chemical abundance analyses (e.g., \citealt{koch_her,ufs,leo4}). Most dwarf galaxies orbit dozens of kpc away in the outer halo and their brightest stars therefore have typical apparent magnitudes of ${\rm V} = 17$ to 18. However, high-resolution spectroscopy is required to investigate the detailed stellar abundance patterns that reflect various enrichment events, and such spectra can only be obtained for faint stars with long integrations on the largest telescopes available. Accordingly, relatively small numbers of stars in most of the classical dwarf spheroidal (dSph) galaxies with $10^{5}\,L_{\odot} \lesssim L \lesssim 10^{7}\,L_{\odot}$ and the ultra-faint dwarfs ($L \lesssim 10^{5}\,L_{\odot}$) have been observed at high spectral resolution. \subsection{The chemical evolution of dwarf galaxies and the Milky Way} In the Milky Way it is well known that low-metallicity halo stars ($\mbox{[Fe/H]}<-1.0$) have enhanced abundances of the $\alpha$-elements (e.g., \citealt{edvardsson93}), while at higher metallicities the [$\alpha$/Fe] ratios smoothly approach the solar ratio \citep[e.g.,][]{tinsley79,mcwilliam97,venn04}. The canonical interpretation of this behavior is that it reflects the timescales of nucleosynthesis from different kinds of supernovae. Massive stars produce large amounts of the $\alpha$-elements both during their stellar evolution and in their explosions as core collapse supernovae. These elements are quickly returned to the interstellar medium because the lifetimes of such stars are short, less than 10\,Myr. Type Ia supernovae, which primarily produce iron, do not begin exploding until a poorly known delay time (typically assumed to be of order $10^{8}$\,yr; \citealt{maoz12}) has elapsed since an episode of star formation. The [$\alpha$/Fe] plateau at $\mbox{[Fe/H]}<-1.0$ then corresponds to the epoch when only core-collapse supernovae contributed significantly to the overall nucleosynthesis, and the decline to $\mbox{[$\alpha$/Fe]} = 0$ occurs when Type\,Ia supernovae begin occurring in significant numbers as well. The turnover from the high [$\alpha$/Fe] plateau in the classical dSph galaxies occurs at lower metallicity than in the Milky Way, [Fe/H]$ \sim -2.5$ (e.g., \citealt{tolstoy03, venn04}), revealing that they have been enriched on slower timescales than what is observed in the halo of the Galaxy (see e.g., \citealt{tolstoy_araa} for a review). Note that, at least in the case of Sagittarius, \citet{mcwilliam13} have questioned whether this explanation for the decline in [$\alpha$/Fe] at high metallicity is correct, and they suggest a top-light initial mass function (IMF) as an alternative. More recently, \citet{kirby08,kirby11} measured metallicities for dozens of individual stars in ultra-faint dwarfs using the medium-resolution spectroscopy from \citet{sg07}. Stars with metallicities of $\mbox{[Fe/H]}<-3.0$ were uncovered in surprisingly large relative numbers, whereas essentially no stars with $\mbox{[Fe/H]}>-1.0$ were found. This general characteristic of overall metal-deficiency correlates with the low luminosities of these galaxies. They extend the metallicity-luminosity relationship for dSph galaxies by several orders of magnitude in luminosity \citep{kirby08,kirby10,kirby13}. \citet{vargas13} then used the same spectra to measure [$\alpha$/Fe] abundance ratios. They found that among their sample of eight ultra-faint dwarfs, only Segue\,1 does not show declining [$\alpha$/Fe] ratios with increasing metallicity\footnote{Figure 4 in \citet{vargas13} indicates that UMa~II contains a single metal-rich ($\mbox{[Fe/H]} \sim -1.0$) and $\alpha$-enhanced ($\mbox{[$\alpha$/H]} \sim 0.4$) star that might place it in this category as well. However, high-resolution spectroscopy of this star by \citet{ufs} showed that it is actually a foreground star rather than a member of UMa\,II.}. Thus, this galaxy is the only dwarf galaxy known to have minimal chemical enrichment from Type\,Ia supernovae. However, medium-resolution spectroscopy is limited in its ability to detect and measure the abundances of some elements, such as the neutron-capture elements. High-resolution spectroscopy can provide highly detailed abundance information for stars that are bright enough. High-resolution spectra with large wavelength coverage of stars down to magnitude of $V\sim19.2$ have been obtained for about a dozen stars in ultra-faint dwarfs by now. Three stars each in Ursa Major\,II and Coma Berenices were observed by \citet{ufs}, \citet{koch_her} observed two stars in Hercules, and other studies reported on one star each in Leo\,IV \citep{leo4}, Bo\"otes\,I \citep{norris10}, Segue\,1 \citep{norris10_seg}, and the stream passing just in front of Segue\,1 that may have originated in an ultra-faint dwarf \citep{frebel13b}. Detailed studies of these stars, nearly all of which are at $\mbox{[Fe/H]}\lesssim-2.0$, revealed close-to-identical chemical abundance patterns compared with halo stars, both in terms of the abundance ratios as well as more global population signatures such as a significant fraction of metal-poor stars being strongly enhanced in carbon relative to iron, and showing low neutron-capture element abundances. It has thus been suggested that the chemical similarity of halo and the ultra-faint dwarf galaxy stars could be due to the stars having formed from early gas that was enriched in the same fashion, i.e., exclusively by massive stars \citep{ufs, leo4, norris10, norris10_seg}. Moreover, if the surviving ultra-faint dwarf galaxies had earlier analogs that were accreted by the Milky Way in its early assembly phases, the chemical similarity of halo and dwarf galaxy stars could also be interpreted as indicating that the early enrichment history of the destroyed dwarfs closely resembled that of the surviving dwarfs observed today, despite the different environments they formed in. In this picture, very low luminosity primordial dwarfs may have provided the now-observed metal-poor ``halo'' stars to the halo. In this context, it is interesting to note that the analysis of deep \emph{HST} color-magnitude diagrams of three ultra-faint dwarf galaxies, Hercules, Leo\,IV, and Ursa Major\,I, by \citet{brown12} shows that they are at least as old as the oldest globular clusters and likely nearly as old as the Universe itself (their age is consistent with that of the globular cluster M92, which on the same scale is measured at 13.7\,Gyr). Preliminary results for three additional ultra-faint dwarfs suggest that the stellar populations of all six galaxies are indistinguishable \citep{brown13}. This demonstrates that the metal-poor stars in these galaxies are as old as their chemical composition (galaxy average metallicities range from $\mbox{[Fe/H]}\sim-2.0$ to $-2.6$; \citealt{kirby08}) suggests. Because of the apparently small age spreads in these systems, their more metal-rich stars also have to be similarly old, suggesting rapid enrichment. This could be due to the low-mass nature of these systems which would lead to a fast, significant build up of metals after only a few supernova explosions. Considering a plausible chemical composition of a first galaxy that may have survived to the present day, \citet{frebel12} thus argued that Segue\,1 (together with Ursa Major\,II, Coma Berenices, Bo\"otes\,I, and Leo\,IV) are candidate systems for such surviving first galaxies. \citet{bovill11} agree that most of the ultra-faint dwarfs are consistent with expectations for reionization fossils, although they do not place Segue~1 in this category as a result of earlier estimates of its metallicity lying above the luminosity-metallicity relation established by brighter dwarfs. The metallicities derived in this paper and improved measurements of the L--Z relation by \citet{kirby13} demonstrate that Segue~1 is in fact consistent with the extrapolated metallicity-luminosity relationship of more luminous systems. Only additional chemical abundance data for more stars in as many of the ultra-faint dwarfs as possible will allow detailed tests of the hypothesis that these objects are fossils of the first galaxies by establishing a detailed account of the chemical composition of each galaxy. Thus, in this study we present chemical abundance measurements for six stars in Segue~1 that are just bright enough to be observable with high-resolution spectroscopy. Segue~1 is the faintest galaxy yet detected, and it has an average metallicity of $\mbox{[Fe/H]} \sim -2.5$ to $-2.7$ \citep{norris10_booseg, simon11}. It was one of five new ultra-faint galaxies discovered by \citet{belokurov07} using a matched filter search of SDSS DR5 and SEGUE photometry. Although Segue~1 contains very few stars, its position $50\degr$ out of the Galactic plane and away from the Galactic center aids in separating member stars from the foreground Milky Way population. It is also close enough (23\,kpc) to permit spectroscopy of stars down to $\sim1$\,mag below the main sequence turnoff \citep[e.g.,][]{geha09,simon11}. Segue 1 was initially presumed to be a globular cluster because of its small half-light radius (30\,pc), but \citet{geha09} presented a strong case based on internal stellar kinematics that Segue~1 is highly dark matter-dominated and therefore a galaxy. \citet{geha09} also demonstrated that Segue~1 lies on or near standard dwarf galaxy scaling relations. \citet{niederste09} found photometric evidence for tidal debris near Segue~1 and proposed that the velocity dispersion of Segue~1 was inflated by contamination from these disrupted structures, but \citet{simon11} showed that contamination is unlikely and that the measured velocity dispersion is robust. The extensive spectroscopy by both \citet{simon11} and \citet{norris10_booseg} also established that Segue~1 has metallicity spreads of 0.7 to 0.8\,dex in [Fe/H] and 1.2\,dex in [C/H]. Along with being extremely underluminous and the most dark matter-dominated and lowest-metallicity object currently known, Segue~1 is not only a galaxy, but perhaps the most extreme galaxy known. With our new observations, our aim is to quantify the chemical evolution of this galaxy by constraining its enrichment processes. This way, we can learn about the limited star formation that occurred in this early system. In \S\,\ref{sec:obs} we describe the observations and in \S\,\ref{sec:analysis} our analysis techniques. We interpret our chemical abundance results (\S\,\ref{signature}) within the context of early galaxy formation and chemical evolution in \S\,\ref{history}. We conclude in \S\,\ref{sec:conc}. | 14 | 3 | 1403.6116 |
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1403 | 1403.1736_arXiv.txt | { One mechanism for the external destruction of protoplanetary discs in young dense clusters is tidal disruption during the flyby of another cluster member. The degree of mass loss in such an encounter depends, among other parameters, on the distribution of the material within the disc. Previous work showed that this is especially so in encounters that truncate large parts of the outer disc. The expectation is that the number of completely destroyed discs in a cluster depends also on the mass distribution within the discs. } { Here we test this hypothesis by determining the influence of encounters on the disc fraction and average disc mass in clusters of various stellar densities for different mass distributions in the discs. } { This is done by performing \nbody simulation of a variaty of cluster environments, where we track the encounter dynamics and determine the mass loss due to these encounters for different disc-mass distributions. } { We find that although the disc mass distribution has a significant impact on the disc losses for specific star-disc encounters, the overall disc frequency generally remains rather unaffected. The reason is that in single encounters the dependence on the mass distribution is strongest if both stars have very different masses. Such encounters are rather infrequent in sparse clusters. In dense clusters such encounters are more common, however, here the disc frequency is largely determined by encounters between low-mass stars such that the overall disc frequency does not change significantly. } {For tidal disrution the disc destruction in clusters is fairly independent of the actual distribution of the material in the disc. The all determining factor remains the cluster density.} | \label{sec:intro} Young stars are initially surrounded by a circumstellar disc. Observations show that with time the circumstellar discs in young clusters become depleted of gas and dust and eventually disappear. It is currently unclear which physical mechanism dominates the evolutionary disc destruction processes. Among the great variety of effects are internal processes such as viscous torques \citep[e.g.][]{1987ARA&A..25...23S}, turbulent effects \citep{2003ApJ...582..869K}, and magnetic fields \citep{2002ApJ...573..749B}, but as well external disc destruction processes like photoevaporation \citep{2001MNRAS.325..449S, 2001MNRAS.328..485C, 2003ApJ...582..893M, 2004RMxAC..22...38J, 2005MNRAS.358..283A, 2006MNRAS.369..229A, 2008ApJ...688..398E, 2009ApJ...699L..35D, 2009ApJ...690.1539G} and tidal interactions \citep{1993ApJ...408..337H, 1993MNRAS.261..190C, 1994ApJ...424..292O, 1995ApJ...455..252H, 1996MNRAS.278..303H, 1997MNRAS.287..148H, 1997MNRAS.290..490L, 1998MNRAS.300.1189B, 2004ApJ...602..356P, 2005ApJ...629..526P, 2006ApJ...653..437M, 2008A&A...487..671K}. In this study we investigate the early embedded phase of stellar cluster development with the scope to understand the general influence of gravitational interactions on the disc frequencies. In contrast to previous investigations \citep{1993MNRAS.261..190C, 1996MNRAS.278..303H, 1998MNRAS.300.1189B, 2004ApJ...602..356P, 2005ApJ...629..526P,2006ApJ...642.1140O, 2006ApJ...653..437M, 2008A&A...487..671K} we concentrate on the influence of the mass distributions in the disc on the resulting disc frequency. Due to the temperature and dust grain size distribution in discs, infra-red observations can only resolve the inner areas ($< 10 \AU$). Alternatively, observations in the sub-millimeter range are limited to the outerskirts ($50 \AU$). So no continuous observational spatial coverage of entire discs with high resolution exist to date. Nevertheless, by fitting resolved millimeter continuum or line emission data with parametric disc structure models \citep[e.g.][]{1996ApJ...464L.169M, 1997ApJ...489..917L} a wide variety of different surface densities profiles have been derived. An other method has been the combination with broadband spectral energy distributions (SEDs) \citep{2000ApJ...534L.101W, 2001ApJ...554.1087T, 2002ApJ...566.1124A, 2002ApJ...581..357K, 2007ApJ...659..705A}. Those studies have profoundly shaped our knowledge of disc structures, however, all have fundamentally been limited by the low angular resolution of available data. Thus to date there is no conclusive knowledge about the typical surface density of protoplanetary discs and how it develops with time. Most previous numerical studies of star-disc encounters have used a theoretically motivated \mbox{$r^{-1}$-dependent} disc-mass distribution \citep{1996MNRAS.278..303H, 1997MNRAS.287..148H, 2004ApJ...602..356P, 2006ApJ...642.1140O, 2006ApJ...653..437M, 2007A&A...462..193P}. Recently \citet{2012A&A...538A..10S} investigated for a wide parameter space the relative disc-mass loss in encounters with special focus on the dependence on the mass distribution in the disc and found differences of up to $40 \, \%$ between the different initial density distributions for the same type of encounter. The aim of this study is to investigate whether this means a comparable difference in the encounter-induced disc frequency in clusters. The likelihood of encounters is a function of the stellar density which varies between different clusters but as well within the considered clusters. To first order the encounter frequency, $\eta$, depends on the stellar number density, $n_{\mathrm{star}}$, as $\eta \propto n_{\mathrm{star}}$ \citep{2008gady.book.....B}. This approximation is valid for systems with equal-mass stars undergoing two-body encounters. For systems with unequal stellar masses effects like gravitational focusing become important \citep{2008gady.book.....B} and for very high stellar densities the two-body approach breaks down \citep{2013A&A...555A.135P}. The cluster-average densities span a wide range from sparse clusters like Taurus with densities of $1-10$ stars per $\pc^{3}$ \citep{2009ApJ...703..399L} to very massive and compact clusters like the Arches cluster with a core density of several $10^5$ stars per $\pc^{3}$ \citep{1999ApJ...525..750F}. Such dense stellar environments lead to strong gravitational interactions between the cluster members and affect as well the protoplanetary discs. The mass (and angular momentum) losses due to gravitational interactions in clusters as a function of stellar densities has been investigated in several studies \citep{2004ApJ...602..356P, 2006ApJ...642.1140O, 2006ApJ...641..504A, 2007A&A...462..193P}. In particular, \citet{2006ApJ...642.1140O} found that star-disc interactions influencing the circumstellar discs are more frequent than previously assumed \citep{2001MNRAS.325..449S}. Not only does the encounter frequency depend on the stellar density, but as well the prevalent type of encounter. In sparse clusters distant parabolic two-body encounters dominate, whereas in dense clusters close encounters often involving several stars at once become increasingly important \citep{2010A&A...509A..63O}. Observations confirm that the cluster disc fraction (CDF) depends strongly on the stellar cluster density. For example, \citet{2008ApJ...675.1375L} found significantly more dissolved discs in the dense IC~$348$ cluster compare to the equal-aged, but sparse Chamaeleon~I cluster. Similarly, \citet{2010ApJ...718..810S} detect a strong decrease of the disc fraction close to the dense centre of the Arches cluster, one of the densest stellar populations in the Milky Way ($\rho_{\mathrm{core}}>10^5 \Msun $pc $^{-3}$. Similar results have been obtained for the starburst cluster NGC $3603$ \citep{2004AJ....128..765S} and the Orion Nebula Cluster \citep[ONC, ][]{1998AJ....116.1816H}. In addition, observed disc frequencies in sparse stellar associations show a slower decrease than in denser clusters \citep{2013A&A...549A..15F}. However, these observations can so far not distinguish whether encounters or photo-evaporation are the dominant environmental process of disc destruction. In the following the question will be adressed how the mass distribution in protoplanetary discs influences encounter-induced losses in young stellar clusters. First, the method and the setup parameters are detailed in Section~\ref{sec:method}. In Section~\ref{sec:results} the influence of a varying initial disc-mass distribution on the encounter-induced losses in a stellar cluster is presented. Finally, a discussion will be given in Section~\ref{Discussion} and the results will be summarised in Section~\ref{sec:summary}. | \label{Discussion} The here presented results can be regarded as upper limits for the influence of encounters on protoplanetary discs in the different stellar environments. One reason is that in above calculations each star was assumed to be initially surrounded by a disc, at the same time only encounters with a disc-less perturbing star have been investigated. However, \citet{2005ApJ...629..526P} showed that star-disc encounter results can be generalised to disc-disc encounters as long as there is no significant mass exchange between the discs. In case of close encounters the discs might be replenished to some extend, which would lead to an overestimate of the losses in strong perturbing encounters. Most affected by this simplification would be discs with shallow mass distributions, which would be replenished to a larger degree . However, the consequence would be an even smaller difference between the fraction of destroyed discs for the various mass distributions. So our general result, that the disc mass distribution has little effect on the disc fraction, would still hold. Another simplification is the focus on prograde, coplanar encounters. If the cluster is not fast rotating, an alignment of the disc and the encounter plane seems rather unlikely. However, as long as the inclination is not larger than $45$ degrees, the disc losses due to inclined encounters are only slightly reduced in comparison to a coplanar encounter \citep{2005A&A...437..967P}. Hence, if the orientations were completely randomly distributed the losses would be overestimated in $75 \%$ of the encounters. This would be the same for any of the considered mass distribution. Similarly, it has been assumed that the relative losses remain unchanged in a consecutive encounter. \citet{2004ApJ...602..356P} showed that for equal-mass perturbers a second encounter results not in the same absolute but the same relative losses as in the first encounter \citep[see also][]{2009DiplomaThesisTackenb}. However, since the perturbations also lead to a steeper surface density profile of the remaining discs, our treatment of repeated encounters might lead again to an overestimate of the losses. Additionally, encounters have been generally treated as parabolic ($\epsilon = 1$) throughout this work. For hyperbolic encounters, $\epsilon > 1$), due to the shorter interaction times, the total disc losses would drop considerably. In sparse clusters such hyperbolic encounters can be generally neglected. By contrast, the average eccentricity of the stellar orbits is higher in case of dense stellar environments, where the massive stars loose their dominating role as encounter partners \citep{2010A&A...509A..63O}. All mass distributions should be affected to the same degree by this simplification. Another significant factor for disc losses is the initial disc size. Small disc sizes lead to higher relative periastron distances $r_{\mathrm{peri}} = r / r_{\mathrm{disc}}$ and therefore lower disc losses in our calculations. In this context, observations give no clear picture, providing a multitude of observed disc-mass distributions and sizes. Thus, here, the discs are assumed to have a radius of $r_{\mathrm{disc}} = 150 \AU$, which is a typical observed value. However, a scaling of the disc size with the mass of the disc-surrounded star by \mbox{$r_{\mathrm{disc}} = 150 \AU \cdot \sqrt{M_1 [\Msun]/\Msun}$}, as it is obtained if a fixed force of the stars at the discs outer radius is assumed, would be equally likely. This would result in an increased disc diameter for massive stars ($m_{\mathrm{star}} > 1 \Msun$) while the disc sizes of low-mass stars ($m_{\mathrm{star}} < 1 \Msun$) are significantly reduced. In the consequence this would lead to a lower fraction of destroyed discs, since the majority of stars in the cluster is located in the low mass regime. All these simplifications might lead to overestimating the disc losses. However, some of the applied assumptions potentially lead to an underestimation. First of all, sub-stellar objects ($M_{\mathrm{star}} < 0.08 \Msun$) have been excluded in the present study. In general, the mass ratios in encounters with such low-mass objects are well below $0.1$, which implies that the disc losses would be sufficiently small ($< 10 \%$). Hence, the effect should be minor for massive stars. If the encounter is non-penetrating the effect can be neglected even for low-mass stellar objects. Furthermore, all encounter processes have been treated as two-body encounters. \citet{2001DiplomaThesisUmbreit} showed that multiple-body encounters result in larger disc losses. However, the effect strongly depends on the mass and periastron distance of the involved stars. For the present calculations the most destructive encounter has been used to obtain the disc losses, while the other encounter partners are most likely either distant or less massive, so that their influence on the losses is less significant. Primordial binaries have not been included, which might significantly underestimate the destruction rates of stellar discs especially for tight binaries. While it is suggested that up to $100\%$ of all stars \citep[e.g.][and references therein]{1995MNRAS.277.1491K} might be initially part of a binary system, it remains unclear how their initial periods are distributed. Assuming the upper limit case of an initially log-uniform period distribution \citep[e.g.][]{2007AJ....134.2272R} a fraction of $50 \%$ of all stars would have had a companion with a semi-major axis $\leq 100 \AU$. Apart from an increased destruction rate of the stellar discs in tight binaries, the cluster dynamics are usually influenced by strong few-body interactions \citep{1975AJ.....80..809H, 1975MNRAS.173..729H}, which potentially leads to underestimating the number of ejections from the cluster. Hence, primordial binaries might have a non-negligible effect on the disc fractions and stellar dynamics and further investigations are needed to give an estimate of the effect. Finally, a large fraction of disc-less stars is ejected after an encounter event within the first few $10^5$ yr with velocities larger than $20\pc/\mathrm{Myr}$, populating regions of $> 20 \pc$ distance from the cluster centre. In the context of planet formation such stellar high-velocity escapers from embedded clusters are expected to show no infrared excess emission and to be less frequently surrounded by planets. Similar results have been obtained from observational \citep{1997AJ....113.1733H, 2004AJ....128.1254L} and numerical studies that assumed primordial mass segregated populations \citep{2008A&A...488..191O}. However, such high-velocity escapers are less frequent for primordial non-mass segregated clusters. Here, a first approach showed that in contrast to evenly distributed clusters, in mass-segregated clusters a lower fraction of disc-less stars remains in the core region as more stars are ejected due to gravitational focusing of the high-mass stars. The consequence is an increased fraction of disc-less stars in the core region of primordial non-mass segregated clusters of up to $10 \%$ in the tested extreme cases. The focus in this work was on the question, in how far the mass distribution within a protoplanetary disc influences the rate of tidally destructed discs in typical cluster environments. Stellar clusters spanning a large range of densities have been modelled and the influence of these different environments on the disc fraction has been investigated. The main results are: \begin{enumerate} \item Surprisingly, even though the initial disc-mass distribution significantly influences individual disc losses induced by stellar interactions, the fraction of discs that are completely destroyed by encounters remains fairly unaffected, as long as the cluster density does not exceed $\rho_{\mathrm{core}} < 10^4 \pc^{-3}$. These are still quite dense clusters, for example the ONC would belong to this group. The reason is that in these clusters the complete destruction of discs happens by interactions with high-mass stars. These type of encounter is rather insensitive to the initial disc-mass distribution. \item By contrast, for very dense clusters, an example would be NGC 3603, the fraction of destroyed discs depends to some degree on the initial disc mass distribution. More specific, $60 \%$ of discs are destroyed assuming initially constant disc-mass distributions while for an initially steep disc-mass distribution ($\Sigma \propto r^{-7/4}$) only 40\% are affected. In such dense clusters, interactions between low-mass stars are not only more frequent in absolute but as well in relative terms. Such encounters between low-mass stars show the strongest dependence on the mass distribution in the disc. However, in general even in this case the fraction of destroyed discs deviates no more than $\sim$ 20\% from an initially $r^{-1}$ disc-mass distribution. \item The initial disc-mass distribution has little influence on the total number of stars, that have a disc that is changed in its structure by a fly-by. However, independently of the initial distribution of the disc material, almost all circumstellar discs (95\%) in the core region ($r_{core}$) of dense clusters are significantly effected by fly-bys. \end{enumerate} This means the most results usually obtained assuming a $r^{-1}$ disc mass distribution can be largely generalised to other mass distributions. The exception might be clusters with densities in excess of $\rho_{\mathrm{core}} > 10^4 \pc^{-3}$ like for example NGC 3603. | 14 | 3 | 1403.1736 |
1403 | 1403.3219_arXiv.txt | { We make use of the frame and gauge independent formalism for scalar and tensor cosmological perturbations developed in Ref.~\cite{Prokopec:2013zya} to show that the physical cutoff for 2-to-2 tree level scatterings in Higgs inflation is above the Planck scale $M_{\rm P}=1/\sqrt{8\pi G_N}$ throughout inflation. More precisely, we found that in the Jordan frame, the physical cutoff scale is $(\Lambda/a)_J\gtrsim \sqrt{M_{\rm P}^2 +\xi\phi^2}$, while in the Einstein frame it is $(\Lambda/a)_J\gtrsim M_{\rm P}$, where $\xi$ is the nonminimal coupling and $\phi$ denotes the Higgs {\it vev} during inflation. The dimensionless ratio of the physical cutoff to the relevant Planck scale is equal to one in both frames, thus demonstrating the physical equivalence of the two frames. Our analysis implies that Higgs inflation is unitary up to the Planck scale, and hence there is no naturalness problem in Higgs inflation. In this paper we only consider the graviton and scalar interactions. } | Higgs inflation \cite{Bezrukov:2007ep,Salopek:1988qh} \cite{Bezrukov:2008ej,Barvinsky:2008ia,DeSimone:2008ei,Bezrukov:2009db,Barvinsky:2009fy,Barvinsky:2009ii,Bezrukov:2013fka} is perhaps the most economical approach to cosmological inflation: it identifies the only known scalar field in the Standard Model (SM) -- the Higgs boson -- with the inflaton, the scalar field that drives the inflationary expansion in the very early universe. The action for Higgs inflation features a non-minimal coupling of the Higgs field to the Ricci scalar. If the non-minimal coupling $\xi$ is large, it leads to a successful period of chaotic inflation, producing primordial power spectra that fit the observational bounds~\cite{Ade:2013uln}. Hence, Higgs inflation can be considered as a "natural" scenario, since it does not seem to require the introduction of new physics to explain the inflationary expansion of the universe. However, the naturalness of the Higgs inflation scenario has been under debate. Refs.~\cite{Barbon:2009ya,Burgess:2009ea} used power-counting techniques to determine the energy scale $\Lambda$ at which perturbation theory breaks down, thus determining the range of validity of Higgs inflation. It was claimed that this cutoff scale $\Lambda$ lies dangerously close to the energy scale of inflation, thereby questioning the naturalness of Higgs inflation. Since then many works have appeared claiming that Higgs inflation is "natural"~\cite{Lerner:2009na,Ferrara:2010in} or "unnatural"~\cite{Burgess:2010zq,Hertzberg:2010dc}. Perhaps the most complete treatment has been done in Ref.~\cite{Bezrukov:2010jz}. It was found that $\Lambda$ is generally field dependent and lies above the typical energy scales in different regions, such that the perturbative (semiclassical) expansion is valid in Higgs inflation. Although there seems to be a consensus about the cutoff scale as computed in Ref.~\cite{Bezrukov:2010jz} (however, see the recent work~\cite{George:2013iia}~\footnote{ The results presented in Ref.~\cite{George:2013iia} use different techniques and arrive at results that are consistent with those presented in this paper and earlier in Ref.~\cite{Weenink:2013oqa}.}), we revisit the computation of the cutoff in this work. The reason is that there are some important aspects that have not been fully taken into account. The most important aspect is that General Relativity contains a large diffeomorphism symmetry, which when truncated resembles the symmetry of a gauge theory. This means that, like in QED, some of the degrees of freedom in the action are actually not physical. As a consequence, some of the interaction vertices obtained after a na\"\i ve perturbative expansion of the action are gauge dependent, and any conclusion that one arrives at by using these vertices can be a gauge artifact. Moreover, it is possible that there are additional vertices that conspire to cancel dominant perturbative contributions. Accounting for these aspects can raise the cutoff scale. Even though it is possible to determine the physical cutoff scale within a gauge dependent formulation, by far the simplest and most reliable way to determine this scale is to use the physical vertices, which can be obtained from the perturbative action in a manifestly gauge invariant way (an alternative is to completely fix the gauge freedom and take account of contributions from {\it all} vertices). This formulation of the action in terms of \textit{gauge invariant perturbations} has been found for a non-minimally coupled scalar field up to third order in perturbations in Refs.~\cite{Weenink:2010rr,Prokopec:2012ug,Prokopec:2013zya}. In this work we use these previously found results in order to demonstrate that the cutoff scale for physical, that is, gauge invariant perturbations is always $\geq M_P$. To be more precise, we find that \begin{eqnarray} \left(\frac{\Lambda}{a}\right)_J \gtrsim \sqrt{M_P^2+\xi\phi^2} \,,\qquad \left(\frac{\Lambda}{a}\right)_E \gtrsim M_P \,, \label{cutoffscalesJordanEinstein} \end{eqnarray} where $a_J$ and $\phi$ are the background scale factor and scalar field in the Jordan frame, and $a_E$ is the Einstein frame scale factor. The extra scale factors have been overlooked in previous computations of the cutoff scale. They appear since $\Lambda^{-1}$ is a comoving scale, and therefore in an expanding universe the corresponding physical length scale, $a/\Lambda$, always includes a scale factor $a$. The cutoffs in Jordan and Einstein frame are different, simply because $\Lambda$ is a dimensionful quantity which differs between the frames, just like the effective Planck mass. If $M_P$ is the energy scale where quantum gravity kicks in in the Einstein frame, then $M_{P,J}\equiv \sqrt{M_P^2+\xi\phi^2}$ can be identified with the scale of quantum gravity in the Jordan frame. Thus in either frame the perturbative (semiclassical) treatment is valid all the way up to the scale at which gravity becomes strong. This means that Higgs inflation is perfectly natural and that no new physics is necessary to explain the inflationary expansion of the universe and the anisotropies in the CMB. In order to arrive at the physical cutoff scales~\eqref{cutoffscalesJordanEinstein}, we first briefly discuss Higgs inflation and physically equivalent frames in section~\ref{sec:Higgs inflation}. In section~\ref{sec: the naturalness debate} we review the naturalness debate. In section~\ref{sec: gauge invariance} we discuss the concept of gauge and frame dependence in cosmology and quote from Ref.~\cite{Prokopec:2013zya} the action for gauge and frame invariant cosmological perturbations. Finally we compute the cutoff scale for physical perturbations in section~\ref{sec: cutoffscale} and conclude in section~\ref{sec:Discussion}. | \label{sec:Discussion} We have used the frame and gauge independent formalism for scalar and tensor cosmological perturbations of Ref.~\cite{Prokopec:2013zya} to show that the physical cutoff for 2-to-2 tree level scatterings in Higgs inflation is above the Planck scale $M_{\rm P}=1/\sqrt{8\pi G_N}$ throughout inflation. More precisely, we found that in the Jordan frame, the physical cutoff scale is $(\Lambda/a)_J\gtrsim\sqrt{M_{\rm P}^2 +\xi\phi^2}$, while in the Einstein frame it is $(\Lambda/a)_E\gtrsim M_{\rm P}$, where $\xi$ is the nonminimal coupling and $\phi(t)$ denotes the Higgs {\it vev}. The physical cutoff in the Jordan frame is illustrated in figure~\ref{fig:cutoffJordan}. The difference between the two frames is immaterial in that it can be fully attributed to the frame dependence of the (physical) cutoff, see Eq.~(\ref{scale factor in two frames}). Our results are incomplete, in that we have not discussed the relevance of: \begin{itemize} \item[$\bullet$] quartic vertices and loops, \item[$\bullet$] vertices containing gauge and fermionic fields, \item[$\bullet$] boundary terms on equal time hypersurfaces (that result from partial integrations), \end{itemize} for the question of naturalness in Higgs inflation. We do however believe that the principal conclusion reached in this paper will not change when these contributions are fully accounted for. | 14 | 3 | 1403.3219 |
1403 | 1403.6861_arXiv.txt | The Space Telescope Imaging Spectrograph (STIS) has measured the flux for Sirius from 0.17--1.01~$\mu$m on the \emph{HST} White Dwarf scale. Because of the cool debris disk around Vega, Sirius is commonly recommended as the primary IR flux standard. The measured STIS flux agrees well with predictions of a special Kurucz model atmosphere, adding confidence to the modeled IR flux predictions. The IR flux agrees to 2--3\% with respect to the standard template of Cohen and to 2\% with the MSX absolute flux measurements in the mid-IR. A weighted average of the independent visible and mid-IR absolute flux measures implies that the monochromatic flux at 5557.5~\AA\ (5556~\AA\ in air) for Sirius and Vega, respectively, is $1.35\times10^{-8}$ and $3.44\times10^{-9}$~erg cm$^{-2}$ s$^{-1}$ \AA$^{-1}$ with formal uncertainties of 0.5\%. Contrary to previously published conclusions, the Hipparcos photometry offers no support for the variability of Vega. Pulse pileup severely affects the Hp photometry for the brightest stars. | Precise stellar flux standards are required for the calibration of the James Webb Space Telescope (JWST) and for the interpretation of dark energy measures with the supernova Ia technique. Cohen et al. (1992a) and, more recently, Engelke et al. (2010, EPK) recommend the use of Sirius as the primary IR standard, because Vega's rapid rotation and dust ring complicate the modeling of its IR flux distribution. Thus, Sirius ($\alpha$~CMa, HD~48915, HR~2491) was observed by \emph{HST/STIS} on 2012 Oct 7 and 2013 Jan 26. The hot WD companion, Sirius B, is 10 mag fainter at V and contributes $<$1\% of the system flux, even at 1300~\AA\ (Holberg et al. 1998, Beuermann et al. 2006). The HST flux system (Bohlin \& Gordon 2014) is based on the flux distribution of NLTE model atmospheres for the pure hydrogen white dwarfs (WDs) GD153 and GD71 and on a NLTE metal line-blanketed model of Rauch et al. (2013, RWBK) for G191B2B. The absolute normalization of each model flux is defined by the STIS net signal in electrons/s from each WD relative to the STIS net signal for Vega at 5557.5~\AA\ (5556~\AA\ in air), where Megessier (1995) found an absolute flux of $3.46\times10^{-9}$~erg cm$^{-2}$ s$^{-1}$ \AA$^{-1}\pm0.7$\%. This paper reconciles the Megessier visible flux with the MSX mid-IR fluxes and derives $3.44\times10^{-9}$~erg cm$^{-2}$ s$^{-1}$ \AA$^{-1}\pm0.5$\% at 5556~\AA\ for Vega's monochromatic flux. This 0.6\% change to the HST fluxes also brings the extrapolated flux for Sirius to within 0.6\% of the average MSX mid-IR absolute flux measures. The STIS Sirius observations and their flux calibration are discussed in Section~2. Section~3 compares the modeled IR spectral energy distribution (SED) with the MSX absolute flux measurements, while Section~4 discusses Vega, its dust rings, and the lack of any evidence for variability in the Hipparcos data. | 14 | 3 | 1403.6861 |
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1403 | 1403.4211.txt | Martian surface morphology implies that Mars was once warm enough to maintain persistent liquid water on its surface. While the high D/H ratios ($\sim 6$ times the Earth's ocean water) of the current martian atmosphere suggest that significant water has been lost from the surface during martian history, the timing, processes, and the amount of the water loss have been poorly constrained. Recent technical developments of ion-microprobe analysis of martian meteorites have provided accurate estimation of hydrogen isotope compositions (D/H) of martian water reservoirs at the time when the meteorites formed. Based on the D/H data from the meteorites, this study demonstrates that the water loss during the pre-Noachian ($> 41-99\ {\rm m}$ global equivalent layers, GEL) was more significant than in the rest of martian history ($> 10-53\ {\rm m\ GEL}$). Combining our results with geological and geomorphological evidence for ancient oceans, we propose that undetected subsurface water/ice ($\simeq 100-1000\ {\rm m\ GEL}$) should have existed, and it exceeds the observable present water inventory ($\simeq 20-30\ {\rm m\ GEL}$) on Mars. | \label{} Mars is generally considered to be a cold and dry planet, with relatively small amounts of water-ice observed at the polar caps \citep[e.g.,][]{Jakosky+Phillips2001,Christensen+2006}. On the contrary, a number of geological observations, such as dense valley networks \citep{Scott+1995,Carr+Chuang1997,Hoke+2011} and deltas \citep{Cabrol+Grin1999,Ori+2000,DiAchille+Hynek2010}, provide definitive evidence that large standing bodies of liquid water (i.e., oceans and lakes) existed in the early history, the presence of which would have profound implications for the early climate and habitability of Mars \citep[e.g.,][]{Carr2007,Head+1999,Dohm+2011}. The geological observations further include the detection of water-lain sediments and a variety of hydrous minerals (e.g., clays) \citep[e.g.,][]{Fialips+2005,Bibring+2006} and evaporites (e.g. gypsum) \citep[e.g.,][]{Osterloo+2008} commonly formed by aqueous processes, implying Earth-like hydrologic activities, with Noachian lakes and/or oceans. Despite such compelling evidence for hydrologic conditions that could support oceans and lakes, there are, however, major gaps in our understanding of the evolution of surface water: e.g., what was the global inventory of martian surficial water/ice, and how did it change through time. The global inventory of ancient surficial water has been estimated based on the size of reported paleo-oceans \citep[e.g.,][]{Head+1999,Clifford+Parker2001,Carr+Head2003,Ormo+2004,DiAchille+Hynek2010}. Topographic features of putative paleo-shorelines suggest that large bodies of standing water once occupied the northern lowlands \citep{Head+1999}. Shoreline-demarcation studies of the northern lowlands point to several contacts that yield variable sizes of paleo-oceans estimated to range from $\sim 2 \times 10^7\ {\rm km^3}$ to $2 \times 10^8\ {\rm km^3}$ (corresponding to global equivalent layers (GEL) of $130\ {\rm m}$ to $1,500\ {\rm m}$, respectively) \citep[][and references therein]{Carr+Head2003}. Though the shoreline demarcations \citep{Parker+1989,Parker+1993}, supported by Mars Orbiter Laser Altimeter (MOLA) topography \citep{Head+1998,Head+1999}, could not be confirmed using Mars Orbiter Camera (MOC) and Thermal Emission Imaging System (THEMIS) image data \citep{Malin+Edgett1999,Malin+Edgett2001,Ghatan+Zimbelman2006}, this variation has been interpreted to reflect the historical change in the ocean volume. For example, two major contacts (contact-1: Arabia shoreline and contact-2: Deuteronilus shoreline) individually represent the larger Noachian and smaller Hesperian oceans, respectively \citep{Parker+1993,Clifford+Parker2001,Carr+Head2003}. Although these geomorphologic studies have provided significant constraints on the history of martian paleo-oceans, they lack information about pre-Noachian \citep{Frey2006} oceans because no geologic records are available. Furthermore, the shoreline-demarcation approaches would not be applicable to the youngest Amazonian (3.1 Ga to present) era, during which the surface water would have occurred mostly as ice \citep{Clifford+Parker2001,Carr+Head2010}. This study endeavors to trace the global inventory of surficial water through time beginning with the embryonic stages of development of Mars (i.e., 4.5 Ga) to present day based on a geochemical approach of hydrogen isotopes (D/H: deuterium/hydrogen). Hydrogen is a major component of water (${\rm H_2O}$) and its isotopes fractionate significantly during hydrological cycling between the atmosphere, surface water, and ground and polar cap ices. Telescopic studies have reported that the hemispheric mean of the martian atmosphere has a D/H ratio of ~6 times (${\rm \delta D} \simeq 5000$ñ) the terrestrial values \citep{Owen+1988}; ${\rm\delta D = [(D/H)_{sample}/(D/H)_{reference} -1] \times 1000}$, where the reference is Standard Mean Ocean Water (SMOW). Because the high atmospheric D/H ratio is interpreted to result from the preferential loss of hydrogen relative to the heavier deuterium from the martian atmosphere throughout the planetfs history \citep{Lammer+2008}, the deuterium enrichment can be used to estimate the amount of water loss due to the atmospheric escape. Compared to a number of geomorphologic studies \citep[e.g.,][]{Scott+1995,Head+1999,Clifford+Parker2001,Carr+Head2003,DiAchille+Hynek2010}, only a few geochemical investigations have been conducted \citep{Chassefiere+Leblanc2011,Lammer+2003}. This is partly because there have been a limited number of reliable D/H datasets for martian meteorites, and the martian meteorites typically have younger ages (typically, $< 1.3\ {\rm Ga}$) \citep{Nyquist+2001}. However, recent technical developments of ion-microprobe analysis of martian meteorites including the 4.1 Ga ALH 84001 pyroxenite have provided more accurate and comprehensive datasets for D/H ratios of martian water reservoirs \citep[e.g.,][]{Greenwood+2008,Usui+2012,Hallis+2012a,Hallis+2012b}, yielding new information helpful for unraveling the origin and evolution of water on Mars. Furthermore, although martian meteorites were derived from limited and highly biased regions of the surface of Mars \citep{McSween+2009,Usui+2010,Christen+2005}, their radiometric ages are more accurate and precise than crater counting ages. Based on the recent D/H dataset from martian meteorites, we estimate the amount of water loss during $4.5\ {\rm Ga}$ to $4.1\ {\rm Ga}$, which we refer to here as Stage-1 in our analysis (approximating the pre-Noachian; Table 1), and consequently demonstrate that the water loss during $4.5\ {\rm Ga}$ to $4.1\ {\rm Ga}$ was more significant than in the rest of the Mars history ($4.1\ {\rm Ga}$ to present, approximating Noachian - Amazonian; Table 1), which we refer to as Stage-2 in our analyses. Combining our results with geological estimates for the volume of martian paleo-oceans, we propose that unidentified surficial water-ice reservoirs should currently exist and the volume ($\simeq 100 - 1000\ {\rm m\ GEL}$) should exceed the estimated present water inventory \citep[20-30 m GEL,][]{Christensen+2006} on Mars. | Geological and geomorphological studies have revealed that Mars once contained large amounts of liquid water on its surface. We estimate the amount of water loss due to atmospheric escape in two stages based on the D/H data of martian meteorites. We demonstrate that the amount of water loss is positively correlated with the present water inventory and that the water loss during $4.5\ {\rm Ga}$ to $4.1\ {\rm Ga}$ (Stage-1) is more significant than that in the rest of the martian history (Stage-2), regardless of the amount of the present water reservoir. Adopting the minimum estimate of the present water inventory based on the estimated extent of the PLD yields the minimum estimates of water loss. The minimum estimates of water loss are comparable with those obtained from the oxygen escape calculations. Combining our results with geological constraints for ancient oceans, we propose a possibility that there should be undetected subsurface water/ice of much greater extent than the collective amounts of the \textquotedblleft visibleh current water inventory. Our study further implies that, because such a large water inventory automatically calls for significant water loss that cannot be explained either by the existing oxygen escape models or the known oxygen sinks, unknown mechanisms that effectively consume the remaining excess oxygen are required. | 14 | 3 | 1403.4211 |
1403 | 1403.3396_arXiv.txt | We use mid-infrared to submillimeter data from the {\it Spitzer}, {\it Herschel}, and APEX telescopes to study the bright sub-mm source OMC-2 FIR 4. We find a point source at 8, 24, and 70 $\mu$m, and a compact, but extended source at 160, 350, and 870 $\mu$m. The peak of the emission from 8 to 70 $\mu$m, attributed to the protostar associated with FIR 4, is displaced relative to the peak of the extended emission; the latter represents the large molecular core the protostar is embedded within. We determine that the protostar has a bolometric luminosity of 37 \Lsun, although including more extended emission surrounding the point source raises this value to 86 \Lsun. Radiative transfer models of the protostellar system fit the observed SED well and yield a total luminosity of most likely less than 100 \Lsun. Our models suggest that the bolometric luminosity of the protostar could be just 12-14 \Lsun, while the luminosity of the colder ($\sim$ 20 K) extended core could be around 100 \Lsun, with a mass of about 27 \Msun. Our derived luminosities for the protostar OMC-2 FIR 4 are in direct contradiction with previous claims of a total luminosity of 1000 \Lsun\ \citep{crimier09}. Furthermore, we find evidence from far-infrared molecular spectra \citep{kama13, manoj13} and 3.6 cm emission \citep{reipurth99} that FIR 4 drives an outflow. The final stellar mass the protostar will ultimately achieve is uncertain due to its association with the large reservoir of mass found in the cold core. | The OMC 2 region in the Orion A star-forming complex is actively forming low- and intermediate-mass stars \citep{peterson08}. It lies in the northern part of the extended Orion Nebula Cluster and is embedded in a 2 pc long, narrow filament extending away from the Orion Nebula itself \citep[][Megeath et al., in preparation]{chini97,carpenter00}. OMC 2 contains some of the most luminous infrared and sub-mm sources in the Orion A molecular cloud outside of the Orion Nebula \citep{johnson90,mezger90}. Over the last few decades, several surveys from infrared to radio wavelengths disentangled the multitudes of sources found in this region, revealing young stellar objects in different evolutionary stages, ranging from deeply embedded protostars to young stars surrounded by disks \citep{gatley74, rayner89, johnson90, mezger90, jones94, ali95, chini97, lis98, reipurth99, nielbock03, tsujimoto03, peterson08, megeath12, adams12}. The first near-IR images of OMC 2 by \citet{gatley74} revealed a small cluster of five bright IR sources in a region 90\arcsec, or 0.2 pc, in diameter. These have subsequently been shown to be young stellar objects with luminosities ranging from 20 to 300~\Lsun\ \citep{adams12}. Subsequent sub-mm and mm imaging \citep{mezger90,chini97,lis98} showed that in the center of this small cluster is a bright sub-mm source. This object, OMC-2 FIR 4, is the brightest sub-mm (350-1300~$\mu$m) source the OMC 2 region. It is connected through filamentary structures to two other adjacent sources that are bright at sub-mm wavelengths and are coincident with two of the bright IR sources of \citet{gatley74}: OMC-2 FIR 3 matches a protostar $\sim$ 28\arcsec\ to the north (also known as SOF 2N or HOPS 370), while OMC-2 FIR 5 agrees with a protostar ~$\sim$ 17\arcsec\ to the south (SOF 4 or HOPS 369, see \citealt{adams12}). Outside of the massive star-forming region OMC-1 in the Orion Nebula, FIR 4 is the brightest 870~$\mu$m source in the Orion A cloud (Stanke et al. 2014, in preparation). Although bright in the sub-mm, FIR 4 was not detected in the near-IR by \citet{tsujimoto03} and only tentatively associated with a near- to mid-IR source by \citet{nielbock03}. The detection of a 3.6 cm source with the VLA toward FIR 4 was the first compelling evidence that the sub-mm source contained a deeply embedded protostar; the elongated radio source was interpreted as free-free emission originating from shock-ionized gas in an outflow launched by a protostar \citep{reipurth99}. FIR 4 also coincides with the IRAS source 05329-0512. Its bolometric luminosity, integrated over an area of 50\arcsec$\times$50\arcsec\ around it, was estimated to be 420 \Lsun\ \citep{mezger90}. FIR 4 was thus identified and studied as an intermediate-mass protostar \citep{johnstone03, crimier09}. \citet{crimier09} constructed a spectral energy distribution (SED) for FIR 4 by retrieving archived mid-infrared to millimeter observations and extracting fluxes. They modeled the SED and derived a total luminosity of 1000 \Lsun. More recently, the infrared emission from a protostar toward FIR 4 (known as SOF 3 or HOPS 108) was resolved by \citet{adams12} using 2\arcsec\ to 19\arcsec\ resolution data from the {\it Spitzer Space Telescope} \citep{werner04}, the {\it Stratospheric Observatory For Infrared Astronomy} \citep[SOFIA;][]{young12}, the {\it Herschel Space Telescope}\footnote{{\it Herschel} is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.} \citep{pilbratt10}, and from the Atacama Pathfinder Experiment (APEX) telescope. This work has cast doubt on the high luminosity of OMC-2 FIR 4; modeling of the SEDs by \citet{adams12} found that the intrinsic luminosity lies in the 30-50 \Lsun\ range. These data also showed that within the beam of IRAS, the other near-IR sources originally found by \citet{gatley74} dominated the flux out to 70 $\mu$m with luminosities varying from 20 to 300~\Lsun; OMC-2 FIR 3 (SOF 2N, HOPS 370) was found to be the most luminous source in the region. Only at wavelengths $\gtrsim$ 160~$\mu$m does FIR 4 dominate; however, it is unclear whether the entire sub-mm emission is associated with the protostar observed at shorter wavelengths. Millimeter interferometry by \citet{shimajiri08} resolved FIR 4 into 11 dusty cores. Furthermore, they found that high-velocity gas traced by CO is dominated by an outflow from FIR 3. They proposed that the motion seen in the dense gas toward FIR 4 could be explained by the interaction of the powerful outflow from FIR 3 with the FIR 4 clump. On the basis of interferometric observations made in both continuum and line, \citet{lopez13} interpreted FIR 4 as containing three distant components, a western core, a southern core and a main core containing a young star, with a total mass of 9.2 to 25.7~\Msun. Noting the lack of the detection of outflow signatures from FIR 4 in their interferometric observations and the proposal of \citet{shimajiri08} that motions in FIR 4 are driven by an outflow from FIR 3, they suggested that the 3.6 cm source is due to photo-ionization of gas by an early-type (B3$-$B4) star with a luminosity of 700-1000 \Lsun\ within one of the three components. In this publication, we use {\it Spitzer}, {\it Herschel}, and APEX imaging of FIR 4 from 3.6 to 870~$\mu$m obtained for the Herschel Orion Protostar Survey (HOPS) to study the protostar associated with FIR 4, with the goal of resolving the large uncertainties in the luminosity of the protostar and its relationship to the sub-mm clump. We use these data to measure the SED of the protostar and constrain its bolometric luminosity and temperature, exploring the effect of the choice of aperture size, or the use of PSF fitting photometry, on the final result. By using radiative transfer models, we explore the range of possible luminosities and source properties and show that a wide range of luminosities are possible. We also investigate the relationship between the protostar and sub-mm clump and the possibility that much of the sub-mm luminosity is due to external heating. We favor a model that has a deeply embedded, protostar with L $<$ 100~\Lsun\ driving an outflow, forming on the side of a massive ($\sim$ 30~\Msun) clump. | OMC-2 FIR 4 is an intriguing protostar whose nature has been debated in the literature; it is likely deeply embedded and thus in an early evolutionary stage, but its properties, like luminosity and envelope mass, were poorly determined. We clearly detect protostellar emission at $\lambda$ $\leq$ 70 $\mu$m, but at longer wavelengths the larger molecular core dominates the emission. We present the most complete analysis to date of this object. Using data from the {\it Spitzer}, {\it Herschel}, and APEX telescopes, we derive new values for the bolometric luminosity of OMC-2 FIR 4 and estimate some of its envelope properties from model fits. Some ambiguities on the detailed nature remain due to the deeply embedded state of the protostar. Our main conclusions are as follows: \begin{itemize} \item We construct the SED of OMC-2 FIR 4 with photometry at 8, 24, 37.1, 70, 100, 160, 350, and 870 $\mu$m, and spectroscopy from 5 to 37 $\mu$m. Thus, the SED is well-sampled, in particular at wavelengths where the emission peaks. We obtain more accurate photometry of the protostar and its envelope by choosing smaller apertures ($\sim$ 10\arcsec) in the 70-870 $\mu$m range than were previously adopted. However, we note an offset of $\sim$~3\arcsec\ in the emission peak for $\lambda$ $\leq$ 70 $\mu$m and $\lambda$ $\geq$ 160 $\mu$m, which suggests that at long wavelengths we actually probe a clump of externally heated dust and thus even our fluxes at 160, 350, and 870 $\mu$m could overestimate the envelope emission. \item The bolometric luminosity of OMC-2 FIR 4 ranges from 37 \Lsun\ to 100 \Lsun, depending on which values are adopted for the far-IR and sub-mm photometry. Given that the extended emission surrounding this object at long wavelengths ($\gtrsim$ 70 $\mu$m) may be dominated by a cold, externally heated clump, the $L_{bol}$ value most closely describing the protostar is likely 37 \Lsun. \item Models that include a protostar surrounded by a disk and envelope with outflow cavities fit the SED well. These models yield different best-fit parameters depending on which photometry values are adopted and which model assumptions are made. Assuming a single protostar with an infalling envelope, we estimate that the envelope density is relatively high ($\rho_1$ $\sim$ 10$^{-13}$ $-$ 10$^{-12}$ g cm$^{-3}$ or $\rho_{1000}$ $\sim$ 3 $\times$ 10$^{-18}$ $-$ 3 $\times$ 10$^{-17}$ g cm$^{-3}$), both for models with polynomial-shaped and streamline-shaped cavities. \item The SED can also be fit by combining a protostellar model that considers fluxes between 8 and 70 $\mu$m and a clump of externally heated dust that fits the longer-wavelength emission. In this model the luminosity is dominated by the clump, and the total luminosity of the protostar alone amounts to $\sim$ 15-25 \Lsun\ (with corresponding $L_{bol}$ values of 12-14 \Lsun). The envelope density is still high ($\rho_1$ close to 10$^{-13}$ or $\rho_{1000}$ close to 3 $\times$ 10$^{-18}$ g cm$^{-3}$), suggesting an early evolutionary state for the protostar (Stage 0). Given the significant contribution of the molecular clump to the long-wavelength emission, the protostar is probably best described by this model. \item We find that the position of OMC-2 FIR 4 measured in our IRAC 4.5 $\mu$m image is offset with respect to the position measured at 8-70 $\mu$m, but matches that of the radio continuum source detected at 3.6 cm by \citet{reipurth99}. Both can be interpreted as emission from shocked gas in an outflow. Furthermore, there is evidence in favor of an outflow from far-IR spectra \citep{manoj13, kama13} in the form of velocity profiles, temperatures, and densities derived from CO lines, although they may contain a contribution from an outflow driven by the nearby protostar OMC-2 FIR~3. These data support the idea that FIR 4 is indeed a protostar, driving a compact outflow. In addition, the centimeter flux is consistent with that observed in outflows from other protostars with luminosities $<$ 100 \Lsun\ \citep{anglada95}. \item Using fluxes measured in a 20\arcsec\ aperture centered on the clump position (i.e., the position of the peak flux at $\lambda$ $\geq$ 160 $\mu$m) and applying a modified blackbody fit, we estimate a temperature of 22 K and a mass of 27 \Msun\ for the clump. This clump could form more protostars, and OMC-2 FIR 4, which lies near its edge, might be the first one formed, but is probably still growing in mass and luminosity. Thus, we agree with the suggestion of \citet{shimajiri08} and \citet{lopez13} that the molecular core of OMC-2 FIR 4 likely fragmented, with one of these fragments currently containing a protostar. However, we find that the data is best explained by a $<$ 100 \Lsun\ protostar and not an intermediate-mass, luminous ($\sim$ 1000 \Lsun) young star as proposed by \citet{crimier09} and \citet{lopez13}. Although the protostar currently has a modest luminosity, the final stellar mass it will obtain is difficult to predict considering that it is embedded in a core with a total mass of 27 \Msun. \end{itemize} Only long-wavelength observations at high spatial resolution, such as the VLA and ALMA can provide, will allow us to better understand this object. In particular, mapping the dust continuum and the outflows at resolutions $\lesssim$ 1\arcsec\ will constrain the envelope structure, including the properties of the cavity and inclination angle. This in turn will settle the question about this object's luminosity. Overall, OMC-2 FIR 4 will further our understanding of the star formation process in complex environments such as OMC 2. | 14 | 3 | 1403.3396 |
1403 | 1403.7440_arXiv.txt | This is continuation of our search for the elusive radio-quiet blazars, by carrying out a systematic programme to detect intranight optical variability (INOV) in a subset of `Weak-Lines-Quasars' (WLQs) which are designated as `high confidence BL Lac candidates' and are known to be radio-quiet. For 10 such RQWLQs, we present here the INOV observations taken in 16 sessions of durations $\ga$ 3.5 hours each. Combining these data with our previously published INOV monitoring of RQWLQs in 13 sessions, gives a set of INOV observations of 15 RQWLQs monitored in 29 sessions each lasting more than 3.5 hours. The 29 differential light curves (DLCs), thus obtained for the 15 RQWLQs, were subjected to an statistical analysis using the F$-$test and the deduced INOV characteristics of the RQWLQs are compared with those published recently for several prominent AGN classes, also using the F$-$test. However, since the RQWLQs are generally 1$-$2 magnitudes fainter, a rigorous comparison has to wait for somewhat more sensitive INOV observations than those presented here. Based on our existing INOV observations, it seems that RQWLQs in our sample show a significantly higher INOV duty cycle than radio-quiet quasars and radio lobe-dominated quasars. Two sessions when we detected rather strong (blazar-like) INOV for RQWLQs are pointed out and both these RQWLQs are therefore candidates for radio-quiet BL Lacs. | The presence of prominent broad emission lines in the optical/UV spectrum is a hallmark of the Active Galactic Nuclei (AGN) designated as quasars. However, such lines can appear much weaker for a class of AGN, called blazars, in which the optical/UV emission is dominated by the Doppler boosted nonthermal continuum from the relativistic jet and is therefore substantially polarized. Specifically, this `weak line' characterization holds for a subclass of blazars, called BL Lac objects (BLOs), in contrast to the other blazar subclass, called `highly polarized quasars' (HPQs) which display the emission lines at a fairly strong level~\citep[e.g.,][and references therein]{Urry1995PASP..107..803U}. Being jet dominated, both blazar subclasses, HPQs and BLOs are radio loud in the sense that the radio-to-optical flux density ratio $R > 10$, where the radio and optical continuum flux densities refer to the rest-frame wavelengths of 6 cm and 2500\AA, respectively ~\citep[e.g.,][]{Kellermann1989AJ.....98.1195K,Stocke1992ApJ...396..487S}. But, whereas HPQs have an abundant population of weakly polarized, radio-quiet counterparts (radio-quiet quasars: RQQs), the existence of radio-quiet analogs of BLOs (RQBLOs) continues to be an open question. The large optical survey SDSS ~\citep{York2000AJ....120.1579Y} was used by~\citet{Collinge2005AJ....129.2542C} and ~\citet{Anderson2007AJ....133..313A} to find candidates for radio-quiet BLOs. They termed such candidates ``Weak-Lines-Quasars'' (WLQs). In this way, dozens of WLQs marked by abnormally weak broad emission-lines~\citep[i.e, rest-frame EW$ < 15.4$\AA~ for the Ly$+$NV emission-line complex,][]{Diamond-Stanic2009ApJ...699..782D} have been reported in the literature as summarized in our first paper of this series ~\citep*[][hereafter Paper I]{Gopal2013MNRAS.430.1302G}. Since many of the WLQs are indeed found to be radio-quiet ~\citep[e.g.,][]{Plotkin2010AJ....139..390P}, they could potentially qualify as the elusive RQBLOs. However, they are generally regarded as weak-lined analogs of RQQs because, in contrast to BLOs (and much like RQQs), RQWLQs exhibit low optical polarization ~\citep{Smith2007ApJ...663..118S} and mild optical continuum variability on time scales ranging from days to years~\citep{Plotkin2010ApJ...721..562P}. This is further corroborated by the similarity observed between the UV-optical spectral indices, $\alpha$ , of WLQs and RQQs. For RQQs the median value of $\alpha$ is $-0.52$ as against $-1.15$ for BLO candidates ~\citep{Diamond-Stanic2009ApJ...699..782D,Plotkin2010AJ....139..390P}. Clearly, the above interpretation of RQWLQs does allow for the possibility that a small subset of them may indeed be the long-sought RQBLOs where the optical continuum is significantly, if not predominantly, contributed by a Doppler boosted relativistic jet. A potentially fruitful approach to explore this possibility was employed in Paper I, where we reported the first search for intranight optical variability (INOV) of RQWLQs. This was motivated by the well established result that BLOs exhibit a distinctly stronger INOV, both in amplitude ($\psi$) and duty cycle (DC), as compared to quasars, specially their more abundant subset, the RQQs~\citep[e.g.,][]{GopalKrishna2003ApJ...586L..25G,Carini2003AJ....125.1811C, 2004MNRAS.350..175S, Gupta2005A&A...440..855G, Carini2007AJ....133..303C, Goyal2012A&A...544A..37G}. It is thus evident that INOV behaviour can be a powerful discriminator between blazars and other powerful AGN, both radio-loud and radio-quiet~\citep[e.g,][]{Carini2003AJ....125.1811C,2004MNRAS.350..175S,Goyal2012A&A...544A..37G,Goyal2013MNRAS.435.1300G}. This point is discussed in Paper I and also in Sect. $4$ below. To pursue the above clue, we extracted from the literature a well-defined sample of 18 RQWLQs suited for our intranight optical monitoring (Paper I). The sample was derived from the list of 86 radio-quiet WLQs published in Table 6 of~\citet[]{Plotkin2010AJ....139..390P}, based on the SDSS Data Release 7~\citep[DR-7,][]{Abazajian2009ApJS..182..543A}. Out of that list, we included in our sample all 18 objects brighter than R$\sim$18.5 which are classified as `high-confidence' BL Lac candidate based on their optical spectra. INOV observations of 8 of the 18 RQWLQs were reported in Paper I; these were carried out in $13$ sessions mainly with the 130-cm Devasthal Fast Optical Telescope (DFOT) of the Aryabhatta Research Institute of observational sciencES (ARIES). As part of the same continuing program, we report here $16$ sessions of INOV observations of 10 RQWLQs with DFOT. This paper is organized as follows. Section $2$ describes the observations and data reduction, while Section $3$ gives details of our statistical analysis. A brief discussion of our results is presented in Section $4$. | \label{wl:sec_dis} This paper extends our work of Paper I which reported the first systematic investigation of the INOV properties of radio-quiet weak-line quasars (RQWLQs). To the 13 DLCs reported in Paper I, we have added here 16 DLCs of durations $\ga 3.5$ hours (Table~\ref{wl:tab_res}), derived for 10 RQWLQs of which three were also included in Paper I. Table 3 presents our INOV results for the 10 RQWLQs. These are based on the $F^{\eta}$-test (Eq. 1) which is a more reliable version of the $F$-test ~\citep{Howell1988AJ.....95..247H,Diego2010AJ....139.1269D}, as shown by GGWSS13 who applied it to determine the INOV status of 262 DLCs of 77 AGN representing 6 prominent classes of AGN (see below). These authors adopted $\eta = 1.5$, as determined by~\citet{Goyal2012A&A...544A..37G} from their analysis of a large set of 262 DLCs of comparison stars. It was also shown by GGWSS13 that the INOV duty cycles determined using the $F^{\eta}$-test are indistinguishable from those found using the `modified C-test', again taking $\eta = 1.5$. The $F^{\eta}$-test applied here to the 16 DLCs of 10 RQWLQs, taking $\eta = 1.5$, yielded an INOV duty cycle of 5\% which rises to 15\% if the single case of `probable' INOV (PV) is included (Table~\ref{wl:tab_res}). The same result is obtained using the `modified C-test', consistent with the finding by GGWSS13, as mentioned above. In order to ascertain the effect of likely uncertainty in $\eta$ value, we have repeated the computation of INOV duty cycle for the 10 RQWLQs, taking two extreme values for $\eta$ (=1.3 and 1.75) reported in the literature~\citep[][and references therein]{Goyal2012A&A...544A..37G}. The INOV duty cycle computed using these extreme values of $\eta$ range up to 15\% which can be treated as an upper limit.\par Next, we have computed the INOV duty cycle for the enlarged sample of 29 DLCs obtained by combining our present INOV observations of $10$ RQWLQs with those reported in Paper I. We thus find the INOV duty cycle for the combined set of $15$ RQWLQs to be $\sim$5\%, rising to $\sim$11\% if the DLCs classified as `probable' INOV (PV) are included. It is interesting to compare these estimates found here for RQWLQs with those reported by GGWSS13 for several other AGN classes, following an essentially identical observing and analysis procedure. The INOV duty cycle inferred by them (using the $F^{\eta}$-test taking $\eta$ = 1.5) is ~ 10\%(6\%) for radio-quiet quasars (RQQs), ~ 18\%(11\%) for radio-intermediate quasars (RIQs), ~ 5\%(3\%) for radio lobe-dominated quasars (LDQs), ~17\%(10\%) for radio core-dominated quasars with low optical polarization (LPCDQs) , ~43\%(38\%) for radio core-dominated quasars with high optical polarization (HPCDQs) and ~45\%(32\%) for BL Lac objects (BLOs) (The values inside parentheses refer to the DLCs showing INOV amplitude $\psi > 3$\%). The INOV duty cycle for Seyfert galaxies is reported to lie between 10\% and 20\%, the higher values being associated with the radio-loud subset~~\citep[e.g., see][]{Carini2003AJ....125.1811C}. Finally, we note that the apparent similarity of the DC estimates found here for the RQWLQs with the afore-mentioned estimates given in GGWSS13 for RQQs, RIQs, LDQs and LPCDQs is likely to be superficial. This is because, in contrast to the INOV detection threshold, $\psi_{lim}$, of 1-2\% characteristic of the observations used in GGWSS13, $\psi_{lim}$ reached in our INOV programme for the RQWLQs is a factor 2-3 higher, essentially because the RQWLQs are typically 1-2 mag fainter compared to the AGN samples covered in GGWSS13. Therefore, the present estimates of INOV duty cycle for the RQWLQs may well have to be revised upwards. A proper comparison has to wait for the availability of about a magnitude more sensitive INOV observations for RQWLQs, compared to those reported here and in Paper I. Such sensitivity matched INOV observations of RQWLQs may well yield substantially higher INOV duty cycles than those estimated here, perhaps approaching the values obtained for HPCDQs or BLOs. Efforts are underway to use larger telescopes for intranight monitoring of RQWLQs. \par As of now, our programme has revealed two instances of RQWLQ exhibiting an INOV amplitude $\psi >$ 3\% in a monitoring session, a level rarely observed in our 2-decade long INOV programme (summarised in GGWSS13), except for BLOs and HPCDQs. The two RQWLQs, J090843.25$+$285229.8 ($\psi \sim$ 31\% on 10-02-2013, Table 3) and J121929.45$+$471522.8 ($\psi \sim$ 7\% on 26-02-2012, Paper I), are thus the best available candidates for the elusive radio-quiet BLOs and both need to be followed up. Further INOV observations of these and several other members of our sample of 18 relatively bright RQWLQs are planned for the next winter months. \begin{table*} \centering \begin{minipage}{500mm} {\small \caption{Observational details and INOV results for the sample of 10 RQWLQs over 16 monitoring sessions.} \label{wl:tab_res} \begin{tabular}{@{}ccc cc rrr rrr ccc@{}} \hline \multicolumn{1}{c}{RQWLQ} &{Date} &{T} &{N} &\multicolumn{1}{c}{F-test values} &\multicolumn{1}{c}{INOV status{\footnote{V=variable, i.e., confidence level $\ge 0.99$; PV=probable variable, i.e., $0.95-0.99$ confidence level; NV=non-variable, i.e., confidence level $< 0.95$.\\ Variability status values based on quasar-star1 and quasar-star2 pairs are separated by a comma.}}} &{$\sqrt { \langle \sigma^2_{i,err} \rangle}$}&{INOV amplitude}\\ & dd.mm.yyyy& hr & &{$F_1^{\eta}$},{$F_2^{\eta}$} &F$_{\eta}$-test &(q-s) &$\psi_1(\%),\psi_2$(\%)&$\frac{}{}$\\ (1)&(2) &(3) &(4) &(5)&(6) &(7) &(8)\\ \hline J081250.79$+$522531.0 &12.11.2012 & 4.49& 50& 0.44, 0.78& NV, NV& 0.04& 10.70, 12.91\\ J084424.24$+$124546.5 &13.11.2012 & 3.93& 25& 0.23, 0.33& NV, NV& 0.04& 3.91, 5.66\\ J084424.24$+$124546.5 &04.11.2013 & 3.23& 38& 0.45, 0.50& NV, NV& 0.02& 6.15, 6.95\\ J090843.25$+$285229.8 &09.02.2013 & 3.90& 32& 0.33, 0.44& NV, NV& 0.04& 5.06, 8.90\\ J090843.25$+$285229.8 &10.02.2013 & 4.02& 33& 3.01, 3.14& V, V& 0.04& 31.73, 30.20\\ J101353.45$+$492757.9 &01.01.2014 & 4.43& 37& 1.96, 1.58& PV, NV& 0.02& 12.79, 11.07\\ J101353.45$+$492757.9 &02.01.2014 & 4.58& 32& 1.10, 0.78& NV, NV& 0.02& 10.68, 7.31\\ J110938.50$+$373611.6 &10.02.2013 & 4.43& 36& 0.54, 0.52& NV, NV& 0.03& 9.89, 9.14\\ J111401.31$+$222211.5 &09.02.2013 & 3.43& 25& 2.15, 2.80& PV, V& 0.04& 28.47, 30.43\\ J115637.02$+$184856.5 &15.01.2013 & 5.05& 41& 0.59, 0.74& NV, NV& 0.03& 7.60, 7.97\\ J121929.45$+$471522.8 &14.01.2013 & 4.13& 33& 0.87, 0.84& NV, NV& 0.02& 7.54, 7.89\\ J121929.45$+$471522.8 &13.03.2013 & 6.22& 44& 1.30, 1.48& NV, NV& 0.04& 15.16, 17.86\\ J121929.45$+$471522.8 &08.04.2013 & 4.18& 30& 0.50, 0.59& NV, NV& 0.05& 14.01, 14.09\\ J212416.05$-$074129.9 &12.11.2012 & 3.40& 37& 1.08, 1.07& NV, NV& 0.07& 33.33, 35.20\\ J224749.56$+$134250.0 &13.11.2012 & 4.42& 29& 0.89, 0.71& NV, NV& 0.05& 15.30, 14.32\\ J224749.56$+$134250.0 &04.11.2013 & 4.69& 35& 0.63, 0.45& NV, NV& 0.04& 20.45, 14.51\\ \hline \end{tabular} } \end{minipage} \end{table*} \begin{figure*} \centering \epsfig{figure=fig1.ps,height=23.5cm,width=16.0cm,angle=00,bbllx=20bp,bblly=161bp,bburx=580bp,bbury=711bp,clip=true} \vspace{-1.0cm} \caption[]{Differential light curves (DLCs), for the $10$ RQWLQs in our sample. The name of the quasar along with the date and duration of the monitoring session are given at the top of each panel. In each panel the upper DLC is derived using the two non-varying comparison stars, while the lower two DLCs are the `quasar-star' DLCs, as defined in the labels on the right side. Any likely outlier point (at $> 3\sigma$) in the DLCs are marked with crosses and those points are excluded from the statistical analysis.} \label{fig:lurve} \end{figure*} \begin{figure*} \centering \epsfig{figure=fig2.ps,height=24.8cm,width=16.0cm,angle=00,bbllx=20bp,bblly=161bp,bburx=580bp,bbury=711bp,clip=true} \vspace{-1.0cm} \caption[]{Same as Figure~\ref{fig:lurve}, for remaining $8$ DLCs.} \label{fig:lurve2} \end{figure*} | 14 | 3 | 1403.7440 |
1403 | 1403.7992_arXiv.txt | {We measure the dust and gas content of the three sub-millimeter galaxies (SMGs) in the GN20 proto-cluster at $z=4.05$ using new IRAM Plateau de Bure interferometer (PdBI) CO(4-3) and 1.2--3.3 mm continuum observations. All these three SMGs are heavily dust obscured, with UV-based star formation rate (SFR) estimates significantly smaller than the ones derived from the bolometric infrared (IR), consistent with the spatial offsets revealed by HST and CO imaging. Based also on evaluations of the specific SFR, CO-to-H$_2$ conversion factor and gas depletion timescale, we classify all the three galaxies as starbursts (SBs), although with a lower confidence for GN20.2b that might be a later stage merging event. We place our measurements in the context of the evolutionary properties of main sequence (MS) and SB galaxies. ULIRGs have 3--5 times larger $L'_{\rm CO}/M_{\rm dust}$ and $M_{\rm dust}/M_\star$ ratios than $z=0$ MS galaxies, but by $z\sim2$ the difference appears to be blurred, probably due to differential metallicity evolution. SB galaxies appear to slowly evolve in their $L'_{\rm CO}/M_{\rm dust}$ and $M_{\rm dust}/M_\star$ ratios all the way to $z>6$ (consistent with rapid enrichment of SB events), while MS galaxies rapidly increase in $M_{\rm dust}/M_\star$ from $z=0$ to 2 (due to gas fraction increase, compensated by a decrease of metallicities). While no IR/submm continuum detection is available for indisputably normal massive galaxies at $z>2.5$, we show that if metallicity indeed decrease rapidly for these systems at $z>3$ as claimed in the literature, we should expect a strong decrease of their $M_{\rm dust}/M_\star$, consistent with recent PdBI and ALMA upper limits. We conclude that the $M_{\rm dust}/M_\star$ ratio could be a powerful tool for distinguishing starbursts from normal galaxies at $z>4$. } | Submillimeter (submm) and millimeter observations are efficient in detecting and studying dusty, star-forming galaxies, due to the effect of negative $K$-correction, which results in nearly constant observed brightness for galaxies with same infrared (IR) luminosity over a broad range of redshifts. However, most current deep submm surveys are limited to the brightest sources and submm-selected galaxies \citep[SMGs;][]{blain02}, due to the limited spatial resolution and sensitivity of submm observations. SMGs are massive, highly dust obscured galaxies with extreme star formation rates (SFRs) of order 10$^3$ $M_\odot$ yr$^{-1}$ \citep[e.g., review by][]{blain02,casey14}, and are generally thought to represent the progenitors of local massive elliptical galaxies. While spectroscopic studies of SMGs originally gave a median redshift of {\em z}$\sim$2.5 \citep{chapman05}, recent deep submm/mm continuum and radio observations show evidence for a significant population of higher redshift massive starbursts \citep[SBs; e.g.,][]{dannerbauer04,smolcic12,swinbank13,dowell14}, extending the redshift peak beyond $z=3$. A substantial number of $z>4$ SMGs have been identified to date \citep[e.g.,][]{dannerbauer08,daddi09a,daddi09b,capak08,capak11,schinnerer08,coppin09,knudsen10,riechers10,riechers13,smolcic11,walter12,combes12,vieira13}. The surface density of these galaxies is found to be significantly higher than that expected from theoretical models \citep[e.g.,][]{baugh05,hayward13}, suggesting that current models of galaxy formation underpredict the number of high-redshift starbursts. Observations of the molecular gas in high-redshift galaxies reveal that while SMGs are highly gas-rich systems \citep{tacconi08}, the gas fractions of these systems are comparable to those of typical massive galaxies at similar epochs \citep[$\sim$40-60\%;][]{daddi08,daddi10}, implying that SMGs have higher star formation efficiencies \citep[SFEs;][]{daddi10,genzel10}. However, these results are complicated by the large uncertainties associated with the CO-to-H$_2$ conversion factor $\alpha_{\rm CO}$ \footnote{{\bf $\alpha_{\rm CO} = M_{\rm H_2} / L'_{\rm CO}$}, with units of M$_\odot$ (K km s$^{-1}$ pc$^2$)$^{-1}$, which are omitted from the text for brevity. Note that the contribution from Helium is included in the $\alpha_{\rm CO}$ estimates.}, which likely changes between normal disk galaxies and starbursts \citep[see review by][]{bolatto13,carilli13}. In the literature, an ``ULIRG-like'' value of $\alpha_{\rm CO}=0.8$ (Downes \& Solomon 1998; but see \citealt{papadopoulos12} for a higher value of $\alpha_{\rm CO}$) is widely adopted for SMGs due to the lack of direct measurements, while a value of $\alpha_{\rm CO}\sim$ 4 is favored for Milky Way and normal galaxies. This carries a significant uncertainty since high redshift SMGs may be dramatically different from local ULIRGs, given the more extended gas distribution and different physical conditions revealed in some SMGs \citep{riechers11,ivison11,carilli13,scoville14}. Therefore, it is of significant importance to obtain a direct calibration of $\alpha_{\rm CO}$, since well-determined molecular gas masses are critical to study the variations in physical properties across the galaxy populations at high redshift. Because of the extreme high specific star formation rates (sSFRs), some of the most luminous SMGs are placed as outliers above the main sequence (MS) of star formation, which is a tight correlation observed between the stellar mass and the SFR over a broad range of redshifts \citep[e.g.,][and references therein]{noeske07,elbaz07,daddi07b,rodighiero10}. While galaxies on the MS are thought to form stars gradually with a long duty cycle and represent the bulk of the galaxy population, starbursts exhibit very intense and rapid star formation activity, likely driven by mergers \citep[e.g.,][]{daddi07a,daddi07b,tacconi08,tacconi10,elbaz11,rodighiero11}. Recent studies on the molecular gas of $z > 3$ Lyman break galaxies (LBGs) found these galaxies to be rather deficient in CO emission for their star formation activity \citep{magdis12b,tan13}. Similar results have also been reported for a luminous LBG at $z=6.595$ called ``Himiko'', for which the 1.2 mm dust continuum and [CII] 158 $\mu$m emission are much lower than predicted by local correlations and measured SFRs \citep{ouchi13}. It has been found that normal galaxies at $z >$ 3 are increasingly metal poor, with metallicities dropping by about 0.6 dex as compared to local galaxies of similar stellar mass \citep{mannucci10,sommariva12,troncoso13}. This may suggest that metallicity effects could be a probable explanation for the deficit of CO emission, since the photodissociation of CO by far-UV radiation is enhanced at low metallicity \citep{leroy11,genzel12,narayanan12,bolatto13}. The decrease of CO emission in $z > 3$ normal galaxies for their IR luminosity is also predicted by simulations with a galaxy-formation model \citep{lagos12}, a result driven by the low metallicities in such objects. Similar detailed study of a local metal poor star-forming galaxy, I Zw 18, concluded that it would be much harder than hitherto anticipated to detect gas and dust in high-redshift galaxies like Himiko \citep[several tens of days of integration with the complete ALMA; see][]{fisher14}, if assuming I Zw 18 is an analog of primitive galaxy population in the early Universe. Dust is expected and observed to be well mixed with gas in the interstellar medium (ISM), because it is composed of metals and regulates the gas phase abundances of the elements through accretion and destruction processes \citep{draine07}. The comparison of dust and gas properties of galaxies at different redshifts is thus crucial to explore the interplay between dust, gas, and metals in the ISM, and allow us to achieve a better understanding of galaxy evolution throughout cosmic time. For galaxies at $z>3$, to date only very few luminous SMGs have been detected in both dust continuum and gas emission \citep[e.g.,][]{dannerbauer08,daddi09a,daddi09b,coppin09,coppin10,walter12,riechers13}, while no dust continuum detection is available for indisputably normal galaxies at $z>3.5$. GN20 is one of the brightest SMGs in the GOODS-N field \citep{pope06}, of which the redshift ($z=4.055$) was established by a serendipitous detection of its CO(4-3) emission \citep{daddi09b}. Two additional SMGs, GN20.2a and GN20.2b, were found to lie within $\sim$25$''$ of GN20 (projected physical separation $\sim$ 170 kpc) and have redshifts of $z\sim$ 4.055$\pm$0.005. These two galaxies are separated by only a few arcseconds and hence are not spatially separated from each other in existing submm images (e.g., SCUBA 850~$\mu$m). \citet{daddi09b} also found 14 B-band dropouts (roughly $z\sim4$) lying within 25$''$ from GN20, which corresponds to an overdensity of 5.8$\sigma$ in the GOODS-N field, suggesting a massive proto-cluster environment at $z\sim4.05$, just 1.6 Gyr after the Big Bang. All three massive SMGs in the GN20 proto-cluster have been detected in CO emission, indicative of large amounts of molecular gas \citep{daddi09b,carilli10,carilli11,hodge12,hodge13}, feeding vigorous ongoing star formation (SFR $\sim$ a few to ten times 100 $M_\odot$ yr$^{-1}$). The deep, high-resolution CO(2-1) observations reveal a clumpy, extended gas disk (14$\pm$4 kpc in diameter) for GN20 \citep{hodge12}, and extended gas reservoirs ($\sim$ 5--8 kpc) for GN20.2a and GN20.2b \citep{hodge13}. \citet{hodge12,hodge13} have attempted to constrain the estimate of CO-to-H$_2$ conversion factor by dynamical analysis, deriving $\alpha_{\rm CO}$ of $\sim$ 1--2 for these three galaxies. For the dust continuum emission, however, only GN20 has been reported in {\it Herschel} and (sub)mm detections \citep{daddi09b,magdis11}. Here we use PACS and PdBI mm data for GN20.2a and GN20.2b to study the dust properties of these two galaxies. By combining with the molecular gas properties and dynamical analysis, we aim to achieve a more comprehensive understanding of the nature of the massive SMGs in the GN20 proto-cluster environment. We further investigate the metallicity effects on molecular gas and dust emission by comparison of CO luminosity-to-dust mass ratio and dust-to-stellar mass ratio between normal galaxies and starbursts. This paper is organized as follows. In Sect.~\ref{obs} we present the new PdBI CO(4-3) observations and the reduction of data for the SMGs GN20, GN20.2a, and GN20.2b. Section~\ref{results} presents the results of CO and millimeter continuum observations, the methods used to compute SFR, dust mass, stellar mass, metallicity, dynamical mass, and CO-to-H$_2$ conversion factor. This section also describes the derived physical properties including sSFR, SFE, radio-IR correlation constraints, gas fraction, and gas depletion timescales. In Sect.~\ref{nature} we discuss the nature of GN20, GN20.2a, and GN20.2b based on the physical properties of optical morphology, molecular gas, dust, and dynamical constraints. We further discuss the implications for the cosmic evolution of dust content in galaxies in sect.~\ref{implication}. Finally, we summarize our results in Sect.~\ref{summary}. We adopt a cosmology with $H_0$=71 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\rm M}$=0.3, $\Omega_\Lambda$=0.7, and a Chabrier (2003) initial mass function (IMF) throughout the paper. \begin{figure*}[htbp] \centering \includegraphics[width=0.32\textwidth]{gn20_co43bcd_gauss_25kms_signal.eps} \includegraphics[width=0.32\textwidth]{gn20a_co43bd_gauss_50kms_signal.eps} \includegraphics[width=0.32\textwidth]{gn20b_co43bcd_gauss_50kms_signal.eps} \caption{CO(4-3) spectra binned in steps of 25 km s$^{-1}$ for GN20 (left), 50 km s$^{-1}$ for GN20.2a (middle) and GN20.2b (right). The yellow color indicates the velocity ranges where line emission is detected. These regions have been used to derive the integrated fluxes. The red lines show best-fitting double Gaussian profiles to the spectra, and the blue dashed lines show the fits with a single Gaussian. Zero velocities correspond to the redshifts listed in Table~1. \label{fig1}} \end{figure*} \begin{table*} \caption{Observed and derived CO emission properties} \label{tbl1} \centering \small {\renewcommand{\arraystretch}{1.5} \begin{tabular}{lccccccc} \hline\hline Source & R.A.$_{\rm CO}$ & Decl.$_{\rm CO}$ & $z_{\rm CO}$ & $z_{\rm keck}$ & FWHM & $I_{\rm CO (4-3)}$ & $L'_{\rm CO (4-3)}$ \\ & (J2000) & (J2000) & & & (km s$^{-1}$) & (Jy km s$^{-1}$) & (K km s$^{-1}$ pc$^2$) \\ \hline GN20 & 12:37:11.91 & 62:22:12.1 & 4.0553$\pm$0.0002 & 4.06$\pm$0.02 & 583$\pm$36 & 1.68$\pm$0.10 & 6.56$\times$10$^{10}$ \\ GN20.2a & 12:37:08.76 & 62:22:01.6 & 4.0508$\pm$0.0013 & 4.059$\pm$0.007 & 760$\pm$180 & 0.65$\pm$0.08 & 2.70$\times$10$^{10}$ \\ GN20.2b & 12:37:09.68 & 62:22:02.2 & 4.0563$\pm$0.0003 & ... & 220$\pm$43 & 0.27$\pm$0.04 & 1.06$\times$10$^{10}$ \\ \hline \end{tabular} } \end{table*} | \label{summary} We have presented results from deep IRAM PdBI CO(4-3) and 1.2--2.2--3.3 mm continuum observations of the GN20 proto-cluster at $z=4.05$. The improved CO spectral profile of GN20, GN20.2a, and GN20.2b allow us to measure the line width more accurately and further constrain the dynamical mass. Combining with the ancillary multiwavelength photometry in the rest-frame UV, optical, and IR, we determine the stellar masses and dust properties of these three sub-mm galaxies (SMGs). With the measured stellar masses, dynamical masses, CO luminosities, dust masses, and indirect metallicity estimates, we inferred the value of conversion factor $\alpha_{\rm CO}$ in each of the three SMGs, using the dynamical modeling and the gas-to-dust ratio methods. Combining with literature data of normal galaxies and starbursts from local to high redshift, we discuss the effect of metallicity evolution on observations of dust and gas emission of galaxies across cosmic time. The main results and implications are summarized as follows: 1. All three SMGs are now detected in CO(4-3) with high S/N ratios. The FWHM of the spectra derived from double Gaussian fits are 583$\pm$36 km s$^{-1}$, 760$\pm$180 km s$^{-1}$, and 220$\pm$43 km s$^{-1}$ for GN20, GN20.2a, and GN20.2b, respectively. With $L'_{\rm CO(4-3)}$ derived from our study and $L'_{\rm CO(2-1)}$ measured by \citet{carilli11}, we find CO(4-3)/CO(2-1) line ratio of $\sim$0.4 for these three SMGs, which is consistent with the mean ratio ($\sim$0.48$\pm$0.10) measured for SMGs at $z\sim2$--4 \citep{bothwell13}. 2. We report 3.3 mm continuum detections in GN20.2a and GN20.2b for the first time, and use continuum measurements at 1.2 and 2.2 mm (Carilli et al. 2010; Riechers et al. 2014, in prep.). The dust masses measured from the far-IR SED fitting are $2.1-5.2\times10^9$ M$_\odot$. The IR-to-radio luminosity ratios for GN20 ($q$=2.41$\pm$0.05) and GN20.2b ($q$=2.60$\pm$0.13) are found to be comparable to the local value ($\sim$2.6), while GN20.2a shows a relatively low value ($q$=1.72$\pm$0.04), suggesting that this galaxy is radio-excess with large amounts of radio emission likely powered by an AGN (see also Daddi et al. 2009). 3. We find that the value of $\alpha_{\rm CO}$ inferred from gas-to-dust ratio method is consistent with the one derived based on the dynamical mass for each galaxy. The $\alpha_{\rm CO}$ derived for these three SMGs ($\sim$1.3-2.8 $M_\odot$ (K km s$^{-1}$ pc$^2$)$^{-1}$) are found to be consistent with the typical value determined for local ULIRGs, but might be well below the value appropriate for normal galaxies at similar redshifts. The high gas fraction ($\sim$40\%-80\%) of these three SMGs at $z$=4.05 are found to be comparable to SMGs at $z$=2--4 and high redshift normal galaxies. 4. Our study clearly distinguishes GN20, GN20.2a (and likely GN20.2b) as starbursts from normal star-forming galaxies by comparing observed physical properties between these galaxies. For GN20 and GN20.2a, the large sSFR-excess (sSFR/sSFR$_{\rm MS} \sim 6$) compared to the normal galaxies at similar epochs place these SMGs as outliers above the main sequence. The extremely large value of SFR$_{\rm IR}$/SFR$_{\rm UV}$ for GN20 and GN20.2a are consistent with the large offset between CO positions and optical counterparts (see Fig.~\ref{counterparts}), suggesting that the UV/optical emission is heavily obscured beyond optically thick dust. Although GN20.2b situates within the MS scatter with sSFR/sSFR$_{\rm MS}\sim 2.4$, both the large value of SFR$_{\rm IR}$/SFR$_{\rm UV}$ ($\sim 6$) and short gas-consumption time-scales ($\sim$116 Myr) suggest that this galaxy could also be a starburst. 5. We find that these three SMGs are likely to experience different evolutionary stages of starburst activity. Compared with GN20 and GN20.2a, GN20.2b displays relatively smaller sSFR-excess, older stellar age, and lower CO excitation. All these properties suggest that GN20.2b is probably observed at a decaying stage of a major merger, while GN20 and GN20.2a are likely to undergo and approach the final coalescence with intense starburst, respectively. 6. We compile a variety of archival data of normal galaxies and starbursts in order to investigate the effect of metallicity evolution on observations of galaxies across the cosmic time. For normal galaxies, the ratio of $L'_{\rm CO}/M_{\rm dust}$ is found to be almost constant from $z=0$ to 3.1. And the same appear to be the case for high-z starbursts, implying that both the CO and dust emission could be affected in the same way by the metals in the ISM. 7. We calculate simple models for the dust emission of normal galaxies based on their properties and find a rapid decrease of dust emission for $z>3$ normal galaxies at a given stellar mass if metallicities indeed decrease rapidly for these galaxies. The model predictions are well-matched to the measurements at $z<2.5$, with a trend of increasing $M_{\rm dust}/M_{\star}$ with redshift. While no dust detection is available for indisputably normal galaxies beyond $z=2.5$, the model based on the assumption of fast metallicity evolution predicts a sharp decline of dust emission for normal galaxies at $z>2.5$. In contrast, the starburst galaxies show an increase of $M_{\rm dust}/M_{\star}$ at high redshift, providing evidence for rapid early metal enrichment in these systems. The different behaviours of normal galaxies lead to a significantly lower $M_{\rm dust}/M_{\star}$ compared to starbursts at $z>4$, implying that the comparison of $M_{\rm dust}/M_{\star}$ ratio could also be used as a powerful tool for distinguishing starbursts from normal galaxies at $z>4$. | 14 | 3 | 1403.7992 |
1403 | 1403.2115_arXiv.txt | {\em Chandra} high-resolution spectra toward eight low-mass Galactic binaries have been analyzed with a photoionization model that is capable of determining the physical state of the interstellar medium. Particular attention is given to the accuracy of the atomic data. Hydrogen column densities are derived with a broadband fit that takes into account pileup effects, and in general are in good agreement with previous results. The dominant features in the oxygen-edge region are \ion{O}{1} and \ion{O}{2} K$\alpha$ absorption lines whose simultaneous fits lead to average values of the ionization parameter of $\log\xi=-2.90$ and oxygen abundance of $A_{\rm O}=0.70$. The latter is given relative to the standard by \citet{gre98}, but rescaling with the revision by \citet{asp09} would lead to an average abundance value fairly close to solar. The low average oxygen column density ($N_{\rm O}=9.2 \times 10^{17}$~cm$^{-2}$) suggests a correlation with the low ionization parameters, the latter also being in evidence in the column density ratios $N$(\ion{O}{2})/$N$(\ion{O}{1}) and $N$(\ion{O}{3})/$N$(\ion{O}{1}) that are estimated to be less than 0.1. We do not find conclusive evidence for absorption by any other compound but atomic oxygen in our oxygen-edge region analysis. | High-resolution X-ray spectroscopy provides a powerful technique for studying the interstellar medium (ISM) since the analysis of absorption features allows the identification of atomic and molecular transitions directly related to its physical and chemical properties. In this context, a chemical element of much interest is oxygen due to its cosmic abundance and foremost spectral features, namely K-edge structures whose models can lead to reliable estimates of its abundance, column densities, and ionization fractions. A prominent oxygen K edge and hints of a resonant $1s\rightarrow 2p$ absorption line were reported in the pioneering work by \citet{sch86} on the Crab Nebula soft X-ray spectrum ($<3$~keV) taken with the Einstein Observatory. No apparent evidence for depletion was therein found thus implying dust grain sizes of $< 4\,\mu$m. A further attempt to exploit the oxygen K-shell absorption region was performed by \citet{jue04}, who analyzed the spectra of seven X-ray binaries taken with the satellite-borne {\it Chandra} High Energy Transmission Grating Spectrometer (HETGS). Their model included two absorption edges ($1s2s^22p^4\ ^4P,\ ^2P)$ and five Gaussians corresponding to K$\alpha$ ($1s\rightarrow 2p$) transitions in \ion{O}{1}, \ion{O}{2}, and \ion{O}{3} and K$\beta$ ($1s\rightarrow 3p$) in \ion{O}{1}. As a result, they managed to constrain the oxygen ionization fractions to $N({\rm O\ II})/N({\rm O\ I})\approx 0.1$ and $N({\rm O\ III})/N({\rm O\ I})\leq 0.1$. \citet{yao05} performed a similar analysis including observations of seven Galactic low-mass X-ray binaries taken with both the High Energy Transmission Grating (HETG) and Low Energy Transmission Grating (LETG) on board {\it Chandra}. The \ion{O}{7} and \ion{O}{8} K$\alpha$ lines and the \ion{O}{7} K$\beta$ detected in three of these sources were associated to the hot interstellar medium (HISM) whose distribution was also estimated; however, due to the few lines of sight, such inference could be biased. \citet{cos05} studied high-resolution spectra of the Cygnus~X-2 low-mass X-ray binary taken with the {\it XMM-Newton} space telescope, concluding that the complexity of the oxygen edge could be explained by absorption of both molecular and ionized atomic species. Moreover, in an analysis of the oxygen K-shell edge in {\it XMM-Newton} spectra towards galaxy clusters, \citet{bau06} determined a high gas-to-dust ratio in the Galaxy, pointing out that the composition of denser clouds could be similar to the diffuse ISM. \citet{mil09b} have fitted {\it Chandra} HETG data from five X-ray binaries with an absorption model referred to as {\tt TBnew}, and suggested that ISM absorption dominated the neutral column density. From similar observations of the line of sight of Cygnus~X-2, \citet{yao09} detected K absorption lines from \ion{O}{1}, \ion{O}{2}, \ion{O}{6}, \ion{O}{7}, and \ion{O}{8}, determining abundances that indicated mild oxygen depletion onto dust grains in the cold phase. From {\it XMM-Newton} Reflection Grating Spectrometer (RGS) spectra of the X-ray binary Sco~X-1, \citet{dev09} have deduced the presence of extended X-ray absorption fine structures (EXAF) and that around $30{-}50\%$ of the oxygen was bound in solid material. However, \citet{gar11} showed that, by using an accurate photoionization cross section for atomic \ion{O}{1}, observations of this source in the $12.5{-}21.0$~\AA\ region could be adequately reproduced with no evidence of additional molecular and dust contributions. \citet{pin10} have considered both the dust and gas components in the ISM absorption features towards the low-mass X-ray binary GS~1826-238; they found oxygen to be over abundant and a gas ionization degree above $5\%$, concluding that at least $10\%$ of the oxygen was found in molecules or dust. More recently, \citet{pin13} have measured oxygen column densities and estimated abundance gradients from {\it XMM-Newton} grating spectra of nine low-mass X-ray binaries, concluding that $15{-}25\%$ of the oxygen is found in dust. They also point out that the ratios between different ionization stages are similar among the lines of sight suggesting large-scale chemical homogeneity. \citet{lia13} have analyzed 36 {\it Chandra} HETG observations from eleven low-mass X-ray binaries taking into consideration a correction for the Galactic rotation velocity relative to the rest frame. Through a Bayesian statistical approach and a combined fit, they detect several spectral features in the oxygen-edge region including K$\alpha$ lines from \ion{O}{1}, \ion{O}{2}, \ion{O}{3}, \ion{O}{4}, \ion{O}{5}, \ion{O}{6}, and \ion{O}{7}. \citet{gat13a} have presented a self-consistent physical model of ISM oxygen K absorption to fit four {\it Chandra} spectra of XTE~J1817-330, a low-mass X-ray binary with high signal-to-noise ratio. The oxygen K-edge region is fitted with a photoionization model derived with the {\sc xstar} computer code \citep{bau01} referred to as {\tt warmabs}. It is found that the K lines and photoionization cross sections must be slightly wavelength shifted in order to match the observed spectra. The resulting low ionization parameter indicate a dominant neutral component with absorption lines from \ion{O}{1} K$\alpha$, K$\beta$, and K$\gamma$ together with K$\alpha$ from \ion{O}{2} and \ion{O}{3}. K$\alpha$ lines from \ion{O}{6} and \ion{O}{7} are also detected, but it is argued that they probably arise in the neighborhood of the source rather than in the ISM; unsurprisingly, molecular features in the O K-edge region are not found in this study. In the present work we refine the building blocks of our model of ISM oxygen photoabsorption, and explore its possibilities in describing the high-resolution {\it Chandra} spectra of eight X-ray binaries. Since this process is dominated by the neutral, we evaluate the impact of the atomic data on model prediction by considering both the new and definitive \ion{O}{1} cross section by \citet{gor13} and previous data of \citet{gar05}. Although dramatic revelations are not expected with the present line-of-sight sampling, we are at least certain to contribute to the current discussion on ISM phase composition and local variability. The outline of the paper is as follows. In Section~\ref{sec_atom} we give details concerning the atomic data sets, and the observational reduction steps are described in Section~\ref{sec_obs}. The fitting procedures of \citet{gat13a} for the broadband and oxygen-edge regions are recapitulated in Section~\ref{sec_fit} followed by the fit results (Sections~\ref{sec_fit_broad}--\ref{sec_fit_oxygen}). A discussion of results is carried out in Section~\ref{sec_ism} in order to draw some conclusions in Section~\ref{sec_conclusion}. | We have carried out an analysis of ISM oxygen K absorption by means of high-resolution X-ray spectra toward eight low-mass Galactic binaries. For this purpose we are employing a physical model, referred to as {\tt warmabs}, that is capable of determining the physical state of the gas. A broadband fit was performed to constrain the hydrogen column density using the {\tt simple\_gpile2.sl}({\tt TBnew}({\tt powerlaw})) model. The pileup effect was estimated from the fit indicating that it must be taken into account in the 11--24~\AA\ region, although it can be safely ignored around the oxygen edge (21--24~\AA). The hydrogen column densities derived from the fits are in good agreement with previous work, although in the case of Cygnus~X-1 it is difficult to constrain it due to the presence of an alleged stellar wind along the line of sight. For each source, the simultaneous fit of the oxygen edge region with the {\tt warmabs} model provides estimates of the ionization parameter and oxygen abundance. The simultaneous fit is implemented to avoid the overlapping between ISM and intrinsic absorption features thus allowing a reliable study through the line of sight. The low ionization degree is consistent with the prevalence of \ion{O}{1} and \ion{O}{2} K$\alpha$ absorption lines, supporting the dominance of the neutral component in the plasma. The fits yield an average oxygen abundance ($A_{\rm O}=0.70$) lower than solar if the standard by \citet{gre98} is assumed, but fairly close to solar when rescaling to the revision by \citet{asp09}. In the case of 4U~1820-30 oxygen enrichment is encountered, a likely consequence of the source location in the metal-rich NGC\,6624 globular cluster. It is important to note that our conclusions are backed by the present benchmark of oxygen atomic data \citep{gor13} which we now confidently recommend as the standard for future X-ray spectroscopy. We do not detect high-ionization lines except in XTE~J1817-330 which, as mentioned by \citet{gat13a}, may arise in the source neighborhood rather than in the actual ISM. Using the \ion{O}{6} column densities obtained by \citet{sem03} and \citet{sav03} from UV data, we have carried out a set data simulations to estimate the typical column densities that would enable a statistically acceptable \ion{O}{6} K$\alpha$ line detection, finding that a minimum of $\approx 1.6\times 10^{15}$~cm$^{-2}$ is required to allow the fitting with a Gaussian. | 14 | 3 | 1403.2115 |
1403 | 1403.1927_arXiv.txt | A novel cooling mechanism is proposed for neutron stars, based on the recent development in the studies of the QCD phase diagram. Possible appearance of the inhomogeneous chiral phase makes the quark beta decay without gluonic interaction. An estimate of the neutrino emissivity shows the order of $10^{24-26}(T/10^9)^6$(erg$\cdot$cm$^{-3}$ $\cdot$ s$^{-1}$) near the phase boundaries, whose efficiency is comparable with the usual quark cooling or pion cooling, but it works only in the limited density region. These features may give another cooling scenario of neutron stars. | The appearance of the inhomogeneous phases near the phase boundary should be rather common phenomenon in many-body systems. Fulde-Ferrell-Larkin-Ovchinikov (FFLO) state is one of the typical examples in superconductivity in the presence of magnetic impurities \cite{super} and has been recently studied in dilute atomic gas \cite{atom}, or within the context of color superconductivity in QCD \cite{raj}. Inhomogeneous phase formation in magnetic materials is another one; spin density wave \cite{sdw,grus} or texture \cite{mag}. Similar subject has been also addressed in the QCD phase diagram. The deconfinement and chiral transition have been studied both theoretically and experimentally in the QCD phase diagram \cite{fuk}. The direct numerical calculation based on the lattice QCD theory should be a most powerful tool for this purpose, but its validity is, for the present, limited to high temperature and low density region due to the sign problem. On the contrary, the phase structure is also important and interesting in the high-density region in the light of recent progress in the observation of compact stars \cite{sch}. Many theoretical studies have been devoted to the chiral transition by the use of the effective models of QCD \cite{fuk}. Consequently, spontaneous symmetry breaking (SSB) should be restored at high density, which is specified by the vanishment of the $q\bar q$ scalar condensate, $\langle{\bar\psi}\psi\rangle$: it is the order parameter in the chiral transition and takes a finite value in the vacuum to generate the quark or nucleon mass. In these studies it is implicitly assumed that the condensate is scalar and uniform, while Lorenz invariance or parity symmetry no more holds at finite densities. Recently there appeared many papers about the possibility of the inhomogeneous chiral phases \cite{chi}, where the condensates are not restricted to the scalar one and they are spatially nonuniform, stimulated by the mathematical discoveries of the Hartree-Fock solutions in the 1+1 dimensions \cite{bas}; it has been shown that analytic solutions are obtained in terms of the elliptic functions in the Gross-Neveu model or two dimensional NJL model in the large $N$ limit. The order parameter or the mean-field is generalized to be complex as $M(x)=\langle\bar\psi \psi\rangle+i\langle\bar\psi i\gamma_5 \psi\rangle=\Delta(x)e^{i\theta(x)}$, they have found the solutions of the self-consistent coupled-equations of quark and $M(x)$ for these models. Its direct application is possible for the one dimensional order in 1+3 dimensions by embedding the one dimensional structure and operating the Lorentz boost in the direction perpendicular to it. Actually Nickel have performed this procedure for the real kink crystal (RKC) \cite{nick}, where $\theta(\br)=0$. Similar procedure may be also possible for the chiral spiral. The chiral spiral has a former history. Nakano and one of the authors (TT) have studied the possibility of the inhomogeneous chiral phase in 1+3 dimensional quark matter within the $SU(2)\times SU(2)$ NJL model \cite{dcdw}. Using $\theta(\br)=\bq\cdot\br$, the chiral condensates take form, $\langle\bar\psi \psi\rangle=\Delta\cos(\bq\cdot\br), \langle\bar\psi i\gamma_5\tau_3 \psi\rangle=\Delta\sin(\bq\cdot\br)$, which is a 1+3 dimensional realization of the chiral spiral in 1+1 dimensions. They called it dual-chiral-density wave (DCDW). Since the spatial displacement of the condensates is compensated by chiral rotation on the quark field, the external degrees of freedom is mixed with the internal ones; the wavefunction changes $\psi\rightarrow e^{i\bk\cdot {\bf d}}{\rm exp}(i\gamma_5\tau_3 \bq\cdot{\bf d}/2)\psi$ following the displacement, $\br\rightarrow \br+{\bf d}$. The physical mechanism has been discussed in ref.\cite{dcdw}; the nesting effect of the Fermi surface may play a key role as in condensed matter physics \cite{sdw,grus,cdw,gruc,grud}. If this is the case, the appearance of the inhomogeneous phase should be rather robust and less model-dependent. However, there are still left many subjects to be elucidated. In ref.\cite{nick} Nickel suggested that RKC is more favorite than DCDW in symmetric quark matter in the chiral limit by comparing the thermodynamic potential. However, it should be an ideal situation and we must carefully compare both cases in realistic situations, including the model dependence \cite{car,mul}. In particular, the effect of the quark current mass \cite{mae,kar} and magnetic field should be important \cite{fro,tat2}. Actually chiral anomaly plays an important role and DCDW develops in a wide region in the presence of the magnetic field \cite{fro,tat2} Asymmetric quark matter or chemical equilibrium is also important in compact stars \cite{ebe}. Thus more elaborate studies are needed to say definite things about the most plausible configuration, the critical density or the critical temperature. On the other hand it should be important to consider their phenomenological implications. Since the order parameter is spatially nonuniform and takes a periodic function, one may expect elasticity like a Coulomb lattice or liquid crystal \cite{gen}. The periodicity of the order parameter may give rise to another effect. The quark wave function accordingly takes a special form dictated by the generalized Bloch theorem \cite{bas}; momentum is not a good quantum number, so that the condensates should modify the momentum conservation in the elementary processes like the Umklapp process in solid \cite{kit}. Moreover, the appearance of the pseudoscalar condensate is related to magnetic properties \cite{dcdw,tat2}. Thus it should be interesting and important to figure out how such features manifest by confronting them with physical phenomena. In the relativistic heavy-ion collisions the formation of quark-gluon plasma has been expected. Some implication of the chiral critical point has been studied theoretically and experimentally \cite{fuk}. If the inhomogeneous phases are realized during the collisions, they might give rise to some phenomena never discussed yet \cite{bas2}. In this paper we consider the cooling process in compact stars as an astrophysical implication of the inhomogeneous phases. Cooling of compact stars has provided us with information about form of matter at high-densities \cite{bec}. Recent observations of the surface temperature of young pulsars have suggested that some compact stars such as 3C58 or Vela seem to have rather low temperature which should be barely explained by the standard scenario. Such stars might require exotic cooling; quark cooling is one of the fast cooling mechanisms in the core region. On the other hand, Cas A also presents important information about the thermal evolution of young pulsars \cite{casa}. Considering the young age of $t=330$yr, the observed effective temperature of Cas A also gives a strong constraint on the equation of state and cooling processes. In the recent paper we have presented models which satisfy both cases of Cas A and other cooler stars by considering the quark matter in the core \cite{nod}. As a cooling mechanism in quark matter, the neutrino emission by way of the direct Urca process is well-known and standard, $d\rightarrow u+e^-+{\bar\nu}_e$ , $u+e^-\rightarrow d+\nu_e$ \footnote{If there develops color superconductivity, the phase space is exponentially restricted due to the pairing gap, so that neutrino emission is inefficient \cite{sch}. } . This process works for interacting quarks, while it is strongly prohibited for free and light quarks due to the kinematical condition ({\it triangular condition}) at low temperature. The neutrino emissivity is then efficient and proportional to $\alpha_s T^6$ with the QCD coupling constant $\alpha_s$\cite{iwa80}. Here we discuss a new cooling mechanism, based on the recent development in understanding of the QCD phase diagram: possible appearance of the inhomogeneous phases near the chiral transition \cite{fuk}. Accordingly the chiral condensates modify the elementary process by supplying the extra momentum at the interaction vertex \footnote{Rough idea has been already presented in ref.\cite{nic}.}. This paper is organized as follows. In Sec.~\ref{sec:framework} we present our framework for calculating the neutrino emissivity, where some characteristic aspects associated with the DCDW phase are pointed out. In Sec.~\ref{sec:phase} numerical results for the neutrino emissivity are demonstrated, and their implications for cooling of hybrid stars are briefly discussed in Sec.~\ref{sec:discussion}. Summary and concluding remarks are given in Sec.~\ref{sec:summary}. Properties of the quark propagator is summarized in Appendix~\ref{sec:a}. The evaluation of the weak matrix element is presented in Appendix~\ref{sec:b}, and details of angular integrals for obtaining the emissivity in two limiting cases are given in Appendices~\ref{sec:c} and \ref{sec:d}. | \label{sec:summary} We have proposed a novel cooling mechanism (DCDW cooling) of hybrid stars, based on the idea of the inhomogeneous chiral phase. It originates from the non-perturbative effect of QCD at moderate densities. We have shown that the beta decay process becomes possible in the DCDW phase due to the momentum supply by DCDW at the weak-interaction vertex. The emissivity is estimated near the phase boundaries of the DCDW phase to be the order of $10^{24-26}T_9^6$ (erg$\cdot$ cm$^{-3}$s$^{-1}$), which value may be comparable with that by the quark cooling \cite{iwa80} or pion cooling \cite{max,mut}. Another important point is that this mechanism works in the limited density region where the DCDW phase appears. This feature is similar to the Cooper pair-breaking-formation (PBF) process, where the limited density region is efficient in the superfluid phase \cite{pbf}. If we incorporate this mechanism in the calculation of the cooling curves of young neutron stars, further works are needed which consider the realistic equation of state (EOS) of cold catalyzed quark matter instead of flavor symmetric quark matter and the numerical values of emissivity over the whole region of the DCDW phase without the restriction to the phase boundaries \cite{mar}. The effects of the magnetic field is also an interesting subject, since there should be large magnetic field inside compact stars. The appearance of DCDW looks to be robust and less model-dependent in the presence of the magnetic field \cite{fro,tat2,nis}. In this paper we considered the DCDW phase as a typical inhomogeneous chiral phase, but the similar mechanism may be possible for other configurations such as RKC. It is also interesting to seek for other phenomenological implications of the inhomogeneous chiral phases by considering their elasticity \cite{sot} or magnetic properties. | 14 | 3 | 1403.1927 |
1403 | 1403.4733_arXiv.txt | The results obtained in the search for possible diurnal effect in the {\it single-hit} low energy data collected by DAMA/LIBRA--phase1 (total exposure: 1.04 ton $\times$ yr) deep underground at the Gran Sasso National Laboratory (LNGS) of the I.N.F.N. are presented. At the present level of sensitivity the presence of any significant diurnal variation and of diurnal time structures in the data can be excluded for both the cases of solar and sidereal time. In particular, the diurnal modulation amplitude expected, because of the Earth diurnal motion, on the basis of the DAMA Dark Matter annual modulation results is below the present sensitivity. | The present DAMA/LIBRA \cite{perflibra,modlibra,modlibra2,modlibra3,pmts,mu,review,alllist} experiment, as the former DAMA/NaI \cite{alllist,RNC,ijmd,allDM4}, has the main aim to investigate the presence of Dark Matter (DM) particles in the galactic halo by exploiting the model independent DM annual modulation signature (originally suggested in Ref. \cite{Drukier,Freese}). In particular, they have cumulatively reached a model independent evidence at 9.3 $\sigma$ C.L. for the presence of DM particles in the galactic halo on the basis of the exploited DM annual modulation signature \cite{modlibra3}. In the present work the DAMA/LIBRA--phase1 data (total exposure: 1.04 ton $\times$ yr) are analysed in terms of possible diurnal variation of the rate of the {\it single-hit} events\footnote{i.e. those events where only one of the 25 detectors in DAMA/LIBRA fires; that is, each detector has all the others as anti-coincidence.} in low energy regions, both where the DM annual modulation signal is observed ($2-6$ keV, see Ref. \cite{modlibra,modlibra2,modlibra3} and references therein) and in the region just above ($6-14$ keV) for comparison. Actually a diurnal effect with the sidereal time is expected for DM because of Earth rotation. In Sect. 2 the diurnal modulation of the DM signal as a function of the sidereal time due to Earth rotation velocity contribution will be discussed and some relevant formulae will be presented; this effect is model-independent and has several requirements as the DM annual modulation effect does. Thus, in Sect. 4 the data have been analyzed using the sidereal time referred to Greenwich, also sometimes called GMST. Since potential environmental backgrounds can be in principle correlated with the solar time, the analysis has been also performed in terms of solar time referred to the LNGS site. | The low energy (2--6) keV {\it single-hit} data collected in the whole DAMA/LIBRA--phase1 (7 annual cycles; exposure: 1.04 ton $\times$ yr) \cite{modlibra,modlibra2,modlibra3} have been analyzed in terms of diurnal effects. At the present level of sensitivity the presence of any significant diurnal variation and of diurnal time structures in the data can be excluded for both the cases of solar and sidereal time. In particular, the diurnal modulation amplitude expected -- because of the Earth diurnal motion -- on the basis of the DAMA DM annual modulation results is below the present sensitivity; it will be possible to investigate this diurnal effect with adequate sensitivity only when a much larger exposure will be available, provided a suitable control of the running parameters at the needed level. At present DAMA/LIBRA is continuously running in its new configuration (named DAMA/LIBRA--phase2) with a lower software energy threshold \cite{pmts} which also can offer an alternative possibility to increase sensitivity to such an effect. | 14 | 3 | 1403.4733 |
1403 | 1403.1099_arXiv.txt | {The braneworld scenario, based on the fact that the four dimension space-time is a hyper-surface of a five dimensional manifold, was shown to deal in a satisfactory way with the hierarchy problem. In this work we study macroscopic stellar properties of compact stars from the braneworld point of view. Using neutron star equations of state, we test the possibility of extra dimensions by solving the brane Tolman-Oppenheimer-Volkoff equations obtained for three kinds of possible compact objects: hadronic, hybrid and quark stars. By comparing the macroscopic solutions with observational constraints, we establish a brane tension lower limit and the value for which the Tolman-Oppenheimer-Volkoff equations in the braneworld converge to the usual Tolman-Oppenheimer-Volkoff equations.} | \label{sec:intro} The four fundamental nature interactions (gravity, electromagnetism, strong and weak nuclear forces) were investigated separately during their initial studies and developments. At some point, it became obvious that an unified theory could help the understanding of the primordial universe and its evolution. Two of these fundamental forces (electromagnetism and weak nuclear forces) were then joined in an unique formalism known as the electroweak interaction by Abdus Salam, Sheldon Glashow and Steven Weinberg, but the unification of the other two is still pursued nowadays. Around 1990's, string theory came up as a possible candidate for the {\it theory of everything} or {\it M-theory} because it presented the advantage of conciliating quantum mechanics with gravity by putting aside the idea of particles as the elementary bricks of the universe and explaining them as particular quantum states of strings. String theory started with bosons only and later incorporated fermions and the requirement of extra dimensions was a key point in its development. M-theory assumes the existence of 11 dimensions, some of them treated as hidden dimensions. These extra dimensions of the space-time have since then been used as an attempt to explain several open problems like the existence of dark matter, dark energy, the accelerated expansion of the universe, etc. The braneworld scenario is based on the assumption that the four dimensional space-time is a hyper-surface of a five dimensional manifold. The gravity in the braneworld is a five dimensional phenomenon and the other fundamental interactions are confined to the brane. The braneworld scenario has attracted a lot of interest, because it tackles the hierarchy problem~\cite{rs1} in an effective way. Another attractive property is that the Newtonian law of gravity with a correction is also given in this braneworld scenario~\cite{rs2}. In the Randall-Sundrum (RS) model~\cite{rs1}, one can further add scalar fields~\cite{wise} with usual dynamics and allow them to interact with gravity in the standard way. In this scenario, the smooth character of the solutions generate thick branes with a diversity of structures~\cite{townsend,tow1,tow2,tow3}. In the braneworld scenario an import issue is how gravity and different observable matter fields of the Standard Model of particle physics are localized on the brane. Recently, the localization of fermions and bosons on the brane have received considerable attention in the literature~\cite{shapo,sha1,sha2,sha3,sha4,single,sin1,sin2,mel,chino1,chi1,chi2,casana,ben1,ben2,landim,lan1,lan2,cruz2,cruz2_1,cruz2_2}. On the other hand, in~\cite{germani,bernhardt,ovalle1}, the idea that neutron stars could be a laboratory for testing extra dimensions was first explored. It was found that the star in the braneworld is less compact that in general relativity and an astrophysical lower limit for the brane tension was established. In~\cite{garcia}, brane theory was utilized to estimate the correction in the waves radiated by a binary system and the observational masses of the PSR B1913+16 were then used to constrain the brane tension. Original neutron star models assume that the dense matter in its interior is composed of hadrons (protons and neutrons only or the complete lowest lying baryonic octet) and leptons, responsible for ensuring charge neutrality and $\beta$-equilibrium~\cite{glen}. On the other hand, the Bodmer-Witten conjecture~\cite{Bodmer_Witten_Itoh,Bodmer_Witten_Itoh2,Bodmer_Witten_Itoh3} states that quarks can be deconfined from the hadrons, forming a stable quark matter under certain conditions. Hence, compact stars can be constituted of pure quark matter or perhaps of hybrid matter, containing in their core a pure quark phase or a mixed phase of quarks and hadrons~\cite{glen,mp1,mp1_1,mp2,bielich,yang}. In order to rule out improbable stellar configurations, observational constraints have been used. While most neutron stars have masses of the order of 1.4 M$_\odot$, at least two pulsars, PSR J1614-2230~\cite{demorest} and PSR J0348+0432~\cite{antoniadis} were confirmed to be very massive objects, with masses of the order of $2 M_\odot$. The theoretical calculation of macroscopic stellar properties, as the masses and radii, is done by solving the Tolman-Oppenheimer-Volkoff (TOV)~\cite{tov} equations, which use equations of state (EOS) as input. In this work, we study the effects of the braneworld scenario on the macroscopic stellar properties of compact stars. In that spirit, we revisit the idea of solving a TOV-like system of equations in the braneworld (brane-TOV) and see if the resulting mass and radius results survive the known observational constraints. We also check weather, with more realistic equations of state than the perfect fluid one used in~\cite{germani,garcia}, limits for the brane tension can be established. Furthermore, we show that the star becomes more compact and that the radii can be adjusted to smaller values depending of the brane-TOV parameters. The paper is organized as follows: In Sec.~\ref{sec2}, we present the standard TOV formalism. In Sec.~\ref{sec3}, we give a brief review of the brane-TOV formalism. In Sec.~\ref{sec4}, we use different EOS as input to the brane-TOV equations, present and discuss our results. Finally, in Sec.~\ref{sec5}, we draw our final conclusions. | \label{sec5} In the present work we have revisited the brane-TOV solutions discussed in~\cite{germani,garcia} for realistic equations of state normally used in the literature and compared the results with the ones obtained from the standard TOV solutions. In order to solve satisfactorily the brane-TOV equations we need an equation of state $p=p(\epsilon)$ and additionally an equation of state-like relation $\mathcal{P}=\mathcal{P}(\mathcal{U})$. We have assumed that the Weyl terms obey the simplest relation $\mathcal{P}=w\mathcal{U}$. We have then chosen appropriate EOS for the description of hadronic, hybrid and quark stars as input to the brane-TOV equations. An interesting aspect related to our results is the fact that the brane tension $\lambda$ clearly controls the values of the maximum star masses, while $w$ influences the corresponding radii. We have established a range for $\lambda$ in between $3.89\times10^{36}<\lambda<10^{38}$~dyn/cm$^{2}$. The lower limit is obtained in such a way that at least a $1.44~M_\odot$ star can be achieved. On the other hand, there is a value for which the solutions encountered reproduce the standard TOV solutions. This fact means that, as far as the equations of state survive the observational constraints when the macroscopic properties are computed from the usual TOV equations, they are also suitable as input to the brane-TOV equations. Once the maximum brane tension value is attained, the results are practically independent of the value of $w$ for hadronic stars and very little dependent for hybrid and quarks stars. It is very important to make some comments on the possible values of neutron stars radii. Based on chiral effective theory, the authors of Ref.~\cite{radii} estimate the radii of the canonical $1.4\,M_\odot$ neutron star to lie in the range 9.7$-$13.9 km. More recently, two different analysis of five quiescent low-mass X-ray binaries in globular clusters resulted in different ranges for neutron star radii. The first one, in which it was assumed that all neutron stars have the same radii, predicted that they should lie in the range $R=9.1^{+1.3}_{-1.5}$~\cite{radii2}. The second calculation, based on a Bayesian analysis, foresees radii of all neutron stars to lie in between 10 and 13.1 km~\cite{radii3}. If one believes those are definite constraints, all hadronic, hybrid and quark stars with the choice of EOS studied in the present work survive the observational constraints for values of $w$ in between $-3<w<2$ (excluding an interval of $w$ values around -0.6) for $\lambda=10^{37}$~dyn/cm$^{2}$). For other values of $w$, the brane-TOV solutions produce mass-radius results which fall within the same interval as the ones obtained within our chosen range. We can conclude that one advantage of using the brane-TOV equations is that the radii can be adjusted to smaller values, as seen, for instance in Figure~\ref{fighad:a}. | 14 | 3 | 1403.1099 |
1403 | 1403.1266_arXiv.txt | We probe the structure and composition of the atmospheres of 5 hot Jupiter exoplanets using the Hubble Space Telescope Wide Field Camera 3 (WFC3) instrument. We use the G141 grism (1.1-1.7 $\mu$m) to study TrES-2b, TrES-4b, and CoRoT-1b in transit, TrES-3b in secondary eclipse, and WASP-4b in both. This wavelength region includes a predicted absorption feature from water at 1.4 $\mu$m, which we expect to be nondegenerate with the other molecules that are likely to be abundant for hydrocarbon-poor (e.g. solar composition) hot Jupiter atmospheres. We divide our wavelength regions into 10 bins. For each bin we produce a spectrophotometric light curve spanning the time of transit and/or eclipse. We correct these light curves for instrumental systematics without reference to an instrument model. For our transmission spectra, our mean $1-\sigma$ precision per bin corresponds to variations of 2.1, 2.8, and 3.0 atmospheric scale heights for TrES-2b, TrES-4b, and CoRoT-1b, respectively. We find featureless spectra for these three planets. We are unable to extract a robust transmission spectrum for WASP-4b. For our dayside emission spectra, our mean $1-\sigma$ precision per bin corresponds to a planet-to-star flux ratio of $1.5\times10^{-4}$ and $2.1\times10^{-4}$ for WASP-4b and TrES-3b, respectively. We combine these estimates with previous broadband measurements and conclude that for both planets isothermal atmospheres are disfavored. We find no signs of features due to water. We confirm that WFC3 is suitable for studies of transiting exoplanets, but in staring mode multi-visit campaigns are necessary to place strong constraints on water abundance. | Transiting exoplanets offer unique opportunities for characterization of their atmospheres. Studying the wavelength-dependent depth of planetary transits and eclipses permits constraints on planetary composition and atmospheric structure. These techniques have been applied broadly in studies of hot Jupiters. Transmission spectroscopy was first used to detect atomic sodium \citep{Charbonneau2002a}, and later used to report the detection of molecules such as water \citep{Barman2007} and planetary hazes \citep{Pont2008}. For a detailed review, see \citet{Seager2010}. Broad-band thermal emission studies with Spitzer have enabled the study of thermal inversions and constrained the atmospheric redistribution of energy (see, for example, \citealt{Knutson2008} and \citealt{Desert2011a}). However, there persist challenges in the interpretation of similar data. The broad photometric bands used in many of these studies span multiple absorbers, leading to degeneracies in the interpretation. \citet{Madhusudhan2010a} show that there further exist degeneracies between composition and thermal structure: for example, they showed that the broad-band emission spectrophotometry of TrES-2b \citep{O'Donovan2006} and TrES-4b \citep{Mandushev2007} can be matched with or without thermal inversions, depending on the assumed composition. Further spectroscopic observations in other wavelength regimes are required to break these degeneracies. \citet{Madhusudhan2010a} highlight the potential of spectroscopy in the NIR for such studies owing to the abundant molecular absorption features in this wavelength regime. Space-based NIR transit studies were previously performed with the Near-Infrared Camera and Multi-Object Spectrometer (NICMOS) instrument on the Hubble Space Telescope (HST). Using this instrument, \citet{Swain2008} reported the detection of H$_2$O, and CH$_4$ in the atmosphere of HD189733b, and \citet{Tinetti2010} reported the detection of CO$_2$, H$_2$O, and CH$_4$ in XO-1b . The NICMOS data contained strong systematics and it was necessary to decorrelate the data using a linear function of optical state vectors. \cite{Gibson2011a} explored alternate means for decorrelating the data by reanalyzing past NICMOS datasets. They experimented with using different out-of-transit orbits to decorrelate the data, using a quadratic instead of linear function for decorrelation, and altering the set of parameters used for decorrelation. They found the resulting shape of the extracted spectrum to depend on the decorrelation technique, and they could not confirm the molecules reported by previous studies. \citet{Crouzet2012} analyzed NICMOS archival data of XO-1b, and concluded the uncertainty in correcting for NICMOS instrument systematics was comparable to expected variations due to atmospheric absorption. In a follow-up study, \citet{Gibson2012} used Gaussian processes to analyze the HD189733b NICMOS data and extracted a spectrum that was consistent with \citet{Swain2008}. However, the uncertainties on this spectrum were much higher, and \citet{Gibson2012} found there was no strong evidence for the molecular detections reported by \citet{Swain2008}. However, it is important to note that this perspective is still debated by the original authors \citep{Swain2011}. \citet{Waldmann2013} use an independent component analysis (ICA) on the NICMOS data to derive a spectrum with uncertainties intermediate to \citet{Swain2008} and \citet{Gibson2012}. \citet{Swain2014} conduct a uniform Bayesian model comparison using multiple retrieval algorithms of these spectra, and find that \citet{Swain2008} and \citet{Waldmann2013} are consistent with molecular detections, but \citet{Gibson2012} is not. Follow-up observations are required to validate or refute the reported detections with NICMOS. The Wide-Field Camera 3 (WFC3) \citep{Dressel2012} is the only space-based NIR spectrometer currently in operation suitable for transiting exoplanet observations. The G141 grism on HST is sensitive to 1.1-1.7 $\mu$m. This wavelength range spans a water-absorption feature at 1.4 microns. For solar composition (oxygen rich) hot Jupiters, this feature is not degenerate with any other major predicted atmospheric absorber. The grism also spans an atmospheric window at 1.6 $\mu$m, where no absorption is predicted. Hence measurements here probe the photospheric emission from the planet and may constrain the planetary energy budget. The wavelength coverage of the WFC3 G141 grism largely overlaps with the 1.2-1.8 $\mu$m range of the NICMOS G141 grism, meaning studies of hot Jupiter atmospheres with WFC3 can test claims based on NICMOS data. For example, \citet{Swain2014} point out that the water abundances predicted for HD189733b by the results of \citet{Waldmann2013} and \citet{Swain2008} should produce a 300-400 ppm signature in the WFC3 IR bandpass. Compared to NICMOS, WFC3 has higher throughput\footnote{See \citet{Dressel2012}, specifically \url{http://www.stsci.edu/hst/wfc3/documents/handbooks/currentIHB/c03_optimum_instr4.html}}, and ground-test studies indicate WFC3 is characterized by more uniform intra-pixel sensitivity response than is NICMOS \citep{McCullough2008}. Observations by the higher-performance WFC3, coupled with ground-based studies (e.g. \citealt{Danielski2014}), offer a means to test reported detections with NICMOS. In this paper, we present results from a study of 5 hot Jupiter atmospheres using WFC3. A comparative study with the same instrument minimizes the risk that instrumental effects or choices in the analysis are introducing systematic differences between spectra, and thus may permit us to begin to make statements about hot Jupiters as a class. Our program is part of a larger study of 16 hot Jupiters. The first results of the larger study were released by \citet{Deming2013} and \citet{Mandell2013}. \citet{Deming2013} presented observations of XO-1b and HD209458b in HST drift-scan mode, whereby 'nodding' the telescope over the course of an exposure alleviates data gaps due to buffer dumps and improves the duty cycle.The observations of WASP-12b, WASP-17b, and WASP-19b presented by \citet{Mandell2013}, by contrast, were obtained in the 'staring' imaging mode used by \citet{Berta2011}.The observations presented in this paper were similarly obtained in staring mode. This work presents results from TrES-2b, TrES-4b, and CoRoT-1b \citep{Barge2008} in transit, TrES-3b \citep{Odonovan2007} in secondary eclipse, and WASP-4b \citep{Wilson2008} in both. Table~\ref{tbl:targetparams} summarizes the physical parameters of these objects, and Figure~\ref{fig:massradius} summarizes these worlds in the context of the known transiting Jovian planets. These 5 planets were chosen for their accessibility (from a signal-to-noise perspective) to transit and eclipse studies, resulting from their short-period orbits, large radii, and high effective temperatures. Our sample includes planets with and without reported thermal inversions from previous measurements, as well as "bloated" hot Jupiters, which are gas giants whose radii are larger than expected from conventional equilibrium models. The degree to which the measured radii of the 5 planets disagree with the expectations from structural models varies, from nearly in agreement (TrES-2b), to observed radii that are substantially larger than predicted (TrES-4b). Measurements of the planetary energy budget and composition via the thermal emission and transmission spectroscopy performed in this paper can inform the physical explanation for their variation in physical radii. \begin{figure}[h] \centering \includegraphics[width=15 cm, angle=0]{f1.eps} \caption{Mass-radius diagram for the known transiting Jovian planets ($R>0.5R_{\rm{Jup}}$) with both mass and radius measurements. The planets in the WFC3 program are filled-in black diamonds. The planets analyzed in this paper are filled-in red diamonds. This figure was generated using planet parameters from the Exoplanet Data Explorer, \url{http://exoplanets.org/} \citep{Wright2011}, except for the parameters for the planets in this study, which are from the references in Table~\ref{tbl:targetparams}. We overplot theoretical mass-radius relations from \citet{Fortney2007} in green. The relations plotted are for 4.5-Gyr-old giant hydrogen-helium planets (helium mass fraction $Y=0.28$) orbiting a Solar-type star at 0.1 AU, for heavy element cores of mass of $0 M_{\Earth}$ (pale green), $25 M_{\Earth}$ (green), and $100 M_{\Earth}$ (olive). These relations are provided for a sense of scale only, and should not be taken to rule on whether the exoplanets presented here are bloated, since such a judgement requires detailed modeling involving parameters beyond the mass and radius.\label{fig:massradius}} \end{figure} \begin{table}[h] \begin{center} \caption{Physical parameters of observed exoplanets and their hosts. \label{tbl:targetparams}} \begin{tabular}{p{1.9 cm}p{1.1cm}p{1.1cm}p{1.1cm}p{0.9cm}p{0.9cm}p{0.7cm}p{0.7cm}p{1.0cm}p{4.5cm}} \tableline\tableline Planet & $M_P$ ($M_{\rm{Jup}}$)& $R_P$ ($R_{\rm{Jup}}$) & Period (Days) & $M_\star$ ($M_{\Sun}$)& Sp. Type & $T_{\rm{eq,P}}$\tablenotemark{a} (K) & $T_{\rm{eff,\star}}$ (K)& $H/R_P$\tablenotemark{b} &References \\ \tableline TrES-2b & 1.20 & 1.20 & 2.47 & 0.992 & G0V & 1700 &5850& 0.0036 & \citet{Kipping2011a}\\ TrES-3b & 1.92 & 1.34 & 1.31 & 0.928 & K0V & 2000 &5650&0.0030& \citet{Sozzetti2009}\\ TrES-4b & 0.92 & 1.71 & 3.55 & 1.388 & F8V & 2100 &6200&0.0083& \citet{Chan2011}\\ WASP-4b & 1.24 & 1.37 & 1.34 & 0.925 & G7V & 2000 &5500& 0.0047& \citet{Gillon2009}, \citet{Winn2009}\\ CoRoT-1b & 1.07 & 1.45 & 1.51 & 1.01 & G0V & 2200 &5950&0.0063&\citet{Gillon2009a}, \citet{Barge2008}\\ \tableline \end{tabular} \tablenotetext{a}{Planetary equilibrium temperature estimate. Assumes blackbody stellar emission at $T_{\rm{eff,\star}}$ and zero albedo atmospheres with no redistribution of energy, and are thus meant only to be comparative.} \tablenotetext{b}{Atmospheric scale height, computed by $H=kT/\mu g$, where $T=T_{\rm{eq,P}}$, $g=GM_P/R_P^2$, and the mean molecular mass $\mu=2.20m_p$, where $m_p$ is the proton mass.} \end{center} \end{table} The paper is organized as follows. In Section~\ref{sec:obs}, we describe the collection of our data. In Section~\ref{sec:extract}, we describe the reduction of our data and the removal of instrumental systematics. In Section~\ref{sec:fitting}, we describe how we fit transit and eclipse models to the data, and in Section~\ref{sec:validation} we describe tests we performed to assess the robustness of our analysis. We interpret the resulting transmission spectra in Section~\ref{sec:prelimres}, and summarize our conclusions in Section~\ref{sec:conc}. | } We have derived transmission spectra for 3 hot Jupiters and emission spectra for 2 using the WFC3 instrument on HST. In cases where out-of-transit orbits are available before and after the event, we are able to decorrelate the data entirely without reference to an instrument mode ($divide-oot$). In cases where only one out-of-transit orbit is available, we have validated a minimal two-parameter linear decorrelation to whiten the data, at the cost of significantly reducing parameter estimate precision ($single-oot$). We have demonstrated these decorrelation techniques to be consistent with each other, as well as with an entirely different instrument parameter-dependent decorrelation technique ($differential-eclipse$). We derive consistent spectra with and without flat-fielding and with different choices for background estimation method. TrES-2b, TrES-4b, and CoRoT-1b are featureless to the precision of our data. Transmission spectra of TrES-2b and TrES-4b are well fit by models of both solar-composition and carbon-rich atmospheres. However, our precision is not high enough to differentiate between these cases. CoRoT-1b is not well fit by either model, and as such particularly merits follow-up observations with an enhanced out-of-transit baseline to enable use of the higher-precision $divide-oot$ methodology. Our WASP-4b transmission spectrum is nonrobust: different treatments of the saturation give significantly different results. Hence we do not report results for this dataset. Follow-up observations of WASP-4b, perhaps using an alternative observation strategy like spatial scan mode, or exposing to levels well below nonlinearity, are required to derive this planet's transmission spectrum. Our emission spectra of TrES-3b and WASP-4b do not show evidence of water, implying either isothermal atmospheres or atmospheres depleted in water. Taken in context with previous broadband measurements of the eclipse depth, isothermal atmospheres are disfavored. A carbon-rich atmosphere is consistent with the WASP-4b emission spectrum, while a low-metallicity atmosphere is consistent with the TrES-3b emission spectrum. Our $1-\sigma$ precision in each of the ten bandpasses corresponds to variations of 2.1, 2.8, and 3.0 scale heights for TrES-2b, TrES-4b, and CoRoT-1b respectively. We can rule out atmospheric variation at the level of 10 scale heights and above at $3\sigma$ for all of our planets. Based on this sample, atmospheric models of the kind reported for XO-1b by \citet{Tinetti2010} are not common. Increased precision is required to resolve water on the hot Jupiters we have studied here. Multi-visit observing campaigns obtaining multiple eclipses and transits of a single object are an obvious way to achieve increased precision, especially given that our observations are dominated by photon noise. Our analysis of WASP-4b in transit demonstrates that saturated data may obfuscate analysis; future programs may wish to consider exposing their data to levels well short of nonlinearity to sidestep challenges of reduction. Our work suggests future campaigns should be planned to include orbits before and after the event, as done in other works (e.g. \citealt{Berta2011}, \citealt{Huitson2013}, \citealt{Swain2013}). Photon collection efficiency can also be improved via the spatial scan mode, which optimizes duty cycle by continuously imaging. \citet{McCullough2012} presents recommendations for observing programs using spatial scan mode, and programs like those of \citet{Deming2013}, \citet{Knutson2014}, and \citet{Kreidberg2014} have been able to use these techniques to extract high-precision atmospheric spectra. For example, \citet{Deming2013} are able to achieve precisions of 35 ppm for HD209458b using this technique. Such campaigns by WFC3 promise to open a new age in the characterization of exoplanet atmospheres. | 14 | 3 | 1403.1266 |
1403 | 1403.4396_arXiv.txt | {We estimate the energy input into the solar corona from photospheric footpoint motions, using observations of a plage region by the Hinode Solar Optical Telescope. Assuming a perfectly ideal coronal evolution, two alternative lower bounds for the Poynting flux are computed based on field line footpoint trajectories, without requiring horizontal magnetic field data. When applied to the observed velocities, a bound based solely on displacements between the two footpoints of each field line is tighter than a bound based on relative twist between field lines. Depending on the assumed length of coronal magnetic field lines, the higher bound is found to be reasonably tight compared with a Poynting flux estimate using an available vector magnetogram. It is also close to the energy input required to explain conductive and radiative losses in the active region corona. Based on similar analysis of a numerical convection simulation, we suggest that observations with higher spatial resolution are likely to bring the bound based on relative twist closer to the first bound, but not to increase the first bound substantially. Finally, we put an approximate upper bound on the magnetic energy by constructing a hypothetical ``unrelaxed'' magnetic field with the correct field line connectivity.} | One of the central questions in solar physics is how the Sun's magnetic field transmits energy through the photosphere to maintain coronal temperatures in excess of a million kelvin. Currently, two broad classes of mechanism are favored: wave heating and magnetic reconnection \citep[see, for example, the reviews by][]{Klimchuk2006a,Reale2010b,Parnell2012f}. Here we focus on heating by magnetic reconnection, and in particular on the magnetic braiding scenario \citep{Parker1972,Parker1983ar}. Parker proposed that convective motions in the photosphere will shuffle the footpoints of coronal magnetic field lines, causing the field lines to become entangled, or braided. Crucially, this will lead to locally intense magnetic gradients in the corona, allowing energy to be released in many small reconnection events, now known as ``nanoflares'' \citep{Parker1988ax}. The heating of the atmosphere is suggested to result from this continual energy release. Rather than braiding of flux tubes around one another, it is also possible for photospheric motions to inject energy by twisting individual flux tube footpoints \citep{Sturrock1981a, Zirker1993b}, although this may be less efficient than braiding \citep{Berger1991q}. Recent studies indicate that the particular braiding pattern may have a significant effect on the resultant heating in the corona \citep{Berger2009, WilmotSmith2011}. Coronal heating mechanisms must account for combined conductive and radiative losses from the active region corona of about $10^7\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ \citep{Withbroe1977}. To determine whether the rate of energy input by photospheric braiding motions is sufficient to supply this, consider the rate of change of magnetic energy \begin{equation} W=\int_V\frac{B^2}{8\pi}\,d^3x \label{eqn:energy} \end{equation} in a coronal volume $V$, which is given by \begin{equation} \frac{dW}{dt}= -\frac{1}{4\pi}\int_V{\bf E}\cdot\nabla\times{\bf B}\,d^3x - \frac{1}{4\pi}\oint_{\partial V}{\bf E}\times{\bf B}\cdot{\bf n}\,d^2x. \label{eqn:poynting} \end{equation} The first term on the right-hand side of \eqref{eqn:poynting} represents the volume dissipation of magnetic energy in the corona, while the second is the Poynting flux through the boundary of $V$. We are interested in the Poynting flux through the photospheric boundary $S_0$, which may be written \begin{align} \frac{1}{4\pi}\int_{S_0}{\bf E}\times{\bf B}\cdot{\bf e}_z\,d^2x &= \frac{1}{4\pi}\int_{S_0}v_z(B_x^2 + B_y^2)\,d^2x \nonumber\\ &\qquad - \frac{1}{4\pi}\int_{S_0}B_z(v_xB_x + v_yB_y)\,d^2x, \label{eqn:poyntingS0} \end{align} where we have assumed an ideal Ohm's law ${\bf E}=-{\bf v}\times{\bf B}$. Determining this quantity from observations requires both vector velocity and vector magnetic field data, which remain challenging to obtain at high cadence and high resolution. Our bounds assume $v_z=0$, so can not be applied to regions with significant flux emergence. The idea is to estimate the last term in \eqref{eqn:poyntingS0} from just $v_x$, $v_y$ and $B_z$, without needing to know $B_x$ or $B_y$. Our bounds assume that the coronal magnetic field evolves ideally during the braiding motions, without dissipation. As a result, if we were to move the photospheric footpoints for longer and longer times, we would accumulate more and more energy in the corona. Previous studies have used numerical MHD simulations \citep[e.g.,][]{Mikic1989,Hendrix1996,Galsgaard1996,Gudiksen2002,Bingert2011} or reduced-MHD simulations \citep{Rappazzo2008} driven by photospheric footpoint motions to determine the level at which the energy input saturates. These models suggest that the braiding process leads to heating rates comparable to that of \citet{Withbroe1977}, although the simulations necessarily have coronal dissipation orders of magnitude too high. Our approach is intended to complement these studies by estimating the energy input by a perfectly ideal evolution. \citet{Parker1983ar} made the simple estimate that $dW/dt\approx 10^7\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ by the following argument. Start with a vertical magnetic field of strength $B=100\,{\rm G}$ between $z=0$ and $z=h=100\,{\rm Mm}$. If we displace the footpoint of a flux tube through distance $vt$, then the tube will gain a transverse flux density $B_h=Bvt/h$. The displacement does work against the magnetic stress $BB_h/(4\pi)$, so the power input will be $dW/dt=vBB_h/(4\pi)=v^2B^2t/(4\pi h)$. Using the speed $v=0.4\,{\rm km}\,{\rm s}^{-1}$ suggested by bright-point observations \citep{Smithson1973}, and an assumed time of $t=1\,{\rm day}$ for the energy build-up, a Poynting flux of $10^7\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ is obtained. Importantly, this is comparable to the input required to balance the coronal losses, lending support to the braiding scenario. Subsequent studies have estimated the Poynting flux due to photospheric motions using various assumptions about the \emph{average} properties of photospheric flows \citep[][and the MHD models cited above]{vanBallegooijen1986b,Berger1991q,Berger1993b,Zirker1993}. The aim of this paper is to make quantitative estimates of the Poynting flux for a \emph{specific} dataset of observed photospheric velocities. We start from two rigorous lower bounds on $W$ for a given sequence $v_x(x,y,t)$, $v_y(x,y,t)$ derived by \citet{Aly}\footnote{also J.-J. Aly (private communication).}. The first bound (Section \ref{sec:first}) is based, like Parker's estimate, on the net displacement between the two footpoints of each field line. The second bound (Section \ref{sec:top}) is more sophisticated and based on the relative twisting between pairs of field lines. It draws on the well-established idea that entanglement of magnetic field lines puts a lower bound on the energy of a magnetic field \citep{Taylor1974s,Moffatt1985c,Freedman1991}. Our work builds on that of \citet{Berger1993b}, who derived a lower bound for the energy of a braided magnetic field in terms of relative winding between field lines. Here, we remove his assumption that ${\bf B}$ has a uniform vertical component, and modify the bound slightly so that it is computable solely from a sequence of photospheric velocities. The observational application of the bounds derived in Section \ref{sec:bounds} is presented in Section \ref{sec:results}. It is important to note that, although our lower bounds for $W$ are strict for the chosen Cartesian domain, they depend on the assumed height $h$ of the domain. Moreover, the real coronal magnetic field from a specific photospheric region will likely fill a different shape of domain, and this will also influence the true magnetic energy. However, the lack of definitive methods for coronal magnetic field extrapolation prevents us from accounting for the precise volume. In view of these uncertainties, we find it useful to compare in Section \ref{sec:comps} with two alternative Poynting flux estimates: one obtained with a vector magnetogram, and a hypothetical magnetic field reconstruction having the correct field line connectivity. In addition, to account for possible limitations of our velocity observations, we apply the technique to horizontal velocities taken from a numerical convection simulation. Conclusions are given in Section \ref{sec:conclusions}. | \label{sec:conclusions} In this Paper we have computed two alternative lower bounds for the magnetic energy injected into the solar corona by photospheric footpoint motions, assuming a perfectly ideal coronal evolution. The first bound is based on the displacement between the two footpoints of each field line, and the second bound is based on the relative pairwise twisting of field lines. The advantage of these bounds is that they do not require observations of horizontal magnetic field components in the photosphere, only the initial vertical magnetic field and a sequence of horizontal velocities. We have computed the bounds for an observed sequence of photospheric velocities derived from correlation tracking in Hinode/NFI line-of-sight magnetograms. For the observed data, we find that the first lower bound is approximately 100 times larger than the second. If the height $h$ of the domain is assumed equal to its horizontal extent $L\approx 12\,{\rm Mm}$, then the first bound gives a Poynting flux of $10^7\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$, which is roughly equal to the observed coronal heating rate. However, it is probably more realistic to take a longer domain, say $h=8L$, in which case the estimated Poynting flux is approximately $10^6\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$. A possible reason for this shortfall, compared with Parker's simple estimate of $10^7\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ \citep{Parker1983ar}, is the slower flow speeds in our observations. However, when we compute the bounds for a numerical convection simulation with faster flows (Section \ref{sec:sim}), the first bound is only slightly increased. On the other hand, the simulations do suggest that smoothing of the observed velocity field -- mainly due to resolution limits of the observations -- could be responsible for the discrepancy between the second bound and the first. This indicates that braiding of flux ropes may be a more important source of energy than the observations suggest. On the other hand, both cases show a roughly linear increase in energy with time. \citet{Berger1991q} suggests that such a linear increase is expected if energy is injected mainly by translations of individual flux tubes, and that if energy were mainly injected by entanglement of multiple tubes, a quadratic increase would be expected (as in our simple example in Section \ref{sec:test}). We have also put a (non-rigorous) upper bound on the magnetic energy by constructing a magnetic field whose field lines are effectively the footpoint trajectories (Section \ref{sec:recon}). At the end of the 12-hour dataset, this gives a Poynting flux of $3.5\times 10^8\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$, essentially independent of $h$. At one particular time during our observations, we were able to compare these estimates against a Poynting flux estimate using horizontal magnetic field components from a Hinode/SP vector magnetogram. Reassuringly, the estimate of $1.67\times 10^7\,{\rm erg}\,{\rm cm}^{-2}\,{\rm s}^{-1}$ falls between our lower and upper bounds. Our assumption of a Cartesian domain, and the lack of information on motions at the opposite end of the field lines, mean that our quantitative estimates can only be taken as indicative. And even if the coronal domain were truly Cartesian, there is no guarantee that our lower energy bounds are tight, in the sense of being attainable by relaxation of the magnetic field without allowing reconnection. However, any more detailed estimate would require a model (or observations) of the three-dimensional evolution of the magnetic field in the coronal volume. Such a model would also be required in order to determine when the energy input saturates due to non-ideal dynamics in the corona. It is encouraging that MHD models, which do include this saturation effect - albeit at the expense of an artificially high non-ideal dissipation in the corona - find heating rates comparable to our estimated Poynting flux. Whilst chosen to match the observed average vertical magnetic field, our assumption of an initially uniform field at the start of the footpoint motions does not account for the concentration of magnetic footpoints in intergranular lanes. Since vorticity is known to peak in the intergranular lanes \citep{Wang1995}, this might affect the injected energy. However, the estimated Poynting flux in the simulations -- where the concentration of footpoints is clearly evident -- is comparable to the observations even after concentration has taken place. Such concentration of field line footpoints must be accompanied by an expansion of flux tubes as they pass through the chromosphere to fill the corona. This expansion will not in itself change the connectivity of field lines, but it is likely to impact on the pattern of energy release in the corona \citep{vanBallegooijen1998d}. Since our study concerns only the build-up of energy, this and other aspects of the energy release remain for further investigation. | 14 | 3 | 1403.4396 |
1403 | 1403.7241_arXiv.txt | We revisit the stability of very massive nonrotating main-sequence stars at solar metallicity, with the goal of understanding whether radial pulsations set a physical upper limit to stellar mass. Models of up to $938$ solar masses are constructed with the \Mesa{} code, and their linear stability in the fundamental mode, assumed to be the most dangerous, is analysed with a fully nonadiabatic method. Models above $100\,\MSun$ have extended tenuous atmospheres (``shelves'') that affect the stability of the fundamental. Even when positive, this growth rate is small, in agreement with previous results. We argue that small growth rates lead to saturation at small amplitudes that are not dangerous to the star. A mechanism for saturation is demonstrated involving nonlinear parametric coupling to short-wavelength g~modes and the damping of the latter by radiative diffusion. The shelves are subject to much more rapidly growing strange modes. This also agrees with previous results but is extended here to higher masses. The strange modes probably saturate via shocks rather than mode coupling but have very small amplitudes in the core, where almost all of the stellar mass resides. Although our stellar models are hydrostatic, the structure of their outer parts suggests that optically thick winds, driven by some combination of radiation pressure, transsonic convection, and strange modes, are more likely than pulsation in the fundamental mode to limit the main-sequence lifetime. | \label{sec:intro} The threshold of hydrogen burning ($\approx 0.08~\MSun$) is generally accepted as a physical lower limit to the masses of stars, one that is independent of the environment in which stars form. Whether there is a definite upper limit to stellar masses, and to what extent the limit may depend on nature (stellar physics) or nurture (star-forming environment), are open questions. The highest well-measured dynamical masses are $\sim 80~\MSun$ \citep{Schnurr2012}, most notably the double-lined eclipsing binary WR~20a \citep{Rauw+etal2004, Bonanos+etal2004}. Statistics of stars in galactic open clusters have been interpreted as evidence for an upper limit $\sim 150~\MSun$ \citep{Weidner+Kroupa2004,Oey+Clarke2005,Figer2005,Koen2006}, while \citet{Crowther+etal2010} present spectroscopic arguments for larger masses among the stars in the cluster R136 of the Large Magellanic Cloud. An empirical mass limit, if such exists, may reflect the environment in which most stars are observed to form: that is to say, molecular clouds, where the density of hydrogen nuclei is typically $n \lesssim 10^{3}\unit{cm^{-3}}$, the temperature $\lesssim 100\unit{K}$, and dust is abundant. One of us has previously argued that the broad-line regions of bright QSO accretion disks are likely self-gravitating and prone to form very massive stars -- at least several hundred solar masses at the onset of gravitational instability, and perhaps $\ga 10^5~\MSun$ after accretion up to the isolation mass \citep{Goodman+Tan2004,Jiang+Goodman2011}. A QSO disk at $\sim 10^3$ gravitational radii from the black hole is a very different environment from a molecular cloud: denser by many orders of magnitude, hotter than the sublimation temperature of dust, rapidly rotating and shearing, and dominated by radiation pressure rather than gas pressure. Hence a different initial-mass function and maximum stellar mass might result in such disks than in giant molecular clouds. On the other hand, it is well known that very massive stars are fragile due to the predominance of radiation over gas pressure, radiatively driven winds, and pulsational instabilities. Thus it is possible that internal physics establishes an upper limit $\lesssim 10^2\text{--}10^3~\MSun$. A presumably fatal relativistic instability sets in above $10^5\text{--}10^6~\MSun$, depending upon internal rotation (\citealt{Chandrasekhar1964,Baumgarte+Shapiro1999,Montero+Janka+Mueller2012}, and references therein). This leaves a gap of several orders of magnitude above the largest observed masses, however. In the present paper, we return to the question of pulsational instabilities driven by the $\kappa$- and $\epsilon$-mechanisms, which are sensitive to composition via opacities and to nuclear reaction rates. This is a problem that has been considered by many authors since the original work by \citet{Schwarzschild+Haerm1959}, and one might have thought it a closed subject. However, the understanding of the opacities and other microphysical inputs has evolved, while the effects of convection on the linear growth rates remain uncertain, as do the mechanisms responsible for nonlinear saturation of the pulsations if they grow at all. We focus on the fundamental radial mode, on the assumption that it is most dangerous. \cite[hereafter GK93]{Glatzel+Kiriakidis1993} have analyzed the stability of solar-metallicity stars up to $120\,\MSun$ and found a host of higher-order modes that grow more quickly than the fundamental. However, the energies of these modes are concentrated in the outer parts of the star, so that they can be expected to reach nonlinear amplitudes before the bulk of the mass is much affected. The fundamental involves the entire star. Its character and scaling with mass are unlike those of other modes. The pulsation period increases $\propto M^{1/2}$, whereas those of higher-order radial modes scale $\propto M^{1/4}$. This is due to the predominance of radiation pressure, $\Prad/\Pgas\propto M^{1/2}$ for $M\gtrsim 100\,\MSun$, which makes very massive nonrotating stars almost neutrally stable against changes in radius even in the adiabatic approximation. Thus at large amplitudes ($\delta r/r\gtrsim 1$), the fundamental mode might disrupt or collapse the entire star. The former requires unbinding the star, which becomes less difficult with increasing mass because of the predominance of radiation pressure and the attendant near-cancellation of gravitational and potential energies in hydrostatic equilibrium. (Indeed, spontaneous disruptions occurred in the simulations of AGN disk fragmentation by \cite{Jiang+Goodman2011}, though they were caused by numerical energy errors rather than pulsations.) Collapse might occur under extreme compression due to electron-positron pairs at central temperatures approaching $10^9\unit{K}$, or due to relativistic corrections to gravity at masses $>10^4\MSun$ \citep{Zeldovich+Novikov1971}. Recently, \citet[hereafter SQA]{Shiode+Quataert+Arras2012} have revisited the $\epsilon$-mechanism. Applying a quasi-adiabatic analysis to equilibrium models constructed with the \Mesa{} code \citep{Paxton_etal2011,Paxton_etal2013}, they concluded that the instability is suppressed by the effective viscosity due to turbulent convection, at least for stars of masses $\la 1000~\MSun$. However, they did not consider any models above $100~\MSun$ with solar or higher metallicity. Since QSO disks appear to be metal rich, with metallicities perhaps up to ten times solar \citep{Hamann+Ferland1999,Dietrich+etal2003,Matsuoka+etal2011,Batra2014}, one motivation for the present work was to repeat SQA's analysis at higher metallicities \emph{and} masses $> 10^2~\MSun$. We also wanted to perform a fully non-adiabatic rather than quasi-adiabatic analysis. This is arguably less important for the $\epsilon$-mechanism because it is driven deep within the star where the thermal time is very long. However, SQA also found evidence for instabilities driven by opacity variations in the envelope which they did not fully explore, perhaps because they had less confidence in the quasi-adiabatic approximation for those modes. Also, at least with modern opacities, the envelopes of high-mass stellar models at solar metallicity differ strikingly from those of corresponding Population~III models, and this has interesting consequences for the mode structures. Linear stability analysis is only a first step toward answering the question posed above. If instabilities are found, one must consider how they may saturate in order to decide whether they are likely to shorten the main-sequence lifetime. Early attempts to address the saturation of instabilities driven by the $\epsilon$-mechanism gave conflicting results \citep{Appenzeller1970,Papaloizou1973b}, but little work has been done along these lines in recent decades. We will argue that even if the uncertain damping effects of convection are neglected, the linear growth rates are so small compared to the real part of the pulsation frequency that the pulsations will saturate by one or another weakly nonlinear mechanism at small amplitudes that do not threaten the survival of these stars, at least not before they have lived out most of the nominal minimum main-sequence lifetime ($\sim 3\times 10^6\unit{yr}$). Instead, in view of the structure of our hydrostatic models, as well as a recent body of work on Wolf-Rayet and O-star winds, radiatively driven mass loss seems more likely likely than pulsational instabilities to limit the lifetimes of the most massive, metal-rich stars. We hope to explore the scaling of the mass-loss timescale (i.e., $\lvert M/\dot{M}\rvert$) with stellar mass in a future paper. The outline of this paper is as follows. Section~2, supplemented by an Appendix, presents the equilibrium \Mesa{} models and our methods for the linear stability analysis. Section~3 highlights the extended atmosphere or `shelf' seen in the higher-mass models. Results for the growth rates and eigenfunction of the fundamental are given in \S4, with particular emphasis on nonadiabatic effects in the shelf. \cite{Glatzel+Kiriakidis1993}'s intrinsically nonadiabatic `strange modes' are shown to extend to higher masses, where they have longer periods than the fundamental. \S5 examines nonlinear saturation of the fundamental through 3-mode or parametric coupling to high-order nonradial g-modes, and (more briefly) saturation of strange modes in shocks. Since the stably-stratified zones of our most massive models are relatively small, and would perhaps disappear entirely at some higher mass, the explicit estimates in \S5 are intended to be illustrative of a larger class of weak nonlinearities that will limit the amplitude of the fundamental when its growth rate is small. A summary of our conclusions and a discussion of future steps follows in \S6. | \label{sec:conclusion} We have re-examined the stability of the fundamental radial mode of very massive main-sequence stars. Although nonradial and higher-order radial modes may also be unstable, we focus on the radial fundamental because collapse or explosion of these radiation-pressure-dominated objects would begin with this mode at linear order. In agreement with \citeauthor{Shiode+Quataert+Arras2012}, we find that the linear growth rate is sensitive to turbulent convective damping. We have extended their results to higher masses at solar metallicity, and we have used a fully nonadiabatic rather than quasi-adiabatic method, which allows us to treat the $\kappa$-mechanism more reliably. The $\epsilon$ mechanism is more important for our most massive models we consider, however. The linear growth rates remain uncertain not only because of the turbulent bulk viscosity, but also because of the tenuous (and possibly unphysical) envelopes possessed by all of our models above $100~\MSun$. In fact we find negative growth rates even without convection, apparently due to radiative damping in the shelf. Nevertheless, the growth rate should in any case be extremely small even if positive, $\omegai/\omegar \sim \Pi_0/\tKH$, due to the relatively low central concentrations of these stars and correspondingly large mode masses. We have then argued from the smallness of the linear growth rate (in case this is positive) that the radial fundamental should saturate at a small amplitude due to any one of a number of weak nonlinearities. To support this claim, we have estimated the saturation amplitude that would result if parametric coupling to high-order g~modes were the most important nonlinearity. For our most massive model, the estimate is $\delta R/R \approx 3\times10^{-3}$. Other nonlinear couplings may stop the growth at even smaller amplitudes, but those we identify would depend on uncertain parameters such as the star's rotation rate or magnetic field. We have also shown that our models, like those of GK93, are subject to a class of intrinsically nonadiabatic modes having much larger growth rates but confined to the shelf: strange modes. These we estimate to saturate at fractional surface displacements of a few percent via shocks. Their contribution to mass loss, if any, can be reliably estimated only in the context of a time-dependent wind model that includes a number of other nonlinear effects, such as line driving. However, even at saturation, the energy of the strange modes in the stellar core is neglegible, and therefore they probably affect the bulk of the star only secularly. A number of physical simplifications and compromises have been made: restriction to solar metallicity; neglect of rotation; and neglect of perturbations to the convective flux. Increased metallicity might produce even more extended ``shelves'' in the equilibrium models, and larger growth rates for the modes driven by the epsilon mechanism. However, presuming that the growth rates of the fundamental mode varied roughly linearly with $Z$, they would remain very small compared to the dynamical time even at metallicities ten times solar, such as may obtain in AGN disks \citep{Dietrich+etal2003,Nagao+etal2006}. Rotation is expected to have a stabilizing influence on the fundamental mode at very high masses because it contributes to the perturbed energy under homologous changes in radius somewhat like gas rather than radiation pressure \citep{Baumgarte+Shapiro1999}. This could be important for very massive stars formed in an AGN disk, and perhaps continually accreting from that disk, since such objects would probably rotate rapidly \citep{Goodman+Tan2004,Jiang+Goodman2011}. Neglect of perturbations to the convective flux has surely caused quantitative errors in the growth rates. \cite{Guzik+Lovekin2012}, using a prescription for such perturbations that incorporates a time delay in the convective response, find that super-Eddington luminosities can occur during part of the pulsation cycle, perhaps leading to mass loss. However, their analysis is limited to the outer parts of the star. More importantly, their prescription relies on mixing-length theory, which may not be reliable in the extremely-radiation-pressure-dominated shelf regions \citep{Jiang+etal2015}. Despite these simplifications and uncertainties, it seems likely that the growth rate of the fundamental mode must be extremely small compared to the reciprocal of the dynamical time, and therefore that pulsations in the fundamental will saturate nonlinearly at small amplitudes too small to disrupt or collapse the star---at least on the main sequence. We conclude that thermally driven pulsations of the radial fundamental mode do not limit the main-sequence lifetimes of very massive stars. The tenuous outer envelopes of the more massive \Mesa{} models, however, which stem from an opacity bump at $\sim 10^5\unit{K}$, lead us to suspect that these stars would have powerful winds if the hydrostatic constraint were lifted, and that the mass-loss timescale ($M_*/\dot{M}$) may be much less than one million years, though necessarily longer than the Kelvin-Helmholtz timescale ($\approx 3000\unit{yr}$). The lower bound would be achieved only if all of the stellar luminosity were converted to the mechanical energy of a wind with vanishing asymptotic velocity at infinity. For a very massive star embedded in a dense AGN disk, continued accretion from the disk might easily exceed the wind losses, perhaps causing it to grow to such a mass as to undergo relativistic instability. These results suggest a few directions for future research. It will be relatively straightforward to explore the effect of super-solar metallicities on the linear growth rates. Changes in the growth rates as the models evolve away from the zero-age main sequence could also be studied, although we have not yet succeeded in evolving our most massive \Mesa{} models to the end of their main-sequence phases. Probably more important, but also more challenging, will be to determine the mass-loss timescale. Several physical mechanisms will have to be considered, including line-driven winds \citep{CAK75}; inhomogeneous optically-thick winds \citep{Owocki2015}; and perhaps winds driven by nonlinear strange modes or other radiation-driven instabilities. Still more mechanisms may operate in late stages of stellar evolution, such as wave-driven winds \citep{Quataert+etal2015}. The range of possibilities is narrowed if one focuses on mechanisms that operate early in the life of a star and that are capable of removing much of its initial mass in much less than the nominal main-sequence lifetime. Even so, multi-dimensional calculations with frequency-dependent radiative transfer may be required. | 14 | 3 | 1403.7241 |
1403 | 1403.7288_arXiv.txt | The recent detection in archival HST images of an object at the the location of supernova (SN) iPTF13bvn may represent the first direct evidence of the progenitor of a Type~Ib SN. The object's photometry was found to be compatible with a Wolf-Rayet pre-SN star mass of $\approx 11$ $M_\odot$. However, based on hydrodynamical models we show that the progenitor had a pre-SN mass of $\approx 3.5$ $M_\odot$ and that it could not be larger than $\approx 8$ $M_\odot$. We propose an interacting binary system as the SN progenitor and perform evolutionary calculations that are able to self-consistently explain the light-curve shape, the absence of hydrogen, and the pre-SN photometry. We further discuss the range of allowed binary systems and predict that the remaining companion is a luminous O-type star of significantly lower flux in the optical than the pre-SN object. A future detection of such star may be possible and would provide the first robust identification of a progenitor system for a Type~Ib SN. | \label{sec:intro} An important remaining problem in astrophysics is finding the links between supernovae (SN) and progenitor stars. For core-collapse SN it is accepted that they arise from massive stars. Of particular interest is the origin of hydrogen-deficient SN (Types Ib and Ic), where the mechanism to remove or deplete the outer hydrogen envelope is not well determined. The most appealing alternatives are strong stellar winds in high-mass massive stars ($M \gtrsim 25 M_\odot$) and mass transfer in close binary systems (see \citet{langer12} for a recent review). Which is the dominant path for this type of SN is still unclear and the answer depends on performing detailed studies of well-observed objects. A young type Ib SN (He-rich, H-deficient), iPTF13bvn, was discovered by the Palomar Transient Factory on 2013 June 16 in the nearby galaxy NGC~5806. Using multi-band pre-explosion images from HST, a source was identified (within the $2 \sigma$ error box of the SN location) as the possible progenitor \citep{cao13}. The luminosity and colors of the progenitor candidate are consistent with some Wolf-Rayet stars \citep{massey06}, one of the proposed progenitors of H-deficient SNe. Based on single stellar evolution models, \citet{groh13b} found that a Wolf-Rayet star with Zero Age Main Sequence (ZAMS) mass of 31--35 M$_\odot$ was able to reproduce the observed pre-SN photometry. According to their model, at the moment of the explosion the star had a mass of 11 $M_\odot$. The search for progenitor stars in deep pre-explosion images is a powerful, direct approach to understand the origin of SNe and it provides a critical test for stellar evolution models. Using this technique it was possible to confirm that type II-P SNe arise from the explosion of red supergiant stars \citep{smartt09}. But so far no firm progenitor identification has been reported for H-deficient SNe \citep{yoon12,groh13a,eldridge13}. iPTF13bvn may be the first case in its class, thus allowing us for the first time to directly link a SN~Ib with its progenitor. In most cases, either because the SN is too distant or simply due to lacking pre-supernova images, other methods are required to infer progenitor properties. One such method is the hydrodynamical modeling of SN observations. It is a well-known fact that the morphology of the light curve (LC) is sensitive to the physical characteristics of the progenitor \citep[e.g. see][]{nomoto93,blinnikov98}. Therefore, modeling of the LC, ideally combined with photospheric velocities or spectra, provides a useful way to constrain progenitor properties such as mass and radius, as well as explosion parameters (explosion energy and production of radioactive material). This methodology is particularly powerful when combined with stellar evolution calculations. A recent example of the predictability of this technique can be seen in our analysis of the Type~IIb SN~2011dh \citep{bersten12,benvenuto13}, which allowed us to provide a self-consistent explanation of the progenitor nature that was later confirmed \citep{vandyk13,ergon14}. Here we use the same approach to address the problem of the progenitor of iPTF13bvn. The observational material used in this work is briefly described in \S~\ref{sec:data}. In \S~\ref{sec:hydro} we present our hydrodynamical modeling of iPTF13bvn with focus on determining the mass and size of the progenitor. In \S~\ref{sec:binary} we further analyze the origin of iPTF13bvn and of the pre-explosion object, and we propose an interacting binary progenitor. The range of allowed binary models is discussed in \S~\ref{sec:companion}, where we also predict the feasibility of detecting of the companion star in future observations. In \S~\ref{sec:conclusion} we present the main conclusions of this work. | \label{sec:conclusion} Our hydrodynamical analysis of iPTF13bvn pointed to the explosion of a low-mass helium star (of $\approx 3.5$ $M_\odot$) with a relatively low explosion energy (of $\approx 7 \times 10^{50}$ erg) and normal production of radioactive material ($M_{\mathrm{Ni}}\approx 0.1$ $M_\odot$). Interestingly, from the LC rise time we could conclude that this relatively normal event managed to produce a quite strong \Ni\ mixing. Our conclusion about the low pre-SN mass is robust because of the strong constraint on the explosion time and it is not affected by the systematic uncertainty of $0.1$ dex in luminosity. Our LC modeling is in contradiction with a Wolf-Rayet progenitor for iPTF13bvn as suggested by \cite{groh13b}. In order to explain the explosion of a low-mass helium star, we proposed the possibility of an interacting binary progenitor. We showed that a system composed of 20~$M_\odot$ + 19~$M_\odot$ stars and an initial orbital period of $4.1$ days can fully satisfy all the observational constraints (pre-explosion mass, chemical composition and HST photometry). The primary star is expected to dominate the flux of the progenitor in the optical, so as a result of the SN explosion we predict that the flux in the observed bands will decrease significantly when the SN fades. We went one step beyond and studied the possible binary configurations that could lead to compatible solutions for all the observational requirements with the focus on making predictions about the putative companion star. We found that the remaining star should necessarily be close to the ZAMS with a range of luminosities of $4.6 \lesssim \mathrm{Log}(L^{\mathrm{f}}_2/L_\odot) \lesssim 5.6$ This means that the companion star may be detected in the future with deep HST imaging in the UV--blue range. The detection of the companion would produce the first robust identification of a hydrogen-deficient SN progenitor as a binary system. While recent evidence suggests a large fraction of massive stars belong to interacting binary systems \citep{sana12}, it is still not clear whether this is the main channel to produce hydrogen-free SN. The combination of hydrodynamical SN models and close binary evolution calculations proves to be a powerful tool for understanding the nature of these events in a self-consistent way. Finally, we studied the implications on the progenitor size by modeling the early $R$-band LC. Contrary to what might be expected from its monotonic rise, we showed that not only compact structures (of a few $R_\odot$) but also relatively extended envelopes ($\lesssim 150$ $R_\odot$) are allowed with the present cadence of the observations. Our calculations suggest that sub-night cadence is required to distinguish among progenitor sizes in the above range. Ongoing surveys such as KISS (Kiso Supernova Survey) or future programs like ZTF (intermediate Palomar Transient Factory and Zwicky Transient Facility) will be able to provide the necessary frequency of observations to solve this kind of problem. | 14 | 3 | 1403.7288 |
1403 | 1403.5244_arXiv.txt | For a narrow band of values of the top quark and Higgs boson masses, the Standard Model Higgs potential develops a shallow local minimum at energies of about $10^{16}$ GeV, where primordial inflation could have started in a cold metastable state. For each point of that band, the highness of the Higgs potential at the false minimum is calculable, and there is an associated prediction for the inflationary gravitational wave background, namely for the tensor to scalar ratio $r$. We show that the recent measurement of $r$ by the BICEP2 collaboration, % $r=0.16 _{-0.05}^{+0.06}$ at $1\sigma$, combined with the most up-to-date measurements of the top quark and Higgs boson masses, reveals that the hypothesis that a Standard Model shallow false minimum was the source of inflation in the early Universe is viable. | 14 | 3 | 1403.5244 |
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1403 | 1403.5134_arXiv.txt | Isospin-violating dark matter (IVDM) provides a possible mechanism to ameliorate the tension among recent direct detection experiments. For IVDM, we demonstrate that the results of direct detection experiments based on neutron-rich target nuclei may depend strongly on the density dependence of the symmetry energy which is presently largely unknown and controls the neutron skin thickness that reflects the relative difference of neutron and proton form factors in the neutron-rich nuclei. In particular, using the neutron and proton form factors obtained from Skyrme-Hartree-Fock calculations by varying the symmetry energy within the uncertainty region set by the latest model-independent measurement of the neutron skin thickness of $^{208}$Pb from PREX experiment at JLab, we find that, for IVDM with neutron-to-proton coupling ratio fixed to $f_n/f_p=-0.7$, the form factor effect may enhance the sensitivity of Xe-based detectors (e.g., XENON100 and LUX) to the DM-proton cross section by a factor of $3$ in the DM mass region constrained by CMDS-II(Si) and even by more than an order of magnitude for heavy DM with mass larger than $80$ GeV, compared with the results using the empirical Helm form factor. Our results further indicate that the form factor effect can significantly modify the recoil spectrum of Xe-based detectors for heavy IVDM with $f_n/f_p=-0.7$. | \label{sec:intro} The possible existence of dark matter (DM) is one of the most intriguing aspects of modern particle physics, astrophysics and cosmology. In order to survey the nature of DM, a number of observations and experiments have been conducted or are underway around the world. The most recent cosmological results based on {\it Planck} measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra indicate that DM comprises about $27\%$ of the energy density of the Universe which also includes about $5\%$ baryon matter and about $68\%$ dark energy~\cite{Plk13}. Many theories beyond the Standard Model of particle physics predict natural candidates for DM, e.g., the weakly interacting massive particles (WIMPs) which are a class of hypothetical stable neutral particles with a huge range in masses from $1$ GeV to $100$ TeV and interaction cross sections with normal matter (proton) from $10^{-40}$ to $10^{-50}$ cm$^{2}$~\cite{Ste85,Jung96}. In terrestrial laboratory, DM might be directly detected through their elastic scattering off nuclei in particle detectors~\cite{Goodman85}. A number of underground DM direct detection experiments have been performed, and among them an excess of events over the expected background has been observed by CoGeNT~\cite{CoGeNT11}, DAMA~\cite{DAMA09}, CRESSTII~\cite{CRESST12} as well as in the recent results presented by the CDMS-II(Si) collaboration~\cite{CDMS13v1,CDMS13v2}. However, these results are in strong tension with the constraints set by some other experimental groups like XENON100~\cite{XENON100v11,XENON100v12}, LUX~\cite{LUX13} and SuperCDMS(Ge)~\cite{SCDMS14}, leaving a confusing situation for the community. This has led to a number of attempts trying to explain the discrepancy by considering atomic uncertainties~\cite{Sav11} or different mechanisms that deviate from standard assumptions about DM interactions or its astrophysical distributions~\cite{Tuc01,Fra12,Mao13,Cot13}. Isospin-Violating Dark Matter (IVDM) provides a very promising mechanism to reconcile the tension among different experiments~\cite{Kur04,Giu05,Cha10,Feng11,Feng13a,Feng13b,Nag13,Vin13}. Within the IVDM framework, DM is assumed to couple differently with protons and neutrons, and this assumption of the isospin violation has been supported by a number of theoretical works~\cite{Fra11,Cli11,Del12,He12,Gao13,Oka13} based on the particle physics point of view. Many parameters need to be specified in the standard method of analyzing DM direct detection experiments~\cite{Lew96} and recently Frandsen~{\it et al.}~\cite{Fran13} presented a systematic discussion on the possible ways to ameliorate the tension among different experiments. They found that the tension between the CDMS-II(Si) results and the XENON100 bounds is independent of the astrophysical uncertainties concerning the DM halo and any momentum- and velocity-dependence of the cross section in particle physics, but it can be largely ameliorated or even resolved within the framework of IVDM. Besides the uncertainties in astrophysics and particle physics concerning the interaction of a DM particle scattering off a single nucleon mentioned above, the uncertainties in nuclear physics describing how the struck nucleon is distributed inside the nucleus may also play an important role in interpreting DM signals. This is because in DM direct detection experiments, the nuclear form factors are generally applied to describe the DM-nucleus cross section and the bounds on DM-nucleon cross section are then obtained accordingly. In particular, the empirical Helm form factor extracted from nuclear charge distributions~\cite{Helm56,Duda07} has been commonly adopted in current direct detection experiments. However, the DM-nucleus interaction should be in principle described by using the form factors of both proton and neutron distributions in the nuclei rather than the charge distributions since the DM particles actually interact with the protons and neutrons in the nuclei. Within the framework of relativistic mean field (RMF) model, Chen~{\it et al.}~\cite{ChenYZ11} derived the nuclear form factor for the spin-independent scattering between the WIMPs and nucleus, and they found that the results can deviate from the empirical Helm form factor by $15\%$ to $25\%$ in a large range of recoil spectrum of $0 \sim 100$ keV. A recent work by Co' {\it et al.}~\cite{Co12} suggests that the use of different distributions for protons and neutrons instead of the commonly used empirical charge distributions for a target nucleus could be important in interpreting DM signals, especially if IVDM is considered. For stable nuclei, the proton distribution can be well determined from the charge distribution which can be accurately measured with electron scattering~\cite{Hof56,Frois77,Dej87}. In contrast, the neutron distribution is usually determined from hadron scattering experiments and the results are generally highly model dependent due to the unclear non-perturbative strong interaction~\cite{PREX12}. Recently, the Lead Radius Experiment (PREX) collaboration at Jefferson Laboratory (JLab) published their results on the measurement of the parity-violating cross section asymmetry in the elastic scattering of polarized electrons from $^{208}{\rm Pb}$~\cite{PREX12}, which provides a model-independent determination of the neutron density distributions in $^{208}{\rm Pb}$. The PREX measurement leads to a value of $\sqrt{\left\langle r_{\rm n}^2 \right \rangle} =5.78_{-0.18}^{+0.16} \,\, {\rm fm}$ for the rms radius of the neutron distributions for $^{208}{\rm Pb}$, implying a large neutron skin thickness, i.e., $\Delta r_{\rm{np}}=\sqrt{\left\langle r_{\rm n}^2 \right \rangle} - \sqrt{\left\langle r_{\rm p}^2 \right \rangle} = 0.33_{-0.18}^{+0.16} \,\, {\rm fm}$ by assuming a point-proton rms radius of $5.45$ fm~\cite{Ong10}. One can see that the obtained value of $\Delta r_{\rm{np}}$ has a large error, indicating a large uncertainty of the neutron distribution relative to the proton distribution in $^{208}{\rm Pb}$. Theoretically, it has been established~\cite{Horo01,Brown01} that the $\Delta r_{\rm{np}}$ is intimately related to the nuclear matter symmetry energy which characterizes the isospin dependent part of the equation of state (EOS) of asymmetric nuclear matter (ANM)~\cite{LCK08}. In particular, it has been shown recently that the $\Delta r_{\rm{np}}$ of heavy nuclei is uniquely determined by the density slope $L(\rho_{\rm c})$ of the symmetry energy at a subsaturation cross density $\rho_{\rm c}\approx0.11$ fm$^{-3}$~\cite{Zha13}. These features imply that the uncertainties of $\Delta r_{\rm{np}}$, especially the neutron distributions, predicted by various nuclear models are essentially due to our poor knowledge about the symmetry energy. The symmetry energy is of critical importance for understanding not only the structure and reaction of radioactive nuclei, but also a number of interesting issues in astrophysics, such as the structure of neutron stars and the mechanism of supernova explosions, and has become a hot topic in current research frontiers of nuclear physics and astrophysics~\cite{EPJAEsym14}. The determination of the symmetry energy provides a strong motivation for studying isospin-dependent phenomena with radioactive nuclei at a number of new/planning rare isotope beam facilities around the world, such as CSR/Lanzhou and BRIF-II/Beijing in China, RIBF/RIKEN in Japan, SPIRAL2/GANIL in France, FAIR/GSI in Germany, SPES/LNL in Italy, RAON in Korea, and FRIB/NSCL and T-REX/TAMU in USA. In this work, using the proton and neutron form factors obtained from Skyrme-Hartree-Fock calculations by varying the symmetry energy slope parameter $L(\rho_c)$ within the uncertainty region set by the PREX experiment, we investigate the form factor effects in the direct detection of dark matter. This article is organized as follows. We briefly introduce in Sec.~\ref{sec:model} the theoretical models and methods used in the present work, and then present the results and discussions in Sec.~\ref{sec:sym}. Finally, a conclusion is given in Sec.~\ref{sec:conclusion}. | \label{sec:conclusion} In the present work, we have shown that isospin-violating dark matter (IVDM) indeed provides a possible mechanism to ameliorate the tension among recent direct detection experiments, including CDMS-II(Si), XENON100, LUX, and SuperCDMS(Ge). For IVDM, we have demonstrated that the results of the DM direct detection experiments based on neutron-rich target nuclei, e.g., Xe-based detector, may strongly depend on the density slope $L(\rho_c)$ of the symmetry energy at a subsaturation cross density $\rho_c \approx 0.11 $fm$^{-3}$, which is presently largely unknown and uniquely determines the neutron skin thickness and thus the relative difference of neutron and proton form factors of the target nuclei. In particular, using the proton and neutron form factors obtained from Skyrme-Hartree-Fock calculations by varying the $L(\rho_c)$ within the uncertainty region set by the latest model-independent measurement of the neutron skin thickness from PREX experiment at JLab, we have found that although the form factor effects on the extracted bounds on DM-proton cross sections are negligible in the direct detection for isospin-invariant DM, they could become critically important in the detection for IVDM. Especially, for IVDM with neutron-to-proton coupling ratio fixed to $f_{\rm n}/f_{\rm p}=-0.7$ in the mass region constrained by CMDS-II(Si), the form factor effect may enhance the sensitivity of Xe-based detectors (e.g., XENON100 and LUX) to the DM-proton cross section by a factor of $3$, compared with the results using the empirical Helm nuclear form factors extracted from charge distributions. This form factor effect can even enhance the sensitivity by more than a factor of $10$ for such kind of IVDM with mass larger than $80$ GeV. Furthermore, we have found that the form factor effect can significantly modify the recoil spectrum of Xe-based detectors for heavy IVDM with $f_{\rm n}/f_{\rm p}=-0.7$. We have also studied how the form factor effects change with the variation of $f_{\rm n}/f_{\rm p}$ and found that the $f_{\rm n}/f_{\rm p}$ value maximumly suppressing the sensitivity of the detector may depend on the form factor, and the form factor effects can either enhance or suppress the sensitivity of the detector relative to the Helm's case depending on the specific value adopted for $f_{\rm n}/f_{\rm p}$. Our results imply that the precise determination of the symmetry energy or the neutron skin thickness (and thus the neutron and proton form factors) of $^{208}$Pb is extremely useful for the direct detection of IVDM based on detectors with neutron-rich targets (e.g., xenon). | 14 | 3 | 1403.5134 |
1403 | 1403.7527.txt | We investigate the amount and spatial distribution of interstellar dust in edge-on spiral galaxies, using detailed radiative transfer modeling of a homogeneous sample of 12 galaxies selected from the CALIFA survey. Our automated fitting routine, FitSKIRT, was first validated against artificial data. This is done by simultaneously reproducing the SDSS $g$-, $r$-, $i$- and $z$-band observations of a toy model in order to combine the information present in the different bands. We show that this combined, oligochromatic fitting, has clear advantages over standard monochromatic fitting especially regarding constraints on the dust properties. We model all galaxies in our sample using a three-component model, consisting of a double exponential disc to describe the stellar and dust discs and using a S\'ersic profile to describe the central bulge. The full model contains 19 free parameters, and we are able to constrain all these parameters to a satisfactory level of accuracy without human intervention or strong boundary conditions. Apart from two galaxies, the entire sample can be accurately reproduced by our model. We find that the dust disc is about 75\% more extended but only half as high as the stellar disc. The average face-on optical depth in the V-band is $0.76$ and the spread of $0.60$ within our sample is quite substantial, which indicates that some spiral galaxies are relatively opaque even when seen face-on. | A part of the interstellar medium (ISM) is made up from dust grains, created mainly in the atmospheres of AGB stars \citep{2006A&A...447..553F, 2011ApJ...727...63D} and during supernova explosions \citep{1998ApJ...501..643D, 2010ASPC..425..237C, 2014ApJ...782L...2I}. Apart from their role in a number of physical and chemical processes, like catalyzing the production of molecular hydrogen and consequently regulating star formation \citep{1971ApJ...163..155H}, dust grains are important as they absorb at least one third of the UV/optical light in galaxies \citep{2002MNRAS.335L..41P}. By using far-infrared (FIR) and submm observations, it has become possible to determine the total dust mass in galaxies with a reasonable accuracy. Especially since the launch of the {\it Herschel} Space Observatory \citep{2010A&A...518L...1P}, the dust mass can be directly estimated by fitting a modified blackbody or more advanced models to the observed spectral energy distribution \citep[e.g.,][]{2011MNRAS.417.1510D, 2012ApJ...745...95D, 2013MNRAS.436.2435S, 2014arXiv1402.3597C}. However, apart from a few nearby targets, these observations lack the spatial resolution to resolve the individual regions and getting a more detailed picture of the dust distribution. An alternative approach consists of determining the dust masses and distribution from the extinction effects caused by dust on UV and optical starlight. In this case, the necessary resolution is easily attained and the observations are cheap and easy to obtain. The drawback is that it is not straightforward to determine the total mass and the distribution of the dust from the observed level of extinction \citep{1989MNRAS.239..939D, 1992ApJ...393..611W, 1994ApJ...432..114B, 1995MNRAS.277.1279D, 2001MNRAS.326..733B, 2005MNRAS.359..171I} . To adequately determine these properties from extinction all the necessary physics like the absorption efficiency, scattering rate, etc. for different dust compositions and distributions have to be accounted for. In other words, one has to rely on dust radiative transfer modeling. Thanks to an increase in computational power and the development of efficient algorithms, dust radiative transfer codes have become increasingly more realistic and powerful. They can now be applied to arbitrary geometries, and include physical processes as absorption, multiple anisotropic scattering, polarization, thermal and non-thermal emission \citep[e.g.][]{2001ApJ...551..269G, 2003MNRAS.343.1081B, 2011ApJS..196...22B, 2006MNRAS.372....2J, 2008A&A...490..461B, 2011A&A...536A..79R}. An overview of the most important developments, advantages and disadvantages of different approaches regarding 3D dust radiative transfer codes can be found in \citet{2013ARA&A..51...63S}. As the creation of these radiative transfer models of spiral galaxies can be an arduous task, most of these studies focus on a very limited number of targets or even a single galaxy \citep[e.g.][]{1987ApJ...317..637K, 2000A&A...362..138P, 2011A&A...527A.109P, 2000A&A...359...65B, 2001ApJ...548..150M, 2001A&A...372..775M, 2010A&A...518L..39B, 2011ApJ...741....6M, 2012MNRAS.419..895D, 2012MNRAS.427.2797D, 2012ApJ...746...70S}. Most of these studies have targeted spiral galaxies with an inclination close to 90 degrees, as these offer some unique advantages. In particular, because of the edge-on projection, the separate components of the galaxy, i.e.\ the stellar disc, dust disc and central bulge, are clearly distinguishable. Unfortunately, the varying observational input used for the modeling, and the different assumptions, geometries and physical ingredients in the radiative transfer models themselves make it almost impossible to compare these studies and draw general implications on the amount and distribution of dust in spiral galaxies. What is needed is a radiative transfer study of a sizable sample of galaxies, all modeled in a homogeneous way based on similar data. There have been only two such efforts in the literature: \citet[][hereafter \citetalias{1999A&A...344..868X}]{1997A&A...325..135X, 1998A&A...331..894X, 1999A&A...344..868X} and \citet[][hereafter \citetalias{2007A&A...471..765B}]{2007A&A...471..765B} both modeled a set of seven edge-on spiral galaxies with prominent dust lanes. The main conclusions of these works are that the dust disc tends to be larger radially than the stellar disc while being thinner in the vertical direction. However, there is still some uncertainty on the ratio of the dust and stellar scale length as different methods to determine the size of the dust disc results in values from being from only 10\% larger \citep{2009ApJ...701.1965M} up to 100\% or even more \citep{2005AJ....129.1396H, 2010A&A...509A..91T, 2011ApJ...741....6M}. In the cases where the FIR/submm observations were able to resolve the dust disc, similar values for the dust scale height and length were found as the ones determined from fitting radiative transfer models to optical/NIR observations \citep{2013A&A...556A..54V, 2014arXiv1402.5967H}. One of the most important quantities concerning the dust distribution in spiral galaxies is the face-on optical depth $\tau_{\text{V}}^{\text{f}}$. A large number of papers looked into this parameter, resulting in often contradicting conclusions \citep{1990Natur.346..153V, 1994MNRAS.266..614V, 1991Natur.353..515B, 1992ApJ...400L..21B, 1993PASP..105..993B, 1995ApL&C..31..143B, 1998A&A...334..772B, 2003AJ....126..158M}. The importance of this value is not to be underestimated: galaxies with $\tau_{\text{V}}^{\text{f}}<1$ would be almost completely transparent when seen face-on, whereas higher values for $\tau_{\text{V}}^{\text{f}}$ would indicate that a significant fraction of the stars in spiral galaxies could be invisible. The latter case has far-reaching consequences for the use of spiral galaxies in a cosmological context, as it would, for example, invalidate most determinations of mass-to-light ratios. Another important aspect to consider is the ratio between the stellar and dust scale height. According to \citet{2004ApJ...608..189D} there should be a clear transition at the critical rotation speed of 120 km\,s$^{-1}$ where the more massive galaxies have a well-defined, thin dust disc, while the less massive galaxies have a more diffuse and bloated dust disc. A similar feature was also observed by \citet{2011ApJ...741....6M} whose radiative transfer models contain a dust disc which has a scale height similar to or larger than the stellar disc and therefore does not have an obvious dust lane, contrary to the relatively much thinner dust discs in galaxies with a higher surface brightness. They suggest that the origin might be a combination of the two possible explanations: either their galaxies have a larger stability against vertical collapse, as expected using the results described in \citet{2004ApJ...608..189D}, or the extraordinary thin nature of the stellar discs in their sample. In this paper we study a set of edge-on spiral galaxies by using detailed radiative transfer models in order to determine their stellar and dust morphology and, subsequently, their face-on optical depth. The selection of our sample, the largest sample so far upon which detailed radiative transfer modeling has been applied, is discussed in Sect.~{\ref{SampleSelection.sec}}. In Sect.~{\ref{RT.sec}} we present our modeling technique, which should be objective and preferably automated. We use an updated version of FitSKIRT \citep{2013A&A...550A..74D}, an automated optimizing code around the radiative transfer code SKIRT \citep{2011ApJS..196...22B} to construct models which accurately reproduce the observations. The most important new feature of the code is the oligochromatic fitting\footnote{oligo- or olig-, as in oligopoly, oligarchy or oligosaccharide, derived from the Greek {\em{ol{\'\i}gos}}, meaning "few" or "a little". So oligochromatic fitting is the modeling of a small number of images simultaneously.}, which is discussed and thoroughly tested on an artificial data. The results of our fits and an individual discussion of each galaxy in our sample is presented in Sect.~{\ref{Results.sec}}. We make some remarks about the quality of the models in general, compare and validate our results against results available from other studies, and discuss the results of both the stellar and dust properties of our sample in Sect.~{\ref{Discussion.sec}}. Our conclusions are presented in Sec.~{\ref{Conclusions.sec}}. | \label{Conclusions.sec} We have selected 12 edge-on, spiral galaxies from the CALIFA survey in order to constrain both their stellar and dust distribution. This was done by computing accurate radiative transfer models to the SDSS $g$-, $r$-, $i$- and $z$-band images simultaneously. As the galaxies are part of the CALIFA survey they already comply to the following criteria: the redshift ranges between $0.005 < z < 0.03$ and the isophotal $r$-band diameter ranges from 45 to 80 arcsec. The galaxies with an obvious dust lane were then selected while avoiding the strongly asymmetrical or interacting ones. As final selection criterium we exclude galaxies with a major axis smaller than 1 arcmin or a minor axis smaller than 8 arcsec as to ensure the dust lane has a high enough resolution to be modeled accurately. Before using our automated fitting routine, FitSKIRT, we have tested and validated its capabilities by applying it to a test case described in \cite{2013A&A...550A..74D}. The mock image was created using the radiative transfer code SKIRT, in order to compare both the ability to reproduce the image as well as the recovery of the input values. We found that FitSKIRT was able to give reasonable constraints on all free parameters describing the stellar disc, stellar S\'ersic bulge and dust disc. It is shown that the oligochromatic fitting, i.e. fitting to a number of bands simultaneously, has clear advantages over monochromatic fitting in terms of accuracy. In particular the parameters describing the dust distribution have a smaller spread as the oligochromatic fitting method is less prone to degeneracies in the free parameters. Of the 25000 most central pixels, about 80\% have a value that deviates 20\% or less from the corresponding pixel in the reference image. With these results we can safely apply the method to real data. The results of the fits to the 12 galaxies in our sample can be found in Table~\ref{Results.tab} while the sample averages, spread and accuracy can be found in Table~\ref{MeanValues.tab}. For only two galaxies (UGC\,4163 and NGC\,5908) in our sample, we found that the model, consisting of a exponential disc to describe the stellar and dust distribution and a S\'ersic profile to model the central bulge, was not able to accurately reproduce the observations. In all other cases we were able to model the galaxies and constrain the parameters to an acceptable accuracy. In all of the residual frames more than half of the pixels show deviations of at most 25 \%. Stellar disc and bulge parameters are determined within 10 and 15\% respectively while the dust parameters are less certain, with error bars rising up to 20 or 30\% for the face-on optical depth. We find that the average disc scale length and intrinsic disc flattening is in good agreement with the results described by \citet{2002MNRAS.334..646K} and \cite{2009MNRAS.393.1531G}. Our sample, on the other hand, does seem to have larger bulges with an average effective radius of $2.31\pm1.59$~kpc. Possible explanations for this difference are the fact that we do not include a bar in our model and a possible selection effect due to the necessity to have a clear dust lane while \cite{2009MNRAS.393.1531G} does not take into account the effect of dust attenuation on the determined bulge parameters. Consequently a slightly higher bulge-to-total ratio is found although we find a similar trend in the ratios as a function of wavelength. For the dust scale length and height we find a good agreement with \citetalias{1999A&A...344..868X} and \citetalias{2007A&A...471..765B}. Also the relative sizes of the dust disc compared to the stellar disc are in good agreement where we find that the dust disc is about 70\% more extended, which is slightly larger than found by \citetalias{1999A&A...344..868X} and \citetalias{2007A&A...471..765B}, but twice as thin as the stellar disc. From \cite{2004ApJ...608..189D} we should expect to see a transition for galaxies with a rotation speed of 120 km\,s$^{-1}$ where the slower rotating ones should have a dust disc scale height similar to the one of the stellar disc. Using the baryonic Tully-Fisher relation to get estimates on the rotation speed based on the stellar mass of the galaxies we do not seem to find a similar trend in our sample. A possible explanation might again be that our sample has a clear tendency for larger bulges compared to the bulgeless galaxies investigated by \cite{2004ApJ...608..189D} and \cite{2011ApJ...741....6M}. An important aspect of the dust distribution in spiral galaxies is the face-on optical depth. A value of higher than 1 means a significant part of the light would be blocked even when the galaxy is seen face-on. In our sample we find a large spread ranging from 0.18 to 1.98 with an average V-band value of $0.76$ and spread within the sample of $0.60$. As a result, a fraction of the galaxies should not be transparent even when seen completely face-on. This is a slightly larger value in optical depth and in spread than what was previously found by \citetalias{1999A&A...344..868X} and \citetalias{2007A&A...471..765B}. This could be the result of our galaxies requiring a visible dust lane while the galaxies are at larger distance compared to the sample investigated by \citetalias{1999A&A...344..868X} and \citetalias{2007A&A...471..765B}. Therefore the galaxies in our sample are relatively more dust rich than galaxies selected on a dust lane at smaller distances. The same difference in distance of this sample and the HRS sample investigated in \cite{2012A&A...540A..52C} could explain why our galaxies reside on the higher side of the relation between the dust-to-stellar mass and the stellar mass. This is an unexpected result, as deriving the dust mass from extinction usually results in values which underestimate the actual dust mass determined from FIR observations by a factor of 3 \citep{2000A&A...362..138P, 2011A&A...527A.109P, 2001A&A...372..775M, 2004A&A...425..109A, 2005A&A...437..447D, 2010A&A...518L..39B}. A useful way to follow up this research would be to investigate this difference by modeling these galaxies by the means of detailed panchromatic radiative transfer simulations covering the entire SED from the UV to the FIR \citep{2010A&A...518L..39B, 2012MNRAS.427.2797D, 2012MNRAS.419..895D}. Comparing the FIR fluxes predicted from the radiative transfer models determined in this paper with the observed fluxes would yield further insights into the dust energy balance of spiral galaxies. | 14 | 3 | 1403.7527 |
1403 | 1403.3238_arXiv.txt | { We report the detection and characterization of two short-period, Neptune-sized planets around the active host star Kepler-210. The host star's parameters derived from those planets are (a) mutually inconsistent and (b) do not conform to the expected host star parameters. We furthermore report the detection of transit timing variations (TTVs) in the O-C diagrams for both planets. We explore various scenarios that explain and resolve those discrepancies. A simple scenario consistent with all data appears to be one that attributes substantial eccentricities to the inner short-period planets and that interprets the TTVs as due to the action of another, somewhat longer period planet. To substantiate our suggestions, we present the results of N-body simulations that modeled the TTVs and that checked the stability of the Kepler-210 system.} | Since the launch of the {\it Kepler} Mission in 2009, a large number of planetary candidates has been found using the transit method in the high precision {\it Kepler} light curves. Specifically, 2321 planetary candidates in 1790 hosts stars have been reported, from which about one third are actually hosted in multiple systems \citep{2012arXiv1202.5852B}. The majority of these {\it Kepler} planetary candidates are expected to be real planets \citep{2012ApJ...750..112L} and therefore those stars present an excellent opportunity for a more detailed study and characterization through the method of transit timing variations (TTVs). Ever since the first proposals of the method by \cite{2005MNRAS.359..567A} and \cite{2005Sci...307.1288H}, TTVs have been widely used to search for smaller, otherwise undetectable planets in systems containing already confirmed planets. In multiple systems this method can be applied in order to confirm the physical validity of the system along with a rough estimate of the components' mass, which can otherwise be obtained only through radial velocity data. For the {\it Kepler} candidates the {\it Kepler} team has carried out and reported this kind of analysis for 41 extrasolar planet systems. For the last announcement of the series see \cite{2013MNRAS.428.1077S}. In this paper we present our in-depth analysis and results for a particular system, Kepler-210 (=KOI-676), which was previously identified and listed as a planet host candidate in the catalog by \cite{2011ApJ...736...19B}. The specific characteristics of Kepler-210 that enticed us to perform a detailed study of this candidate system were the high activity of its host star coupled with the fact that the system harbors two transiting planets, which we validate using spectral and TTVs analysis, as well as stability tests. The plan of our paper is as follows. In the first section we describe the methods used to determine the stellar and planetary properties. In the second section we discuss various scenarios to explain the detected discrepancies in the orbital elements of the planets. Furthermore, we describe the results of our TTVs analysis for both planets, and finally, we summarize with what we believe is the most probable scenario. \begin{figure}[tp] \includegraphics[width=\linewidth]{lcls} \caption{The Lomb-Scargle Periodogram for the raw lightcurve as logarithmic power (on y axis) vs. period. A polynomial fit was applied to remove systematics related to the rotation of the telescope.}\label{lsstar} \vspace{-0.4cm} \end{figure} \begin{figure*}[htp] \label{stellaract} \includegraphics[width=\textwidth]{fluxndet.eps} \caption{A fraction of the Kepler-210 lightcurve. Top: Part of the raw lightcurve demonstrating the activity of Kepler-210. Bottom: The transits of planet a (green) and b (red) for that particular time, with the stellar activity removed by using the kepflatten routine of the Pyke package for pyraf.}\label{stellaract} \end{figure*} | \subsection{Examination of stellar properties} \label{sect:age} In order to better determine the stellar parameters of Kepler-210, a high resolution spectrum was acquired, using the CAFE instrument on the 2.2 m telescope of the Calar Alto Observatory in Spain. For our analysis we also used two spectra of Kepler-210, taken from the CFOP\footnote {https://cfop.ipac.caltech.edu} web page. We specifically inspected the spectra for a second set of lines indicating the existence of a close unresolved companion but found none. For the same purpose we also examined the pixel area around the star using the Kepler target fits frames, but found again no evidence of any variable star in the vicinity of the central star that could create a contaminating signal. To measure the color index B-V, we observed Kepler-210 together with with two standard stars (HD 14827 and HD 195919), using the 1.2 m Oskar-L\"uhning-Telescope (OLT) from Hamburg Observatory and found B-V$_{Kepler-210}$ = 1.131 $\pm$ 0.064, consistent with the color derived from CFOP (1.088 $\pm$ 0.037) and other sources; thus the spectral type of Kepler-210 is in the late K range. We then proceeded to estimate the stars age using the gyrochronology expression \ref{age} derived by \cite{2007ApJ...669.1167B} \begin{eqnarray}\label{age} log(t_{gyro}) &=& {1\over n}\{log(P)-log(\alpha)-[\beta \cdot log(B-V-0.4)]\}, \end{eqnarray} where t is in Myr, B-V is the measured color, P (in days) is the rotational period, $n = 0.5189$, $\alpha = 0.7725\pm 0.011$ and $\beta = 0.601\pm 0.024$. By using Eq.\ref{age} with P = 12.33 days and the B-V = 1.131, we estimate an age of 350 $\pm$ 50 Myrs for Kepler-210; this estimate appears reasonable given its high degree of activity. \subsection{Mean stellar density} When a planet is transiting in front of its parent star, we have the opportunity to accurately derive the ratio between the stellar radius $R_{\star}$ and the orbital semimajor axis $a$ (cf., Table \ref{planetkeys}). Combining this information with Kepler's third law, we can compute an expression for the mean density $\rho _{mean}$ of the host star through \begin{equation} \label{rhomean} \varrho _{\star,mean} = \frac{3 \pi} {G} \frac {a^3} {R^3_{\star} \ P^2}, \end{equation} \noindent with $G$ denoting the gravitational constant in addition to the terms containing only {the observed quantities a/R$_{\star}$ and period P. The value for a/R$_{\star}$ is derived from the transit modeling, given the large number of transits, for both planets, the values of a/R$_{\star}$ and P can be estimated with relatively high accuracy.} Carrying out this computation using the observed parameters for planets b and c (cf., Table \ref{planetkeys}) we obtain densities of $\varrho_{\star,b}$ = 0.27 $\pm$ 0.004 $g/cm^3$ and $\varrho_{\star,c}$ = 0.46 $\pm$ 0.038 $g/cm^3$ , respectively for the host. On the other hand, based on the nominal stellar parameters of the host star we expect a mean density of $\varrho_o $ $\approx$ 2.6 $g/cm^3$. Thus the mean host star densities derived from planets b and c are, first, inconsistent with each other, and second, differ by almost an order of magnitude from the expected host star density. Since we firmly believe in Kepler's third law, there must be a physical explanation for both discrepancies. \subsubsection{Ellipticity of planetary orbits} \label{sec:Elipt} \begin{figure}[tp] \includegraphics[width=\columnwidth]{phodegen.eps} \caption{Contour plot of eccentricity versus true anomaly during the mid-transit ($\phi$). For a circular system (e = 0) the density should equal $\varrho_o \; \backsimeq$ 2.6 $g/cm^3$, as can be calculated for the given values of $R_{\star}$ and $M_{\star}$. The TBD derived from the $a/R_{\star}$ values of $\varrho_{\star}$ for the planets Kepler-210b (black line) and Kepler-210c {(gray line)} can be explained for eccentricities $\gtrsim$ 0.4 and $\gtrsim$ 0.51 respectively, depending on the true anomaly of the planet during the mid-transit. The dashed lines represent the uncertainty limits.} \label{phidegen} \end{figure} \begin{figure}[bp] \includegraphics[width=\columnwidth]{new_i_rs_rp.eps} \caption{The variation of inclination, $R_{\star}$ and $R_{p}$, assuming third light interference $F^3$ for Kepler-210c} \label{newirsrp} \end{figure} So far our analysis has implicitly assumed circular orbits for both planets. For elliptical orbits the orbital speed and hence the transit duration change during the orbit and therefore there is no unique relation between transit duration and stellar and planetary dimensions. Assuming that the orbital velocity is constant during the actual transit, \cite{2005ApJ...627.1011T} relate the transit duration $D_{ell}$ to the period $P$ and the impact parameter $b$ of a transit through the expression \begin{equation} \label{dur} D_{ell} = \frac{\sqrt{(1 - e^{2})}} {1 + e\cdot cos(\phi _t)} \frac{P}{\pi} \frac{\sqrt{(R_{\star}+R_{pl})^2 - b^2)}}{a}, \end{equation} \noindent where $\phi _t$ denotes the true anomaly at the mid-transit, while $R_{\star}$, $R_{pl}$ and $a$, denote stellar and planetary radii and semi-major axis respectively. Consequently, the transit duration $D_{ell}$ of an elliptical orbit scales with the transit duration $D_{circ}$ of a circular orbit (for the same system geometry and the same period) through \begin{equation} \label{circel} D_{ell} = \frac{\sqrt{(1 - e^{2})}} {1 + e\cdot cos(\phi _t)} \times D_{circ} = g(e, cos(\phi _t)) \times D_{circ}. \end{equation} \noindent It is straightforward to convince oneself that the derived sizes for star and planet scale with the scaling function $g(e, cos(\phi _t))$ introduced in Eq.\ref{circel}. Since the mean stellar density scales with $R^3_{\star}$, we find \begin{equation} \label{mdenro} \varrho_{\star ,ell} = \varrho_{\star, circ} \cdot\left({\sqrt{1-e^2}} \over {1+e \cdot cos \phi _t} \right)^{-3} \end{equation} \noindent with $\varrho_{\star, circ} = \varrho_{\star, mean}$ from Eq.\ref{rhomean}. Hence the discrepant stellar densities can be explained by introducing suitable eccentricities and true transit anomalies. By solving \ref{mdenro} for different values of $e$ and $\phi _t$ it is thus possible to to constrain the range of permissible eccentricities as well as values for $\phi _t$, for which the derived stellar density becomes equal to the density expected for the spectral type of the star for both planets; the corresponding curves are shown in Fig. \ref{phidegen}, where we plot for each planet the combination of $e$ and $\phi _t$ resulting in a nominal stellar density of 2.7 $g\ cm^{-3}$. Fig. \ref{phidegen} shows that eccentricities of 0.4 (for planet b) and 0.5 (for planet c) are required to produce the expected stellar densities. \subsubsection{Second (third) light scenario} \begin{figure}[bp] \includegraphics[width=\columnwidth]{3rdl.eps} \caption{Derived stellar density versus assumed third light contribution $F_3$} \label{3rdl} \end{figure} Despite the fact that neither the optical spectrum nor the centroid analysis of the {\it Kepler} data have shown any evidence for a companion or blend, it might still be possible that some {third} object in the background or foreground with flux $F_3$ contributes to the system flux in a way that the observed total flux $F_{obs}$ is given by \begin{equation} F_{obs} = F^\star + F_3 , \end{equation} \noindent where $F^\star$ is the desired planet host's flux, which has to be used for the transit modeling. If this {hypothetical} third light contribution $F_3$ is substantial, the true transit depth $d_{true}$ would be underestimated and {an incorrect radius for the Kepler-210 host star would be derived}. Assuming that the limb darkening coefficients are identical and equal to the values presented in Table \ref{stellarkeys} for all system sources, we calculate the influence of the third light source on the derived stellar density (as shown in Fig.\ref{3rdl}), {considering the following non-linear system of equations}, which allows computing the stellar and planetary radii (each scaled by the semi-major axis) $\tilde{R}_\star$ and $\tilde{R}_p$ and, $i$, the inclination of the orbit normal with respect to the line of sight, given the observed period $P$, the observed time between the first and forth contact, $T_{14}$, the time between the second and third contact, $T_{23}$ and the observed (relative) transit depth at mid-transit $d_{obs}$. \begin{eqnarray} \label{seteq3rdl} sin^{2}i\:cos^2 \left({{\pi}\over{P}}T_{14}\right) &=& 1-(\tilde{R}_\star + \tilde{R}_p)^{2} \\ sin^{2}i\:cos^2 \left({{\pi}\over{P}}T_{23}\right) &=& 1-(\tilde{R}_\star - \tilde{R}_p)^{2} \end{eqnarray} and \begin{eqnarray} \label{seteq3rdl2} d_{true} = \frac{(1- c_1-c_2)+(c_1+2c_2)\:\mu_c-c_2\mu_c^{2}}{1-{c_1\over 3}-{c_2\over 6}}\left(\tilde{R}_p\over \tilde{R}_\star\right)^{2} \end{eqnarray} \noindent Here $c_1$ and $c_2$ denote the quadratic limb darkening coefficients and $\mu_c$ denotes the expression \begin{equation} \mu_c = \sqrt{1-\frac{cos^{2}i}{\tilde{R}_\star^{2}}}. \end{equation} \noindent We clearly need the true transit depth $d_{true}$ to compute the values of $\tilde{R}_\star$, $\tilde{R}_p$ and $i$, yet only the observed transit depth $d_{obs}$ is available; the two depths are related, however, through \begin{equation} d_{true} = (1 + d_{obs})\frac{F_3}{F^\star}. \end{equation} {Therefore, given the observed values of $d_{obs}$, $T_{14}$ and $T_{23}$ and the observed periods $P$ for both planets}, the derived values for $\tilde{R}_\star$ and hence $\varrho_{\star }$ will depend on the assumed third light contribution $F_3/F^{\star}$. {The resulting system of equation is quite non-linear. In order to provide a feeling on how sensitive the solutions depend on the third light contribution $F_3/F^{\star}$, we plot in Fig. \ref{newirsrp} the variation of the derived values for the inclination and stellar and planetary radii (for the planet Kepler-210c), relative to the case of no third light. As is clear from Fig. \ref{newirsrp}, the inclination increases only slightly (it cannot exceed 90 degrees), while the stellar radius decreases (as desired) and the planetary radius increases. Finally, we can derive the stellar density, for which} our results are shown in Fig. \ref{3rdl}, where we plot the derived stellar densities for both planets as a function of the assumed third light contribution $\frac{F_3}{F^\star}$. As is clear from Fig. \ref{3rdl}, the third light contribution would have to be substantial, and in fact {the third light would have to dominate the total system flux in order to obtain values of $\varrho_{\star c}$ as expected for stars on the main sequence in the relevant spectral range.} Yet, the two planets still yield discrepant densities of their host, so one would have to introduce yet another host for the second planet, which appears at least a little contrived. Therefore we conclude that the introduction of a third light source does not lead to a satisfactory solution of inconsistency in the derived stellar parameters. \subsubsection{Inflated star} Another possible scenario explaining the {\it Kepler} observations of Kepler-210 would be the assumption that the host is not on the main sequence, but rather evolved and in fact a giant or sub-giant. Such stars are usually not active, however, there are some classes of evolved stars which are quite active, for example, variables of the FK Com type. Those stars are highly active G-K type sub-giant stars with surface gravities log(g) of $\sim$ 3.5. They show strong photometric rotational modulations caused by a photosphere covered with inhomogeneously distributed spots. An other important characteristic of these objects is their rapid rotation. Generally the $v\:sini$ derived from their spectra is between $\sim$ 50 and 150 $km\cdot s^{-1}$ \citep{2005LRSP....2....8B}. In the case of Kepler-210 $v\:sini$ is $\sim$ 4 $km\cdot s^{-1}$, and thus we believe that a FK-com scenario does not provide a suitable explanation for the observed density discrepancy. \subsection{Kepler-210 TTVs} \hspace{3 ex} As described in sec. \ref{sec:ttvs}, TTVs are detected in both planets. In order to further examine the properties of these variations we searched for any periodicities in the O-C data by constructing a Lomb-Scargle periodogram on every set. For the outer and larger planet, the Lomb-Scargle periodogram shows a leading period of about 690 days, which is apparent in the modulation of the O-C curve in Fig.\ref{ocdiag}, while for the inner and smaller planet the periodicity results remain ambiguous, most probably due to the large scatter in its O-C diagram. \begin{table}[bp] \begin{center} \caption{$\chi^2$ results of the model for 2 eccentric planets hypothesis, 3 non eccentric planets and 3 eccentric planets. In the square brackets are listed the degrees of freedom.}\label{ttvchisqr} \begin{tabular}{rrrr} \hline \hline \\[-8pt] & 2 ecc Planets & 3 non ecc Planets & 3 ecc Planets\\ \hline \\[-6pt] b & 489.57 [420] & 447.9 [415] & 443.9 [415] \\ c & 116.22 [86] & 112.4 [81] & 117.59 [81] \\ \hline \end{tabular} \end{center} \end{table} What would be a physical scenario consistent with these O-C diagrams? We first note that the orbital period ratio of the system is very close to a 13/4, if we consider that the errors in periods in Table \ref{planetkeys} are also affected by the TTVs. This ratio is not close to any low order mean motion resonance so the amplitude of any TTVs is expected to be relatively small for both planets \citep{2005MNRAS.359..567A}. In order to verify this and to model the TTVs we use the N-body code as presented in the same paper. The N-body code requires the planetary masses which are unknown. {Assuming ad hoc that the planetary densities are below 5 g/cm$^3$, it is clear that the masses of the two planets are substantially below 0.5 M$_J$. Furthermore, in order to roughly estimate the planetary masses below that limit,} we use a general mass vs. radius law as described by \cite{2011ApJS..197....8L} in the form \begin{eqnarray}\label{eqmasrad} M_{p} = R_{p}^{2.06} \end{eqnarray} \begin{figure}[tp] \includegraphics[width=\columnwidth]{2eccplmodel.eps} \caption{TTVs expected for two planets assuming eccentric orbits {with e$_b$ = 0.44 and e$_c$ = 0.50.}} \label{2ecc} \end{figure} \noindent With the masses thus specified, we first considered only the two transiting planets for our TTVs simulations. Assuming non-eccentric orbits resulted in TTVs of less than a minute, which is far from the observed variations for both planets. The TTVs would remain in that state even if we assume higher masses, under the limit of 12 M$_{J}$. As discussed in detail by \cite{2012ApJ...761..122L}, the TTVs amplitude can also be affected by eccentricity. Implementation of eccentric orbits for both planets, Kepler-210b and Kepler-210c, improved the fit substantially; the modeled TTVs together with the data are shown in Fig.\ref{2ecc}, the fit results in terms of fit quality measured through $\chi ^2$ are given in Table \ref{ttvchisqr}. Clearly, also the TTVs analysis supports a scenario of two planets with rather eccentric orbits similar to our discussion in \ref{sec:Elipt}. However, in order to produce the observed TTVs the system configuration must be such that the true anomaly, of both planets at the time of transit, $\phi_{t}$, should exceed 40$^{\circ}$, while also the difference in true anomaly $\Delta\phi_{t}$ should be $\sim$ 60$^{\circ}$, However, this configuration appears impossible due to the physical constraints in Fig.\ref{phidegen}. Furthermore, our stability tests, (which performed with the ${\bf swift\_rmvs3}$ algorithm \citep{1994Icar..108...18L}, show that this configuration is unstable on time scales in excess of $\sim$ 1 Myear. {Finally we note that the probability of observing a transit is higher for small values of true anomaly, i.e., for the times near periastron passage.} We therefore conclude that a scenario with only two planets with eccentric orbits is unlikely and introduce a third, hypothetical planet KOI-676.03 in order to stabilize the system. {We consider both eccentric and non-eccentric orbits for Kepler-210b and Kepler-210c. In order to determine period, mass and eccentricity for the hypothetical planet KOI-676.03, we considered several possible system configurations.} {We emphasize that we cannot derive a unique solution for the physical parameters of this hypothetical planet. Most importantly, we need to assume a mass for this planet, which controls the strength of the gravitational interaction with the observed planets Kepler-210b and Kepler-210c. Thus, given the observed TTVs amplitude and given the assumed mass of KOI-676.03, a certain value of semi-major axis and hence period is derived. The higher the assumed mass, the longer the resulting period, and thus there is more than one configuration to account for the detected TTVs signal.} {In order to produce possible candidate systems, we carried out simulations assuming some given mass for KOI-676.03, considering periods between 20 to 300 days, masses in the range $M_{03} \sim$ 0.1-0.6 M$_J$ and eccentricities e $\simeq$ 0.1-0.3. A particularly promising configuration, but by no means unique solution, consistent with all {\it Kepler} data, has a period P $\simeq$ 63 days;} in Fig.\ref{3noecc} and again Table \ref{ttvchisqr} (for the case with zero eccentricity) and in Fig.\ref{3ecc} and Table \ref{ttvchisqr} (for the eccentric case) we show that such a scenario provides results consistent with the available {\it Kepler} data. As is clear from Fig.\ref{3noecc} and Fig.\ref{3ecc}, as well as Table \ref{ttvchisqr}, the difference between the non-eccentric and eccentric case is marginal at best, while (statistically) preferable over a two planets scenario. In addition, the eccentricities of the planets Kepler-210b and Kepler-210c give a high frequency TTVs signal, which might better explain the higher dispersion of the TTVs in Kepler-210b. In that case the model also suggests $\phi_t$ values around zero with $\Delta\phi <$ 30 $^\circ$, which are in line with Fig.\ref{phidegen}. Also the system's stability exceeds 10$^7$ years. \begin{figure}[tp] \includegraphics[width=\columnwidth]{3noeccplmodel.eps} \caption{TTVs expected for three planets with non-eccentric orbits {for all components of the system. The third planet's period for that case is P$_{03}$= 63.07 days.}} \label{3noecc} \end{figure} \begin{figure}[tp] \includegraphics[width=\columnwidth]{3eccplmodel.eps} \caption{TTVs expected for three planets assuming eccentric orbits {with e$_b$ = 0.45, e$_c$ = 0.51 and e$_{03}$ = 0.23. The Third planet's period for that case is P$_{03}$ = 63.29 days.}} \label{3ecc} \end{figure} In the case of non eccentric orbits the system would reach fatal instability once masses above 5 M$_J$ are chosen. For eccentric orbits the upper limit for the masses of the system becomes lower. While this fact suggests a planetary nature of the system components, it also introduces an additional factor of concern about the long term stability of the system. We do point out that this third stabilizing planet does produce a radial velocity signal in the system. For our nominal case we plot in Fig.~\ref{rv} the expected RV signal in a synthetic radial velocity diagram, which shows peak-to-peak variations in excess of 60 m/sec; clearly such RV variations ought to be detectable despite the high activity level of the host star, and therefore, the detection of a RV-signal would significantly constrain the possible configuration space of the system. | 14 | 3 | 1403.3238 |
1403 | 1403.4768_arXiv.txt | We apply the jet model developed in the preceding paper of Zdziarski et al.\ to the hard-state emission spectra of Cyg X-1. We augment the model for the analytical treatment of the particle evolution beyond the energy dissipation region, and allow for various forms of the acceleration rate. We calculate the resulting electron and emission spectra as functions of the jet height, along with the emission spectra integrated over the outflow. The model accounts well for the observed radio, infrared, and GeV fluxes of the source, although the available data do not provide unique constraints on the model free parameters. The contribution of the jet emission in the UV--to--X-ray range turns out to be in all the cases negligible compared to the radiative output of the accretion component. Nevertheless, we find out that it is possible to account for the observed flux of Cyg X-1 at MeV energies by synchrotron jet emission, in accord with the recent claims of the detection of strong linear polarization of the source in that range. However, this is possible only assuming a very efficient particle acceleration leading to the formation of flat electron spectra, and jet magnetic fields much above the equipartition level. | \label{intro} \begin{figure*} \centerline{\includegraphics[width=11.5cm]{model1.eps}} \centerline{\includegraphics[width=11.5cm]{model2.eps}} \caption{The hard-state broad-band spectrum of Cyg X-1 shown together with our jet models (a) 1 and (b) 2. Fluxes in the radio/mm range from \citet{pandey07} and \citet{fender00}, along with the total IR fluxes \citep{persi80,mirabel96}, are denoted with black circles. The IR spectra of the jet component from \citet{rahoui11} are given as black curves. Small black squares correspond to the X-ray data points from \sax\/ \citep{ds01}, and soft \g-ray data points from \integral\/ IBIS \citep{zls12} and \gro\/ COMPTEL \citep{mcconnell02}. Note that the spectrum below 20 keV represents a typical hard state spectrum of the source (which is absorbed by an intervening medium). Finally, black squares and arrows at high energies denote the detected fluxes and the derived upper limits from \fermi-LAT (30 MeV--0.3 TeV; MZC13) and MAGIC \citep[$>0.1$ TeV;][]{magic}. The green short-dashed curve corresponds to the stellar blackbody continuum. The dotted cyan curve shows the estimated unabsorbed accretion spectrum with (a) and without (b) a hybrid Comptonization tail \citep{pv09}. The red solid curves give the model jet-synchrotron spectra. The magenta dotted, cyan short-dashed, green long dashed, and blue solid curves illustrate the pair-absorbed SSC, BBC, XC, and the sum of the SSC+BBC+XC jet components, respectively. (a) The model 1 with soft electron injection spectrum ($p=2.5$), in which the MeV tail is due to hybrid Comptonization in the accretion flow (cyan dotted curve). (b) The model 2 with hard electron injection spectrum ($p=1.4$), in which the observed MeV tail is due to the jet synchrotron emission. } \label{spectra} \end{figure*} Upper limits on the flux from Cyg X-1 at photon energies $>30$ MeV and a detection of 0.1--10 GeV emission in the hard spectral state of Cyg X-1 have recently been reported using the \fermi\/ Large Area Telescope (LAT; \citealt*{mzc13}, hereafter MZC13). Although the detection has a limited statistical significance, it has been confirmed by the independent work of \citet{bodaghee13}, who found variable emission using the LAT data in the hard and intermediate states, but not in the soft state. The spectra and upper limits of MZC13 complement the previously known radio--to--hard X-ray spectra of Cyg X-1 in the hard state, e.g., the average one compiled in \citet*{zls12} and shown in Fig.\ \ref{spectra}. We apply to these data the jet model developed in \citet{z14}, hereafter Paper I. We take into account, in particular, the possibility that the MeV tail in the hard state of the source is due to the jet synchrotron emission, as implied by the recent claims of very strong linear polarization in that energy range \citep{l11,jourdain12}. We find that the combination of a high flux around MeV energies (if interpreted as synchrotron radiation) and a low flux above 30 MeV requires rather strong jet magnetic field (much above the equipartition level), necessary to reduce the strength of Compton scattering in high-energy \g-rays. We note that the statistical significance of the result of \citet{l11} appears rather low, since the distribution of the azimuthal scattering angle presented in their fig.\ 2 is independent only up to $180\degr$. There is also a disagreement regarding the polarization in the 250--400 keV band, which was found weak and consistent with null by \citet{l11}, whereas \citet{jourdain12} found it to be $\simeq 50$ per cent. In addition, \citet{l11} found the polarization above 400 keV to be $67\pm 30$ per cent compared to the best fit at $>100$ per cent in the 370--850 keV band found by \citet[see figure\ 4 therein]{jourdain12}. The agreement of the polarized fraction with \citet{l11} at $76\pm 15$ per cent claimed by \citet{jourdain12} was obtained only by adding the two channels within the 230--850 keV range. The results regarding the 230--370 keV band are thus quantitatively different between the two papers. This could be, in principle, due to the somewhat different observation periods on which the two works are based, 2003--2009 for \citet{l11} vs.\ 2006--2009 for \citet{jourdain12}. Then, in the 370--850 keV band of \citet{jourdain12}, the minimum $\chi^2$ appears to be obtained at the polarization fraction of $\sim 150$ per cent. If we compare the $\chi^2$ not at this unphysical value but at $\sim 70$ per cent polarization (consistent with the stated fractions of \citealt{l11} and \citealt{jourdain12}) with the $\chi^2$ at null polarization, the resulting $\Delta\chi^2$ is $\la 5$ for 41500 degrees of freedom. Thus, the statistical significance of the presence of strong polarization at that channel appears weak. Therefore, we also consider models in which the jet does not account for the MeV tail. In Section \ref{method}, we outline the method applied to model the data, and specify the adopted parameters of Cyg X-1. We extend the model presented in Paper I for an analytical treatment of the particle evolution beyond the energy dissipation region (see Appendix \ref{advection}). Sections \ref{soft}--\ref{gammamin} give results of the application of our model to the average hard-state spectrum of Cyg X-1. We present here a number of alternative models fitting the data. In Section \ref{magic_flare}, we present two models reproducing the spectrum of the TeV flare detected by MAGIC \citep{magic}. We discuss our results in Section \ref{discussion}, and give our conclusions in Section \ref{conclusions}. \begin{table*} \begin{center} \caption{Parameters of Cyg X-1 adopted in this work. } \begin{tabular}{cccccccccccccccc} \hline $P$ & $M$ & $M_*$ & $r_*$ & $T_*$ & $i$ & $D$ & $\beta_{\rm j}$ & $\Theta_{\rm j}$ & $z_{\rm M}$ & $E_{\rm t0}$ & $F$(15 GHz)& $L_*$ & $a$ & $\Gamma_{\rm j}$ & $R_{\rm g}$\\ d & $\msun$ & $\msun$ & $\rsun$ & K & deg & kpc & & deg & cm & eV & mJy & erg s$^{-1}$ & cm & & cm\\ \hline 5.6 & 16 & 27 & 19 & $2.8\times 10^4$ & 29 & 1.86 & 0.6 & 2 & $10^{15}$ & 0.15 & 13 & $8\times 10^{38}$ & $3.2\times 10^{12}$ & 1.25 & $2.36\times 10^6$ \\ \hline \end{tabular} \end{center} \label{cygx1} \end{table*} \setlength{\tabcolsep}{3.5pt} \begin{table*} \begin{minipage}{17.7cm} \caption{The free parameters of the models and the derived quantities.} \begin{tabular}{@{}lcccccccccccccccccc} \hline model & $p$ & $\gamma_{\rm m}$ & $B_0$ & $z_{\rm m}/ R_{\rm g}$ & $a/z_{\rm m}$ & $\gamma_{\rm t0}$ & $\gamma_{\rm b0}$ & $\lg(\beta_{\rm eq})$ & $\lg(\sigma_{\rm eq})$ & $\lg(P_{\rm e})$ & $\lg(P_{\rm i})$ & $\lg(P_B)$ & $\lg(P_{\rm inj})$ & $\lg(P_{\rm ad})$ & $\lg(P_{\rm S})$ & $\lg(P_{\rm BBC})$ & $\lg(R_{\rm inj})$ & $\lg(R_{\rm e})$\\ &&&$\times 10^4$ &&&$@z_{\rm m}$ &$@z_{\rm m}$ &$@z_{\rm M}$ & $\leq $ &$@z_{\rm M}$ &$\geq $ &&&&&&& $\geq$\\ \hline 1 & 2.5 & 2 & 0.9 & 777 & 1760 & 29 & 78 & 1.2 & $-3.7$ & 34.7 & 36.6 & 33.5 & 35.7 & 35.6 & 34.0 & 33.6 & 40.9 & 40.0\\ 1m & 2.5 & 300 & 7 & 341 & 4010 & 10 & 2.9 & $-0.42$ & $-0.60$ & 34.1 & 34.4 & 34.6 & 35.0 & 34.8 & 34.6 & 33.7 & 38.0 & 37.8 \\ 2 & 1.4 & 2 & 50 & 285 & 4800 & 3.9 & 0.07 & $-1.6$ & 2.4 & 34.5 & 33.8 & 36.1 & 35.8 & 34.7 & 35.8 & 33.6 & 37.8 & 37.3\\ 2a & 1.43 & 2 & 50 & 271 & 5060 & 3.9 & 0.07 & $-1.6$ & 3.6 & 34.5 & 33.9 & 36.1 & 35.8 & 34.7 & 35.8 & 33.7 & 38.0 & 37.3\\ 2m & 1.5 & 300 & 100 & 167 & 8180 & 2.8 & 0.03 & $-1.7$ & 3.8 & 34.5 & 33.7 & 36.3 & 35.8 & 34.7 & 35.8 & 33.5 & 37.2 & 37.1\\ \hline MZC-1 & 3.2 & 2 & 0.25 & 829 & 1650 & 55 & 950 & 3.8 & $-6.5$ & 36.3 & 38.3 & 32.4 &--& 37.1 & 33.8 & 34.2 & -- & 41.7 \\ MZC-2 & 2.3 & 2 & 4 & 1110 & 1230 & 14 & 2.8 & $-1.7$ & $-0.52$ & 33.4 & 34.9 & 35.1 &--& 34.2 & 35.8 & 33.1 & -- & 38.3\\ \hline \end{tabular} {\it Notes:} Parameters of the different models discussed in Sections \ref{soft}--\ref{gammamin} of this paper are compared with those of the models 2, 1 presented in MZC13 (denoted here as MZC-1 and MZC-2). In the models 1, 1m, and MZC-1 the MeV tail of Cyg X-1 is assumed to originate in the accretion flow, whereas in the models 2, 2a, 2m, and MZC-2 it is accounted by the jet synchrotron emission. The model 2a is a variant of 2 with the advection taken into account. The models 1m and 2m are variants of models 1 and 2, respectively, with high low-energy cutoff in the electron injection function. The first four listed quantities are the model free parameters, and the remaining ones are the model-derived parameters. The values of $\sigma_{\rm eq}$ and $P_B$ are for tangled magnetic field. Various components of the jet power provided here can be compared to the average hard-state bolometric accretion luminosity of Cyg X-1, $\lg(L_{\rm accr})\simeq 37.3$, and the Eddington luminosity, $\lg(L_{\rm E})\simeq 39.3$. The units of $B$, $P$ and $R$ are G, erg s$^{-1}$, s$^{-1}$, respectively. \label{t:models} \end{minipage} \end{table*} | \label{conclusions} In this paper, we have applied the jet model developed in Paper I to the average broad-band spectrum of Cyg X-1 in the hard state. We take into account the new measurements and upper limits in the 30 MeV--300 GeV range by \fermi-LAT of MZC13. We have found that in $\gamma$-rays, the Compton scattering of blackbody photons dominates over the SSC process, and that the resulting evaluated jet emission accounts well for the observed LAT spectrum of the source. In the context of the recent controversial claim of a strong polarization of Cyg X-1 at MeV photon energies, we have considered two different variants of the developed jet model. In one, the observed MeV tail is assumed to originate in the accretion flow. This model returns `standard' parameters including soft injection index of the radiating electrons, $p \ga 2$, and the jet magnetic field which can be close to the equipartition level. In the other model, the MeV tail is accounted for by the jet synchrotron emission, so that its strong (maximum) polarization is not, in principle, implausible. We find that in this case the \fermi-LAT measurements impose very tight constraints on the jet magnetic field, which has to be significantly above the equipartition level in order to avoid an overproduction of GeV-energy $\gamma$-rays. Also, the electron injection index has to be hard, $p\sim 1.5$. Importantly, however, the bulk of the MeV jet synchrotron emission turns out to originate in the same regions as the jet radio emission. The strong observational upper limit on the radio linear polarization ($\la 8$ per cent) rules therefore out any strong MeV polarization in our model. We have also modelled the TeV flare of Cyg X-1 observed by MAGIC \citep{magic}. We have speculated that it could have been due to a magnetic reconnection event temporarily decreasing the jet magnetic field, but only assuming hard electron injection. Alternatively, it could have been due to a temporary increase of the acceleration rate by a factor of, at least, $\sim 10^2$, around $\gamma\ga 10^5$, in models with soft electron injection. Finally, in Appendix \ref{advection}, we have derived equations describing the electron distribution in jet regions above the dissipation region, where the distribution is governed solely by the advection and radiative losses. These equations allow for a very simple treatment of jet models with acceleration taking place only close to the jet base \citep{kaiser06,pc09}, in which case advection is of a crucial effect at higher heights. This provides an important extension to the results of Paper I. | 14 | 3 | 1403.4768 |
1403 | 1403.6071_arXiv.txt | Neon emission lines are good indicators of high-excitation regions close to a young stellar system because of their high ionization potentials and large critical densities. We have discovered [Ne {\sc iii}] $\lambda3869$ emission from the microjets of Sz 102, a low-mass young star in Lupus III. Spectroastrometric analyses of two-dimensional [Ne {\sc iii}] spectra obtained from archival high-dispersion ($R\approx 33,000$) Very Large Telescope/{\sc Uves} data suggest that the emission consists of two velocity components spatially separated by $\sim0\farcs3$, or a projected distance of $\sim60$ AU. The stronger redshifted component is centered at $\sim +21$ km\,s$^{-1}$ with a line width of $\sim 140$ km\,s$^{-1}$, and the weaker blueshifted component at $\sim -90$ km\,s$^{-1}$ with a line width of $\sim 190$ km\,s$^{-1}$. The two components trace velocity centroids of the known microjets and show large line widths that extend across the systemic velocity, suggesting their potential origins in wide-angle winds that may eventually collimate into jets. Optical line ratios indicate that the microjets are hot ($T\lesssim1.6\times10^4$ K) and ionized ($n_e\gtrsim5.7\times10^4$ cm$^{-3}$). The blueshifted component has $\sim13\%$ higher temperature and $\sim46\%$ higher electron density than the redshifted counterpart, forming a system of asymmetric pair of jets. The detection of the [Ne {\sc iii}]$\lambda3869$ line with the distinct velocity profile suggests that the emission originates in flows that may have been strongly ionized by deeply embedded hard X-ray sources, most likely generated by magnetic processes. The discovery of [Ne {\sc iii}] $\lambda3869$ emission along with other optical forbidden lines from Sz 102 support the picture of wide-angle winds surrounding magnetic loops in the close vicinity of the young star. Future high sensitivity X-ray imaging and high angular-resolution optical spectroscopy may help confirm the picture proposed. | \label{introduction} Understanding the launching processes and the excitation mechanisms is crucial in studies of jets and outflows from low-mass young stellar objects (YSOs). Theoretical studies have shown that jets are launched from inner disks of young stars. High-resolution spectroscopy and imaging have revealed forbidden emissions from ``microjets'' on scales of a few tens of AU. High-dispersion spectroscopy has helped to examine these properties through velocity-resolved line profiles and line ratio diagnostics even with moderate spatial resolutions. The low-mass YSO Sz 102 \citep{Sz77}, located in the Lupus III cloud, was first identified as an emission-line star (Th 28) by \citet{The62}. Its $377$ \AA\ equivalent width H$\alpha$ emission line is among the largest in the Lupus star-forming regions \citep{Hughes94}. Low-resolution optical spectroscopy of Sz 102 shows forbidden emission lines resembling those from Herbig--Haro (HH) objects, superimposed on a weak red continuum \citep{Krautter84}. The stellar emission from Sz 102 is underluminous ($0.03\,L_\odot$) for a K- or M-type pre-main sequence star \citep{MOD11}, which suggests that the disk is observed close to edge-on and obscures the star. The observed spectral energy distribution, from which a disk thermal emission of $\sim0.13\,L_\odot$ was derived \citep{MOD11,Merin08}, has a rising infrared index \citep[$\alpha\approx0.72$;][]{Chapman07,Evans09}. The geometry inferred from outflow knots is also consistent with that inferred from the continuum emission. Along the position angle of 98\degr, at least three HH knots were identified, two on the east side and one on the west side, designated as HH 228 E1, E2, and W \citep{Krautter86,GH88}. Spectroscopy of [S {\sc ii}] and [N {\sc ii}] emission lines shows that knots E1 and E2 are blueshifted from the systemic velocity by $-67$ and $-87$ km\,s$^{-1}$, and knot W is redshifted by $+33$ km\,s$^{-1}$ \citep{GH88}. Proper motions of the HH knots are $\sim0\farcs5$\,yr$^{-1}$ for the blueshifted knots and $\sim0\farcs4$\,yr$^{-1}$ for the redshifted knots. With an inferred distance ranging between 150 and 200 pc, the outflow is inclined at $\sim 5\degr$ -- $10\degr$ from the plane of sky \citep{Krautter86,WH09,CF10}. This corresponds to an inclination angle between $80\degr$ and $85\degr$. Spectra of Sz 102 show signatures of asymmetry in its pair of microjets. The east and west components have projected lengths of $\sim12\farcs4$ and $\sim13\farcs8$ \citep{Krautter86} and radial velocities $\sim-78$ and $\sim+23$ km\,s$^{-1}$ relative to the star \citep{GH88}, respectively. High-dispersion ($R\approx33,000$) spatially unresolved spectra with the {\sc Ultraviolet and Visual Echelle Spectrograph (Uves)} on the Very Large Telescope (VLT) by \citet{CF10} show most of the forbidden line profiles consist of a strong peak at $\sim+23$ km\,s$^{-1}$ and a blueshifted wing extended to $\sim-350$ km\,s$^{-1}$. \citet{CF10} interpreted the redshifted peak as the receding microjet but the high-velocity blueshifted wing as an uncollimated stellar wind. The physical conditions of the Sz 102 microjets have been studied with optical spectroscopy at various spectral resolutions. Low-dispersion spectra show strong nebular lines such as [O {\sc i}] $\lambda\lambda6300,6363$, [N {\sc ii}] $\lambda\lambda6548,6583$, and [S {\sc ii}] $\lambda\lambda6716,6731$. High-excitation lines including [O {\sc iii}] $\lambda\lambda4959,5007$ and [S {\sc iii}] $\lambda6312$ are also detected. High electron density $\gtrsim 10^4$ cm$^{-3}$ is indicated by strong [S {\sc ii}] $\lambda\lambda4068,4076$ and moderate [O {\sc i}] $\lambda5577$ and [N {\sc ii}] $\lambda5755$ lines \citep{Krautter84}. The redshifted component was studied by \citet{BE99} at a spatial scale of $\sim2\arcsec$ and by \citet{Cof08} at $\sim0\farcs3$ from the source, while the blueshifted component is too faint for a reliable inference. The [S {\sc ii}] $\lambda\lambda6716,6731$ doublet ratio is saturated close to the base of the red component, suggesting a high electron density $\gtrsim 1\times10^4$ cm$^{-3}$. The average temperature inferred from [O {\sc i}] $\lambda6300$/[S {\sc ii}] $\lambda6731$ reaches $2\times10^4$ K and ionization fraction inferred from [N {\sc ii}] $\lambda6583$/[O {\sc i}] $\lambda6300$ gives a high value of $\sim0.3$ at $0\farcs3$ \citep{Cof08}. Here we reanalyze the archival VLT/{\sc Uves} spectra of Sz 102, using the spatial sampling along the slit to separate the velocity components and examine the spectrally-resolved kinematics. In particular, we focus on the [Ne {\sc iii}] $\lambda$3869 emission. A noble gas, neon has high ionization potentials, so its emission lines of multiple ionization states are good indicators of high-energy processes. Ionization of the first valence electron requires 21.6 eV and the second for 41.0 eV. Alternatively, neon can be ionized through inner-shell photoionization, which requires 0.87 and 0.88 keV for $K$-shell electron ejection for neutral and singly-ionized neon, respectively. These properties suggest that photons within or beyond the energy range of the extreme ultraviolet (EUV, $13.6$ eV $<h\nu \lesssim100$ eV) are necessary for ionizing the outer electrons \citep{GH08}. Hard X-rays with energies on the order of keV are important and efficient in neon ionization since the $K$-shell photoionization has its maximal cross section at $\sim0.9$ keV and it is followed by consequent Auger electron ejections \citep{GNI07}. Jump shocks stronger than 100 km\,s$^{-1}$ \citep{HG09}, which typically occur at large bow shocks in HH objects \citep{HRH87}, provide another possible source of ionization. Sz 102 is one of the six YSOs for which both [Ne {\sc ii}] 12.81\micron\ and [Ne {\sc iii}] 15.55\micron\ were detected in the {\it Spitzer}/Infrared Spectrograph (IRS) surveys \citep{Lahuis07,Esp13}. Although the low mid-infrared (MIR) [Ne {\sc iii}]/[Ne {\sc ii}] ratio \citep[0.064,][]{Lahuis07} is consistent with model predictions of an X-ray--irradiated disk and photoevaporative wind \citep{MGN08,EO10}, other evidence suggests that neon lines from Sz 102 may be associated with its microjets \citep{Shang10}. \citet{Gudel10} demonstrated a clear bimodal distribution of [Ne {\sc ii}] 12.81\micron\ luminosities among those YSOs detected with the IRS. Along with other jet-driving sources including T Tau and DG Tau, Sz 102 has a larger [Ne {\sc ii}] 12.81\micron\ luminosity that is roughly 1 dex larger than the average value of $\sim 2\times10^{28}$ erg\,s$^{-1}$ from disk sources. Calculations with X-wind jet models in \citet{Shang10} support the notion that the higher luminosities of [Ne {\sc ii}] 12.81\micron\ line in the bimodal distribution correlate well with the presence of stronger [O {\sc i}] $\lambda6300$ emission, which is an indicator of jet activity. Additionally, [Ne {\sc ii}] emission was not detected in Sz 102 with the VLT/VISIR long-slit spectroscopy, as the slit orientation was perpendicular to the jet axis. This non-detection supports the interpretation that the IRS-detected [Ne {\sc ii}] 12.81\micron\ might come from the jet \citep{PS09}. Further constraints require velocity-resolved spectra of both [Ne {\sc ii}] and [Ne {\sc iii}] in the MIR. Since high-dispersion observations of the MIR [Ne {\sc iii}] line are not viable from the ground, the optical [Ne {\sc iii}] $\lambda\lambda3869,3968$ doublet, with critical electron density of $\sim10^7$ cm$^{-3}$, stands out as a critical tracer for the jet origins of neon emission from low-mass YSOs. In this work, we report the velocity-resolved [Ne {\sc iii}] $\lambda3869$ line from the Sz 102 microjets. This is the first detection of optical [Ne {\sc iii}] $\lambda3869$ emission in the near vicinity of a low-mass YSO. The paper is organized as follows. In Section \ref{smarts}, we present [Ne {\sc iii}] $\lambda3869$ detection in low-dispersion blue ($3500\lesssim\lambda/{\rm \AA}\lesssim5500$) SMARTS/CTIO spectra of Sz 102. The rest of the paper is devoted to studies in the optical wavelengths from archival high-dispersion spectra obtained with the VLT. Basic properties and reduction of the two-dimensional optical spectra are presented in Section \ref{data_reduction}. In Section \ref{results}, [Ne {\sc iii}] $\lambda3869$ and selected forbidden line profiles are analyzed, and physical conditions from optical forbidden line ratios are derived. Based on the information obtained from multiple forbidden emission lines as well as the optical [Ne {\sc iii}] $\lambda3869$ line itself, we discuss origins of the emissions and physical conditions of the microjets. We also explore scenarios that could lead to the irradiation by X-rays in the Sz 102 system in Section \ref{discussion} and summarize the perspectives in Section \ref{summary}. | \label{discussion} Sz 102 drives a pair of microjets that are peculiar compared to other microjets from low-mass YSOs. The optical [Ne {\sc iii}] $\lambda3869$ is clearly and uniquely detected in the jets. Its velocity-resolved line profile provides the unprecedented probe of the innermost region where wide-angle winds may be launched in the system. The physical conditions inferred from [Ne {\sc iii}] $\lambda3869$ and other forbidden emission lines suggest line excitation should occur in relatively hot and dense part of the flows. We discuss scenarios that would produce the neon ions and the excitation of the lines in the flows in this section. Put into perspectives, the origins of the optical [Ne {\sc iii}] emission would elucidate an important role of X-rays in the irradiation of the system. We discuss the sources of the X-rays in a system such as Sz 102 and their implications. \subsection{Kinematics of the Sz 102 Microjets} The forbidden emission line profiles of the Sz 102 microjets, including the large line widths and the ``excess'' spectral features, may be explained by a wide-angle wind whose density is stratified along the jet axis, such as one in the X-wind model \citep[e.g.,][]{XWI,XWV,Shang98,Shang02,Shang10}. \citet{Shang10} illustrated synthetic line profiles of [O {\sc i}] $\lambda6300$, [Ne {\sc ii}] 12.81\micron\, and [Ne {\sc iii}] 15.55\micron\ of an approaching jet from a low-mass YSO at various inclination angles. For an approaching jet, the predicted profiles have typical full widths at zero intensity extended from $\sim -200$ to $+100$ km\,s$^{-1}$ and a blueshifted intensity peak corresponding to the projected terminal velocity of the jet. The diverging streamlines of the wide-angle wind give rise to the large line widths. The intensity peaks toward the jet terminal velocity, which comprises of largely the densest part of the flow that has collimated into jet. Part of the diverging streamlines points away from the observer near the base, allowing the radial velocities to extend to the red, producing the so-called excess emission as described in \citet{Pyo06}. As the inclination angle increases, position of the peak intensity shifts toward the systemic velocity. The shapes of the theoretical line profiles can be flipped about the systemic velocity to represent those of a receding jet. The shape and widths of the line profiles from the redshifted microjet of Sz 102 are consistent with such theoretical profiles seen close to edge-on. A wide-angle wind may account for the large blueshifted velocity centroid in Sz 102. If the approaching side of a wide-angle wind is properly ionized and excited near the base, one may be able to see through the diverging streamlines and probe the dense region that contribute to the emission. In this case, the effective viewing angle to the flow volume would be less than the inclination angle determined from radial velocities and proper motions of the outer knots after the flow has already collimated into a jet. Assume the flow speed of the blueshifted wind is similar to that determined from outer knots, $\sim320$ km\,s$^{-1}$ \citep{Krautter86}, the large blueshifted centroid would be better explained if it corresponds to streamlines directed toward the line of sight with angles $\lesssim80\degr$. The most blueshifted velocity in the profile, $\sim-300$ km\,s$^{-1}$, which can be seen from [Ne {\sc iii}] and other line profiles, is also consistent with the maximum radial velocity achievable from the blue wide-angle wind. Further constrained by the high critical density of [Ne {\sc iii}] $\lambda3869$, the observed wide-angle wind may come from within the innermost region of the disk of Sz 102. Consider a cylinder as an approximation to the innermost part of the jet with cylindrically stratified density profile, from within which the wind is launched and the streamlines are threaded over the outer area $A\approx 2\pi r h$. The radius of this hypothetical cylinder may be regarded as the upper limit of the cylindrical distance of the wind launching region from the outflow axis. It can be estimated, in an order-of-magnitude way, if the density within the cylinder is assumed to be the inferred jet density: \[ R_m \sim \frac{\dot{M}_w x_e}{2\pi h v_w m_{\rm H} n_e} \sim \left(\frac{\dot{M}_w}{10^{-8}M_\odot\,{\rm yr}^{-1}}\right) \left(\frac{x_e}{0.1}\right) \left(\frac{v_w}{100\,{\rm km\,s^{-1}}}\right)^{-1} \left(\frac{n_e}{5\times10^4\,{\rm cm^{-3}}}\right)^{-1} \left(\frac{h}{50\,{\rm AU}}\right)^{-1}\; {\rm AU}. \] Assuming a cylinder with a height of $h \sim 50$ AU, mass-loss rate $\dot{M}_w \sim 2\times10^{-8}$ $M_\odot\,{\rm yr}^{-1}$, $v_w \sim 300$ km\,s$^{-1}$ the maximum wind speed, inferred electron density $n_e \approx 5\times10^4$ cm$^{-3}$, and $x_e \sim 0.3$ the ionization fraction of the wind, one derives $R_m \sim 2$ AU. The uncertainties introduced by $n_e$ from $A_V$ determination and by $x_e$ from the [N {\sc ii}]/[O {\sc i}] ratio would be of the same order of magnitude. Line profile modeling of a wide-angle wind with cylindrical stratified density suggested that most of the MIR neon emission corresponding to spectral bins that builds up the large line width originates from within cylindrical distances 1 AU from the jet axis \citep{Shang10}. \subsection{Physical Conditions of the Sz 102 Microjets} The detection of [Ne {\sc iii}] $\lambda3869$ from Sz 102 makes it possible to estimate the physical conditions for doubly ionized neon emitting gas for the first time. The IRS [Ne {\sc iii}] 15.55\micron\ flux is $2.3\times10^{-15}$ erg\,cm$^{-2}$\,s$^{-1}$ \citep{Lahuis07} and the [Ne {\sc iii}] $\lambda3869$ flux is $7.4\times10^{-15}$ erg\,cm$^{-2}$\,s$^{-1}$. At the thermal limit ($n_e \gtrsim n_{\rm cr}$), one may approximate the [Ne {\sc iii}] $\lambda3869/15.55\,\micron$ ratio as a function of $T$: \[ \frac{L({\rm 3869\,\AA})}{L({\rm 15.55\,\micron})} = 2000 e^{-30945/T}, \] which would be valid for $n_e \approx 10^6$--$10^7$ cm$^{-3}$. The line ratio is $\sim3$ and $\sim100$ for adopted extinctions of $A_V=0.0$ and 2.5 mag, respectively, which corresponds to temperatures of $\sim5000$ and $\sim10,000$ K. This order-of-magnitude estimate of the temperature for the neon emitting gas is consistent with that derived from [N {\sc ii}] and [S {\sc ii}] line ratios emitted from the jet. This consistency implies that the emitting volumes for [Ne {\sc iii}] and other forbidden emission may share similar physical conditions, which sustains the temperature and density that are needed for collisional excitation of the lines. Properties revealed by the {\sc Uves} spectra suggest that asymmetry in the Sz 102 jet persists down to scales within $\sim50$ AU. At a scale beyond $\sim 10\arcsec$ (or $\sim 2000$ AU), the redshifted outflow appears brighter and more extended than the blueshifted outflow \citep{Cof10}. Long-slit spectroscopy of the outer knots at $\sim 30\arcsec$ revealed a blue-to-red speed ratio of $\sim 2$ \citep{GH88}. This velocity asymmetry persists in the near-infrared [Fe {\sc ii}] spectra \citep{Cof10} and optical spectra from {\it HST}/STIS \citep{Cof12} and {\sc Uves}. The asymmetry in excitation conditions, inferred from the {\sc Uves} spectra, can be combined with the velocity asymmetry to elucidate physical conditions of the jets. The blueshifted jet is more ionized but less dense. It is brighter in those highly ionized lines compared with the redshifted jet, but less extended since the density drops off faster. The smaller density may in turn lead to a higher temperature if equal energy is dissipated in the same volume. Similar asymmetries have also been observed in several other T Tauri jets \citep{Hirth94}. RW Aur A \citep{LS12} and FS Tau B \citep{Liu12}, in which 60\% and 30\% differences in velocities were found, are two well known systems driving asymmetric bipolar jets. In the context of the X-wind model, different mass loading operates on the opposite side of the disk in response to the asymmetric magnetic configuration as was suggested in the case of the RW Aur A system \citep{LS12}. The mechanism automatically adjusts the dynamics across the disk such that the averaged linear momentum is conserved in the system and the density ratio is approximately the reciprocal of the velocity ratio. The reasons for the asymmetry, however, are largely unknown, and perhaps are attributable to the detailed dynamo process inside a specific star. Other causes such as misaligned magnetic and rotation axes may also be plausible but will introduce other observable traces. \subsection{Origins of the [Ne {\sc iii}] $\lambda3869$ Emission} Detection of [Ne {\sc iii}] $\lambda3869$ in the Sz 102 microjets posts strong constraints not only on physical conditions of the flow where the specific line is excited but also on the sources of ionization of neon up to the doubly ionized state. From discussion in the previous subsections, one can infer that the optical [Ne {\sc iii}] $\lambda3869$ line itself is most likely excited locally {\it in situ} inside the denser and hotter part of wide-angle winds, along with other detected forbidden transitions. How the neon is ionized and how it remains in the doubly ionized state place stringent requirements on the sources of ionization and the properties of the local flow. For the considerations of producing doubly ionized neon in an environment of low-mass YSO, one naturally looks into {\it in situ} ionization by fast shocks \citep{HRH87,HG09}, external irradiation by EUV \citep{GH08,HG09}, and X-rays \citep{GNI07,Shang10}, for sources of high-energy radiation. We discuss how each of the mechanisms may work in a system such as Sz 102. Neon can be collisionally ionized {\it in situ} by strong shocks that heat the flow to temperatures exceeding those of the ionization potentials. For Ne$^{2+}$, it is 62.5 eV, or $\sim 0.73$ MK. To reach a postshock temperature of $T\approx0.14[v_s/100\,\mbox{km\,s$^{-1}$}]^2$ MK \citep{Shock_ARAA93} requires a shock velocity $v_s$ of $\sim230$ km\,s$^{-1}$. Ionization from UV photons produced by the shock may reduce the required shock speed to $\gtrsim100$ km\,s$^{-1}$ \citep{HRH87,HG09}. This may account for the [Ne {\sc iii}] $\lambda3869$ detections from several large bow shocks of HH objects \citep[e.g., HH 1, 2, 32, 34;][]{BBM81,DBS82,Morse93}. The inferred shock speed of the large bow shocks in HH 34, for example, is $\sim140$ km\,s$^{-1}$ \citep{Morse92}. [Ne {\sc ii}] 12.81\micron\ detection at the northwestern knot $\sim2\farcs5$ from T Tau S suggests that shocks would be important in line formation at large distances from the star \citep{vB09}. In the case of Sz 102, the almost edge-on orientation of the system should have projected the radial component of the needed jump to be $\sim 10$ -- $20$ km\,s$^{-1}$, which may be resolved but is not present in the PV diagrams. Other signatures of strong shocks $\gtrsim100$ km\,s$^{-1}$ near the bases of the jets have not been detected or resolved up to date. It might also be that the places where these shocks occur are heavily extincted. Fast shocks would heat the gas up to 0.1 -- 1 MK, and emit in the UV to X-ray wavelengths (see below for discussions on the X-ray source detected in Sz 102). An average gas temperature of $2\times10^4$ K is inferred in this work from optical line ratios without the correction for extinction. If an extinction correction of 2.5 mag is adopted, the inferred temperature would be lowered to $9\times10^3$ K. Excitation temperature inferred from [Ne {\sc iii}] $\lambda3869$/15.55\micron\ also suggests a range between $5\times10^3$ and $10^4$ K with possible extinction corrections. The observables of the Sz 102 system thus far do not seem to support an origin of {\it in situ} ionization by fast shocks. This would imply that the ionization of neon may be done by some external high-energy photons and the local conditions of the flow will affect the excitation and formation mechanisms of the lines. The ionization state of the neon depends on the local dynamical conditions of the flow and how fast recombination is competing, if ionization of the neon happens away from the line-emitting volume. For the inferred temperature $T\sim2\times10^4$ K and electron density $n_e\sim6\times10^4$ cm$^{-3}$, the recombination timescale is one-half to one year. A flow speed of $\sim300$ km\,s$^{-1}$ can maintain the frozen-in neon ionization on a scale of up to 50 AU if the ionization takes place deeply inside. This is compatible with the current data set. If one adopts an extinction correction of $A_V=2.5$, the inferred lower temperature and higher density reduce the neon recombination timescale by nearly an order of magnitude. This would further disfavor strong shocks operating {\it in situ} as they would have to repeatedly ionize the neon on timescales of several months, and one would easily see tell-tale traces of the events, such as very bright knots adjacent to the driving source that resemble those at the terminal bow shocks. To sustain the ionization of neon in the flow, temporally repetitive or spatially extended sources of ionization are in fact preferred by the evidences shown, and those would not significantly heat up the gas in the jets above a few tens of thousand degrees as inferred in this work. EUV (13.6 eV $<$ $h\nu$ $<$ 100 eV) emission from hot spots produced by accretion shocks is one source that can remove the valence electrons of neon. The EUV photons are easily absorbed by neutral hydrogen in the interstellar medium, and direct observation and determination of the ionizing flux are difficult. For sources without strong jet activities, the existence of EUV irradiation can be obtained by MIR line diagnostics such as [Ar {\sc ii}]/[Ne {\sc ii}] and [Ne {\sc iii}]/[Ne {\sc ii}] ratios \citep{GH08,HG09}, or by free--free emission and radio hydrogen recombination lines from the disk \citep{PGH12}. Among the few MIR {\it Spitzer} [Ne {\sc iii}] disk (jet-free) sources, the generally small MIR [Ne {\sc iii}]/[Ne {\sc ii}] ratios are not positively (nor strongly) correlated with the X-ray luminosity $L_{\rm X}/L_{\rm bol}$ \citep{Esp13}. However, in jet-driving sources, the models based on the X-winds would have also predicted a small ratio of [Ne {\sc iii}]/[Ne {\sc ii}], but show correlations with X-ray parameters \citep{Shang10}. The MIR neon lines alone can not definitely establish the sources of ionization, especially in YSOs wherein both X-rays and EUV radiations may well be present. In a source where the mass accretion rate is larger than $1\times 10^{-8}M_\odot$\,yr$^{-1}$ \citep{HG09}, not only would the EUV photons have trouble escaping from the winds, but also be absorbed by the accretion funnels before they reach the inner winds \citep{GNI07,MGN08,Shang10}. In a system such as Sz 102 in which the ionization is seeded by external radiation sources, any EUV radiation that is able to penetrate the winds will simply add on top of the ionization that has been produced by the primary source of irradiation. Sz 102 has been known as a soft X-ray ($kT_{\rm X} < 1$ keV) emitter \citep{PJC_Gudel}. Analysis of the archival X-ray spectra of Sz 102 obtained with both {\it XMM-Newton} \citep[2003 September;][]{Xray2006} and {\it Chandra} \citep[2009 June;][]{PJC_Gudel} show soft X-ray profiles which peak at $\sim 0.6$ keV. Spectral energy fitting to the two X-ray spectra shows that the emission is produced by a plasma of $\sim 2$ MK ($kT_{\rm X} \approx 0.173$ keV) attenuated by hydrogen column of $4$--$5\times10^{21}$ cm$^{-2}$, which corresponds to $A_V \sim 2.5$ \citep[$N_{\rm H} \sim 2\times10^{21}\,A_V$ cm$^{-2}$,][]{Vuong03}. The recovered unabsorbed X-ray flux is $2.3\times10^{-13}$ erg\,s$^{-1}$\,cm$^{-2}$, or an X-ray luminosity of $1.1\times10^{30}$ erg\,s$^{-1}$ at a distance of 200 pc. This X-ray component is spatially indistinguishable from the Two Micron All Sky Survey source associated with Sz 102 within the positional uncertainty of 0\farcs4. Such a temperature, if produced in a shock, would come from an impact velocity of $\sim 380$ km\,s$^{-1}$, only achievable in the accretion funnels. The alternative would be corona trapped in the closed magnetic loops, which is known to produce soft X-ray emission in quiescence as well. \citet{CF10} noted a large equivalent width of H$\alpha$ and a maximum redshifted tail up to $+450$ km\,s$^{-1}$ in several permitted lines but absent in the forbidden lines, which they attributed to magnetospheric accretion \citep[e.g.,][]{MCH98}. A mass of 0.6--0.9 $M_\odot$ was derived, and an accretion rate of 4.2--6.3 $\times 10^{-8}$ $M_\odot$\,yr$^{-1}$ was estimated by using width of Ca {\sc ii} triplets in \citet{Com03}. If this X-ray component is produced by magnetospheric accretion, the contribution of the EUV photons would be superseded in this scenario. If the soft X-ray component is rooted in the magnetic loops, it may be easily absorbed by the accretion funnels or the bases of the winds. Regardless of the production mechanisms, the existing observations may contain contributions from both. The derived total X-ray luminosity is typical of the time-averaged value from the characteristic state \citep[defined as typical emission state between isolated flares by][]{Wolk05_COUP} of revealed low-mass pre-main sequence stars \citep[$\sim2\times10^{30}$ erg\,s$^{-1}$; see, e.g.,][]{FGP02,Wolk05_COUP}. However, a thermal spectrum at a temperature of 0.6 keV does not produce enough X-ray photons at the peak of the neon photoionization cross section \citep[$\sim0.9$ keV,][]{GNI07} for the level of the optical [Ne {\sc iii}] emission reported in this work. The flat-spectrum source DG Tau, famous for its bright optical and infrared jet, tells a different story. It has a ``two-absorber'' X-ray spectrum that contains two unrelated emission components. There is a hard flaring component located at the stellar position and a soft static component elevated at $\sim0\farcs2$ along the jet axis \citep{SS08}. An extended soft X-ray ``knot'' is identified at $\approx 5\arcsec$ further down \citep{Gudel08,Gudel12}. This knot has a proper motion of $\sim0\farcs28$\,yr$^{-1}$, similar to those of the bright optical [S {\sc ii}] and UV H$_2$ knots \citep{DGTau_RadioJet,Sch13}. The X-ray knot seems to originate in the inter-knot region that has a velocity jump of $\sim100$ km\,s$^{-1}$ identified in \citet{LCD00}, if tracing back in time and position locations. The inferred temperature of the soft X-ray knot is $\sim 2.7$ MK, which is $\sim 1$ MK lower than the inner soft component \citep{Gudel12}. Based on the similar hardness, \citet{Gudel08} suggested that the inner soft component originates in the base of the outflow. \citet{GML09} showed that the temperature of the inner soft component requires strong shocks of $\sim450$ km\,s$^{-1}$ produced by the fastest portions of the jet of density $\sim 10^5$ cm$^{-3}$. The lower-temperature outer knot may be produced by collisions with previous ejecta. This scenario is consistent with its weaker shock strength and proper motion \citep{Gudel08,GML09}. The strong shocks of $\gtrsim300$ km\,s$^{-1}$ inferred along the DG Tau jet may provide some {\it in situ} ionization of neon and further excitation of the neon forbidden lines. If the luminosity of the shock-induced soft X-ray allows for enough ionization, extended neon emission and ``knot'' coinciding with the X-ray emitting jet and knot would be detected. The caveat here is that the hard flaring component is more luminous than the soft X-ray jet by almost two orders of magnitude, and even if any extended neon emission is detected along the jet, it would still not be a clean case for shock ionization. \subsection{X-Ray Flares in Sz 102} A potential source of ionizing radiation in Sz 102 is (unseen) hard X-rays. Hard ($kT_{\rm X} \gtrsim 1$ keV) X-rays can penetrate the denser region of the flows, and have sufficient ionizing power. How might such a component, if it exists, remain undetected? This component could be obscured by the optically thick disk, or it could simply be temporally variable, with the extant X-ray observations insufficient to have caught any large flares. The fact that [Ne {\sc iii}] $\lambda3869$ has been caught by two observations $\sim8$ yr apart shows that either the hard sources have flared during the two observations ({\sc Uves} and SMARTS) or the ionization has remained frozen-in within the flow and the temperature has not cooled during the time lapsed. Searching for the missing flaring components in Sz 102 may be helpful in identifying the ionization sources of its jet. Flares in YSOs can generate copious X-rays that are harder than those generated by plasma gyrating around the closed magnetic loops of the magnetosphere or those produced by magnetospheric accretion. Reconnection events release energies from the twisted magnetic field lines and can heat up the gas to 10 -- 100 MK \citep[as shown in, e.g., Figure 42 of][]{PF02}, whose thermal spectra are peaked at keV ranges \citep{Wolk05_COUP,Favata05_COUP}. Studies of our Sun show that flares may occur on small scales close to the star or on larger sizes extending up to the scale of the solar radius \citep[see the review in, e.g.,][]{PF02}. The former is usually called the impulsive flares, which are more frequent and less luminous, and the latter is associated with the coronal mass ejections or prominence eruptions, which release a large amount of energy. Flares in YSOs have been monitored by various X-ray satellites, and have been found to show similar characters, with elevated strengths, to those on the Sun. \citet{Wolk05_COUP} found those similar to the impulsive flares can have an average luminosity of $6\times10^{30}$ erg\,s$^{-1}$, with rise times of a day or two. Large flares are relatively rare in YSOs, but they do exist, and can have energy releases on the order up to $\sim 10^{32}$ erg\,s$^{-1}$ and temperatures exceeding 100 MK at their peak intensities \citep[see, e.g.,][]{Imanishi01,Grosso04,Favata05_COUP,Getman08a_COUP,Getman08b_COUP}. They have been interpreted to involve large loops of sub-AU sizes, which are believed to connect to both the star and the inner circumstellar disk \citep{Favata05_COUP}. This picture supports the analogies of ``coronal mass ejections'' that take place around the ``helmet streamers'' in star--disk interacting systems \citep{Shu97Sci}. These large though less frequent flares that arise high above the disk plane may release enough energy to ionize enough neon to their doubly-ionized states in the surrounding wide-angle winds (irrespective of their detailed origins). The discussions on the relative fast flow time and not-so-fast recombination time scales would help in maintaining the ionization that has been seeded by irradiation. A flaring hard component, similar to that detected at the stellar position of DG Tau, may help. {\it Chandra} observations during 2004 and 2006 showed that this component has a temperature ranging from 25 to 35 MK, and {\it XMM-Newton} observations in 2004 showed an even higher average temperature of $\sim70$ MK \citep{Gudel08}. Temporal analysis revealed 20 ks scale flares in the hard component \citep{Gudel07} that can recur in days \citep{Gudel12}. During the rise of the flare, energy can be released at beyond a rate of $L_{\rm X}\approx10^{30}$ erg\,s$^{-1}$; the gas is heated to $\gtrsim 100$ MK and the X-ray spectrum is hardened between 1 and 10 keV \citep{Gudel07}. This deeply embedded ($N_{\rm H}\approx2\times10^{22}$ cm$^{-2}$) X-ray source is interpreted as hot coronal gas confined in closed loops of magnetosphere that is heated by recurring flares \citep{Gudel07,Gudel08}. For Sz 102, an analog of this recurring hard X-ray component would be an ideal source of irradiation. The flux-calibrated SMARTS spectrum observed in 2011 has a [Ne {\sc iii}]$\lambda3869$ flux of $4.9\pm1.0\times10^{-15}$ erg\,s$^{-1}$\,cm$^{-2}$. This corresponds to a $\sim35\%$ drop of flux compared to the {\sc Uves} spectrum observed in 2003. If no fresh ionization has been supplied during the two events, this implies a recombination timescale of $\sim20$ yr for the doubly-ionized neon. This may be achieved if the gas in flows stays at a temperature of $\sim10^4$ K and the electron density is below $2\times10^3$ cm$^{-3}$. However this density would be too low for the observed [Ne {\sc iii}] $\lambda3869$ and other high-density lines such as [S {\sc ii}] $\lambda4068$. Although no clear history of the optical [Ne {\sc iii}] flux variation can be made from existing data, at least another event of strong flare prior to the 2011 SMARTS observations would be needed. Whether the occurrence and energetics of the flares in the system are asymmetric on the opposite sides of the disk remains unclear. As discussed in Section 5.2, different mass loading in the magnetocentrifugal winds may further introduce different velocity and density profiles across the disk \citep[e.g.,][]{LS12}, which subsequently will affect the ionization fractions, if the flares are symmetric (i.e., same luminosity). If the asymmetry exists in the magnetic field configurations across the disk plane, the energetics of the flares may also be asymmetric. However, the asymmetric character of the system is not required for the scenarios of external irradiation; whether it can enhance the level of X-ray flares will be investigated in the future. | 14 | 3 | 1403.6071 |
1403 | 1403.2558_arXiv.txt | A first new luminosity functions of galaxies can be built starting from a left truncated beta probability density function , which is characterized by four parameters. In the astrophysical conversion, the number of parameters increases by one, due to the addition of the overall density of galaxies. A second new galaxy luminosity function is built starting from a left truncated beta probability for the mass of galaxies once a simple nonlinear relationship between mass and luminosity is assumed; in this case the number of parameters is six because the overall density of galaxies and a parameter that regulates mass and luminosity are added. The two new galaxy luminosity functions with finite boundaries were tested on the Sloan Digital Sky Survey (SDSS) in five different bands; the results produce a "better fit" than the Schechter luminosity function in two of the five bands considered. A modified Schechter luminosity function with four parameters has been also analyzed. | The standard luminosity function for galaxies (LF) in the last forty years has been represented by the Schechter LF \begin{equation} \Phi (L) dL = (\frac {\Phi^*}{L^*}) (\frac {L}{L^*})^{\alpha} \exp \bigl ( {- \frac {L}{L^*}} \bigr ) dL \quad , \label{equation_schechter} \end {equation} where $\alpha$ sets the slope for low values of $L$ , $L^*$ is the characteristic luminosity and $\Phi^*$ is the normalization, see \cite{schechter}. This LF is defined in the in the interval $[0, \infty]$ and has replaced other LFs presented by \cite{Zwicky1957,kiang1961,Abell1965,Arakelyan1970}. The goodness of the fit can be evaluated by the merit function $\chi^2$ \begin{equation} \chi^2 = \sum_{j=1}^n ( \frac {LF_{theo} - LF_{astr} } {\sigma_{LF_{astr}}})^2 \quad , \label{chisquare} \end{equation} where $n$ is number of data and the two indexes $theo$ and $astr$ stand for theoretical and astronomical, LF respectively. The value of $ \chi_S^2 $ which characterizes the Schechter LF for a given astronomical catalog, i.e. the Sloan Digital Sky Survey (SDSS) in five different bands, represents a standard value to improve. Many new LFs has been derived in the last years and we report some examples. A two-component Schechter-like function is , see~\cite{Driver1996} \begin{eqnarray} L_{max} > L > L_{Dwarf} : \quad \Phi (L) dL = (\frac {\Phi^*}{L^*}) (\frac {L}{L^*})^{\alpha} \exp \bigl ( {- \frac {L}{L^*}} \bigr ) dL \quad, \nonumber \\ \\ L_{Dwarf} > L > L_{min} : \quad \Phi (L) dL = (\frac {\Phi_{Dwarf}}{L^*}) (\frac {L}{L_{Dwarf}})^{\alpha_{ Dwarf}} dL \quad, \nonumber \end {eqnarray} where \begin{eqnarray} \Phi_{Dwarf} = \Phi^* (\frac {L_{Dwarf} }{L^*})^{\alpha} \exp \bigl ( {- \frac {L_{Dwarf} }{L^*}} \bigr ) \quad. \nonumber \end{eqnarray} This two-component LF defined between the maximum luminosity, $L_{max}$, and the minimum luminosity, $L_{min}$, has five parameters because two additional parameters have been added: $L_{Dwarf}$ which represents the magnitude where dwarfs first dominate over giants and ${\alpha_{Dwarf}}$ which regulates the faint slope parameter for the dwarf population. In order to fit the case of extremely low luminosity galaxies a double Schechter LF with five parameters, see~\cite{Blanton_2005}, was introduced: \begin{equation} \Phi(L) dL = \frac{dL}{L_\ast} \exp(-L/L_{\ast}) \left[ \phi_{\ast,1} \left( \frac{L}{L_{\ast}} \right)^{\alpha_1} + \phi_{\ast,2} \left( \frac{L}{L_{\ast}} \right)^{\alpha_2} \right] \quad, \end{equation} where the parameters $\Phi^*$ and $\alpha$ which characterize the Schechter LF have been doubled in $\phi_{\ast,1}$ and $\phi_{\ast,2}$. The strong dependence of LF on different environments such as voids, superclusters and supercluster cores was analyzed by \cite{Einasto_2009} with \begin{equation} F (L) \mathrm{d}L \propto (L/L^{*})^\alpha (1 + (L/L^{*})^\gamma)^{(\delta-\alpha)/\gamma} \mathrm{d}(L/L^{*}), \label{eq:abell} \end{equation} where $\alpha$ is the exponent at low luminosities $(L/L^{*}) \ll 1$, $\delta$ is the exponent at high luminosities $(L/L^{*}) \gg 1$, $\gamma$ is a parameter of transition between the two power laws, and $L^{*}$ is the characteristic luminosity. Another LF starts from the probability density function (PDF) that models area and volumes of the Voronoi Diagrams and introduces the mass-luminosity relationship, see \cite{Zaninetti2008}; in the SDSS case $ \chi^2 > \chi_S^2$. A last example is represented by three new LFs deduced in the framework of generalized gamma PDF, see \cite{Zaninetti2010f}; in the SDSS case $ \chi^2 < \chi_S^2$. All the previous LFs cover the range $[0, \infty]$ and therefore the analysis of finite upper and lower boundaries can be a subject of investigation. Another interesting observational fact is that at low values of luminosity (high absolute magnitude) the observed LF has an approximate constant value. The left truncated beta with scale PDF recently derived , see equation (34) in \cite{Zaninetti2013a}, satisfies the two issues previously raised. In order to explore the connection between LF and evolution of galaxies see \cite{vandenBosch2003,Yang2003,Cooray2005a,Cooray2005b, Cooray2005c,Tinker2005,Tinker2007}. Here we analyze in Section \ref{lflinear} a left truncated beta LF for galaxies and in Section \ref{lfnonlinear} a left truncated beta for mass which transforms itself in a LF for galaxies through a nonlinear mass-luminosity relationship. Section \ref{secbrazilian} reports a recent LF for galaxies which has a finite boundary at the bright end. | {\bf Motivations} The observational fact that the LF for galaxies spans from a minimum to a maximum value in absolute magnitude makes attractive the exploration of the left truncated beta LF. We derived two LFs adopting the framework of the linear M-L relationship , see eqn. (\ref{lfmagnibeta}) , and the framework of the non linear M-L relationship , see eqn. (\ref{lfmagnibetaml}). {\bf Goodness of fit tests} We have computed $\chi^2$ and $ \chi_{red}^2 $ for two LFs here derived and compared the results with the Schechter LF, see Tables \ref{databetalf} and \ref{databetalfml}. In the linear M-L case $\chi^2$ and $ \chi_{red}^2 $ are greater of that of the Schechter LF. In the non linear M-L case $\chi^2$ and $ \chi_{red}^2 $ , $u^*$ and $i^*$ , are smaller in two bands over five in respect to those of the Schechter LF. The non linear case suggests a power law behavior with an exponent $1.1 < c < 1.52$ and therefore M-L relationship has an exponent greater than 1 but smaller than 4 , the theoretical value of the stars. {\bf Modified Schechter LF} The modified Schechter LF when $\eta <1$ , which is the case of SDSS , has by definition an upper boundary, see \ref{secbrazilian}. The $\chi^2$ and $ \chi_{red}^2 $ are smaller in five bands over five in respect to those of the Schechter LF. This goodness of fit is due to the flexibility introduced by the fourth parameter $\eta$ as outlined in \cite{Alcaniz2004}. {\bf Physical Motivations} The Schechter LF is motivated by the Press-Schechter formalism on the self-similar gravitational condensation. Here conversely we limited ourself to fix a lower and an upper bound on the mass of a galaxy and we translated this requirement in a PDF for mass and then in LF. Finite-size effects on the luminosity of SDSS galaxies has also been explored in \cite{Taghizadeh-Popp2012}. \providecommand{\newblock}{} | 14 | 3 | 1403.2558 |
1403 | 1403.0900_arXiv.txt | Sagittarius A$^{\star}$ harbors the supermassive black hole that lies at the dynamical center of our Galaxy. Sagittarius A$^{\star}$ spends most of its time in a low luminosity emission state but flares frequently in the infrared and X-ray, increasing up to a few hundred fold in brightness for up to a few hours at a time. The physical processes giving rise to the X-ray flares are uncertain. Here we report the detection with the {\em NuSTAR} observatory in Summer and Fall 2012 of four low to medium amplitude X-ray flares to energies up to 79 keV. For the first time, we clearly see that the power-law spectrum of Sagittarius A$^{\star}$ X-ray flares extends to high energy, with no evidence for a cut off. Although the photon index of the absorbed power-law fits are in agreement with past observations, we find a difference between the photon index of two of the flares (significant at the 95\% confidence level). The spectra of the two brightest flares ($\sim$55 times quiescence in the 2--10 keV band) are compared to simple physical models in an attempt to identify the main X-ray emission mechanism, but the data do not allow us to significantly discriminate between them. However, we confirm the previous finding that the parameters obtained with synchrotron models are, for the X-ray emission, physically more reasonable than those obtained with inverse-Compton models. One flare exhibits large and rapid ($<$ 100~s) variability, which, considering the total energy radiated, constrains the location of the flaring region to be within $\sim$10 Schwarzschild radii of the black hole. | \label{sec:intro} Sagittarius A$^{\star}\,$ (\SgrA), at a distance of $\sim8$~kpc, is a $\sim4 \times10^6$ solar mass supermassive black hole (SMBH) that marks the dynamical center of the Milky Way \citep{ghez.2008ys,gillessen.2009vn}. Although \SgrA is a fairly bright radio and submillimeter (sub-mm) source, it is not detected in the optical and UV due to over 30 magnitudes of visual extinction, and it is very dim in X-rays. Its bolometric luminosity $L_{\rm bol}$ is only 550 times that of the Sun, corresponding to $\sim10^{-9}$ times the Eddington luminosity \citep{narayan.1998kx}. Most of this is radiated in the sub-mm, with the X-ray luminosity being $3.6 \times 10^{33}$ erg s$^{-1}$ \citep{nowak.2012fk} in the 2--10 keV energy band ($\sim 2 \times 10^{-3} \, L_{\rm bol}$). This low luminosity implies that matter falls onto the black hole in a radiatively-inefficient manner, perhaps in a hot, geometrically thick, optically thin flow \citep{narayan.1998kx,yuan.2003qf,wang.2013fk}. A few times per day in the near infrared (NIR) and about once per day in X-rays, \SgrA flares up to a few hundred times its quiescent level for intervals lasting up to a few hours, with the strong flares being less common than the weak ones. The NIR emission is strongly polarized \citep{eckart.2006kl}, indicating a synchrotron origin, and therefore a population of relativistic electrons. The source of the X-ray emission is uncertain; possibilities include both synchrotron radiation with a cooling break \citep[SB,][]{yuan.2003qf, yuan.2004uq, dodds-eden.2009dq} and inverse Compton (IC) up-scattering of lower energy photons by energetic electrons. Two IC scenarios involve the NIR emitting electrons up-scattering either ambient sub-mm photons \citep[external Compton, EC,][]{markoff.2001ve,eckart.2004oq,yusef-zadeh.2006ij} or the NIR synchrotron emission itself \citep[synchrotron self-Compton, SSC, e.g.][]{markoff.2001ve,eckart.2006zr,marrone.2008hc}. A third IC scenario involves NIR flare photons up-scattered by the electrons radiating in the sub-mm domain \citep{yusef-zadeh.2009fk,yusef-zadeh.2012fk}. The physical cause of the episodic particle acceleration is not understood, and suggestions include a hot spot in the accretion flow \citep[due, for example, to a magnetic reconnection event, see e.g.][]{dodds-eden.2010fk}, enhanced mass accretion \citep{tagger.2006uq}, magnetohydrodynamic turbulence or shocks in the inner accretion flow \citep{yuan.2003qf}, a jet \citep{markoff.2001ve}, or episodic outflow triggered by magnetic reconnection \citep{yuan.2009fk}. Tidal disruption of asteroids has also been proposed as possible origin of the flares \citep{cadez.2008uq, kostic.2009kx, zubovas.2012fk}. Numerous flares have now been observed in X-rays \citep{baganoff.2001qy,porquet.2003bh,porquet.2008uq,degenaar.2013cr,neilsen.2013fk}, in NIR \citep{genzel.2003fj,witzel.2012dq}, and in both bands simultaneously \citep{eckart.2004oq,yusef-zadeh.2006ij,eckart.2006zr,marrone.2008hc,dodds-eden.2009dq,trap.2011fk,eckart.2012bh}. Above 10~keV, only upper limits exist due to a combination of limited instrumental sensitivity and spatial resolution \citep{yusef-zadeh.2009fk,trap.2011fk}. Short, high-amplitude temporal substructures, with variability timescales as short as 47~s, have been seen during NIR flares \citep{dodds-eden.2009dq}, indicating a compact origin for this emission component. In the X-ray, variability on 100--200~s timescales has been reported, although at low relative amplitude \citep{porquet.2003bh, nowak.2012fk}. The fastest timescale observed to-date for significant (more than a factor of a few) X-ray variability is 600~s \citep{baganoff.2001qy}. We report here on {\it NuSTAR} observations of four flares detected in Summer and Fall 2012. This paper is organized as follows. Section \ref{sec:observations} details the observations, and section \ref{sec:BB} presents the method to search for flaring activity. In section \ref{sec:variability}, we quantify the variability amplitude and time scale exhibited during one of the flares. Section \ref{sec:spectralanalysis} describes the spectral analysis of the flares. Then, in section \ref{sec:sed}, we introduce the models that are compared to the SEDs of the two brightest flares, and the results are discussed in section \ref{sec:discussion}. Finally, in section \ref{sec:energybalance}, we derive a constraint on the location of the flaring region. | \begin{deluxetable}{lcccccc} \tabletypesize{\small} \tablecaption{Best fit parameters for the EC, SSC and SB models of flares J21\_2 and O17. \label{tab:SEDparam}} \tablewidth{0pt} \tablehead{Parameters & \colhead{EC$_{\rm J21\_2}$} & \colhead{EC$_{\rm O17}$} & \colhead{SSC$_{\rm J21\_2}$} & \colhead{SSC$_{\rm O17}$} & \colhead{SB$_{\rm J21\_2}$} & \colhead{SB$_{\rm O17}$} } \startdata $n_e$ (cm$^{-3}$) & $4.2\times10^{7}$ & $3.7\times10^{8}$ & $3\times10^{10}$ & $3.4\times10^{10}$ & $> 2.9 - 1.9 \times 10^3$ & $> 5.7 - 5.6 \times 10^2$ \\ $R$ (cm) & $4.6\times10^{10}$ & $3.2\times10^{10}$ & $5.4\times10^{9}$ & $5.4\times10^{9}$ & $ < 3 \times 10^{12}$ & $ < 3 \times 10^{12}$ \\ $R_{\rm sub-mm}$ (cm) & $1.1\times10^{11}$ & $6.4\times10^{10}$ & ... & ... & ... & ... \\ $B$ (G) & ... & ... & 3200 & 2300 & $2.7 - 24$ & $6.3 - 56$ \\ $T_e$ (K) & $1.0\times10^{12}$ & $1.4\times10^{12}$ & $1.0\times10^{11}$ & $1.4\times10^{11}$ & ... & ... \\ $ \tau_{\rm inj} (s)$ & ... & ... & ... & ... & 100 & 100 \\ NIR flux (mJy) & ... & ... & 5.5 & 5.1 & $1 - 27$ & $1 - 27$ \\ $\chi^2/{\rm dof}$ & $7.3/7$ & $5.4/7$ & $7.2/7$ & $4.8/7$ & $4.1/7$ & $4.4/7$ \\ CDF & 0.60 & 0.39 & 0.59 & 0.31 & 0.23 & 0.27 \\ \enddata \tablecomments{The NIR flux is the value for the $K_s$ band (2.2 $\mu$m); in the case of the SSC model, the NIR flux is the prediction from the model. In the case of the SB model, it is simply the range of past observations \citep{trap.2011fk}. The EC model does not allow a NIR flux prediction, as it only depends on the magnetic field strength given the number of electrons and their temperature. In the SB case, the number of electrons is calculated for $\gamma_{\rm min}=1000$ and $\gamma_{\rm max} =3 \times 10^5$. A range of electron densities and magnetic field strengths are quoted, which produce the same X-ray flux but cover the range of NIR flux measured in past flares. The size of the emitting region does not play a role. The flux only depends on the total number of electrons. However, for consistency, we use the upper limit on the flaring region size that we derived for flare J21\_2 to estimate the lower limit on the electron density (see Section \ref{sec:energybalance}). The last row, CDF, gives the cumulative distribution function for the $\chi^2$ distribution, given the $\chi^2$ value and the degree of freedom (dof). } \end{deluxetable} Work to date combining NIR and X-ray data does not definitively rule out any of the above mechanisms. The narrow bandpasses of {\em Chandra} and {\em XMM-Newton} and the strong absorption in the soft X-ray band have made it impossible to distinguish between a power-law spectrum, naturally explained by a synchrotron process, and a curved spectrum that would be characteristic of straightforward EC or SSC emission models. {\em NuSTAR}, with its larger bandpass, clearly shows that the spectrum extends to high-energy X-rays, but we are limited by statistics in the highest part of the energy range. The fit to flare J21\_2 is somewhat conclusive with a rejection probability for the SB model of 23\% versus 60\% and 59\% for the EC and SSC models, respectively. However, the fit to flare O17 is clearly inconclusive with no model standing out. We nonetheless note that the best fit parameters for the EC and SSC models are unrealistic, while the SB model gives reasonable ranges of electron density and magnetic field strength. The EC process requires an electron density several orders of magnitude higher than expected for the accretion flow around \SgrA, and the high density required for the sub-mm photons leads to a very small sub-mm volume, over an order of magnitude smaller than the quiescent emission region as observed by VLBI \citep{fish.2011fk}. The SSC model needs even higher electron density along with extremely high magnetic field strengths. Thus, we reach identical conclusions to \citet{dodds-eden.2009dq}: we favor the SB model primarily based on physical arguments. Within the synchrotron picture, {\em NuSTAR}'s high-energy detection implies either a higher magnetic field strength or a particle distribution with a higher maximum Lorentz factor ($E_{\rm max}\propto B\gamma_{\rm max}^{2}$) than previously assumed. With a magnetic field strength of 50~G, flare J21\_2 requires $\gamma_{\rm max}$$\sim$$3\times 10^{5}$, which implies a synchrotron cooling time as short as $\sim$1\,s for the most energetic X-ray emitting particles. Thus, continuous acceleration of high-energy particles is required to produce a $\sim$3,000\,s flare, even if the magnetic field were more than an order of magnitude lower than the value given above. The rapid X-ray variability detected by {\em NuSTAR} also puts important constraints on flare models. In the SB model with a cooling break between the NIR and X-ray, the NIR variability is primarily due to changes in the magnetic field strength, while any X-ray variability is driven by sporadic injection of high-energy particles into the emission region \citep{dodds-eden.2010fk}. Thus, the amplitude changes (rise and decay) within 100~s measured during flare J21\_2 require that the particle injection rate can either drop or rise dramatically on a timescale of 100~s (see section \ref{sec:variability}). Given that we observe these fast variations at the beginning and at the end of sub-flare J21\_2b (separated by 30 minutes), we assume that the emitting region keeps the same size throughout the flare. For this given flare, this assumption puts constraints on the adiabatically expanding blob model for the X-ray emission \citep{van-der-laan.1966kx,eckart.2006zr,eckart.2012bh,yusef-zadeh.2006fk,yusef-zadeh.2008uq,yusef-zadeh.2009fk}. Four flares were detected during this observation campaign, two of medium amplitude, J21\_2 and O17, and two weaker ones, J20 and J21\_1. For the first time, we clearly see that the power-law spectrum of \SgrA X-ray flares extends to high energy, with no evidence for a cut off; flare O17 is detected up to 79 keV and flare J21\_2 up to 60 keV. The SED fit slightly favors the SB model for flare J21\_2 but is inconclusive for flare O17 due to limited statistics at high energy. However, we confirm previous reports that physical arguments favor the SB model over the two simplified IC models we tested. This implies that efficient particle acceleration takes place continuously over the duration of the flares, as the synchrotron cooling time is of the order of 1~s. Flare J21\_2 was detected over a long enough time to search for spectral evolution, but we find none. We detect a variation of photon index between two individual flares at the 95\% confidence level. Flare O17 ($\Gamma=2.04^{+0.22}_{-0.20}$), which is also stronger, is harder than flare J21\_1 ($\Gamma=2.84^{+0.64}_{-0.54}$). This is opposite to the finding of \citet{degenaar.2013cr} who reported on one bright flare that was softer than the average of five weak flares. Keeping in mind that the present result and that of \citet{degenaar.2013cr} have low significance, this indicates that the photon indices of flares can take a range of values, even for a given flux, which is suggestive of magnetic reconnection as acceleration mechanism. Variability with a timescale of 100~s was observed during flare J21\_2, both in rise (factor of at least $3.8 \pm 1.1$) and decay (factor of $3.4 \pm 1.8$). This suggests that the flaring region keeps the same size throughout the flare, and it allows us to put an upper limit of 2.5 $R_{\rm S}$ on its radial size. Assuming that flares are powered by magnetic energy, this flaring region size places a constraint on the location of the region: energetics show that there is only enough energy to power flare J21\_2 within 10 $R_{\rm S}$ of the event horizon. | 14 | 3 | 1403.0900 |
1403 | 1403.2134_arXiv.txt | We report the discovery of MOA-2013-BLG-220Lb, which has a super-Jupiter mass ratio $q=3.01\pm 0.02\times 10^{-3}$ relative to its host. The proper motion, $\mu=12.5\pm 1\,\masyr$, is one of the highest for microlensing planets yet discovered, implying that it will be possible to separately resolve the host within $\sim 7$ years. Two separate lines of evidence imply that the planet and host are in the Galactic disk. The planet could have been detected and characterized purely with follow-up data, which has important implications for microlensing surveys, both current and into the LSST era. | Because microlensing planet detections are based on observations of a background source that is lensed by the planetary system, rather than observations of the planetary system itself, microlensing is unique in its ability to detect planets orbiting extremely dim or dark hosts or even planets without hosts \citep{sumi11}. For the same reason, however, microlensing planet hosts are often difficult to characterize. This can in principle be done by simultaneously measuring two higher-order effects during the event, yielding the Einstein radius $\theta_\e$ and the ``microlens parallax'' $\pi_\e$. Then the lens mass $M$ and lens-source relative parallax $\pi_\rel$ are given by \citep{gould92} \begin{equation} M = {\theta_\e\over \kappa \pi_\e}; \qquad \pi_\rel = \pi_\e\theta_\e; \qquad \kappa\equiv {4G\over c^2\au}\simeq 8.1\,{{\rm mas}\over M_\odot}. \label{eqn:mpirel} \end{equation} This has been successfully carried out for a significant minority of microlensing planets to date, and actually verified in one case by direct imaging \citep{ob06109,ob06109b}. However, while $\theta_\e$ has been measured in the great majority of published planetary events, $\pi_\e$ usually proves too difficult to measure. In this case, one only has the mass-distance constraint, \begin{equation} M \pi_\rel = {\theta_\e^2\over \kappa}. \label{eqn:mpirel2} \end{equation} An alternate approach is to directly observe the lens in high-resolution images, either under the ``glare'' of the source while they are still superposed, provided that the lens is sufficiently bright \citep{mb11293B}, or by waiting for the lens and source to separate (Batista et al.\ 2014b, in preparation; Bennett et al.\ 2014, in preparation). Of course, direct imaging is ill-suited to detecting dark hosts, but it can at least verify that they are dark, particularly if the mass-distance constraint (Equation~(\ref{eqn:mpirel2})) is available. Here we present MOA-2013-BLG-220Lb, with super-Jupiter planet/host mass ratio $q=3.0\times 10^{-3}$. Although the host (and so planet) mass is presently unknown, we show that it is moving rapidly away from the source ($\mu_\rel=12.5\pm 1\,\masyr$) and so can be imaged separately within $\sim 7\,$yrs. | We have presented the discovery of a planet with relatively high mass ratio $q=0.0030$, i.e., three times that of Jupiter and the Sun. The underlying event has a relatively high proper motion, $12.5\,\masyr$. Two lines of argument show the planet lies in the Galactic disk. First, the measured Einstein radius $\theta_\e=0.45\,$mas, together with an upper limit on the lens flux, implies that the lens lies at least 1.7 kpc in front of the source. Second, the source (actually, ``baseline object'') proper motion is $\sim 6\,\masyr$ counter to Galactic rotation, implying that typical disk-lens motion of $\sim 6.5\,\masyr$ would naturally produce the observed lens-source relative proper motion. The actual lens mass and distance can be measured in the short term by looking for excess flux at the position of the lens in {\it HST} or ground-based AO observations provided it is at least 10\% of the source brightness and otherwise by $\sim 2021$, i.e., once the lens and source have moved far enough apart to be separately resolved. | 14 | 3 | 1403.2134 |
1403 | 1403.3242_arXiv.txt | We explore bounce cosmology in $F(\mathcal{G})$ gravity with the Gauss-Bonnet invariant $\mathcal{G}$. We reconstruct $F(\mathcal{G})$ gravity theory to realize the bouncing behavior in the early universe and examine the stability conditions for its cosmological solutions. It is demonstrated that the bouncing behavior with an exponential as well as a power-law scale factor naturally occurs in modified Gauss-Bonnet gravity. We also derive the $F(\mathcal{G})$ gravity model to produce the ekpyrotic scenario. Furthermore, we construct the bounce with the scale factor composed of a sum of two exponential functions and show that not only the early-time bounce but also the late-time cosmic acceleration can occur in the corresponding modified Gauss-Bonnet gravity. Also, the bounce and late-time solutions in this unified model is explicitly analyzed. | 14 | 3 | 1403.3242 |
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1403 | 1403.4979_arXiv.txt | {} {We aim at constraining the assembly history of clusters by studying the intra cluster light (ICL) properties, estimating its contribution to the fraction of baryons in stars, f$_*$, and understanding possible systematics/bias using different ICL detection techniques.} {We developed an automated method, {\it GALtoICL}, based on the software GALAPAGOS to obtain a refined version of typical BCG+ICL maps. We applied this method to our test case MACS J1206.2-0847, a massive cluster located at z$\sim$0.44, that is part of the CLASH sample. Using deep multi-band SUBARU images, we extracted the surface brightness (SB) profile of the BCG+ICL and we studied the ICL morphology, color, and contribution to f$_*$ out to R$_{500}$. We repeated the same analysis using a different definition of the ICL, {\it SBlimit} method, \ie a SB cut-off level, to compare the results.} {The most peculiar feature of the ICL in MACS1206 is its asymmetric radial distribution, with an excess in the SE direction and extending towards the 2$^{nd}$ brightest cluster galaxy which is a Post Starburst galaxy. This suggests an interaction between the BCG and this galaxy that dates back to $\tau\leq1.5$Gyr. The BCG+ICL stellar content is $\sim8$\% of M$_{*,\,500}$ and the (de-) projected baryon fraction in stars is f$_{*}=0.0177 (0.0116)$, in excellent agreement with recent results. The {\it SBlimit} method provides systematically higher ICL fractions and this effect is larger at lower SB limits. This is due to the light from the outer envelopes of member galaxies that contaminate the ICL. Though more time consuming, the {\it GALtoICL} method provides safer ICL detections that are almost free of this contamination. This is one of the few ICL study at redshift z $>$ 0.3. At completion, the CLASH/VLT program will allow us to extend this analysis to a statistically significant cluster sample spanning a wide redshift range: 0.2$\lesssim$z$\lesssim$0.6.} {} | \label{Sec:Int} Since its first discovery by \citet{Zwicky1951} to the most recent works \citep{Guennou2012,Burke2012,Adami2012} the intra cluster light (ICL) has gained increasing interest because it can help us understanding both the assembly history of galaxy clusters and its contribution to the baryonic budget. The ICL consists of stars which are bound to the cluster potential after being stripped from member galaxies as they interacted and merged with either the brightest cluster galaxy (BCG) or the other member galaxies \citep{Murante2004,Sommer2005,Monaco2006,Murante2007,Conroy2007,Puchwein2010,Rudick2011,Cui2013,Contini2013}. The ICL signature can be seen in the surface brightness (SB) profile of the BCG as an excess of light with respect to the typical r$^{1/4}$ law \citep{DeVaucouleurs1953}. \citet{Gonzalez2005} showed that a double r$^{1/4}$ model provides a better fit to the BCG+ICL SB profile and that the ICL has a more concentrated profile than that of the total cluster light \citep[see also][]{Zibetti2005}. The origin of the ICL strictly connects it to the evolutionary history of the clusters, thus, we can recall the assembly history of the clusters by studying the ICL properties. The ICL colors can provide us information on the timescales involved in ICL formation and on its progenitors when compared to BCG colors. Some works found that ICL colors are consistent with those of the BCG \citep[\eg][]{Zibetti2005,Krick2007,Pierini2008,Rudick2010}, suggesting that the ICL has been originated by ongoing interactions among cluster members and the BCG. The merging cluster in the sample of \citet{Pierini2008} and some compact groups \citep{DaRocha2005} represent an exception showing bluer colors for the ICL, hinting to either {\it in-situ} star formation or blue dwarf disruption after interaction. Usually the ICL is found to be strongly aligned with the position angle (PA) of the BCG \citep{Gonzalez2005,Zibetti2005}, but there are cases of misalignment and/or prominent features/plumes \citep{Mihos2005,Krick2007}. Studying the connections between the ICL spatial distribution and the presence of cluster substructures can shed a light on the origin of the ICL and its connection to the assembly history of the cluster. ICL plume-like structures bridging together the BCG and other galaxies, arcs and tidal streams of ICL have been found by many works \citep[\eg][]{Gregg1998,Calcaneo2000,Feldmeier2004,Krick2006,DaRocha2008}. According to simulations these features trace recent interactions and/or merger events between galaxies and/or clusters and they are supposed to last only $\sim$1.5 times their dynamical timescale because of disruption by cluster tidal field \citep{Rudick2009}. \citet{Adami2005,Krick2007} also found an association between ICL sources and infalling groups of galaxies and they used it to infer the dynamical evolution of the clusters. Beside characterizing the ICL properties and the specific evolution of a single cluster, the ICL can be put in a much more comprehensive context by determining its contribution to the total stellar cluster mass and, as a consequence, to the baryon fraction. Observational studies show fractions of ICL ranging from few percent of the total light up to half of it \citep{Feldmeier2004,DaRocha2005,Zibetti2005,Krick2007,Gonzalez2007,DaRocha2008,Guennou2012,Burke2012,Adami2012}, depending on enclosing radius, and/or cluster mass. On top of this there is no common definition of ICL both among observational works and simulations. Ideally the ICL consists of the residual light after having subtracted the contribution of all galaxies, including the BCG. However both choosing the separation between the BCG and the ICL, and determining the best fit model of member galaxies is a difficult task. As a consequence some studies prefer to focus on a BCG+ICL map and mask other members \citep{Gonzalez2005,Gonzalez2007}, while other authors chose to mask all galaxies down to different arbitrary surface brightness levels, \citep{Zibetti2005,Krick2007,Burke2012}, and finally \citet{DaRocha2005,Guennou2012} remove all the galaxy contribution via a wavelet technique. Different ICL detection methods can suffer from different systematics/bias thus providing discordant ICL fractions as shown for simulations \citep{Cui2013}. This variety of ICL definitions can explain part of the lack of a general consensus on the effective role played by the ICL in the cluster baryon budget. Moreover the fraction of ICL can correlate with global cluster properties such as mass, projected distance and redshift depending on the dominant process and epoch at which they occur \citep[see][for a comprehensive description of the origin of these correlations]{Krick2007}. \citet{Guennou2012} found only a weak correlation between the ICL content and the cluster velocity dispersion/mass and there is no variation in the amount of ICL between z = 0.4 and z = 0.8. The absence or mildness of these trends is confirmed also at lower redshifts, \ie z $<$ 0.3, \citep{Zibetti2005,Krick2007}. These findings are inconsistent with most of the previous results from both cosmological and analytical simulations which generally agree with an increasing ICL fraction as cluster mass grows \citep{Murante2004,Lin2004,Purcell2007,Watson2012}. However recent simulations suggest a much weaker dependence of the ICL fraction on cluster mass \citep{Murante2007,Dolag2010,Puchwein2010,Martel2012,Cui2013}. Apparently ICL is a promising and complementary way to understand the mechanisms occurring in galaxy cluster and their constituents, however there are two main disadvantages. First the ICL features typically have extremely faint surface brightnesses of $\sim$1\% of the brightness of the night sky, making their study extremely difficult. Secondly, the surface brightness dimming increases with redshift as: $(1 + z)^4$. As a consequence, detecting the ICL is very difficult and there are only few detections at $z>0.3$ \citep{Jee2010,Guennou2012,Burke2012,Adami2012,Giallongo2013}. In this paper we present our ICL detection and measurement method and the results we obtained from optical images of MACS1206.2-0847 (hereafter MACS1206), one cluster in the Cluster Lensing And Supernova survey with Hubble (CLASH) sample \citep{Postman2012}. Overall this cluster is one of the most massive, M$_{200}$ = 1.41$\times$10$^{15}$ \Msun, among the CLASH sample and it is located at a medium-redshift, z$\sim$0.44, with plenty of ancillary information, so it is a suitable case in order to test the performances of our ICL detection method. The CLASH survey comprises 25 massive clusters of galaxies in the redshift range $0.2 \lesssim z \lesssim 0.9$. Among these, 14 have been selected for spectroscopic follow-up at the VLT. At completion, both photometric and dynamical properties of each cluster will be available allowing the study of ICL and its connection to cluster properties over a wide redshift range. Using deep multi-band images from SUBARU, we studied the colors and the morphology of the ICL in MACS1206, as well as its connection to cluster substructures and its contribution to the total baryon budget. We then compare these results with those we obtain applying different ICL detection methods, in order to explore advantages/disadvantages of each method and to reveal possible systematics in each method. In Sect. \ref{Sec:data} we show the data set we used and the details of the reduction, in Sect. \ref{Sec:method} we explain our ICL detection and measurement method. Sect. \ref{Sec:results_M1206} describes our results in terms of both ICL properties and its contribution to the total cluster light/mass. We discuss our results in Sect. \ref{Sec:discussion} and in Sect. \ref{Sec:conclusions} we draw our conclusions and future prospects. Throughout this paper we use \hnot = 70 \kmsecmpc, \omegaM = 0.3, and \omegaL = 0.7, which gives 5.685 \kpcharc at z=0.44, the distance of MACS1206. | \label{Sec:conclusions} In conclusions we have developed an authomated method to extract BCG+ICL light maps in a refined way: {\it GALtoICL}. Applying this technique to MACS1206: \begin{enumerate} \item We have highlighted the presence of an extra component, \ie the ICL, when studying the SB profile of the BCG. This component appears to be asymmetric in radial distribution and we interpret it as an evidence of a past merger. We have linked the ICL properties to those of the cluster substructures and this way we have reconstructed the most recent cluster assembly history. \item We have estimated the BCG+ICL mass fraction and the (de-) projected f$_*$ of MACS1206 to be in good agreement with recent literature results suggesting a lowering in star formation efficency at higher cluster masses. \item We have estimated the sole ICL contribution with two different methods, {\it GALtoICL} and the {\it SBlimit} methods, and compared their results. The {\it SBlimit} method provide ICL fractions systematically larger than those obtained with the {\it GALtoICL} method due to member galaxies, other than the BCG, light contamination. The {\it GALtoICL} method removes this contamination by fitting simultaneously galaxies, thus providing safe ICL detection and it also highlights the presence of features/plumes in the ICL. As a con, the {\it GALtoICL} method is much more time consuming compared to simpler methods such as the SB limit definition and it can only be applied to small field of view. \item Based on the {\it SBlimit} method, we have obtained the first temptative ICL global SED. The ICL mass fraction we obtained by the SED fitting are in qualitative good agreement with those simply obtained by fluxes in the single reference broadband filter Rc. \end{enumerate} The high-quality dataset, the new refined ICL detection method, and the comparison of different ICL detection methods are the most striking novelties of this work. Deep multiband photometry allowed us to securely detect the ICL at a relatively high redshift, z=0.44, while the spectroscopic information allowed us to select cluster members, determine their masses down to $\log$(M/M$_\odot$)=9.5 and thus obtain an accurate estimate of the cluster stellar mass, BCG+ICL stellar mass, and f$_*$. The wide spectroscopic dataset also permit to associate the ICL properties to the dynamical analysis of MACS1206 and thus reconstruct its assembly history. While a single data point can not give statistical relevance to our results and/or allow to draw strong conclusions, at completion the CLASH/VLT survey will provide a high quality dataset over a wide redshift range, thus enabling us to constrain both the role of the ICL in the baryon budget and the f$_*$-M$_{500}$ relation. This work has also highlighted the importance of a common definition of ICL to allow comparison among both observational and numerical works. Simple ICL definition such as the {\it SBlimit} method might be easier to compare but they do not retrieve the real ICL properties because of contamination effects. | 14 | 3 | 1403.4979 |
1403 | 1403.1586_arXiv.txt | I make a short revision of Cosmology questions which ALMA was built to address. Without diving into much detail, I point out the ALMA specifications and strategies which are expected to provide a better handle of: the temperature evolution of the Cosmic Microwave Background (CMB) and the properties of its secondary anisotropies (such as the thermal and kinetic Sunyaev-Zel'dovich and the Ostriker-Vishniac effects); variability of dimensionless fundamental constants; H$_0$ and galaxy initial mass function by means of strong gravitational lensing; black hole science with the greatly expected Event Horizon Telescope. | Introduction} In my (still short) experience as an extra-galactic Astronomer, I got used to associating the question ``What Cosmology are they using?'' to mere three parameters: vaccum or dark energy density ($\Omega_\Lambda$), baryonic plus dark matter density ($\Omega_{\rm M}$), and the Hubble ``constant'' (H$_0$). As we all know, this simplification hides a whole lot of information. With the thirst to know where do we come from, Mankind characterized the Universe as best as possible in order to understand it. It did so by discovering or creating \cite{Duff02a,Duff02b} parameters and equations, which enabled a better description of the Universe's behaviour, but not always its nature \cite{Alexeevich10}. To be accepted, such theories were tested against observations \cite{Danjon46,Dyson20}. It goes without saying that the instrumentation available to Mankind played a key role in this quest for knowledge. While improved instrumentation and statistical work keep breaking degeneracies between models, theoreticians implement changes to their theories or propose new ones. This manuscript deviates from my presentation's title at Cosmosur\,II, but not from its content. I focus on key subjects of Cosmology and how the Atacama Large (sub-)Millimetre Array (ALMA) may help us take a step forward towards understanding our Universe. | 14 | 3 | 1403.1586 |
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1403 | 1403.4476_arXiv.txt | We study the multi-dimensional properties of neutrino transfer inside supernova cores by solving the Boltzmann equations for neutrino distribution functions in genuinely six dimensional (6D) phase space. Adopting representative snapshots of the post-bounce core from other supernova simulations in three dimensions, we solve the temporal evolutions to stationary states of neutrino distribution functions by our Boltzmann solver. Taking advantage of the multi-angle and multi-energy feature realized by the S$_n$ method in our code, we reveal the genuine characteristics of spatially three dimensional (3D) neutrino transfer such as non-radial fluxes and non-diagonal Eddington tensors. In addition, we assess the ray-by-ray approximation, turning off the lateral-transport terms in our code. We demonstrate that the ray-by-ray approximation tends to propagate fluctuations in thermodynamical states around the neutrino-sphere along each radial ray and overestimate the variations between the neutrino distributions on different radial rays. We find that the difference in the densities and fluxes of neutrinos between the ray-by-ray approximation and the full Boltzmann transport becomes $\sim20\%$, which is also the case for the local heating rate, whereas the volume-integrated heating rate in the Boltzmann transport is found to be only slightly larger ($\sim2\%$) than the counterpart in the ray-by-ray approximation due to cancellation among different rays. These results suggest that we had better assess carefully the possible influences of various approximations in the neutrino transfer employed in the current simulations on supernova dynamics. Detailed information on the angle and energy moments of neutrino distribution functions will be profitable for the future development of numerical methods in neutrino-radiation hydrodynamics. | Neutrinos play an essential role in the mechanism of core-collapse supernovae as a driving force in the dynamics starting from the gravitational collapse of massive stars. Transport of energy and lepton number via neutrinos is particularly crucial to determine their outcomes, i.e. explosions with an energy of 10$^{51}$ erg \citep{bet90,kot06,jan07}. Electron-type neutrinos are produced by electron captures in the collapsing phase and are trapped inside the central core to give pressure support. Pairs of neutrinos are created after bounce as a part of the thermal energy converted from the gravitational energy. Emissions of the trapped neutrinos result in an energy release of $\sim$10$^{53}$ erg in the form of supernova neutrinos. The release of this huge energy in neutrinos was indeed vindicated in the observed events of SN 1987A \citep{hir87}. The emitted neutrinos carry valuable information of the mechanism of explosion as well as the properties of dense matter inside compact stars and progenitors (see \citet{nak13}, for example, and references therein). Interactions of neutrinos with material in the supernova core contribute to the energy transfer in a significant size. The shock wave generated by core bounce stalls soon after the launch and fizzles later in the case of strictly spherical geometry. Without such an artificial restriction in geometry, multi-dimensional hydrodynamical instabilities occur and push the stalled shock so that it could hover at larger radii. A portion of the emitted neutrinos is absorbed by the matter behind the stagnant shock wave and may lead eventually to its outward propagation again. This so-called neutrino heating mechanism \citep{bet85} combined with the multi-dimensional hydrodynamical instabilities is one of the most promising ways to trigger the explosion particularly under a marginal condition. In fact, energy gain by the neutrino heating amounts to $\sim$10$^{51}$ erg, which is comparable to the observed explosion energy of supernovae \citep{jan96}. Whether the neutrino heating mechanism is the essential cause of explosion or not remains an unsolved issue, though \citep{jan12,bur13}. In order to advance further our understanding of the role of neutrinos in the intrinsically multi-dimensional dynamics, the evaluation of neutrino heating and cooling should be as accurate as possible. Neutrinos interact with matter very frequently and diffuse outward only gradually inside the proto-neutron star just born after the bounce. Since the temperatures are high in the proto-neutron star, neutrinos are coolant there. On the other hand, a partial absorption of the emitted neutrinos takes place outside the neutrino-sphere below the stalled shock wave before they stream out of the star freely, which heats the matter there. Quantitatively accurate treatment of neutrino transfer is hence mandatory to provide correct rates of cooling and heating since the energy transport proceeds across the region, where neither diffusion nor free-streaming approximation is applied. The emergent fluxes and energy spectra of neutrinos are determined by the neutrino-matter interactions around the energy-dependent neutrino-spheres. We need to do multi-energy group computations, since the interactions strongly depend on the neutrino energy. In the evaluation of the heating rate, on the other hand, the local number density of neutrinos are important in addition to the energy spectra. It is hence the angular distributions of neutrinos in their momentum space that should be given precisely. Although they are isotropic near the center and become forward-peaked at large radii, the angular distributions are highly non-trivial in the transitional region, which includes the heating region. The treatment of neutrino transfer should, therefore, be as accurate as possible, particularly in the description of the energy and angle distributions. In most of multi-dimensional numerical simulations of supernovae, however, some approximations are employed at the moment. This is simply because the full description of neutrino distributions is a six-dimensional (three spatial coordinates and three momenta of neutrinos) problem, which is formidable even for modern supercomputing resources. While computations with the multi-energy groups are becoming a standard nowadays, angular distributions are still commonly approximated one way or another. Since such approximations can be eliminated in spherically symmetric simulations, the influences of the approximations have been extensively studied \citep{jan92,mes98,yam99,lie05}. It is well known that the diffusion approximation with a flux-limiter tends to overestimate the degree of forward-peak and thus underestimate the heating rate \citep{jan92,mes98}. Although the difference is not so drastic, such a small change may be crucial, tipping the balance for explosion particularly in the marginal conditions \citep{jan96}. Validation of the approximate methods in multi-dimensions has growing importance, since the post-shock conditions obtained in multi-dimensional simulations appear more marginal for successful explosion. The diffusion approximations (including its variants such as IDSA) and/or the ray-by-ray methods are frequently used in the currently state-of-the-art 2D/3D simulations \citep{suw10,mul12b,bru13,tak12,han13,knak14a,suw14b,bru14}. Although they have reported a considerable number of successful explosions produced by the neutrino heating combined with the neutrino-driven convection and/or the standing accretion shock instability (SASI), their approximate treatments of neutrino transfer introduce a certain level of uncertainty. The influences of these approximations should be examined carefully before drawing any conclusion. In the past years we have indeed seen the multi-dimensional treatment of neutrino transfer progress substantially, keeping pace with the rapid increase of supercomputing resources. In two dimensions, multi-angle and multi-energy groups neutrino radiation-hydrodynamics have been performed to follow the post-bounce evolution of supernova cores \citep{liv04,ott08,bra11}. They adopted the discrete-ordinate (S$_n$) method to fully describe angle distributions in 2D space \citep{liv04}. \citet{ott08} reported the comparisons with the diffusion approximation. % They demonstrated that the multi-angle transport is needed to describe the neutrino distributions in globally aspherical supernova cores. \citet{bra11} analyzed further the neutrino heating and showed that the multi-angle transfer leads to less lateral variations in the neutrino distributions owing to an averaging effect. Such a detailed study has been limited to 2D. In three dimensions, there has been a remarkable progress in the multi-energy group transport, but not in the multi-angle group transport \citep{tak12,han13,tak14,tam14,mez14,hor14}. These simulations commonly adopted the ray-by-ray approximations although the radial transport was treated differently: the isotropic diffusion source approximation (IDSA) is employed by \citet{tak12,tak14} whereas the moment equations are solved together with a variable Eddington factor obtained from the solution of the 1D model Boltzmann equations in \citet{han13,tam14}. Results obtained by the two groups differ in many respects, most notably on the success or failure of explosion (see e.g. their 11.2M$_{\odot}$ model). Note, however, that the origin of the differences might be the employed neutrino reactions \citep{tak14b}. Provided that the number of reported models is still small and the employed physics and numerics are considerably different among them, it is still premature to draw a firm conclusion from these 3D simulations and further studies should be done systematically with the assessment of the influences from the approximations in 3D neutrino transfer. The purpose of this study is hence to explore the basic features of 3D neutrino transfer in realistic supernova cores with the multi-angle and multi-energy group Boltzmann solver for the first time. Adopting a set of profiles from 3D numerical simulations by \citet{tak12,hor14,tak14b}, we run our newly developed code \citep{sum12} to obtain stationary neutrino distribution functions for those fixed matter configurations. Taking advantage of the multi-angle treatment of our code, we explore the non-radial (polar and azimuthal) transport in the globally and locally aspherical matter distributions. Note that in our previous paper \citep{sum12} the background models were constructed by artificially deforming spherically symmetric models. We pay particular attention to the behavior of the angle moments of neutrino distribution functions in the transitional regime, which will be useful for development of numerical codes using the moment formalism. % Employing our Boltzmann code, we can study the quality of the ray-by-ray approximation, which is routinely used in many simulations in 2D and 3D\footnote{Some simulations implemented the ray-by-ray plus approximation, in which the lateral coupling is partially taken into account. }. As a matter of fact, simply dropping the polar and azimuthal advection terms, we can emulate the ray-by-ray approximation without changing other settings. We examine the non-radial transport, which will not be fully described in the ray-by-ray approximation. As we will show, the contributions of polar and azimuthal fluxes are significant even outside the optically thick region. It is also found that the ray-by-ray approximation tends to exaggerate the contrast between different radial rays, which may affect local neutrino-heating rates. The paper is organized as follows. We describe the methodology in \S \ref{section:3D-nu}. The realization of the ray-by-ray approximation in our code is also explained there. The 3D profiles taken from \citet{tak12,hor14,tak14b} are presented in \S \ref{section:3D-hyd}. We report in \S \ref{section:d-boltz} the basic features of 3D neutrino transfer, showing density, radial and non-radial fluxes obtained by the 6D Boltzmann solver. The corresponding results by the ray-by-ray approximation are presented in \S \ref{section:d-ray} for comparison. We investigate the heating rates obtained by both the 6D Boltzmann solver and the ray-by-ray approximation in \S \ref{section:h-boltz-ray}. In \S \ref{section:h-boltz-ray.others}, we present the results for other profiles and demonstrate that our findings are generic. The volume-integrated heating rates are examined in \S \ref{section:h-total} to discuss the global influences of 3D neutrino transfer on the supernova dynamics. In \S \ref{section:moments}, we show the angle and energy moments of the neutrino distribution functions. Discussions and implications of our study are given in \S \ref{section:discuss} followed by the summary in \S \ref{section:summary}. | \label{section:discuss} We discuss here some possible implications of our finding for the supernova mechanism and associated phenomena. % The 6D Boltzmann solver provides a seamless description of the neutrino transfer from optically thick to thin regions in 3D space. Non-radial neutrino transfer occurs in general up to large distances from the center beyond the neutrino-sphere, which can have influences on the convective motions of neutrino-rich matter inside the proto-neutron star as well as the emission properties around the neutrino-sphere. These may in turn affect the neutrino heating in the gain region and ultimately the revival of shock wave. Although the diffusion approximation can describe the non-radial transfer of neutrinos in the optically thick regime, the transition to the transparent regime is handled by a prescribed flux limiter, which is not easy to justify \citep{jan92,mes98}. The non-radial neutrino flux at large radii in the semi-transparent and transparent regimes, which we have seen above, can not be properly described by the diffusion-based approximation, since the flux in these regimes is not determined by the local gradient of neutrino density but is obtained non-locally as a superposition of neutrinos flying in different directions from distant points. The 6D Boltzmann treatment is a unique solution to treat such circumstances rigorously. It is, of course, more desirable to conduct the neutrino-radiation hydrodynamics simulations, which will be a future work, though. A recent study by the multi-energy group flux-limited diffusion approximation in 2D reported non-explosions for 12--25M$_{\odot}$ stars \citep{dol14}, being different from the successful 2D simulations by other groups \citep{suw10,mul12b,bru13,knak14a,suw14b}. This example again casts a light on uncertainties due to different approximations in neutrino transfer, which might lead to totally different outcomes. The 6D Boltzmann code will be helpful to decipher the discrepancies among them. (See \citet{lie09} for the validation of IDSA in 1D. ) The comparison of the ray-by-ray approximation with the 6D Boltzmann evaluation is beneficial for the supernova research, since this approximation is routinely used for the currently state-of-the-art numerical simulations in 2D and 3D spatial dimensions but its validation is rather scarce. While the ray-by-ray approximation is an efficient way to handle the neutrino transfer in multi-dimensions, it inevitably neglects some of the non-radial neutrino transport (See \citet{bura06} for partial coupling) and, as a consequence, tends to enhance artificially the contrast among different radial rays. These features found by the 6D Boltzmann solver in this paper are in accord with the comparison in 2D between the Boltzmann transport and the flux-limited diffusion approximation by \citet{ott08} and \citet{bra11} (See also \citet{dol14} for the discussions with a formal solution). It remains to be seen if this effect persists in 3D dynamical simulations. If the artificial enhancement of neutrino anisotropy lasts for a long period, it may have impact on the hydrodynamics. We have actually seen that it lasts at least for $\sim$10 ms. A larger neutrino-heating rate along a certain radial ray will give a strong push to the stalled shock wave locally in that direction. The opposite situation can arise in another direction, where neutrino heating is suppressed erroneously. The ray-by-ray approximation, therefore, may enhance the deformation of shock wave and might induce stronger hydrodynamical instabilities. In the 6D Boltzmann treatment, such anisotropies tend to be smoothed by the non-radial transport. It is advisable to pay an appropriate attention to this effect when one studies the anisotropy of neutrino distributions produced by local matter inhomogeneities. It remains to be seen whether the improvement by the 6D Boltzmann treatment indeed changes the behavior of hydrodynamical instabilities such as SASI \citep{blo07a,iwa08,nor10,han12,tak12,han13}. Very recently \citet{tam14} reported with the ray-by-ray approximation a new instability named Lepton-number Emission Self-suitained Asymmetry (LESA), which produces self-sustained, globally dipolar configurations. Note, however, that \citet{dol14} have found no such instability with the flux-limited diffusion approximation. LESA may hence be an artifact of the approximation. In fact, since it is claimed that the global coupling of anisotropy between the neutrino-sphere and shock wave is the key to the instability, accurate evaluations of the neutrino anisotropy may be crucial. It is hence interesting to see what the Boltzmann transport would produce. It may be that eventually only by performing full neutrino-radiation hydrodynamics simulations with Boltzmann transport can we disentangle this new twist. Our results suggest that the errors by the ray-by-ray approximation may be moderate for most of the cases. This will be a good news for the supernova research in 3D, since the current supercomputing resources are limited and allow only the 3D simulations with an approximate neutrino transfer. In future, however, it is necessary to remove even such moderate uncertainties. In fact, even a $\sim10\%$ error in the heating rate may have an impact on the revival of shock wave particularly when it is marginal. The neutrino distributions in the transparent regions are determined not locally but globally as a superposition of neutrinos flying in different directions from various distant points. The Boltzmann solver can fully take this into account in sharp contrast to other approximate methods. The neutrino spectra are also affected by such non-local features in neutrino transfer, reflecting thermodynamical states not just at a single point but in a wide region on the neutrino-sphere. It may hence be possible that the Boltzmann solver reveals new features in the neutrino spectra. It would then be also interesting to examine its influences on the nucleosynthesis of heavy elements via neutrino processes. This will be particularly the case when the proto-neutron star is strongly deformed due to rapid rotation. Since the core is globally asymmetric, the resulting fluxes are intrinsically non-radial. Such an effect was pointed out by \citet{ott08} in the case of a rapidly rotating 2D supernova core. Its observational consequences were studied \citep{bra11}. In the case of 3D the neutrino-sphere may be globally non-axisymmetric if the core rotates very rapidly. It would be interesting then to study its possible observational implications with the 6D Boltzmann transport. The main limitation of the current Boltzmann code is the angular resolution in describing the forward-peaked neutrino distribution functions in the optically thin region. A large number of grid points would be required if one were to fully resolve such configurations, which is simply unaffordable. Fortunately, the area, which we are most concerned with and where the Boltzmann solver is most needed, is the region from beneath the neutrino-sphere up to the stalled shock wave and the neutrino distribution function is not so forward-peaked yet there; the moderate angular resolution we can afford will be acceptable particularly for the evaluations of heating and cooling rates although detailed convergence tests are certainly necessary. If one wants to obtain the neutrino luminosities and spectra at different viewing angles quantitatively, one may need a finer angular mesh, which may require prohibitive computing resources in the current approach. (See, however, \S 4 in \citet{kot12} for the scaling of computational load. ) It would then be necessary to develop alternative techniques such as the variable angle mesh \citep{yam99} or the Monte Carlo method \citep{abd12}. Although the current study employs only the snapshots from the 3D supernova simulations with the ray-by-ray IDSA \citep{tak12,tak14,hor14,tak14b}, it is desirable to investigate other background models, since the neutrino transfer may be somewhat affected indirectly by the approximation employed in the supernova simulations. It will be also preferable to study the influences of the numerical grid employed (ex. spherical-polar vs 3D-cartesian as well as its resolution) and progenitor models. World wide collaborations will be indispensable in order to fully understand the 3D neutrino transfer. It may become possible then to choose suitable tool for a given problem (See \citet{ili06} for the cosmological radiative transfer codes, for example). The validation of the approximate methods currently used in 3D supernova simulations will be a necessary first step in that direction. The Boltzmann solver can be combined with the magneto-hydrodynamical code with no problem to study magneto-hydrodynamics scenarios of core-collapse supernovae in more realistic settings. The application will not be limited to the supernova. The neutrino transfer in the collapsar, which originates from more massive stars, for example, will be important for the jet formation in the gamma ray burst. The Boltzmann transport is particularly suitable to study such highly anisotropic and non-local problem. In particular information on the angle moments of neutrino distribution functions will be very helpful to develop a closure relation for the moment formalism, another approximate method. These issues are now under investigation with the 6D Boltzmann solver and will be reported elsewhere. Improvements of the current 6D Boltzmann code are certainly needed and may somewhat change the results. Among other things, the implementation of the modern reaction rates instead of the conventional set is mandatory to investigate the post-bounce dynamics quantitatively further as demonstrated in the previous papers \citep{bura06,len12a}. The modifications of the emission and absorption rates affect directly the cooling and heating rates. Addition of inelastic scatterings of neutrinos will modify their energy spectra and, as a result, anisotropy as well. Even the electron captures on nuclei affect the post-bounce dynamics by setting the initial stage. The proper account of relativistic corrections is another issue toward the ultimate realism \citep{lie04,sum05,bura06,len12b}. Implementations of the special relativistic effects such as the Doppler shift and aberration have been actually done recently \citep{nag14}. Combined with a Newtonian hydrodynamics code, it is now applied to the 2D supernova simulation and the results will be reported elsewhere. The incorporation of general relativistic corrections to the present code is also currently underway (See also \citet{car13b,shi14}). Its coupling to a general relativistic hydrodynamics code and a solver of the Einstein equation in 3D will be a grand challenge. We have explored the 3D properties of the neutrino transfer in supernova cores by solving the Boltzmann equation in 6 dimensions (3 in space and 3 in momentum space). We have performed the numerical simulations to obtain the stationary state of neutrino distribution functions in 6D phase space for the fixed backgrounds of the 3D supernova core. We used the typical profiles of the supernova core taken from the 3D supernova simulations of 11.2M$_{\odot}$ and 27.0M$_{\odot}$ stars by \citet{tak12,hor14,tak14b}. The numerical code to solve the Boltzmann equation in 6D handles the neutrino transfer in multi-energy and multi-angle group for three neutrino species. The three dimensional propagation of neutrinos is described by the S$_n$ method. The standard set of neutrino reactions is implemented in the collision term together with the table of equation of state. This is the application of the 6D Boltzmann solver to the realistic profiles of the 3D supernova cores for the first time. The 6D Boltzmann equation directly provides the energy and angle distributions of neutrinos in the whole region of the 3D supernova cores. Most importantly, the transport of neutrinos in the multi-angle description provides the information of the non-radial (polar and azimuthal) directions as well as the radial one. We have demonstrated that the 6D Boltzmann solver describes the 3D features of neutrino transfer, removing the approximations often used in the currently state-of-the-art simulations. The numerical results show that the non-radial fluxes are generally seen inside the proto-neutron star and can extend over the wide region beyond the optically thick region. We find that the ray-by-ray approximation, which is a popular approximation in the current supernova simulations, provides enhanced directional variations in neutrino distributions. We have computed the 3D neutrino transfer in the ray-by-ray approximation by using our numerical code, dropping off the non-radial transport terms. We have examined the characteristics of the ray-by-ray approximation for the same 3D profiles through the comparison with the 6D Boltzmann evaluation. In the ray-by-ray approximation, the non-spherical profiles of neutrino densities and fluxes tend to prevail from center to large distances. % This is in marked contrast to the 6D Boltzmann evaluation in which the integral from many directions provides the nearly spherical distribution outside the proto-neutron star. Our analysis has revealed that the ray-by-ray evaluation provides noticeable overestimation or underestimation of densities and fluxes along the radial ray. By examining the relative differences of the ray-by-ray evaluation with respect to the 6D Boltzmann evaluation, the deviations of $\sim20\%$ was found to develop depending on the environment. Once the neutrino emission is enhanced due to a local hot spot of the neutrino chemical potential, this modification continues along the radial ray. The reduced neutrino emission is similarly maintained. Therefore, we find alternate distributions of the rays with underestimation and overestimation outside the proto-neutron star. This behavior is seen commonly for $\nu_e$ and $\bar{\nu}_e$ distributions, which reflect the non-uniform distribution of the neutrino degeneracy. The sign of the deviations for the two species is opposite each other because of the opposite effects on the emission through the degeneracy. We have also found that the heating rates evaluated by the ray-by-ray approximation have deviations along the radial ray. The relative differences from the 6D Boltzmann evaluation amount to $\sim20\%$ in some regions but smaller than the case of the densities and fluxes in wide regions. This is because the overestimation and underestimation of the heating rates by $\nu_e$ and $\bar{\nu}_e$ cancel each other due to their opposite deviations in many cases. Significant deviations occur in the regions where the neutrino degeneracy is prominent from the average distribution, for example, in the narrow channels between the two mushroom-like outflows. This hot spot provides the enhanced heating rate along the particular radial ray. The hot spot effect may last for $\sim$10 ms as found in our study using the time series of the profile. We have found that the total amount of heating in the whole heating region in the ray-by-ray evaluation is slightly smaller than that in the 6D Boltzmann evaluation. These features of the ray-by-ray characteristics are common for the adopted profiles from the 11.2M$_{\odot}$ and 27.0M$_{\odot}$ stars, which represent the exploding and stalled shock situations. Our study calls for careful assessment of the angle-dependent heating effects which may affect the hydrodynamics. We remark that these features are found in the fixed background profiles and further studies in neutrino-radiation hydrodynamics are necessary. We have examined the basic features of the angle moments and the Eddington tensor in the 3D supernova cores. We show that the angle moments of the neutrino distribution functions obtained by the 6D Boltzmann solver have rather spherical profiles. The relative differences of the ray-by-ray evaluation appear in some regions, but limited within the inner part. % The components of the Eddington tensor exhibit deformed distributions in more wide regions than the case of angle moments. Since we have the 6D neutrino distribution functions, we can compute all components of the Eddington tensor and clarify the behavior of the diagonal and non-diagonal elements. We have demonstrated that there are regions with appreciable non-diagonal components in one of the snapshots as an example. Studies of these basic quantities will be helpful to develop new closure relations for the moment formalism in largely deformed profiles such as collapsars. The current study is a step toward the complete treatment of neutrino-radiation hydrodynamics implementing the full list of neutrino reactions in the general relativistic framework. It is of great interest how the 6D Boltzmann treatment affects the neutrino heating mechanism in hydrodynamical instabilities. The coupling of the 6D Boltzmann solver with the hydrodynamics is made recently \citep{nag14} and numerical studies to explore the dynamical outcome for explosions are currently underway. | 14 | 3 | 1403.4476 |
1403 | 1403.4530_arXiv.txt | {We study the Rayleigh--Taylor instability (RTI) at a prominence--corona transition region in a non-linear regime. Our aim is to understand how the presence of neutral atoms in the prominence plasma influences the instability growth rate, and the evolution of velocity, magnetic field vector and thermodynamic parameters of turbulent drops. We perform 2.5D numerical simulations of the instability initiated by a multi-mode perturbation at the corona--prominence interface using a single-fluid MHD approach including a generalized Ohm's law. The initial equilibrium configuration is purely hydrostatic and contains a homogeneous horizontal magnetic field forming an angle with the direction in which the plasma is perturbed. We analyze simulations with two different orientations of the magnetic field. For each field orientation we compare two simulations, one for the pure MHD case, and one including the ambipolar diffusion in the Ohm's law (AD case). Other than that, both simulations for each field orientation are identical. The numerical results in the initial stage of the instability are compared with the analytical linear calculations. We find that the configuration is always unstable in the AD case. The growth rate of the small-scale modes in the non-linear regime is up to 50\% larger in the AD case than in the purely MHD case and the average velocities of flows are a few percent larger. Significant drift momenta are found at the interface between the coronal and the prominence material at all stages of the instability, produced by the faster downward motion of the neutral component with respect to the ionized component. The differences in temperature of the bubbles between the ideal and non-ideal case are also significant, reaching 30\%. There is an asymmetry between large rising bubbles and small-scale down flowing fingers, favoring the detection of upward velocities in observations.} | Solar prominences are composed of cool, dense, and partially ionized plasma and their large-scale magnetic structure remains stable for days, or even weeks, in the solar corona. Prominence material is believed to be supported by the magnetic field \citep[see reviews by][]{Tandberg-Hanssen1995, Mackay+etal2010}. There are several large-scale models that address the problem of the global stability of prominences, and of the origin of their mass that may explain observational properties \citep{Pneuman1983, vanBallegooijen1989, Priest+etal1989, Antiochos+Klimchuk1991, Rust+Kumar1994, Antiochos1994, Aulanier1998, DeVore2000, Gibson2006, Aulanier+etal2006}. On the top of the global stability, prominences are extremely dynamical at small scales, showing a variety of shapes, moving with vertical and horizontal threads \citep{Berger2010, Ryutova+etal2010}. The dynamical appearance of prominences depends on whether these are located above active or quiet regions, and on the relative orientation with respect to the observer. Quiescent prominences usually occur in quiet regions at high latitudes. They usually reach larger heights than active region prominences, and often show very characteristic vertical threads of less than 1 Mm size, and downflow velocities of about 10--20 \kms\ along them\footnote{Due to their peculiar appearance, quiescent prominences with vertical threads are also known as `hedgerow prominences''.}. The origin of these downflowing drops has been addressed in many studies \citep{Gilbert2002, Gilbert2007, Ballegooijen2010, Haerendel2011}, aiming to explain the apparent material motion across the magnetic field lines, the speed of the drops, and the amount of the mass loss and gain. \citet{Berger2010} find large-scale 20--50 Mm arches, expanding from the underlying corona into the prominences. At the top of these arches, at the prominence--corona transition region (PCTR), there are observed dark turbulent upflowing channels of 4-6 Mm maximum width with a profile typical of the Rayleigh--Taylor (RT) and Kelvin--Helmholtz (KH) instabilities. The upflows rise up to 15--50 Mm, with an average speed of 13--17 \kms, decreasing at the end. Lifetimes of the plumes are about 300--1000 sec. These numbers fit well into the theoretical predictions from the classical theory of plasma instabilities \citep{Isobe+etal2005, Berger+etal2008, Heinzel+etal2008, Ryutova+etal2010, Berger2010, Berger+etal2011} and can therefore be used to derive plasma parameters of the prominences \citep{Hillier+etal2012c}. Plumes and spikes are seen at any time and any possible orientation of the limb portion of a prominence, but they are specially evident in quiescent hedgerow prominences. An alternative explanation for the upflowing plumes was recently proposed by \citet{Dudik+etal2012}, as due to the presence of separatrix layers and reconnection, arguing that RTI can not happen for the magnetic field orientation and plasma parameters expected for prominences. From the theoretical point of view, the existence of the instabilities at the PCTR is easily explained since the two media have clearly different densities, temperatures and relative velocities. The analytical linear MHD theory of these instabilities is well developed \citep[see, for example ][]{Chandrasekhar1981, Priest1982}. Numerical simulations in the non-linear regime have been performed for different astrophysical contexts in two and three dimensions \citep{Jun+etal1995a, Jun+etal1995b, Arber2007, Stone+Gardiner2007a, Stone+Gardiner2007b, Isobe+etal2006}. Recent numerical MHD simulations of the RTI in prominences by \citet{Hillier+etal2012a, Hillier+etal2012b}, including a rising buoyant tube in a Kippenhahn--Schl\"{u}ter prominence model show a good agreement with observations. Prominences are relatively cool and dense objects, with values of temperature and density in the chromospheric range \citep{Tandberg-Hanssen1995}. Therefore, a prominence material is expected to be only partially ionized. The presence of a large number of neutrals must affect the overall dynamics of the plasma, since neutrals do not feel the influence of the magnetic Lorentz force directly, but only through the collisional coupling to ions. The aim of our work is to model the dynamics of the Rayleigh--Taylor instability in the partially ionized prominence plasma in the non-linear regime. The linear theory of the Rayleigh--Taylor and Kelvin--Helmholtz instabilities in a partially ionized plasma has been recently developed by \citet{Soler+etal2012, Diaz+etal2012, Diaz+etal2013}. Different approaches have been used, including a two-fluid and a single fluid modeling. It is known from the ideal MHD that the magnetic field parallel to the perturbation interface stabilizes the system, up to some threshold wavelength $\lambda_c$: \begin{equation} \label{eq:lambdac} \lambda_c=\frac{4\pi B_0^2\cos^2\theta}{(\rho_2-\rho_1)g\mu_0} \end{equation} where $B_0\cos\theta$ is the value of the magnetic field in the plane of the perturbation, and $\rho_2-\rho_1$ is the density contrast between the two media. For a given value of the magnetic field, perturbations with a wavelength shorter than $\lambda_c$ are stable, while large wavelength perturbations remain to be unstable. The results of the linear theory show that, in a partially ionized plasma, there is no critical wavelength, and perturbations in the whole wavelength range are always unstable \citep{Soler+etal2012, Diaz+etal2012, Diaz+etal2013}. The growth rate of a given perturbation in a partially ionized plasma depends (among other parameters) on the ionization fraction and keeps being rather small for the ionization fractions expected for the prominence plasma. The linear instability theory has the advantage of being analytical, but then a number of simplifications is necessary, limiting the range of its validity. In order to consider the fully non-linear evolution of the Rayleigh--Taylor instability, and to include more complex physics, numerical simulations have to be performed. Here we report on 2.5D numerical simulations of the RTI at the boundary between the hot corona and a cool prominence taking into account plasma partial ionization by means of the generalized Ohm's law. \begin{figure}[t] \center \includegraphics[width=9cm]{ms_fig1-eps-converted-to} \caption{{\footnotesize Sketch of the initial configuration. The instability develops in the $XZ$ plane containing the perturbation vector $\vec{k}$; the initial magnetic field $\vec{B}_0$ forms an angle $\theta$ with the $XZ$ plane. $\vec{B}$ is initially lying in $XY$ plane, parallel to the interface separating the prominence and coronal plasma, with $B_z=0$, $B_x=B_0\cos(\theta)$ and $B_y=B_0\sin(\theta)$.} }\label{fig:sketch} \end{figure} \begin{table}[!b] \begin{center} \centering \caption{ Parameters of the equilibrium configuration, showing the values of temperature ($T$), density ($\rho$), Alfv\'en ($v_a$) and sound ($c_s$) speeds, Ohmic diffusion coefficient ($\eta$, Eq. \ref{eq:etac}), ambipolar diffusion coefficient ($\eta_A$, Eq.~\ref{eq:etaa}), and fraction of neutrals ($\xi_n=\rho_n/\rho$).} \label{tab:model} \begin{tabular}{ccc} \hline & Corona & Prominence \\ \hline $T$ [kK] & 400 & 5 \\ $\rho$ [kg m$^{-3}$] & 3.7$\times$10$^{-12}$ & 2.9$\times$10$^{-10}$ \\ $v_a$ [km s$^{-1}$] & 450 & 53 \\ $c_s$ [km s$^{-1}$] & 75 & 8.3 \\ $\eta$ [m$^2$ s$^{-1}$] & 7.3 & 3.3$\times$10$^3$ \\ $\eta_A$ [m$^2$ s$^{-1}$] & 0 & 2.3$\times$10$^8$ \\ $\xi_n$ & 0 & 0.9 \\ \hline \end{tabular} \end{center} \end{table} \begin{figure*}[!ht] \center \includegraphics[width=16cm]{ms_fig2a-eps-converted-to} \includegraphics[width=16cm]{ms_fig2b-eps-converted-to} \caption{{\footnotesize Time evolution of density (top) and pressure (bottom) in the AD simulation with $\theta=90$\degree. The size of each snapshot is 250$\times$1000 km, the elapsed time is given at the bottom of each panel. The velocity field is indicated by arrows. Note the asymmetry between the large-scale rising bubbles and small-scale downflowing fingers in the density images. } }\label{fig:tevol90} \end{figure*} \begin{figure*}[!ht] \center \includegraphics[width=16cm]{ms_fig2a_mhd-eps-converted-to} \includegraphics[width=16cm]{ms_fig2b_mhd-eps-converted-to} \caption{{\footnotesize Same as Fig. \ref{fig:tevol90} but for the MHD simulation.} }\label{fig:tevol90mhd} \end{figure*} | We have studied how the presence of neutral atoms in a prominence plasma influences the development of the Rayleigh--Taylor instability at the coronal-prominence interface by means of numerical 2.5D simulations. Our approach consisted in solving the single-fluid quasi-MHD equations including physical diffusion term (ambipolar diffusion) in the induction and energy equations. Such approach is justified in the regime of strong collisional coupling of the plasma. Our main goal was to investigate the RTI in partially ionized plasmas in the non-linear regime to verify and extend the conclusions from the linear theory. Our main finding is that the configuration containing neutral atoms is always unstable on small scales. While in the completely ionized plasma the growth rate of the small-scale harmonics is lowered (or becomes zero) due to the action of magnetic forces, this is not like that if neutral atoms are present. We obtain an increase in the growth rate of the small scale harmonics, up to 50\%, when partial ionization effects are taken into account (Fig.~\ref{fig:scales89}). This result is in good agreement with the linear theory \citep[][see our Fig.~\ref{fig:linear}]{Soler+etal2012, Diaz+etal2012, Diaz+etal2013}. We show that, relaxing the approximations of the linear analysis, the growth rate is still large in the non-linear regime of the RTI. A statistical comparison reveals that this fast growth rate at small scales produces, on average, a 2--3 percent larger flow velocities in the model with ambipolar diffusion term ``on'' compared to the purely MHD model (Fig.~\ref{fig:vzlinear89}). Another action of the ambipolar diffusion is the dissipation of currents in the direction perpendicular to the magnetic field. Such dissipation allows to transform magnetic energy into internal energy \citep{Khomenko+Collados2012, MartinezSykora+etal2012}, and this results in heating of the plasma in the prominence part of the domain. The temperature increase due to this effect is about 5--10\% inside the prominence, and about 10--20\% at the PCTR, compared to the model without ambipolar diffusion (Fig.~\ref{fig:dt89}). While the heating is produced, we observe that the amplitude of perpendicular currents, $J_{\perp}$, becomes progressively lower in the model with ambipolar diffusion, reaching 20--30\% difference with the pure MHD case. The ambipolar diffusion introduces an anisotropy in the system since, with time, perpendicular currents get dissipated and the longitudinal ones are unaltered. Such anisotropic dissipation tends to create force-free structures, as was shown in the simulations by \citet{Leake+Arber2006, Arber2009}. As the instability evolves, the initially sharp interface gets smoother and is filled with a mixture of coronal and prominence material. In this transition layer, the density, ionization fraction, collisional frequency, and other parameters vary strongly from prominence to coronal values. Due to the decrease of density, the collisional coupling becomes less strong. As a consequence of that, a non-negligible drift momentum appears at this layer (Eq~\ref{eq:momw}, Fig.~\ref{fig:omega89}), with a value of 10--15\% of the individual ion and neutral momenta. The sign of the drift momentum indicates that the neutral atoms at the bottom part of the downflowing drop move with slightly larger downward velocities. The neutrals feel the presence of the magnetic Lorentz force only through the collisions with the ionized particles and, once the collisional coupling weakens, this relative motion between the components becomes possible. Perpendicular currents also reach maximum values inside the transition layer between the prominence and coronal material. Therefore, the action of partial ionization effects on the RTI is localized in space to a small zone. This explains why the inclusion of these effects in our current modeling only alters the global parameters of the flow (thermodynamic parameters, velocities, magnetic field) by no more than a few tens of percent. In a different, non current-free equilibrium configuration, the action of partial ionization effects could be significantly amplified. Our initial equilibrium configuration is the simplest possible, purely hydrodynamical with a homogeneous magnetic field. Such configuration is different from the equilibrium usually thought to exist in prominences producing their large-scale stability \citep{Tandberg-Hanssen1995, Mackay+etal2010}. The support of the prominence material is thought to be provided by the magnetic tension. Contrarily, we neglect the effects of the magnetic field curvature in our analysis. Our choice was motivated by two reasons. On the one hand, such equilibrium is a natural choice for the 2.5D modeling that does not allow to include the effects of magnetic field curvature perpendicular to the perturbation plane \citep[as Kippenhahn-Schl{\"u}ter model, see][]{Hillier+etal2012a, Hillier+etal2012b}. We have presented here an exploratory study to investigate the importance of partial ionization effects, and 2.5D simulations, instead of full 3D, allow for faster calculations. On the other hand, we have also pursued with this work an adequate comparison with the linear theory, where the same equilibrium is adopted \citep{Diaz+etal2013}. Our equilibrium model causes several limitations. Since the temperature in the prominence part of the domain is rather low, the pressure scale height is only a few hundreds of km, and we are unable to extend the model in height to have a large slab of prominence material, since the pressure and density quickly drop to coronal values. This limits the size of the computational box, making impossible the direct comparison to observations of the whole prominence structure. The current-free equilibrium is another drawback, since, as already mentioned above, the action of the partial ionization effects is only limited to a narrow transition zone, decreasing its potential influence. As a consequence of our equilibrium model, the force balance developed in the simulations is different from the one found in \citet{Hillier+etal2012a, Hillier+etal2012b}. The main force to balance gravity in the downflowing drop in Fig.~\ref{fig:tevol89} is found to be the magnetic pressure force (Fig.~\ref{fig:vdrop}), unlike the magnetic tension force in the aforementioned papers. Since we have not introduced any buoyant rising material, as in \citet{Hillier+etal2012a, Hillier+etal2012b}, the distribution of upflows and downflows is significantly more symmetric in our case (Fig.~\ref{fig:vz90}). However, due to mass conservation, the upflowing rising bubbles of the coronal material have significantly larger sizes than the downflowing fingers of dense prominence material (Fig.s~\ref{fig:tevol90} and \ref{fig:tevol89}). Therefore, assuming the density to be a proxy for the intensity in $H_{\alpha}$ imaging observations, observational detection of upflows is easier and could cause the observed asymmetry \citep{Berger2010, Ryutova+etal2010}. The simulations described above are only done for two orientations of the magnetic field, one normal to the perturbation plane, $\theta=90$\degree, and another one skewed by just one degree from the normal, $\theta=89$\degree. It might seem surprising that the structures developed in both cases are so different. Such behavior is nevertheless expected from the properties of the non-linear flow cascade and are observed in many other simulations of the RTI in different astrophysical contexts in 2 and 3 dimensions \citep{Jun+etal1995b, Wang+Robertson1985, Isobe+etal2006, Stone+Gardiner2007a, Stone+Gardiner2007b, Hillier+etal2012a}. The increase of the dominant scale with time (Fig.~\ref{fig:maxscale}) is in a good agreement with other works \citep{Jun+etal1995b}. Since the maximum perturbation wavelength was of the size of the computational domain, $\lambda=$250 km, it is natural that with time the perturbation of this scale dominates. The results of our initial calculations in a larger box \citep{Khomenko+etal2013} show that the same perturbation develops several drops on the same time scale. There, a simulation with $\theta=88$\degree\ was also analyzed and essentially lead to the same conclusions as for the enhanced growth rate of small scale modes with the ambipolar diffusion term ``on''. The disappearance of small scales in the $\theta=89$\degree\ simulation is caused by the cut-off wavelength introduced by the component of the magnetic field in the perturbation plane and is also in agreement with other numerical works \citep{Stone+Gardiner2007a}. One also has to keep in mind that the size of our computational box is relatively small compared to the cut-off wavelength introduced by magnetic field skewed by just 1\degree\ away from normal, $\lambda_c=38$ km. The main issue of our modeling is the use of the Saha equation to update the electron density and neutral fraction at each time step of the simulations. At prominence temperatures of the plasma, the deviations from the instantaneous ionization equilibrium can be significant, and the use of Saha equation may lead to an underestimation of the electron density. A more appropriate approach would be to consider a time-dependent ionization balance. \citet{Leenaarts2006, Leenaarts2007, Wedemeyer2011} have shown that, while the ionization process happens rapidly, the recombination is slow, so the ionization fraction is maintained rather constant in time and space even when significant temperature fluctuations are present. The calculations of the impact of time-dependent ionization balance on the development of the RTI in partially ionized plasma needs a thorough study. However, such calculations require significant computational resources and are beyond the scope of the present explorative work. Besides the Rayleigh-Taylor instability per se, the posterior time evolution of the downflowing drop from Fig.~\ref{fig:tevol89} deserves a separate discussion. After the downward motion of the drop stops at $t\approx160$ sec, it remains oscillating around the equilibrium position, extending in the horizontal direction. The evolution of the drop brings close the magnetic field lines at the coronal part of the domain and reconnection happens at about 200 sec of the simulation. The plasmoid formed after this reconnection is visible at time 237 sec in Fig.~\ref{fig:tevol89}. The layer of plasma linking the drop to the main part of the prominence becomes thinner and finally another reconnection happens in the chromospheric part of the domain. Another magnetic island is formed at the location of the drop, and the drop becomes almost completely disconnected from the rest of the prominence, extending even more in the horizontal direction and forming a thread (not shown in Fig.~\ref{fig:tevol89}). The reconnections and the formation of the horizontal thread will need further analysis in a separate paper. The process of the drop falling across the horizontal magnetic field lines under the action of gravity, its disconnection from the magnetic field of the rest of the prominence and forming a finite plasma island may resemble the mechanism proposed by \cite{Haerendel2011}. Summarizing all above, we conclude that partial ionization effects on the Rayleigh-Taylor instability in prominences are non-negligible and have to be taken into account in models of prominence dynamics. In the future, we will consider larger simulation boxes in three dimensions to perform the comparison with observations, and will investigate the development of the instability for different ionization fractions and initial equilibrium configurations. | 14 | 3 | 1403.4530 |
1403 | 1403.7705_arXiv.txt | Winking (oscillating) filaments have been observed for many years. However, observations of successive winking filaments in one event have not been reported yet. In this paper, we present the observations of a chain of winking filaments and a subsequent jet that are observed right after the X2.1 flare in AR11283. The event also produced an Extreme-ultraviolet (EUV) wave that has two components: upward dome-like wave (\speed{850}) and lateral surface wave (\speed{554}) which was very weak (or invisible) in imaging observations. By analyzing the temporal and spatial relationships between the oscillating filaments and the EUV waves, we propose that all the winking filaments and the jet were triggered by the weak (or invisible) lateral surface EUV wave. The oscillation of the filaments last for two or three cycles, and their periods, Doppler velocity amplitudes, and damping times are 11 -- 22 minutes, \speed{6 -- 14}, and 25 -- 60 minutes, respectively. We further estimate the radial component magnetic field and the maximum kinetic energy of the filaments, and they are 5 -- 10 Gauss and $\sim 10^{19} \, {\rm J}$, respectively. The estimated maximum kinetic energy is comparable to the minimum energy of ordinary EUV waves, suggesting that EUV waves can efficiently launch filament oscillations on their path. Based on our analysis results, we conclude that the EUV wave is a good agent for triggering and connecting successive but separated solar activities in the solar atmosphere, and it is also important for producing solar sympathetic eruptions. | A solar filament or prominence is made up of cool plasma, often in a loop shape, extending outward from the Sun's surface into the extremely hot corona. It is typically one hundred times cooler and denser than the surrounding coronal plasma. The filament and prominence are the same entities with the former against the solar disk and latter over the limb, and they appear darker and brighter than their surrounding backgrounds, respectively. Hereafter, we use the term ``filament'' throughout the paper. Previous studies indicate that magnetic field always plays a key role in the whole lifetime of a filament \citep{kipp57,kupe74,tand95}, and typically, whose eruption is often accompanying with flares and coronal mass ejections (CMEs) \citep[e.g.,][]{shen11b,shen12d,yan12a,yan12b,bi12,bi13a,chen13}. So far, many questions about filaments and their eruptions remain unresolved, and the investigation of those questions, such as how and why are they formed, as well as their stability, eruption mechanisms, and potential impact on physical condition of the terrestrial space, have attracted a lot of attentions of solar physicists in recent decades. The phenomenon of filament oscillation is important due to the possible application in filament seismology that is a new and promising technique for estimating physical parameters of filaments and their surrounding coronal plasma. As early as in the 1930s, solar physicists have noted the existence of periodic oscillating motion in filaments \citep{dyso30,newt35}. Since then, a number of observational and theoretical studies have been performed for understanding the physical nature of the filament oscillation \citep[e.g.,][]{dods49,more60,hyde66,rams66}. According to the velocity amplitude, filament oscillations can be classified into two categories, i.e., small and large amplitude oscillations. The former is quite common in filaments, which is often observed in a restricted volume of the filament body and is not related to flare activities. Such kind of oscillation usually has small velocity amplitudes of \speed{2 -- 3} and periods of 10 -- 80 min \citep{arre12,hill13}. The report of large amplitude oscillation is relatively scarce. It is often triggered by large-scale magnetohydrodynamics (MHD) waves or shocks (e.g., Moreton waves \citep{more60}, or ``EIT'' waves \citep{okam04}) in association with remote flaring activities \citep{atha61,hyde66,rams66,eto02,okam04,asai12,shen12b,shen12c,jack13}, or near-by micro-flares and jets \citep{jing03,jing06,vrsn07,li12}. The velocity amplitude of large amplitude oscillation is often of tens of \speed{}, while the period is typically of 6 -- 150 minutes \citep{trip09}. Particularly, long and ultra-long period (8 -- 27 hours) of oscillations are also observed in filaments \citep{foul04,foul09}. In a special case, oscillation was observed before and during the slow-rising, pre-eruption phase of an erupting filament \citep{isob06,isob07,pint08,chen08}. The authors proposed that the fast magnetic reconnection that changes the equilibrium of the supporting magnetic system could be the possible trigger mechanism, and such kind of activity is important for diagnosing and forecasting filament eruptions. On the other hand, according to the oscillating direction relative to the filament's main axis, large amplitude oscillation could also be divided into longitudinal \citep[e.g.,][]{zirk98,jing03,vrsn07,zhan12,zhan13,luna12a,luna12b}, horizontal \citep[e.g.,][]{klec69,hers11,shen12b}, and vertical oscillations \citep[e.g.,][]{hyde66,eto02,okam04}. For vertical (horizontal) large amplitude oscillation of a filament close to (far away from) the disk center, one can observe the alternative appearance and disappearance of the filament body in H$\alpha$ center and line-wings due to the oscillating movement of the filament, which causes the Doppler shift from the H$\alpha$ center to the red wing and then the blue wing. This process repeats periodically and for this reason suck kind of oscillating filament was dubbed ``winking filament'' in history. \cite{rams66} and \cite{hyde66} studied 11 winking filaments and found that the oscillation periods are not related to the filament dimensions and the power and distance of the disturbing flare, namely, filaments always oscillate with their characteristic periods. \cite{hers11} also confirmed such a result, and they further proposed that large amplitude filament oscillations are actually a collection of separate but interacting fine threads. As mentioned above, there are several possible agents that can trigger large amplitude filament oscillations. For winking filaments, they are often triggered by large-scale MHD waves or shocks in association with remote flare/CME activities. \cite{eto02} studied a winking filament that is associated with both a Moreton and an EUV waves. They found that the speed of the Moreton wave is approximately three times of the EUV wave, and the arriving of the inferred Moreton wave front is consistent with the start time of the filament oscillation, which suggests that the trigger of the filament oscillation should be the Moreton wave. In a statistical study performed by \cite{okam04}, the authors found that some winking filaments are triggered by EUV waves rather than Moreton waves, which lead the conclusion that EUV waves could be another possible trigger of winking filaments. In some events, one can not detect notable Moreton waves in chromosphere, even though the EUV wave is remarkable in coronal observations. Therefore, the observation of winking filaments can be used to diagnose the existence and the properties of invisible (weak) Moreton waves \citep[e.g.,][]{rams66,eto02,okam04}. For example, based on observations of winking filaments, \cite{eto02} found that the Moreton wave was inconsistent with the corresponding coronal EUV wave. \cite{gilb08} found that there is a delay in the filament rebound accompanying the initial compression of the wave front, which suggests the filament is sensitive to the width of the wavefront. Their study also indicated that the wavefront topology should be slightly forward-inclined with respect to the surface, confirming the speculation of \cite{rams66} and the theoretical prediction in the numerical model of Moreton wave \citep{uchi68}, where the Moreton wave is explained as the intersection line between an expanding coronal wave front surface and the dense chromosphere. A few recent studies using high-resolution observations also confirm the forward-inclined topology of Moreton waves \citep[e.g.,][]{liu12,liu13}. The study of winking (oscillating) filaments opens a new discipline called filament seismology. In general, the filament seismology technique is based on the application of theoretical knowledge and inversion techniques using the observed periods, damping times, and flow speeds to estimate the physical parameters of the filaments and the surrounding coronal plasma. With the application of \cite{kipp57} model of filaments into winking filaments reported by \cite{rams66}, \cite{hyde66} obtained the radial components of the filament magnetic fields ($B_{\rm r}$) are ranging from 2 to 30 Gauss, while the effective coefficients of viscosity ($\eta$) is from $4 \times 10^{-10}$ to $1.6 \times 10^{-9}$ poise. By assuming the temperature ($T = 10^{6}$ K) and electron number density ($n_{\rm e} = 10^{9}$ ${\rm cm}^{-3}$) in the lower corona, the author further derived the coronal magnetic fields ($B_{\rm e}$) surrounding the filaments, which is about 0.09 -- 0.18 Gauss. The inferred magnetic fields of filaments are in agreement with those obtained from direct measurements \citep[e.g.,][]{ziri61,lee65} and from the analysis of the polarization of H$\alpha$ and \ion{He}{1} $D_{\rm 3}$ lines \citep[e.g.,][]{hyde65,warw65}. The study of \cite{hyde66} demonstrates that filament seismology is a reasonable method for deriving various physical parameters of filaments. In addition, filament oscillations are also important for diagnosing the stability and eruption mechanism of filaments \citep{isob07,pint08}. For more background knowledge on filament oscillation and the application in filament seismology, we refer to several recent reviews \citep{oliv02,trip09,arre12}. In this paper, we present an interesting observational study of a chain of winking filaments that was in association with a {\it GOES} X2.1 flare in NOAA active region AR11283 (N13W18) on September 06, 2011. The flare produced with a remarkable EUV wave propagating mainly in the northwest direction, which not only triggered the oscillation of three filaments in the northwest of AR11283, it also launched the oscillation of a long filament and the occurrence of a small jet in the eastern hemisphere where the wave signature is very weak or even invisible. Thanks to the excellent observations obtained by the Solar Magnetic Activity Research Telescope \citep[SMART;][]{ueno04}, and the {\it Solar Dynamics Observatory} \citep[{\it SDO};][]{pesn12}, we are able to study the winking filaments and the EUV wave in great detail. In Section 2, observations and measuring methods are described briefly. Section 3 is the main analysis results. Conclusions and Discussions are given in Section 4. | In this paper, we present an observational study of a chain of winking (oscillation) filaments and a small jet that occurred in a proper time order but separated far away from each other. The event initiated from an X2.1 flare in AR11283, after which a remarkable EUV wave is observed mainly in the northwest direction, which swept over three filaments in the west hemisphere and launched there oscillations. It is interested that oscillation of a long filament and a small jet in the east hemisphere are also observed following the flare. With the excellent observations taken by the SMART and the {\it SDO} instruments, we find that all these successive solar activities, including four oscillating filaments and a jet, were dynamically connected to the global EUV wave. The main analysis results could be summarized as follows. \begin{enumerate} \item A remarkable EUV wave is observed a few minutes after the start of the X2.1 flare, which propagates outward mainly in the northwest side of AR11283 and with an average projection speed (deceleration) of about \speed{850} (\acc{-224}). Behind the EUV wave, we detect another slow wave whose speed is about \speed{338}. In the east of AR11283, the wave signature is very weak or even invisible in the imaging observations, and the average speed is about \speed{554}. Based on our analysis, we propose that the shape of the EUV wave should be like a dome as what has been reported in \cite{vero10}. In this line of thought, we propose that the prominent wave structure in the northwest of AR11283 should be the upward expanding dome structure, while the weak wave signature in the east hemisphere should be the surface EUV wave that is driven by the associated CME at the initial stage and then propagates freely on the surface. In addition, we note that there is no detectable chromosphere Moreton wave associated with the EUV wave, which may imply that the downward compression to the dense chromosphere of the fast EUV wave is too weak, maybe it is possibly due to a large angle of the EUV wave to the solar surface \citep{tama13}. \item In the SMART H$\alpha$ line-wing observations, four successive winking (oscillating) filaments are observed, and the start of their oscillations are in a proper time order depending on their distances to the flare kernel. All the filaments oscillated for about two or three cycles and then regained their equilibriums instead of eruptions. The intensity fluctuation amplitudes in the H$\alpha$ line-center and the EUV observations are very subtle, which suggests a relative small oscillation amplitudes of the filaments. By analyzing the temporal and spatial relationships between the oscillating filaments and the EUV wave, we propose that all the filament oscillations are triggered by one common agent, i.e., the weak (or invisible) surface EUV wave. It is also noted that some filaments did not disturbed during the event, no matter how close they are to the flare kernel (for example, F6, see \fig{fig1} (a)). Such phenomenon is also noted by \cite{okam04}, and the detailed reasons need further investigations. \item Using the Beckers' cloud model, Some physical parameters of the oscillating filaments are derived. The results show that the oscillation periods of the filaments range from 11 to 22 minutes, the Doppler velocity amplitudes are from \speed{6 to 14}, and the damping times are from 25 to 60 minutes. These results may indicate inherent property of the filaments, namely, a filament always oscillates with its own characteristic parameters. It is noted that the filament oscillation launched by large-scale EUV wave often has a large amplitude at the very beginning, but it will quickly reduce to a moderate amplitude and then undergoes an ordinary damping oscillation process. This characteristic could be recognized as an observational characteristic of filament oscillations that are trigged by pulse-like EUV waves. \item A small jet is observed close to the southern boundary of a large trans-equatorial coronal hole following the sequence of the successive filament oscillations. Considering the magnetic configuration around the jet-base and the ejection details of the jet, we propose that this jet should be caused by the magnetic reconnection between the biple and the ambient open fields in the coronal hole, which were pushed down by the EUV wave and thereby trigger the reconnection. \item Based on the analyzing of the temporal and spatial relationships among the EUV waves and the oscillating filaments, as well as the small jet. We propose that all the observed filament oscillations and the jet are triggered by the large-scale surface EUV wave, which could be the physical linkage of many successive but separated solar activities. Even though the EUV wave is very weak or even invisible in coronal imaging observations, it also can trigger the occurrence of many different solar activities. The oscillation of F1 and the occurrence of the jet in the present case could be a good example for such a conclusion. Vice versa, the observation of winking (oscillation) filaments can provide an effective way to diagnose the arriving and the property of weak or invisible waves in the solar atmosphere. \end{enumerate} Many studies have indicated that EUV waves often have their chromospheric counterparts, i.e., Moreton waves. It seems that how deep a coronal wave can reach down to the lower dense atmosphere depends on its strength and the angle between the wave and the solar surface. For example, in a powerful X6.9 flare event, \cite{shen12c} found that the EUV wave can reach down to the upper photosphere or the bottom of the chromosphere. In the present case, however, no chromosphere Moreton wave can be detected in H$\alpha$ observations, suggesting that the observed fast EUV should be a weak one (at least for the surface wave), or it has a large angle relevant to the solar surface \citep{tama13}. A slow wave behind the fas EUV wave was often interpreted as a pseudo-wave in previous studies \citep[e.g.,][]{chen02,shen12c}. So far there are several interpretations for such an EUV wave, which are related to a current shell or successive restructuring of field lines caused by the associated CME \citep[e.g.,][]{chen02,dela07,attr07}. In addition, some authors claimed that both the wave and non-wave models are required to explain the EUV waves \citep[e.g.,][]{cohe09,liu10,down11}. Recently, \cite{gosa12} found that a filament is triggered by both the fast and slow EUV waves successively in a flaring event, in which the slow EUV wave resulted in a phase change of the filament oscillation. Their observation seems supporting the scenarios that such a slow EUV wave should be a real MHD wave. In the present case, the observed slow EUV wave is possibly a secondary wave triggered by the fast EUV wave when it interacts with other magnetic structures on the path. On the other hand, since the northwestward wave structure is considered as the upward dome structure of the EUV wave, there is another possible that the slow wave may represent the surface wave launched by the associated CME. In this sense, one can interpret the slow EUV wave observed in the present case as a real MHD wave in the physical nature. For the oscillating filaments, the observed parameters could be applied into filament seismology to estimate the other important filament parameters that are difficult to obtain with direct measuements. With the method proposed by \cite{hyde66} and the measured oscillation parameters, one can derive the radial component of the filament magnetic field which supports the filament mass. In Hyder's method, the relation between the radial magnetic field and the oscillation period and damping time can be written as $B_{\rm r}^{2} = \pi \rho \, r_{\rm 0}^{2} \, [4 \, \pi ^{2} \, (\frac{1}{T})^{2} + (\frac{1}{\tau})^{2}]$, where $B_{\rm r}$ is the radial magnetic component, $\rho$ is the density of the filament mass, $r_{\rm 0}$ is the scale height of the filament, $T$ is the filament oscillation period, and $\tau$ is the damping time. If we use the value $\rho = 4 \times 10^{-14} \, {\rm gm/cm^{3}}$, i.e., $n_{\rm e} = 2 \times 10^{10} \, {\rm cm^{-3}}$, the above equation can be rewritten as the form $B_{\rm r}^{2} = 4.8 \times 10^{-12} \, r_{0}^{2} \, [(\frac{1}{T})^{2} + 0.025 \, (\frac{1}{\tau})^{2}]$. With the measured oscillation periods and damping times, we obtain that the value of the radial component of the filaments' magnetic fields $B_{\rm r}$ are 5.0, 10.0, 7.0, and 7.0 Gauss for the filaments F1 -- F4, respectively. In the calculation, we use the value $r_{\rm 0} = 3 \times 10^{9}$ cm, the same with \cite{hyde66}. The estimated filament magnetic fields are in agreement with the values obtained by direct measuring or inferred from the analysis of polarization of filament lines \citep[e.g.,][]{ziri61,warw65,lee65}. In addition, one can also estimate the total maximum kinetic energy of the oscillating filaments by using the measured maximum Doppler velocities. The maximum kinetic energy of an oscillating filament is equal to the work done by the pressure gradient force in the wave as it accelerates the filament. Here, we take the values measured at P1 on F1 as an example. The maximum redshift velocity at P1 is \speed{21}, and therefore, the maximum kinetic energy is $E = \frac{1}{2} \, m v^{2} \approx 9.0 \times 10^{19} \, {\rm J}$, where $m$ is the mass of the filament and we assume it as $4 \times 10^{14} \, {\rm g}$ \citep{gilb06}. The obtained value of the oscillating filament is in agreement with the predicted energy required to induce the oscillations of a quiescent filament, namely, $\sim 10^{19}$ -- $10^{20} \, {\rm J}$ \citep{klec69}. The maximum kinetic energy of the oscillating filament is comparable with the value of the minimum energy of EUV waves, which is of the order of $10^{19} \, {\rm J}$ \citep{ball05}. These results indicate that the energy of the EUV wave is sufficient to launch filament oscillations on the path. The event presented in this paper is a good example of the so-called sympathetic solar eruptions, i.e., a number of successive but separated solar eruptive activities occurring within a short timescale. The key question of sympathetic eruptions is whether the close temporal correlation between successive solar activities is purely coincidental or causally linked. Therefore, the searching for the physical linkage among the successive solar activities are important for interpreting sympathetic eruptions. Many studies have shown that most of sympathetic eruptions are dynamically connected, and the basic mechanism is often of a magnetic nature. For example, \cite{schr11} found that successive events could be connected by a system of separatrices, separators, and quasi-separatrix layers. \cite{shen12d} found that magnetic reconnection is important for the production of sympathetic filament eruptions. In addition, these studies also indicate the importance of the magnetic topological structure of the global coronal field in the production of sympathetic eruptions \citep[see also,][]{jian08,toro11,tito12,lync13,schr13,kong13}. In the present case, our analysis results indicate that EUV waves can be a good agent for connecting successive but separated solar activities. | 14 | 3 | 1403.7705 |
1403 | 1403.0580_arXiv.txt | \noindent This article investigates the construction of fermions and the formulation of the Standard Model of particle physics in a theory in which the Lorentz signature emerges from an underlying microscopic purely Euclidean $SO(4)$ theory. Couplings to a clock field are responsible for triggering the change of signature of the effective metric in which the standard fields propagate. We demonstrate that Weyl and Majorana fermions can be constructed in this framework. This construction differs from other studies of Euclidean fermions, as the coupling to the clock field allows us to write down an action which flows to the usual action in Minkowski spacetime. We then show how the Standard Model can be obtained in this theory and consider the constraints on non-Standard Model operators which can appear in the QED sector due to CPT and Lorentz violation. | Part of the art of theoretical physics is to find the mathematical structures that allow us to formalize and simplify the laws of nature. These structures include the description of spacetime (dimension, topology, \ldots) and matter and their interactions (fields, symmetries, \ldots). While there is a large amount of freedom in the choice of these mathematical structures, the developments of theoretical physics have taught us that some of them are better suited to describe certain classes of phenomena. However, these choices are only validated by the mathematical consistency of the theory and, in the end, by the agreement of their predictions with experiments. Among all of these structures, and in the framework of metric theories of gravitation, the signature of the metric is in principle arbitrary. It seems that on the scales that have been probed so far there is the need for only one time dimension and three spatial dimensions. It is also now universally accepted that the relativistic structure is a central ingredient of the construction of any realistic field theory, in particular as the cleanest way to implement the notion of causality. Spacetime enjoys a locally Minkowski structure and, when gravity is included, the equivalence principle implies (this is not a theoretical requirement, but an experimental fact, required at a given accuracy) that all the fields are universally coupled to the same Lorentzian metric. Thus, we usually take for granted that spacetime is 4-dimensional manifold endowed with a metric of mixed signature, e.g.~$(-,+,+,+)$. While the existence of two time directions may lead to confusion \cite{V4,V42}, several models for the birth of the universe \cite{nothing,nothing2,nothing3,nothing4} are based on a change of signature via an instanton in which a Riemannian and a Lorentzian manifold are joined across a hypersurface. While there is no time in the Euclidean region, with signature $(+,+,+,+)$, it flips to $(-,+,+,+)$ across this hypersurface, which may be thought of as the origin of time from the Lorentzian point of view. Eddington even suggested \cite{G85} that it can flip across some surface to $(-,-,+,+)$ and signature flips also arise in brane or loop quantum cosmology \cite{lqc,lqc2,lqc3}. It is legitimate to investigate whether the signature of the metric is only a convenient way to implement causality or whether it is just a property of an effective description of a microscopic theory in which there is no such notion. In Ref.~\cite{Mukohyama:2013ew,*emergentessay}, two of us have proposed that at the microscopic level the metric is Riemannian and that the Lorentzian structure, usually thought of as fundamental, is in fact an effective property that emerges in some regions of a 4-dimensional space with a positive definite metric. There has been some related work in the past --- for instance, the work by Barbero \cite{BarberoG.:1995ud} (with more than second-order derivatives in the equations of motion, however), or in Einstein-Aether theory \cite{BarberoG.:2003qm,*Foster:2005ec} (although without an order parameter connecting the Euclidean and Lorentzian theories) and scalar gravity \cite{Girelli:2008qp}. We argued that a decent classical field theory for scalars, vectors, and spinors in flat spacetime can be constructed, and that gravity can be included under the form of a covariant Galileon theory instead of general relativity. This mechanism of emergent Lorentz signature may also serve as a new way to circumvent the issue of non-unitarity in some higher-derivative quantum gravity theories \cite{Mukohyama:2013gra, Muneyuki:2013aba}. Among the gaps emphasized in this work, we have pointed out that (1) the construction is restricted to classical field theory and the spinor sector suffers from a severe fine-tuning to ensure CPT invariance (see e.g.~Ref.~\cite{Toma:2012xa} and references therein for recent constraints on CPT violation), and that (2) it requires the construction of Majorana and Weyl spinors in order to formulate the Standard Model (SM) and its extensions. It is well known that Majorana fermions are technically impossible to construct in a 4d Euclidean theory, but several authors have found alternative constructions \cite{Mehta:1986mi, Mehta:1991ve, vanNieuwenhuizen:1996tv, vanNieuwenhuizen:1996ip, Wetterich:2010ni}. However, these techniques are often aimed at a Wick rotation to or from a Lorentzian theory and can involve doubling the fermion degrees of freedom or other aspects which are ill suited to our application. With the aim of developing a theory which flows to the usual actions in Minkowski space (which may look very different in Euclidean space) and the available couplings to the clock field, we arrive at a new formulation for Weyl and Majorana spinors. As our goals and setting are different than in previous studies, we do not need to use the techniques employed there, such as fermion doubling or the ad hoc construction of different spinors. The Weyl spinors and coupling to the clock field allow us to directly construct an emergent version of the SM, with its chiral and metric structure inherited from an originally Euclidean theory. This article is organized as follows. In Section \ref{sec:emerg-lorentz-sign} we briefly review the construction given in Ref.~\cite{Mukohyama:2013ew,*emergentessay}. Following that, in Section \ref{sec:weyl-major-ferm} we extend the fermion sector to include Weyl and Majorana fermions, which is quite distinct from the usual considerations in Euclidean space. For fermions, an alternative ``derivation'' of several of the choices in this construction are detailed in the Appendix. In Section \ref{sec:standard-model} we then show how to construct the Standard Model in this framework of an emergent Lorentzian metric. There are additional operators which can arise in this theory and, in Section \ref{sec:constraints-qed}, we categorize and analyze the constraints on such operators in the QED sector of the SM. Finally, we gather further comments, conclusions, and future directions in Section \ref{sec:disc-concl-outl}. | \label{sec:disc-concl-outl} This article follows the idea that the apparent Lorentzian dynamics of usual field theories is an emergent property and that the underlying field theory is in fact strictly Riemannian. This requires the introduction of the clock field, a scalar field playing the role of the physical time. The microscopic theory is Euclidean, and time evolution is just an effective and emergent property, which holds on some energy scales, and in some regions of the Euclidean space. Through interactions with the clock field the effective theory flows to the standard Lorentzian picture. In Ref.~\cite{Mukohyama:2013ew,*emergentessay}, we were able to perform a construction in flat spacetime for scalar, vector, and Dirac spinors restricted to classical fields. In order for all the fields to propagate in the same emergent Lorentzian metric, the couplings to the clock field needed to be adjusted with care. This work was a proof of concept in constructing a model with the Lorentzian metric only emerging at energies below the vev of the gradient of the clock field, with many open and interesting questions. In this work we have addressed several of these questions. The present analysis has shown that it is possible to construct a Euclidean theory with fermions that reduce, once the gradient of the clock field has a vev on ${\cal M}_0$, to Lorentzian Weyl and Majorana fermions. This completes the basic fields needed in the Standard Model and common extensions. The clock field allows us to avoid the typical difficulties in constructing Euclidean theories of these types of fermions. We then showed that it is possible to construct a Euclidean theory leading to an emergent version of the Standard Model by adding the Standard Model structure to the dynamics necessary for the emergence of a Lorentzian metric. To finish, we have analyzed with care the fine-tuning required to ensure CPT and Lorentz invariance. One crucial point is that the terms necessary in our model do not induce CPT violation. Bounds on the deviations from the adjusted couplings to the clock field, as well as other possible interaction terms in this framework, can be obtained from experimental QED constraints. Forbidding additional operators and ensuring the value of the necessary coupling constants is an open question. There are still many interesting future directions to pursue in this framework for emergent Lorentz symmetry. One would like to move beyond the classical level and quantize the theory, as well as understand the mechanism which leads to the vev of the clock field. The possible violation of CPT and Lorentz symmetry also needs to be investigated further. Even with these and other open questions, we now have a basic model which can reproduce the Standard Model and its Lorentzian background with time evolution from a purely Riemannian theory with no concept of time. | 14 | 3 | 1403.0580 |
1403 | 1403.0852_arXiv.txt | We use the optimised skew-spectrum as well as the skew-spectra associated with the Minkowski Functionals (MFs) to test the possibility of using the cross-correlation of the Integrated Sachs-Wolfe effect (ISW) and lensing of the cosmic microwave background (CMB) radiation to detect deviations in the theory of gravity away from General Relativity (GR). We find that the although both statistics can put constraints on modified gravity, the optimised skew-spectra are especially sensitive to the parameter $\rB_0$ that denotes the the {\em Compton wavelength} of the scalaron at the present epoch. We investigate three modified gravity theories, namely: the Post-Parametrised Friedmanian (PPF) formalism; the Hu-Sawicki (HS) model; and the Bertschinger-Zukin (BZ) formalism. Employing a likelihood analysis for an experimental setup similar to ESA's Planck mission, we find that, assuming GR to be the correct model, we expect the constraints from the first two skew-spectra, $S_{\ell}^{(0)}$ and $S_{\ell}^{(1)}$, to be the same: $\rm B_0<0.45$ at $95\%$ confidence level (CL), and $\rm B_0<0.67$ at $99\%$ CL in the BZ model. The third skew-spectrum does not give any meaningful constraint. % We find that the optimal skew-spectrum provides much more powerful constraint, giving $\rm B_0<0.071$ at $95\%$ CL and $\rm B_0<0.15$ at $99\%$ CL, which is essentially identical to what can be achieved using the full bispectrum. | \label{sec:intro} The observations of type Ia supernovae imply that our Universe is undergoing a phase of accelerated expansion \citep{Riess98,Perl99}. Cosmic acceleration can arise from either an exotic form of energy with negative pressure, referred to as ``dark energy", or a modification of gravity manifesting on large scales. As shown by various authors \citep{Bertschinger:2006aw,Song:2006ej,Brax:2008hh,2013arXiv1312.5742H}, determining the cause of the acceleration os hampered by the fact that the background dynamics in dark energy and modified gravity models are nearly indistinguishable. To lift this degeneracy, one can test the evolution of perturbations in these models. The perturbative approach to growth of structure in modified gravity can, in principle, be classified in two different frameworks: parametric and non-parametric, an example of the latter being principal component analysis~\citep{Zhao:2008bn,Zhao:2009fn,Zhao:2010dz,Hojjati:2011xd}. In this paper we focus on the former. There exist several phenomenological parametrizations of modified gravity including the Bertschinger-Zukin \citep{BZ08} parametrization, and that of \cite{Staro07}). These parametrizations are suitable for the quasi-static regime, where the time evolution of the gravitation potentials is negligible compared with their spatial gradient. Furthermore, if we focus on the linear fluctuation dynamics for which the equations in Fourier space can be reduced to simple algebraic relations, these techniques allow us to perform some analytic calculations which make the parametrization technically efficient. However, if we want to go further beyond the quasi-static scale, while remaining in the linear perturbation framework, the parametrization of modified gravity becomes more complex. This is because on the largest scales, especially the super- or near-horizon scales, the time evolution of the gravitational potentials is no longer negligible. In fact, the time derivative terms dominate the dynamical equations, which means that we need to solve some temporal ordinary differential equations. All in all, the inclusion of time derivative terms makes the parametrization of modified gravity not so manifest anymore Actually, there exists some debate about the range of validity of the various parametrizations; on the one hand, as shown by \cite{Zuntz:2011aq}, using a parametrization with insufficient freedom significantly tightens the apparent theoretical constraints. On the other hand, for some specific modified gravity models some phenomenological parametrizations work quite well; for instance \cite{Hojjati:2012rf} recently demonstrated that for small Compton wavelength in the $f(\rR)$ model, the Bertschinger-Zukin parametrization is in practice good enough for current data analysis. This is because, for small Compton wavelengths, the most significant modifications w.r.t. GR occur in the sub-horizon regime, while the modification on the super-horizon scales are subdominant. In addition to the above explicit parametrizations, some quite generic frameworks have been proposed, such as the parametrized Post-Friedmann (PPF) formalism, including the Hu-Sawicki approach \citep{Hu:2007pj,Fang:2008sn}, its calibration version \citep{Lombriser:2013aj} and Baker-Ferreira-Skordis-Zuntz algorithm \citep{Baker:2011jy,Baker:2012zs}, and the Effective Field Theory (EFT) formalism \citep{Gubitosi:2012hu,Bloomfield:2012ff,2013arXiv1312.5742H}. These formalisms are devoted to build up a ``dictionary'' of modified gravity theories and their PPF or EFT correspondence. Since the purpose of these generic formalisms is to construct a unified way to include all the modified gravity/dark energy models, they contain more arbitrary functions/coefficients, which usually lead to looser constraints. Besides the recent progress on the construction of parametrizations, many observational windows have recently been proposed, such as the Integrated Sachs-Wolfe (ISW) effect~\citep{Sachs:1967er} in Cosmic Microwave Background (CMB) anisotropies~ \citep{Zhang:2005vt,Song:2007da,2008PhRvD..78d3519H}, the power spectrum of luminous red galaxies~\citep{2010PhRvD..81j3517Y,2012PhRvD..86j3505H,2013PhRvD..88d4050A}, cluster abundance~\citep{Jain:2007yk,2009PhRvD..80h3505S,Lombriser:2010mp,2011PhRvD..83f3503F}, Coma cluster \citep{2013arXiv1312.5083T}, galaxy peculiar velocities~\citep{Li:2012by}, redshift-space distortions~\citep{Jennings:2012pt,2013MNRAS.436...89R}, weak-lensing~\citep{Heavens2007,Zhang:2007nk,2010Natur.464..256R,2008PhRvD..78d3520H,2010PhRvD..81l3508D,2011A&A...530A..68T,2012MNRAS.423.1750L,2013MNRAS.429.2249S}, $21$cm observations~\citep{Hall:2012wd}, matter bispectrum~\citep{GilMarin:2011xq,2013JCAP...03..034B}, {\it etc}. In addition, recently some N-body simulation algorithms in modified gravity models have been developed~\citep{Zhao:2010qy,Li:2010zw}. As shown by \cite{Song:2007da} and \cite{Lombriser:2010mp}, with WMAP resolution the modification effects on the CMB mainly come from the ISW effect, which becomes prominent on the super-horizon scales. However, due to the unavoidable cosmic variance on large scales, the constraints from these effects are not significant. On the other hand, since the typical modification scales are on sub-horizon scales, several studies show that the most stringent constraints come from the large-scale structure data sets. For example, the strongest current constraint on $f(\rR)$ gravity (${\rm log}_{10}{\rm B}_0<-4.07;\ 95\%{\rm CL}$)~\citep{2014arXiv1401.3980D} is driven by the galaxy spectrum from WiggleZ data sets~\citep{2012PhRvD..86j3518P}. Various previous results show that the main constraint on modified gravity comes from galaxy or cluster scales which corresponds to the multipole range $\ell\gtrsim 500$ in CMB data, where lensing effects are no longer negligible. The recent release of {\it Planck} % data \citep{Ade:2013ktc} provides us with a fruitful late-time information both on ISW and lensing, which is encoded in the CMB temperature power-spectrum \citep{Ade:2013kta}, the lensing potential power-spectrum \citep{Ade:2013tyw}, and the CMB temperature ISW-lensing bispectrum \citep{Ade:2013ydc,Ade:2013dsi}. The full sky lensing potential map has been constructed and the amplitude of the lensing potential power-spectrum has been estimated at the $25\sigma$ level. The ISW-lensing bispectrum is also detected with nearly $3\sigma$ confidence level. Although the ISW-lensing bispectrum data have not yet been released, forecasts of constraints on modified gravity models through this novel observational statistic have been investigated \citep{DiValentino:2012yg,HLBM12}. These studies show that the ISW-lensing bispectrum is an effective tool to constrain modified gravity. Also notice that \cite{Hu13} analysed CMB temperature power-spectrum data alone and improved the previous constraint from WMAP9's ${\rm B}_0<3.37$ at $95\%$ CL to ${\rm B}_0<0.91$. Inclusion of the lensing potential power spectrum improved it to ${\rm B}_0<0.12$. The lensing-ISW bispectrum is known to be uncorrelated to the power-spectrum and thus it can further tighten the constraint on ${\rm B}_0$. Inspired by these results, in this paper we use the recently introduced optimum skew-spectra and the skew-spectra associated with the Minkowski Functionals (MFs) to constrain departures from GR. Since their introduction in cosmology by \cite{MBW94}, MFs have been extensively developed as a statistical tool for non-Gaussianity in a cosmological setting for both two-dimensional (projected) and three-dimensional (redshift) surveys. Analytic results are known certain properties of the MFs of a Gaussian random field making them suitable for identifying non-Gaussianity. Examples of such studies include CMB data \citep{Schmalzing98,Novikov00,HikageM08,Natoli10}, weak lensing (\cite{Matsubara01,Sato01,Taruya02,MuWaSmCo12}), large-scale structure \citep{Gott86,Coles88,Gott89,Melott89,Gott90,Moore92,Gott92,Canavezes98,SSS98, Schmalzing00,Kerscher01,Hikage02,Park05,HKM06,Hikage08}, 21cm \citep{Gleser06}, frequency cleaned Sunyaev-Zel'dovich (SZ) maps \citep{MuSmJoCo13} and N-body simulations \citep{Schmalzing00,Kerscher01}. The MFs are spatially-defined topological statistics and, by definition, contain statistical information of all orders in the moments. This makes them complementary to the poly-spectra methods that are defined in Fourier space. It is also possible that the two approaches will be sensitive to different aspects of non-Gaussianity and systematic effects, although in the weakly non-Gaussian limit it has been shown that the MFs reduce to a weighted probe of the bispectrum \citep{HKM06}. The skew-spectrum is a weighted statistic that can be tuned to a particular form of non-Gaussianity, such as that which may arise either during inflation at an early stage or from structure formation at a later time. The skew-spectrum retains more information about the specific form of non-Gaussianity than the (one-point) skewness parameter alone. This allows not only the exploration of primary and secondary non-Gaussianity but also the residuals from galactic foreground and unresolved point sources. The skew-spectrum is directly related to the lowest-order cumulant correlator and is also known as the two-to-one spectra in the literature \citep{Cooray01}. In a series of recent publications the concept of skew-spectra was generalized to analyse the morphological properties of cosmological data sets or in particular the MFs \citep{MuSmCooReHeCo13, MuWaSmCo12,MuSmJoCo13,PratMun12}. The first of these three spectra, in the context of secondary-lensing correlation studies, was introduced by \cite{MuVaCoHe11} and was subsequently used to analyse data release from WMAP by \cite{Cala10}. The layout of the paper is as follows. In \textsection\ref{sec:mod_grav} we briefly outline various models and parametrization of modified gravity. Next, in \textsection\ref{sec:isw_lensing}, we review the non-Gaussianity, at the level of bispectrum, introduced by cross-correlaion of secondaries and lensing of CMB. In \textsection\ref{sec:MF} we introduce the skew-spectra associated with the Minkowski Functionals (MFs) and compute them for various modified gravity scenarios. \textsection\ref{sec:like} is devoted to likelihood analysis using MFs. In \textsection\ref{sec:result} we discuss our results. Finally \textsection\ref{sec:disc} is reserved for concluding remarks as well as discussing the future prospects. | \label{sec:disc} The correlation between ISW and lensing of the CMB generates a specific signature in the CMB bispectrum. Analysis of first-year data from the Planck satellite has detected this signature with a moderate level of signal to noise ($2.6\sigma$). The ISW-lensing bispectrum is unique as it depends on the CMB power-spectrum generated at recombination and cross-spectra of the lensing potential and the ISW effect generated at late times. Both ISW and lensing are sensitive to the underlying model of gravity, and thus the resulting bispectrum provides an opportunity to constrain any departure from GR. We consider various formulations of the modified gravity models which include HS, BZ and PPF models to compute the bispectrum. {\bf Topological Estimators: }The non-Gaussianity in CMB maps are often studied using moment-based approaches or alternatively using their harmonic counterparts, namely the multi-spectra. Extending previous results we have studied how topological descriptors such as the MFs can provide a complementary role, paying special attention to Planck-type experiments. The MFs are interesting as they have different responses to various systematics. We have considered the three MFs that are used for describing the topological properties of CMB temperature maps. We compute analytically the covariance associated with the skew-spectra associated to the MFs, and our results also include cross-covariance among different skew-spectra. In agreement with previous results we find that the skew-spectra are highly correlated. Constructing the MFs for Planck type experiments (143 GHz). We find that the constraints are tighter for the first two MFs $S_{\ell}^{(0)}$ and $S_{\ell}^{(1)}$, which both give ${\rm B}_0<0.67$ at $95\%$ CL. We do not get any meaningful constraints using $S^{(2)}_{\ell}$. The constraints can be further improved by considering Wiener filtering instead of Gaussian smoothing. We provide simple analytical results for the three different Wiener filtering techniques that have been considered previously in the literature. We also incorporate the optimum estimator and its covariance for construction of the corresponding likelihood. The MFs do not fare particularly well in comparison with the optimal estimators, which are predicted to give much tighter constraints: ${\rm B}_0<0.071$ at $95\%$ CL and ${\rm B}_0<0.15$ at $99\%$ CL. These are very close to the predictions from the full bispectrum \citep{Hu13}, showing their optimal nature. We have not considered the possibility of combining results from different channels which can further improve the constraints. \begin{figure} \begin{center} {\epsfxsize=10 cm \epsfysize=7 cm {\epsfbox[31 319 586 716] {new_cross.eps}}} \end{center} \caption{The confusion from unresolved point sources is plotted for determination of optimum ISW-Lensing skew-spectrum. The normalisation for point source is fixed at ${\rm b}_{\rm PS}=10^{-29}$. The line-styles used for various models are same as that of Figure \ref{fig:clTT}.} \label{fig:confusion} \end{figure} {\bf Contamination from Point Sources and Galactic Foregrounds:} Galactic contamination are a major source of concern which can affect any study involving the CMB. They are usually dealt with masking or by using component separation techniques \citep{Leach08}. The residual bias in the estimation of primordial non-Gaussianity was found to be small \citep{Hikage08,Komatsu11}. However, other studies were more conservative in interpreting the results \citep{Chiang03}. Techniques also exists that involve marginalising over foregrounds \citep{Komatsu02,Komatsu11}. Point sources are an additional source of contamination for any study involving MFs. The resolved point sources with sufficient signal-to-noise can be removed by application of an appropriate mask, but there will be low-flux, unresolved and unsubtracted sources, comprising radio-galaxies and active galactic nuclei that emit in radio frequencies through the synchrotron process, and dusty starburst galaxies which emit thermally. However integrated emission from the Cosmic Infrared Background (CIB) has recently been detected by Planck collaboration using the skew-spectrum \citep{Ade:2013dsi}. Any contamination from unresolved point sources can be estimated using Eq.(\ref{eq:opt}). Some of the issues involving mask and inhomogeneous noise can be dealt with by computing the {\em cumulant correlators} that represent MFs in the real-space or in the {\em needlet} basis \citep{MuSmCooReHeCo13}. The contamination from unresolved point sources (PS) can be estimated using Eq.(\ref{eq:opt}) with $\rm X=ISW$-$lensing$ and $\rm Y=Point\;\; Sources$. The contamination is shown in Figure \ref{fig:confusion}. For normalisation $b_{\rm PS}=10^{-29}$ the contamination is several orders of magnitude lower compared to the optimum skew-spectrum depicted in Figure \ref{fig:opt_hs}. We have ignored the contamination from primordial non-Gaussianity which is expected to be negligible. \cb{{\bf RS-Lensing and tSZ-Lensing skewspectrum:} The ISW-Lensing cross-correlation at the level of bispectrum has been the focus of our study in this article. The same techniques can in principle be used to analyse skew-spectra associated with the Rees-Sciama(RS)-lensing or thermal Sunyaev Zeldovich(tSZ)-lensing bispectrum to constrain $\rm B_0$. However, the tSZ-lensing bispectrum depends on detailed modeling of underlying ``gastrophysics'' and the S/N of RS-lensing skew-spectrum is below the detection threshold for ongoing surveys such as the Planck.} {\bf Beyond the bispectrum:} The results that we have derived here are based on MFs and the optimum skew-spectrum. Going beyond third-order correlation functions, it is possible to incorporate the power-spectrum of the lensing potential $\myC^{\phi\phi}_{\ell}$ in constraining $\rm B_0$. Optimized kurt-spectrum introduced in \cite{Mu11} and later used to analyse 7-year data released by WMAP team \citep{Sm11} can be valuable for studies in this direction. These results when combined with results from power-spectrum data alone can improve the constraints by an order of magnitude. The possibility of using polarised CMB maps will be explored elsewhere. \cb{{\bf Constraints on $\rm B_0$ from other cosmological data-sets:}Constraints from CMB can provide independent confirmations of constraints derived from studies of BAOs, studies of galaxy clusters or that from weak lensing studies, though constraints from galaxy power-spectrum can be significantly tighter compared to the constraints derived here $\rm log_{10} B_0 < -4.07$. The scales and redshift probed by galaxy surveys and CMB observations are very different and are affected by different set of observational systematics. Hence, these observations play complimentary roles in constraining $\rm B_0$.} {\bf \cb{Wiener and Wiener-like Filtering and Minkowski Functionals:}} {\em Wiener} and {\em Wiener-like} filtering are generally used for analysing realistic data to confront issues related to component separation, point-source and galactic masks \citep{Du13}. The expressions for MFs in Eq.(\ref{sl1})-Eq.(\ref{sl3}) can be modified by replacing the bispectrum by ${\tilde B}_{\ell_1\ell_2\ell_3} = B_{\ell_1\ell_2\ell_3}W_{\ell_1}W_{\ell_2}W_{\ell_3}$. Various forms of the filters $W_{\ell}$ that were found useful in analysing realistic data are: $W^{(\rm M)}_\ell= {\myC_{\ell}b^2_{\ell}/\myC^{\rm tot}_{\ell}};$ $W^{(\rm D1)}_\ell= \sqrt{\ell(\ell+1)}{\myC_{\ell}b^2_{\ell}/\myC^{\rm tot}_{\ell}};$ $W^{(\rm D2)}_\ell= {\ell(\ell+1)}{\myC_{\ell}b^2_{\ell}/\myC^{\rm tot}_{\ell}}$. They correspond to Wiener-filtering ({\rm M}) and Wiener-like filtering using first ({\rm D1}) and second derivatives ({\rm D2}) of the map. The expression for the covariance can be derived by replacing the power-spectrum by the filtered power spectrum $\tilde\myC_{\ell} =W_\ell^2\myC_{\ell}$ in Eq.(\ref{eq:covSij}). By definition, the optimum estimator includes inverse covariance weighting and its performance cannot be improved by filtering - inclusion of weights in the definition of optimum estimator in the numerator and denominator cancel out. As a final remark, the information content of the skew-spectrum is independent of the power spectrum, as at the lowest order the resulting cross-correlation will involve five-point spectra which vanish for a Gaussian CMB map. | 14 | 3 | 1403.0852 |
1403 | 1403.1968_arXiv.txt | A new compilation of {\it UBV} data for stars near the Cepheid S~Vul incorporates {\it BV} observations from APASS and NOMAD to augment {\it UBV} observations published previously. A reddening analysis yields mean colour excesses and distance moduli for two main groups of stars in the field: the sparse cluster Turner~1 and an anonymous background group of BA stars. The former appears to be $1.07\pm0.12$ kpc distant and reddened by $E_{B-V}=0.45\pm0.05$, with an age of $10^9$ yrs. The previously overlooked latter group is $3.48\pm0.19$ kpc distant and reddened by $E_{B-V}=0.78\pm0.02$, with an age of $1.3\times 10^7$ yrs. Parameters inferred for S~Vul under the assumption that it belongs to the distant group, as also argued by 2MASS data, are all consistent with similar results for other cluster Cepheids and Cepheid-like supergiants. | } The variability of S~Vulpeculae was first recognized in 1836-37 with an estimated cycle length of $\sim$68 days. The star was at times classified as either semi-regular or RV Tauri-type (e.g., Joy 1952). A study by Nassau \& Ashbrook (1943) appears to be the first to identify the variations as those of a long-period Cepheid. Photoelectric studies by Fernie (1970) and others (Berdnikov 1993, 1994; Heiser 1996) subsequently confirmed the Cepheid nature of S~Vul, making it the longest period classical Cepheid recognized in the Galaxy. A few other Cepheid-like supergiants (e.g., V810~Cen, HD~18391) have periods in excess of 100 days. Like S~Vul, they have small light amplitudes. In the 1970s the possibility was raised that S~Vul might be a member of the association Vul OB2 (Tsarevskii 1971; Turner 1980), a link that would provide a means of establishing both the luminosity and intrinsic colour of S~Vul from the distance and reddening of association stars. Circa 1980 the author noticed that S~Vul lies in an anonymous open cluster (Fig.~\ref{fig1}), now catalogued as Turner~1 (Turner 1985). A photometric study of the cluster was subsequently performed using photoelectric and photographic photometry (Turner et al.~1986), the latter calibrated using stars in the photoelectric sequence and secondary images offset by $\sim$4$^{\rm m}.6$ from the primary images using a Racine-Pickering wedge on the 3.6-m Canada-France-Hawaii Telescope. Interpreting the photometry was complicated, but it was possible to isolate an old cluster of FG dwarfs $\sim$650 pc distant reddened by $E_{B-V}\simeq0.50$, as well as possible background B stars of larger reddening. The presence of the background group of B dwarfs was later confirmed from 2MASS infrared photometry (Turner 2011), but has not yet been studied using optical photometry. This paper attempts to rectify that omission. \begin{figure}[t] \centerline{ \epsfig{file=turner12f1.eps, scale=0.60} } \caption{\small{The 15$^{\prime}\times15^{\prime}$ field of S~Vul from the Palomar Observatory Sky Survey blue image.}} \label{fig1} \end{figure} | 14 | 3 | 1403.1968 |
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1403 | 1403.3476_arXiv.txt | We discuss possible candidates for non-radial modes excited in a mass accreting and rapidly rotating neutron star to explain the coherent frequency identified in the light curves of a millisecond X-ray pulsar XTE J1751-305. The spin frequency of the pulsar is $\nu_{\rm spin}\cong435$Hz and the identified coherent frequency is $\nu_{\rm osc}=0.5727595\times\nu_{\rm spin}$. Assuming the frequency identified is that observed in the corotating frame of the neutron star, we examine $r$- and $g$-modes in the surface fluid layer of accreting matter composed mostly of helium, and inertial modes and $r$-modes in the fluid core and toroidal crust modes in the solid crust. We find that the surface $r$-modes of $l^\prime=m=1$ and 2 excited by $\epsilon$-mechanism due to helium burning in the thin shell can give the frequency ratio $\kappa=\nu_{\rm osc}/\nu_{\rm spin}\simeq0.57$ at $\nu_{\rm spin}=435$Hz, where $m$ is the azimuthal wave number of the modes. As another candidate for the observed ratio $\kappa$, we suggest a toroidal crustal mode that has penetrating amplitudes in the fluid core and is destabilized by gravitational wave emission. Since the surface fluid layer is separated from the fluid core by a solid crust, the amplitudes of an $r$-mode in the core, which is destabilized by emitting gravitational waves, can be by a large factor different from those in the fluid ocean. We find that the amplification factor defined as $f_{\rm amp}=\alpha_{\rm surface}/\alpha_{\rm core}$ is as large as $f_{\rm amp}\sim 10^2$ for the $l^\prime=m=2$ $r$-mode at $\nu_{\rm spin}=435$Hz for a typical $M=1.4M_\odot$ neutron star model, where $\alpha$'s are the parameters representing the $r$-mode amplitudes, and $l^\prime$ is the harmonic degree of the mode. Because of this significant amplification of the $r$-mode amplitudes in the surface fluid layer, we suggest that, when proper corrections to the $r$-mode frequency such as due to the general relativistic effects are taken into consideration, the core $r$-mode of $l^\prime=m=2$ can be a candidate for the detected frequency, without leading to serious contradictions to, for example, the spin evolution of the underlying neutron star. | A recent report of the detection of a coherent frequency from a mass accreting millisecond X-ray pulsar XTE J1751-305 (Strohmayer \& Mahmoodifar 2014) suggests the existence of a nonradial mode excited in the neutron star. The spin frequency of the pulsar is $\nu_{\rm spin}\cong 435$Hz and the identified frequency is $\nu_{\rm osc}=0.5727595\times\nu_{\rm spin}=249.332609$Hz. If the frequency is really associated with a non-radial mode of a neutron star, we may be able to rule out $p$-modes for the frequency, since their oscillation frequencies are higher than kHz in the case of neutron stars and are too high to be consistent with the detected frequency. We may also rule out the $g$-modes residing in the core, since they usually have much lower frequencies than the spin frequency of the star because of nearly isentropic structure of the core (e.g., McDermott et al 1988). Therefore, possible candidates remained for the detected frequency will be a $g$-mode or a rotational mode propagating in the surface fluid layer, or a rotational mode in the fluid core, or a toroidal crust mode in the solid crust. Note that low frequency $g$-modes and crust modes can be strongly modified by the rapid rotation of the star. Accretion powered millisecond pulsars show small amplitude X-ray oscillations with periods equal to their spin periods, which are assumed to be produced by a hot spot on the surface of the star (e.g., Lamb et al 2009). Numata \& Lee (2010) suggested that global oscillations of neutron stars can periodically perturb such a hot spot so that the oscillation mode periods could be observable as X-ray flux oscillations. They also suggested that since the hot spot on the neutron star surface is corotating with the star, the oscillation frequencies should be equal to those observed in the corotating frame of the star. In this paper, we pursue the possibility that the detected frequency in the pulsar is caused by an unstable non-radial mode of the rapidly rotating neutron star. To obtain the oscillation frequency $\omega$ of pulsationally unstable non-radial modes of neutron stars, we calculate the surface $r$-modes and $g$-modes excited by nuclear helium burning in the surface layer for $|m|=1$ and 2, and toroidal crust modes in the solid crust and rotational modes such as inertial modes and $r$-modes in the fluid core for $m=2$, where $m$ is the azimuthal wave number of the modes. Here, $\omega$ denotes the frequency observed in the corotating frame of the star and is given by $\omega=\sigma+m\Omega$, where $\sigma$ is the oscillation frequency in an inertial frame and $\Omega=2\pi\nu_{\rm spin}$ is the angular spin frequency of the star. To calculate surface $r$-modes and $g$-modes, we construct mass accreting and nuclear burning thin shells in steady state. On the other hand, we use a neutron star model composed of a surface fluid ocean, a solid crust, and a fluid core, to compute crust modes in the solid crust and rotational modes in the fluid core. Note that the crust mode and the core $r$-mode are expected to be destabilized by emitting gravitational waves. Assuming $\nu_{\rm osc}=\omega/2\pi$ and $\nu_{\rm spin}=\Omega/2\pi$, we look for non-radial oscillation modes that are pulsationally unstable and give the ratio $\kappa\equiv\omega/\Omega\simeq0.57$ at $\nu_{\rm spin}=435$Hz. | We have discussed candidates of non-radial modes for the detected frequency $\nu_{\rm osc}= 0.5727\times \nu_{\rm spin}$ at $\nu_{\rm spin}=435$Hz found for the millisecond X-ray pulsar XTE J1751-305. We have shown that the $r_1$-modes and $g_1$-modes propagating in the surface fluid layer of accreting matter composed mostly of helium with a small mixture of hydrogen are pulsationally unstable and can be responsible for the frequency detected. We have found that toroidal crustal modes of $l^\prime=m=2$, which have appreciable amplitudes in the fluid core because of the effects of rapid rotation, are destabilized by emitting gravitational waves, although the strength of the destabilization is weaker that that for the $r$-mode of $l^\prime=m=2$. We have also suggested a possibility that an unstable toroidal crust mode of a neutron star model can be responsible for the observed periodicity in the pulsar. We have shown that for the $r$-mode of $l^\prime=m=2$ there occurs a strong amplification of the amplitudes between the fluid core and the surface fluid ocean, an amplification as large as $f_{\rm amp}\equiv \alpha_{\rm surface}/\alpha_{\rm core}\sim 10^2$, where $\alpha$'s are the parameters representing the $r$-mode amplitudes. As discussed by Strohmayer \& Mahmoodifar (2014), the strength of the detected frequency indicates the amplitude of $\alpha_{\rm surface}\sim 10^{-3}$, for which the $r$-mode amplitudes in the fluid core becomes $\alpha_{\rm core}\sim 10^{-5}$ for $f_{\rm amp}\sim 10^2$. This significant reduction in the $r$-mode amplitudes in the core will render much less serious the difficulty met in the $r$-mode interpretation for the detected frequency, since the spin change rate and heating rate of the star due to the $r$-mode excitation become much smaller than those inferred from the detection of the frequency. Note that, as Andersson et al (2014) discussed, if various frequency corrections such as due to the general relativity are taken into account (see e.g. Yoshida \& Lee 2002; Lockitch, Friedman \& Andersson 2003), it is possible to obtain the ratio $\kappa\simeq 0.57$ for the $l^\prime=m=2$ $r$-mode, for which the ratio tends to $\kappa=2/3$ in the limit of $\Omega\rightarrow 0$ in the Newtonian gravity. Probably, we need a larger amplification factor $f_{\rm amp}$ to completely remove the difficulty, since Mahmoodifar \& Strohamyer (2013), for example, suggested the $r$-mode amplitudes ranging from $\alpha\sim10^{-8}$ to $\sim10^{-6}$. We need more careful discussions and calculations for the determination of the factor $f_{\rm amp}$ for the $r$-modes of neutron star models with a solid crust. The factor $f_{\rm amp}$ may depend on the structures of the ocean and the crust. We need to compute the $r$-mode in the general relativistic frame work with proper treatments of the jump conditions at the interfaces between the solid crust and the fluid regions. The existence of a weak magnetic field possibly affects the amplification. To estimate the effects of the viscous boundary layer on the stability we use an extrapolation formula (Bildsten \& Ushomirsky 2000; Andersson et al 2000; Yoshida \& Lee 2001) given by \be {1\over\tau_{\rm VBL}}={1\over \tilde\tau_{\rm VBL}}\left({10^8~{\rm K}\over T_c}\right) \left({\Omega^2\over \pi G\bar\rho}\right)^{1/4}, \ee where $\bar\rho=M/(4\pi R^3/3)$. If we take the value $\tilde\tau_{\rm VBL}=3.7\times10$ (e.g., Yoshida \& Lee 2001), we have $\tau_{\rm VBL}\sim 10^2$ for $T_c\simeq 2\times 10^8$K, which is shorter than the growth timescales of the $l^\prime=m=2$ $r$-mode and toroidal crust mode computed in this paper, suggesting that these modes are damped by the viscous boundary layer effects. If the transition between the solid crust and the fluid core is not sharp enough for a thin viscous boundary layer to form, the effects of viscous dissipations at the boundary will be weak and probably the destabilized $r$- and crust modes by emitting gravitational waves remain unstable (e.g., Bondarescu \& Wasserman 2013). If the frequency detected in the X-ray pulsar XTE J1751-305 is really produced by a non-radial mode of the underlying neutron star and if it is possible to obtain a correct mode identification for the frequency, we will be able to use the mode to probe the physical properties of the star, such as the mass $M$, the radius $R$, the shear modulus $\mu_{\rm crust}$, and equation of state. If the frequency is due to a toroidal crustal mode or an $r$-mode destabilized by emitting gravitational waves, the detection of the oscillation frequency can be regarded as an evidence for the existence of a neutron star radiating gravitational waves with detectable amplitudes, which will be useful for understanding the physics expected in strong gravity environment. | 14 | 3 | 1403.3476 |
1403 | 1403.6123_arXiv.txt | Starlight from galaxies plays a pivotal role throughout the process of cosmic reionisation. We present the statistics of dwarf galaxy properties at $z > 7$ in haloes with masses up to $10^9 \Ms$, using a cosmological radiation hydrodynamics simulation that follows their buildup starting with their Population III progenitors. We find that metal-enriched star formation is not restricted to atomic cooling ($\tvir \ge 10^4 \unit{K}$) haloes, but can occur in haloes down to masses $\sim10^6 \Ms$, especially in neutral regions. Even though these smallest galaxies only host up to $10^4 \Ms$ of stars, they provide nearly 30 per cent of the ionising photon budget. We find that the galaxy luminosity function flattens above $M_{\rm UV} \sim -12$ with a number density that is unchanged at $z \la 10$. The fraction of ionising radiation escaping into the intergalactic medium is inversely dependent on halo mass, decreasing from 50 to 5 per cent in the mass range $\log M/\Ms = 7.0-8.5$. Using our galaxy statistics in a semi-analytic reionisation model, we find a Thomson scattering optical depth consistent with the latest {\it Planck} results, while still being consistent with the UV emissivity constraints provided by \lya~forest observations at $z = 4-6$. | Cosmic reionisation is an extended process as individual \hii~regions grow around ionising sources that gradually coalesce, culuminating in a fully ionised universe by $z \sim 6$ \citep[e.g.][]{Gnedin97, Razoumov02, Sokasian03, Ciardi03, Furlanetto04, Iliev06, Robertson10, Zahn11, Trac11, So13}. However, there is still some tension between observational constraints on the timing and duration of reionisation. First, the transmission fraction of $z \sim 6$ quasar light blueward of \lya~through the intergalactic medium (IGM) indicates that the universe was mostly ionised by this epoch \citep[e.g.][]{Gunn65, Fan02, Fan06_QSO, Willott07, Mortlock11}. Second, observations of the cosmic microwave background (CMB) from the {\it Wilkinson Microwave Anisotropy Probe (WMAP)} and {\it Planck} have measured the optical depth to Thomson scattering $\tau_e = 0.089^{+0.012}_{-0.014}$, which corresponds to the universe being $\sim$50 per cent ionised at $z = 11.1 \pm 1.1$ \citep{Planck13_Cosmo}. But the ionising emissivity measured at $z = 4-6$ through \lya~forest observations cannot account for this measured $\tau_e$, indicating that the end of reionisation must be photon-starved \citep{Bolton07} and that the emissivity must have been higher during reionisation. Third, the duration% \footnote{\citet{Zahn12} defines $\Delta z$ as the redshift elapsed between 20 and 99 per cent ionised.} % of reionisation has been constrained to occur within $\Delta z < 7.9$ by measuring the kinetic Sunyaev-Zel'dovich effect with the {\it South Pole Telescope} \citep[SPT;][]{Zahn12}. These observations suggest that reionisation was an extended process, mainly occurring at $6 \la z \la 15$. What population of ionising sources drives this global and extended transition? It is clear that quasars and the very brightest galaxies, both of which are too rare, do not significantly contribute to the overall ionising photon budget of reionisation \citep[e.g.][]{Shapiro86, Dijkstra04, Willott10, Grissom14}. Starlight from galaxies are thought to provide the vast majority of the ionising photon budget from extrapolating the observed $z > 6$ galaxy luminosity function (LF) to low luminosities \citep[e.g.][]{Madau99, Bouwens12_Reion, Haardt12, Shull12, Fontanot12, Robertson13}. Alternatively, massive, metal-free (Population III; Pop III) stars can contribute on the order of 10 per cent of the budget \citep{Ricotti04_P3, Greif06, Trac07, Wise08_Reion, Ahn12, Wise12_Galaxy, Paardekooper13, Johnson13} because they are short-lived \citep[e.g.][]{Tumlinson00, Schaerer02} and can be suppressed by chemical enrichment and \hh-dissociating radiative feedback \citep[e.g.][]{Haiman97, Haiman00, Machacek01, Wise08_Gal}. Finally, X-ray radiation from X-ray binaries and accreting massive black holes partially ionise the IGM and may contribute a small amount to the Thomson scattering optical depth \citep{Ricotti04_Xray, McQuinn12, Power13, Fragos13}. Deep galaxy surveys, such as the {\it Hubble Ultra Deep Field} \citep[HUDF;][]{Beckwith06, Koekemoer13} and CANDELS \citep{CANDELS, Koekemoer11}, can probe $z \ga 6$ galaxies up to absolute UV magnitudes $M_{\rm UV} < -18$ or equivalently a stellar mass $M_\star \ga 10^8 \Ms$. Future deep surveys using the {\it James Webb Space Telescope (JWST)} and 30-m class ground-based telescopes will push this limit down to $M_{\rm UV} \sim -15.5$. At these high redshifts, the faint-end LF slope is steepening with redshift and is around $-2$ at $z \sim 8$ \citep[e.g.][]{Bouwens11, Bradley12, Oesch12_LF}. The least massive galaxies can be suppressed through supernovae (SNe) and/or radiative feedback, and this process should materialise as a flattening or turn-over in the LF, but starting at which limiting magnitude? Any change in the LF behavior should be related to the star formation efficiency, i.e. $M_\star/M_{\rm gas}$, which is also connected to the effectiveness of gas cooling and the halo mass in principle. For instance, starting at the lowest mass haloes, the primary coolants in the interstellar medium (ISM) are molecular hydrogen and metals (e.g. C, O, Si), whereas above a virial temperature $\tvir \sim 10^4 \unit{K}$, they change to atomic hydrogen. Negative feedback in these small haloes is also a concern on whether they can sustain efficient star formation. Examples of such feedback include photo-evaporation, \hh~dissociation, and gas blowout from \hii~regions and SN, which all depend on halo mass \citep[e.g.][]{Gnedin00, Wise09, Stinson13, Hopkins13_FIRE}. In the \hh-cooling haloes with $M \sim 10^6 \Ms$, \hh~can be dissociated by a moderate Lyman-Werner (LW; 11.2--13.6~eV) background. But in more massive haloes with $M \sim 10^7 \Ms$, cold gaseous reservoirs can form even in the presence of a strong LW radiation field \citep{Wise07_UVB, Johnson08, OShea08, Safranek12}. Progressing up the mass scale, even atomic cooling haloes are prone to negative feedback; for example, haloes with masses $M \lsim 2 \times 10^9 \Ms$ can be photo-evaporated by an external radiation field, gradually boiling away their star-forming gas reservoir \citep{Efstathiou92, Thoul96, Dijkstra04, Shapiro04, Okamoto08, Finlator11}. How does the LF limiting magnitude $M_{\rm lim}$ affect reionisation histories? Recently, a few groups \citep{Kuhlen12, Finkelstein12, Robertson13} have explored this question among other variations in their reionisation models. \citeauthor{Kuhlen12} found a nearly linear dependence between $\tau_e$ and $M_{\rm lim}$, increasing $\tau_e$ from $\sim$0.06 to 0.08 when $M_{\rm lim}$ increases from --13 to --10. \citeauthor{Robertson13} found little dependence on $M_{\rm lim}$ above --13. Whereas \citeauthor{Finkelstein12} showed that the escape fraction must be greater than 30 and 50 per cent to sustain reionisation at redshifts 6 and 7, respectively, if only the observed CANDELS galaxies contribute to the emissivity. Additional constaints on reionisation can be gained from the inferred ionising flux in the \lya~forest at $z = 4-6$ \citep{Bolton07, Kuhlen12}. Extrapolating the LF down to $M_{\rm UV} = -13$ and assuming that the escape fraction \fesc~is independent of halo mass, \citeauthor{Finkelstein12} also found that $\fesc < 0.13$ is constrained by the measured ionising photon emissivity in \lya~forest observations at $z = 6$. It is clear from these studies that a population of unobserved dwarf galaxies are primarily responsible for driving cosmic reionisation. To further refine reionisation models, it is pertinent to determine the characteristic properties of these unobserved dwarf galaxies. In particular, the stellar fraction, $M_\star/M_{\rm vir}$, and \fesc~of high-redshift galaxies are the largest sources of uncertainty in reionisation models\footnote{Other properties that could affect the ionising emissivity originating from such galaxies are the gas fraction, initial mass function (IMF), gaseous and stellar morphology, and the strength and duration of star formation events.}. Current reionisation models favor scenarios that have a luminosity-weighted average escape fraction that increases with redshift to match the observed $\tau_e$ value while being photon-starved at $z \sim 6$ \citep{Alvarez12, Haardt12, Kuhlen12, Shull12, Mitra13}. For example, the model of \citeauthor{Alvarez12} considers a scenario where galaxies in haloes of mass $10^8 \le M/\Ms \le 2 \times 10^9$ with $\fesc = 0.8$ dominate the ionising emissivity at early times and are gradually photo-suppressed \citep[also see][]{Sobacchi13}. Then at $z \la 6.5$, galaxies greater than $2 \times 10^9 \Ms$ with lower average escape fractions become sufficiently abundant to produce the majority of ionising photons, keeping the universe ionised in a photon-starved scenario. Before moving forward, it should be stressed that the UV escape fraction is an intrinsic quantity for a given galaxy not an entire population. Galaxies with the same mass can have very different escape fractions, arising from, e.g., complex gaseous and stellar morphologies, dust content, and cosmological mass inflow. Furthermore, variable star formation rates (SFRs) and the associated radiative feedback in the ISM can result in an escape fraction that is highly time-dependent. The ionising escape fraction is a notoriously difficult quantity to measure both in high-redshift galaxy observations and theoretical studies. Nevertheless, this topic has been a subject of great interest to constrain the reionisation history of the universe. On the observational side, it is nearly impossible to detect Lyman continuum (LyC) emission at $z > 4$ because the number density of Lyman limit systems rapidly increases with redshift \citep{Inoue08}. However at $z \sim 3$ when the IGM optical depth is around unity, detection of intrinsic LyC radiation becomes feasible. Deep narrow-band galaxy imaging and spectroscopy have uncovered LyC emission in 10--20 per cent of Lyman-break galaxies, which can be interpreted as the mean ionising radiation escape fraction \citep{Steidel01, Shapley06, Iwata09, Nestor11, Jones13}, but see \citet{Vanzella12}. Theoretical efforts have focused on the calculation of \fesc~for over a decade, using analytical and numerical techniques with varying model complexities. The galaxies studied in these cumulative works span over six orders of magnitude in halo mass and are considered out to $z = 15$. Models of the escape fraction found that $\fesc \la 0.06$ for Milky Way like galaxies \citep{Dove00}, and, in general, it depends on the density structure of the ISM and SFR \citep{Ciardi02, Clarke02, Wise09, Fernandez11, Benson13}. At high redshift, \citet{Ricotti00} found higher escape fractions $\fesc \ga 0.1$ in haloes with masses $M \le 10^7 \Ms$, but they posed the valid question of whether these low-mass haloes can host star formation. This paper will address this exact question, utilising a cosmological radiation hydrodynamics simulation of dwarf galaxy formation. Conversely, because of the higher mean densities at high redshift, \citet{Wood00} argued that $\fesc \le 0.01$, and \citet{Fujita03} found that $\fesc \le 0.1$ from dwarf starburst disc galaxies with total masses between $10^8$ and $10^{10} \Ms$. \citet{Paardekooper11} found similar results for isolated high-redshift disc galaxies with total masses of $10^8$ and $10^9 \Ms$. All of the aforementioned models were idealised calculations of isolated galaxies; however \citet{Razoumov06, Razoumov07} and \citet{Gnedin08} used cosmological simulations of galaxy formation with radiative transfer to conclude that $\fesc = 0.01-0.1$ and $\fesc \sim 0.01 - 0.03$, respectively, in haloes with $M \ge 10^{11} \Ms$ at $z = 3-5$. If these low escape fractions were present in lower mass galaxies before reionisation, insufficient LyC emission would escape from them to reionise the universe by $z = 6$ \citep{Gnedin08L}. In radiation hydrodynamics simulations of isolated dwarf irregular galaxies at $z = 8$, \citet{Wise09} found that $\fesc \ga 0.3$, which was confirmed by several other groups with numerical simulations shortly afterward \citep{Razoumov10, Yajima11, Paardekooper13, Ferrara13}. These works imparted momentum to the idea that protogalaxies could be the dominant driver of reionisation, as originally proposed by \citet{Ricotti00}. Semi-analytic models of reionisation tested these ideas and further constrained the required escape fraction in high-redshift dwarf galaxies to be increasing with redshift, suggesting that low-mass galaxies with high \fesc~contributed a significant amount of the ionising photon budget \citep{Haardt12, Alvarez12, Mitra13}. Unfortunately, not even {\it JWST} has the capability to directly detect the lowest-luminosity galaxies that could provide the majority of ionising photons during the earlier epochs of reionisation. Comparisons to local dwarf galaxies can be made, but in principle, similarities could be few because some form in a neutral and cool environment, largely unaffected by the ensuing inhomogeneous reionisation. In addition, some are directly affected by radiative and SN feedback from Pop III stars \citep{Johnson06, Wise08_Gal, Greif10, Maio10_Pop32, Wise12_Galaxy, Pawlik13, Muratov13}. Thus for the time being, this problem is best approached theoretically. This paper focuses on these early dwarf galaxies that are sensitive to feedback effects in haloes with $M \lsim 10^9 \Ms$. The primary goal of this paper is to quantify the mean stellar and gaseous properties, the ionising escape fractions, and LFs of high-redshift dwarf galaxies, and their contribution to global reionisation. In the next section, we outline our simulation set-up and methods. Then, in Section 3, we present scaling relations for stellar mass, gaseous fractions, intrinsic UV magnitudes, and ionising escape fractions of the simulated dwarf galaxies. Next, in Section 4, we apply our mean scaling relations to a semi-analytic reionisation model and show the resulting reionisation history when low-luminosity galaxies are considered. We discuss the implications of our results and possible observational signatures of the first galaxies in Section 5, where we also compare our results to previous studies. Lastly, we summarise our findings in Section 6. | \label{sec:conclusions} We present the characteristic properties and abundances of dwarf galaxies at high-redshift and their absolute contribution to cosmic reionisation. To obtain our results, we use a cosmological radiation hydrodynamics simulation that considers Pop II and III star formation with a self-consistent transition with their radiative feedback modeled with the radiation transport module \moray. In a previous paper (W12), we showed that the star formation history and stellar population of the most massive dwarf galaxy in the simulation analysed here agreed with the local dwarf galaxy metallicity-luminosity relation. We have further analysed this simulation that captures the buildup of the first galaxies, starting with their Pop III progenitors, focusing on their global properties, LF, UV escape fraction, and role during reionisation, and the highlights of our work are as follows: \begin{enumerate} \item Low-luminosity galaxies with stellar masses up to $3 \times 10^4 \Ms$, SFRs of $10^{-3}~\hsfr$, and absolute UV magnitudes of --12 are able to form in metal-line cooling (MC) haloes ($T_{\rm vir} \le 10^4 \unit{K}$). This usually occurs in one burst, which then suppresses any further star formation through stellar feedback, and star formation will recommence after sufficient gas has (re-)accreted into the potential well. \item Gas fractions in the MC haloes have a large spread and are, on average, $\sim$5--7 per cent, where $\sim$0.3--3 per cent of this gas form stars. In addition to internal suppression, they are subsequently photo-suppressed by an external radiation field. \item The early dwarf galaxy LF flattens to $\sim$3 mag$^{-1}$ Mpc$^{-3}$ at $M_{\rm UV} \ga -12$. The galaxies in this plateau form in MC haloes usually with one star formation event that produces an initial magnitude around $M_{\rm UV} = -12$ and then increases as the stellar population ages. \item The luminosity-weighted escape fraction decreases with halo mass with $\fesc \simeq 0.5$ in haloes with $M \le 2 \times 10^7 \Ms$, $\fesc \simeq 0.3$ in haloes with $2 \times 10^7 \le M/\Ms \le 2 \times 10^8$, and $\fesc \simeq 0.05$ in larger haloes. The escape fraction is highly time dependent and is correlated with the SFR with an average delay of $\sim$10 Myr. \item The amount of ionising photons per unit mass escaping from the halo, i.e. $\fesc f_\star f_{\rm gas}$, shows little evolution with halo mass with a mean value of $10^{-3.6}$ over the mass range captured in our simulation. \item Low-luminosity galaxies hosted in MC haloes propel the early epochs of reionisation, providing 75 per cent of the instantaneous emissivity at $z = 14$ when our reionisation model has an ionisation fraction of 20 per cent. These faintest galaxies contribute nearly 30 per cent of the ionising photon budget by $z = 6$. \item Photo-suppression of low-luminosity galaxies leads to a photon-starved reionisation scenario by $z = 6$, agreeing with emissivities inferred from \lya~forest observations. By utilizing calibrated galaxy properties in our reionisation model, we obtain an optical depth to Thomson scattering $\tau_e = 0.093$, agreeing with the latest WMAP and Planck results. \item The luminosity-weighted escape fraction and host halo mass smoothly decline and increase, respectively, with time, and we have given functional fits (Equations \ref{eqn:fesc} and \ref{eqn:mvir}) to these trends for use in future studies. \end{enumerate} We have shown that the faintest galaxies contribute a significant amount to the ionising photon budget during cosmic reionisation. Their consideration in reionisation calculations is essential in order to adhere to observational constrains, such as $\tau_e$, the duration of reionisation, a mostly ionised IGM by $z \sim 6$, and the ionisation background at $z = 4-6$. We are currently following up this study with a larger dataset with more massive galaxies \citep{Xu13} to further constrain galaxy scaling relations and galaxy observables during reionisation, which is timely with the future launch of JWST and commissioning of 30-m class ground-based telescopes. | 14 | 3 | 1403.6123 |
1403 | 1403.3530_arXiv.txt | We use detailed numerical simulations of a turbulent molecular cloud to study the usefulness of the \ci~609~$\mu$m and 370~$\mu$m fine structure emission lines as tracers of cloud structure. Emission from these lines is observed throughout molecular clouds, and yet they have attracted relatively little theoretical attention. We show that the widespread \ci~emission results from the fact that the clouds are turbulent. Turbulence creates large density inhomogeneities, allowing radiation to penetrate deeply into the clouds. As a result, \ci~emitting gas is found throughout the cloud. We examine how well \ci~emission traces the cloud structure, and show that the 609~$\mu$m line traces column density accurately over a wide range of values. For visual extinctions greater than a few, \ci~and $^{13}$CO both perform well, but \ci~performs better at $A_{\rm V} \leq 3$. We have also studied the distribution of \ci~excitation temperatures. We show that these are typically smaller than the kinetic temperature, indicating that the carbon is subthermally excited. We discuss how best to estimate the excitation temperature and the carbon column density, and show that the latter tends to be systematically underestimated. Consequently, estimates of the atomic carbon content of real GMCs could be wrong by up to a factor of two. | Giant molecular clouds (GMCs) are the sites where the majority of Galactic star formation occurs, and hence it is important to understand their properties if we are to understand how star formation proceeds within our Galaxy. The two most abundant chemical species in molecular clouds are molecular hydrogen (H$_{2}$) and atomic helium, and between them they are responsible for the vast majority of the mass of the clouds. However, neither of these species can easily be observed within molecular clouds, as the gas temperature is too low to excite their internal energy levels. Observational studies of GMCs are therefore forced to focus on less abundant tracers that can be observed at typical GMC temperatures. The most popular such tracer is carbon monoxide (CO).\footnote{Unless otherwise stated, when we refer to CO in this paper, we mean $^{12}$CO, the most abundant isotopologue.} Unfortunately, CO is not without its problems as a molecular gas tracer. At high column densities, the problem is one of opacity: the CO rotational transitions start to become optically thick, breaking the relationship between CO emission and column density \citep[see e.g.][]{pin08}. Fortunately, this problem can be avoided to a large extent by observing less common isotopic variants of CO, such as $^{13}$CO or C$^{18}$O, which remain optically thin up to much higher column densities. At low column densities, on the other hand, the problem is one of abundance: in low extinction regions, CO is strongly photodissociated by the interstellar radiation field (ISRF), making it very difficult to observe any CO emission from these regions \citep[see e.g.][]{vdb88,gold08}, let alone to learn anything about the thermal state or kinematics of this gas. It is therefore worthwhile examining other possible tracers of the gas within molecular clouds. One particularly interesting possibility is neutral atomic carbon. Spin-orbit coupling splits the atomic carbon ground state into three fine structure levels with total angular momenta $J = 0, 1, 2$, and forbidden transitions between these three levels give rise to two prominent fine structures lines: the \ci~$^{3}P_{1} \rightarrow \mbox{}^{3}P_{0}$ transition at 609~$\mu$m (hereafter written simply as the $1 \rightarrow 0$ transition) and the \ci~$^{3}P_{2} \rightarrow \mbox{}^{3}P_{1}$ transition at 370~$\mu$m (hereafter the $2 \rightarrow 1$ transition). The energy difference between the $^{3}P_{1}$ and $^{3}P_{0}$ levels is only $\Delta E_{10} / k \simeq 24$~K, while between the $^{3}P_{2}$ and $^{3}P_{0}$ levels it is $\Delta E_{20} / k \simeq 60$~K. Therefore, at typical molecular cloud temperatures of 10--20~K, both of the fine structure lines can be excited. So far, however, neutral atomic carbon has attracted much less attention than CO as a molecular cloud tracer. There are several reasons for this. Observationally, the \ci~lines are harder to study than the low $J$ rotational transitions of CO: they typically have lower brightness temperatures, and are also situated in a wavelength regime where the effects of atmospheric absorption can be highly significant. Theoretically, it was originally thought that neutral atomic carbon would be abundant only at the edges of clouds \citep{langer76}, limiting its usefulness as a tracer of the bulk of the cloud. Subsequent observations have shown that this expectation is incorrect, and that \ci~609~$\mu$m emission is widespread within clouds \citep{frerking89,little94,sch95,kra08}, and yet the perception of \ci~as a tracer of cloud surfaces has proved difficult to shift. In the past few years, however, there has been renewed interest in the prospects of \ci~as a molecular gas tracer. The CHAMP+ and FLASH instruments on the APEX telescope\footnote{http://www.apex-telescope.org/} have allowed both \ci~lines to be studied with reasonable sensitivity from one of the best sites on the planet, and ALMA\footnote{http://www.almaobservatory.org/} will allow these lines to be studied with much greater sensitivity and angular resolution once Bands 8 and 10 are commissioned. Moreover, in the longer term, CCAT\footnote{http://www.ccatobservatory.org} will be able to rapidly map \ci~emission over large areas of the sky with good sensitivity. The time is therefore ripe for an in-depth look at what \ci~emission can tell us about molecular clouds, using state-of-the-art numerical simulations. In this paper, we take the first steps towards this goal. We present results from a simulation of the chemical, thermal and dynamical evolution of a $10^{4} \: {\rm M_{\odot}}$ turbulent molecular cloud illuminated by the standard interstellar radiation field, and examine in detail how the neutral atomic carbon is distributed in this cloud. We also make synthetic emission maps of the resulting \ci~lines, and investigate how much we can learn about the cloud by looking at this emission. Although our focus in this paper is the detailed analysis of a single simulation, we plan to follow this up in future work with a much broader parameter study. The plan of the paper is as follows. In Section~\ref{method}, we present the numerical approach used to simulate the cloud and generate the synthetic emission maps. We also outline the initial conditions used for our simulation. Our main results are presented in Section~\ref{res}, where we examine the chemical and thermal state of the gas in the cloud, and investigate what we can learn about the properties of the cloud from the \ci~emission. Finally, in Section~\ref{conc} we present our conclusions. | \label{conc} In this paper, we have examined in detail the distribution of neutral atomic carbon within a model of a turbulent molecular cloud illuminated by the standard local interstellar radiation field, and have also studied the \ci~fine structure emission produced by these carbon atoms. We show that the density substructure created by the turbulence naturally leads to widespread, spatially extended \ci~emission, in good agreement with observations of real molecular clouds. Most of the neutral carbon in our model is located in gas with a density in the range $100 < n < 10^{4} \: {\rm cm^{-3}}$, and with an effective (angle-averaged) visual extinction $A_{\rm V, eff} > 1$. This gas is relatively cold -- around 80\% of the neutral carbon is found in regions with $T < 30$~K -- and so \ci, like CO, is primarily a tracer of the cold, dense phase within molecular clouds, and not the warm, space-filling phase traced by \cii. Our results suggest that \ci~$1 \rightarrow 0$ emission is a promising tracer of low column density gas in molecular clouds. Although it is easier to detect the molecular gas using $^{12}$CO emission than using \ci~emission, the relationship between $^{12}$CO integrated intensity and the column density of the gas is highly non-linear, owing to the effects of CO photodissociation at low $A_{\rm V}$ and line opacity at high $A_{\rm V}$. One can avoid the worst of the opacity effects by using $^{13}$CO in place of $^{12}$CO, but the effects of photodissociation are not so easily overcome. We find that $^{13}$CO emission is a roughly linear tracer of column density for line-of-sight visual extinctions in the range $3 < A_{\rm V} < 10$, although we caution that the fact that we are neglecting CO freeze-out onto dust grains may affect our results at high $A_{\rm V}$. In comparison, the integrated intensity of the \ci~$1 \rightarrow 0$ line is a linear tracer of column density for visual extinctions in the range $1.5 < A_{\rm V} < 7$. Observing \ci~in place of $^{13}$CO therefore allows one to better study the gas with visual extinctions $1.5 < A_{\rm V} < 3$, which in practice accounts for around 20\% of the total mass of the cloud. However, at $A_{\rm V} > 3$, $^{13}$CO is as good a tracer of the cloud as \ci, while also being significantly easier to observe. Our results are consistent with previous work that has suggested that \ci~emission is a good tracer of molecular gas \citep[see e.g.][]{gp00,ptv04}, although whether this is still true for clouds in other environments (e.g.\ lower metallicities, higher radiation fields) remains to be seen. We have studied several different ways of estimating the excitation temperature of \ci~based on the observed emission. We find that the best results are obtained if we use the \citet{dick78} method for computing $T_{\rm ex}$ along sight-lines with integrated intensities $W_{\rm CI, 1-0} > 3 \: {\rm K} \: {\rm km} \: {\rm s^{-1}}$ and adopt a constant value of $T_{\rm ex}$ for the fainter sight-lines, derived by averaging the estimated values for the bright sight-lines. The resulting excitation temperatures are typically $T_{\rm ex} \sim 11$--13~K, and are generally smaller than the kinetic temperature of the emitting gas, indicating that most of the carbon atoms are not in local thermodynamic equilibrium. Using our estimate for $T_{\rm ex}$, we can determine the column density of neutral atomic carbon, $N_{\rm C}$, with reasonable accuracy in the regime where $N_{\rm C}$ is less than a few times $10^{16} \: {\rm cm^{-2}}$. Comparison of the true and estimated column densities shows that although the error along any particular line of sight may be as high as a factor of two, there is no systematic offset between the estimated and real values. At higher carbon column densities, however, our estimate becomes inaccurate because it neglects the effects of line opacity, and we start to significantly underestimate the true value of $N_{\rm C}$. We find that in practice, we typically miss about half of the total atomic carbon when using this procedure. We have also explored whether using the $^{12}$CO excitation temperature as a proxy for the \ci~excitation temperature can allow us to better reconstruct $N_{\rm C}$ in the optically-thick regime. We find that it does allow us to partially correct for the effects of opacity, although we still miss as much as a third of the total atomic carbon. We therefore recommend that if one wants to estimate $N_{\rm C}$ based on observations of the \ci~fine structure lines, then the following procedure should be adopted: \begin{enumerate} \item Determine the excitation temperature of the $1 \rightarrow 0$ line of $^{12}$CO using Equation~\ref{tx_co}. \item Using this excitation temperature as a proxy for that of \ci, estimate the optical depth in the \ci~$1 \rightarrow 0$ transition using Equation~\ref{tau_est}. \item Compute the column density of atomic carbon in the $J = 1$ level, $N_{1}$, using Equations~\ref{fcorr} and \ref{n1_corr}. \item Repeat steps 2 and 3 for the $J = 2$ level, using the integrated intensity of the $2 \rightarrow 1$ transition in place of that of the $1 \rightarrow 0$ transition, and using $E_{21}$, $\nu_{21}$ and $A_{21}$ in place of $E_{10}$, $\nu_{10}$ and $A_{10}$. \item Use the excitation temperature estimate together with Equation~\ref{tex_defn} to compute the column density of carbon in the $J = 0$ level. \item Sum the column densities of the three levels to obtain the final estimate for $N_{\rm C}$. \end{enumerate} If, as is often the case, the atomic carbon column density is estimated without correcting for opacity effects and with the assumption that the levels have LTE populations, then our study suggests that the resulting values could be in error by as much as a factor of two. A major limitation of our present study is the fact that we have restricted our attention to a single example of a turbulent cloud. In future work, we plan to examine a wider sample of clouds, and to explore whether \ci~emission remains a good tracer of the H$_{2}$ column density as we reduce the metallicity of the cloud and/or increase the strength of the ambient interstellar radiation field. It will also be interesting to explore how the ability of \ci~emission to trace H$_{2}$ changes over time as the cloud evolves, as we have seen in previous studies that the CO emission from clouds that are in the process of forming can change quickly on a relatively short timescale. | 14 | 3 | 1403.3530 |
1403 | 1403.5316_arXiv.txt | The components of blazar jets that emit radiation span a factor of $10^{10}$ in scale. The spatial structure of these emitting regions depends on the observed energy. Photons emitted at different sites cross the lens plane at different distances from the mass-weighted center of the lens. Thus there are differences in magnification ratios and time delays between the images of lensed blazars observed at different energies. When the lens structure and redshift are known from optical observations, these constraints can elucidate the structure of the source at high energies. At these energies, current technology is inadequate to resolve these sources and the observed light curve is thus the sum of the images. Durations of $\gamma$-ray flares are short compared with typical time delays; thus both the magnification ratio and the time delay can be measured for the delayed counterparts. These measurements are a basis for localizing the emitting region along the jet. To demonstrate the power of strong gravitational lensing, we build a toy model based on the best studied and the nearest relativistic jet M87. | Strong gravitational lensing is a powerful tool for exploring the universe \citep{1992grle.book.....S}. It magnifies distant objects and provides a way to observe their structure and detailed properties (e.g. \citet{2012ApJ...759...66Y,2012ApJS..199...25P,2012A&A...542L..31L}). Blazars are the most luminous energy source in the universe; they are also among the most mysterious. Strongly lensed blazars offer a new window for elucidating their structure. The components of blazars that emit radiation from the radio to the $\gamma$-ray span a factor of $10^{10}$ in scale. The images of lensed blazars are resolved in the radio and in the optical \citep{2013A&A...558A.123M,1992AJ....104.1320O,1995MNRAS.274L...5P,1997MNRAS.289..450K}. Their sizes are from sub parsec up to megaparsec. Radio interferometry resolves the details of blazar radio emission from the core, the jets, and the extensive lobes \citep{2008Natur.452..966M}. Improved angular resolution of current X-ray satellites demonstrates that the X-ray emission from the jet forms structures as large as hundreds of kpcs \citep{2006ARA&A..44..463H,2007ApJ...662..900T,2002ApJ...570..543S}. At high energies, the technology is inadequate to resolve the sources. However, the short variability timescales suggest that the sources of the high energy radiation during a flare is of the order of $10^{-3}$~parsec \citep{2011AdSpR..48..998S}. It remains unclear whether the radiation source is the same at all energies. The source of radiation may be close to the base of the jet or it may originate from blobs moving along the jet at relativistic speed. Strong lensing provides a potential tool for distinguishing among the possible emission sites. These strongly lensed sources may thus provide fundamental discriminants among models for high energy emission in blazars. Photons emitted at the different sites cross the lens plane at different distances from the mass-weighted center of the lens. Thus the magnification ratios, and the time delays between the images depend on the location where the radiation originates. Because the site of the emission may be energy dependent, the magnifications ratios and time delays may differ from one wavelength range to another. They may even differ from one flare to another in the same source if the radiation originates from knots in the jet. Here, we develop a method for using strong gravitational lensing as a tool to constrain the internal structure of blazar jets. We use the detailed observations of M87 to construct a toy model of the source (Section~\ref{sec:M87}). We discuss the range of projected physical scales relative to the Einstein radius size (Section~\ref{sec:Scales}). The first step in the process is the determination of the lens properties from the spatially resolved radio and optical images (Section~\ref{sec:Application}). Within the context of the well-constrained $\Lambda$CDM cosmology \citep{2013arXiv1303.5076P}, distances to the lens and source are also known. In $\gamma$-rays, the observed light curve is the sum of the lensed images. We show that the properties of distinct flares enable retrieval of the properties of the source even though the images are unresolved. The crucial $\gamma$-ray observations are the amplitude and time delay of the flares (Sections~\ref{sec:VarR} and \ref{sec:VarDT}). \begin{figure} \includegraphics[width=8.5cm,angle=0]{1.eps}% \caption{\label{fig:sketch} Steps in the application of strong gravitational lensing to unresolved jet structures. 1) Blazar jets extend from sub-parsec up to megaparsec scales. 2) A galaxy located close to the line-of-sight between the source and the observer acts as a lens with an Einstein radius of a few kpcs. Radiation emitted in different regions of the jet crosses the lens plane at different distances from the center of mass of the lens. Differences in path length result in a different magnification ratio and time delay for each image of lensed blazar. 3) Observations at radio and optical wavelengths provide resolved images. They also provide redshifts of the lens and source. 4) The images shows the lensed system B2~0218+35 observed in optical and radio (Images from: \citep{2000MNRAS.311..389J,1995MNRAS.274L...5P,1999MNRAS.304..349B}). 5) The resolved images and the known distances allow retrieval of the mass distribution of the lens. 6) The location of emitting region at high energies cannot be resolved with current instruments, but variability time scales as short as a few hours suggest that the region have to be compact. 7) The $\gamma$-ray variability timescale is short compare to the time delay. Thus the time delay and corresponding magnification ratio for the delayed counterparts of the radiation source can be estimated. 8) Measurement of the time delay and magnification ratio for the lensed flare can be used to limit the location the high energy emitting region along the kpc jet. % % } \end{figure} | Strong gravitational lensing is a potentially powerful tool for investigating the structures of jets at $\gamma$-ray energies where the angular resolution of instruments is insufficient to resolve the source. Observations of strongly lensed sources can discriminate among models where the $\gamma$-ray emission comes from the region close to the core and along those where it originates from knots along the jet. Two gravitationally-lensed blazars have been detected at high energies \citep{2011A&A...528L...3B,HujCheung}; both have flared \citep{2010ATel.2943....1C,2012ATel.4158....1C,2012ATel.4411....1C}. Measurements of time delays and magnification ratios for the lensed counterparts provide a unique opportunity to investigate the origin of the $\gamma$-ray emission. The M87 toy model that we have constructed shows that constraining the emission site to a 60~pc projected distance requires an accuracy in the time delay measurement of 0.4~days, and an accuracy in the magnification ratio of a few percent. Currently, these quantities can be measured to this accuracy at $\gamma$-rays, and in the near future measurements with this precision will be possible at shorter wavelengths. Shortly, dozens of gravitationally-lensed systems will be detected at energies $\lesssim 100$ GeV. In the coming years, these sources will have dozens of sets of flares. This statistical ensemble of flaring sources will allow a systematic study constraining the sites of $\gamma$-ray emission. At energies $\gtrsim$ 100~GeV (VHE), absorption by the Extragalactic Background Light precludes detection of sources at $z \gtrsim$ 1. Even at these energies, the number of known gravitationally-lensed systems should increase very rapidly in the future. Euclid and SKA will reveal blazars at redshift low enough to be detected at VHE. Observations of flaring sources with ground-based Cherenkov telescopes like VERITAS \citep{2002APh....17..221W}, or, eventually, the Cherenkov Telescope Array, CTA \citep{2011ExA....32..193A}, will provide the time delays and magnification ratios necessary to limit the emission region. | 14 | 3 | 1403.5316 |
1403 | 1403.2700_arXiv.txt | Both the broad iron (Fe) line and the frequency of the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low-mass X-ray binaries (LMXBs) can potentially provide independent measures of the inner radius of the accretion disc. We use \textit{XMM-Newton} and simultaneous \textit{Rossi X-ray Timing Explorer} observations of the LMXB 4U~1636--53 to test this hypothesis. We study the properties of the Fe-K$\alpha$ emission line as a function of the spectral state of the source and the frequency of the kHz QPOs. We find that the inner radius of the accretion disc deduced from the frequency of the upper kHz QPO varies as a function of the position of the source in the colour-colour diagram, in accordance with previous work and with the standard scenario of accretion disc geometry. On the contrary, the inner disc radius deduced from the profile of the iron line is not correlated with the spectral state of the source. The values of the inner radius inferred from kHz QPOs and iron lines, in four observations, do not lead to a consistent value of the neutron star mass, regardless of the model used to fit the iron line. Our results suggest that either the kHz QPO or the standard relativistic Fe line interpretation does not apply for this system. Furthermore, the simultaneous detection of kHz QPOs and broad iron lines is difficult to reconcile with models in which the broadening of the iron line is due to the reprocessing of photons in an outflowing wind. | The energy and power density spectra of low-mass X-ray binaries (LMXBs) change with time in a correlated way, generally following changes of the source luminosity, supporting the scenario in which these changes are a function of mass accretion rate in the system \citep[e.g., ][]{Wijnands97, Mendez99, GierlinskiDone02}. Evolution of the broad-band energy spectrum in low-luminosity systems is thought to reflect changes in the configuration of the accretion-disc flow \citep[see review by][and references therein]{Done07}. \citet{GierlinskiDone02} find a strong correlation in the LMXB 4U 1608--52 between the position of the source in the colour-colour diagram and the truncation radius of the inner accretion disc, which is likely driven by the average mass accretion rate through the disc. At low luminosity, the spectrum is consistent with emission from an accretion disc truncated far from the neutron star; as the luminosity increases the spectrum softens and the inner radius of the accretion disc moves inwards. \noindent In a very similar way, changes of the power density spectra appear to be driven by mass accretion rate. At low luminosity, when the energy spectrum of the source is hard, all timing components in the power spectrum have relatively low characteristic frequencies. These frequencies increase as the energy spectrum softens and the inferred mass accretion rate through the disc increases \citep[see e.g.,][]{vdKlis97, Mendez97,Mendez99,Mendez01, Homan02,Straaten02,Straaten03,Straaten05,Altamirano05, Altamirano08a, Altamirano08b, Linares05,Linares07}. The fact that fits to the energy spectra suggest that the accretion disc moves closer to the NS, and that the characteristic frequencies in the power density spectra increase as the luminosity increases, supports the idea that those frequencies are set by the dynamical frequencies in the accretion disc. The kilohertz quasi-periodic oscillations (kHz QPOs) are especially interesting because of the close correspondence between their frequencies and the Keplerian frequency at the inner edge of the accretion disc \citep[e.g.,][]{MillerLambPsaltis98,Stella98}. On short time-scales (within a day or less), the frequency of the kHz QPOs increases monotonically as the source brightens, and the inferred mass accretion rate increases. However, on longer time-scales this correlation breaks down and the intensity-frequency diagram shows the so-called ``parallel tracks'' \citep{Mendez99}. Broad asymmetric iron (Fe) lines have been often observed in accreting systems with the compact object spanning a large range of masses, from supermassive black holes in AGNs \citep[see][for an extensive review]{Fabian00} to stellar-mass black holes \citep[e.g.,][]{Miller02,Miller04} and neutron star systems \citep{Bhattacharyya07}. The Fe K-$\alpha$ emission line at 6--7 keV is an important feature of the spectrum that emerges from the accretion disc as a result of reflection of the corona and the NS surface/boundary layer photons off the accretion disc. The mechanism responsible for the broad asymmetric profile of the line is still under discussion. \citet{Fabian89} proposed that the line is broadened by Doppler and relativistic effects due to motion of the matter in the accretion disc. \citet{diSalvo05} and \citet{Bhattacharyya07} discovered broad iron lines in the NS LMXBs 4U 1705--44 and Serpens X-1, respectively. \citet{Cackett08} confirmed \citet{Bhattacharyya07} results using independent observations, and also discovered broad, asymmetric, Fe K-$\alpha$ emission lines in the LMXBs 4U 1820--30 and GX 349+2. All these authors interpreted the broadening of the line as due to relativistic effects. Relativistic Fe lines have been observed at least in a dozen NS binary systems in the last decade \citep{diSalvo05,Bhattacharyya07,Cackett08, Pandel08, Cackett09b, Papitto09,diSalvo09, Reis09, Iaria09,DAi09,Cackett10,DAi10,Egron11,Cackett12,Sanna13}. A different interpretation for the broadening of the line has been suggested by \citet{Ng10} who re-analysed the data of several NS systems showing Fe K-$\alpha$ emission lines. \citet{Ng10} claim that for most of the lines there is no need to invoke special and general relativity to explain the broad profile, and that Compton broadening is enough. If the relativistic interpretation of the Fe line is correct, we can directly test accretion disc models by studying the line properties, as the shape of the profile depends on the inner and the outer disc radius. We expect then the iron line to be broader in the soft state -- when the inner radius is smaller and the relativistic effects stronger -- than in the hard state. Accretion disc models can also be tested using simultaneous measurements of kHz QPOs and iron lines \citep{Piraino00,Cackett10}. If both the Keplerian interpretation of the kHz QPOs frequency and the broadening mechanism (Doppler/relativistic) of the Fe line are correct, these two observables should provide consistent information about the accretion disc. Furthermore, if the changes in the spectral continuum also reflect changes of the inner edge of the accretion disc, the Fe line should vary in correlation with the frequency of the kHz QPOs \citep[see, e.g.,][]{Bhattacharyya07}. Understanding the relation between kHz QPOs, Fe emission line and spectral states may have an impact beyond accretion disc physics. As discussed by \citet{Piraino00}, \citet{Bhattacharyya07}, and \citet{Cackett08}, measurements of the line could also help constraining the mass and radius of the neutron star \citep{Piraino00}, parameters needed to determine the neutron star equation of state. \citet{Cackett10}\footnote{At about the same time, Altamirano et al. (2010) presented a similar analysis in a manuscript that was eventually never published (c.f. \S 5 in \citet{Cackett10})} tested this idea using three observations of 4U 1636--53. With all of this in mind, in this paper we investigate the correlation between the iron line, kHz QPOs and spectral states in the LMXB 4U 1636--53, with the aim of understanding whether the existing interpretations of these phenomena are consistent. The fact that 4U 1636--53 is well sampled with \textit{XMM-Newton}, and \textit{Rossi X-ray Timing Explorer (RXTE)} observations, is one of the most prolific sources of kHz QPOs, shows strong Fe-K$\alpha$ lines, and shows regular hard-to-soft-to-hard state transitions on time scales of weeks, makes this source an excellent target for this study. | We detected kHz QPOs in all the \textit{RXTE} observations simultaneous with the six \textit{XMM-Newton} observations of the NS LMXB 4U 1636--53 for which \citet{Sanna13} studied the broad iron line in the X-ray spectrum. Combing the measurements of the frequency of the kHz QPOs and the parameters of the iron lines in 4U 1636--53 we investigated the hypothesis that both the iron line and the kHz QPOs originate at (or very close to) the inner radius of the accretion disc in this system. From these observations we found that the inner disc radius, deduced from the upper kHz QPO frequency, decreases as the spectrum of the source softens, and the inferred mass accretion rate increases. On the other hand, the inner radius estimated from the modelling of the relativistically-broadened iron line did not show any clear correlation with the source state, except for the line model \textsc{laor} for which the inferred inner disc radius consistently decreases going from the transitional state to the soft state (see Table~\ref{tab:line_radius}). Combining the disc radius inferred from the frequency of the upper kHz QPO and the iron line profile, we found that the mass of the NS in 4U 1636--53 deduced from the four observations are inconsistent with being the same. A similar conclusion was drawn by \citet{Cackett10} from the first three observations in the sample that we studied here. The latter result implies that either the upper kHz QPO frequency does not reflect the orbital frequency at the inner edge of the disc, the Fe line profile is not (only) shaped by relativistic effects, the models used to fit the iron line are incorrect, or the the kHz QPOs and the Fe line are not produced in the same region of the accretion disc. We assumed that the upper kHz QPO is the one which reflects the orbital frequency at the inner edge of the accretion disc \citep[e.g.,][]{MillerLambPsaltis98, Stella98}. There are, however, alternative models that associate instead the lower kHz QPO to the orbital disc frequency \citep[e.g.,][]{Meheut09}. If this is the case, then the radius profile showed in Figure~\ref{fig:radius_qpo} would shift to higher values of $R_{in}$, and therefore, the mass for which $R_{in}$ from kHz QPOs and iron lines would match will also shift to higher values. Since the difference in frequency between upper and lower kHz QPOs in 4U 1636--53 is more or less constant across the colour-colour diagram \citep[e.g.,][]{Mendez98, Jonker02}, using the lower kHz QPOs would lead to similar results as those shown in Figure~\ref{fig:masses}, with NS masses shifted toward higher values. Under the assumption that the kHz QPOs are generated in the accretion disc, and considering circular orbits in the equatorial plane for Kerr space-time, the only characteristic frequencies (other than the orbital frequency) that match the observed kHz QPO frequency range are the periastron precession and the vertical epicyclic frequencies. Interpreting the upper kHz QPO as the vertical epicyclic frequency and combining the inner radius estimates with the iron line findings we found results consistent with the ones reported above. On the other hands, interpreting the upper kHz QPO as the periastron precession frequency led to meaningless NS mass values (lower than 0.1 M$_\odot$). The kHz QPOs may still reflect the orbital (quasi-Keplerian) frequency at a radius far from the inner edge of the disc. A possible scenario to reconcile this idea, for instance, could be a mechanism that amplifies the orbital frequencies of matter orbiting within a narrow ring in the disc to produce the QPO. The process could be similar to the lamp-post model by \citet{Matt91}. Such mechanism, however, must be able to pick a narrow range of radii in order to reproduce the observed high QPO coherence values \citep[e.g.,][]{Barret05b}. For instance, for a 1.8 solar mass neutron star with a QPO at 800 Hz, if this is the Keplerian frequency in the disc, the putative mechanism should pick a ring of $\sim$600 m to produce a QPO with $Q = 200$. Besides generating the kHz QPOs, this mechanism should also affect other properties of the disc, such as the emissivity index or the ionisation balance, which would in turn affect the properties of the iron emission line. From the behaviour of the time derivative of the frequency of the lower kHz QPO, \citet{Sanna12a} found that the kHz QPOs (both the lower and the upper) in 4U 1636--53 are consistent with the orbital frequency at the sonic radius in the accretion disc. We also note that the frequency of the upper kHz QPO increases monotonically across the colour-colour diagram. All this lends support to the interpretation of the kHz QPO reflecting the orbital frequency at the inner edge of the accretion disc. \begin{figure*} \begin{center}$ \begin{array}{cc} \includegraphics[scale=0.23]{figure12.ps} & \includegraphics[scale=0.23]{figure13.ps}\\ \includegraphics[scale=0.23]{figure14.ps}& \includegraphics[scale=0.23]{figure15.ps} \\ \includegraphics[scale=0.23]{figure16.ps}& \includegraphics[scale=0.23]{figure17.ps}\\ \end{array}$ \end{center} \caption{Marginal probability distribution functions of the NS mass in 4U 1636--53 inferred from simultaneous measurements of the upper kHz QPO and the iron emission line, for four different observations represented with different colours. Different panels represent different models used to fit the iron line profile. } \label{fig:masses} \end{figure*} Besides Doppler and relativistic effects, the iron emission line can be broadened by other processes. For example, the broadening may be ( partially) due to Compton scattering in a disc corona (\citealt{Misra98}; \citealt{Misra99}; see also \citealt{Reynolds00}; \citealt{Ruszkowski00}; \citealt{Turner02}, and \citealt{Ng10}). However, \citet{Sanna13} showed that Compton broadening alone cannot explain the broad profile of the iron emission line in 4U 1636--53. \citet{Titarchuk03} argued that the red wing of the Fe-K$\alpha$ lines is not due to Doppler/relativistic effects, but to relativistic, optically-thick, wide-angle (or quasi-spherical) outflows (\citealt{Laming04}; \citealt{Laurent07}, see however \citealt{Miller04}; \citealt{Miller07}, and \citealt{Pandel08}). As explained by \citet{Titarchuk09}, in this scenario the red wing of the iron line is formed in a strong extended wind illuminated by the radiation emanating from the innermost part of the accreting material. One of the main predictions of this model is that all high-frequency variability should be strongly suppressed. The fact that we detected kHz QPOs and broad iron lines simultaneously in 4U~1636--53 casts doubt on this interpretation. Although our findings contradict this scenario, the model under discussion has been developed for black holes, so it is not clear how the boundary layer or the neutron star surface could change these predictions. Compared to other sources, the iron line in 4U 1636--53 shows unusual properties; for instance, the best-fitting inclination is $i \gtrsim 80^\circ$ \citep{Pandel08,Cackett10,Sanna13}, which is at odds with the lack of dips or eclipse in the light curve. \citet{Pandel08} proposed that the line profile could be the blend of two (or more) lines, for example, formed at different radii in the disc, or due to separate regions with different ionisation balance. If this is correct, the total line profile would be the result of iron lines at different energies. To proceed further with this idea would require to solve the ionisation balance in the accretion disc where the line is formed. \citet{Sanna13} investigated this scenario by fitting the reflection spectrum with a self-consistent ionised reflection model, but they did not find any supporting evidence for this idea \citep[see also][]{Cackett10}. The fact that in Obs.~3 and 5 the kHz QPO frequency significantly varied within the 20-30~ksec required to detect the iron line suggests that the iron line profile we model may be affected by changes of the disc during those 20-30~ksec. If the kHz QPO frequency depends upon the inner disc radius, the iron line profile we observe would be the average of different line profiles, one for each value of the inner disc radius. This is independent of whether the kHz QPO frequency reflects the orbital disc frequency, or whether the relation between frequency and inner radius is more complicated. The line energy or the disc emissivity could also vary if the inner disc radius changes. To proceed further, detailed simulations (assuming scenarios in which only the $R_{in}$ changes with time, as well as scenarios in which all line parameters change) are needed to test to what extent changes in the accretion flow on timescales of $\sim$30~ksec (approximately the time needed with present instruments to fit the line accurately) can affect the final line profile. A similar consideration applies to the inner radius inferred from the kHz QPO frequency. As mentioned in Section~\ref{sec:qpo_analysis}, in Obs.~3 and 5 the frequency of the lower kHz QPO spanned a frequency range of $\sim$200 Hz during the $\sim$25 ks observation. Although, we did not directly see the upper kHz QPO changing frequency with time, it is likely that the upper kHz QPO followed the lower one. If this was the case, then the full width at half maximum (FWHM) of the upper kHz QPO observed contains information on the frequency range covered by the QPO during the observation. To bring this information into the inner disc radius estimates, we should use the QPO FWHM instead of the frequency error (which is relatively small) to calculate the probability distribution function of the inner radius of the accretion disc. In Figure~\ref{fig:diskline_fwhm} we show the marginal probability distribution functions of the NS mass inferred from the four observations combining the upper kHz QPOs and the iron lines modelled with \textsc{diskline}. Solid and dotted lines represent the marginal probability distribution functions using the error in the QPO frequency and the half-width half-maximum (HWHM) as error, respectively. In the latter case the marginal probability distribution functions of the NS mass show a broader profile, and the range of mass values where they are consistent increases (although the overlapping area is still small). By combining the marginal probability distribution functions we get the mass profile (joint probability) for which, in the 4 observations, kHz QPO and iron line estimates of the inner disc radius are consistent. This is shown in the inset of Figure~\ref{fig:diskline_fwhm}. The most likely value of the NS mass, for this specific case, ranges between $\sim$1.1 and $\sim$1.5 M$_\odot$, which is consistent with theoretical NS mass predictions \citep[e.g.,][]{Lattimer07}. However, it should be noticed that in Figure~\ref{fig:diskline_fwhm}, two out of the four PDFs (Obs.~1 and 2) marginally overlap, therefore the final joint probability function is likely not fully representative of all observations. Statistically speaking, the overlapping area between the intersecting marginal distributions in Figure~\ref{fig:diskline_fwhm} represents the likelihood of measuring 4 values $M_i$ of the NS mass $M_0$ (assuming the mass is always the same), and the hypothesis $H$ that one of the kHz QPOs is Keplerian, the Fe line is relativistic, and both phenomena arise from the same region of the accretion disc is valid. In Table~\ref{tab:probability} we report the the NS mass values and the likelihood for the different models used to fit the Fe line profile. It is interesting to notice that the highest likelihood of the data given the model is obtained when the Fe-K$\alpha$ emission line is modelled with \textsc{diskline}. \begin{table} \resizebox{0.9\columnwidth}{!}{\begin{minipage}{\columnwidth} \begin{tabular}{lcccc}\hline \multicolumn{1}{c}{} & \multicolumn{2}{c}{$\delta \nu$} & \multicolumn{2}{c}{HWHM}\\\hline \multicolumn{1}{c}{Fe line model} & \multicolumn{1}{c}{$M_0(M_\odot)$} & \multicolumn{1}{c}{$\mathcal{L}$} & \multicolumn{1}{c}{$M_0(M_\odot)$} & \multicolumn{1}{c}{$\mathcal{L}$} \\\hline \textsc{Diskline} & 1.4$\pm$0.2 & 8.2\e{-3} &1.3$\pm$0.2 &1.4\e{-1} \\ \textsc{Laor} &2.6$\pm$0.6& \textless\, 1\e{-9} &3.0$\pm$1.2& 1.8\e{-6} \\ \textsc{Kyrline} a$_{*}$=0 &0.9$\pm$0.3 &\textless\, 1\e{-9} &0.9$\pm$0.3& \textless\, 1\e{-9}\\ \textsc{Kyrline} a$_{*}$=0.27&0.8$\pm$0.2 & \textless\, 1\e{-9} &0.7$\pm$0.1& 3.1\e{-3}\\ \textsc{Kyrline} a$_{*}$=1&0.8$\pm$0.2 & \textless\, 1\e{-9}&0.8$\pm$0.1 &1.9\e{-3}\\ \textsc{Reflection} &0.6$\pm$0.1 & 3.7\e{-3} &0.6$\pm$0.1& 2.5\e{-2}\\\hline \end{tabular} \end{minipage}} \caption{Likelihood ($\mathcal{L}$) values of measuring the 4 values NS $M_i$ if the NS mass $M_0$ is always the same and under the hypothesis $H$, for different models of the Fe emission line. The two columns represent the likelihood measured from the marginal probability distribution functions of the NS mass in 4U 1636--53 calculated using the error in the QPO frequency ($\delta \nu$) and the half-width half-maximum of the upper kHz QPOs (HWHM), respectively.} \label{tab:probability} \end{table} The frequency of the kHz QPO and the source intensity (likely the mass accretion rate) are degenerate on long (longer than $\sim$ a day) time-scales \citep[``parallel tracks'',][]{Mendez99}: The same QPO frequency may appear at very different source intensities. It remains to be seen whether this phenomenon can affect some properties of the disc, such as the emissivity index or the ionisation balance, which would affect the profile of the iron line, and hence the inferred value of the inner radius of the accretion disc. \begin{figure} \resizebox{1\columnwidth}{!}{\rotatebox{0}{\includegraphics[clip]{figure18.ps}}} \caption{Marginal probability distribution functions of the NS mass in 4U 1636--53 using the iron line model \textsc{Diskline}. Solid and dotted lines are calculated using the error in the QPO frequency and the half-width half-maximum of the upper kHz QPOs, respectively. Colours are as in Figure~\ref{fig:masses}. The inset shows the joint probability distribution function for the four observations with Fe line and upper kHz QPO, using the half-width half-maximum as the error in the frequency. The area under the probability function shown in the inset represents the likelihood of measuring the masses $M_i$ of the NS mass $M_0$ under the hypothesis $H$ that one of the kHz QPOs is Keplerian, the Fe line is relativistic, and both phenomena arise from the same region of the accretion disc is valid.} \label{fig:diskline_fwhm} \end{figure} | 14 | 3 | 1403.2700 |
1403 | 1403.0369_arXiv.txt | We examine the radiation spectra from relativistic electrons moving in a Langmuir turbulence expected to exist in high energy astrophysical objects by using numerical method. The spectral shape is characterized by the spatial scale $\lambda$, field strength $\sigma$, and frequency of the Langmuir waves, and in term of frequency they are represented by $\omega_0 = 2\pi c/\lambda$, $\omega_\mathrm{st}=e\sigma/mc$, and $\omega_\mathrm{p}$, respectively. We normalize $\omega_\mathrm{st}$ and $\omega_{p}$ by $\omega_0$ as $a \equiv \omega_\mathrm{st}/\omega_0$ and $b \equiv \omega_\mathrm{p}/\omega_0$, and examine the spectral shape in the $a-b$ plane. An earlier study based on Diffusive Radiation in Langmuir turbulence (DRL) theory by Fleishman \& Toptygin showed that the typical frequency is $\gamma^2\omega_\mathrm{p}$ and that the low frequency spectrum behaves as $F_\omega \propto \omega^1$ for $b>1$ irrespective of $a$. Here, we adopt the first principle numerical approach to obtain the radiation spectra in more detail. We generate Langmuir turbulence by superposing Fourier modes, inject monoenergetic electrons, solve the equation of motion, and calculate the radiation spectra using Lienard-Wiechert potential. We find different features from the DRL theory for $a>b>1$. The peak frequency turns out to be $\gamma^2 \omega_\mathrm{st}$ which is higher than $\gamma^2\omega_\mathrm{p}$ predicted in the DRL theory, and the spectral index of low frequency region is not $1$ but $1/3$. It is because the typical deflection angle of electrons is larger than the angle of the beaming cone $\sim 1/\gamma$. We call the radiation for this case "Wiggler Radiation in Langmuir turbulence" (WRL). | \label{int} The radiation mechanisms of many high energy astrophysical objects are still an active issue since they often contain features which are not easily explained by the conventional synchrotron and inverse Compton emissions. Recently, much attention has been paid to the radiation signatures from the turbulent electromagnetic fields (e.g., Medvedev 2000, Fleishman 2006, Kelner, Aharonian, \& Khangulyan 2013, Mao \& Wang 2013, Teraki \& Takahara 2013). The main scene of the emission regions of high energy astrophysical objects is collisionless shocks, and the turbulent electromagnetic fields would be generated in the shock region. Therefore, the electromagnetic turbulence should be taken into account when we consider the radiation. However, for the major emission mechanisms of synchrotron radiation and inverse Compton scattering, effects of small scale turbulence are not taken into account. There is a room for novel emission signatures in the consideration of turbulence, which may be of relevance to observations. By reproducing the observed spectra, we can extract physical parameters of astrophysical objects. Thus, researches of radiation signatures from the turbulent field would play a key role for the understanding of physical mechanisms of the high energy astrophysical objects. Radiation spectra from a small scale turbulent magnetic field have been well studied as the "jitter radiation" or "Diffusive Synchrotron Radiation" (Medvedev et al. 2011, Fleishman \& Urtiev 2010 and references therein). Differences from the synchrotron radiation become significant when the typical spatial scale of an eddy $1/k_\mathrm{typ}$ is smaller than the Photon Formation Length (PFL) of the synchrotron photons $r_\mathrm{L}/\gamma$, where $r_\mathrm{L}$ is the Larmor radius and $\gamma$ is the Lorentz factor of the electron. Such a small scale magnetic field is thought to be generated by Weibel instability around the shock front. When the strength of this small scale turbulent magnetic field is dominant, the radiation spectra are determined by the turbulence and reveal various signatures of the turbulent field. For example, when $2\pi/k_\mathrm{typ}\ll r_\mathrm{L}/\gamma$ the peak frequency in $\nu F_\nu$ spectrum becomes $\gamma^2k_\mathrm{typ}c$, and the spectrum in the highest frequency region shows a power law $\nu F_\nu\propto \nu^{-\mu+1}$ when the turbulence exists up to the maximum wave number $k_{\rm max}\gg k_{\rm typ}$. The power law index $\mu$ reflects that of the turbulent magnetic field $B^2(k)\propto k^{-\mu}$. The spectra show more complex signatures when $2\pi/k_\mathrm{typ}\sim r_\mathrm{L}/\gamma$ (Medvedev 2011, Reville \& Kirk 2010, Teraki \& Takahara 2011). We note that the anisotropy of turbulence also affects the radiation spectra (e.g. Kelner et al. 2013, Reynolds \& Medvedev 2012, Medvedev 2006). The radiation from an electron which moves in non-uniform magnetic field in a laboratory is well studied using the insertion device of synchrotron orbital radiation factory, where a series of magnets are line-upped to make the particle deflect periodically. It is called "Wiggler" or "Undulator" (Jackson 1999). For Undulator, the strength of magnets $B$ and gaps between them $\lambda$ are chosen to satisfy the condition that the observer is always in the beaming cone. On the other hand, for Wiggler, the observer is periodically in and off the beaming cone. We estimate the critical distance $\lambda_{\rm c}$ which divides Wiggler and Undulator. The deflection angle in one deflection is $\theta_{\rm def}= \lambda/r$, where $r\simeq \gamma mc^2/eB$ is the typical curvature radius of the orbit. The radiation from a relativistic particle is concentrated into small cone with opening angle $\sim 1/\gamma$. Therefore, the critical condition dividing Wiggler and Undulator is $\theta_{\rm def} = 1/\gamma$, which is rewritten as $\lambda_{\rm c} = r/\gamma$. Thus, the device is called Undulator when $\lambda<\lambda_{\rm c}$, while it is called Wiggler when $\lambda>\lambda_{\rm c}$. The radiation spectrum of Undulator shows a sharp peak at $\gamma^2 2\pi c/\lambda$, while Wiggler shows a broad spectrum with peak frequency $\sim \gamma^2 eB/mc$. The relation between typical frequencies and deflection angle is a key point for understanding of the radiation spectra. Perturbative jitter radiation or perturbative DSR is recognized as extensions of the Undulator radiation, since the spatial scale of turbulence $\lambda$ is assumed to be much smaller than $mc^2/eB$. The fact that $\theta_{\rm def}$ determines the radiation feature was also noted in astrophysics in early seventies by, e.g., Rees, (1971), and Getmantsev \& Tokarev (1972). Rees assumed that the strong electromagnetic wave is emitted from the Crab pulsar with frequency $\Omega$ (30Hz) according to the "oblique rotator" model by Ostriker \& Gunn (1969), and argued that the radiation from an electron moving in the strong wave is not inverse Compton scattering (with frequency $\gamma^2\Omega$) but synchrotron-like (synchro-Compton) radiation, because the deflection angle $\theta_{\rm def}$ is estimated as $\theta_{\rm def}>10/\gamma$, where the factor $10$ comes from the ratio of cyclotron frequency to the wave frequency $eB_{\rm eq}/mc\Omega$. The magnetic field strength $B_{\rm eq}$ is estimated by equating the spindown luminosity and power of magnetic dipole radiation of the Crab pulsar and by considering the distance from the pulsar. He argued that the radiation signature of synchro-Compton radiation resembles that of the synchrotron radiation. The typical frequency is determined by the field strength as $\gamma^2eB_{\rm eq}/mc$, and the low frequency spectral index is roughly $1/3$. Getmantsev \& Tokarev (1972) studied the radiation spectra under general electromagnetic fields and stated that the radiation signature from a single charged particle is determined by the frequency or wavelength of the field for $\theta_{\rm def}\ll1/\gamma$, while it is determined by the field strength for $\theta_{\rm def}\gg1/\gamma$ in the same way as synchrotron radiation. Note that they did not discussed explicit expressions of the radiation spectra from a single electron for $\theta_{\rm def}\sim 1/\gamma$, they presented a general expression of radiation spectrum from an ensemble of electrons with a power spectrum. Thirty years after these pioneering works, radiation spectra from a relativistic particle interacting with turbulent fields are gathering a renewed attention. For example, the radiation mechanism from Langmuir turbulence treated in the present paper has become an interesting topic. The Langmuir turbulence has been pointed out to be generated around the shock front of the relativistic shocks (Silva 2006, Dieckmann 2005, Bret, Dieckmann, \& Deutch 2006), so it should be as important as the radiation from turbulent magnetic field. Fleishman \& Toptygin (2007a,b) have made a systematic treatment of diffusive radiation in Langmuir turbulence (see references cited in Fleishman \& Toptyigin 2007b for other earlier relevant works). Their method is the most sophisticated treatment for Langmuir turbulence, which is based on Toptygin \& Fleishman (1987). For later discussions, we shortly review their treatment. They treat the electron motion by a statistical approach and use a perturbative treatment for calculation of the radiation. The calculation formula for the radiation spectra is based on the one written in Landau \& Lifshitz (1971). For $\theta_{\rm def}\ll 1/\gamma$, a rectilinear trajectory with constant velocity is assumed, but non-zero acceleration from the external field is taken into account. The wavenumber of the Langmuir waves is assumed to satisfy the condition $k_{\rm typ} <\omega_{\rm p}/c$, where $\omega_\mathrm{p}$ is the plasma frequency. They calculate the correlation between the acceleration and the Langmuir waves. The peak frequency is $\gamma^2\omega_\mathrm{p}$. The spectrum shows an abrupt cutoff above the peak, and becomes $F_\omega \propto \omega^{-\mu}$ in higher frequencies when the turbulence exists up to the maximum wavenumber $k_{\rm max}\gg c/\omega_{\rm p}$ for a power law turbulent spectrum $E^2(k)\propto k^{-\mu}$. The spectrum just below the peak is $F_\omega\propto \omega^1$, and becomes $F_\omega \propto \omega^0$ in lower frequencies and $F_\omega \propto \omega^{1/2}$ in even lower frequency region.\footnote{$F_\omega \propto \omega^2$ spectrum is predicted in the lowest frequency region, which comes from the effect of wave dispersion in the plasma. We do not discuss such effects in this paper.} $F_\omega \propto \omega^{1/2}$ spectrum comes from the effect of multiple scattering. The angle between the velocity and observer direction becomes larger than the beaming cone after many deflections even when the deflection angle in one deflection $\theta_{\rm def}$ is much smaller than $1/\gamma$, and the approximation of rectilinear trajectory is broken. Therefore, this treatment is beyond the perturbative treatment, and they call it "non-perturbative treatment". They treat the changing of direction of motion in many deflections by diffusion approximation. In consequence, a spectral break emerges in the low frequency region with a suppression of low frequency photons. The spectrum becomes $F_\omega \propto \omega^{1/2}$ from this effect and the index of $1/2$ comes from the diffusivity. They claimed that the break frequency approaches the peak frequency as $\theta_{\rm def}$ becomes large and the break and peak merge for $\theta_{\rm def}\sim 1/\gamma$. They stated that even for $\theta_{\rm def}\gg1/\gamma$the spectrum in frequency region just below the peak of $\gamma^2\omega_{\rm p}$ is $F_\omega \propto \omega^{1/2}$. This is inconsistent with the statement by Getmantsev \& Tokarev (1972). This is one of the objectives of investigations in the present paper. The effect of large angle deflection would come into play in forming the radiation spectra for Langmuir turbulence as in the Wiggler radiation for $\theta_{\rm def}>1/\gamma$. This point has been discussed for magnetic turbulence in Kelner et al. (2013), Medevev et al. (2011), and Teraki \& Takahara (2011). In this paper, we investigate general properties of the radiation spectra from relativistic electrons in a Langmuir turbulence for various cases including this regime. Before proceeding to the formulation of the calculation employed in the present paper, we point out the differences between the magnetic field generated by Weibel instability (entropy modes) and the Langmuir waves. The first is time variability. The entropy mode does not oscillate, so the typical timescale is determined by the turnover time of an eddy. It is longer than the crossing time of a relativistic electron if we assume that the background plasma is sub-relativistic. Therefore, we can treat the magnetic field as a static field when we calculate the radiation spectra for the zeroth-order approximation. On the contrary, we should not treat the Langmuir turbulence as a static field even for the zeroth-order approximation. The crossing time can be comparable to or longer than the period of the Langmuir waves, because the typical spatial scale is about inertial length $c/\omega_{\rm p}$, governed by the plasma frequency $\omega_\mathrm{p}$ (Diekmann 2005). Therefore, the time variability of the electric field can not be ignored. This effect is well studied by Fleishman \& Toptygin (2007a,b). The second is the energy change of the radiating electrons. For the case of turbulent magnetic field, the energy of electrons is conserved if we ignore the radiation back reaction. However, the energy change cannot be ignored for the Langmuir turbulence, because the electric field can accelerate the electrons parallel to their velocity. The Lorentz factor of the electron can change in a short time by strong Langmuir waves. This effect may play a role for calculation of the radiation spectra. The calculation of electron trajectory for the strong turbulence by analytical approach is hard to perform. Thus, we calculate the radiation spectra by numerical approach from first principle. We calculate radiation spectra for a wide range of the field parameters. We study about three factors, the scale length, time variability, and strength. By sweeping the parameter plane, we generally investigate the radiation spectra from a relativistic electron moving in Langmuir turbulence. In section 2, we describe calculation method, and we show the results in section 3. In section 4, we give the physical interpretations of the discovered spectral features using radiation for a spatially uniform plasma oscillation. In section 5, we make a summary and some discussions. | 14 | 3 | 1403.0369 |
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1403 | 1403.5585_arXiv.txt | Recently, BICEP2 measurements of the cosmic microwave background (CMB) $B$-mode polarization has indicated the presence of primordial gravitational waves at degree angular scales, inferring the tensor-to-scalar ratio of $r=0.2$ and a running scalar spectral index, provided that dust contamination is low. In this {\em Letter}, we show that the existence of the fluctuations of cosmological birefringence can give rise to CMB $B$-mode polarization that fits BICEP2 data with $r<0.11$ and no running of the scalar spectral index. When dust contribution is taken into account, we derive an upper limit on the cosmological birefringence, $A\beta^2<0.0075$, where $A$ is the amplitude of birefringence fluctuations that couple to electromagnetism with a coupling strength $\beta$. | 14 | 3 | 1403.5585 |
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1403 | 1403.0086_arXiv.txt | The Chinese Small Telescope ARray (CSTAR) is a group of four identical, fully automated, static $14.5\,\rm{cm}$ telescopes. CSTAR is located at Dome A, Antarctica and covers $20\,\rm deg^2$ of sky around the South Celestial Pole. The installation is designed to provide high-cadence photometry for the purpose of monitoring the quality of the astronomical observing conditions at Dome A and detecting transiting exoplanets. CSTAR has been operational since 2008, and has taken a rich and high-precision photometric data set of 10,690 stars. In the first observing season, we obtained 291,911 qualified science frames with 20-second integrations in the $i$-band. Photometric precision reaches $\sim 4\,\rm{mmag}$ at 20-second cadence at $i=7.5$, and is $\sim 20\,\rm{mmag}$ at $i=12$. Using robust detection methods, ten promising exoplanet candidates were found. Four of these were found to be giants using spectroscopic follow-up. All of these transit candidates are presented here along with the discussion of their detailed properties as well as the follow-up observations. | The detection and study of exoplanets is one of the most exciting and fastest growing fields in astrophysics. At the present time, several different detection methods have yielded success. Two of most productive methods among them have been the radial velocity method and the transit method. Even though among the confirmed exoplanets, the radial velocity method has been more productive, the transit method also has its own advantages. The spectroscopic radial velocity method measures the doppler velocity signatures of individual stars at multiple epochs, which is a very time consuming procedure. The photometric transit method can yield the light curves of thousands of stars simultaneously. More importantly, the photometric transit method provides information on planetary radius and the inclination of the planetary orbit relative to the line of sight, not possible from radial velocity detections. In addition, a wide array of studies are possible for transiting exoplanets, which cannot be done with non-transiting systems, e.g. the study of planetary atmospheres \citep{Sing2009}, temperature, surface brightness \citep{Snellen2007, Snellen2010}, and the misalignment between the planetary orbit and the stellar spin \citep{Win2005}. Ideally, to search for transit exoplanet requires high-quality, wide-field, long-baseline continuous time-series photometry. This kind of monitoring can be achieved effectively by the ambitious space-based programs such as \textit{CoRoT} \citep{Baglin2006} and \textit{Kepler} \citep{Borucki2010} or complicated longitude-distributed network programs such as HATNet \citep{Bakos2004} and HATSouth \citep{Bakos2013}. However, the circumpolar locations offer a potentially comparable alternative. The circumpolar locations provide favorable conditions for a wide and diverse range of astronomical observations, including photometric transiting detections. Thanks to the extremely cold, calm atmosphere and thin turbulent surface boundary layer, as well as the absence of light and air pollution, we can obtain high quality photometric images in circumpolar locations \citep{Burton2010,steinbring2010,steinbring2012,steinbring2013}. Furthermore, the long polar nights offer an opportunity to obtain continuous photometric monitoring. As shown by a series of previous thorough and meticulous studies (cf. Pont \& Bouchy 2005; Crouzet et al. 2010; Daban et al. 2010; Law et al. 2013), it greatly increases the detectability of transiting exoplanets, particularly those with periods in excess of a few days. Additionally, decreased high-altitude turbulence will result in reduced scintillation noise that will lead to superior photometric precision \citep{Kenyon2006}. The significant photometric advantages of the polar regions have been proven and utilized by the observing facilities at different polar sites such as two AWCam \citep{Law2013} at Canadian High Arctic, SPOT \citep{Taylor1988} at the South Pole, small-IRAIT \citep{Tosti2006}, ASTEP-South \citep{Crouzet2010} and ASTEP-400 \citep{Daban2010} at Dome C. Dome A, located in the deep interior of Antarctica, with the surface elevation $4,093\,\rm{m}$, is the highest astronomical site on the continent and is also one of the coldest places on Earth. In a study that considered the weather, the boundary layer, airglow, aurorae, precipitable water vapor, surface temperature, thermal sky emission, and the free atmosphere, \citet{Saunders2009} concluded that Dome A might be the best astronomical site on Earth. In order to take the advantage of these remarkable observing conditions at the Dome A, the Chinese Small Telescope ARray (CSTAR) was established at Dome A in 2008 January. CSTAR undertook both site testing and science research tasks. In 2008, 291,911 qualified \textit{i}-band photometric images were acquired. Based on these data, the first version of photometric catalog has been released by \citet{Zhou2010a}, and updated three times \citep{Wang2012, Wang2013, Meng2013} to correct for various systematic errors. The resulting CSTAR photometric precision typically reaches $\sim 4\,\rm{mmag}$ at 20-second cadence at $i=7.5$, and is $\sim 20\,\rm{mmag}$ at $i=12$ (see Figure~\ref{fig1}), which is sufficient for the detection of giant transiting exoplanets around F, G, K, dwarf stars. In this paper, we present ten exoplanet candidates to come from 10,690 high precision light curves selected from the CSTAR data of 2008 \citep{Wang2013}. From all these candidates four were found to be giants using spectroscopic follow-up. Since this is the first effort to find exoplanets from these data, we describe the CSTAR instrument, observations, previous data reductions and the methods used for the transit searching in detail, as well as the procedures used to eliminate the false positives. The layout of the paper is as follows. A brief description of the CSTAR instrument, observations and previous data reduction, as well as the photometric precision of the light curves, is presented in Section 2. In Section 3, we detail the techniques we used for transit detection and the robust procedures of data validation. The spectroscopic and radial velocity follow-up are briefly described in Section 4. We report the exoplanet candidates along with the detailed properties for each system in Section 5. Lastly, the work is summarized and prospects for future work are discussed in Section 6. | In 2008, more than 100 days of observations for a $20\,\rm{deg}^2$ field centered at the South Celestial Pole with the Antarctic CSTAR telescope provided high-precision, long-baseline light curves of 10,690 stars with a cadence of 20 seconds. From this data set we found ten bright exoplanet candidates with short period. Subsequent spectral follow-up showed that four of these were giants, leaving six candidates. Med-resolution radial velocity showed none of the six candidates have radial velocity variation great than $2\,\rm{km\,s^{-1}}$. These detections have enriched the relatively limited optical astronomy fruit in Antarctica and indirectly reflects the favorable quality of Dome A for continuous photometric observations. However, the real strength of CSTAR will be realized when the 2008 data are combined with the multi-color observations of following years. We expect to find many more candidates, especially those with longer periods and small radii, as a result of longer baseline along with higher signal to noise ratio. The photometric data, including all of the CSTAR catalog and the light curves, are a valuable data set for the study of variable stars as well as hunting for transit exoplanets. | 14 | 3 | 1403.0086 |
1403 | 1403.7173_arXiv.txt | In this paper we constrain the cosmological parameters, in particular the tilt of tensor power spectrum, by adopting Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 (P13) and Wilkinson Microwaves Anisotropy Probe 9-year Polarization (WP) data. We find that a blue tilted tensor power spectrum is preferred at more than $3\sigma$ confidence level if the data from B2 are assumed to be totally interpreted as the relic gravitational waves, but a scale invariant tensor power spectrum is consistent with the data once the polarized dust is taken into account. The recent Planck 353 GHz HFI dust polarization data imply that the B2 data are perfectly consistent with there being no gravitational wave signal. | 14 | 3 | 1403.7173 |
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1403 | 1403.7203_arXiv.txt | {We studied the chronology of galactic bulge and disc formation by analysing the relative contributions of these components to the $B$--band rest--frame luminosity density at different epochs. We present the first estimate of the evolution of the fraction of rest--frame $B$--band light in galactic bulges and discs since redshift $z\sim 0.8$. We performed a bulge--to--disc decomposition of HST/ACS images of 3266 galaxies in the zCOSMOS--bright survey with spectroscopic redshifts in the range $0.7 \leq z \leq 0.9$. We find that the fraction of $B$--band light in bulges and discs is $(26 \pm 4)\%$ and $(74 \pm 4)\%$, respectively. When compared with rest--frame $B$--band measurements of galaxies in the local Universe in the same mass range ($10^{9} M_{\odot}\lessapprox M \lessapprox 10^{11.5} M_{\odot}$), we find that the $B$--band light in discs decreases by $\sim30\%$ from z$\sim 0.7-0.9$ to z$\sim0$, while the light from the bulge increases by $\sim30\%$ over the same period of time. We interpret this evolution as the consequence of star formation and mass assembly processes, as well as morphological transformation, which gradually shift stars formed at half the age of the Universe from star--forming late--type/irregular galaxies to earlier types and ultimately into spheroids. } | Several physical processes are at work to assemble mass and shape galaxies during cosmic time, but their relative contributions and effective time--scales are as yet unclear. In the hierarchical dark--matter halo assembly picture, galaxies obtain their baryonic mass through different processes that include major and minor mergers or continuous gas accretion, and lose mass when subject to strong feedback from supernovae and/or AGN \citep[e.g][]{Cattaneo:06,Croton:06,Somerville:08,Benson:10}. While mergers are directly observed to act on galaxies, their numbers and associated star formation seem to remain insufficient to sustain the high star formation rate observed at the peak in the star formation history. Cold gas accretion fueling star formation has therefore been proposed \citep{Keres:05,Sancisi:08,Dekel:09,Carilli:10}, but the extent of this process is yet to be confirmed from direct observational evidence \citep{Bouche:13}. The strong decrease in the star formation rate (SFR) density since $z\sim1$ \citep[e.g.,][]{Lilly:96,Madau:96,Tresse:07,Bouwens:11,Cucciati:12} calls for an active process to quench the star formation. While its origin is still unknown, it might be produced either by mass--dependant internal processes or be related to the environments in which galaxies reside. Each physical process that builds galaxies during cosmic time is expected to leave specific observational signatures, even if simulations cannot reliably predict them. % Given this context, it is necessary to seek quantitative galaxy properties that describe how stellar mass has been assembled in the different components of galaxies. A key signature of galaxy evolution is the strong change in the morphological properties, with galaxies evolving from small irregular shapes at early epochs to the well--structured sequence of Hubble types at the present epoch. Because the main components of galaxies today are bulges and discs, it is crucial to trace the onset of these components since early times. The evolution of the luminosity density in galactic bulge and disc components is a powerful method to follow galaxy build--up, which may indicate when and how stars have been transferred into these components. From a subset of the Sloan Digital Sky Survey data \citet{Tasca:11} have shown that, averaging over the galaxy population as a whole, $(54 \pm 2)\%$ of the local cosmic luminosity density comes from discs and $(32 \pm 2)\%$ from ``pure bulge'' systems. Of the remaining $(14 \pm 2)\%$ half comes from the light in the spheroidal component of spiral galaxies and the other half from light in bars of systems with detectable discs. The COSMOS survey \citep{Scoville:07a} provides a unique opportunity to make these measurements at about half the age of the Universe by combining high--resolution HST/ACS imaging data \citep{Koekemoer:07} and accurate spectroscopic redshifts from the zCOSMOS survey \citep{Lilly:07}. In this letter we present for the first time an estimate of the luminosity functions (LF) of galaxy bulges and discs , and the relative contribution of the associated luminosity densities (LD) of these galactic components to the global $B$--band rest--frame LD at redshift $z\sim 0.8$. We discuss the evolution of the fraction of $B$--band light in bulges and discs since $z\sim 0.8$ as well as the implication for the general picture of galaxy formation and evolution. Throughout this letter we adopt a concordance cosmology with $\Omega_M = 0.27$, $\Omega_{\Lambda} = 0.73$ and $H_0= 70$ Km s$^{-1}$ Mpc$^{-1}$. All magnitudes are quoted in the AB system. | \begin{figure}% \centering \includegraphics[width=8cm]{aa23699fg2.ps} \caption{Evolution of the $B$--band rest--frame light since $z\sim0.8$. The local results at a redshiftl z~0 are taken from \citet{Tasca:11}. Filled red circles and blue triangles represent the whole $B$--band rest--frame light in the bulge and disc components. The empty stars and squares stand for the pure bulge and the spheroid populations, while the empty triangles are for bulgeless galaxies and the disc components of spirals. The lines help to guide the eyes.} \label{fig:ev_LD} \end{figure} Using the LF presented in Section \ref{sec:LF}, we explored for the first time at a median redshift $\sim 0.8$ the fraction of $B$--band light contained in the bulge and disc components of galaxies brigher than $I_{AB}=22.5$. We computed the luminosity density (LD) as a simple sum of the $1/V_{max}$ up to $M_{B}=-20.2$, since we are complete for this population. We find that for galaxies at redshifts $0.7 \leq z \leq 0.9$, $(26\pm4)\%$ of the $B$--band luminosity is in bulges, and $(74\pm4)\%$ in discs. The bulge and disc contributions of galaxies fainter than $M_{B}=-20.2$ were not investigated. We note that this represents $\sim 5\%$ of their global LD when computed as the sum of $1/V_{max}$. Since most galaxies fainter than the bias are disc dominated and we observe that the B/T distribution evolves with magnitude towards lower values at lower luminosities, we can therefore speculate that the computed disc LD is a lower limit. Various studies have computed the LD in bulges and discs in the local Universe using different samples, selections, and methods \citep[e.g.,][]{Schechter:87,Benson:07,Driver:07,Gadotti:09,Tasca:11}. There is a general agreement that about $50\%$ of the $B$--band light in the local Universe is contributed by stars in discs. In Figure\,\ref{fig:ev_LD} we compare our measurements at $z\sim0.8$ with the measurements of \citet{Tasca:11} at $z\sim0.1$. The fraction of $B$--band light in discs decreases from $(74\pm4)\%$ to $(54\pm2)\%$, a $\sim30\%$ decrease over 6 Gyr. In contrast, the fraction of $B$~--band light in bulges follows a reverse evolution, increasing from $(26\pm4)\%$ to $(41 \pm 2)\%$ during the same period of time. The evolution of the fraction of light in different morphological components is a key signature of physical processes that shape galaxies during cosmic time, with the advantage of being a direct observable that does not require any assumption or simulation. Our results indicate that the $B$--band emissivity has massively shifted from discs to bulges since $z\sim0.8$. Furthermore, by splitting the contribution of the bulge light into the luminosity coming from pure bulges, meaning elliptical galaxies, and the luminosity produced by late--type bulges, identified with the central component of spiral galaxies, we are able to follow their different evolution. While elliptical galaxies and the bulges of spirals have been commonly studied as a single population, it is now evident that the stellar populations in these two components follow a distinct evolution, which indicates that different physical processes must be at work. In Figure\,\ref{fig:ev_LD} it is clearly visible that while the fraction of light in late--type bulges since $z\sim0.8$ remains almost constant, the luminosity density in pure bulges increases during the same period from $(18\pm4)\%$ to $(32\pm2)\%$, determining the global behaviour of the $B$--band light in the bulge component. We point out that our estimate of the fraction of light in all bulges at $\sim0.8$ is an upper limit because it includes the contribution of bars, which is out of the scope of this paper to study, while the value in the local Universe was computed without the bar contribution, which is separately estimated to be $(6\pm2)\%$ \citep{Tasca:11}. The estimate of the fraction of light in the discs of spirals and in the pure discs, meaning bulgeless galaxies, shows that the strong evolution since $z\sim0.8$ of the luminosity density in the global disc component is mainly caused by the considerable evolution of bulgeless galaxies. In late--type galaxies the $B$--band emissivity is tightly related to the SFR \citep[e.g.,][]{Tresse:02}, and therefore traces the on--going instantaneous star formation. The strong diminution of the fraction of $B$--band light in discs is then connected to the sharp decrease of the star formation rate observed since $z\sim1$. In contrast, for bulges the $B$--band emissivity is mainly dominated by long--lived stars from older stellar populations instead of on--going starburst, and represents an integrated SFR along the time life of the bulge. Thus the galaxy population is decreasing its SFR density within all discs, either via a fading of the stellar population and/or a decrease in number density. While at $z\sim1$ the Hubble sequence is already in place, \citet{Tasca:09} reported a sizeable growth of the fraction of irregular galaxies towards higher redshifts, % balanced by the continuous decrease of the elliptical fraction from $\sim30\%$ at low redshift to $\sim20\%$ at $z\sim1$. The fraction of spiral galaxies instead remains rather constant at $\sim50\%$. When this morphological evolution is related to the behaviour of the evolution of the $B$--band emissivity shown in Figure\,\ref{fig:ev_LD} we conclude that while for the disc component the fading of the stellar population is not the main factor responsible for the observed trend, an important morphological change is still on--going from $z\sim1$ to $z\sim0$, mainly driven by the transformation of irregular galaxies and their strong decrease in number density and the consequent increase of the bulge component $B$--band emissivity. We emphasise the importance of extending the analysis of bulge and disc components, or their progenitors, to earlier cosmic epochs to obtain better insight into physical processes that drive galaxy formation and evolution. Our results provide an observational reference to test theoretical model predictions. In particular, forming bulgless galaxies have until very recently been a major challenge for hydrodynamical simulations \citep[see][]{Scannapieco:09,Marinacci:14}; our results provide the reference observed number density for these models to test against. | 14 | 3 | 1403.7203 |
1403 | 1403.0938_arXiv.txt | Spinning black holes tend to expel magnetic fields. In this way they are similar to superconductors. It has been a persistent concern that this black hole ``Meissner effect'' could quench jet power at high spins. This would make it impossible for the rapidly rotating black holes in Cyg X-1 and GRS 1915+105 to drive Blandford-Znajek jets. We give a simple geometrical argument why fields which become entirely radial near the horizon are not expelled by the Meissner effect and may continue to power jets up to the extremal limit. A simple and natural example is a split-monopole field. We stress that ordinary Blandford-Znajek jets are impossible if the Meissner effect operates and expels the field. Finally, we note that in our general relativistic magnetohydrodynamic simulations of black hole jets, there is no evidence that jets are quenched by the Meissner effect. The simulated jets develop a large split monopole component spontaneously which supports our proposal for how the Meissner effect is evaded and jets from rapidly rotating black holes are powered in nature. | \label{sec:intro} Spinning black holes tend to expel magnetic fields. Astrophysical jets are believed to be powered by magnetized, spinning black holes. Magnetic fields need to thread the horizon to extract the black hole's rotational energy (a point we will return to later). So if the black hole Meissner effect prevents rapidly rotating black holes from becoming magnetized, it could quench jet power. Until recently, one might have argued that astrophysical black holes do not achieve the high spins where the Meissner effect is important. However, there is now reliable evidence for rapidly rotating black holes. In particular, the spin parameters of the black holes in Cyg X-1 and GRS 1915+105 have been measured to be $a/M>0.95$ \cite{2006ApJ...652..518M,2011ApJ...742...85G,2013SSRv..tmp...73M}. Jets from these black holes could be quenched by the Meissner effect. It is important to understand this possibility. The discovery of the black hole Meissner effect predates astrophysical jet modeling. Wald \cite{1974PhRvD..10.1680W} found a solution for a Kerr black hole immersed in a uniform magnetic field aligned with the black hole spin axis. The magnetic field is treated as a test field. It is a vacuum field; there are no currents. The simplicity of Wald's solution makes it very useful for understanding the interaction of black holes with magnetic fields. King, Lasota, and Kundt \cite{1975PhRvD..12.3037K} noted that the flux of Wald's solution through the black hole horizon drops to zero in the extremal limit (see Figure \ref{fig:waldfields}), in a way that is similar to the Meissner effect of superconductors \cite{1980PhRvD..22.2933B,1998PhRvD..58h4009C}. \begin{figure*}[!ht] \begin{center} \includegraphics[width=0.45\textwidth]{wald05_final.pdf} \includegraphics[width=0.45\textwidth]{wald1_final.pdf} \caption{The Wald magnetic field \cite{1974PhRvD..10.1680W} for black hole spin parameters $a/M=0.5$ (left panel) and $a/M=1$ (right panel). At $a/M=1$, the field is completely expelled from the horizon.} \label{fig:waldfields} \end{center} \end{figure*} If the field was only expelled at the extremal limit, one could dismiss the effect as a pathology of $a/M=1$. It is impossible to achieve extremal spins in nature, so the implications of the Meissner effect would be limited. However, the flux is expelled in a continuous way as the black hole is spun up. It is not a discontinuous effect that only appears exactly at $a/M=1$. The flux threading the northern hemisphere of the horizon is \beq \Phi = 2 \pi \int_0^{\pi/2} F_{\theta\phi} d\theta. \eeq The integral is restricted to one hemisphere of the horizon because the flux over the entire horizon is trivially zero (because the magnetic monopole charge of the black hole is zero). Plugging in the Wald solution gives \cite{1974PhRvD..10.1680W,1975PhRvD..12.3037K} \beq \Phi = \pi r_+^2 B (1-a^4/r_+^4), \eeq where $r_+=M+\sqrt{M^2-a^2}$ is the radius of the horizon and $B$ is the field strength at infinity. Figure \ref{fig:waldfluxes} shows how $\Phi$ drops as the black hole is spun up. The drop is partly coming from the fact that the black hole is shrinking as it spins up. This contribution is not particularly interesting, as even in flat space the flux of a uniform field through a sphere depends on its surface area. However, the area-normalized flux, $\Phi/(4 \pi M r_+)$, also drops with spin (the area of the northern hemisphere of the horizon is $4 \pi M r_+$). \begin{figure*}[!ht] \begin{center} \includegraphics[width=0.45\textwidth]{waldflux1.pdf} \includegraphics[width=0.45\textwidth]{waldflux2.pdf} \caption{The flux threading the northern hemisphere of the black hole horizon drops continuously as $a/M\rightarrow 1$. We have set $B=1$.} \label{fig:waldfluxes} \end{center} \end{figure*} One might worry that the Meissner effect relies on a peculiar feature of the Wald solution. This solution is a test field, but the effect persists for non-test fields \cite{bicak1989,1991JMP....32..714K,1998PhRvD..58h4009C,2000PhyS...61..253K}. The Wald solution is a vacuum field and the vector potential is a Killing vector, so it is a very special configuration. However, Bi{\v c}{\'a}k and Dvo{\v r}{\'a}k \cite{1976GReGr...7..959B} have found solutions which vastly generalize the Wald solution and their solutions also display the Meissner effect \cite{1985MNRAS.212..899B}. They found a general multipole expansion which can be adapted to (almost) any axisymmetric, stationary magnetic field in the Kerr metric, including non-vacuum fields sourced by current distributions. Their result is often summarized as proving \cite{2007IAUS..238..139B} \begin{proposition*} ``All stationary, axisymmetric magnetic fields are expelled from the Kerr horizon as $a/M\rightarrow 1$.'' \end{proposition*} The standard Blandford-Znajek (BZ) model \cite{bz77} of spin-powered black hole jets is stationary and axisymmetric, so this result appears to rule out BZ jets at high spins. Our first observation is that stationary and axisymmetric fields which become entirely radial near the horizon are not expelled by the Meissner effect and may continue to power jets up to the extremal limit. This is an important possibility because early work on the BZ model and recent simulations both suggest the fields of black hole jets have a large split monopole component \cite{bz77,1979AIPC...56..399L,1982MNRAS.198..345M,phinney1983,2012MNRAS.423.3083M,2012JPhCS.372a2040T,2013MNRAS.436.3741P}. This provides a natural mechanism to power jets from Cyg X-1 and GRS 1915+105. It appears to be consistent with the perturbative solutions constructed by \cite{2011MNRAS.412.2417T}, which describe slowing rotating fields threading extremal Reissner-Nordstr{\" o}m horizons. One can imagine embedding the Bi{\v c}{\'a}k and Dvo{\v r}{\'a}k solutions in a conductive magnetosphere. Conductivity does not enter into Maxwell's equations, so for a fixed current distribution, turning on conductivity does not affect whether the field lines thread the horizon. However, a conductive magnetosphere may redistribute the current. The final current distribution might thread the horizon with flux even if the initial current distribution did not (or vice versa). Simulations suggest conductive magnetospheres choose current distributions which evade the Meissner effect \cite{2007MNRAS.377L..49K}. The result of \cite{1985MNRAS.212..899B} suggests such current distributions must be nonstationary or nonaxisymmetric. Our observation is that the field may remain stationary and axisymmetric (as in the original BZ model) provided it becomes radial at the horizon. One might argue that a sufficiently powerful accretion disk can drag any field onto an extremal horizon despite the Meissner effect. We give a simple geometrical reason why this is impossible unless the field becomes radial at the horizon. It has been argued that jets can be powered directly by the ergosphere, so that even if the Meissner effect operated it would not be relevant for BZ jets \cite{1990ApJ...354..583P,2007MNRAS.377L..49K}. We argue that this suggestion is incorrect unless the BZ model is significantly modified. Finally we note that in our simulations of black hole jets there is no evidence for the Meissner effect. We have observed previously that the fields in our simulations have a large split monopole component \cite{2013MNRAS.436.3741P}. So this is consistent with our observation that fields which become radial at the horizon evade the Meissner effect. Furthermore, simulations generate split monopole fields spontaneously, which suggests this mechanism is naturally occurring. Our paper is organized as follows. In Sec. \ref{sec:jets} we review the physics underlying the black hole Meissner effect and debunk two proposals for evading the Meissner effect. In Sec \ref{sec:evade} we discuss three ways the black hole Meissner effect can be evaded. Of these, split-monopole fields provide a particularly natural solution. In Sec. \ref{sec:conc} we summarize and conclude. | \label{sec:conc} We have revisited the black hole Meissner effect, whereby a spinning black hole tends to expel magnetic fields. We have argued that if the Meissner effect operates, then electromagnetic spin-powered jets will be quenched. This argument has a simple explanation in the membrane paradigm. In this picture, the black hole's rotational energy is stored on the horizon. Fields extract the black hole's energy by torquing the horizon. If the field does not thread the horizon, then there is no torque and it is impossible to extract the black hole's rotational energy. A subtlety is that the membrane is described by a teleological Green's function (which reflects the global nature of the event horizon), so the ``response'' precedes the torque. This means the field need not thread the horizon until after the energy is extracted. The membrane paradigm makes it clear that if the Meissner effect operated, then it would prevent the field from torquing the black hole and there could be no jets. We have explained how to understand this claim without using the membrane paradigm. The key fact is that all negative energy geodesics eventually cross the horizon. Our claim can be understood as a generalization of this fact from particles to magnetic fields. A magnetic field configuration which is not on a horizon crossing trajectory cannot be a negative energy configuration. If all stationary axisymmetric fields were prevented from crossing the horizon by the Meissner effect, then there could be neither energy extraction nor BZ jets. Given the importance of the Meissner effect, it is crucial to understand whether astrophysical jets can avoid it and continue to operate at high spins. One might argue that a sufficiently powerful accretion disk or conductive magnetosphere would simply overwhelm the Meissner effect and drag any field configuration onto the horizon. We have shown that this is impossible unless the field becomes radial near the horizon. A simple example of such a field is a split-monopole. The jets in our simulations spontaneously develop a large split-monopole component. So this provides a natural mechanism to power jets from rapidly rotating black holes such as Cyg X-1 and GRS 1915+105. This addresses a long-standing concern that the black hole Meissner effect quenches jet power at high spins. It would be good to find a simple explanation for why simulated black hole fields tend to have a large split-monopole component. Also, as we have noted, simulations have trouble resolving the black hole throat for $a/M\gtrsim 0.95$. The Meissner effect is a manifestation of the throat, at least from the perspective of an observer who remains outside the black hole. (It is not clear how to understand the Meissner effect from the perspective of an infalling observer.) So it would be good to find a way to simulate jets in a way that resolves the throat. Perhaps the near-horizon extremal Kerr geometry could be useful \cite{1999PhRvD..60j4030B}. | 14 | 3 | 1403.0938 |
1403 | 1403.6033_arXiv.txt | We present our astrometric observations of the small near-Earth object 2011~MD ($H \sim 28.0$), obtained after its very close fly-by to Earth in June 2011. Our set of observations extends the observational arc to $73$ days, and together with the published astrometry obtained around the Earth fly-by allows a direct detection of the effect of radiation pressure on the object, with a confidence of $5\sigma$. The detection can be used to put constraints on the density of the object, pointing to either an unexpectedly low value of $\rho = (640\pm330) \unrho$ ($68\%$ confidence interval) if we assume a typical probability distribution for the unknown albedo, or to an unusually high reflectivity of its surface. This result may have important implications both in terms of impact hazard from small objects and in light of a possible retrieval of this target. | The small near-Earth asteroid 2011~MD was discovered on 2011 June 22 by the Lincoln Near-Earth Asteroid Research (LINEAR) survey in New Mexico, USA \citep{2011MPEC....M...23B}. Within 24 hours of discovery it was obvious that the object was going to have an extremely close approach to Earth in a few days, at about $18\,700 \un{km}$ from the Earth's center ($12\,300 \un{km}$ from its surface, flying over the Southern hemisphere). Around its closest approach the object's magnitude peaked at about $V=11$, and it remained brighter than $V=19$ for four days before and after the peak. As a result, more than $1500$ individual astrometric positions were obtained and reported to the Minor Planet Center (MPC) in a period of less than $8$ days. However, the object rapidly became faint while receding from Earth, and no further observations were reported after 2011 July 3, only $11$ days after discovery.\\ Around that time we realized that the object was still fading at a reasonably slow rate of less than $0.5$ magnitudes per week, and we would have the capability to observe it for at least two more months using the telescopes to which we have access on Mauna Kea. We were able to obtain astrometric positions of the object on $5$ nights in August and early September 2011, therefore extending the observed arc on the object from $11$ to $73$ days, or about a factor of $6.5$. In this work we present these observations, together with an accurate analysis of the object's dynamics made possible by this extended observational arc. We also discuss the implications of this result on the object's physical properties. \subsection{Previous work} The case of 2011~MD shares some resemblance with other very small NEOs observed in the past. Of about $200$ known small objects in this size range (diameter around or below $10 \un{m}$), only a handful remained observable from the ground for more than a few days, because of their intrinsic faintness. Only some peculiar characteristic of the close approach can allow for an extended observability window, enough to characterize their dynamical behavior in good detail. The first example of one such object was probably 2006~RH120, an even smaller NEO that was temporarily captured in Earth orbit in 2006-2007 \citep{2008MPEC....D...12B,2009A&A...495..967K}. In that case, the long orbital phase allowed for 9 months of almost continuous observations from the ground. A second case was 2009~BD, that happened to have two very close approaches with Earth (and a couple of more distant but observable ones) in less than 3 years \citep{2009MPEC....B...14B,2012NewA...17..446M}. We recently presented our observational data and analysis of a third such object, 2012~LA \citep{2012MPEC....L...06H,2013Icar..226..251M} All these objects, together with 2011~MD, share the property of having very Earth-like orbits, with very modest eccentricities and inclinations. As a result, they usually have very low relative orbital velocity with respect to our planet ($\Delta v < 4 \un{km}/\unp{s}$), making their close encounters last unusually long. This same property also implies that these same objects are also among the easiest to fly-by or rendezvous with a spacecraft launched from Earth; together with the small size, this makes them plausible candidates for a Asteroid Robotic Retrieval Mission (ARRM) such as the one currently under study by NASA. However, the 2011~MD case is peculiar because it had only a single and short close encounter with Earth, and it was therefore observable for a much shorter timespan. Furthermore, being discovered only around the time of close approach, only the second half of the observability window was available.% | From the observational data presented above we obtained a statistically significant detection of the action of radiation pressure on the small object 2011~MD, based on a relatively short observational arc (only $73$ days). To our knowledge this is the first detection of a non-gravitational effect on a natural object observed during a single close encounter with our planet, and shows the value of high-precision astrometry and of a proper statistical treatment of astrometric data. It is worth noting that the data used in this work are only optical, without any radar detection. The most relevant scientific result of this work is the low density value $\rho = (640\pm330) \unrho$ obtained for 2011~MD under assumptions of a typical albedo probability distribution. While well above typical bunk densities of man-made objects, it still unexpectedly low for a natural object, and would imply either an extremely high bulk porosity, or an estimate biased by an unusually high albedo, and therefore a significantly smaller diameter (about $5\un{m}$ if we assume $p_V\sim0.5$). Both these interpretations can have significant implications in terms of impact hazard from small objects, but also in light of a possible ARRM to this target or to others with comparable properties. | 14 | 3 | 1403.6033 |
1403 | 1403.7451.txt | {}{}{}{}{} % 5 {} token are mandatory \abstract % context heading (optional) { NGC 4815 is a populous $\sim$ 500 Myr open cluster at \rgc $\sim$ 7 kpc observed in the first six months of the Gaia-ESO Survey. Located in the inner Galactic disk, NGC 4815 is an important potential tracer of the abundance gradient, where relatively few intermediate age open clusters are found.} % aims heading (mandatory) {The Gaia-ESO Survey data can provide an improved characterization of the cluster properties, such as age, distance, reddening, and abundance profile. } % methods heading (mandatory) {We use the survey derived radial velocities, stellar atmospheric parameters, metallicity, and elemental abundances for stars targeted as potential members of this cluster to carry out an analysis of cluster properties. The radial velocity distribution of stars in the cluster field is used to define the cluster systemic velocity and derive likely cluster membership for stars observed by the Gaia-ESO Survey. We investigate the distributions of Fe and Fe-peak elements, alpha-elements, and the light elements Na and Al and characterize the cluster's internal chemical homogeneity comparing it to the properties of radial velocity non-member stars. Utilizing these cluster properties, the cluster color-magnitude diagram is analyzed and theoretical isochrones are fit to derive cluster reddening, distance, and age.} % results heading (mandatory) {NGC 4815 is found to have a mean metallicity of [Fe/H]$=+0.03 \pm 0.05$ dex (s.d.). Elemental abundances of cluster members show typically very small internal variation, with internal dispersions of $\sim$ 0.05 dex. The alpha-elements [Ca/Fe] and [Si/Fe] show solar ratios, but [Mg/Fe] is moderately enhanced, while [Ti/Fe] appears slightly deficient. As with many open clusters, the light elements [Na/Fe] and [Al/Fe] are enhanced, [Na/Fe] significantly so, although the role of internal mixing and the assumption of LTE in the analysis remain to be investigated. From isochrone fits to color-magnitude diagrams, we find a cluster age of 0.5 to 0.63 Gyr, a reddening of $E(B-V) = $ 0.59 to 0.65, and a distance modulus $(m-M)_0 = 11.95$ to 12.20, depending on the choice of theoretical models, leading to a Galactocentric distance of 6.9 kpc.} % conclusions heading (optional), leave it empty if necessary {} | The Gaia-ESO Survey \citep{GES1,GES2} is an ambitious high-resolution public spectroscopic survey of stars in the Galaxy carried out with the FLAMES multi-object spectrograph on the ESO Very Large Telescope. Over its 5-year lifetime, the survey will target up to 90 to 100 open clusters of a wide range of properties, ages, and locations in the Galaxy (Randich et al. 2014, in prep.). Survey data are processed and analyzed in a homogeneous way to ensure a final data set of stellar kinematic, atmospheric, and chemical abundance properties that are derived in a uniform and consistent manner (Lewis et al. 2014, in prep., Sacco et al. 2014, submitted., Smiljanic et al. 2014, in prep.). Among the many long-term goals of the survey are an improved understanding of the formation and chemical evolution of the Galactic disk as traced by the open cluster population. Most stars are born in aggregates of stars, most of which are unbound and dissolve into the field population \citep{lada03}. Those clusters that remain serve as important indicators that permit the study of a wide variety of issues in cluster formation and Galactic evolution, including investigations of the mass function and survivability of star clusters \citep{larsen09}, the process of cluster dispersal especially as traced by the chemical tagging of former cluster members \citep{FB2002,BKF2010}, and the development and evolution of the abundance gradients in the Galactic disk \citep{magrini10, jpf}. Key to addressing these last issues on chemical evolution is the question of the chemical homogeneity of the surviving clusters, and by implication those that have dispersed into the field population. Careful work by \citet{deSilva06,deSilva07,deSilva11}, for example, has demonstrated the chemical homogeneity in clusters such as the Hyades and Cr261, as well as the potential to trace dispersed cluster members into the surrounding field. It remains an open question whether all elements display such uniformity in open clusters, however. Light elements such as Na may show the effects of internal nucleosynthesis and mixing to the surface in evolved stars \citep{sm12}, although the situation is complicated by the potential influence of non-LTE effects. Open clusters do not appear to share the common (anti-)correlations between the light and alpha-elements seen in the globular cluster population \citep{carretta10}. Work by \citet{deSilva09} and \citet{brag12}, for example, finds no evidence of an O-Na anti-correlation or the presence of the extreme O-depletions or Na-enhancements see in in the globulars. The unusual cluster NGC 6791 has prompted much attention for some first signs of globular cluster-like Na-O anti-correlations \citep{Geisler12}, but further studies are not finding evidence for intrinsic abundance dispersions in the cluster \citep{n6791_14}. Larger and uniform samples of abundances in open clusters offer the potential to distinguish these behaviours and define chemical characteristics that separate cluster populations. If open clusters are to trace these disk properties and their evolution, we must first be able to securely define the cluster members and distinguish them from the surrounding field population. And we must place the cluster properties such as age, abundance, and location in the disk on uniform and consistently determined scales so that details of distributions can be probed with confidence that we are not simply exploring systematic differences between approaches or methodology. With these basic properties well characterized, clusters become indicators of both their initial environments (through their chemical signatures) and their current environments, allowing the possibility of using them to explore their migration through the Galactic disk. The Gaia-ESO survey aims to address all of these scientific goals based on substantial samples of clusters and cluster members and, most importantly, cluster properties and abundances on a uniform and internally consistent scale. The observations of the first three intermediate-aged clusters allow us to explore the adequacy of the survey data and establish procedures that will yield a uniform set of cluster parameters. Progress on the larger Galactic context of the cluster data must await the samples to come, but the initial survey data allow the first steps to be taken. The first six months of GES survey observations included three intermediate-age clusters that allow us to begin to explore these issues. The clusters Trumpler 20, NGC 4815, and NGC 6705 (M11) differ in many ways, but all are located inside the solar circle. This location makes them important probes of the abundance gradient in the inner regions of the Galaxy, but also means that their study will be complicated by high and possibly variable reddening, a potentially large and complex field population, and the contamination of many non-members superimposed on the cluster field. As a result, the basic properties of these clusters are often poorly constrained. The Gaia-ESO survey data allow us to define these properties, particularly by comparison to the surrounding field, understanding the chemical profile of these clusters and improving the cluster parameters such as age, distance, and reddening, which are critical to their use in tracing abundance gradients in the disk. This paper presents the results of data for stars in the field of NGC 4815. Similar analysis of the other early Gaia-ESO Survey cluster observations are presented in companion papers (Tr 20 in \citealt{pdTr20}; NGC 6705 in Cantat-Gaudin et al. 2014, in prep.). Each of these clusters presents a particular characteristic (Tr 20 shows an unusual morphology of the red giant clump; NGC 6705 is unusually massive for an open cluster; NGC 4815 is embedded in a rich field population) that allows the focus on different aspects of the analysis and interpretation of the GES data in the context of available information from the literature. The three clusters are considered together in the broader context of chemical evolution in the Galaxy in \citet{magrini14}. NGC 4815 is an intermediate age cluster located inside the solar Galactocentric radius, at RA=12:57:59, Dec=$-$64:57:36 and Galactic coordinates $\ell = 303.6$, $b = -2.1$. It shows distinctly against a crowded field at this low latitude. Located approximately 2.5 kpc away, the line of sight to the cluster passes through both the Sagittarius and the Scutum-Centaurus spiral arms, with the cluster located beyond, but close to, the Sagittarius arm. The cluster has been the subject of several photometric studies, but has not been observed spectroscopically until now. The paper is organized as follows: In Sec. 2 we briefly describe our understanding of the properties of NGC 4815 based on past studies. Sec. 3 discusses the results from the Gaia-ESO Survey data, beginning with a description of the observed sample, followed by an analysis of the radial velocities and then the stellar abundances. Sec. 4 utilizes the results on cluster membership and metallicity to derive cluster properties based on fitting of theoretical isochrones. Finally, Sec. 5 summarizes our results. | We have used the results from Gaia-ESO Survey spectroscopic data and published photometric data to carry out a study of the intermediate age cluster NGC 4815. Observations of 218 stars in the field of the cluster provide radial velocities from which we estimate the cluster systemic velocity to be $-29.4$ \kms. The radial velocity distribution is, however, quite broad, suggesting significant contribution by field stars, which is also indicated by the Besan\c{c}on Galactic stellar populations model. Selecting stars within 4 \kms~ of this mean velocity as potential cluster members results in only $\sim$30\% of the observed Gaia-ESO Survey targets having velocities consistent with membership. Stellar abundances from the UVES observations for the five evolved stars that are likely members yield a mean cluster metallicity of [Fe/H] = +0.03 $\pm$ 0.02 dex (error in the mean). Elemental abundances also show a small dispersion about the mean values, indicating homogeneous chemical composition in the cluster. Among the $\alpha$-elements, [Ca/Fe] and [Si/Fe] appear solar, while [Mg/Fe] appears somewhat enhanced and [Ti/Fe] slightly depleted. Iron-peak elements [Ni/Fe] and [Cr/Fe] are slightly underabundant relative to solar. Consistent with findings for many other open clusters, the light elements Na and Al are enhanced over solar, but what role the effect of inadequacies in the assumed LTE analysis or internal stellar mixing might have in explaining these abundances remains to be investigated. Abundances for radial velocity non-members of NGC 4815, sampling the disk field population, show typically much larger dispersions, but have abundance distributions that generally overlap with the cluster values at the same metallicity, particularly for the $\alpha$-elements. There are indications, once all elements are considered, that the detailed abundance pattern of the cluster is distinguished from those of the field stars. Obtaining abundances for additional elements will help clarify this picture. Future releases will include the determination of more elements; the neutron-capture elements will be especially interesting in this regard. It is expected that as the survey proceeds, the internal precision of the GES abundances may be improved through analysis of an increased number of calibrating benchmark stars and a fine-tuning of the homogenization process leading to recommended parameters. In addition, for many clusters sample sizes will be larger; as one of the less massive open clusters, the number of potential targets in NGC 4815 is limited. However, it is clear that the uniformity of the Gaia-ESO Survey analysis and the homogeneity of the resultant abundances offers the opportunity to explore the potential systematic chemical differences between the cluster and the field at a new level of detail, for many open clusters, in many lines of sight. These data combined with proper motions from Gaia will also enable a more thorough kinematic selection and dynamical investigation of the cluster and its surrounding field population. Finally, using the information on radial velocity membership, and with the cluster metallicity constrained by the Gaia-ESO Survey determinations, theoretical isochrones were fit to the published $BV$ and $VI$ photometry of NGC 4815 to derive more robust estimates of the cluster parameters. Utilizing three different sets of isochrones and fitting both the $VI$ and $BV$ color-magnitude diagrams provided an assessment of uncertainty in these parameters. We conclude that NGC 4815 has an age of between 0.5 to 0.63 Gyr, a reddening $E(B-V) = 0.59$ to 0.65, and distance modulus $(m-M)_0$ of 11.95 to 12.20, placing it at a distance of 2.45 to 2.75 kpc, or 6.9 kpc from the Galactic center. The isochrones provide a good fit to the shape of the main-sequence and the luminosities of the turnoff and the red clump stars, but are less successful in matching simultaneously the $BV$ and $VI$ colors. Possible reasons for this mismatch could rest in differences in the accuracy of the photometric zero points, or the difficulty of transforming the isochrones from the theoretical to the observational plane. | 14 | 3 | 1403.7451 |
1403 | 1403.4941_arXiv.txt | {The UX Ori type variables (named after the prototype of their class) are intermediate-mass pre-main sequence objects. One of the most likely causes of their variability is the obscuration of the central star by orbiting dust clouds.} {We investigate the structure of the circumstellar environment of the UX~Ori star V1026~Sco (HD~142666) and test whether the disk inclination is large enough to explain the UX~Ori variability. } {We observed the object in the low-resolution mode of the near-infrared interferometric VLTI/AMBER instrument and derived {\textit H}- and {\textit K}-band visibilities and closure phases. We modeled our AMBER observations, published Keck Interferometer observations, archival MIDI/VLTI visibilities, and the spectral energy distribution using geometric and temperature-gradient models. } {Employing a geometric inclined-ring disk model, we find a ring radius of $0.15 \pm 0.06$~AU in the {\textit H} band and $0.18 \pm 0.06$~AU in the {\textit K} band. The best-fit temperature-gradient model consists of a star and two concentric, ring-shaped disks. The inner disk has a temperature of $1257^{+133}_{-53}$~K at the inner rim and extends from $0.19 \pm 0.01$~AU to $0.23 \pm 0.02$~AU. The outer disk begins at $1.35^{+0.19}_{-0.20}$~AU and has an inner temperature of $334^{+35}_{-17}$~K. The derived inclination of $48.6^{+2.9}_{-3.6}${\degr} approximately agrees with the inclination derived with the geometric model ($49 \pm 5\degr$ in the {\textit K} band and $50 \pm 11\degr$ in the {\textit H} band). The position angle of the fitted geometric and temperature-gradient models are $163 \pm 9\degr$ ({\textit K}~band; $179 \pm 17\degr$ in the {\textit H}~band) and $169.3^{+4.2}_{-6.7}$\degr, respectively.} {The narrow width of the inner ring-shaped model disk and the disk gap might be an indication for a puffed-up inner rim shadowing outer parts of the disk. The intermediate inclination of $\sim$50{\degr} is consistent with models of UX~Ori objects where dust clouds in the inclined disk obscure the central star.} | The UX Ori (UXOr) phenomenon of Herbig Ae/Be stars (HAeBes) is attributed to obscuration by circumstellar dust in an inclined disk \citep{1994grithe,1997natgri,2001grikoz,2003dulvan} or unsteady accretion \citep{1999hershe}. The Herbig Ae star \object{V1026~Sco} (HD~142666) has a spectral type of A8Ve \citep{2003domdul} and is classified as a UX~Ori object \citep{1998meewae}. The UX~Ori variability has been confirmed by \citet{2009zwikal}. \citet{2003domdul} and \citet{2005vanmin} report distances of 116~pc and $145 \pm 43$~pc, respectively. We adopt the Hipparcos-based measurement of 116~pc and the associated parameters for our work. The object V1026~Sco shows large, non-periodic \citep{2005lecnit} brightness variations ($>$1.2~mag) and a pulsational variability on the milli-magnitude level \citep{2009zwikal}. It reddens with decreasing apparent magnitude \citep{1998meewae}. These authors suggest that dense dust clouds in an inclined disk cause the stellar reddening. \citet{2013alewad} report on the magnetic properties of V1026~Sco (and several other Herbig Ae/Be stars). The object V1026~Sco belongs to the Meeus group IIa \citep{2010juhbou} and might, therefore, have a self-shadowed disk. The stellar parameters \citep{2003domdul} of V1026~Sco are listed in Table~\ref{tabpro}. By modeling the spectral energy distribution (SED), \citet{2003domdul} found that the circumstellar disk of V1026~Sco has an inclination of approximately 55\degr. \citet{2005monmil} have performed Keck Interferometer (KI) measurements of V1026~Sco and found an inner disk diameter of 2.52~mas (0.29~AU at 116~pc). In a recent publication, \citet{2013schrat} have reported mid- and near-infrared interferometric observations (archival MIDI/VLTI \& IOTA data), and performed radiative transfer modeling of V1026~Sco, and derived a disk structure with a gap from 0.35~AU to 0.80~AU. In this paper, we analyze the circumstellar environment around V1026~Sco by taking new interferometric near-infrared (NIR) VLTI/AMBER and archival mid-infrared (MIR) VLTI/MIDI measurements into account. We describe our observations and the data reduction in Sect.~\ref{kapobs}. The modeling is presented in Sect.~\ref{kapmod}, and our results are discussed in Sect.~\ref{kapdis}. \begin{table}[t] \caption{The adopted stellar parameters of HD142666.} \label{tabpro} \centering \begin{tabular}{rcl} \hline\hline Parameter & Value \\ \hline spectral type & A8Ve \tablefootmark{a} \\ age [Myr] & $6.0 \pm 1.5$ \tablefootmark{b} \\ distance [pc] & 116 \\ $M_* [M_\odot]$ & 1.8 \\ $L_* [L_\odot]$ & 11 \\ $T_* [\mathrm K]$& 8500 \\ $log(\dot M [M_\odot \mathrm{yr}^{-1}])$ & $-6.73 \pm 0.26$ \tablefootmark{c} \\ \hline \end{tabular} \tablefoot{The values are taken from \citet{2003domdul} unless otherwise noted. The error bars are shown where available. \citet{2003domdul} estimate the uncertainty of the luminosity to be $\pm50\%$ (due to the Hipparcos distance error) and the mass uncertainty to be 5 -- 10\%. Other authors find slightly different parameters for the alternative distance of $145 \pm 20$~pc. For example \citet{2013alewad} derived $5.0^{+1.6}_{-1.1}$~Myr, $2.15^{+0.20}_{-0.19} M_\odot$, $27.5^{+7.9}_{-7.1} L_\odot$, and $7900 \pm 200$~K. Other references: \tablefoottext{a}{\citet{1998meewae}}, \tablefoottext{b}{\citet{2012folbag}}, \tablefoottext{c}{\citet{2011mencal}}. } \end{table} | We observed the UX~Ori star V1026~Sco with VLTI/AMBER in the \textit{H} and \textit{K} bands. With a geometric ring-shaped model consisting of the star and an inclined ring, we found a radius of $r_\mathrm{ring,in}=0.18 \pm 0.06$~AU in the \textit{K} band. In the context of the size-luminosity diagram, this radius is found to be consistent with the theory of a passive circumstellar disk with an inner hole and a rim at the dust sublimation radius. We further derived an inclination of $50 \pm 11\degr$ and $49 \pm 5\degr$ and a PA of the semi-major axis of the inclined disk of $179 \pm 17\degr$ and $163 \pm 9\degr$ in the \textit{H} and \textit{K} bands, respectively. We found a two-component-disk temperature-gradient model that is able to reproduce all visibilities and the SED. The inner radius of the inner disk is $0.19 \pm 0.01$~AU and similar to the one found with a geometric ring fit. The two disk components are separated by a gap, which may be explained by a shadow cast by a puffed-up inner rim and agrees with the type II classification of the object. The derived inclination of $48.6^{+2.9}_{-3.6}${\degr} and the PA of $169.3^{+4.2}_{-6.7}${\degr} are consistent with the values found by geometric modeling. Our inclination of $\sim 49\degr$ is probably not consistent with a model where rim fluctuations cause the UXOr variability, because the expected rim height is not high enough, as discussed above. The unsteady accretion theory cannot be excluded with our measurements, because the model is inclination-independent. Finally, the measured intermediate disk inclination is within the range predicted from UXOr models with orbiting dust clouds in the disk or in centrifugally-driven disk winds. | 14 | 3 | 1403.4941 |
1403 | 1403.4170_arXiv.txt | The exact location of the $\gamma$-ray emitting region in blazars is still controversial. In order to attack this problem we present first results of a cross-correlation analysis between radio (11\,cm to 0.8\,mm wavelength, F-GAMMA program) and $\gamma$-ray (0.1--300\,GeV) $\sim$\,3.5 year light curves of 54 {\it Fermi}-bright blazars. We perform a source stacking analysis and estimate significances and chance correlations using mixed source correlations. Our results reveal: (i) the first highly significant multi-band radio and $\gamma$-ray correlations (radio lagging $\gamma$ rays) when averaging over the whole sample, (ii) average time delays (source frame: 76\,$\pm$\,23 to 7\,$\pm$\,9\,days), systematically decreasing from cm to mm/sub-mm bands with a frequency dependence $\tau_{\mathrm{r,\gamma}}(\nu)\propto\nu^{-1}$, in good agreement with jet opacity dominated by synchrotron self-absorption, (iii) a bulk $\gamma$-ray production region typically located within/upstream of the 3\,mm core region ($\tau_{\mathrm{3mm,\gamma}}=12\pm8$\,days), (iv) mean distances between the region of $\gamma$-ray peak emission and the radio ``$\tau=1$ photosphere'' decreasing from $9.8\pm3.0$\,pc (11\,cm) to $0.9\pm1.1$\,pc (2\,mm) and $1.4\pm0.8$\,pc (0.8\,mm), (v) 3\,mm/$\gamma$-ray correlations in 9 individual sources at a significance level where one is expected by chance (probability: $4\times 10^{-6}$), (vi) opacity and ``time lag core shift'' estimates for quasar 3C\,454.3 providing a lower limit for the distance of the bulk $\gamma$-ray production region from the supermassive black hole (SMBH) of $\sim$\,0.8--1.6\,pc, i.e. at the outer edge of the Broad Line Region (BLR) or beyond. A 3\,mm $\tau=1$ surface at $\sim$\,2--3\,pc from the jet-base (i.e. well outside the ``canonical BLR'') finally suggests that BLR material extends to several pc distances from the SMBH. | Since the era of the Energetic Gamma-ray Experiment Telescope (EGRET) on-board the Compton Gamma-ray Observatory, the relation between the $\gamma$-ray and radio emission in Active Galactic Nuclei (AGN) has been intensively discussed. In particular, the location of the $\gamma$-ray production and dissipation region in AGN jets is still a matter of active debate -- recently re-activated and intensified thanks to the Large Area Telescope (LAT) on board the {\it Fermi Gamma-ray Space Telescope} ({\it Fermi}). The LAT is a pair-conversion $\gamma$-ray telescope sensitive to photon energies from about 20\,MeV up to $>$\,300\,GeV. Due to its unprecedented sensitivity and all-sky monitoring capabilities, {\it Fermi}/LAT is providing for the first time $\gamma$-ray light curves and spectra resolved at a variety of time scales for a large number ($\sim\,10^{3}$) of AGN since its launch in 2008 \citep[e.g.][]{2010ApJ...722..520A,2011ApJ...743..171A}. Different theoretical models and observational findings suggest different locations of the $\gamma$-ray emitting region, either at (i) small distances from the central supermassive black hole (SMBH), i.e. inside the Broad Line Region (BLR, sub-parsec) or even within a few 100 Schwarzschild radii, very close to the accretion disk \citep[e.g.][]{1995ApJ...441...79B} or (ii) at larger distances, e.g. in regions of radio shocks, shock-shock interaction, in various jet layers or turbulent cells parsecs downstream of the jet \citep[e.g.][]{1995A&A...297L..13V,2010arXiv1005.5551M,2012A&A...537A..70S,2013arXiv1304.2064M}. The knowledge of the $\gamma$-ray emission location, however, is of great importance for any model trying to explain the origin of the processes responsible for bulk $\gamma$-ray photon production and energy dissipation \citep[e.g.][]{2009MNRAS.397..985G,2014ApJ...782...82D}. In leptonic models, for instance, the exact location of the dissipation region constrains the origin of the main seed photon fields available for Inverse Compton (IC) up-scattering to high energies, i.e. either accretion disk/BLR/jet synchrotron photons ($\lesssim$\,1\,pc) or dust torus and/or jet synchrotron photons ($\gtrsim$\,1\,pc). Observationally, several findings disfavor the ``large distance'' scenario, for instance: (i) rapid ($\le$\,hours) MeV/GeV variability observed in a few sources \citep[e.g.][]{2010MNRAS.405L..94T,2010MNRAS.408..448F,2013A&A...557A..71R} suggests ultra-compact emission regions and, assuming that the emission region is taking up the entire jet cross-section in a conical jet geometry, a location not too far from the central engine; (ii) the high-energy spectral breaks observed by {\it Fermi} have been interpreted as $\gamma$-ray photo-absorption via He\,II Lyman recombination in the BLR \citep[][]{2010ApJ...717L.118P,2011MNRAS.417L..11S}, (iii) SED modeling can often describe well the high energy emission within leptonic scenarios by external Compton scattering of seed photons from the BLR and/or accretion disk \citep[e.g.][]{2010ApJ...714L.303F}. On the other hand, detailed multi-wavelength studies of single sources including cross-band (radio, optical, X-ray, $\gamma$-ray, and polarisation) and relative timing analysis of outbursts and{\bf /or} VLBI component ejection/kinematics suggest relativistic shocks, shock-shock interaction and/or multiple jet regions on pc scales as sites of the $\gamma$-ray emission \citep[e.g.][]{2001ApJ...556..738J,2010ApJ...710L.126M,2010ApJ...715..362J, 2011ApJ...735L..10A,2012A&A...537A..70S,2013A&A...552A..11R,2013MNRAS.428.2418O,2013MNRAS.436.1530R}. For instance, the joint occurrence of a $\gamma$-ray flare and an optical polarization position angle swing observed in 3C\,279 provides evidence for co-spatial emission regions along a curved trajectory at a significant distance from the central engine \citep[][]{2010Natur.463..919A}. Similarly, joint $\gamma$-ray and mm-band flares and (mm/optical) polarization peaks along with jet kinematics also suggest co-spatial emission regions many parsecs downstream of the jet in OJ\,287 \citep[][]{2011ApJ...726L..13A}. Finally, rapid variability on time scales of minutes in the few hundred GeV to TeV energy range can not be produced within the BLR due to high pair production $\gamma$-ray opacity \citep*[e.g.][]{2009ApJ...703.1168B,Tavecchio:2012vn}. \citet{2012ApJ...758L..15D} presented a new method to locate the energy dissipation region via the energy dependent decay times of flares in the different cooling regimes of the BLR (Klein-Nishina regime) and the pc-scale molecular torus region (Thomson regime). However, this method is limited to the most powerful $\gamma$-ray events providing enough photon statistics to detect significant differences in {\it Fermi} light curves at two different energy bands. Alternatively, detailed multi-wavelength and cross-correlation studies of large samples are capable of providing additional constraints on the location of the $\gamma$-ray emitting region. For instance, different studies aim at detecting time delays between $\gamma$ rays and 15\,GHz radio single-dish as well as long-term VLBI data of large samples \citep[e.g.][]{2010ApJ...722L...7P,2013arXiv1303.2131M}, indicating that cm-band radio flares are generally delayed w.r.t. $\gamma$ rays \citep[see also][]{2009ApJ...696L..17K}. Parsec-scale distances have been inferred from delays of $\gamma$-ray peak emission w.r.t. 37\,GHz radio flare onsets in a sample of sources monitored by the Mets\"ahovi group \citep[][]{2011A&A...532A.146L}, in-line with earlier results of similar studies conducted during the EGRET era \citep[e.g.][]{2003ApJ...590...95L}. Here, we present the first results of a cross-correlation analysis of a larger blazar sample based on multi-frequency radio (cm, mm and sub-mm wavelengths) light curves obtained by the F-GAMMA program \citep[e.g.][]{2007AIPC..921..249F,fuhrmann2013} and $\sim$\,3.5 year $\gamma$-ray light curves of 54 {\it Fermi}-bright blazars. The study aims at (i) establishing statistically significant correlations between the radio and $\gamma$-ray bands in a sample average sense by estimating correlation significances and chance correlations using mixed source correlations as well as a cross-correlation stacking analysis, and (ii) further constraining the location of the $\gamma$-ray emitting region in these sources. The paper is structured as follows: In Sect.~\ref{data} the sample and data sets are introduced. Sect.~\ref{DCCF_analysis} describes the applied cross-correlation methods and analysis, whereas Sect.~\ref{results} and \ref{discussion} present and discuss the results. A summary and concluding remarks are given in Sect.~\ref{conclusions}. \begin{figure*}% \centering \includegraphics[width=176mm,angle=0]{figure1.eps} \caption{The $\gamma$-ray (top) and radio (bottom) light curves (flux vs. modified julian date, MJD) for four selected, bright $\gamma$-ray sources of the studied sample: J1504+1029 (PKS\,1502+106, top left; redshift: 1.84), J2253+1608 (3C\,454.3, top right; redshift: 0.86), J1159+2914 (4C\,29.45, bottom left; redshift: 0.73) and J0222+4302 (3C\,66A, bottom right; redshift: 0.44). The top two and bottom left sources demonstrate cases of possible correlations between both bands, whereas no correlated variability is evident for J0222+4302 (bottom right).} \label{fgamma_lat_LCs} \end{figure*} | We have presented first results of a detailed cross-correlation analysis between radio (cm, mm and sub-mm wavelengths of the F-GAMMA program) and $\gamma$-ray variability in the $\sim$\,3.5 year light curves of 54 {\it Fermi}-bright blazars. Our results for the studied sample can be summarized as follows: \begin{enumerate} \renewcommand{\theenumi}{(\arabic{enumi})} \item The 3.5 year light curves often display strong outbursts (time scales of months) and extended periods of activity (months to 1--2 years) at both radio and $\gamma$ rays, whereas the $\gamma$-ray variability usually appears to be more rapid. \item In order to increase the significance and sensitivity for correlations, a DCCF stacking analysis was performed using the whole sample and a new method to estimate correlation significances and chance correlations via a ``mixed source correlation'' method. For the latter analysis, we used a total of 131 $\gamma$-ray light curves including additional 77 reference blazars. This yields for the first time strong, statistically significant multi-band radio (11\,cm to 0.8\,mm) and $\gamma$-ray correlations. The radio emission is typically lagging the $\gamma$ rays with sample average time lags ranging between 76\,$\pm$\,23 and 7\,$\pm$\,9\,days, systematically decreasing from the longer cm wavelengths to the mm/sub-mm bands. \item The radio/$\gamma$-ray delay frequency dependence is well described by a power law $\tau_{\mathrm{r,\gamma}}(\nu)\propto\nu^{-1}$, as expected for synchrotron self-absorption (SSA) dominated opacity effects (with $\tau\propto\nu^{1/k_{{\mathrm r}}}$, $k_{{\mathrm r}}\simeq 1$). \item Although the time lag rapidly decreases towards shorter wavelengths, a still positive delay at 3\,mm with $\tau_{\mathrm{3\,mm,\gamma}}=12\pm8$\,days suggests that the bulk $\gamma$-ray emission is coming from inside or even upstream of the (optically thick) 3\,mm-core region. \item The mean spatial distances between the region of $\gamma$-ray peak emission and the radio ``$\tau=1$ photosphere'' are found to decrease from $9.8\pm3.0$\,pc at 110\,mm to $0.9\pm1.1$\,pc and $1.4\pm0.8$\,pc at 2 and 0.8\,mm wavelength, respectively. \item Previous studies have shown that the multi-frequency radio variability observed in our sample is in overall good agreement with shocks and their three-stage evolution. Given the strong radio/$\gamma$-ray correlations presented here, we thus conclude that the enhanced, bulk $\gamma$-ray emission is likely also connected to these shocked jet structures. \item We obtain 3\,mm/$\gamma$-ray correlations for 9 individual sources at a significance level where we expect one occurring by chance (chance probability: $4\times 10^{-6}$). These sources exhibit 3\,mm/$\gamma$-ray time lags $\tau_{{\mathrm 3mm,\gamma}}$ in the source frame ranging between $-4\pm10$ and $93\pm16$\,days. No significant case of radio leading $\gamma$ rays is found. \item The observed opacity/SSA effects allow us to further constrain the location of the $\gamma$-ray emitting region in individual sources using a new method which combines the radio/$\gamma$-ray as well as radio/radio time lags. Together with VLBI proper motion measurements and assuming a conical jet, ''time lag core shifts'' then reveal the absolute, de-projected distance of the bulk $\gamma$-ray emitting region from the jet-base. Applied to 3C\,454.3 we consequently obtain a lower limit for the $\gamma$-ray distance to the SMBH of 0.8--1.6\,pc. \item For typical bulk BLR radii of $\lesssim$\,1\,pc observed in AGN and a value of $\sim$\,0.2\,pc obtained for 3C\,454.3, we place the $\gamma$-ray emitting region in this source at the outer edge or beyond the BLR. Our finding of the $\tau=1$ surface at 3\,mm being at $\sim$\,2--3\,pc from the jet-base (i.e. well outside the canonical BLR) together with recent findings of \citet{2013ApJ...763L..36L} suggests that BLR material in 3C\,454.3 extends to several pc distances from the SMBH. \end{enumerate} Our overall findings suggest a scenario where the bulk light curve flare emission is produced in shocks moving down the jet, whereas the $\gamma$ rays are escaping instantaneously from the shocked jet region and the optically thin radio emission from the same region reaches the observer successively delayed due to opacity effects and travel-time along the jet. The current low detection rate of significant single-source correlations clearly demonstrates the need for longer data trains and a correspondingly better ``event statistic'' to study the correlation properties and $\gamma$-ray location for a larger number of individual sources in detail. Our stacking analysis will furthermore enable more detailed studies of the radio/$\gamma$-ray correlation properties of the sample exploring possible differences of the correlation behavior between different source classes (e.g. FSRQs vs. BL Lacs) and testing dependencies on different physical parameters such as black hole mass, BLR size, luminosity, jet opening angle and Doppler factor (Fuhrmann et al., Larsson et al. in prep.). We stress that the overall situation is complex. The strong and significant multi-band correlations presented here are statistical in nature and often no simple, detailed one-to-one correlation of single radio and $\gamma$-ray flares is observed. In addition, our correlation method and data sets are mostly sensitive to the maxima and minima of the most prominent, long-term variability/flares in the studied sample. The radio/$\gamma$-ray correlation properties of the more rapid $\gamma$-ray flares often observed in these sources on time scales of $\lesssim$\,hours or days to a few weeks (and not resolved with our data sets and analysis) may be different. These events may be produced also at different locations. However, the very smooth and continuous behavior of the observed time lag in agreement with SSA all the way to the mm and sub-mm bands may provide some evidence against the ``43\,GHz standing shock and turbulent extreme multi-zone scenario'' \citep[e.g.][]{2010arXiv1005.5551M,2013arXiv1304.2064M}. Future, more detailed studies of single sources will shed further light on this topic. Neither our stacking method nor single-source results provide strong evidence for cases of radio leading $\gamma$ rays. This demonstrates the limited predictive power of radio flares to reliably trigger {\it Fermi} observations of flaring $\gamma$-ray sources (whereas the detection of a $\gamma$-ray flare by {\it Fermi} likely signals an impending high state at radio bands). This statement holds unless radio (mm/sub-mm) flare onsets occur simultaneously with or even before $\gamma$-ray flare onsets, which is unclear at the moment. This needs to be addressed in future studies. | 14 | 3 | 1403.4170 |
1403 | 1403.6015.txt | A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation of the corresponding Gaussian density. In the $n$-dimensional setting, however, it requires the inversion of an $n \times n$ covariance matrix, $C$, as well as the evaluation of its determinant, $\det(C)$. In many cases, such as regression using Gaussian processes, the covariance matrix is of the form $C = \sigma^2 I + K$, where $K$ is computed using a specified covariance kernel which depends on the data and additional parameters (hyperparameters). The matrix $C$ is typically dense, causing standard direct methods for inversion and determinant evaluation to require $\mathcal O(n^3)$ work. This cost is prohibitive for large-scale modeling. Here, we show that for the most commonly used covariance functions, the matrix $C$ can be hierarchically factored into a product of block low-rank updates of the identity matrix, yielding an $\mathcal O (n\log^2 n) $ algorithm for inversion. More importantly, we show that this factorization enables the evaluation of the determinant $\det(C)$, permitting the direct calculation of probabilities in high dimensions under fairly broad assumptions on the kernel defining $K$. Our fast algorithm brings many problems in marginalization and the adaptation of hyperparameters within practical reach using a single CPU core. The combination of nearly optimal scaling in terms of problem size with high-performance computing resources will permit the modeling of previously intractable problems. We illustrate the performance of the scheme on standard covariance kernels. | % Computer Society journal papers do something a tad strange with the very % first section heading (almost always called "Introduction"). They place it % ABOVE the main text! IEEEtran.cls currently does not do this for you. % However, You can achieve this effect by making LaTeX jump through some % hoops via something like: % %\ifCLASSOPTIONcompsoc % \noindent\raisebox{2\baselineskip}[0pt][0pt]% % {\parbox{\columnwidth}{\label{sec:introduction}\par %\fi % % Admittedly, this is a hack and may well be fragile, but seems to do the % trick for me. Note the need to keep any \label that may be used right % after \section in the above as the hack puts \section within a raised box. % The very first letter is a 2 line initial drop letter followed % by the rest of the first word in caps (small caps for compsoc). % % form to use if the first word consists of a single letter: % \IEEEPARstart{A}{demo} file is .... % % form to use if you need the single drop letter followed by % normal text (unknown if ever used by IEEE): % \IEEEPARstart{A}{}demo file is .... % % Some journals put the first two words in caps: % \IEEEPARstart{T}{his demo} file is .... % % Here we have the typical use of a "T" for an initial drop letter % and "HIS" in caps to complete the first word. \IEEEPARstart{A} common task in probability and statistics is the computation of the numerical value of the posterior probability of some parameters $\btheta$ conditional on some data $\bx, \by \in \mathbb R^n$ using a multivariate Gaussian distribution. This requires the evaluation of \begin{equation} p(\btheta | \bx, \by) \propto \frac{1}{ | \det(C(\bx; \btheta)) |^{1/2}} e^{-\frac{1}{2} \by^t C^{-1}(\bx;\btheta) \by} \, p(\btheta), \end{equation} where $C(\bx;\btheta)$ is an $n \times n$ symmetric, positive-definite {\it covariance} matrix. The explicit dependence of $C$ on particular parameters $\btheta$ is shown here, and may be dropped in the proceeding discussion. In the one-dimensional case, $C$ is simply the scalar variance. Thus, computing the probability requires only the evaluation of the corresponding Gaussian. In the $n$-dimensional setting, however, $C$ is typically dense, so that its inversion requires $O(n^3)$ work as does the evaluation of its determinant $\det(C)$. This cost is prohibitive for large $n$. In many cases, the covariance matrix $C$ is assumed to be of the form $C(\bx) = \sigma^2 I + K(\bx)$, where $K_{ij}(\bx) = k(x_i,x_j)$. This happens when the model for the data assumes some sort of uncorrelated additive measurement noise having variance $\sigma^2$ in addition to some structured covariance described by the kernel $k$. The function $k(x_i,x_j)$ is called the covariance function or covariance kernel, which, in turn, can depend on additional parameters, $\btheta$. Covariance matrices of this form universally appear in regression and classification problems when using Gaussian process priors~\cite{rasmussen2006gaussian}. Because many covariance kernels are similar to those that arise in computational physics, a substantial body of work over the past decades has produced a host of relevant fast algorithms, first for the rapid application of matrices such as $K$~\cite{greengard1987fast, fastgauss, fong2009black, gimbutas2003generalized, ying2004kernel}, and more recently on their inversion~\cite{greengard2009fast, ambikasaran2013fastdirect, amirhossein2014fast, chandrasekaran2006fast, fong2009black, borm2003hierarchical, martinsson2005fast, ho2012fast}. We do not seek to further review the literature here, except to note that it is still a very active area of research. Using the approach outlined in~\cite{ambikasaran2013fastdirect}, we will show that under suitable conditions, the matrix $C$ can be hierarchically factored into a product of block low-rank updates of the identity matrix, yielding an $\mathcal O (n\log^2 n) $ algorithm for inversion. More importantly (and perhaps somewhat surprising), we show that our factorization enables the evaluation of the determinant, $\det(C)$, in $\mathcal O (n\log n)$ operations. Together, these permit the efficient direct calculation of probabilities in high dimensions. Previously existing methods for inversion and determinant evaluation were based on either rough approximation methods or iterative methods \cite{murray,smola,snelsongh,anitescu,anitescu2}. These schemes are particularly ill-suited for computing determinants. Although bounds exist for sufficiently random and diagonally dominant matrices, they are often inadequate in the general case \cite{brent}. We briefly review existing accelerated methods for Gaussian processes in Section~\ref{sec-accel} and present a cursory heuristic comparison with our covariance matrix factorization. Gaussian processes are the tool of choice for many statistical inference or decision theory problems in machine learning and the physical sciences. They are ideal when requirements include flexibility for the modeling of continuous functions. However, applications are limited by the computational cost of matrix inversion and determinant calculation. Furthermore, the determinant of the covariance matrix is required for Gaussian process likelihood evaluations (i.e., computation of any actual value of the probability of the data under the covariance hyperparameters, or evidence). Existing linear algebraic schemes for direct matrix inversion and determinant calculation are prohibitively expensive when the likelihood evaluation is placed {\it inside} an outer optimization or Markov chain Monte Carlo (MCMC) sampling loop. In this paper we will focus on describing and applying our new methods for handling large-scale covariance matrices (dense and full- or high-rank) to avoid the computational bottlenecks encounters in regression, classification, and other problems when using Gaussian process models. We motivate the algorithms by explaining where their need arises only in Gaussian process regression, but similar calculations are frequently encountered in other regimes under Gaussian process priors. Other applications, such as marginalization and adaptation of hyperparameters are relatively straightforward, and the computational bottlenecks of each are highly related. The paper is organized as follows. Section~\ref{sec-gp} reviews some basic facts about Gaussian processes and the resulting formulas encountered in the case of a one-dimensional regression problem. Prediction, marginalization, adaptation of hyperparameters, and existing approximate accelerated methods are also discussed. Section~\ref{sec-matrices} discusses the newly developed matrix factorization for Hierarchical Off-Diagonal Low-Rank (HODLR) matrices, for which factorization requires only $\mathcal O (n \log^2 n)$ work. Subsequent applications of the operator and its inverse scale as $\mathcal O (n \log n)$. Many popular covariance functions used for Gaussian processes yield covariance matrices satisfying the HODLR requirements. While other hierarchical methods could be used for this step, we focus on the HODLR decomposition because of its simplicity and applicability to a wide range of covariance functions. We would like to emphasize that the algorithm will work for any covariance kernel, but the scaling of the algorithm might not be optimal; for instance, if the covariance kernel has a singularity or is highly oscillatory without damping. Further, in Section~\ref{sec-deter}, we show that the determinant of an HODLR decomposition can be computed in $\mathcal O(n \log n)$ operations. Section~\ref{sec-numerical} contains numerical results for our method applied to some standard covariance functions for data embedded in varying dimensions. Finally, in Section~\ref{sec-conclusions}, we summarize our results and discuss any shortcomings and other applications of the method, as well as future avenues of research. The conclusion contains a cursory description of the corresponding software packages in C++ and Python which implement the numerical schemes of this work. These open-source software packages have been made available since the time of submission. | \label{sec-conclusions} In this paper, we have presented a fast, accurate, and nearly optimal hierarchical direct linear algebraic algorithms for computing determinants, inverses, and matrix-vector products involving covariances matrices encountered when using Gaussian processes. Similar matrices appear in problems of classification and prediction; our method carries over and applies equally well to these problems. Previous attempts at accelerating these calculations (inversion and determinant calculation) relied on either sacrificing fidelity in the covariance kernel (e.g. thresholding), constructing a global low-rank approximation to the covariance kernel, or paying the computational penalty of dealing with dense, full-rank covariance matrices. Our HODLR-based algorithm obviates the need for this compromise. Our {\it observation} that many covariance matrices of mathematical statistics have fine-grained, compressible hierarchical structure that provides access to the inverse may find use in many applications in the future. The source code for the algorithm has been made available on GitHub. The HODLR package for solving linear systems and computing determinants is available at \url{https://github.com/sivaramambikasaran/HODLR}~\cite{HODLR} and the Python Gaussian process package~\cite{dfm_gp}, {\it george}, has been made available at \url{https://github.com/dfm/george}. Both packages are open source, the HODLR package is released under the MPL2.0 license and {\it george} is released under the MIT license. Details on using these packages are available at their respective online repositories. In its present form, our method degrades in performance when the $n$-dimensional data has a covariance function based on points in $\mathbb R^d$ with $d >3$, as well as when the covariance function is oscillatory. Part of the performance loss cannot be avoided due to the curse of dimensionality. High-dimensional data is simply more complicated than low-dimensional data causing the off-diagonal blocks to have larger ranks (at least in the scenario of more and more data samples). The other part of the performance loss is in the compression. For high-dimensional data, analytic interpolatory low-rank approximations will provide faster and more robust approximations. Extensions of our approach to these cases is a subject of current research. We are also investigating high-dimensional anisotropic quadratures for marginalization and moment computation. % use section* for acknowledgement \ifCLASSOPTIONcompsoc % The Computer Society usually uses the plural form | 14 | 3 | 1403.6015 |
1403 | 1403.2389_arXiv.txt | In a recent contribution, \citet{2014MNRAS.438.2916B} investigated the incidence of planar alignments of satellite galaxies in the Millennium-II simulation, and concluded that vast thin planes of dwarf galaxies, similar to that observed in the Andromeda galaxy (M31), occur frequently by chance in $\Lambda$-Cold Dark Matter cosmology. However, their analysis did not capture the essential fact that the observed alignment is simultaneously radially extended, yet thin, and kinematically unusual. With the caveat that the Millennium-II simulation may not have sufficient mass resolution to identify confidently simulacra of low-luminosity dwarf galaxies, we re-examine that simulation for planar structures, using the same method as employed by Ibata et al. (2013) on the real M31 satellites. We find that 0.04\% of host galaxies display satellite alignments that are at least as extreme as the observations, when we consider their extent, thickness and number of members rotating in the same sense. We further investigate the angular momentum properties of the co-planar satellites, and find that the median of the specific angular momentum derived from the line of sight velocities in the real M31 structure ($1.3\times10^4 \kms \kpc$) is very high compared to systems drawn from the simulations. This analysis confirms that it is highly unlikely that the observed structure around the Andromeda galaxy is due to a chance occurrence. Interestingly, the few extreme systems that are similar to M31 arise from the accretion of a massive sub-halo with its own spatially-concentrated entourage of orphan satellites. | \label{sec:Introduction} The so-called $\Lambda$-CDM cosmology \citep{2011ApJS..192...18K}, in which the universe is dominated by dark energy and cold dark matter (CDM), accurately describes the large scale properties and evolution of the cosmos. On the scale of the halos of large galaxies, this model predicts copious CDM sub-structures, the most massive of which are identified with the dwarf satellite galaxies that are observed to inhabit such regions \citep{2011MNRAS.417.1260F}. Numerical simulations that adopt this framework \citep{2008Springel,2010Cooper} generally reveal that the sub-halos that could host visible dwarf galaxies are distributed roughly spherically about the large galaxy. Observationally however, the distribution of dwarf galaxies within the Local Group appears to be more complicated. \citet{1976MNRAS.174..695L} and \citet{1976RGOB..182..241K} first noted that several prominent dwarf galaxies are correlated with streams of \ion{H}{1} emission, and suggested that the outer halo globular clusters of the Milky Way may represent `ghostly' indicators of ancient accretions \citep{1995MNRAS.275..429L}. More recent analyses \citep{2007MNRAS.374.1125M,2008ApJ...680..287M,2009MNRAS.394.2223M,2012MNRAS.423.1109P} that include the faint dwarf galaxies detected during the past decade in the Sloan Digital Sky Survey (SDSS) support the earlier results, although concerns remain about the spatial selection biasses given the SDSS sky coverage. Interestingly, the satellites appear to be rotationally stabilized, orbiting within the plane defined by their spatial alignment \citep{2013MNRAS.435.2116P}. It has been claimed that the proposed planes of satellites are not predicted within $\Lambda$-CDM, and cannot simply represent a memory of past coherent accretion \citep{2005A&A...431..517K,2012MNRAS.423.1109P,2013MNRAS.435.1928P}, although other studies dispute this conclusion \citep{2005ApJ...629..219Z,2011MNRAS.413.3013L,2013MNRAS.429.1502W}. In a previous contribution we showed that our nearest large companion, the Andromeda galaxy, possesses an immense, kinematically coherent, thin plane of dwarf galaxies, representing $\sim 50\%$ of the total dwarf population of Andromeda (\citealt{2013Natur.493...62I}; see also \citealt{2013ApJ...766..120C}), confirming previous studies \citep{2006AJ....131.1405K,2007ApJ...670L...9M,2007MNRAS.374.1125M,2008ApJ...676L..17I,2009MNRAS.394.2223M} that had hinted at potential spatial correlations of dwarfs in M31. \begin{figure*} \begin{center} \includegraphics[viewport= 75 155 560 640, clip, height=13cm]{fig01.pdf} \end{center} \caption{Real and simulated alignments. Panel (a) shows the sky positions of the real sample of 15 satellite galaxies of M31 that display a planar alignment. (For objects at a distance of $780\kpc$, the top and right margins show the corresponding length scale, and dashed circles mark $50$, $100$ and $150\kpc$). The irregular polygon marks the outer limit of the Pan-Andromeda Archaeological Survey (PAndAS) \citep{2009Natur.461...66M}, while the inner (continuous) circle marks a $2\degg5$ region that was masked out by \citet{2013Natur.493...62I} to avoid incompleteness due to high stellar density. The side-on view in (b) shows the most likely positions of the satellites \citep{2012ApJ...758...11C}. The line of sight velocities of the satellites from \citet{2013ApJ...768..172C} are also displayed (a velocity of $1\kms$ has length $1\kpc$); the red arrows mark objects that share the same sense of rotation. The small dots in panels (c) and (d) show, respectively, the same information as in (a) and (b), but for all the satellites extracted from the Millennium-II simulation. In (d) we also overlay (large symbols) one of the two satellite systems that was more extreme than the observed M31 system. The green circle marks the position of the most massive sub-halo in that system, whose baryonic mass ($1.8\times10^{10}\msun$) significantly exceeds that of any satellite in the Local Group.} \label{fig:observations} \end{figure*} A scenario that has been proposed to explain these alignments is that the present-day satellites are the remnants of tidal dwarf galaxies formed in ancient major mergers \citep{2012MNRAS.423.1109P,2013MNRAS.431.3543H}. This explanation is problematic, however, as it requires that the dwarfs are not dark matter dominated. It is in this context that \citet[][hereafter BB14]{2014MNRAS.438.2916B} recently analyzed the Millennium-II simulation \citep{2009MNRAS.398.1150B}, to investigate the incidence of satellite alignments in that large $10^6 h^{-3} \mpc^3$ volume of a $\Lambda$-CDM universe. They concluded that due to the spatial correlation between satellites in $\Lambda$-CDM, structures similar to that observed are relatively common, arising in approximately 2\% of the halos they investigated. The aim of the present paper is to examine the validity of the BB14 analysis, and to extend our earlier analysis to make better use of the accurate kinematic information available for the real satellites. In Section~\ref{sec:Sample_Selection}, we discuss how the samples were selected from the simulation. Section~\ref{sec:Results} presents the analysis and results, and conclusions are drawn in Section~\ref{sec:Conclusions}. | \label{sec:Conclusions} We have carefully reanalyzed the large-scale ``Millennium-II'' $\Lambda$-CDM simulation, searching for alignments of satellites similar to that observed around the Andromeda galaxy. We consider M31-like host galaxies in a range of a full decade in stellar mass around the M31 value and require that they reside in parent dark matter halos that are no more massive than plausible values for the Local Group. By applying the PAndAS spatial selection function we derive views of planes of 15 satellites that are comparable to the observed configuration. We analyzed the perpendicular thinness, radial extent, coherent kinematics and angular momentum properties of the simulated samples together, and found cases similar to the observed planar structure to be extremely rare, occurring in only 0.03--0.04\% of the samples. This shows that the observed alignment discovered by \citet{2013Natur.493...62I} is surprising in $\Lambda$-CDM, if one assumes that the Millennium-II simulation has sufficient resolution to reliably detect counterparts of the observed satellites. Nevertheless, the extreme rarity of analogs to the M31 system in the Millennium-II simulation does not necessarily preclude the possibility that planar structures may exist around different types of hosts in $\Lambda$-CDM simulations. By relaxing our search criteria that are specific to M31, such as the adopted virial and baryonic mass constraints, and the requirement that there be no nearby large neighbor, the number of candidate systems increases from 679 to over 2000 for virial masses in the range $1$--$5\times10^{12}\msun$. While a thorough analysis of such simulated satellite systems is beyond the scope of the present paper, we believe that it will be of great importance to ascertain the incidence of satellite alignments in nature for galaxies beyond the Local Group. | 14 | 3 | 1403.2389 |
1403 | 1403.0942_arXiv.txt | We study metal absorption around \ngaltotal\ $z\approx2.4$ star-forming galaxies taken from the Keck Baryonic Structure Survey (KBSS). The galaxies examined in this work lie in the fields of 15 hyper-luminous background QSOs, with galaxy impact parameters ranging from 35~proper kpc (pkpc) to 2~proper Mpc (pMpc). Using the pixel optical depth technique, we present the first galaxy-centred 2-D maps of the median absorption by \osix, \nfive, \cfour, \cthree, and \sifour, as well as updated results for \hone. At small galactocentric radii we detect a strong enhancement of the absorption relative to randomly located regions that extend out to at least 180~pkpc in the transverse direction, and $\pm240$~\kmps\ along the line-of-sight (LOS, $\sim1$~pMpc in the case of pure Hubble flow) for all ions except \nfive. For \cfour\ (and \hone) we detect a significant enhancement of the absorption signal out to 2~pMpc in the transverse direction, corresponding to the maximum impact parameter in our sample. After normalising the median absorption profiles to account for variations in line strengths and detection limits, in the transverse direction we find no evidence for a sharp drop-off in metals distinct from that of \hone. We argue instead that non-detection of some metal line species in the extended circumgalactic medium is consistent with differences in the detection sensitivity. Along the LOS, the normalised profiles reveal that the enhancement in the absorption is more extended for \osix, \cfour, and \sifour\ than for \hone. We also present measurements of the scatter in the pixel optical depths, covering fractions, and equivalent widths as a function of projected galaxy distance. Limiting the sample to the \ngalmf\ galaxies with redshifts measured from nebular emission lines does not decrease the extent of the enhancement along the LOS compared to that in the transverse direction. This rules out redshift errors as the source of the observed redshift-space anisotropy and thus implies that we have detected the signature of gas peculiar velocities from infall, outflows, or virial motions for \hone, \osix, \cfour, \cthree, and \sifour. | 14 | 3 | 1403.0942 |
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1403 | 1403.5560_arXiv.txt | Metallicity is a fundamental parameter that contributes to the physical characteristics of a star. However, the low temperatures and complex molecules present in M dwarf atmospheres make it difficult to measure their metallicities using techniques that have been commonly used for Sun-like stars. Although there has been significant progress in developing empirical methods to measure M dwarf metallicities over the last few years, these techniques have been developed primarily for early- to mid-M dwarfs. We present a method to measure the metallicity of mid- to late-M dwarfs from moderate resolution ($R\sim2000$) $K-$band ($\simeq2.2$~\um) spectra. We calibrate our formula using 44 wide binaries containing an F, G, K, or early M primary of known metallicity and a mid- to late-M dwarf companion. We show that similar features and techniques used for early M dwarfs are still effective for late-M dwarfs. Our revised calibration is accurate to $\sim0.07$~dex for M4.5--M9.5 dwarfs with $-0.58<$[Fe/H]$<+0.56$ and shows no systematic trends with spectral type, metallicity, or the method used to determine the primary star metallicity. We show that our method gives consistent metallicities for the components of M+M wide binaries. We verify that our new formula works for unresolved binaries by combining spectra of single stars. Lastly, we show that our calibration gives consistent metallicities with the \citet{Mann:2013gf} study for overlapping (M4--M5) stars, establishing that the two calibrations can be used in combination to determine metallicities across the entire M dwarf sequence. | \label{sec:intro} M dwarfs have become attractive targets for exoplanet searches \citep[e.g.,][]{Fischer:2012lr}. M dwarfs represent $\sim75\%$ of stars in the solar neighborhood \citep{2006AJ....132.2360H} so their planets weigh heavily on any Galactic planet occurrence calculations. Stellar companions, which can impede giant planet formation \citep{2012ApJ...745...19K}, dilute transits detections, and make Doppler detections more difficult, are less common around M dwarfs than for solar-type stars \citep{Figueira:2012fk}. M dwarf's low masses and small radii enhance Doppler and transit signals, thereby increasing the feasibility of detecting of Earth-sized planets in their habitable zones. These enhancements strengthen considerably from early- to late- M dwarfs. Early M-type dwarfs have masses and radii about half that of the Sun, while late-M dwarfs can have masses and radii $\sim10\%$ that of the Sun \citep{2010ApJ...721.1725D,Boyajian:2012lr} resulting in deeper transit depths and stronger transit signals for an equal size/mass planet. Further, the habitable zone for a late M-type dwarf is 5-10 times closer to the star than for an early M-type dwarf \citep{Kopparapu2013}, resulting in a larger Doppler signal and more likely and frequent transits. Studies of M dwarfs have already advanced the study of planet occurrence with stellar mass \citep[e.g.,][]{Johnson:2010lr, Gaidos:2013b} and metallicity \citep{Mann:2012, Mann:2013vn}. Their low masses give additional leverage on any correlation between stellar mass and planet properties, and their large convective zones dilute any metallicity changes from pollution of the photosphere \citep{1997MNRAS.285..403G, 2001ApJ...556L..59P}. However, fully exploiting M dwarfs to advance our knowledge of planet occurrence requires accurate metallicities for the entire sequence of M dwarfs, which are currently unavailable. The advantages discussed above, among others, have motivated a number of planet surveys specifically targeting mid- to late-M dwarfs, most of which are coming online in the next few years. This includes near-infrared radial velocity surveys like CARMENES \citep{2012SPIE.8446E..0RQ} and the Habitable-Zone Planet Finder \citep{2012SPIE.8446E..1SM}, transit surveys like APACHE \citep{2013EPJWC..4703006S} and MEarth \citep{Nutzman:2008gf, Charbonneau:2009rt}, and direct imaging searches like PALMS \citep{2012ApJ...753..142B}. Some of these surveys are directed at M dwarfs generally, but many are aimed at mid- to late-M dwarfs specifically. The Habitable-Zone Planet Finder, for example, is targeting M4-M9 dwarfs \citep{2012SPIE.8446E..1SM}. Our knowledge of planet parameters are directly linked to our understanding of their host stars. Thus, these surveys require reliable stellar masses, radii, and metallicities to properly characterize orbiting planets that are discovered. The {\it Gaia} spacecraft \citep{2012Ap&SS.341...31D} is expected to measure parallaxes for the majority of the M dwarfs targeted by these surveys \citep{Bailer-Jones:2013aa}, and distances can be used to derive luminosities and infer masses and radii \citep[e.g.,][]{2000A&A...364..217D, 2006ApJ...651.1155B}, but not metallicities. M dwarfs have sufficiently cool atmospheres to enable the formation of molecules with complex absorption bands. These bands are difficult to model but dominate the visible spectrum, making continuum identification difficult and creating line confusion. The result is that model-dependent methods such as spectral synthesis and curve of growth analysis that work well on solar-type stars are ineffective for M dwarfs \citep[although improvements are ongoing, e.g.,][]{Onehag:2012lr}. An alternative approach is to measure the metallicity of M dwarfs using empirical techniques. Such methods include measuring the position on a color-magnitude diagram \citep[e.g.,][]{Schlaufman:2010qy, 2012A&A...538A..25N}, the strength of molecular lines in the optical \citep[e.g.,][]{Woolf:2006uq, Dhital:2012lr}, or atomic lines in the optical or near-infrared \citep[e.g.,][]{2010ApJ...720L.113R,Mann:2013gf}. Colors such as $g-r$ \citep[e.g.,][]{West:2004qy, Bochanski:2013lr} or $JHK$ \citep[e.g.,][]{Johnson:2012fk,Newton:2014} can be used for predicting metallicity, but the errors are higher than other approaches and are subject to additional systematic errors \citep{Mann:2012}. These methods are typically calibrated using wide binaries containing a solar-type primary \citep[e.g.,][]{2005A&A...442..635B}. This assumes that wide binaries formed from the same molecular cloud and therefore have the same metallicity, which is well-established for solar-mass binaries \citep{2004A&A...420..683D,2006A&A...454..581D}. To date, calibrations of these empirical techniques have been created only for early and mid M-type dwarfs. The calibration from \citet[][henceforth M13]{Mann:2013gf} utilized the largest sample, but it contained only one M5, one M6, and nothing later. \citet{Newton:2014} focused on cooler M dwarfs for the MEarth survey, but included no M6 dwarfs, a single M7, and nothing cooler. As a result, the effectiveness of these calibrations for the coolest M dwarfs remains untested. The faintness at optical wavelengths of the coolest M dwarfs makes them less likely to show up in long-time baseline proper motion surveys, because they generally rely on detections in the optical. Thus, until recently, it was difficult to locate wide, common proper motion pairs containing a late-type M dwarf. However, the problem has been mitigated significantly thanks to wide-field digital sky surveys such as the Sloan Digital Sky Survey \citep{Aihara:2011ly, West:2011fj}, the Two-Micron All-Sky Survey \citep[2MASS][]{Skrutskie:2006lr}, and the Panoramic Survey Telescope and Rapid Response System \citep[PAN-STARRS][]{2010SPIE.7733E..12K}, which have provided proper motions and photometry for cooler and fainter objects than were previously accessible. Furthermore, now that methods to estimate the metallicity of early-M types are established, we can use pairs of early-M and late-M type dwarfs to extend the calibration to cooler temperatures. In this paper we investigate methods to measure the metallicities of M4.5--M9.5 dwarfs. We use 44 wide binaries containing an F, G, K, or early M dwarf primary and an M4.5--M9.5 companion. We determine metallicities for the primary stars by combining those from the literature with our own observations. Following the techniques of M13, we derive empirical calibrations between features in $K-$band spectra and the metallicity of ultracool dwarfs. In Section~\ref{sec:sample} we present our wide binary sample. In Section~\ref{sec:obs} we describe our observations of the primary and companion stars. In Section~\ref{sec:analysis} we detail our calculations of metallicities for the primary stars and spectral classifications of the companions. We test how prior metallicity calibrations work on our ultracool dwarf sample in Section~\ref{sec:priorcal} then derive a new calibration in Section~\ref{sec:newcal}. We investigate the reliability of the calibration by employing a number of tests in Section~\ref{sec:tests}. We conclude with a brief summary of our work in Section~\ref{sec:discussion}. All wavelengths used in this work are stated as vacuum values. | \label{sec:discussion} We have used wide binaries containing an F, G, K, or early M dwarf primary with a M4.5--M9.5 companion to calibrate spectroscopic metallicity diagnostics for the coolest M dwarfs. Although many calibrations already exist, based either on spectroscopy or absolute magnitude, none have been calibrated with the latest M-type dwarfs. We showed that these prior spectroscopic calibrations yield systematically inaccurate metallicities for the coolest M dwarfs (Figure~\ref{fig:cal_comp}). We derived a new calibration for late-M (M4.5-M9.5) dwarfs and found that the Na~I doublet and Ca~I triplet were the most effective metallicity indicators for late-M dwarfs. We found that our calibration (Equation~\ref{eqn:cal}) predicts metallicities accurate to $\simeq0.07$~dex for $-0.58<$[Fe/H]$<+0.56$. The error is comparable to that reported by M13 for the K5--M5 sample. By combining this work with that of M13 ,it is possible to measure metallicities of stars across the entire M dwarf sequence. For the F, G, and K dwarf primaries [Fe/H] is generally measured directly using the plethora of Fe lines present in their spectra. However, measuring metallicities of M dwarfs generally relies on Ca and Na. We would therefore expect to get a smaller scatter relating the strength of these features to [$\alpha$/H], [M/H], and [Na/H]. Unsurprisingly, this was seen in previous studies using similar features \citep[e.g.][]{Rojas-Ayala:2012uq,Mann:2013gf}. This also may be the source of the higher scatter between primary and companion metallicity seen at lower metallicity (M13). However, most of the literature sources we use only report [Fe/H]. Although calibrations exist to determine [M/H] for early M dwarfs, these calibrations use almost identical lines to the [Fe/H] calibrations, which may complicate the result. Thus we would be left with only 18 stars, which is not enough for a meaningful investigation. Future analysis of this issue would require a more homogenous analysis of the primary stars. We performed a number of tests to assess the quality and applicability of the calibration. We verified that: \begin{itemize} \item Despite the use of a large line list and many free parameters, the precision of the calibration cannot be due to chance ($P\ll0.001$). \item The metallicities predicted by Equation~\ref{eqn:cal} are free of significant trends as a function of spectral type, metallicity, or source of metallicity for the primary. \item The calibration (and that of M13) is unaffected by unresolved binaries (triples) in the calibration sample. \item Both this calibration and that of M13 yield consistent metallicities for each component of M+M wide binaries. \item The calibration from M13 and this work predict metallicities for M4-M5 dwarfs (where the calibration samples overlap) that are in agreement. \end{itemize} Another potential source of error is the presence of false common-proper-motion companions (chance alignment) in the calibration sample. Presumably two unassociated stars will have random metallicities, and therefore appear as outliers in our relation. The lack of outliers in Figure~\ref{fig:calibration} suggests our sample is relatively free of false binaries. Based on the published proper motions and statistical arguments from \citet{Lepine:2007qy} and \citet{Tokovinin:2012fj} we expect the false-binary rate to be $\ll8\%$. The true number is probably significantly lower than this, as many pairs from the literature are identified using distance and radial velocity information in conjunction with proper motions. Although the Na~I and Ca~I lines are strong metallicity indicators for M dwarfs, the Na~I doublet becomes significantly weaker and the Ca~I triplet is essentially not detectible in L dwarfs at this S/N and resolution. It is promising that our current calibration works for a single L dwarf, however it is hard to draw conclusions from a single star. Extending this calibration further into the L dwarf regime may require fine-tuning the calibration and/or using an entirely different set of lines. We will investigate measuring the metallicities of L dwarfs in a future paper. | 14 | 3 | 1403.5560 |
1403 | 1403.2801_arXiv.txt | The new wide-field radio telescopes, such as: ASKAP, MWA, LOFAR, eVLA and SKA; will produce spectral-imaging data-cubes (SIDC) of unprecedented size -- in the order of hundreds of Petabytes. Servicing such data as images to the end-user in a traditional manner and formats is likely going to encounter significant performance fallbacks. We discuss the requirements for extremely large SIDCs, and in this light we analyse the applicability of the approach taken in the JPEG2000 (ISO/IEC 15444) standards. We argue the case for the adaptation of contemporary industry standards and technologies vs the modification of legacy astronomy standards or the development new from scratch. | Spectral-imaging data-cubes (SIDCs), from the new radio telescopes that are currently in various stages of construction or commissioning -- Australian Square Kilometre Array Pathfinder (ASKAP) \citep{ASKAP..09}, Murchison Widefield Array (MWA) \citep{TINGAY}, LOFAR \citep{2013A&A...556A...2V}, MeerKAT~\citep{2009arXiv0910.2935B}, eVLA ~\citep{2011ApJ...739L...1P} -- are expected to be in the range of tens of GBs to several TBs. The Square Kilometre Array (SKA) Design Reference Mission, SKA Phase 1 \citep{SPDO2011}, defines at least one survey, namely the ``Galaxy Evolution in the Nearby Universe: HI Observations", for which the SKA pipeline will produce hundreds of SIDCs, of tens of terabytes each. In its first year the SKA Phase 1 is expected to collect over 8 EB of data. The data volumes for the full SKA are expected to be by at least an order of magnitude larger. Even taking into account projected advances in HDD/SSD and network technologies, such large SIDCs cannot be processed or stored on local user computers. Most of the imaging data will be never seen by a human, but rather processed automatically \citep{2012MNRAS.421.3242W, 2012PASA...29..318P, 2012PASA...29..352J, 2012PASA...29..371W}. However, there will still be a number of cases where visualisation is going to be required, e.g. data quality control/assessment or detailed studies of individual objects. Visual exploration of such large data volumes requires a new paradigm for the generation and servicing of the higher level data products to the end-user. In this paper we present a straw man of the functionality required to enable working with extremely large radio astronomy imagery. We consider the JPEG2000 industry standard as a suitable example that addresses many similar requirements, even though it was originally developed for medical and remote sensing imagery. Currently, most radio astronomy imaging data is stored and distributed in one of three formats: FITS (Flexible Image Transport System) \citep{2010A&A...524A..42P}; CASA Image Tables~\footnote{\href{http://ascl.net/1107.013}{http://ascl.net/1107.013}} and newly developed by LOFAR HDF5-based format \citep{2011ASPC..442...53A}. FITS and HDF5 are, in general, single self-describing files containing the image data, as well as metadata. CASA, on the other hand, uses a different approach representing any data as a hierarchical structure of directories and files. CASA data is usually distributed as an archived file created by using common archiving software, such as \texttt{tar}\footnote{\href{http://en.wikipedia.org/wiki/Tar(computing)/}{http://en.wikipedia.org/wiki/Tar(computing)/}}. These formats provide both, portability and access to image data. Currently, image files or CASA tar-balls are normally retrieved from an archive and stored on a local computer for exploration, analysis or processing purposes. Alternatively, a specified part of an image-cube (cutout) is produced in one of the image formats, and presented to the user as a download. If coterminous regions are required, several cutout files would be produced and downloaded. The example of such a framework is Simple Image Access Protocol (SIAP)\footnote{\href{http://www. ivoa.net/Documents/SIA/}{http://www. ivoa.net/Documents/SIA/}} of the International Virtual Observatory Alliance (IVOA)\footnote{\href{http://www.ivoa.net}{http://www.ivoa.net}} that provides a uniform interface for retrieving image data from a variety of astronomical image repositories. By using SIAP the user can query compliant archives in a standardised manner and retrieve image files in one or more formats, depending on the archive capabilities (e.g. FITS, PNG or JPEG). The resulting files can then be stored on a local computer or a virtual network storage device that is provided through VOSpace, which is another IVOA standard. In the paper we discuss the use case of extremely large SIDCs in the context of the limitations of the current standard astronomy file formats. We present the analysis of the applicability of the approach taken in developing JPEG2000 standards to addressing the new requirements of extremely large astronomical imagery. We also present some interesting benchmarks from using JPEG2000 on large radio astronomy images. The rest of paper is structured as follows. In Section~\ref{cha:use-case}, we discuss the specific requirements of extremely large imaging. Section~\ref{cha:JPEG2000} discusses JPEG2000 standards, and how they have addressed the requirements of extremely large imaging. We specifically discuss the image interaction protocol in detail as the alternative to the used in astronomy cutout framework. Section~\ref{cha:Bench1} presents benchmarks for JPEG2000 compression for radio astronomy images. In Section~\ref{cha:adopting} we discuss the strategic approaches for improving the existing astronomy standards or the adoption of new industry standards. Finally, we conclude in Section~\ref{cha:conc}. | \label{cha:conc} New telescopes, such as the SKA, will produce images of extreme sizes. Providing adequate performance and level of convenience when serving such images to the end-user is going to be beyond the capabilities of current astronomy image formats. Improvements of the existing image and data formats can not solve the deficiencies inherently there, due to the fundamental limitations at the time of development. New advanced technologies are necessary. Technologies such as JPEG2000 have the potential to powerfully pave the way to a contemporary solution that will adequately address the challenges of extremely large imagery. Substantial reductions in storage/archive requirements can be achieved by losslessly encoding data into JPEG2000 images. Even greater saving may be achieved through lossy compression. JPIP provides a standard powerful way for interaction with the imagery data reducing the bandwidth, storage, and memory requirements, and increasing the mobility of future astronomy application. The results of our benchmarks demonstrate the viability of JPEG2000 compression for storing and distributing radio astronomy images. JPEG2000 is not just about compression -- it has the potential to enable an entirely new paradigm for working with radio astronomy imagery data. | 14 | 3 | 1403.2801 |
1403 | 1403.8112_arXiv.txt | {FU Orionis objects are a class of young stars with important bursts in luminosity and which show evidence of accretion and ejection activity. It is generally accepted that they are surrounded by a Keplerian circumstellar disk and an infalling envelope. The outburst would occurs because of a sudden increase in the accretion rate.} {We aim at studying the regions closer to the central star in order to observe the signs of the accretion/ejection activity.} {We present optical observations of the H$_{\alpha}$ line using the Integral Field Spectrograph OASIS, at the William Herschel Telescope, combined with Adaptive Optics. Since this technique gives the spectral information for both spatial directions, we carried out a two-dimensional spectro-astrometric study of the signal. } {We measured a clear spectro-astrometric signal in the North-South direction. The cross-correlation between the spectra showed a spatial distribution in velocity suggestive of scattering by a disk surrounding the star. This would be one of the few spatial inferences of a disk observed in a FU Orionis object. However, in order to fully understand the observed structure, higher angular and spectral resolution observations are required. V1515 Cyg appears now as an important object to be observed with a new generation of instruments to increase our knowledge about the disk and outflows structure in FU Orionis objects.} {} | FU Orionis objects (FUor) are a class of young stellar objects showing important outbursts, increasing in luminosity about 5 magnitudes and changing their spectral type in short timescales. The typical rise time is over one year, whereas the time scale for the lifetime of the high phase is decades. Two main theories were proposed to explain their nature. The first one favors a scenario where an unstable star is rotating near breakup, which would cause the outburst. A rapidly rotating G supergiant photosphere overlaid with a rising cooler shell could explain the observed spectral properties of these objects \citep{Herbig2003}. The second model, more widely accepted nowadays, considers a proto-stellar object surrounded by a Keplerian circumstellar disk and an infalling envelope. The outburst would occur because a sudden increase in the accretion rate through the disk. In this scenario, all young stars experience FUor phases during their evolution \citep{Hartmann1985,Hartmann1996}. Many studies during the last years investigated the accretion phenomenon in this class of objects from both an observational and theoretical point of view. Despite the effort the origin of the episodic accretion and outburst is poorly understood. A detailed review is presented by \citet{Audard2014}, including future promising directions. Evidence of outflows in FUor objects have already been reported before by different authors and using different observational tracers, both in the optical and in the infrared \citep{Croswell1987}, showing P Cygni profile in different lines, such several hydrogen lines, lower excitation lines of neutral metals and TiO bands \citep{Hartmann1996} and continuum radio observations \citep{Rodriguez1992}. In particular for the Z\,CMa system (Herbig Be star and FUor object), \citet{Whelan2010} detect jets driven by each of the components in the [FeII] lines . At much smaller scales \citet{Benisty2010} detect collimated Br$\gamma$ from the Be component. Typical observed wind velocities are in the range of 300--400~\kms with mass-loss rates in the order of $\sim$10$^{-5}$--10$^{-6}$M$_{\sun}$~yr$^{-1}$, even if this is a very variable parameter from one source to another. In the case of V1515 Cyg, discovered by \citet{Herbig1977}, evidence of winds and outflows were found. Both \citet{Bastian1985} and \citet{Croswell1987} showed spectra with a clear H$_{\alpha}$ P Cygni profile and \citet{Croswell1987} determined a mass loss rate of 10$^{-5}$ M$_{\sun}$/yr from the spectral energy distribution. This value was then confirmed by \citet{Kenyon1991}. They compared the mid- and far-infrared SED to the predictions of standard accretion disk models and concluded that the presence of an infalling envelope in this object is needed to fit the model, but the presence of a cavity in the envelope, through which the central optical source is seen, is also required. More recently \citet{Green2006} obtained similar conclusions. Using IR Spitzer IRS observations, they also conclude that the envelope model requires an outflow hole with a large opening angle. They suggested that this cavity should be the result of the high mass-loss rate accompanying rapid accretion in the FUor outburst state. Despite the evidence of the existence of winds/outflows and accretion activity in these objects, a detailed study of their physical properties have been difficult to carry out with high resolution instruments manly due to the faintness of these objects and their distance to us, for instance V1515 Cyg is 1 kpc away \citep{Racine1968}. Here, we present a new approach through an Integral Field Spectroscopy study at medium spatial resolution which allows us to astrometricaly probe scales typically in the order of 100-1000 AU to the central star and carry out a spectroscopic study in the both spatial directions simultaneously. This article is organized as follows: in Sec.~\ref{sec:obs} we describe the observations and the data reduction, in Sec.~\ref{sec:results} we present our results in terms of detection and reality of the detection. Section~\ref{sec:discussion} we propose some explanations for the observed signal in the context of the previous works and summarize our conclusions. | \label{sec:discussion} We showed a clear spectro-astrometric signal observed in the H$_{\alpha}$ emission of the FUor star V1515 Cyg. The signal was tested for bias and we conclude that the observed velocity structure observed in H$_{\alpha}$, shown in Figs.~\ref{fig:cross-correlation1} and~\ref{fig:cross-correlation2}, is real, with a physical origin and characteristic of the H$_{\alpha}$ line, since none other emission is detected in other lines typically tracing outflows such as [OI]$\lambda$6300\AA, [NII]$\lambda$6584\AA~or [SII]$\lambda$$\lambda$6716,6716. The velocity distribution of the observed structure suggests a rotating disk around the young star, that we can observe because of the scattering of the light by the disk. The FUor objects are assumed to be similar to T Tauri stars, consisting in a surrounding disk, maybe a remaining envelope, and an outflow. In fact what we observe here is very similar to the observed velocity gradients in $^{12}$CO images of protoplanetary disks with keplerian rotation in several T Tauri stars \citep[e.g.,][]{Simon2000}. In addition, several previous works on V1515 Cyg concluded about the need of an infalling envelope in order to fit the observed SED, in fitting the excess at 10 $\mu$m, and to explain the low K-band visibilities observed \citep{Millan-Gabet2006,Green2006,Zhu2008}. The models by \citet{Zhu2008} and by \citet{Green2006} also require the existence of an outflow cavity in the envelope. As shown by \citet{Kospal2011} this star is also surrounded by a nebula. Hence, the environmental medium in this star is a plausible option to produce scattering by dust either on the disk or on the envelope. However, where is the light coming from? It may be stellar radiation scattered in a disk in keplerian rotation, scattering by a dusty halo or it may be the light coming from an outflow. We briefly discuss these options in base of the results presented here. \paragraph{{\it 1) Disk in keplerian rotation:}} as said before, the observed morphology of the structure strongly suggest scattering in a disk in keplerian rotation. However, for the 1 kpc distance of this object and a typical velocity ($V_k$) of 10 \kms~observed in Figs.~\ref{fig:cross-correlation1} and~\ref{fig:cross-correlation2} at a distance for the star of 1\arcsec ($r$), the expected central star mass, $M_*=V_k^2\times r/G$, is in the order of $\sim$100 M$_{\sun}$ which is too large for this class of objects. Even in the regions where the observed velocity is $\sim$4 \kms, the derived star mass is $\sim$20 M$_{\sun}$ which is still too high. In the case of FU Ori a mass of 0.3 M$_{\sun}$ has been estimated by \citet{Zhu2007}. Assuming a higher mass of $\sim$2 M$_{\sun}$, in the order of the highest masses observed in T Tauri stars \citep{Calvet2004}, the keplerian velocity only explains $\sim$1 \kms~of the observed values. An additional contribution is needed. \paragraph{ {\it 2) Dusty halo:}} The scattering light can also be produced by dusty haloes, remnants of the original envelopes. \citet{Wheelwright2010} carried out a spectro-astrometric study over several Herbig Ae/Be (HAe/Be) stars. They observed in several of them a behavior similar of that observed here in V1515 Cyg. Large FWHM features occurred over absorption features in the emission profiles within small positional signatures (bottom and top panels of Figs.~\ref{fig:spectroastrometry69} and~\ref{fig:spectroastrometry70}). They suggested that these signatures could trace extended structures which scatter the light, such as a disk/stellar wind \citep{Azevedo2007}, haloes \citep{Leinert2001,Monnier2006}, or nebulosity. They considered the presence of dusty haloes and carried out a simple model. In spite of the limits of their model, such as for example the unknown amount of light scattered and the extend of the halo, they reproduced quite well the spectro-astrometric signatures observed for the PCygni profile observed over the H$_{\alpha}$ line in AB Aur (their Fig.~4). In our case, however, the positional signature in the vertical direction is very different from the horizontal one and comparable with the FWHM features. This asymmetry could be caused by an outflow or by projection effects. \paragraph{ {\it 3) Outflow:}} \citet{Azevedo2007} showed that the observed spectro-astrometric signal could also result from a wind. Some authors favor a nearly pole-on orientation of the system \citep{Kenyon1991,Millan-Gabet2006,Zhu2008}, in which case we would be seeing the outflow coming to us through the predicted cavity. The peak at $\sim$8-10 \kms (Figs.~\ref{fig:cross-correlation1} and~\ref{fig:cross-correlation2}) could be caused by a shock in the outflow itself or against the envelope cavity on the disk or the ambient medium. To explain the rest of the velocity structure, one simple explanation is that we are seeing % the projected $\Delta V$ produced by rotation of an inner disk-wind. Disk-wind models predict rotation of the outflow, points at different sides of the jet with different velocities would be scattered by the disk or an envelope producing an observed $\Delta V$. The projected $\Delta V$ of rotation from the outflow will be $\sim$10 \kms which corresponds to the lower typical velocity differences measured by \citep{Coffey2007} in the case of DG Tau and interpreted as possible rotation signatures. However, for the regions with lower observed velocities the derived velocities are too low for relating them with rotation signatures.\\ Unfortunately, this object is very faint, the signal to noise of our H$_{\alpha}$ line and the strong stellar continuum emission, do not allow a more detailed analysis of this detection in order to extract more quantitative results and the disk parameters. In addition, the exact inclination of the system is unknown, so projection effects could play an important role in the interpretation. In conclusion, the spatial distribution of the velocity structure observed in H$_{\alpha}$ suggests scattering by a disk/envelope surrounding the star. In that case, this would be one of the few spatial inferences of disks in FUor. Unfortunately our resolution does not allow a detailed parametrization of the emission observed in order to satisfactorily explain the velocity values observed. Observations at higher angular and spectral resolution are required. Since little is known about the exact structure of the disk and outflows in this class of objects, V1515 Cyg appears now as an excellent candidate for future instruments with higher angular and spectral resolution. | 14 | 3 | 1403.8112 |
1403 | 1403.4420_arXiv.txt | {% \nolinenumbers % We discuss the chemical pre-conditions for planet formation, in terms of gas and ice abundances in a protoplanetary disk, as function of time and position, and the resulting chemical composition and cloud properties in the atmosphere when young gas giant planets form, in particular discussing the effects of unusual, non-solar carbon and oxygen abundances. Large deviations between the abundances of the host star and its gas giants seem likely to occur if the planet formation follows the core-accretion scenario. These deviations stem from the separate evolution of gas and dust in the disk, where the dust forms the planet cores, followed by the final run-away accretion of the left-over gas. This gas will contain only traces of elements like C, N and O, because those elements have frozen out as ices. {\sc ProDiMo} protoplanetary disk models are used to predict the chemical evolution of gas and ice in the midplane. We find that cosmic rays play a crucial role in slowly un-blocking the CO, where the liberated oxygen forms water, which then freezes out quickly. Therefore, the C/O ratio in the gas phase is found to gradually increase with time, in a region bracketed by the water and CO ice-lines. In this regions, C/O is found to approach unity after about 5\,Myrs, scaling with the cosmic ray ionisation rate assumed. We then explore how the atmospheric chemistry and cloud properties in young gas giants are affected when the non-solar C/O ratios predicted by the disk models are assumed. The {\sc Drift} cloud formation model is applied to study the formation of atmospheric clouds under the influence of varying premordial element abundances and its feedback onto the local gas. We demonstrate that element depletion by cloud formation plays a crucial role in converting an oxygen-rich atmosphere gas into carbon-rich gas when non-solar, premordial element abundances are considered as suggested by disk models. } \keyword{ \nolinenumbers % astrochemistry; element abundances; extra-solar planets; gas giants; planet formation; cloud formation} \begin{document} \nolinenumbers % | \noindent Element abundances are critical parameters to predict the atmospheric composition of exoplanets and to understand their formation and evolution, including potentially the emergence of life. Extrasolar gas giants are commonly assumed to have elemental abundances similar to those of their host stars. These stars themselves can be reasonably well measured, for example (in case of the Sun) by high-resolution spectroscopy in combination with time-dependent numerical simulations of the photosphere, meteorite studies, or astroseismology \cite{asp09}. However, when considering the process of planet formation in a protoplanetary disk, which involves a segregation of gas, dust and ice phases, the assumption that the element mix of the host star must be the same as in the gas giants' atmospheres becomes questionable. This has far-reaching consequences for the spectroscopic analysis of planetary spectra, including the search for bio-signatures \cite{hwt08,wit09,bi2013}. Following the standard core-accretion model of planet formation \cite{Wetherill96,Ida2004}, the refractory elements are initially present mostly in form of $\mu$m-sized dust particles, which undergo a complex evolution eventually leading to km-sized planetesimals. The planetesimals are gravitationally attracted to each other, and collide to form larger parental bodies that later become planetary cores \cite{Kokubo1998,Fortier2013}. At the end of the evolution from dust to planet cores, the planet feeding zone is expected to be mostly devoid of smaller dust particles \cite{Dullemond2005}, and the remaining gas in the planet feeding zone is expected to contain only minor traces of refractory elements. Elements which are able to form ices on the surface of the refractory grains in protoplanetary disks, in particular oxygen, carbon and nitrogen, will also be depleted to an extent, depending on local temperature, though less than the refractory elements. The ices play an essential role in the dust growth process as ``glue'' or ``cement'' during planet formation \cite{Bridges1996}. The dust particles have been in contact with the gas in the disk for $>\!10^6$\,yrs, which is certainly long enough to cause most of the gaseous oxygen in the disk midplane to form H$_2$O ice outside the water ``ice-line'' and for most of the gaseous carbon to form CO ice outside the CO ``ice-line'' \cite{Chaparro2012a}. The elements bound in those ices should then rather follow the dust than the gas dynamical evolution. Only at the very end of the planet formation process, the overwhelming majority of the mass of the gas giant will be accreted onto the proto-planet in a rapid run-away phase \cite{Pollack1996}, using up the remaining gas in the planet feeding zone and possibly forming a gap. The timescale for gas accretion onto the proto-planet is about two orders of magnitude shorter than the growth timescale of the solid core \cite{Machida2010}. At this late stage, the gas should contain only traces of refractory elements, and possibly also very little amounts of the ``ice elements'' O, C and N, depending on local temperature, i.e.\ position in the disk. The resulting planetary atmosphere will hence be extremely metal-poor in the first place. Late bombardment with left-over planetesimals \cite{Zhou2007,Bergin2013} will cause an element re-enrichment leading once more to a change of the atmospheric composition. The opacity of the atmosphere surrounding the planetary core plays an important role for the critical mass that inhibits further accretion \cite{hase2014}. Thus, the formation of gas giants via core-accretion means that, first, the ice and volatile elements segregate. Then the gas and icy dust evolves separately. Finally, the icy dust and the gas combine in a specific order, forming a planet. It would be a strange coincidence if all these complicated processes would result in gas giant surface element abundances that resemble those of their host stars. We should rather expect a large variety of the atmospheric element abundances of gas giants, depending on when and where the planets form. In this paper, we first study the segregation and evolution of gas and ice in protoplanetary disk models to predict the element abundances of the gas that will finally be accreted onto the proto-planets (Sect.~\ref{s:disk}). We show that the resulting carbon-to oxygen ratio (C/O) is expected to be larger than the primordial value, and increase further with time, in particular between the water snowline ($\approx\!150$\,K) and the CO ice-line ($\approx\!20$\,K), where mostly water freezes out. Similar results have been recently obtained in \cite{Oberg2011}, who schematically discussed the relative segregation of carbon, oxygen, and nitrogen in the disk, causing the C/O and C/H ratios to differ significantly from those of the host stars. Gaseous C/O ratios close to unity between the water and CO ice-lines, mainly driven by the formation of water, CO and CO$_2$ ices \cite{Oberg2011}. The time-dependent ice composition in the midplane of T\,Tauri disks has been studied by \cite{Chaparro2012a,Chaparro2012b}, who found agreement with measured chemical compositions of comets in their model, after long integration times (10\,Myrs) at 10\,AU, using a relatively high cosmic ray ionization rate of $5\times10^{-17}\rm\,s^{-1}$ and a sophisticated treatment of the secondary cosmic ray induced photo reactions, the rates of which are enhanced due to an increased ratio of UV gas absorption with respect to dust absorption, driven by dust growth with respect to interstellar conditions. We expect the metal-poor gas in protoplanetary disks to lead to unusual element abundances in planets, in particular the element abundances in gas giant atmospheres, although the dynamical details of the actual planet formation process need further investigation \cite{hase2014}. Tentative detections of carbon-rich planets have been announced, concerning the planets WASP\,12b and 55\,Cancri\,e, respectively \cite{Madhusudhan2011, Madhusudhan2012}. However, 65 orbits of WFC3-IR grism observations could not find any evidence for $\rm C/O\!>\!1$ in the atmosphere of WASP\,12b \cite{Swain2013}, as was reported \cite{Madhusudhan2011}. And in the case of 55\,Cancri\,e, is was shown that the abundance analysis of the host star 55\,Cancri \cite{Delgado2010} (used in \cite{Madhusudhan2012}) was probably erroneous due to a unsuitable choice of a zero-excitation oxygen line \cite{Nissen2013}. Most of the presently known extrasolar planets orbit somewhat metal-rich host stars \cite{buch12}. However, this simple relation holds only for giant gas planets, but not for Neptune-sized planets. It was argued that the Sun has a depletion of refractory to volatile elements of about 20\% with respect to planet-free solar twins \cite{mel09}. This abundance deficit roughly matches the mass of the terrestrial planets. One possible explanation for these deficiencies is to assume an early formation of $\sim 10$\,km bodies, which later formed the terrestrial planets before the majority of the Sun's mass (excluding the $\sim 10$ km bodies) was accreted from the proto-solar disk. The abundance peculiarities can also be found in solar-like stars that are known to have close-in giant planets \cite{mel09}. Our knowledge about the chemical composition of exoplanet atmospheres is prompted by transit observations of close-in planets, e.g.~\cite{cros2013, wil14, nik14}, or by bulk properties like global density estimates, e.g.~\cite{fort11}. Recent observation of the four directly imaged HD 8788 planets, however, suggest spectral diversity amongst co-eval objects of similar luminosity. The authors report on tentative detections of CH$_4$, C$_2$H$_2$, CO$_2$ and HCN \cite{opp13}. A more complete understanding of exoplanet atmospheres hinges on the detailed atmosphere modeling that must include cloud formation, photochemistry and global circulation. The element abundances are essential parameters to all those models, and a simple scaling of a metallicity parameter, e.g. from \cite{mos13,cros2013}, is far from realistic, as we will demonstrate in Sect.~\ref{s:cloudmod} of this paper. Planetary atmosphere chemistry does not only depend on the initial element abundances but also on the cloud formation process that depletes condensable elements and hence determines the remaining gas composition and radiative cooling processes. Cloud formation will impact all elements involved (Fe, Ti, Al, O, $\ldots$ \cite{hwt08, wit09}) and thereby change the C/O-ratio in such atmospheres (see Figs. 2 \& 3 in \cite{bi2013}). Cloud layers have a large impact on the atmospheric structure and the spectral appearance of ultra-cool low-mass objects, like brown dwarfs and planets. Thus, a direct abundance analysis of exoplanets like WASP\,12b, possibly with future instruments like JWST, must take these effects into account carefully. Different cloud models make different predictions for the remaining gas-phase abundances resulting in different molecular abundances \cite{hell08b}. Clouds are expected to occur in a variety of physical phases and chemical compositions, depending on temperature and pressure, from cold icy hazes, over liquid droplets, to hot solid gemstones. Beside temperature and pressure, the cloud formation process is controlled by the elemental composition of the atmospheric gas, which in turn is drastically reduced by the consumption of condensable elements into cloud particles and subsequent rain-out~\cite{hwt08}. Section~\ref{s:disk} summarizes the disk chemistry model that we use to predict gas and ice elemental abundances in proto-planetary disks. Section~\ref{s:cloudmod} introduces our model for planetary atmospheres and cloud formation. Inspired by the results of the disk models, we consider unusual element abundances, in particular large ratios $\rm C/O\!\lesssim\!1$ in young gas giant atmospheres. In Sect.~\ref{s:cloudeps}, we demonstrate that such non-standard oxygen abundances have a strong impact on the atmospheric structure and cloud properties in the atmosphere, like the cloud base, cloud particle number densities, and mean grain sizes. We further show that condensation of oxygen-rich dust may cause the C/O ratio to tip over locally, $\rm C/O\!>\!1$, and we show that the abundances of astrobiologically interesting molecules like H$_2$O, CH$_4$, NH$_3$, C$_2$H$_2$, C$_2$H$_6$ may increase near the cloud top. | \noindent We have discussed the chemical preconditions for planet formation in protoplanetary disks, with emphasis on the time-dependent segregation of carbon, nitrogen and oxygen into gas and ice phases. We obtained the following results: \begin{itemize} \item The segregation into gas and ice phases beyond the water ice-line (the ``snowline'') result in a rich variety of gaseous oxygen, carbon, and nitrogen abundances in the midplanes of protoplanetary disks, depending on time, position in the disk, and cosmic ray ionization rate. The resulting gas element abundances can vastly differ from that of the host star. \item Inside of the snowline ($\gtrsim\!150\,$K) all considered ice phases are thermally unstable, and the gas phase abundances remain primordial. \item Beyond the CO ice-line ($\lesssim\!20\,$K) oxygen, carbon and nitrogen freeze out quickly, and already after $\ll\!10^3\,$yrs, the outer midplane barely contains any molecules other than H$_2$. This may be different though, for the outermost midplane which is transparent to interstellar UV and X-ray irradiation, as well as for scattered stellar UV and X-ray irradiation. \item Between the snowline and the CO ice-line, a slow transition from O-rich to $\rm C/O\!\to\!1$ takes place, on timescales of $\sim$\,3\,Myrs. This timescale is related to the cosmic-ray induced un-blocking of O$_2$ and CO, and scales with the cosmic ray ionization rate assumed. \item For very long-lived protoplanetary disks, or disks exposed to an unusually high cosmic ray ionization rate, the carbon-to-oxygen ratio C/O would eventually exceed unity, leading to a sudden occurrence of organic molecules in the midplane, and providing the chemical pre-conditions for the formation of carbon planets. \end{itemize} Following the standard core-accretion model, it is this element-depleted gas that will be finally accreted onto the proto-planet in a rapid run-away phase, to eventually form the planetary atmosphere, although many difficult questions remain open, like the subsequent bombardment with left-over planetesimals, or the previous internal heating and outgasing of the planetesimals due to radioactive decay of $^{26}$Al. However, in agreement with \cite{Oberg2011}, we conclude that a super-solar C/O ratio (but $\rm C/O\!\lesssim\!1$) is the most likely result from the gas-ice segregation in the disk, between the snowline and the CO ice-line. In the remainder of this paper, we have studied how the cloud formation in young planetary atmospheres is affected by decreased oxygen abundances. Our results are applicable to directly imaged planets like HB~8799b,c,d,e, GQ Lupi or $\beta$ Pic b, and free-floating planets. But the issue of non-solar element abundances has biased also our understanding of the atmospheres of the large number of close-in, irradiated planets. Cloud formation depends strongly on the local element abundances involved (Fe, Ti, Si, O, $\ldots$) and it strongly affects the local elements by element depletion or enrichment. The consequence is a strong influence of the cloud formation on the local opacity, and hence on the atmosphere's temperature structure. The oxygen abundance has a strong impact on the seed particle formation rate which initiates the cloud formation process. The reduced number of seed particles leads to a lower number density of cloud particles which hence grow to larger sizes throughout most of the cloud in an atmosphere with $\rm C/O\!\lesssim\!1$. This sequence of processes leads to a more transparent haze layer on low-C/O planet compared to a solar abundance (or solar-abdundance scaled) atmospheres. However, an increasing oxygen abundance does not automatically cause more cloud particles to be formed because the nucleation rate is determined by the monomer density, not by the oxygen abundance alone. We further observe the appearance of a semi-detached cloud layer with C/O$\rightarrow$1. We conclude that the differences in element abundances with radial distance in protoplanetary disk have broad implications for the cloud properties in planetary atmospheres. The element abundances are, however not a multiple of the set of solar abundances. Using the results of our disk models as input for our cloud and chemistry calculation did only result in C/O $\approx 2$, and and we can not confirm element abundances in planetary atmospheres as high as 100x the solar values. Planetary atmospheres might still carry signatures of the initial abundances of the gas in the protoplanetary disks from which they were once formed. However, it seems difficult to detect these signatures from spectroscopy directly, because cloud formation changes the gaseous element abundances. We further have demonstrated that it is not straight-forward to argue for the formation of carbon-rich planets (Figs.~\ref{fig:epsDisk_UMIST2012},~\ref{fig:epsDisk_OSU2010}) and that some fine-tuning would be necessary in order to end up with a planet that exhibits spectral signatures typical for a carbon-rich gas. So far, only additional processes like element depletion by dust cloud formation and condensation adequately explain observations of planetary atmospheres rich in carbon-binding molecules. | 14 | 3 | 1403.4420 |
1403 | 1403.6613_arXiv.txt | Extreme UltraViolet images of the corona contain information over a large range of spatial scales, and different structures such as active regions, quiet Sun and filament channels contain information at very different brightness regimes. Processing of these images is important to reveal information, often hidden within the data, without introducing artifacts or bias. It is also important that any process be computationally efficient, particularly given the fine spatial and temporal resolution of \textit{Atmospheric Imaging Assembly} on the \textit{Solar Dynamics Observatory} (AIA/SDO) , and consideration of future higher-resolution observations. A very efficient process is described here which is based on localized normalizing of the data at many different spatial scales. The method reveals information at the finest scales, whilst maintaining enough of the larger-scale information to provide context. It also intrinsically flattens noisy regions and can reveal structure in off-limb regions out to the edge of the field of view. The method is also successfully applied to a white light coronagraph observation. | Extreme UltraViolet (EUV) observations currently provide the most important source of information on the low solar corona. As new EUV instruments are developed, the temporal, spatial and spectral resolution becomes ever finer, giving new insight on the coronal and chromospheric structure and dynamics. The \textit{Atmospheric Imaging Assembly} (AIA: \opencite{lemen2011}) aboard the \textit{Solar Dynamics Observatory} (SDO: \opencite{pesnell2012}) provides very fine temporal and spatial resolution of the Sun at multiple wavelengths, and is having a large impact on the field. Even as the community develop methods to digest the huge volume of data from AIA/SDO, new instruments are planned and tested with even finer resolution (e.g. \textit{High-Resolution Coronal Imager} (Hi-C), see \opencite{cirtain2013}). Despite the development of automated detection tools for EUV observations (e.g. \opencite{martens2012}), most scientific works begin from visual inspection of images. In particular, the volume of data provided by AIA/SDO is so high that low-resolution images are often used as a starting point to find features of interest. The higher-resolution data are then used for further analysis. Image processing is therefore an important step in analysing the data. The scientific return can be improved by the application of processing which better reveals features in the data, particularly in the early stages of analysis where visual inspection is most important. A common approach to process EUV images is simply to display the square root (or a gamma curve transformation), or alternatively the logarithm, of the original pixel values. This is a quick and easy way of reducing the dominance of the image contrast range by a few small bright regions. To reveal dynamic features, time-differencing is used, where a previous image is subtracted from the current image. Such simple processes are commonly used not due to the quality of the output, but due to their simplicity. More advanced image processing methods are not so commonly used due to their complexity and computational expense. Wavelet-based techniques have been used by \inlinecite{stenborg2003} and \inlinecite{stenborg2008} to greatly improve the visual information available from the \textit{Extreme Ultraviolet Imaging Telescope} (EIT: \opencite{Delaboudiniere1995}) aboard the \textit{Solar and Heliospheric Observatory} (SOHO) and the \textit{Extreme UltraViolet Imagers} (EUVI: \opencite{howard2002}) aboard the \textit{Solar Terrestial Relations Observatory} (STEREO: \opencite{kaiser2005}) . The technique involves the decomposition of images into different spatial scales, and the filtering/enhancements of features at the multiple resolutions. The technique is computationally expensive yet gives very good results. A less sophisticated yet very efficient technique to reveal features above the limb is based on techniques originally developed for coronagraphs \cite{morgan2006,druckmullerova2011}. Most relevant to this work is the recently-developed Noise Adaptive Fuzzy Equalization (NAFE) method \cite{druckmuller2013}. The method is inspired by adaptive histogram equalization, where local statistics govern the output value of a pixel. The method uses a fuzzy membership function of a Gaussian-weighted local set to enhance structural detail, preserve contextual detail, and to reduce noise. The NAFE method results in very clear images without artifacts and with excellent noise reduction. Its one downside is computational expense. This work summarizes the problems in visualising features in EUV images (Section \ref{observation}), introduces the new method (section \ref{method}), applies the method to several images from various instruments (section \ref{results}) and closes with a brief summary (section \ref{summary}). | \label{summary} The MGN method normalizes an image by using the local mean and standard deviation calculated using a Gaussian-weighted sample of local pixels. This normalised image is transformed by the $\arctan$ function (similar to a Gamma transformation). This is applied over several spatial scales, and the final image is a weighted combination of the normalized components. The results compare well with multiresolution wavelet enhancement or the NAFE procedure, but is far more computationally efficient. We hope that the MGN will become an established tool for researchers, offering a good compromise between computational time and clarity of the final images. The method is simple to implement, and the author is happy to provide the IDL code by email request. \begin{acks} We are grateful for comments by the anonymous referee which improved this work. Huw Morgan is grateful for funding from the Coleg Cymraeg Cenedlaethol to Prifysgol Aberystwyth and support of SHINE grant 0962716 and NASA grant NNX08AJ07G to the Institute for Astronomy, University of Hawaii. The work of Miloslav Druckm\"uller was supported by Grant Agency of Brno University of Technology, project FSI-S-11-3. We acknowledge the High resolution Coronal Imager instrument team for making the flight data publicly available. MSFC/NASA led the mission and partners include the Smithsonian Astrophysical Observatory in Cambridge, Mass.; Lockheed Martin's Solar Astrophysical Laboratory in Palo Alto, Calif.; the University of Central Lancashire in Lancashire, England; and the Lebedev Physical Institute of the Russian Academy of Sciences in Moscow. \end{acks} | 14 | 3 | 1403.6613 |
1403 | 1403.6878_arXiv.txt | We present a detailed investigation of the $\gamma$-ray emission in the vicinity of the supernova remnant (SNR) W28 (G6.4$-$0.1) observed by the Large Area Telescope (LAT) onboard the {\it Fermi Gamma-ray Space Telescope}. We detected significant $\gamma$-ray emission spatially coincident with TeV sources \A, B, and C, located outside the radio boundary of the SNR. Their spectra in the 2--100~GeV band are consistent with the extrapolation of the power-law spectra of the TeV sources. We also identified a new source of GeV emission, dubbed \W, which lies outside the boundary of TeV sources and coincides with radio emission from the western part of W28. All of the GeV $\gamma$-ray sources overlap with molecular clouds in the velocity range from 0 to 20~km~s$^{-1}$. Under the assumption that the $\gamma$-ray emission towards \A, B, and C comes from $\pi^0$ decay due to the interaction between the molecular clouds and cosmic rays (CRs) escaping from W28, they can be naturally explained by a single model in which the CR diffusion coefficient is smaller than the theoretical expectation in the interstellar space. The total energy of the CRs escaping from W28 is constrained through the same modeling to be larger than $\sim$~2~$\times$~10$^{49}$~erg. The emission from \W~can also be explained with the same CR escape scenario. | Diffusive shock acceleration (DSA) operating at the shocks of supernova remnants~\citep[SNRs;][and references therein]{Reynolds08} is the most likely mechanism to convert the kinetic energy released by supernova explosions into high energy particles (cosmic rays; CRs) that obey a power-law type distribution. Evidence of the CR proton acceleration in SNRs has emerged from the detection of GeV $\gamma$ rays from some SNRs interacting with molecular clouds such as W51C, W44, and IC 443~\citep{W51C,W44,IC443} by the Large Area Telescope (LAT) on board the {\it Fermi Gamma-ray Space Telescope}. The intense GeV emission from those SNRs is naturally explained by $\pi^0$ decay produced in inelastic collisions of the accelerated protons with dense gas. This was recently confirmed by the detection of the characteristic spectral feature produced by the decay of $\pi^0$s in W44 and IC 443~\citep{W44_AGILE, W44_Science}. In DSA theory, CRs accelerated at the shock are scattered by self-generated magnetic turbulence. Since the highest-energy CRs in the shock precursor at the upstream are prone to lack self-generated turbulence, they are expected to escape from the shock~\citep{Ptuskin03}. However, it has been unclear how the CRs escape from SNRs and propagate into the interstellar medium (ISM) because the interplay among the CRs, the magnetic turbulence, and the surrounding environment of SNRs is not well understood. If an SNR is in a dense environment, we can expect an enhancement of the $\pi^0$-decay $\gamma$ rays from molecular clouds illuminated by the escaping CRs in the vicinity of the SNR~\citep{Aharonian96,Gabici07}. For example, the $\gamma$-ray emissions near middle-aged SNRs G8.7$-$0.1 and W44 are naturally explained by the above scenario~\citep{G8.7,Uchiyama12}. The energy dependence of the diffusion coefficient of the CRs alters their spectrum, which affects the spectral shape of the resulting $\gamma$-ray emission~\citep{Aharonian96,Gabici09,Ohira11}. Thus, we can constrain the diffusion coefficient by measuring the wide-band $\gamma$-ray spectrum of the emission around SNRs. W28 (also known as G6.4$-$0.1) is a mixed-morphology SNR whose age is estimated to be (3.5--15)~$\times$~10$^4$~yr~\citep{Kaspi93}. In this paper, we adopted the same age of 4~$\times$~10$^4$~yr as used in~\citet{W28}. The SNR is located within a molecular cloud complex with a mass of 1.4~$\times$~10$^{6}$~$M_\odot$~\citep{Reach05} and interacts with some parts of the cloud, traced by the detection of OH (1720~MHz) masers~\citep{Frail94,Claussen97,Claussen99}. Observations of molecular lines placed W28 at a distance of $\sim$1.9~kpc~\citep{Velazquez02}. GeV $\gamma$-ray emission associated with W28 has been detected by the LAT and the Gamma-Ray Image Detector (GRID) onboard {\it AGILE}~\citep{Tavani08}. A natural explanation is the decay of $\pi^0$s due to the interaction of the cloud and CRs accelerated in the SNR~\citep{W28,AGILE_W28}. W28 is considered to have entered the radiative phase~\citep{Lozinskaya92} as indicated by optical filaments~\citep{Lozinskaya74}. Thus, we can expect that CRs have escaped into the surrounding ambient medium. H.E.S.S. observations of W28 have revealed four TeV $\gamma$-ray sources~\citep{Aharonian08}: HESS~J1801$-$233, located along the northeastern boundary of W28, and a complex of three sources, \A, B, and C, located to the south, outside the radio boundary. The southern H.E.S.S. sources spatially correspond with molecular clouds whose distances are consistent with that of W28~\citep{Aharonian08}, suggesting the possibility that their origins are due to runaway CRs from the SNR. Thus, this region is one of the best sites to study CR diffusion. Although \cite{W28} detected only one source associated with \B\ in the first year of observations, there are two LAT sources in the southern region listed in the second {\it Fermi}-LAT catalog~\citep[2FGL;][]{2FGL}. If the GeV and TeV emissions originate from CRs escaping from W28, we can constrain the diffusion coefficient of the particles in this region. In this paper, we report a detailed analysis of the LAT sources surrounding W28, based on 4 years of data. First, we give a brief description of the observations and data selection in Section~\ref{obs}. The analysis procedure and results are presented in Section~\ref{ana_res}, along with the spectra of the LAT sources. The discussion is given in Section~\ref{discussion} followed by conclusions in Section~\ref{conclusion}. | \label{conclusion} We analyzed the GeV $\gamma$-ray emission in the vicinity of SNR W28 using 4 years of LAT data. We detected GeV $\gamma$ rays spatially coincident with the TeV sources \A~, B, and C, located south of the radio boundary of W28. Their spectra in the 2--100~GeV band are consistent with the extrapolation of power-law emission from the TeV $\gamma$-ray sources. We also detected GeV emission from \W, located outside the boundary of the TeV emission and coinciding with radio emission from the western shell of W28. All of the GeV $\gamma$-ray sources overlap with the molecular clouds in the velocity range from 0 to 20~km~s$^{-1}$. Assuming that the $\gamma$-ray emissions from the three H.E.S.S. sources are due to the decay of $\pi^0$s produced by the interaction of the molecular clouds with CRs escaping from W28, the GeV--TeV spectra can naturally be explained by a single model. We constrain the diffusion constant at 10~GeV~c$^{-1}$ and the power-law index of the energy dependence to be 0.5--5~$\times$~10$^{27}$~cm$^2$~s$^{-1}$ and 0.1--0.35, respectively, with a negative correlation between them. These values are smaller and harder than those of the Galactic CR propagation model. Considering the masses of the molecular clouds responsible for the emission, the lower limit on the total energy of the escaped CRs is constrained to be $\sim$~2~$\times$~10$^{49}$~erg, in agreement with the conjecture that SNRs are the main sources of the Galactic CRs. The $\gamma$ rays from \W~can be also interpreted to be the emission originating from the interaction of the runaway CRs and molecular clouds with the same diffusion coefficient as obtained for the H.E.S.S. sources. | 14 | 3 | 1403.6878 |
1403 | 1403.1496_arXiv.txt | Using the {\it Hubble Space Telescope}/Advanced Camera for Surveys data in the COSMOS field, we systematically searched clumpy galaxies at $0.2<z<1.0$ and investigated the fraction of clumpy galaxies and its evolution as a function of stellar mass, star formation rate (SFR), and specific SFR (SSFR). The fraction of clumpy galaxies in star-forming galaxies with $M_{\rm star} > 10^{9.5} M_{\odot}$ decreases with time from $\sim 0.35$ at $0.8<z<1.0$ to $\sim 0.05$ at $0.2<z<0.4$ irrespective of the stellar mass, although the fraction tends to be slightly lower for massive galaxies with $M_{\rm star} > 10^{10.5} M_{\odot}$ at each redshift. On the other hand, the fraction of clumpy galaxies increases with increasing both SFR and SSFR in all the redshift ranges we investigated. In particular, we found that the SSFR dependences of the fractions are similar among galaxies with different stellar masses, and the fraction at a given SSFR does not depend on the stellar mass in each redshift bin. The evolution of the fraction of clumpy galaxies from $z\sim 0.9$ to $z\sim0.3$ seems to be explained by such SSFR dependence of the fraction and the evolution of SSFRs of star-forming galaxies. The fraction at a given SSFR also appears to decrease with time, but this can be due to the effect of the morphological K-correction. We suggest that these results are understood by the gravitational fragmentation model for the formation of giant clumps in disk galaxies, where the gas mass fraction is a crucial parameter. | In the present universe, most bright galaxies have regular and symmetric morphologies, which can be classified in the framework of the Hubble sequence \citep{hub36}. On the other hand, using the high-resolution imaging capability of the {\it Hubble Space Telescope} ($HST$), it has been found that many star-forming galaxies at $z>1$ have irregular shapes with asymmetric structures, (e.g., \citealp{cow95}; \citealp{ste96}; \citealp{kaj01}; \citealp{elm07}; \citealp{cam11}). Although these high-redshift irregular galaxies show a variety of morphologies, they commonly have giant (kpc scale) star-forming clumps (e.g., \citealp{elm09a}; \citealp{for11}). Recent NIR integral field spectroscopy observations of star-forming clumpy galaxies at $z\sim2$ revealed that a significant fraction of these galaxies show coherent rotation with a relatively large turbulent velocity in their ionized gas kinematics (e.g., \citealp{for06}; \citealp{wri07}; \citealp{gen08}; \citealp{cre09}; \citealp{for09}). Several studies of the radio CO line observations also found that actively star-forming galaxies at $1\lesssim z \lesssim 3$ have large gas mass fractions of $\sim 0.3$ -- 0.8 (\citealp{dad10}; \citealp{tac10}; \citealp{tac13}). While some of these galaxies are galaxy mergers (e.g., \citealp{som01}; \citealp{lot04}; \citealp{pue10}), these results can be explained by theoretical models where gas-rich rotational disks are gravitationally unstable for the fragmentation and lead to the formation of giant star-forming clumps (e.g., \citealp{nog98}; \citealp{imm04}; \citealp{bou07}; \citealp{dek09}). The high gas mass fraction of these galaxies is considered to be maintained by the rapid and smooth cosmic infall of gas along large-scale filaments. Since the accretion rate of gas is expected to decrease with time, especially at $z\lesssim 1$, the gas fraction of these clumpy galaxies declines at lower redshifts as the gas consumption by the star formation proceeds, which results in the stabilization of the gas disks \citep{cac12}. In this view, these high-redshift clumpy galaxies are considered to be progenitors of normal (disk) galaxies at low redshifts. Therefore, it is important to study the evolution of these clumpy galaxies in order to understand the formation process of normal galaxies in the present universe. However, the number of systematic surveys for clumpy galaxies is very limited, because wide-field imaging data with high spatial resolution are required. While \cite{elm07} claimed that clumpy galaxies are dominated at high redshift based on the morphological analysis of galaxies in the HUDF field, \cite{tad14} reported that $\sim $40\% of 100 H$\alpha$ emitters at $z\sim 2.2$ and $z\sim 2.5$ in the UKIDSS/UDS-CANDELS field show clumpy morphologies. \cite{wuy12} measured the fraction of clumpy galaxies in star-forming galaxies with $M_{\rm star} > 10^{10} M_{\odot}$ at $z\sim2$ in the GOODS-South field, and found that the fraction is 74\% for clumps selected at the rest-frame 2800 \AA\ and 42\% for those selected at the rest-frame $V$ band, which suggests that the morphological K-correction can be important for the selection of clumpy galaxies. Although systematic surveys of clumpy galaxies at lower redshifts are also important for understanding the connection between clumpy galaxies at high redshifts and normal galaxies in the nearby universe, there is few survey for clumpy galaxies at $z\lesssim 1$. In this paper, we systematically search clumpy galaxies at $0.2<z<1.0$ in the COSMOS field \citep{sco07} and investigate their physical properties. The high spatial resolution images taken with $HST$/Advanced Camera for Surveys (ACS) over the very wide field allow us to construct a large sample of clumpy galaxies at $z<1$ and to investigate the fraction of clumpy galaxies and its evolution as a function of physical properties such as stellar mass and star formation rate for the first time. Section \ref{sec:ana} describes our sample and details of the selection method for clumpy galaxies. We present the physical properties of clumpy galaxies and investigate the fraction of these galaxies and its evolution in Section \ref{sec:result}. In Section \ref{sec:dis}, we summarize our results and discuss their implications. Throughout this paper, magnitudes are given in the AB system. We adopt a flat universe with $\Omega_{\rm matter}=0.3$, $\Omega_{\Lambda}=0.7$, and $H_{0}=70$ km s$^{-1}$ Mpc$^{-1}$. \begin{figure*} \begin{center} \includegraphics[width=180mm]{f1.ps} \caption{ $HST$/ACS $I_{\rm F814W}$-band images of galaxies with more than two components as a function of the flux ratios among the brightest three clumps in each galaxy. $f_{\rm 2}/f_{\rm 1}$ is the ratio between the second brightest and the brightest clumps, while $f_{\rm 3}/f_{\rm 2}$ is that between the third and second brightest clumps. The red line shows the criteria for clumpy galaxies ($f_{\rm 2}/f_{\rm 1} \ge 0.3$ \& $f_{\rm 3}/f_{\rm 2} \ge 0.3$). These galaxies are randomly selected from those with each range of the parameters. } \label{fig:monclump} \end{center} \end{figure*} \begin{figure*} \begin{center} \includegraphics[width=170mm]{f2.ps} \caption{ Examples of clumpy galaxies in the redshift bins. Galaxies are randomly selected in each redshift bin and are shown in the order of their stellar mass. The number in each panel shows $\log(M_{\rm star}/M_{\odot})$. } \label{fig:clumpy} \end{center} \end{figure*} \begin{figure*} \begin{center} \includegraphics[width=170mm]{f3.ps} \caption{ The same as Figure \ref{fig:clumpy} but for non-clumpy galaxies. } \label{fig:nonclumpy} \end{center} \end{figure*} \begin{figure*} \begin{center} \includegraphics[width=50mm,angle=-90]{f4_1.ps} \includegraphics[width=50mm,angle=-90]{f4_2.ps} \caption{ SFR vs. stellar mass for clumpy galaxies (top panels) and non-clumpy galaxies (bottom panels) in each redshift bin. The dashed line shows a constant SSFR of 0.1 Gyr$^{-1}$, above which galaxies are classified as star-forming ones. } \label{fig:mstar} \end{center} \end{figure*} | \label{sec:dis} In this study, we constructed a large sample of clumpy galaxies at $0.2<z<1.0$ in the COSMOS field using the $HST$/ACS data and investigated the fraction of these galaxies and its evolution as a function of stellar mass, SFR, and SSFR. This is the first systematic search for clumpy galaxies at $z<1$. Our main results are as follows. \begin{itemize} \item The fraction of clumpy galaxies in star-forming galaxies decreases with time from $\sim 0.35$ at $0.8<z<1.0$ to $\sim 0.05$ at $0.2<z<0.4$ irrespective of stellar mass, although the fraction tends to be slightly lower at $M_{\rm star}>10^{10.5} M_{\odot}$ in each redshift bin. \item The fraction of clumpy galaxies increases with increasing both SFR and SSFR in all the redshift ranges we investigated. In particular, the SSFR dependences of the fractions are similar among galaxies with different stellar masses. Moreover, the fraction at a given SSFR does not depend on stellar mass in each redshift bin. \item The fraction of clumpy galaxies at a given SSFR decreases with time at $SSFR > 0.1$ Gyr$^{-1}$. This can be explained by the effect of the morphological K-correction. \end{itemize} We discuss these results and their implications for both origins and evolution of clumpy galaxies in the following subsections. \subsection{SSFR dependence of the fraction of clumpy galaxies} We found that the fraction of clumpy galaxies increases with increasing both SFR and SSFR. The similar fractions at a given SSFR among galaxies with different stellar masses may indicate that the SSFR is more important and fundamental physical parameter for the origin of the clumpy morphology. Among previous studies on clumpy galaxies, \cite{bou12} studied 14 clumpy galaxies and 13 smooth disk galaxies at $z\sim0.7$ selected by an eyeball classification, and found that the average and median SSFRs of clumpy galaxies are higher than those of smooth disk galaxies. \cite{sal12} also reported that clumpy galaxies at $0.5<z<1.3$ have systematically higher SSFRs than the other star-forming galaxies at the same redshifts. They selected clumpy galaxies with a quantitative clumpiness parameter, but their measurement of the clumpiness includes the surface brightness fluctuation on relatively small scales. The SSFR dependence of the fraction of clumpy galaxies seen in Figure \ref{fig:msfrac} is consistent with the results of these previous studies, although the selection methods for clumpy galaxies are different among the studies. Since the SSFR is a current birth rate of stars relative to the integrated past star formation rate, it can be considered to represent the evolutionary stages of the stellar mass assembly by the star formation. In this view, the relatively high SSFRs of clumpy galaxies indicates that these galaxies may be systematically in younger stages in their star formation history. We can also consider the SSFR as a proxy for the gas mass to stellar mass ratio, M$_{\rm gas}$/M$_{\rm star}$, if we naively assume that the SFRs of galaxies roughly reflect their gas mass. Clumpy galaxies are expected to be (probably young) objects with relatively high gas mass fraction in this case. Recently, the gravitational instability and fragmentation in gas-rich disks is often proposed as a possible origin of the clumpy morphology of high-redshift galaxies, which show both coherent rotation and relatively large velocity dispersion in their gas (e.g., \citealp{imm04}; \citealp{bou07}; \citealp{dek09}; \citealp{bou10}; \citealp{gen12}). Gas-rich rotational disks are gravitationally unstable for the fragmentation and lead to the formation of large clumps. In this framework, the gas mass fraction is a key physical parameter. The stability for the gravitational fragmentation of the disks and the maximum unstable mass scale strongly depend on the gas mass fraction (e.g., \citealp{esc08}; \citealp{cac12}). If the SSFR is closely related to the gas mass fraction, the strong SSFR dependence of the fraction of clumpy galaxies in Figure \ref{fig:msfrac} can be explained by the relationship between the gravitational fragmentation and the gas mass fraction of the rotational disks. \cite{esc11} also discussed that a large maximum unstable mass of gas-rich disks corresponds to a large velocity dispersion of turbulent motions of gas in the self-regulated quasi-stationary state with the Toomre parameter $Q\sim1$. They also claimed that the large velocity dispersion can cause an enhancement of star formation activity. In fact, the correlation between the mass of the most massive clump of galaxies and their surface SFR density has been observed at $z\gtrsim 1$ (\citealp{liv12}; \citealp{swi12}). This scenario may explain the relatively higher SSFRs of clumpy galaxies. Another possible origin of the clumpy morphology is the galaxy merger (e.g., \citealp{som01}; \citealp{lot04}). For example, \cite{dim08} performed extensive numerical simulations of major mergers and found that gas-rich major mergers can cause the greater disk fragmentation than the cases of isolated gas-rich galaxies. Morphological studies of high-redshift galaxies and comparisons of these objects with merger galaxies in the nearby universe suggested that some fraction of clumpy and irregular galaxies at $z\gtrsim 1$ are ongoing mergers (e.g., \citealp{lot08}; \citealp{pet09}; \citealp{ove10}). \cite{man13} suggested that a non-negligible fraction of large clumps in high-redshift clumpy galaxies come from minor mergers, based on a numerical cosmological simulation of disk galaxies. \cite{pue10} reported that a significant fraction of intermediate-mass clumpy galaxies at $z\sim0.6$ have complex kinematics, which is compatible with major mergers. In this scenario, the SSFR dependence of the fraction of clumpy galaxies can be understood by the enhancement of star formation caused by the galaxy mergers. The galaxy interaction/merger does not only cause disturbed and clumpy morphologies, but also triggers intense star formation. Thus the SSFRs of clumpy galaxies tend to be enhanced from the main sequence of star-forming galaxies. However, it is unclear whether such starbursts by mergers are consistent with the relatively tight SFR-M$_{\rm star}$ relation or not (e.g., \citealp{noe07}; \citealp{elb07}; \citealp{ren09}; \citealp{wuy11}; \citealp{rod11}). \begin{figure} \begin{center} \includegraphics[width=90mm]{f11.eps} \caption{{\bf left:} Evolution of the fraction of clumpy galaxies in star-forming galaxies ($SSFR > 0.1$ Gyr$^{-1}$) with different stellar masses. {\bf right:} The same as the left panel but for all galaxies with $I_{\rm F814W} < 22.5$ including passively evolving galaxies. } \label{fig:down} \end{center} \end{figure} \subsection{Evolution of the fraction of clumpy galaxies} We found that the overall fraction of clumpy galaxies in star-forming galaxies with $M_{\rm star} > 10^{9.5} M_{\odot}$ decreases from $\sim 0.35$ at $z\sim0.9$ to $\sim 0.05$ at $z\sim0.3$. While many actively star-forming galaxies with clumpy morphologies have been observed at $z>1$ (e.g., \citealp{elm07}; \citealp{gen08}; \citealp{for11}), most relatively bright galaxies belong to the Hubble sequence and clumpy galaxies are very rare at $z\sim0$ (e.g., \citealp{ove10}). Our result naturally connects between these previous studies in the early universe and those in the nearby universe, although the morphological K-correction may affect the result (Section \ref{sec:bias}). \cite{wuy12} reported that the fraction of clumpy galaxies in star-forming galaxies at $z\sim1$ is 27 \% when the selection for clumps was performed at the rest-frame $V$ band. Our result at $0.8<z<1.0$ ($\sim 30$\%), which was obtained at the rest-frame $B$ band (see Section \ref{sec:bias}), is consistent with their result, although the selection criteria for clumpy galaxies are different. Several authors pointed out that the clumpy morphology persists to lower redshifts in lower-mass galaxies, so called ``down-sizing effect'' in the clumpy morphology (e.g., \citealp{elm09b}; \citealp{elm11}). There are many bright/massive clumpy galaxies at $z\gtrsim1$, while such clumpy morphology can be seen only in low-mass systems such as dwarf irregular galaxies in the present universe. In Figure \ref{fig:down}, we show the evolution of the fraction of clumpy galaxies with different stellar masses in order to investigate the down-sizing effect. The evolution is similar among the different mass samples, while the fraction of clumpy galaxies is slightly lower in massive galaxies with $M_{\rm star} > 10^{10.5} M_{\odot}$. The differences of the fraction among galaxies with different masses become larger when we include passive galaxies with $SSFR < 0.1$ Gyr$^{-1}$ into the samples (the right panel of Figure \ref{fig:down}). If we extrapolate the trend in Figure \ref{fig:down} to the present, the fraction of clumpy galaxies in more massive galaxies is expected to become negligible earlier. Therefore, our result is not inconsistent with the down-sizing picture, but the mass dependence of the evolution is weak in the stellar mass range we investigated. The lower fraction of clumpy galaxies in massive star-forming galaxies with $M_{\rm star} > 10^{10.5}M_{\odot}$ at each redshift may be explained by lower SSFR of these massive galaxies (Figure \ref{fig:msbias}). \begin{figure} \begin{center} \includegraphics[width=90mm]{f12.ps} \caption{ Fraction of clumpy galaxies in star-forming galaxies with $M_{\rm star} > 10^{10} M_{\odot}$ and the fractions of barred spiral galaxies from \cite{she08} as a function of redshift. Diamonds show the fraction of all barred spiral galaxies, while triangles represent that of strong barred galaxies. These fractions of barred galaxies are measured in face-on spiral galaxies with inclination angles of $i > 65^\circ$ (see \citealp{she08} for details). } \label{fig:bar} \end{center} \end{figure} Another our result of the SSFR dependence of the fraction of clumpy galaxies seen in all the mass and redshift ranges indicates that the evolution of the SSFRs of galaxies leads to the evolution of the fraction of clumpy galaxies. In fact, the median SSFR of star-forming galaxies decreases by $\sim 1$ dex from $z\sim 0.9$ to $z\sim 0.3$ (Figure \ref{fig:msfrac}). For example, if we assume the relation between the fraction of clumpy galaxies and SSFR at $0.8<z<1.0$ shown in Figure \ref{fig:fssfr}, the decrease of the SSFR from $SSFR \sim 10^{0.25}$ Gyr$^{-1}$ (median value at $z\sim0.9$) to $SSFR \sim 10^{-0.75}$ Gyr$^{-1}$ (that at $z\sim0.3$) corresponds to the evolution of the fraction from $\sim 0.35$ to $\sim 0.05$. Thus the evolution of the fraction of clumpy galaxies in star-forming galaxies at $0.2<z<1.0$ appear to be explained by the evolution of the SSFR. On the other hand, from such correlation between the fraction of clumpy galaxies and SSFR, the fraction of clumpy galaxies is expected to be higher at higher redshifts, because galaxies tend to have higher SSFRs than those at $z\lesssim1$. \cite{wuy12} found that the fraction of clumpy galaxies in star-forming galaxies with $M_{\rm star} > 10^{10} M_{\odot}$ at $1.5<z<2.5$ is 42\% when the morphological selection was done at the rest-frame $V$ band. \cite{tad14} also reported that 42\% of H$\alpha$ emitters at $z\sim 2.2$ and 2.5 have clumpy morphology, although their clump selection was performed with both rest-frame UV and optical-bands images. The average SSFRs of star-forming galaxies at $z\sim2$ in both studies are $\sim 10^{0.5}$ Gyr$^{-1}$, and therefore the fractions of clumpy galaxies of $\sim 40$\% in these studies seem to be consistent with the relation between the fraction of clumpy galaxies and SSFR at $0.8<z<1.0$ shown in Figure \ref{fig:fssfr}. In the gravitational fragmentation model for the formation of giant clumps in disk galaxies, the rapid and smooth streams of gas along filaments effectively penetrate halos of galaxies at high redshift (e.g., \citealp{ker05}; \citealp{dek09b}). This ``cold accretion'' keeps active star formation and a high gas mass fraction of these galaxies, which leads to the formation of the clumpy morphology. In fact, such high gas mass fraction of star-forming galaxies at $z\sim2$ have been observed (e.g., \citealp{dad10}; \citealp{tac13}), and the observed high turbulent velocity of gas in high-redshift clumpy galaxies also supports this scenario (e.g., \citealp{cre09}; \citealp{for09}). Using an analytic model, \cite{cac12} predicted that such disks tend to stabilize at $z \lesssim 1$ mainly due to the decrease of the gas mass fraction. They suggested that the decrease is attributed to the gradual decline of the cosmological accretion rate into halos of galaxies with time (e.g., \citealp{gen08}), the gas consumption by the star formation, the inflows of clumps into the center of galaxies by the gravitational torque (e.g, \citealp{dek09}), and the gas outflows by the supernova feedback. If the SSFRs of galaxies are closely related to the gas mass fraction as discussed above, the evolution of the fraction of clumpy galaxies at $0.2<z<1.0$ could be explained by this scenario. The decrease of the gas mass fraction with time at $z\lesssim 1$ causes the stabilization of galactic disks, while it also leads to the decrease of the SSFRs of these galaxies. Interestingly, several studies reported that the fraction of barred spiral galaxies increases with time in the same redshift range (e.g., \citealp{abr99}; \citealp{she08}; \citealp{mel14}). The bar instability is considered to occur in ``mature''systems where stellar disk is dynamically cold and rotationally supported, and the surface stellar density is sufficiently high. Clumpy galaxies may evolve to these barred galaxies when the gas fraction becomes lower and the stellar disk is stabilized (e.g., \citealp{imm04}; \citealp{she12}; \citealp{kra12}). In Figure \ref{fig:bar}, we compare the fraction of clumpy galaxies with the fraction of barred spiral galaxies in the same COSMOS field from \cite{she08}. Note that since the bar fraction in \cite{she08} is the fraction of barred galaxies in face-on spiral galaxies with $i > 65^\circ$ excluding irregular galaxies, it is difficult to directly compare the absolute values of the both fractions. Nevertheless, we can see the fraction of barred spiral galaxies increases with time, as the fraction of clumpy galaxies decreases in the figure. The transition from clumpy galaxies to barred spiral galaxies may gradually occur from $z\sim1$ to $z\sim0$. \begin{figure} \begin{center} \includegraphics[width=90mm]{f13.ps} \caption{ Comparison between the observed fraction of clumpy galaxies and that expected from wet major merger rate by \cite{lop13}. The solid lines show the major merger rate multiplied by a time scale of 3, 4, 5, and 6 Gyr, while the dashed line represents that multiplied by a time scale of 0.5 Gyr. } \label{fig:merger} \end{center} \end{figure} On the other hand, in the major merger scenario for the origin of the clumpy morphology, the evolution of the major merger rate may explain the evolution of the fraction of clumpy galaxies at $0.2<z<1.0$. Many observational studies have found that the major merger rate decreases with time at $z\lesssim 1$ (e.g., \citealp{lef00}; \citealp{con03}; \citealp{lin08}; \citealp{der09}; \citealp{xu12}; see also \citealp{lot11}). In particular, several studies reported that the gas-rich wet major merger, which is considered to be important for making the clumpy morphology \citep{dim08}, decreases with time in the redshift range (\citealp{cho11}; \citealp{pue12}; \citealp{lop13}). Figure \ref{fig:merger} compares the observed fraction of clumpy galaxies at $0.2<z<1.0$ with that expected from the wet major merger rate of galaxies with $M_{\rm star} \sim 10^{10}-10^{10.5} M_{\odot}$ by \cite{lop13}. We multiplied the major merger rate from \cite{lop13} by an arbitrary time scale when the merged galaxies are seen as clumpy galaxies to estimate the expected fraction of clumpy galaxies. The evolution of clumpy galaxies can be roughly explained by the evolution of the major merger rate with the time scales of $\sim$ 3--6 Gyr. However, these time scales seem to be too long for the merger time scale during which the morphology is disturbed and clumpy (e.g., \citealp{dim08}; \citealp{lot10}). If we assume a typical merger time scale of $\sim 0.5$ Gyr, the expected fraction of clumpy galaxies become much lower than the observed fraction at $z\gtrsim 0.5$ (the dashed line in Figure \ref{fig:merger}). It seems to be difficult to explain the fraction of clumpy galaxies at $0.2<z<1.0$ only by the wet major merger. Finally, we note that the fraction of clumpy galaxies at a given SSFR decreases with time from $z\sim 0.9$ to $z\sim0.3$. This can be due to the morphological K-correction because we selected clumpy galaxies at the observed $I_{\rm F814W}$ band as discussed in Section \ref{sec:bias}. If this is the case, the intrinsic fraction of clumpy galaxies at a given SSFR could not depend on redshift. There may be the universal relation between the fraction of clumpy galaxies and SSFR. \vspace{1pc} We would like to thank the anonymous referee for valuable comments and suggestions. We also thank Tsutomu T. Takeuchi at Nagoya University for his generous support to K. L. M. and for useful discussion. The HST COSMOS Treasury program was supported through NASA grant HST-GO-09822. We greatly acknowledge the contributions of the entire COSMOS collaboration consisting of more than 70 scientists. This work was financially supported in part by the Japan Society for the Promotion of Science (Nos. 17253001, 19340046, 23244031, and 23740152). | 14 | 3 | 1403.1496 |
1403 | 1403.3487_arXiv.txt | {}{ We compute the emergent stellar spectra from the UV to far infrared for different viewing angles using realistic 3D model atmospheres for a large range in stellar parameters to predict the stellar limb darkening. }{We have computed full 3D LTE synthetic spectra based on 3D radiative hydrodynamic atmosphere models from the \textsc{Stagger}-grid in the ranges: $T_{\mathrm{eff}}$ from $4000$ to $7000\,\mathrm{K}$, $\log g$ from $1.5$ to $5.0$, and $\left[\mathrm{Fe}/\mathrm{H}\right]$, from $-4.0$ to $+0.5$. From the resulting intensities at different wavelength, we derived coefficients for the standard limb darkening laws considering a number of often-used photometric filters. Furthermore, we calculated theoretical transit light curves, in order to quantify the differences between predictions by the widely used 1D model atmosphere and our 3D models. }{The 3D models are often found to predict steeper darkening towards the limb compared to the 1D models, mainly due to the temperature stratifications and temperature gradients being different in the 3D models compared to those predicted with 1D models based on the mixing length theory description of convective energy transport. The resulting differences in the transit light curves are rather small; however, these can significant for high-precision observations of extrasolar transits, and are able to lower the residuals from the fits with 1D limb darkening profiles. }{We advocate the use of the new limb darkening coefficients provided for the standard four-parameter non-linear power law, which can fit the limb darkening more accurately than other choices.} | } The emergent intensity across the surface of late-type stars diminishes gradually from the center of the stellar disk towards the edge (limb), since the optical depth depends on the angle of view. Rays crossing the stellar photosphere near the limb reach optical depth unity in layers at higher altitude and at typically lower densities and temperatures than rays crossing the stellar disk near the center. The intensity is very sensitive to the temperature, therefore, one observes darker brightness from the limb, which emerges from higher and cooler regions of the stellar atmosphere. This effect is known as limb darkening \citep{Gray2005oasp.book.....G}. An accurate knowledge of the surface brightness distribution is essential for the analysis of light curves from stars with transiting objects in the line of sight, such as exoplanets and eclipsing stellar companions in binary systems. Furthermore, the precise determination of stellar angular diameters with stellar interferometry relies also on the theoretical limb darkening predictions \citep{Davis2000MNRAS.318..387D}. The variation in surface intensity with angular distance from the stellar disk center is usually expressed in the form of limb darkening laws \citep{Claret:2000p12465}. Multiple functional basis have been used in the past, from simple linear to higher order non-linear laws, in order to fit the surface brightness variations predicted by theoretical model atmospheres leading to so-called limb darkening coefficients (LDC). For example, the individual shape of a light curve for transiting exoplanets is important, because it contains information about the structure of the external layers of the occulted stellar object \citep[e.g.,][]{Southworth:2008p23114}. The observed light curves are interpreted by comparisons with theoretical transit light curves that are based on limb darkening predictions arising from model atmospheres. More accurate theoretical atmosphere models will reduce the uncertainties in the comparison, and thereby improving the quality of the analysis in favor of other transit-parameters like planet-to-star ratio or the inclination of the orbit. Also, the goodness of the transmission-spectroscopy of exoplanet atmospheres relies on the underlying theoretical atmospheres of the host stars \citep[e.g.,][]{Seager:2000p14757}. The first estimates of the intensity variation over the disk were performed with a simple linear law \citep{Milne1921MNRAS..81..361M}. However, with theoretical 1D model atmospheres it was shown that a linear law is insufficient to describe the limb darkening of a real star adequately \citep[e.g.,][]{vanHamme:1993p22403}. Then, various alternatives with a two-parameter law was introduced starting from a quadratic, over square root to a logarithmic, and finally an exponential law \citep[e.g. see][]{DiazCordoves:1995p22374,Claret:1995p22394}. These restricted functional bases are only marginally accurate for a certain range in effective temperatures, therefore, \citet{Claret:2000p12465} introduced a new non-linear power law with four coefficients, which is powerful enough to fit the LDC for a broad range in stellar parameters, while conserving the flux to a high accuracy. Later on, limb darkening variations were fitted and provided for the community derived from extensive grids with the latest model atmospheres (e.g, \textsc{MARCS, ATLAS} and \textsc{PHOENIX}) for several broad band filters, e.g. the SDSS \citep{Claret:2004p12494}, Kepler and CoRoT \citep{Sing:2010p21961}. An extensive comparison of the various limb darkening laws has been performed by \citet{Southworth:2008p23114}. All of these developments revealed that a well-considered choice of an appropriate functional basis is mandatory for a precise description of the intensity variations. The next step in improving the systematic errors prevailing in the predicted limb darkening laws was yielded in the underlying model atmospheres, since the limb darkening is mainly determined by the temperature gradient \citep[see][]{Knutson:2007p22139,Hayek:2012p21944}. Therefore, flaws in the theoretical atmospheric temperature stratification will directly propagate into the predicted limb darkening. The hydrostatic 1D models make use of several simplifications, the most prominent one being the use of the mixing length theory to account for convective energy transport \citep{BohmVitense:1958p4822}. Cool late-type stars feature a convective envelope, thereby convective motions are present in the thin photospheric transition region due to overshooting of convective flows. These stars exhibit a typical granulation pattern in its emergent intensity due to inhomogeneities arising from the asymmetric up- and downflowing stellar plasma. Therefore, only 3D atmosphere models are able to predict these properties accurately. With the advent of 3D atmosphere modeling \citep{Nordlund:1982p6697}, which solves from first-principle the hydrodynamic equations coupled with a realistic radiative transfer, the deficiencies of the 1D models were revealed and quantified \citep[e.g.,][ and references therein]{Nordlund:2009p4109}. Comparisons of the 3D models with the Sun showed that these models can predict accurately the intensity distribution \citep{Pereira:2013arXiv1304}, while 1D models overestimate the limb darkening of our resolved host star. \citet{Bigot:2006p23513} studied the limb darkening of $\alpha$ Centauri B by comparing its interferometrically observed visibility curves with theoretical predictions. The latter is sensitive to the limb darkening, and they found an significant improvement with the predictions from 3D models. Furthermore, \citet{Hayek:2012p21944} showed on the basis of the extremely accurately measured light curves of the transiting exoplanet HD 209458 that the intrinsic residuals of the 1D models can be resolved with the more realistic 3D model atmospheres. The largest differences were found close to the limb, hence during the ingress and egress of the transition. With 1D model predictions, the well-studied close-orbit Jupiter-like transit planet HD 209458 exhibited priorly systematic residuals due to the simplified treatment of convection leading to insufficient temperature stratifications \citep[see][]{Knutson:2007p22139}. For another well-studied star, Procyon, and four K giants \citet{Chiavassa:2010p6257,Chiavassa:2012p22493} could also find the limb darkening and stellar diameter predictions to be coherent with independent asteroseismic observations \citep[see also][]{AllendePrieto:2002p22280,Aufdenberg2005ApJ...633..424A}. After the first detection of a Jupiter-like extra solar planet through radial velocity detection \citep{Mayor:1995p23118}, five years later, eventually a transiting exoplanet around a solar-like star was also found \citep{Charbonneau:2000p22468}. These spectacular landmark discoveries triggered literally a gold-rush in the hunt for new exoplanets. With advanced satellite missions, like Kepler and CoRoT, nowadays up $1491$ transiting extra solar planets have been detected \citep{Wright2011PASP..123..412W}. Both of the mentioned satellite missions operate in the visible spectral range, therefore, the effects of limb darkening are strong. These sophisticated observations evoke rightfully a demand in more accurate theoretical limb darkening predictions. In order to fulfill this call, we present in this work LDCs derived from realistic full 3D synthetic spectra based on a comprehensive grid of 3D RHD atmosphere models. In Sects. \ref{sec:Methods} and \ref{sec:Deriving-limb-darkening}, we explain the methods we utilized to obtain the LDC. Subsequently, the resulting theoretical limb darkening variations (Sec. \ref{sec:Limb-darkening-laws}) and transit light curves (Sec. \ref{sec:Transit-light-curves}) are presented and discussed. We compare our results with previous predictions from 1D ATLAS models in Sec. \ref{sec:Comparison-with-1D}. Finally, we conclude our findings in Sec. \ref{sec:Conclusions}. | } We derived on the basis of the \textsc{Stagger}-grid, a large grid of 3D RHD atmosphere models, the limb darkening coefficients for the various bi-parametric and non-linear limb darkening laws. The four-parameter non-linear power law introduced by \citet{Claret:2000p12465} is the only limb darkening law that is sufficiently versatile to express the intensity distribution with an excellent accuracy, while all other limb darkening laws are insufficient, in particular at the limb. Therefore, we recommend the use of the four-parameter functional basis only, in particular for the comparison with high-precision measurements in the hunt of extrasolar planets. We discussed the limb darkening in the Kepler filter for various stellar parameters, and outlined systematical variations that exposed the complex changes of the brightness distribution, in particular with the effective temperature. We compared also our new LDC with predictions from widely used 1D ATLAS models, and the largest differences are given towards the limb. The 1D models are often brighter than 3D predictions, only for giant models with solar-metallicity we find opposite differences. Furthermore, we displayed the systematic (anti-)correlations between the coefficients $a_{k}$ between half-integer and integer exponents of the four-parameter law. We found the coefficient of linear limb darkening law, $u$, to scale with the temperature gradient and the Planck function. Theoretical transit light curves indicate similar systematical differences between 1D and 3D as the limb darkening variations implied, which are relatively small. However, as observations indicate \citep{Knutson:2007p22139,Hayek:2012p21944}, these can be measured with high-precision observations. Therefore, we advise to use of of the new LDC. | 14 | 3 | 1403.3487 |
1403 | 1403.2212_arXiv.txt | {The Hertzsprung-Russell diagram is an essential diagnostic diagram for stellar structure and evolution, which has now been in use for more than 100 years. } {We introduce a new diagram based on the gravity-effective temperature diagram, which has various advantages. } {Our spectroscopic Hertzsprung-Russell (sHR) diagram shows the inverse of the flux-mean gravity versus the effective temperature. Observed stars whose spectra have been quantitatively analyzed can be entered in this diagram without the knowledge of the stellar distance or absolute brightness. } {Observed stars can be as conveniently compared to stellar evolution calculations in the sHR diagram as in the Hertzsprung-Russell diagram. However, at the same time, our ordinate is proportional to the stellar mass-to-luminosity ratio, which can thus be directly determined. For intermediate- and low-mass star evolution at constant mass, we show that the shape of an evolutionary track in the sHR diagram is identical to that in the Hertzsprung-Russell diagram. We also demonstrate that for hot stars, their stellar Eddington factor can be directly read off the sHR diagram. For stars near their Eddington limit, we argue that a version of the sHR diagram may be useful where the gravity is exchanged by the effective gravity. } {We discuss the advantages and limitations of the sHR diagram, and show that it can be fruitfully applied to Galactic stars, but also to stars with known distance, e.g., in the LMC or in galaxies beyond the Local Group. } | The Hertzsprung-Russell (HR) diagram has been an important diagram for the understanding of stellar evolution for more than a hundred years (Nielsen 1964). Hertzsprung (1905) and later independently Russell (1919) realized that the knowledge of the absolute brightness of stars together with their spectral type or surface temperature allowed fundamentally different types of stars to be distinguished. Hertzsprung and Russell had already realized that the apparent stellar brightness was insufficient to draw conclusions, but that the absolute brightnesses, i.e., the distances, are required to properly order the stars in the HR diagram. Order can also be achieved for stars in star clusters where the distance may still be unknown, but the distances of all stars are roughly equal, in what we now call color-magnitude diagrams because the apparent and absolute brightness differences are equal. Hertzsprung and Russell pointed out that the HR diagram contains information about the stellar radii, with the giant sequence to be found at a larger brightness but similar surface temperatures to the cools stars of the dwarf or main sequence. And indeed, it remains one of the main advantages of the quantitative HR diagram that stellar radii can be immediately determined, thanks to the Stefan-Boltzmann law. Later, with the advent of stellar model atmosphere calculations, it became possible to quantitatively derive accurate stellar surface gravities (see, e.g., Auer and Mihalas 1972 and references therein). This allowed stars to be ordered in the surface gravity-effective temperature ($g-T_{\rm eff}$) diagram (sometimes called the Kiel diagram), since a larger surface gravity for stars of a given surface temperature can imply a larger mass (Newell 1973, Greenstein and Sargent 1974). The main advantage of the $g-T_{\rm eff}$ diagram is that stars can be compared to stellar evolution predictions without the prior knowledge of their distance (a first example is given in Kudritzki 1976). However, the radius or any other stellar property can not be directly identified from the $g-T_{\rm eff}$ diagram. Moreover, the comparison with stellar evolution calculations is often negatively affected by the relatively large uncertainties of the spectroscopic gravity determinations. In this paper, we want to introduce a diagnostic diagram for stellar evolution which combines the advantages of the Hertzsprung-Russell and of the $g-T_{\rm eff}$ diagram. We introduce the spectroscopic Hertzsprung-Russell (sHR) diagram in Sect.~2 and compare it with the Hertzsprung-Russell and the $g-T_{\rm eff}$ diagram in Sect.~3. We discuss stars with changing mass and helium abundance in Sect.~4, and focus on stars near the Eddington limit in Sect.~5, and on low- and intermediate-mass stars in Sect.~6. Finally, we give an example for the application of the sHR diagram in Sect.~7, and close with concluding remarks in Sect.~8. | 14 | 3 | 1403.2212 |
|
1403 | 1403.0956_arXiv.txt | The observations of jet breaks in the afterglows of short gamma-ray bursts (SGRBs) indicate that the jet has a small opening angle of $\lesssim 10^{\circ}$. The collimation mechanism of the jet is a longstanding theoretical problem. We numerically analyze the jet propagation in the material ejected by double neutron star merger, and demonstrate that if the ejecta mass is $\gtrsim 10^{-2} M_{\odot}$, the jet is well confined by the cocoon and emerges from the ejecta with the required collimation angle. Our results also suggest that there are some populations of choked (failed) SGRBs or low-luminous new types of event. By constructing a model for SGRB 130603B, which is associated with the first kilonova/macronova candidate, we infer that the equation-of-state of neutron stars would be soft enough to provide sufficient ejecta to collimate the jet, if this event was associated with a double neutron star merger. | \label{sec:intro} \begin{figure} \vspace{15mm} \epsscale{0.9} \plotone{cartoon2.eps} \caption{The schematic picture of the NS-NS merger scenario for SGRBs. Phase (I): Inspiral phase of NS-NS binary. Phase (II): The mass ejection by the coalescence of NS-NS, and a hypermassive star (HMNS) is formed as a merger remnant, which expels further material from the system. Phase (III): The HMNS collapses to a black hole, and forms the black hole plus torus system. Phase (IV): The central engine starts to operate and the jet propagates through the ejecta. \label{f1}} \end{figure} \begin{table*} \centering \caption{\label{tab:model} Models} \begin{tabular}{lcccccccccc} \hline\hline Model~~ & ~$M_{\rm{ej}}$ ($M_{\odot}$)\tablenotemark{a}~ & ~$t_{\rm{i}}$ (ms)\tablenotemark{b}~ & ~$\theta_{0}$ ($^{\circ}$)\tablenotemark{c}~ & ~$L_{\rm{j50}} $\tablenotemark{d}~ & ~$r_{\rm{esc}}$ ($10^{8}$cm)\tablenotemark{e}~ & ~$r_{\rm{max}}$ ($10^{8}$cm)\tablenotemark{f}~ & ~$t_{\rm{b}}$ (ms)\tablenotemark{g}~ & ~$r_{\rm{b}}$ ($10^{9}$cm)\tablenotemark{h}~ & ~$\theta_{\rm{ave}}$ ($^{\circ}$)\tablenotemark{i}~ \\ \hline {\sl M-ref} & $10^{-2}$ & 50 & 15 & 2 & 1.2 & 6.1 & 231 & 3.7 & 5.4 \\ {\sl M-L4} & $10^{-2}$ & 50 & 15 & 4 & 1.2 & 6.1 & 195 & 3.2 & 5.4 \\ {\sl M-th30} & $10^{-2}$ & 50 & 30 & 2 & 1.2 & 6.1 & 626 & 8.9 &5.8 \\ {\sl M-th45} & $10^{-2}$ & 50 & 45 & 2 & 1.2 & 6.1 & - & - & - \\ {\sl M-ti500} & $10^{-2}$ & 500 & 15 & 2 & 5.6 & 60.1 & 899 & 17.5 & 10.1\\ {\sl M-M3} & $10^{-3}$ & 50 & 15 & 2 & 1.2 & 6.1 & 105 & 2.0 & 12.6 \\ {\sl M-M2-2} & 2 $\times 10^{-2}$ & 50 & 15 & 2 & 1.2 & 6.1 & 320 & 5.0 & 4.7 \\ {\sl M-M1} & $10^{-1}$ & 50 & 15 & 2 & 1.2 & 6.1 & 750 & 11.0 & 3.4 \\ \hline\hline \end{tabular} \tablecomments{(a) Ejecta mass, (b) Onset timing of jet injection, (c) Initial jet opening angle, (d) Jet power ($L_{\rm{j50}} \equiv L_{\rm{j}}/(10^{50}$erg/s)), (e) Escape radius, (f) Dynamical ejecta front at the time of jet injection, (g) jet breakout time, (h) the radius where the jet head reaches the edge of the ejecta, (i) $\theta_{\rm{ave}}$ at the end of simulations.} \end{table*} Recent afterglow observations of short gamma-ray bursts (SGRBs) have provided various information about their environments which can be interpreted as circumstantial evidence linking SGRBs with mergers of compact binaries such as double neutron stars (NS-NS) \citep{1986ApJ...308L..43P,1986ApJ...308L..47G,1989Natur.340..126E} and black hole-neutron star (BH-NS) (see \cite{2013arXiv1311.2603B} for a latest review). On the other hand, the compact binary merger scenario is challenged by the detection of jet breaks in the afterglow of some SGRBs and the deduced small jet opening angle of $\lesssim 10^{\circ}$ \citep{2006ApJ...650..261S,2006ApJ...653..468B,2011A&A...531L...6N,2012ApJ...756..189F,2013arXiv1309.7479F}. The formation of such a collimated jet in compact binary merger has not been clarified yet (see e.g., \citet{2005A&A...436..273A,2012MNRAS.419.1537B}). One of the most interesting features in the latest numerical-relativity simulations \citep{2013PhRvD..87b4001H} is that NS-NS mergers in general are accompanied by a substantial amount of dynamical mass ejection. Interestingly, the excess in near-IR band observed by {\it Hubble Space Telescope} in {\it Swift} SGRB 130603B (\citet{2013Natur.500..547T,2013ApJ...774L..23B}) is explained by the kilonova/macronova model \citep{1998ApJ...507L..59L,2010MNRAS.406.2650M,2013ApJ...774...25K,2013ApJ...775...18B,2013arXiv1307.2943G,2013ApJ...775..113T} provided that a large amount of mass $\gtrsim 2 \times 10^{-2} M_{\odot}$ is ejected in the NS-NS merger and it is powered by the radioactivity of r-process nuclei \citep{2013ApJ...778L..16H,2013Natur.500..547T,2014arXiv1401.2166P}. Such massive ejecta will have a large impact on the dynamics of the jet and the observed collimation could be naturally explained by their interactions. In this {\it Letter}, we numerically investigate the jet propagation in the material ejected by double neutron star mergers based on a scenario indicated both by our latest numerical-relativity simulations and the observations of SGRB 130603B. The scenario is summarized as follows (see Fig.\ref{f1}). \begin{itemize} \item According to latest numerical relativity simulations adopting equations of state (EOSs) which are compatible with the recent discovery of massive neutron stars with $M\sim 2M_{\odot}$ \citep{2010Natur.467.1081D,2013Sci...340..448A}, a hypermassive neutron star (HMNS) is the canonical outcome formed after the NS-NS merger for the typical binary mass ($2.6$--$2.8 M_{\odot}$) \citep{2011PhRvL.107e1102S,2013PhRvD..87b4001H,2013ApJ...773...78B}. \item During and after the merger a large amount of mass $\mathrm{O}(0.01 M_{\odot})$ is ejected (phase (II)) . This size of ejecta is required to explain the kilonova candidate associated with SGRB 130603B. According to our numerical-relativity simulations \citep{2013PhRvD..87b4001H}, the morphology of the ejecta is quasi spherical for the case of the HMNS formation. In particular, the regions along the rotational axis is contaminated significantly by the mass ejection. \item Such a large amount of mass can be ejected only if the EOS of neutron-star matter is relatively soft \citep{2013PhRvD..87b4001H,2013PhRvD..88d4026H,2013ApJ...773...78B}. In this case, the massive NS formed after the merger is expected to collapse to a BH {\it within several tens of milli seconds} (phase (III)), forming a massive torus around it. \item After the formation of the BH-torus system, a jet would be launched and it propagates through the expanding merger ejecta (phase (IV)). A SGRB will be produced only if the jet successfully breaks out of the ejecta. \end{itemize} Note that our scenario is different from that explored by previous studies \citep{2005A&A...436..273A} based on the Newtonian studies \citep{1999A&A...341..499R}, in which the mass ejection is not isotropic but is concentrated along the orbital plane. In this case, there will be little interaction with the jet and ejecta, and no collimation by the ejecta is expected. Indeed, \citet{2005A&A...436..273A} found no strong collimation by the disk wind (see also \citet{2000PhRvL..85..236L}), since their simulations were carried out in rather dilute ejecta ($< 10^{-3} M_{\odot}$). After studying the dynamics of the jet in the presence of the expanding ejecta, we discuss the canonical model for explaining a particular event, SGRB 130603B. With the observationally consistent parameter set, we show that relativistic jets successfully break out of the dynamical ejecta and travel with the required collimation angle. | \label{sec:summary} In this {\it letter}, we investigate the jet propagation in the dynamical ejecta after the NS-NS merger. Similar to the collapsar model, the interaction between the jet and the merger ejecta generates the hot cocoon and the jet undergoes collimation at least by the deepest and densest layers of the ejecta, which is qualitatively consistent with the criterion $\tilde{L} \lesssim \theta_{0}^{-4/3}$. Importantly, models except for quite large initial opening angle ($\theta_{0}=45$) succeed in the breakout with smaller opening angle than the initial one. We also, for the first time, show the possibility that there are some populations for the choked SGRBs or low-luminous new types of event. Using only the duration of the prompt emission, the jet opening angle, and ejecta mass, we argue for the canonical model for SGRB 130603B. Under the assumption of spherically symmetric ejecta, {\sl M-M2-2} model satisfies all observational constraints. In reality, however, the ejecta profile is not exactly spherically symmetric, and its mass contained in the equatorial region tends to be larger. According to this, the ejecta mass in the realistic system would be larger than in our spherical models by a factor of a few. Therefore, {\sl M-ref} and {\sl M-L4} could also be candidates for SGRB 130603B \citep{2013ApJ...778L..16H,2013Natur.500..547T,2014arXiv1401.2166P}. The result of this study and \citet{2013ApJ...778L..16H} suggest that the EOS of neutron stars may be soft among several models of EOS with its maximum mass $> 2 M_{\odot}$ if the central engine of this SGRB is a NS-NS merger. The required condition for the central engine is that the jet should be collimated $ \lesssim 15^{\circ}$ before reaching the ejecta, and its life time should be $\sim 300$ms with $L_{\rm{j}} \gtrsim 2 \times 10^{50}$erg/s as the average jet power, and the time lag between merger and jet launching should not be much longer than several tens of milli seconds. As discussed in this {\it{letter}}, the cocoon confinement changes the conventional picture of jet propagation for the production of SGRBs, and reinforces the scenario of NS-NS binary merger for SGRBs. In BH-NS merger, the morphology of dynamical ejecta is non-spherical, i.e, concentrates on the equatorial plane (see \citet{2013PhRvD..88d1503K}), so the jet never undergoes the strong collimation unless neutrino or magnetic driven winds from the accretion disk provide enough baryons in the polar region. | 14 | 3 | 1403.0956 |
1403 | 1403.0398_arXiv.txt | Extensive optical and ultraviolet (UV) observations of the type Ia supernova (SN Ia) 2012fr are presented in this paper. It has a relatively high luminosity, with an absolute $B$-band peak magnitude of about $-19.5$ mag and a smaller post-maximum decline rate than normal SNe Ia [e.g., $\Delta m _{15}$($B$) $= 0.85 \pm 0.05$ mag]. Based on the UV and optical light curves, we derived that a $^{56}$Ni mass of about 0.88 M$_{\sun}$ was synthesized in the explosion. The earlier spectra are characterized by noticeable high-velocity features of \ion{Si}{2} $\lambda$6355 and \ion{Ca}{2} with velocities in the range of $\sim22,000$--$25,000$ km s$^{-1}$. At around the maximum light, these spectral features are dominated by the photospheric components which are noticeably narrower than normal SNe Ia. The post-maximum velocity of the photosphere remains almost constant at $\sim$12,000 km s$^{-1}$ for about one month, reminiscent of the behavior of some luminous SNe Ia like SN 1991T. We propose that SN 2012fr may represent a subset of the SN 1991T-like SNe Ia viewed in a direction with a clumpy or shell-like structure of ejecta, in terms of a significant level of polarization reported in \citet{Maund12frp}. | \label{sect:Intro} Type Ia supernovae (SNe Ia) are widely accepted as the results of thermonuclear explosion of accreting carbon-oxygen white dwarf (WD) with a mass close to the Chandrasekhar limit ($\sim$1.4 M$_{\odot}$) in a binary system \citep{HiNi,Bow12,Maoz14}. They play important roles in many aspects of astrophysics, especially in observational cosmology because of their use as distance indicators probing the expansion history of the universe \citep{Riess98,Schmidt98,Perl99}. Observationally, most of the SNe Ia show strikingly similar photometric and spectroscopic behavior (i.e., \citealp{Sun96,Filip97}), and the remained scatter can be better understood in terms of an empirical relation between light-curve width and luminosity (i.e., \citealp{Phillip93}). Nevertheless, there is increasing evidence for the observed diversity that cannot be explained with such a relation. The representative subclasses include: (1) overluminous group like SN 1991T characterized by weak \ion{Si}{2} absorption and prominent iron in the near-maximum light spectra \citep{Filip92a,Phillip92}; (2) underluminous events like SN 1991bg that exhibit strong \ion{Si}{2} $\lambda$5972 and $\sim$4000\AA~Ti features (i.e.,\citealp{Filip92b,Ben05}); (3) peculiar objects like SN 2002cx which have extremely low ejecta velocities and luminosities \citep{Li02cx}; (4) super-Chandrasekhar mass SNe Ia like SN 2007if \citep{Scalzo} and SN 2009dc\citep{Silver11}, which are characteristic of extremely high luminosity but relatively low expansion velocity. In addition, there are also reports of circumstellar interaction in some SNe Ia such as SN 2002ic \citep{Hamuy} and PTF 11kx \citep{Dilday}, though their classifications are still controversial because of bearing similarities to type IIn supernovae. The existence of above peculiar subtypes indicate that there are possibly multiple channels leading to SN~Ia explosions. Besides peculiar SN Ia events, specific classification schemes have recently been proposed to highlight the diversity of relatively normal SNe Ia. For example, \citet{Ben05} found that normal SNe Ia can be further subclassified by the temporal velocity gradient of the \ion{Si}{2} $\lambda$6355 line, i.e., the group with a high-velocity gradient (HVG) and the group with a low-velocity gradient (LVG). Based on the equivalent width (EW) of the absorption features of \ion{Si}{2} $\lambda$5972 and \ion{Si}{2} $\lambda$6355, \citet{Branch06,Branch09} suggested dividing the SN Ia sample into four groups: cool (CL), shallow silicon (SS), core normal (CN), and broad line (BL); the CL and SS groups mainly consist of peculiar objects like SN 1991bg and SN 1991T, respectively. \citet{Wang09a} proposed using the expansion velocity of the \ion{Si}{2} $\lambda$ 6355 line to distinguish the subclass with a higher \ion{Si}{2} velocity (HV) from that with a normal velocity (NV). In spite of different criteria adopted in these classifications, the respective subsamples show some overlap with each other. For example, the FAINT subclass from \citet{Ben05} tend to match the SN 1991bg/CL subclass. The HV subclass overlap with the BL and the HVG ones, as suggested by the Berkeley and CfA spectral datasets of supernova \citep{Blondin12,Silver12}. In particular, the HV SNe Ia are found to have redder $\bv$ colors \citep{Wang09a} and different locations within host galaxies in comparison to the NV ones \citep{Wang13}, suggesting that the properties of their progenitors may be different. SN 2012fr is a type Ia supernova discovered at a relatively young phase in nearby galaxy NGC 1365 \citep{Klotz,CEBT3277}. Owing to its brightness, extensive follow-up observations were performed in multi-wavebands for this object immediately after the discovery. Childress et al. (2013, hereafter C13) have presented observations of earlier optical spectra for SN 2012fr, showing clear signatures of high-velocity features (HVFs) that are detached from the photospheric components. After comparing with subclasses of SNe Ia defined in different classification schemes, they suggested that SN 2012fr may represent a transitional event between nominal spectroscopic subclasses of SN Ia, with important dissimilarities with the overluminous SN 1991T-like subclass of SNe Ia. \citet{Maund12frp} presented the spectropolarimetric observations of this object, spanning from $-$11 days to +24 days with respect to $B$-band maximum light. They found that the high-velocity components of the spectral features are highly polarized in the earlier phases but the polarization decreases as these features become weaker. However, the continuum polarization for the SN is always low $<$0.1\%, suggestive of an overall symmetry of the photosphere for SN 2012fr. In this paper, we present extensive optical and ultraviolet (UV) observations of SN 2012fr. The large dataset of SN 2012fr can help us further understand diversity of SNe Ia, its physical origin, and impact on cosmological applications. The paper is organized as follows. Observations and data reductions are described in Section \ref{sect:obs}. Section \ref{sect:LV} presents the UV and optical light and color curves, while Section \ref{sect:Spe_analy} presents the spectral evolution. In Section \ref{sect:Discu} we constructed the bolometric luminosity of SN 2012fr and discussed its classification. The conclusions are given in Section \ref{sect:con}. | \label{sect:con} We have presented the ultraviolet and optical observations of SN 2012fr from the $Swift$ UVOT and the Li-Jiang 2.4-m telescope. Our observations show that SN 2012fr is a luminous SN Ia. The maximum bolometric luminosity deduced from the UV and optical light curves is $(1.82\pm 0.15) \times 10^{43}$ erg s$^{-1}$, corresponding to a synthesized nickel mass of 0.88 $\pm$ 0.08 M$_{\sun}$. Generally, the spectral evolution of SN 2012fr show some similarities to the HV SNe Ia in the early phase because of showing detached HVFs but it becomes more similar to the 91T-like subclass in the near-maximum and later phases. In the very earlier phases, strong HVFs are present in the \ion{Ca}{2} IR triplet, \ion{Ca}{2} H\&K, and \ion{Si}{2} $\lambda$6355 lines at velocities of 22,000--25,000 km s$^{-1}$. The absorption of \ion{Si}{2} and \ion{Ca}{2} formed from the photosphere has a velocity of 12,000 km s$^{-1}$ and exhibits an unusually narrow line profile. A comparison with other SNe Ia indicates that SN 2012fr is characterized by narrow-lined, photospheric component near the maximum light. We found that the SNe Ia similar to SN 2012fr are usually slow-decliners with $\Delta m_{15}$ (B)$\lesssim$ 1.0 mag, and they show a large overlap with the members of the shallow-silicon/SN 1991T-like subclasses in the Branch et al. and Wang et al. classification schemes. These results, together with the asymmetric high-velocity material, suggest that SN 2012fr may represent a subset of 91T-like SNe Ia viewed at different angles. A larger sample of SN 2012fr-like explosions with very early spectral observations as well as polarization measurements will help us understand the frequency of objects that show detached HVFs and their geometry (e.g., Childress et al. 2014), which will finally enable us to set stringent constraints on the nature of the progenitor system for some particular types of SNe~Ia. | 14 | 3 | 1403.0398 |
1403 | 1403.5268_arXiv.txt | We consider the ability of three models -- impacts, captures, and collisional cascades -- to account for a bright cloud of dust in Fomalhaut b. Our analysis is based on a novel approach to the power-law size distribution of solid particles central to each model. When impacts produce debris with (i) little material in the largest remnant and (ii) a steep size distribution, the debris has enough cross-sectional area to match observations of Fomalhaut b. However, published numerical experiments of impacts between 100~km objects suggest this outcome is unlikely. If collisional processes maintain a steep size distribution over a broad range of particle sizes (300~\mum\ to 10~km), Earth-mass planets can capture enough material over 1--100~Myr to produce a detectable cloud of dust. Otherwise, capture fails. When young planets are surrounded by massive clouds or disks of satellites, a collisional cascade is the simplest mechanism for dust production in Fomalhaut b. Several tests using HST or JWST data -- including measuring the expansion/elongation of Fomalhaut b, looking for trails of small particles along Fomalhaut b's orbit, and obtaining low resolution spectroscopy -- can discriminate among these models. | \label{sec: intro} Fomalhaut b is a faint object orbiting at a distance of $\sim$ 120~AU from the nearby A-type star Fomalhaut. Originally detected on {\it Hubble Space Telescope} (HST) images at 0.6~\mum\ and 0.8~\mum\ \citep{kalas2008}, the source lies inside the orbits of a bright belt of dust particles at 130--150~AU from the central star \citep[e.g.,][]{holl2003,stap2004,kalas2005,marsh2005,ricci2012,acke2012,boley2012,su2013}. Recent re-analyses of the original HST data confirm the detections at 0.6--0.8~\mum\ and identify the source on images at 0.435~\mum\ \citep{currie2012,galich2013}. New optical HST data recover the object in 2010--2012 \citep{kalas2013}. In all of these studies, the optical colors are similar to those of the central star. Despite the robust optical data, Fomalhaut b is not detected at infrared (IR) wavelengths. Attempts to identify the source have failed at 1.25~\mum\ \citep{currie2012}, 1.6~\mum\ \citep{kalas2008,currie2013}, 3.6--3.8~\mum\ \citep{kalas2008,maren2009}, and 4.5~\mum\ \citep{maren2009,janson2012}. Each upper limit lies well above the IR fluxes expected for an object with the optical-infrared colors of an A-type star. Although the brighter IR fluxes expected from a 2--10~\mjup\ (Jupiter mass) planet are excluded by these data, the IR data are consistent with emission from lower mass planets \citep[e.g.,][]{janson2012,currie2012}. However, the measured optical fluxes in Fomalhaut b are a factor $\gtrsim$ 100 larger than expected for a 1~\mjup\ planet at a distance of 7.7 pc from the Earth \citep[e.g.,][]{currie2012}. Thus, the optical flux requires a different source. Without a clear IR detection, the simplest explanation for the emission from Fomalhaut b is scattered light from an ensemble of dust grains with a collective cross-sectional area of roughly $10^{23}$ cm$^2$ \citep[e.g.,][]{kalas2008}. A single, high velocity collision between two objects with radii of 10--1000~km is a plausible source for the dust \citep{wyatt2002,kb2005,kalas2008,galich2013,kalas2013}. In this picture, the collision disperses objects with sizes ranging from a fraction of a micron to tens of meters or kilometers \citep[see, for example, the discussions in][]{wyatt2002,kb2005}. A collisional cascade within a circumplanetary cloud \citep{kw2011a} or debris disk \citep{kalas2008} is another plausible source of dust grains in Fomalhaut b \citep[e.g.,][] {currie2012,galich2013,kalas2013}. In this model, dynamical processes place a massive cloud of satellites around a newly-formed 1--100~\mearth\ planet \citep[e.g.,][]{nesv2007}. Subsequent collisions among 1--100~km satellites produce copious amounts of dust \citep[e.g.,][]{bottke2010,kw2011a}. Aside from the nature of the collisions, this mechanism probably produces dust grains with properties similar to those derived from a single giant impact. Material continuously captured from Fomalhaut's circumstellar disk provides a third source for dust in Fomalhaut b. In this picture \citep[e.g.,][]{ruskol1961,ruskol1963,ruskol1972}, material orbiting Fomalhaut loses energy and is captured by a massive planet. Collisions among captured objects produce a cloud of dust grains orbiting the planet. If the grains within this disk remain small, their properties are probably similar to dust produced in a single collision or in a collisional cascade. In this paper, we develop a framework for analyzing dusty clouds of debris and apply this framework to available data for Fomalhaut b. We begin in \S2 with a summary of relevant data for this system. In \S3, we consider a novel approach for deriving properties of the debris from the observed cross-sectional area (\S3.1) and apply this approach to dust produced in a giant impact (\S3.2), captured from the protoplanetary disk (\S3.3), and generated in a collisional cascade (\S3.4). After exploring uncertainties, tests, and improvements of these mechanisms for dust production (\S4), we conclude with a brief summary (\S5). | In \S3, we considered three generic models -- impacts, captures, and collisional cascades -- for the origin of a cloud of dust in Fomalhaut b. In the simplest model, a single giant impact within the circumstellar disk produces an expanding cloud of dust orbiting the central star. As another simple alternative, dynamical processes during the earliest stages of planet formation leave a massive cloud or disk of solid particles surrounding a planet. Collisions among the largest satellites maintain a swarm of dust particles around the planet. The capture model is an interesting combination of these ideas, where a planet continuously captures the debris from giant impacts within its Hill sphere. If the cloud of debris becomes massive enough, a balance between material gained through capture and lost by a collisional cascade sets the properties of the circumplanetary dust cloud. Each of these models makes predictions for the mass and cross-sectional area of the dust cloud. Our analysis in \S3 establishes these predictions. To summarize the constraints on each model, we collect the derived parameters for the slope of the dust size distribution ($q$) and the maximum radius of the size distribution (\rmax, for captures and cascades) or the radii of two impactors ($R_1$). For simplicity, we consider steps of 0.2 in $q$ and 0.25 in log radius. The open symbols in Fig.~\ref{fig: summary} show combinations of $q$ and $\rmax, R_1$ which match the observed $\ab \approx 10^{23}$~cm$^2$. Although the allowed parameter space is broad, simple physical arguments limit the parameter space considerably. For giant impact models (\S3.2), collisions among pairs of objects with $R \gtrsim$ 100~km happen too rarely. Collisions among smaller objects occur more often, but standard collision outcomes produce debris with too little cross-sectional area to match observations. Non-standard outcomes with little debris in large particles can match the observed area with large $q$. Current numerical experiments of collisions suggest this option is improbable \citep[e.g.,][]{durda2004,lein2012}. Thus, giant impacts seem an implausible way to produce a dust cloud in Fomalhaut b. Capture models appear somewhat more viable (\S3.3). Earth-mass planets orbiting Fomalhaut at 120~AU can attract up to $10^{23}$~g of solids in 100~Myr. If this material maintains a steep size distribution, then the cross-sectional area of the cloud matches observations of Fomalhaut b. Although many combinations of $q$ and \rmax\ yield a model \ad\ which can match the observed \ab\ for \md\ $\approx 10^{21} - 10^{23}$~g, the collision time precludes models with $q \gtrsim$ 4.6. When $q$ is too large, the largest particles have short collision times. Short collision times limit the mass of the cloud to $M_d \lesssim 10^{21}$~g, which is insufficient to produce the observed \ab\ with \rmin\ $\approx$ 10--1000~\mum. With this constraint, we limit the allowed parameter space to the four filled diamonds in Fig.~\ref{fig: summary}. Collisional cascade models are also reasonable \citep[\S3.4, see][]{kw2011a}. Within the allowed parameter space, size distributions with \rmax\ $\gtrsim$ 500~km can maintain the cascade for the age of Fomalhaut. In systems with smaller \rmax\ and larger $q$, there is too little material in the most massive objects. Thus, the cascade cannot survive for the 200--400~Myr age of Fomalhaut. Discounting these options limits the allowed parameter space to the three filled circles in Fig.~\ref{fig: summary}. Within $(q, \rmax)$ space, there are two main regions. Collisional cascade models permit $q \approx$ 3.5--3.7 and $\rmax \approx$ 500--3000~km. Systems with smaller $q$ require larger \rmax. Capture models allow $q \approx$ 4.0--4.6 and $\rmax \approx$ 2--50~km. Systems with smaller $q$ require larger total mass. Both of these pictures require 1--10 Earth-mass planets. Our analysis strongly favors these options over a giant impact. Plausible giant impacts occur too rarely, require unlikely collision outcomes, or both. These conclusions generally agree with previously published results. For giant impacts, \citet{kalas2005} and \citet{tamayo2013} derive similarly low probabilities for collisions among 100--1000~km objects. Although \citet{galich2013} revise the collision probability upward, their estimate is based on the surface density of material within the belt. Given the newly measured trajectory of Fomalhaut b \citep{kalas2013,beust2014} and the short lifetime of the debris cloud, any giant impact capable of producing Fomalhaut b must occur at distances $r \lesssim$ 120~AU where the surface density is at least a factor of six smaller than in the belt (\S2.1). Thus, the \citet{galich2013} estimate of the collision frequency is overly optimistic. Compared to \citet{galich2013}, our approach to the outcomes of high velocity collisions between two protoplanets yields more ejected mass but less surface area. By using approximations appropriate for cratering collisions between a small object and a much larger one, \citet{galich2013} underestimate dust production from collisions between objects with roughly equal masses (\S3.2). With the ejected mass known, \citet{galich2013} set \rmin, \rmax, and $q = 3.5$ to yield the observed area. Our estimates for \ad\ hinge on numerical experiments which derive the size of the largest fragment as a function of the ejected mass. After associating the size of the largest fragment with \rmax, we derive \ad\ as a function of $q$. Despite the larger ejected mass, this approach yields much larger \rmax\ and much smaller \ad. Given current collision theory \citep[e.g.,][and references therein]{lein2012}, our results seem more realistic. Discriminating between the two methods requires new numerical experiments of high velocity collisions. Coupled with recent dynamical results, our collision analysis in \S3.2 enables stronger limits on the impact hypothesis. \citet{tamayo2013} infers that collisions between two large objects are unlikely to lead to the large $e$ orbit in Fomalhaut b. He favors a collision between a small planetesimal and a much larger protoplanet already on a large $e$ orbit. However, collisions between one small and one large object produce enough dust only when the large object has $R \gtrsim$ 1000~km (\S3.2). These collisions are very unlikely. Along with the need to produce the apparent apsidal alignment of Fomalhaut b and the main belt, these constraints challenge our ability to develop a viable impact model \citep[e.g.,][]{tamayo2013,beust2014}. Capture models applied to Fomalhaut b have a limited history. \citet{kw2011a} consider capture of material which strikes the central planet and ejects dust from the planet's surface. Based on our analysis, we agree with their conclusion that the cross-section of a 1--10~\mearth\ planet is too small to accrete enough mass for the Fomalhaut b dust cloud. Our results in \S3.3 generally confirm their estimates for the amount of mass ejected in the collision. In our picture, the larger cross-section of the Hill sphere enables a larger capture rate. Both approaches ignore likely captures from circumstellar material striking orbiting satellites \citep{durda2000,stern2009,poppe2011}; this process likely adds captured material to the circumplanetary environment. Addressing the viability of this model in more detail requires numerical simulations. Finally, we agree with previous studies supporting the collisional cascade model \citep{kw2011a,galich2013,kalas2013,tamayo2013}. Most studies derive similar properties for the central planet, 1--100~\mearth, and the surrounding circumplanetary cloud, $\sim$ 0.01~\mearth. The stability, surface area, and lifetime of the cloud set the lower mass limit on the planet \citep{kw2011a,galich2013}; minimizing disruption of the main dust belt sets the upper mass limit \citep{chiang2009,kw2011a,tamayo2013,beust2014}. Our approach expands the allowed range of slopes for the size distribution of particles in a circumplanetary cloud or disk. Because the slope correlates with the dust mass, future dynamical studies can provide additional constraints on these parameters. To explore the available parameter space for these models in more detail, we now examine plausible uncertainties (\S4.2), tests (\S4.3), and improvements (\S4.4) of our approach. \subsection{Uncertainties} \subsubsection{Observations} To examine how uncertainties impact our results, we begin with the derivation of the cross-sectional area from the observations. As outlined in \S2, we assume that all radiation from Fomalhaut b is scattered light from Fomalhaut. The minimum cross-sectional area is then derived from the ratio of the scattered flux to the flux from Fomalhaut. The uncertainty is these quantities is small, $\sim$ 10\%. Thus, the uncertainty in the minimum cross-sectional area is small. Establishing an upper limit on the cross-sectional area requires an accurate estimate for the optical depth. Our analysis in \S2.5 safely precludes $\tau \gtrsim$ 1 for giant impact models. Optically thick clouds orbiting a massive planet have collision times roughly $10^{10}$ times shorter than the age of Fomalhaut, robustly eliminating this possibility. With $\tau \lesssim$ 1, the observed \ab\ yields an accurate estimate of the true \ab. Deriving the true cross-sectional area of the dust requires an estimate of the albedo $Q$. Among Kuiper belt objects in the solar system, the albedo is typically $Q \approx$ 0.04--0.20 \citep{marcialis1992,roush1996,stansberry2008,brucker2009}. Choosing $Q \approx$ 0.1 thus yields a reasonable estimate for the actual cross-sectional area, $\ab \approx 1.25 \times 10^{23}$~cm$^2$, with a factor of two uncertainty. This uncertainty has little impact on our results (e.g., Fig.~\ref{fig: area-mdust}). For configurations with large \rmax/\rmin, changing \ab\ by a factor of 2 modifies $M_d$ by a factor of $2^{2/3}$ = 1.6. For giant impacts with fixed $q$, this uncertainty implies a 20\% variation in the derived target radius, a factor of two difference in the collision rate, and minimal revision to our conclusions. If the target radius is held fixed, a factor of two uncertainty in \ab\ implies a 0.1--0.2 change in $q$. We infer similar adjustments to $q$ and \rmax\ for captures or collisional cascades. Thus, allowing for observational error in the cross-sectional area leads to minimal changes in the allowed parameter space of Fig.~\ref{fig: summary}. \subsubsection{Size Distribution} On the theoretical side, we assume that the size distribution is a power law with a slope $q$ and a clear minimum size \rmin\ and maximum size \rmax. Adopting a single largest remnant in a giant impact is reasonable. In a collisional cascade, the largest objects resist erosion by accreting smaller objects \citep[e.g.,][]{kb2008,kb2010,kb2012}. For the slopes inferred from our analysis, the next two largest objects have radii $R \approx$ 0.75--0.85~\rmax\ and $R \approx$ 0.65--0.75~\rmax. Thus, a single largest object is appropriate for impact, capture, and cascade models. Establishing the proper \rmin\ is somewhat more involved. When giant impacts yield small dust grains orbiting Fomalhaut at $r \approx$ 100~AU, setting the minimum radius equal to or larger than the blowout radius -- \rmin\ $\gtrsim$ 5~\mum\ -- is sensible. If small ($R \lesssim \rmin$), icy grains at 120~AU have impurities of carbon or silicates, radiation pressure probably ejects them on the orbital or a smaller time scale \citep{arty1988,gust1994}. Independent of their total mass, grains with $R \lesssim \rmin$ probably contain a large fraction of the cross-sectional area of the ejecta. With velocities much larger than the escape velocity of the impactors, they produce a rapidly expanding halo around the main ejecta. While visible for several years, very small grains become invisible on time scales much longer than a decade \citep[e.g.,][] {galich2013,kalas2013}. For capture and cascade models, isolated small particles are ejected when radiation pressure overcomes the gravity of the planet. For $M_p \approx$ 1--10~\mearth, \rmin\ $\approx$ 300~\mum\ \citep{burns1979,kw2011a}. Although smaller particles might participate in the collisional processing of either mechanism, typical collision times are much longer than the planet's orbital period. Thus, particles with $R \lesssim \rmin$ leave after several orbits of the planet around Fomalhaut \citep{poppe2011}. For impact models, adding more complexity to the size distribution is not warranted. As long as there is a broad range of sizes between \rmin\ and \rmax, a single power-law provides a reasonably good way to relate the cross-sectional area, the mass, and the parameters -- $q$, \rmin, and \rmax\ -- of the size distribution. Thus, this uncertainty seems minimal. For viable capture models, a single power-law may not completely characterize the size distribution from 100~\mum\ to 50--100~km. In our picture, capturing the fragments of giant impacts yields a steep size distribution with $q \gtrsim 4$ \citep[e.g.,][]{durda2004,lein2012}. Collisional evolution among fragments tends to produce shallower size distributions with $q \approx$ 3.5--3.7 \citep{obrien2003,koba2010a}. While a single power-law may not capture all details of capture and collisional evolution, it is probably sufficient to establish allowed values for $q$ and \rmax. In collisional cascades, the proper equilibrium size distribution is uncertain \citep[e.g.,][and references therein]{bely2011}. However, it is somewhat inaccurate to adopt a single power-law to describe the numbers of objects from a few microns to a few thousand kilometers. In long-term numerical simulations of cascades, the size distribution is better represented by separate power-laws at small ($ R \lesssim$ 0.1--1 ~km), intermediate ($R \approx$ 1--100~km), and large sizes \citep[$R \gtrsim$ 10--100~km; e.g.,][]{kb2004c,kbod2008,bottke2010,kb2012}. Analytic studies support this conclusion \citep{pan2005,schlicht2013}. Wavy patterns are often superimposed on these power-laws \citep[e.g.,][]{campo1994, obrien2003,bely2011}. The slopes of the power laws for the small and large objects are similar, with $q_S \approx 3.5-4.0$ and $q_L \approx$ 2.5--4.5; the slope of the intermediate power law is small, with $q_I \approx$ -1 to 1. Observations of Kuiper belt objects in the solar system reveal fairly strong evidence for a break in the size distribution at $\sim$ 20--100~km \citep[e.g.,][]{fuentes2008,fraser2010b} and some evidence for another break at small radii \citep[e.g.,][]{schlicht2012}. Observed slopes are generally consistent with theoretical predictions \citep{bottke2010,kw2011b,schlicht2012}. Quantifying how a somewhat wavy, multi-component power law approximation to the size distribution impacts our conclusions requires exploring a vast parameter space. To place an initial limit, we examine a few general cases for a typical outcome, $q_S \approx$ 3.5--4.0 and $q_I \approx$ 1. Compared to models of a single size distribution with $q \approx$ 3.5--3.7 and \rmax\ $\approx$ 500--3000~km, multiple power laws with $q_L > q_S$ match the observed \ab\ with an \rmax\ which is larger by a factor of 1.5--2. When $q_L < q_S$, matching \ab\ requires a steeper slope, with $q_S \approx q + \delta q$ and $\delta q \approx$ 0.4--0.5. Because the intermediate part of the size distribution contains little area or mass, multiple power law models require a factor of 2--4 more mass to achieve the same surface area. Although a factor of 2--4 uncertainty in the mass certainly impacts the size distribution and the lifetime of a collision cascade \citep[e.g.,][]{wyatt2008,kb2008,kriv2008,kw2010,kb2010}, it has little impact on the general viability of collisional cascade models. From eq.~(\ref{eq: coll-time}), the collision time scales inversely with the mass and linearly with $M_p^{2/3}$. For a fixed cascade lifetime, changing the mass involved in the cascade requires a corresponding adjustment to $M_p$. With current observations requiring $M_p \lesssim 0.5 M_J$, it is fairly straightforward to adjust the mass required for the collisional cascade and meet the broad range of allowed planet masses. \subsubsection{Collision Physics} Aside from the physical parameters of the size distribution, the physics of collisions and collision outcomes plays a major role in our analysis. Our results for impacts hinge on understanding debris production during collisions between large objects. Analyses of captures and cascades also rely on swarms of solid particles finding stable equilibrium size distributions over long periods of time. Although each mechanism depends on an accurate parameterization of the binding energy of icy objects, the uncertainties in \qdstar\ probably have little impact on our results. In a collisional cascade, satellites lose mass when the collision energy exceeds \qdstar\ \citep[e.g.,][]{dohn1969,obrien2003,kb2008,koba2010a}. Because $Q_c$ varies with the orbital velocity, it is possible to compensate for changes in \qdstar\ simply by changing the mass of the planet. For a reasonably large range in planet masses, the subsequent evolution of the cascade is largely unchanged. The binding energy has little impact on capture models. In our picture, \qdstar\ helps to set the collision time for the largest objects (eqs. [\ref{eq: rd1}--\ref{eq: t-large}]). Although factor of two uncertainties in \qdstar\ can lead to similar uncertainties in the rate particles lose mass, the collision time for the largest objects depends mainly on the cross-sectional area. Thus, our assumptions for \qdstar\ have a relatively small, $\sim$ 10\% to 20\%, impact on the collision time and the total mass of the cloud. Viable impact models are more sensitive to \qdstar. Changing \qdstar\ by a factor of two changes debris production by a similar factor. Less debris (larger \qdstar) makes giant impacts less viable. Although more debris adds to the viability of giant impacts, these models still require steep size distributions with little mass in the largest remnant. These outcomes are still unlikely. Our assumption of a head-on giant impact has little impact on our conclusions. When impacts are off-center, the center-of-mass impact energy is smaller by a factor $b$, the impact parameter \citep[e.g.,][]{asphaug2006,lein2012,sstew2012}. With less energy available in a collision and the same energy required to unbind half the colliding protoplanets, off-center collisions lose less mass than head-on collisions. Thus, allowing for off-center collisions reduces the likelihood that a giant impact is responsible for the dust in Fomalhaut b. For captures and cascades, the outcomes of collisions have little impact on the results. For sizes where collisions produce destruction or growth, the rate particles diminish or grow depends on the collision rate much more than collision outcomes \citep{koba2010a,koba2010b,koba2011}. Simple physics constrains the collision rates. Our conclusions for giant impacts rely heavily on the published outcomes of numerical experiments of high energy collisions \citep[e.g.,][]{benz1999,durda2004,lein2012}. So far, different approaches yield similar results: high velocity collisions between objects with substantial self-gravity always leave behind large remnants with a significant fraction of the debris. Because the dust cloud in Fomalhaut b appears to require debris with little mass in the largest remnants, a large impact seems an unlikely way to produce the dust cloud. If numerical simulations identify collision parameters capable of producing the debris required in Fomalhaut b, an impact becomes much more plausible. \subsubsection{Orbital Dynamics} Finally, several aspects of orbital dynamics might modify our conclusions. In a planet with a highly elliptical orbit, for example, the size of the Hill sphere is smaller at periastron than at apoastron. Satellites with circumplanetary orbits at semimajor axes of 0.3--0.4~\rhill\ might be stable at apoastron but unstable at periastron. Because these satellites have orbital periods comparable to the orbital period of Fomalhaut b around Fomalhaut, it should take many Fomalhaut b orbits to develop unstable satellite orbits \citep[e.g.,][]{shen2008}. Indeed, \citet{kalas2013} showed that planets with $M_p \gtrsim 5 \times 10^{24}$ g on Fomalhaut b-like orbits can retain satellites with semimajor axes of 0.3--0.4 \rhill. Thus, the elliptical orbit has little impact on the stability of captured satellites or satellites involved in a collisional cascade. Dynamical interactions among satellites also play a role in the viability of capture and collisional cascade models. In an ensemble of satellites, gravitational interactions produce random velocities comparable to the escape velocity of the largest satellite \citep[e.g.,][]{gold2004}. When these random velocities exceed the orbital velocity, satellites are ejected. In the transneptunian region of the solar system, these interactions produce the scattered disk -- an ensemble of 10--500~km icy objects with perihelia near the orbit of Neptune and large orbital eccentricity \citep[e.g.,][]{gladman2008}. Managing the cascade around 1--10~\mearth\ planets with much larger satellites is challenging. Massive satellites with $R \approx$ 500--1500~\kms\ have escape velocities, $v_{esc} \approx$ 0.5--1.5 \kms, much larger than the local orbital velocity. On a few dynamical time scales, these objects eject smaller satellites orbiting within 2--3 Hill radii \citep[e.g.,][]{glad1993,gold2004}, which is roughly 0.05--0.06 AU. For a satellite system with an outer radius of 0.25--0.5~AU, 5--10 massive satellites can eject all small objects on very short time scales. Maintaining a roughly spherical cloud of dust in a capture or cascade model is also challenging. For any initial geometry, energy loss and angular momentum transport from inelastic collisions eventually produce a prograde disk with angular momentum similar to the initial angular momentum of the cloud \citep{brah1976}. If the initial orbits within the cloud are roughly balanced between prograde and retrograde, material gradually falls onto the planet instead of landing in a large disk. This evolution probably enhances the mass loss rate from a roughly spherical collisional cascade, shortening the lifetime. \subsection{Tests} The simplest ways to deduce the source of the optical emission in Fomalhaut b involve polarimetry or spectroscopy. Imaging polarimetry excels at probing the underlying geometry of dusty clouds or disks \citep[e.g.,][]{whit1993,whit1997,olof2012}. Optical or IR spectroscopy might reveal absorption features from the central A-type star \citep{lagr1995,hemp2003} or silicate features from dust \citep{teles1991,wein2003}. Measuring the velocity of cloud material with high resolution spectroscopy \citep[e.g.,][]{olof2001,brand2004} would discriminate between expanding and orbiting geometries. Unfortunately, these observations are far in the future. The HST and the {\it James Webb Space Telescope} (JWST) have no polarimetric capabilities. Although the source is too faint for HST spectroscopy, the prototype exposure time calculator\footnote{ http://jwstetc.stsci.edu/etc/input/nirspec/spectroscopic/} for NIRSPEC on JWST yields an 8$\sigma$ detection for an A-type continuum with an exposure time of 3600 sec. Although JWST is scheduled for launch no sooner than 2018, low resolution NIRSPEC spectra may enable accurate tests of dust models for Fomalhaut b. Extending photometry to longer wavelengths also tests these models \citep[e.g.,][]{currie2012,currie2013}. JWST NIRCAM observations will enable better than 10$\sigma$ detections\footnote{http://jwstetc.stsci.edu/etc/input/nircam/imaging/} at 1--3~\mum\ \citep[e.g.,][]{tamayo2013}. On a somewhat longer time scale, ground-based imaging with 20-m to 40-m class telescopes might provide independent measures of the spectral energy distribution at 1--5~\mum. Until JWST launches, other approaches are possible. To develop tests for giant impact models, we assume an unbound cloud of dust particles with an expansion velocity exceeding the escape velocity of a pair of impactors with $R \approx$ 50~km, $v_{esc} \approx 5 - 6 \times 10^3 ~ \cms$. \begin{itemize} \item Expansion of the cloud is detectable on short time scales. If all of the material expands at $v_{esc}$, the expansion rate is roughly 0.01~AU~yr$^{-1}$ \citep[e.g.,][]{galich2013,kalas2013}. However, the ejecta probably have a range of velocities with $f(>v) \propto (v / v_{esc})^{-\alpha}$ \citep{gault1963,stoff1975, housen2003,housen2011}. Adopting $\alpha$ = 1.5, roughly 20\% (50\%) of the material has $v \gtrsim 3 ~ v_{esc}$ ($1.6 ~ v_{esc}$). If 35\% of the dust expands at twice $v_{esc}$, the diameter grows roughly 0.4~AU (1--2 pixels on HST images) in 10~yr. Although current efforts to resolve the source are inconclusive \citep[e.g., \S2;][]{galich2013,kalas2013}, improving the resolution and placing robust limits on the expansion rate should be possible in the next decade \citep[e.g.,][]{tamayo2013}. \item Shearing of the cloud is also detectable. For particles expanding at median velocity $v$ from a guiding center with orbital velocity $v_K$, the velocity dispersion is roughly $\delta v \approx v$ \citep[e.g.,][]{gault1963,housen2003}. Among particles expanding tangentially to the orbital motion, some lag the orbit; others move ahead of the orbit. Thus, the sphere shears into a ring \citep[e.g.,][]{kb2005}. When $\delta v / v_K \approx v / v_K \approx 0.01 - 0.02 $, the differential motion is $\delta r / r \approx 0.01 - 0.02$. Over 10 yr, the guiding center moves roughly 8~AU \citep{kalas2013}, resulting in a predicted shear of 0.15--0.3~AU. In the next decade, HST and JWST data can test this prediction. Our large estimate for the shearing rate -- a few decades instead of 100--1000~yr \citep{currie2012,galich2013,kalas2013,tamayo2013} -- is based on the larger internal velocity dispersion of debris clouds suggested by laboratory and numerical experiments. Performing SPH simulations of collisions between pairs of 50--200~km objects \citep[e.g.,][]{lein2012} in a Keplerian reference frame would test these ideas. \item Collisions with other circumstellar disk particles enhance these rates. For a typical relative velocity of 0.4~\kms, it takes roughly 10~yr for a disk particle to cross the cloud. During this period, one in $10^3$ disk particles collides with a cloud particle. If the surface density of the disk at $r \approx$~120~AU is 1\% to 10\% ($d = 0.01 - 0.10$) of the initial surface density, roughly $10^{21}$~g to $10^{22}$~g of disk material mixes with particles in the expanding cloud every decade. Because orbits in the disk differ from orbits of the cloud, these collisions enhance the rate of expansion and orbital shear by factors of three or more. Even very modest amounts of mixing -- $\sim 10^{18}$~g, corresponding to a disk with $d \approx 10^{-5}$ -- can easily increase the expansion and shear by roughly 50\%. Any mixing thus increases the chances of detecting expansion or shearing very soon. If Fomalhaut b enters the dust belt \citep{galich2013,kalas2013}, the enhanced collision rate should produce an obvious shear on very short time scales. \end{itemize} Without high quality polarimetry or spectroscopy, robust tests of the capture or cascade pictures are more challenging. Still, several tests allow promising tests of either scenario. \begin{itemize} \item Although significant expansion or contraction of captured or cascading material is unlikely, measurements of Fomalhaut b's size place important constraints on the models. As noted in \S2, unambiguous resolution of the disk of Fomalhaut b places a robust lower limit on the mass of a central planet. \item Placing better limits on the azimuthal structure of material at 20--130~AU also constrains models for Fomalhaut b. If dust in the inner disk is smoothly distributed \citep[as in the model of][]{acke2012}, capture models are more viable. Detecting patchy dust increases the likelihood of massive planets in the inner disk and decreases the likelihood of significant capture of small solids by planets in the inner disk. \item Collisional cascades should leave behind a trail of small particles \citep[e.g.,][]{kalas2013}. Because particles with $R \approx$ 5--300~\mum\ are blown out of circumplanetary -- but not circumstellar -- orbits, these particles should take up orbits along the path of Fomalhaut b. Assuming 10$\sigma$ detections from existing observations of Fomalhaut b, the brightest detectable cloud of small dust particles is a factor of 5--10 fainter than Fomalhaut b. With roughly 1000 resolution elements along the elliptical orbit, it is possible to discriminate a trail from the background if an ensemble of small dust particles has a total cross-sectional area $A_{d,s} \approx 1000 / 5-10 \approx$ 100--200 times the cross-sectional area of the dust observed in Fomalhaut b. If it is possible to coadd data convincingly in an annulus along the orbit, a robust algorithm could detect fainter trails. Although there are many uncertainties, this level of emission from 5--300~\mum\ particles is plausible. For size distributions with $q \approx$ 3.5--4.0, the cross-sectional area of the small particles is 7--20 times larger than the area of the circumplanetary debris disk. If the particles do not drift too far away from the orbit and if collisions do not destroy small particles ejected well before the current epoch, it is possible to enhance this surface area by factors of 3--10 \citep[see, for example][and references therein]{wyatt2008,kb2008,kb2010,kw2010,kw2011a}. Unambiguous limits on this trail would enable stern tests of capture and cascade models. \item Fomalhaut b's possible entry into Fomalhaut's dust belt provides another opportunity to test cascade \citep[e.g.,][]{kalas2013} and capture models. By analogy with Saturn's rings \citep[e.g.,][]{dur1989} and Kuiper belt objects \citep[e.g.,][]{stern2009}, we expect several classes of behavior when particles from the dust belt interact with circumplanetary dust: (i) large objects from the belt will carry away small circumplanetary particles and (ii) collisions between small belt objects and large circumplanetary objects will produce debris. For small objects in a captured cloud or disk, entry into the dust ring will be dramatic: we expect an initial loss of captured material on 10 yr time scales, followed by a slow increase as the rare collisions of larger objects produce debris which repopulates the smaller sizes. Because collisional cascades have a shallower dust distribution, we expect much less dramatic changes: as large objects remove small particles from the cloud or the disk, collisions between larger objects rapidly restore lost material. The time scale for any variations, however, should be similar, $\sim$ 10--100~yr. \end{itemize} \subsection{Improvements} As observations continue to probe the nature of Fomalhaut b, new approaches can hone theoretical predictions. Although clear improvements in analytic approaches are possible, here we outline several numerical calculations to clarify expectations. For all dust models, it is crucial to add to our understanding of interactions between the dust cloud and ambient material in the disk. If the surface density of the disk at 30--100~AU is roughly 1\% to 10\% of the initial surface density, then disk material inevitably interacts with the cloud. From our earlier estimates, disk material with a total mass comparable to the mass of the cloud interacts with cloud material every 10--100 yr (for impact and capture models) to every $10^4 - 10^5$ yr (for cascade models). If these interactions add material to the cloud, they make (i) capture and cascade models more viable and (ii) impact models less viable. Interactions which remove material from the cloud tend to decrease the viability of all models. Despite the wealth of analytic and numerical work \citep[e.g.,][]{dones1993,kort2005,jewitt2007a,nesv2007, pires2012}, estimating the amount of material a planet can capture throughout the history of a planetary system remains uncertain. For Fomalhaut b, its elliptical orbit through the inner disk and main belt of dust might lead to substantial differences in the capture rate. Numerical simulations can place stronger constraints on our simple estimates. Numerical experiments could clarify the long-term collisional evolution of circumplanetary debris. Our estimates for the viability of the capture hypothesis rest on the development of an equilibrium between the rate captures add mass to the cloud and the rate collisions remove mass from the cloud. More sophisticated calculations can address this issue. Finally, numerical calculations can illuminate the relative importance of cloud and disk geometries for collisional cascades around massive planets. During the early evolution of the solar system, dynamical interactions between the gas giants strongly favor cloud geometries for swarms of captured particles \citep[e.g.,][]{nesv2007}. In a dynamically quiet environment, however, growing planets might easily capture large disks of particles. Unless these disks are disrupted by the gravity of another massive planet, massive satellite formation and the onset of a collisional cascade is inevitable. Understanding common features and differences of circumplanetary cascades in clouds and disks might enable new tests of the cascade model. | 14 | 3 | 1403.5268 |
1403 | 1403.4352_arXiv.txt | Recent studies in different types of galaxies reveal that the product of the central density and the core radius ($\rho_cr_c$) is a constant. However, some empirical studies involving galaxy clusters suggest that the product $\rho_cr_c$ depends weakly on the total dark halo mass. In this article, we re-analyse the hot gas data from 106 clusters and obtain a surprisingly tight scaling relation: $\rho_c \propto r_c^{-1.46 \pm 0.16}$. This result generally agrees with the claims that $\rho_cr_c$ is not a constant for all scales of structure. Moreover, this relation does not support the velocity-dependent cross section of dark matter if the core formation is due to the self-interaction of dark matter. | The dark matter problem is one of the key issues in modern astrophysics. The existence of cold dark matter (CDM) particles is the generally accepted model to tackle the dark matter problem. N-body simulations show that the dark matter density should follow a universal density profile (NFW profile), which goes like $r^{-\alpha}$ towards the center of the structure with $\alpha \sim 1-1.5$ \citep{Navarro,Moore}. However, observations in many dwarf galaxies and a few clusters indicate that flat cores of dark matter exist in those structures \citep{Tyson,Gentile,Sand,deBlok,Newman}. This discrepancy can be reconciled in many possible scenarios. For example, the feedback from baryonic processes such as supernova explosion can generate core-like structure in dark matter profile \citep{Weinberg,Maccio}. However, some studies point out that these processes cannot produce enough feedback to get the observed core size \citep{deBlok,Penarrubia,Vogelsberger}. Another suggestion is that dark matter particles are not collisionless, but weakly self-interacting. Burkert(2000) showed that a core could be produced if the dark matter cross-section per unit mass is about $\sigma/m \sim 1$ cm$^2$ g$^{-1}$. The resulting dark matter profile is known as the Burkert profile. Moreover, recent studies in a wide range of galaxies (including dwarf galaxies) report an interesting relation if the dark matter density profile is fitted with a cored density profile: $\rho_cr_c=$ constant, where $\rho_c$ and $r_c$ are the central density and core radius of the dark matter density profile respectively. This relation is first noticed by Kormendy and Freeman(2004). They obtained $\rho_cr_c \sim 100M_{\odot}$ pc$^{-2}$, which is almost a constant by using the data from 55 rotation curves in spiral galaxies \citep{Kormendy}. Later, Spano et al.(2008) analysed the mass distribution of 36 spiral galaxies and got $\rho_c \propto r_c^{-1.04}$. Furthermore, Donato et al.(2009) use the data from 1000 spiral galaxies and obtained $\rho_cr_c \approx 141M_{\odot}$ pc$^{-2}$ for a wide range of different galaxies. Gentile et al.(2009) also show that this interesting relation can be applied in baryonic component of galaxies. Recently, Salucci et al.(2012) use the kinematic surveys of the dwarf spheroidal satellites of the Milky Way to tighten the relation $\rho_c \propto r_c^{-a}$ with $0.9<a<1.1$. However, all the above results are only based on the observations from galaxies. Some studies including the data from galaxy clusters suggest that the product $\rho_cr_c$ is not really a constant, but depends weakly on the total mass of dark matter halo $M_{\rm halo}$. Boyarsky et al.(2009) and Del Popolo et al.(2013) obtained $\rho_cr_c \propto M_{\rm halo}^{0.21}$ and $\rho_cr_c \propto M_{\rm halo}^{0.16}$ respectively by extending the sample data to cluster scale. Moreover, recent observation from cluster Abell 611 reports a very large $\rho_cr_c \sim (2350 \pm 200)M_{\odot}$ pc$^{-2}$ \citep{Hartwick}. Although the data from clusters are still not enough to draw any conclusions, these results begin to challenge the universality of dark column density ($\rho_cr_c=$ constant). In fact, the potential relation between $\rho_c$ and $r_c$ suggests that some strong constraints or intrinsic properties may exist in dark matter. Chan(2013a) suggests that the existence of a universal `optical depth' $\tau= \rho_c(\sigma/m)r_c=$ constant in galaxies can explain the observed relation. However, there is no strong fundamental reason or physical principle why there exists a universal `optical depth'. Therefore, it would be very useful to understand the properties of dark matter if we could examine whether the universality of dark matter column density is also true in galaxy clusters. However, the mass density profile probed by gravitational lensing cannot provide accurate core radius and central density of dark matter profile. Although the method of weak and strong lensing can give a good direct estimation of projected mass, the 3-D mass function still depends strongly on the dark matter functional form, which is usually assumed to be the NFW profile or generalized NFW profile \citep{Bartelmann,Mahdavi,Giocoli}. However, as mentioned above, the NFW profile deviates from the observed profile significantly for small radius and an additional free parameter is needed to indicate the inner slope of the density profile \citep{Giocoli}. Moreover, the generalized NFW profile can give us the density scale only, but not the central density for our analysis. Although \citet{Bartelmann,Shan} are able to obtain a large sample of enclosed cluster mass by strong lensing, we still need to assume some cored-profile (with $\rho_c$ and $r_c$) to de-project the enclosed mass for our purpose. The result, however, would be highly dependent on the assumed profile. Alternatively, observations in cluster hot gas provide a good tool to probe the dark matter density profile. Although we need to assume that the hot gas particles are in hydrostatic equilibrium and the distribution is spherically symmetric, we need not assume any cored-profile in the analysis to get the $\rho_c$ and $r_c$. Since the dark matter mass dominates the total mass, the resulting profile can be regarded as the dark matter mass profile. However, the spherical asymmetry, cooling flow in hot gas and the AGN feedbacks may significantly affect the estimated profile. In particular, the cooling flow and AGN feedbacks mainly affect the central part of the density profile in clusters by a factor of 2-4 \citep{Arabadjis,Martizzi}. Although these effects are not negligible, it is the only way to obtain a large sample of clusters with corresponding $\rho_c$ and $r_c$. Moreover, we can divide the analysis into subsets such that the cooling-flow clusters can be ruled out in the empirical fits. In this article, we still use this traditional method to get a universal dark matter density profile for 106 galaxy clusters from observations based on the ROSAT All-Sky Survey \citep{Reiprich}. By relating the central densities and the core radii of these density profiles, we can test the universality of dark column density for the whole sample and its subsets of clusters. | In this article, we obtain the central density and core radius of dark matter in a cluster by using the hot gas profile. The resulting scaling relation is $\rho_c \propto r_c^{-1.46 \pm 0.16}$. This result is basically different from that obtained in galaxies: $\rho_c \propto r_c^{-1}$. Also, this result gives a tighter scaling relation in clusters compared with the fits from previous studies such as $\beta \propto r_c^{0.11^{+0.03}_{-0.02}}$ and $T \propto r_c^{0.03^{+0.05}_{-0.07}}$ \citep{Ota}. On the other hand, the fitted slope for cooling flow clusters (slope$=-1.30 \pm 0.07$) are slightly different from non-cooling flow clusters (slope$=-1.50 \pm 0.24$). This suggests that the cooling flow in clusters may affect the inner structure of dark matter, which is consistent with some suggestions about the baryonic feedbacks in galaxies \citep{Weinberg,Maccio}. The scaling relation in clusters consists of three basic parameters in hot gas profile, $\beta$, $r_0$ and $T$. These parameters should be independent of each other in hot gas. However, the gravitational interaction between dark matter and hot gas particles relates the three parameters to form a tight scaling relation. Therefore, this scaling relation may reflect some intrinsic properties of dark matter in clusters. If the core formation is due to the self-interaction of dark matter, as suggested by Spergel and Steinhardt(2000), the scattering cross section $\sigma$ should be related to $(\rho_cr_c)^{-1}$. In galactic scale, since $\rho_cr_c$ is a constant, $\sigma$ is also a constant for galaxies. This supports the constant (velocity independent) self-interaction cross section scenario \citep{Peter,Rocha,Zavala}. However, recent studies in clusters have already revealed that $\sigma$ should be velocity-dependent ($\sigma$ decreases as the velocity of dark matter particle increases) \citep{Loeb,Chan2}. By using our result from cluster data, since $\rho_cr_c^{1.46}$ is a constant, we have $\sigma \sim (\rho_cr_c)^{-1} \propto r_c^{0.46}$. Generally, the velocity of dark matter particle $v$ increases with $r_c$ \citep{Rocha}. That means $\sigma$ should increase with $v$, which contradicts to the observations and the prediction from velocity-dependent cross section scenario \citep{Colin,Vogelsberger}. Therefore, the formation of cores in clusters and galaxies may not be caused by the self-interaction of dark matter particles. Finally, the two very different scaling relations in galaxies and clusters suggest that some different constraints in dark matter may exist in galaxies and clusters. Therefore, probably there will be no universal dark matter density profile exist in different scales as predicted by numerical simulations. | 14 | 3 | 1403.4352 |
1403 | 1403.3091_arXiv.txt | We present a study on the gender balance, in speakers and attendees, at the recent major astronomical conference, the American Astronomical Society meeting 223, in Washington, DC. We conducted an informal survey, yielding over 300 responses by volunteers at the meeting. Each response included gender data about a single talk given at the meeting, recording the gender of the speaker and all question-askers. In total, 225 individual AAS talks were sampled. We analyze basic statistical properties of this sample. We find that the gender ratio of the speakers closely matched the gender ratio of the conference attendees. The audience asked an average of 2.8 questions per talk. Talks given by women had a slightly higher number of questions asked (3.2$\pm$0.2) than talks given by men (2.6$\pm$0.1). The most significant result from this study is that while the gender ratio of speakers very closely mirrors that of conference attendees, women are under-represented in the question-asker category. We interpret this to be an age-effect, as senior scientists may be more likely to ask questions, and are more commonly men. A strong dependence on the gender of session chairs is found, whereby women ask disproportionately fewer questions in sessions chaired by men. While our results point to laudable progress in gender-balanced speaker selection, we believe future surveys of this kind would help ensure that collaboration at such meetings is as inclusive as possible. | All scientific gatherings, from conferences to colloquia, should seek to be welcoming venues for intellectual exchange. Such meetings are, along with publications, the primary means by which scientists communicate. As we seek to improve the diversity of the body scientific, making our field more approachable to women, minorities, and other traditionally underrepresented peoples, we must ensure that our meetings also foster interaction between all members. Anecdotal observations during a recent astronomy meeting noted a difference in the gender distribution between conference attendees, invited speakers, and the attendees that asked questions. More specifically, while the conference as a whole seemed well balanced in gender, as were the invited speakers, the questions appeared to be preferentially asked by men. Specifically, it appeared that men were asking the majority of the questions for every talk. We wondered the significance of this observation, and sought to gather more data on the subject. Here we present findings from a semi-formal survey of oral presentations at a recent major astronomical conference, the 223rd Meeting of the American Astronomical Society (AAS), held in January 2014. The survey was a volunteer effort throughout the meeting, with submissions coming from anonymous attendees. The analysis was conducted as part of the AAS ``Hack Day'' program, which provided an excellent forum for discussion and creative input on the project. We hope this informal report will encourage further discussion and study of diversity and gender equality within our community. | The primary results of this study are as follows: \begin{enumerate} \item Men ask disproportionally more questions than women in talks, despite the gender ratio of the speakers matching that of the conference attendees.\vspace{0.04in} \item Women are asked slightly more questions per talk than men (3.28 versus 2.64, respectively.) \item The gender of the session chair appears to have a strong correlation with the gender ratio of the questioners. \end{enumerate} We believe the first result may be explained by a simple line of reasoning: in the past the gender distribution of astronomers was very lopsided (strongly male). More senior scientists may simply be more likely to ask questions as deep experts. Speakers are instead drawn from a younger sample of scientists who are more often advertising new and novel work. This is supported by the recent Demographics Survey of 2013 US AAS Members, which found that the female/male split for astronomers born before 1980 was 21\%/79\%, while those born after 1980 were 40\%/60\%. These numbers very closely match the gender distributions we show in Figure \ref{fig:q}. Given the modest effort in advertisement and organization before the meeting for our survey, we are encouraged by the participation and coverage of AAS talks (26\%) sampled here. Further, introspective studies of our profession are clearly supported by our community. In the immediate future, we would like to have a larger scale study, with particular focus one the impact of session format and session chair involvement. We believe this could be conducted by the AAS with very low organizational overhead and volunteer labor. Our pilot study has shown the great value of volunteer submitted data, and with minimal advertisement we believe data could be gathered for nearly 100\% of the conference talks. Near term, we seek to improve meeting organization, striving to find the right scenario for presenting scientific advances between peers in a manner that is most inclusive and inviting to underrepresented peoples in our field. A recent demographic survey conducted by the AAS indicates that, while several major hurdles for equality in our field still exist, gender ratios are flattening with time. In the not-too long term, we hope that the advancement of scientific knowledge will be a truly inclusive endeavor which benefits from contributions of all groups of scientists. | 14 | 3 | 1403.3091 |
1403 | 1403.6820.txt | We present the results of the atmospheric optical turbulence (OT) measurements performed atop Mt.~Shatdzhatmaz at the installation site of new 2.5-m telescope of Sternberg Astronomical Institute. Nearly 300\,000 vertical OT profiles from the ground up to an altitude of 23~km were obtained in the period November 2007--June 2013 with the combined multi-aperture scintillation sensor (MASS) and differential image motion monitor (DIMM) instrument. The medians of the main OT characteristics computed over the whole dataset are as follows: the integral seeing $\beta_0 = 0.96$~arcsec, the free-atmosphere seeing $\beta_{free} = 0.43$~arcsec, and the isoplanatic angle $\theta_0 = 2.07$~arcsec. The median atmospheric time constant is $\tau_0 = 6.57 \mbox{ ms}$. The revealed long-term variability of these parameters on scales of months and years implies the need to take it into account in astroclimatic campaign planning. For example, the annual variation in the monthly $\theta_0$ estimate amounts up to 30\% while the time constant $\tau_0$ changes by a factor of 2.5. Evaluation of the potential of Mt.~Shatdzhatmaz in terms of high angular resolution observations indicates that in October--November, this site is as good as the best of studied summits in the world. | The potential of a ground-based telescope is basically defined by the size $\beta$ of the image distorted by the earth's atmosphere. In classical astronomical observations, the telescope efficiency, in the sense of the detection limit, depends mainly on the $D/\beta$ ratio \citep{Bowen1964,Shcheglov1980}. Other resources concerning improvement in the telescope optics quality and detector efficiency are already nearly exhausted. Further, the telescope yield relates to the same ratio being squared. Finally, the resolution-limited tasks are fully constrained by the image quality achievable at a given site. The capabilities of ground based telescopes may be significantly boosted using various active and passive high angular resolution (HAR) techniques. Since they are quite complex to implement, it is important to assess and optimize their efficiency in advance. In turn, this requires one to be armed with statistically reliable and comprehensive information on atmospheric optical turbulence (OT) including its vertical distribution, \citep[see for e.g.,][]{Vernin1991, Roddier1999, Wilson2003, Fuensalida2004}. Over the past two decades, such measurements are being conducted both at operating observatories \citep{Tokovinin2003MN,DaliAli2010,Wilson2009,Catala2013} and at potential extra-large-telescopes installation sites \citep{Shoeck2009,Vernin2011,Ramio2012,Thomas-Osip2008}. On this basis, we set in 2006 the long-term program of monitoring of the OT vertical distribution along with other astroclimatic parameters at Mt.~Shatdzhatmaz in the Northern Caucasus, Russia, which is the site selected for the installation of new 2.5-m telescope of Sternberg Astronomical Institute (SAI). Regular measurements were begun towards the end of 2007 and preliminary conclusions were presented in a paper two years later \citep{2010MNRAS}. This study, apart from the explicit goal to optimize the performance of the 2.5-m telescope, is also more generally motivated towards a better understanding of the astroclimatic properties of the Northern Caucasus. Although site testing campaigns were conducted several times in this region \citep[full description is available in][]{Panchuk2011T}, their results are currently only of historical value. The aim of this paper is to describe the main results of the six-year period of OT measurements (from November 15, 2007 to June 15, 2013) and to assess the stability of the main atmospheric parameters in this time span. The second section presents the basic terms and definitions in use to describe OT, and the principles of the MASS and DIMM instruments widely used in OT monitoring throughout the world. Next, a brief description of the site and the campaign layout are outlined along with the main characteristics of the particular equipment used in the monitoring. The fourth section presents the main results of the OT parameter measurements and the analysis of their temporal behaviour. The last section focuses on the discussion of the determined properties of the OT at Mt.~Shatdzhatmaz. In particular, we focus attention on the suitability of this site for the application of HAR techniques. In this article, we do not consider the results of the measurements of the main meteorological parameters, fraction of clear night sky, night-sky brightness, and atmospheric extinction as they are to be published in an upcoming paper. | The results of the campaign at Mt.~Shatdzhatmaz in 2007--2013 again confirm the high efficiency of OT monitoring in the automatic mode. In terms of the total amount of data collected on OT vertical distribution, this study is among the most representative ones. What is important is the location of the site in the Northern and Eastern hemispheres at mid-latitudes. As such, the closest analogues among actively tested observatories are those at San Pedro Martir and Mt.~Maidanak. We list the most significant results of this six-year monitoring. Here, we report on the median estimates of each OT parameter and view the season as a year-long period starting on July 1. Over the whole period, the integral seeing $\beta_0$ is $0.96$\asec. For 25\% of time, $\beta_0 < 0.74$\asec\ while the most probable value is $0.81$\asec. The seeing in the free atmosphere (1~km and above) $\beta_{free}$ is $0.43$\asec, and the most probable one is $0.28$\asec. From season to season, the changes in the seeing estimates have a relative range of $14$\% (which corresponds to $\sim\!\!23$\% in the OT intensity), both in the whole and in the free atmosphere. The best images are observed in October--November when the median $\beta_0$ is as low as $0.83$\asec. Strongest turbulence is encountered in March ($1.34$\asec) due to a significant wind shear in the lower atmosphere. The isoplanatic angle is $2.07$\asec, which is typical for many observatories. Its estimates vary from season to season quite mildly, by $\sim\!\!10$\% of the general median. Peak-to-peak variations of monthly estimates approach 35\%, and in October, $\theta_0$ reaches $2.50$\asec. The atmospheric time constant $\tau_0$ for the whole campaign period is $6.57$~ms. The season-to-season spread of the median estimates amounts up to 27\% while during a year $\tau_0$ changes between $4.2$~ms in March and $10.8$~ms in October. A considerable variability in the basic OT parameters expressed both as annual and as season-to-season changes, confirms the need to conduct long-term site monitoring campaigns. Short-term calibration campaigns yield only rough estimates of the OT properties at a given location. This particularly applies to the atmospheric time constant whose variations are affected by several factors. The coherence \'etendue factor $G_0$ \citep{Lloyd2004} that is considered a sensitive parameter in AO-related studies, exhibits the most considerable annual variation. In our case, it changes by an order of magnitude, reaching a value $\sim\!\!0.8$ in autumn. In this period, the Mt.~Shatdzhatmaz HAR capabilities are the same as those of Mauna Kea and Armazones. | 14 | 3 | 1403.6820 |
1403 | 1403.1577_arXiv.txt | Modal noise in optical fibers imposes limits on the signal to noise and velocity precision achievable with the next generation of astronomical spectrographs. This is an increasingly pressing problem for precision radial velocity (RV) spectrographs in the near-infrared (NIR) and optical that require both high stability of the observed line profiles and high signal to noise. Many of these spectrographs plan to use highly coherent emission line calibration sources like laser frequency combs and Fabry-Perot etalons to achieve precision sufficient to detect terrestrial mass planets. These high precision calibration sources often use single mode fibers or highly coherent sources. Coupling light from single mode fibers to multi-mode fibers leads to only a very low number of modes being excited, thereby exacerbating the modal noise measured by the spectrograph. We present a commercial off-the-shelf (COTS) solution that significantly mitigates modal noise at all optical and NIR wavelengths, and which can be applied to spectrograph calibration systems. Our solution uses an integrating sphere in conjunction with a diffuser that is moved rapidly using electrostrictive polymers, and is generally superior to most tested forms of mechanical fiber agitation. We demonstrate a high level of modal noise reduction with a narrow bandwidth 1550 nm laser. Our relatively inexpensive solution immediately enables spectrographs to take advantage of the innate precision of bright state-of-the art calibration sources by removing a major source of systematic noise. | \label{introsection} High-resolution fiber fed spectrographs are being used for demanding astrophysical applications, including the detection of low mass planets (eg. \citealt{dumusque12}) using precise radial velocity (RV) measurements. The promise of detecting rocky planets around M dwarfs has led to the development of stabilized high resolution near-infrared (NIR) spectrographs such as the Habitable Zone Planet Finder (HPF, \citealt{mahadevan12}) and CARMENES \citep{quirrenbach12}, while ambitious instruments like ESPRESSO \citep{megevand12} seek to achieve 10 cm s$^{-1}$ RV precision to find true Earth-analogs around G and K stars. These instruments require extremely stable and accurate calibration sources like laser frequency combs and stabilized Fabry Perot etalons that are now being developed and tested. The finite number of electromagnetic modes in an optical fiber leads to a form of noise that, if left unmitigated, limits the achievable signal to noise and adds a source of RV noise. This {\it modal noise} is worst with narrow emission line sources, and at longer wavelengths, and can significantly hinder the ability to achieve the high signal to noise needed to search for biomarkers in the atmosphere of transiting planets \citep{snellen13} in the NIR. In this paper we experimentally demonstrate a commercially available and easy to implement solution to modal noise that is applicable to calibration sources. This solution is immediately useful to multiple groups attempting to push forward the limits of precision spectroscopy in the optical and NIR. The development of such techniques is closely related to the growing field of {\it Astrophotonics} \citep{2009OExpr..17.1880B}. | We have demonstrated a commercial off-the-shelf solution to the fiber modal noise problem that has previously limited the use of narrow emission line calibration sources with high resolution astronomical spectrographs. Our solution uses a dynamic diffuser \citep{blum12} and integrating sphere to randomize the modes. The dynamical diffuser changes the mode distribution at a timescale much shorter than the typical spectrograph exposure, and the integrating sphere further randomizes this distribution. Our solution is also quite general in that any combination of a dynamic mode re-distributor and a mode mixer will help mitigate modal noise, though not necessarily as well as the setup we present. For example a galvano scanner may be used as a replacement to the dynamic diffuser in conjuction with an integrating sphere. Experiments coupling light from the diffuser directly to a multimode fiber achieve a total light throughput of $\sim$0.2\%, with modal noise mitigation exceeding the mechanical agitation case. Such solutions are useful with calibration sources like Th-Ar and U-Ne where minimizing light loss becomes important. The commercial Optotune diffuser is made of polycarbonate, and has shallow absorption bands at certain wavelengths ($\sim$ 1180nm \& 1400nm)\footnote{Optotune Data Sheet: http://www.optotune.com/images/products/Optotune\%20LSR-3000\%20Series.pdf}. It is possible to create custom engineered diffusers made of glass or fused silica \citep{sales06} that do not exhibit such absorption. Light weight diffusers can be agitated with the electroactive polymers, while heavier diffusers can utilize a rotating mount, albeit at lower frequencies. While light loss with the use of a integrating sphere makes it impractical to use with starlight, modal noise is less problematic in this case due to lower visibility ($\nu$). Some modal mixing may be accomplished with custom diffusers between two fibers, but requires very small diffusion angles to minimize light loss and focal ratio degradation. While exploration of such techniques may be fruitful, our opinion is that the star fiber modal noise is likely best addressed with a small amount of gentle agitation \citep{baud01,plavchan}, while a solution to the calibration fiber modal noise problem is presented in this paper for all optical and NIR wavelengths. | 14 | 3 | 1403.1577 |
1403 | 1403.1607_arXiv.txt | We show that the spectrum of radial pulsation modes in luminous red giants consists of both normal modes and a second set of modes with periods similar to those of the normal modes. These additional modes are the red giant analogues of the strange modes found in classical Cepheids and RR Lyrae variables. Here, we describe the behaviour of strange and normal modes in luminous red giants and discuss the dependence of both the strange and normal modes on the outer boundary conditions. The strange modes always appear to be damped, much more so than the normal modes. They should never be observed as self-excited modes in real red giants but they may be detected in the spectrum of solar-like oscillations. A strange mode with a period close to that of a normal mode can influence both the period and growth rate of the normal mode. | Luminous red giant stars are known to exhibit periods of variation that fall on 7 or more roughly parallel period-luminosity sequences \citep[e.g.][]{woo99,ita04,fra05,sos07}. Some of these sequences are known to be due to different radial pulsation modes \citep{woo99,sos07,tak13}. While exploring the periods and stability of radial pulsation modes in luminous red giants, we encountered situations where we found two radial modes with identical pulsation periods. It turned out that there are two independent sets of radial pulsation modes occurring in luminous red giants, one set being the well-known normal modes and the second set being the strange modes encountered in classical Cepheid and RR Lyrae variables \citep*{buc97,buc01}. Related strange modes also appear in luminous main-sequence stars \citep*{sai98}. Here we describe the behaviour of the strange modes in red giants and how they depend on the surface boundary conditions. | We have shown that in luminous red giant stars, a series of radial strange modes exists in addition to the series of radial normal modes of pulsation. At high luminosities, strange modes can have periods as long as that of the first overtone for plausible luminosities, especially if an extended outer atmosphere in included in the calculations. The periods of the strange modes increase faster with $\log L/{\rm L}_{\odot}$ (and hence surface radius) than the periods of the normal modes. This means that normal and strange modes in a given star can have identical periods at certain luminosities. In some cases, avoided crossings in period occur leading to a given mode (identified by continuity as the luminosity is varied) changing back and forth between a normal and strange mode character as the luminosity changes. In cases where the modes cross in period, the growth rates of each mode is affected by the near-resonance condition. The strange modes are always damped, and more so than the normal modes. We should not expect to see self-excited strange modes in real stars but strange modes may be observed in the spectrum of solar-like oscillations. The periods and growth rates of normal modes may be influened by resonances with strange modes. Fortunately, the normal modes periods are essentially unaffected by the placement of the outer boundary. On the other hand, the strange mode periods increase as the outer boundary is placed at larger radii. Finally, we note that although these calculations were performed for radial modes, we expect that strange modes should also exist in the nonradial case. | 14 | 3 | 1403.1607 |
1403 | 1403.4214_arXiv.txt | We discuss the effects of destruction of wide binaries in the nuclei of the lower mass giant elliptical galaxies. We show that the numbers of barium stars and extrinsic S stars should be dramatically reduced in these galaxies compared to what is seen in the largest elliptical galaxies. Given that the extrinsic S stars show strong Wing-Ford band and Na I D absorption, we argue that the recent claims of different initial mass functions from the most massive elliptical galaxies versus lower mass ellipticals may be the result of extrinsic S stars, rather than bottom-heavy initial mass function. | Despite the fact that most stars are members of binary systems, binary stellar evolution is usually neglected in modelling of the spectral energy distributions of galaxies (although see e.g. Han et al. 1995). This decision is made as a basic simplication, in part because it has not, to date, been clear how binary evolution would affect most of what is seen in optical light, and in part because binary population synthesis is extremely complicated, with large numbers of parameters which are not particularly well-constrained by observations (see e.g. Belczynski et al. 2008 for a discussion of a particular binary population synthesis code). Furthermore, while we will show evidence to the contrary in this paper, one might initially expect that the effects of binary evolution would not vary much from galaxy to galaxy. Heggie's Law (1975) states that hard binaries get harder while soft binaries get softer -- i.e. binaries whose binding energy is larger than the mean kinetic energy of single stars in their local neighborhood will tend to become closer with time, while binaries with binding energies less than the local mean stellar kinetic energy will tend to become wider with time until they are eventually dissolved into two single stars. The consequences of Heggie's Law are generally well-appreciated, if not fully understood, in the context of globular clusters. For example, the hardening of binaries in globular clusters supplies kinetic energy to the single stars in the clusters, holding up the collapses of star clusters in a manner somewhat analogous to the manner in which nuclear fusion holds up the collapses of stars (see e.g. Sugimoto \& Bettweiser 1983; Fregeau 2008). In the context of field populations of galaxies, it has been shown that the absence of wide binaries in the Galactic halo can be taken as evidence against massive compact halo objects (i.e. MACHOs) supplying the bulk of the dark matter in the Milky Way (Yoo et al. 2004). There has been relatively little appreciation, however, of how removing long period binaries from a stellar population affects integrated stellar light. Traditionally, in fact, stellar population synthesis models for understanding galaxy evolution have ignored binaries almost entirely, except with respect to binary models for producing the ultraviolet upturn in elliptical galaxies (e.g. Han et al. 2002; Han et al. 2007), and, of course population synthesis calculations aimed at unequivocally binary populations like X-ray binaries and double neutron stars (e.g. Belczynski et al. 2008). In this Letter, I will show that the cutoff period varies considerably through different classes of stellar systems, and that this difference affects whether Roche lobe overflowing red giants will be present in different classes of galaxies. I will show further that these binary systems may then have profound implications for the observational appearance of different classes of galaxies. | Binary destruction in the cores of the smaller giant elliptical galaxies is expected. A lack of S stars in these galaxies can provide an alternative explanation for the recent claims of steeper initial mass functions in the biggest giant elliptical galaxies than in smaller ellipticals, eliminating the need to deal with the conflict between those results and other estimates of the dark matter content of the Universe. This idea can be tested by searching for the ZrO bands in giant elliptical galaxies, and by spectroscopic follow-up of giants in the center of the Milky Way relative to giants elsewhere in the Milky Way. If the Wing Ford band can be confirmed to be dominated, or even affected, by the S stars, the results from Cappellari et al. (2012) showing higher M/L in higher velocity dispersion galaxies remain unaffected by the conclusions of this work. However, the results of Cappellari et al. (2012) have some degeneracies between the functional form of the dark matter density distribution and the stellar mass-to-light ratio. They can also produce higher-than-standard M/L ratios either through top heavy or bottom heavy initial mass functions, with the former producing high M/L ratios due to having more compact objects, and the latter due to having more low luminosity M-dwarfs. Understanding all the systematic effects in stellar population models is thus a key for understanding the root cause of the results of Cappellari et al (2002). | 14 | 3 | 1403.4214 |
1403 | 1403.6027_arXiv.txt | {Previous works indicate that the frequency ratio of second and first harmonics of kink oscillations has tendency towards 3 in the case of prominence threads. This is not a straightforward result, therefore it requires adequate explanation.} {We aim to study the magnetohydrodynamic oscillations of longitudinally inhomogeneous prominence threads and to shed light on the problem of frequency ratio.} {Classical Sturm--Liouville problem is used for the threads with longitudinally inhomogeneous plasma density. We show that the spatial variation of total pressure perturbations along the thread is governed by the stationary Schr\"{o}dinger equation, where the longitudinal inhomogeneity of plasma density stands for the potential energy. The Schr\"{o}dinger equation appears as the equation of quantum harmonic oscillator for a parabolic profile of plasma density. Consequently, the equation has bounded solutions in terms of Hermite polynomials. } {Boundary conditions at the thread surface lead to transcendental dispersion equation with Bessel functions. Thin flux tube approximation of the dispersion equation shows that the frequency of kink waves is proportional to the expression $\alpha(2n+1)$, where $\alpha$ is the density inhomogeneity parameter and $n$ is the longitudinal mode number. Consequently, the ratio of the frequencies of second and first harmonics tends to $3$ in prominence threads. Numerical solution of the dispersion equation shows that the ratio only slightly decreases for thicker tubes in the case of smaller longitudinal inhomogeneity of external density, therefore the thin flux tube limit is a good approximation for prominence oscillations. However, stronger longitudinal inhomogeneity of external density may lead to the significant shift of frequency ratio for wider tubes and therefore the thin tube approximation may fail.} {The tendency of frequency ratio of second and first harmonics towards 3 in prominence threads is explained by the analogy of the oscillations with quantum harmonic oscillator, where the density inhomogeneity of the threads plays a role of potential energy.} | \label{S-Introduction} Filaments or prominences are cold clouds of dense plasma imbedded in the tenuous hot solar corona, probably supported by the prominence magnetic field against the gravity. Observations show that prominences are made up of many tube-like fine structures very likely smaller than the currently achievable resolution ($\approx\!\!\!150$~km). The structures are called fibrils or threads and they have a length of 10$^3$--10$^4$~km, which is much shorter than the longitudinal extent of prominence itself (Lin et al. \cite{Lin2005}, Labrosse et al. \cite{Labrosse2010}). Therefore, it is likely that the threads are concentrations of cold plasma at the middle of much longer magnetic tube, while the remaining part of the tube is filled with hot coronal plasma. Small-amplitude magnetohydrodynamic (MHD) waves and oscillations are frequently observed in solar prominence threads (Oliver et al. \cite{Oliver2002}, Lin et al. \cite {Lin2005}, Lin et al. \cite {Lin2007}, Lin et al. \cite{Lin2009}, Mackay et al. \cite {Mackay2010}, Arregui et al. \cite {Arregui2012}). MHD oscillations in prominences are well studied by both, slab and tube approximations (Roberts \cite{Roberts1991}, Joarder and Roberts \cite{Joarder1992a,Joarder1992b}, Oliver et al. \cite{Oliver1993}, Joarder et al. \cite{Joarder1997}, D\'iaz et al. \cite{Diaz2002,Diaz2005}, Dymova and Ruderman \cite{Dymova2005}, Terradas et al. \cite{Terradas2008}, Oliver \cite{Oliver2009}, Arregui et al. \cite{Arregui2011,Arregui2012}). It turns out that the longitudinal density stratification significantly influences the oscillation spectra of simple homogeneous tubes (D\'iaz et al. \cite{Diaz2004,Diaz2010}, Andries et al. \cite{andries1,Andries2009}, Dymova and Ruderman \cite{Dymova2005}, McEwan et al. \cite{McEwan2006}, Zaqarashvili et al. \cite{Zaqarashvili20072,Zaqarashvili2013}). However, the oscillations in coronal loops and prominence threads are very different. The difference is caused by the density profile: coronal loops have denser plasma at footpoints probably due to the stratification, while prominence threads (fibrils) are denser at the midpoint of magnetic tube (or slab). The density contrast between the tube center and footpoints is by an order larger in prominences than in coronal loops. The different physical parameters lead to different oscillation spectra in these two structures. For example, the ratio between the periods of first and second harmonics in homogeneous coronal loops is near 2 (Edwin and Roberts \cite{Edwin1983}), while the stratification may lead to the significant shift of the ratio (Andries et al. \cite{andries2}, McEwan et al. \cite{McEwan2006}). There are several observational examples of simultaneous existence of first and second harmonics of MHD oscillations in coronal loops, which indeed show the deviation of the ratio from 2 (Van Doorsselaere et al. \cite{van1, Van2}, Verwichte et al. \cite{Verwichte}, De Moortel and Brady \cite{demoo}, Srivastava et al. \cite{Srivastava, Srivastava2013}, Inglis and Nakariakov \cite{Inglis}). On the other hand, the period ratio of first and second harmonics is not 2 in the prominence case. Early calculations showed that the asymptotic frequency of internal kink mode in the prominence case is proportional to $2n+1$, where $n$ is the mode number (Joarder and Roberts \cite{Joarder1992b}). Then, the period ratio of first and second harmonics is 3, in contrast with coronal loops. The similar ratio can be seen on the plots of other papers concerning the prominence oscillations (Dymova and Ruderman \cite{Dymova2005}, D\'iaz et al. \cite{Diaz2010}). However, the authors did not clearly note this fact and consequently did not explain why the period ratio has tendency towards 3 in prominences. On the other hand, the frequency dependence of $2n+1$ found by Joarder and Roberts (\cite{Joarder1992b}) suggests that the quantum mechanical analogy may stand behind the result. All these authors used piecewise profiles to study the prominence oscillations. Consequently, the concentration of density in the middle of tube can be considered as a potential energy, which may lead to the problem of quantum harmonic oscillator. In this paper, we reconsider the oscillation of prominence threads using parabolic density profile in the longitudinal direction. Solution of Sturm-Liouville problem allows us to obtain the equation of a quantum harmonic oscillator. The solution of the equation leads to the frequency dependence of $2n+1$, therefore, we may conclude that the enhancement of plasma density (both, piecewise and parabolic profiles) at the middle of flux tube allows to quantify waves analogously with quantum mechanics. The paper is organized as follows: In Sect. 2 we describe the physical model of the considered problem. In Sect. 3 we give the Sturm-Liouville solution that leads to the dispersion equation described in Sect. 4. Analytical and numerical solutions of the dispersion equation are given in Sects. 4.1 and 4.2. We shortly summarize the paper in Sect. 5. | % \label{S-Conclusion} The period ratio of second and first harmonics is near 2 in weakly inhomogeneous coronal loops, however it is quite different in the case of prominences. Considering piecewise profiles of density concentration at the tube midpoint, several authors found that the ratio tends to 3. First, Joarder and Roberts (\cite{Joarder1992b}) found that the asymptotic frequency of internal kink mode is proportional to $2n+1$ (see Eq.~(21) in the paper), which yields that the period ratio of first and second harmonics of kink mode is 3 in the prominence case. Second, one can see in Figs.~4 and 5 in Dymova and Ruderman (\cite{Dymova2005}) that the period ratio tends to 3 when $W/L$ approaches to $0.2$, where $W$ is the half length of thread and $L$ is the half length of the tube itself. Third, Fig.~6 in D\'iaz et al. (\cite{Diaz2010}) shows that the period ratio of first and second harmonics of kink mode tends to 3 for $W/L > 0.1$. Joarder and Roberts (\cite{Joarder1992b}), Dymova and Ruderman (\cite{Dymova2005}) and D\'iaz et al. (\cite{Diaz2010}) did not explicitly note this fact and consequently did not explain why the period ratio has tendency towards $3$ in prominences. In this paper, we showed that the tendency of period ratio towards $3$ is the result of analogy between prominence oscillations and oscillations of quantum harmonic oscillator. The density enhancement at the midpoint of longer tube, which appears as a prominence thread, plays a role of potential energy. We used the method of separation of variables and solve the Sturm-Liouville problem of bounded oscillations in a prominence thread with longitudinally inhomogeneous density of parabolic profile. We found that the spatial variation of total pressure along the tube axis is governed by the stationary Schr\"{o}dinger equation, where the term with the longitudinal inhomogeneity of density stands for the potential energy. The equation is transformed into the equation of parabolic cylinder for the parabolic profile of the density. Consequently, the solutions are found in terms of Hermite polynomials, which are a set of orthogonal polynomials over the domain $(-\infty, \infty)$. Therefore, the solutions form an orthogonal basis of the Hilbert space. The solutions are bounded in infinity, therefore the oscillations are trapped inside the thread and hence are localised much higher than the footpoints. Then, using the continuity of velocity and total pressure at the tube surface, we derived the transcendental dispersion equation for MHD oscillations in terms of Bessel functions. The dispersion equation is solved analytically in thin flux tube approximation for kink waves. It is obtained that the normalized frequency of a fundamental kink mode depends on the inhomogeneity parameter $\alpha$ as ${\omega_n}\sim \alpha (2n+1)$, where $n$ is the longitudinal wave mode. This expression shows that the stronger inhomogeneity leads to the higher frequency of kink waves. However, the ratio of second and first harmonics of kink waves does not significantly depend on $\alpha$ in the thin tube approximation and it tends to 3 as it is suggested by the analogy with quantum mechanics. We solved the dispersion equation numerically for kink and sausage waves. The numerical solutions agree with the analytical estimations. We found that the frequency ratio of second and first harmonics of kink waves tends to 3 in thin flux tubes. The ratio depends slightly on the width to length ratio of the tube (Fig.~4). The wider tubes lead to bit smaller ratio of the frequencies when the inhomogeneity parameter inside and outside the tube is the same. Therefore, the thin flux tube approximation is a good approximation for the estimation of the ratio in this case. However, when the external inhomogeneity of plasma density is stronger then the ratio significantly depends on the inhomogeneity for wider tubes and the thin tube approximation may fail. Numerical solution of the dispersion equation shows that the frequency ratio slightly depends on the longitudinal inhomogeneity and decreased for stronger $\alpha$ (Fig.~5) for thin tubes, which is in good agreement with analytical formulas. The calculation in this paper is performed for straight tubes, while the curvature may significantly affect the oscillation spectrum (Selwa et al. \cite{Selwa2005}, D\'iaz et al. \cite{Diaz2006}). It would be also interesting to study the case of parabolic longitudinal inhomogeneity, when the denser plasma is located near the tube ends. In this case, the tube is analog of coronal loops rather than of prominence threads. The both problems should be studied in the future. | 14 | 3 | 1403.6027 |
1403 | 1403.1431_arXiv.txt | LIGO and Virgo recently completed searches for gravitational waves at their initial target sensitivities, and soon Advanced LIGO and Advanced Virgo will commence observations with even better capabilities. In the search for short duration signals, such as coalescing compact binary inspirals or ``burst'' events, noise transients can be problematic. Interferometric gravitational-wave detectors are highly complex instruments, and, based on the experience from the past, the data often contain a large number of noise transients that are not easily distinguishable from possible gravitational-wave signals. In order to perform a sensitive search for short-duration gravitational-wave signals it is important to identify these noise artifacts, and to ``veto'' them. Here we describe such a veto, the bilinear-coupling veto, that makes use of an empirical model of the coupling of instrumental noise to the output strain channel of the interferometric gravitational-wave detector. In this method, we check whether the data from the output strain channel at the time of an apparent signal is consistent with the data from a bilinear combination of auxiliary channels. We discuss the results of the application of this veto on recent LIGO data, and its possible utility when used with data from Advanced LIGO and Advanced Virgo. | \label{sec:intro} The LIGO and Virgo laser interferometric gravitational-wave (GW) detectors recently completed their observations in their initial design configurations. While GWs were not observed, important upper limits have been established in searching for signals from coalescing compact (neutron star and black hole) binaries~\cite{S6inspiral,S6BHinspiral}, burst events~\cite{S6burst} (core collapse supernova~\cite{Ott}, cosmic strings~\cite{S6string}, etc.), rapidly spinning neutron stars~\cite{S5CW}, and a stochastic GW background~\cite{S5stoch}. Searches were also made for GW signals in association with gamma ray bursts~\cite{S6gamma} and high energy neutrinos~\cite{S5neutrinos}. By 2015 Advanced LIGO~\cite{aLIGO} will begin operating with a significant improvement in sensitivity, followed soon thereafter by Advanced Virgo~\cite{aVirgo1,aVirgo2} coming on-line in 2016-2017~\cite{Commissioning}. A world-wide network of advanced interferometric GW detectors will be operating in the near future; a Japanese detector, KAGRA~\cite{KAGRA}, is currently under construction, and a third LIGO detector may also be constructed in India. Interferometric GW detectors are highly complex instruments; the data to date have often contained a large number of noise transients or noise frequency lines that were not easily distinguishable from possible GW signals. Noise artifacts can be created from imperfections or events within the detector itself, or caused by disturbances in the physical environment around where the detectors are located, which can couple to the output strain channel (the ``GW channel'') through various coupling mechanisms. In order to perform a sensitive search for GW signals, it is important to identify these noise artifacts, and to ``veto'' them. For the initial LIGO and Virgo detectors, numerous techniques were developed in order to identify and remove data from time periods when problems with the detector or its physical environment could be detected~\cite{S6DQ,VSR23DQ}. Similarly, specific noise frequency lines were also identified and removed from searches for GW signals from rapidly spinning neutron stars and the stochastic GW background~\cite{noise-lines}. Short duration noise transients, or \emph{glitches}, are especially problematic for compact coalescing binary and burst GW signal searches. During the recent LIGO (S6) and Virgo (VSR2, VSR3) scientific runs a number of vetoes were defined in order to identify and remove glitches from the interferometers' output strain GW channel, $H$. During these recent scientific runs data from numerous interferometer auxiliary channels and physical environment monitoring (PEM) devices were recorded, and searched for glitches. The glitch search tool used was a wavelet-based program called \emph{KleineWelle} (KW)~\cite{KleineWelle}. The various vetoes were developed by looking for statistical association between glitches in the interferometer auxiliary channels and the PEM devices and events in the interferometer's output strain channel. For example, the hierarchical (``hveto'') pipeline~\cite{hveto} and the ``used percentage veto''~\cite{UPV} were effective in identifying noise events in the GW channel due to glitches that appeared in multiple channels in LIGO and Virgo data, while the ``SeisVeto''~\cite{MacLeod:2011up} was effective in eliminating glitches that originated due to fluctuations in the seismic noise. Another veto compared KW triggers from the two quadrature phases of Virgo's output strain channel, and when associations could be made between events in the in-phase and quadrature channels, then the in-phase events were vetoed~\cite{PQveto}~\footnote{Another veto method making use of a similar idea, implemented for the GEO\,600 detector, is described in~\cite{Hewitson:2005wr}.}. The ``{traditional}'' veto methods mentioned above all search for a time coincidence between a glitch in an interferometer's output strain channel, and an event in an interferometer auxiliary or PEM channel. The \emph{bilinear-coupling veto}, which we are describing in this paper, was developed with the goal to see if the data from an interferometer's output GW strain channel at the time of an apparent signal is consistent with the data from the interferometric detector's auxiliary channels. The consistency check is based on the observation of the coupling of different noise sources to the interferometer output strain channel. This veto was applied on LIGO S6 data~\cite{S6inspiral,S6BHinspiral}, and can be applied on data from Advanced LIGO and Advanced Virgo. In this paper we will fully describe the bilinear-coupling veto, and summarize its results when used on LIGO S6 data. We will also discuss its potential capabilities when used with data from Advanced LIGO and Advanced Virgo. The organization of the paper is as follows. In Section~\ref{sec:vetomethod} we describe the veto method. The results of the bilinear-coupling veto when applied to LIGO S6 data are given in Section~\ref{sec:veto_analysis_s6}. In Section~\ref{sec:future_work} we discuss how the bilinear-coupling veto can be used as a potential diagnostic tool with the advanced detectors. Concluding observations are given in Section~\ref{sec:conclusions}. | \label{sec:conclusions} In this paper we have presented a description of a novel veto method that was recently used to eliminate short duration noise transients (glitches) in data from the LIGO detectors during the S6 science run~\cite{S6inspiral,S6BHinspiral}. The unique aspect of the bilinear-coupling veto, as opposed to other vetoes used by LIGO and Virgo~\cite{hveto,UPV,PQveto}, is that it provides a means to identify and eliminate glitches in a detector's output GW channel that are associated with non-optimal states of interferometer sub-systems; these non-optimal states are observed in slow auxiliary channels, like the ones studied in this paper. This veto was also developed with the goal to see if the data from an interferometric detector's output GW strain channel at the time of an apparent signal is consistent with the data from a detector auxiliary channel, or a combination of auxiliary channels. Results were presented demonstrating the effectiveness of this veto with LIGO S6 data. For the case of the upcoming advanced detectors like Advanced LIGO~\cite{aLIGO} and Advanced Virgo~\cite{aVirgo1,aVirgo2}, the severity of noise glitches in the GW strain channels is presently unknown. If such glitches are found to limit the ability to detect GW transient events, the the bilinear-coupling veto can be implemented as a means to reduce the number of noise transients. It should be noted, however, that Advanced LIGO and Advanced Virgo will reach their target sensitivities over a number of years of commissioning~\cite{Commissioning}. During this period it will be of critical importance to have tools that allow for the identification and characterization of noise. As demonstrated in this paper, the bilinear-coupling veto can be used as a means to diagnose sources of noise. Another avenue for the improvement of the bilinear-coupling veto will be through the use of improved glitch trigger generators. The KW~\cite{KleineWelle} pipeline will continue to be used to generate triggers. However, new trigger pipelines with improved resolution at low frequencies are being developed. We also note that several other noise regression methods using linear/bilinear coupling models are being investigated within the LIGO-Virgo collaboration~\cite{Tiwari:2012,Klimenko:2012,Drago:2012}. We expect the bilinear-coupling veto to be a powerful noise diagnostic tool and veto generator for the next generation of laser interferometric GW detectors. | 14 | 3 | 1403.1431 |
1403 | 1403.5212_arXiv.txt | { So called superluminous supernovae have been recently discovered in the local Universe. It appears possible that some of them originate from stellar explosions induced by the pair instability mechanism. Recent stellar evolution models also predict pair instability supernovae from very massive stars at fairly high metallicities (i.e., $Z \sim 0.004$). } { We provide supernova models and synthetic light curves for two progenitor models, a 150~\Msun{} red-supergiant and a 250~\Msun{} yellow-supergiant at a metallicity of $Z = 0.001$, for which the evolution from the main sequence to collapse, and the initiation of the pair instability supernova (PISN) itself, has been previously computed in a realistic and self-consistent way. } { We are using the radiation hydrodynamics code STELLA to describe the supernova evolution of both models over a time frame of about 500 days. } { We describe the shock-breakout phases of both supernovae which are characterized by a higher luminosity, a longer duration and a lower effective temperature than those of ordinary Type~IIP supernovae. We derive the bolometric as well as the \emph{U}, \emph{B}, \emph{V}, \emph{R} and \emph{I} light curves of our pair instability supernova models, which show a long-lasting plateau phase with maxima at $M_{\rm bol}\simeq -19.3$~mag and $-21.3$~mag for our lower and higher mass model, respectively. While we do not produce synthetic spectra, we also describe the photospheric composition and velocity as function of time. } { We conclude that the light curve of the explosion of our initially 150~\Msun{} star resembles those of relatively bright type~IIP supernovae, whereas its photospheric velocity at early times is somewhat smaller. Its $^{56}$Ni mass of 0.04~\Msun{} also falls well into the range found in ordinary core collapse supernovae. The light curve and photospheric velocity of our 250~\Msun{} models has a striking resemblance with that of the superluminous SN~2007bi, strengthening its interpretation as pair instability supernova. We conclude that pair instability supernovae may occur more frequently in the local universe than previously assumed. } | \label{sect:conclusions2} We carried out simulations of shock breakouts and light curves of pair instability supernovae using two evolutionary models of 150~$M_\odot${} and 250~$M_\odot${} at metallicity $Z=10^{\,-3}$ \citep{2007A&A...475L..19L,2014paper1..K}. We used the radiation hydrodynamics code {\sc STELLA} for this purpose \citep{2006A&A...453..229B}. The considered metallicity ($Z = 10^{\,-3}$) is among the highest of PISN models that have been so far presented in the literature \citep{1990A&A...233..462H,2013arXiv1312.5360W}. Therefore, our models may serve as useful references for future studies on PISNe observed in the local Universe, as well as in the early Universe. From our qualitative comparison to ordinary core collapse SNe we conclude that it is difficult to distinguish low mass pair instability explosions from hydrogen-rich core collapse explosions. The photometric and spectroscopic observations, including X-ray and ultraviolet (for detection of shock breakout events), should be very detailed from the earliest epoch to help shedding light on this. The increasing number of SN surveys allows to increase the number of discovered SNe and detailed data from the very early epoch after explosion, especially those missions which have the short cadences (e.g. PTF). Given the low-mass preference of the stellar initial mass function, a large fraction of PISNe that will be observed in the local Universe could resemble our 150~$M_\odot${} model, which represents PISNe from the low-mass end of the PISN regime. These PISNe are predicted to have the following characteristics: \begin{enumerate} \item The progenitors are likely to be red-supergiants having very extended envelopes ($R\sim 3000~\mathrm{R_\odot}${}), if they can retain some fraction of the hydrogen envelopes by the time of explosion. Our 150~$M_\odot${} model has the final mass of 94~$M_\odot${} and the envelope mass is 29~$M_\odot${}, which is significantly smaller than in the corresponding case of zero or extremely low metallicity ($\sim 70~M_\odot${}). The hydrogen mass fraction in the envelope is only about 0.25. \item The resulting PISN would appear to be a bright type~IIP supernova like SN~2009kf. Its luminosity at the visual maximum would be typically higher by 2-3~magnitudes than average SNe~IIP, although the total amount of radioactive nickel would be more or less similar to those from usual hydrogen-rich core-collapse supernovae ($\sim 0.05~M_\odot${}), depending on the final mass of the progenitor. \item The plateau duration would be similar to those of ordinary SNe~IIP, but much shorter than in the corresponding case at extremely low metallicity because of the relatively low mass of the envelope and the low hydrogen mass fraction. \item The shock breakout duration would be somewhat longer ($\sim 6$~hrs) and redder ($0.07$~keV) than those of ordinary SNe~IIP. \item The photospheric color temperature would be systematically higher than those of ordinary SNe~IIP, and its evolution would look quite similar to that of SN~2009kf, which is an unusually bright SN~IIP with a NUV-excess. \item Because of the very large radius of the progenitor, the photospheric velocity at early times would be systematically lower than those of ordinary SNe~IIP (Figure~\ref{figure:uph}). \end{enumerate} \begin{figure} \centering \includegraphics[width=0.5\textwidth]{uph_PISN250_vs_SLSN} \caption[The photospheric velocity of our 250~$M_\odot${}~PISN model and of several SLSN~Ic.] {The photospheric velocity of our 250~$M_\odot${}~PISN model and of several SLSN~Ic. The observed data are taken from \citet{2010A&A...512A..70Y,2011ApJ...743..114C}. SN~2007bi points show the lower velocity limit measured from O~I~$\lambda~7774$ which we use as a best estimate for the photospheric velocity. The observed data are shifted to the maximum phase of the theoretical curve (day~175). The bold part of the theoretical curve (green) covers the maximum phase (from day~175) and the successive decline phase.} \label{figure:uphsnIc} \end{figure} We also conclude that some observed luminous SNe~Ic could have emerged from a pair instability explosion. Careful and deep photometric and spectroscopic observations would help to differentiate a pair instability explosion from SN~Ic, in particular for the rise epoch and the tail. A general property of PISN explosions from the high mass regime is a slow light curve evolution due to massive ejecta. This causes a long rise to the peak luminosity and a long transition to the radioactive tail. It was previously noted \citep{2005ApJ...633.1031S,2011ApJ...734..102K,2013ApJ...777..110W, 2013MNRAS.428.3227D} that a PISN from the high mass end of the PISN regime does not resemble any of the observed supernovae so far. However, we demonstrated that SLSNe~2007bi and PTF10mnm may fit well to our high mass PISN Model~250M. This concerns the light curve shape, the peak luminosity, the photospheric velocity and the bulk ejecta masses. We suggest the following criteria to distinguish high mass PISN from CCSN: \begin{enumerate} \item A short precursor in \emph{U}, \emph{B}, \emph{V}-bands at about $-19$~mag lasting less than 40~days which can appear itself as a SN long before (e.g. half a year -- a year before) the main maximum. \item The pronounced rise time is larger than 200~days, which is significantly longer than for ordinary SN~Ic. \item A PISN may evolve from hydrogen-rich to hydrogen-poor type. \item The nebular luminosity is powered by radioactive nickel decay and determined by the amount of produced nickel. Large amounts of radioactive nickel, tens of solar masses, produced in PISN significantly exceed typical 0.05~--~0.5~$M_\odot${} of nickel left by ordinary SNe~Ic. \item The photospheric velocity is lower than the velocities of SNe~Ic during the whole evolution. On top of that the PISN photospheric velocity has a peculiar evolution during the rise to maximum light. \end{enumerate} Increasing SN statistics allows to discover the brightest SNe together with others \citep{2002SPIE.4836..154K,2008arXiv0805.2366I,2009PASP..121.1395L}. According to \citet{2007A&A...475L..19L} one pair instability explosion in the local Universe occurs among one thousand core collapse SNe. At present the number of discovered SNe per year surpasses one thousand, therefore, we expect several PISNe among the large number of discovered SNe. However, their unambiguous identification may be challenging, which we hope to facilitate with our present study. | 14 | 3 | 1403.5212 |
|
1403 | 1403.2742_arXiv.txt | We analyze age distributions of two nearby rich stellar clusters, the NGC 2024 (Flame Nebula) and Orion Nebula Cluster (ONC) in the Orion molecular cloud complex. Our analysis is based on samples from the MYStIX survey and a new estimator of pre-main sequence (PMS) stellar ages, $Age_{JX}$, derived from X-ray and near-infrared photometric data. To overcome the problem of uncertain individual ages and large spreads of age distributions for entire clusters, we compute median ages and their confidence intervals of stellar samples within annular subregions of the clusters. We find core-halo age gradients in both the NGC 2024 cluster and ONC: PMS stars in cluster cores appear younger and thus were formed later than PMS stars in cluster peripheries. These findings are further supported by the spatial gradients in the disk fraction and $K$-band excess frequency. Our age analysis is based on $Age_{JX}$ estimates for PMS stars, and is independent of any consideration of OB stars. The result has important implications for the formation of young stellar clusters. One basic implication is that clusters form slowly and the apparent age spreads in young stellar clusters, which are often controversial, are (at least in part) real. The result further implies that simple models where clusters form inside-out are incorrect, and more complex models are needed. We provide several star formation scenarios that alone or in combination may lead to the observed core-halo age gradients. | } While considerable insights have been gained regarding the formation of stars on small scales, the formation of rich stellar clusters dominated by OB stars is quite uncertain. Debate has waged for decades over the relative importance of rapid `top-down' fragmentation or a slower `bottom-up' process involving merging of subcomponents \citep{Clarke00}. In the former model, cluster formation would occurring within $1-2$ core free-fall times, $t_{ff} \simeq 10^5$~yr \citep{Elmegreen00}. Rapid gravitational collapse is characteristic of clouds with weak turbulence on small scales \citep[]{VazquezSemadeni03}. In the latter model, cluster formation can be extended over millions of years, delayed by strong turbulence in the natal cloud. \citet{Krumholz07} argue for slow cluster formation, in part on extensive evidence for strong turbulence in giant molecular clouds \citep{MacLow04} and in part on empirical evidence from Hertzsprung-Russell diagrams (HRDs) of revealed clusters showing a wide age spread in the apparent ages of pre-main sequence (PMS) stars. However, the interpretation of HRD age spreads is quite controversial for both observational and theoretical reasons, as reviewed by \citet{Preibisch12}. For example, \citet{Huff06} construct a model of the Orion Nebula Cluster (ONC) where star formation accelerates slowly over millions of years in both the cluster core and outer regions. From a detailed analysis based on optical photometry and spectroscopy, \citet{Reggiani2011} report a characteristic age of 2.2~Myr, and an intrinsic age spread of 2~Myr, after accounting for various sources of age uncertainties. \citet{Jeffries2011} argue that the similar apparent age distribution of disk-bearing and disk-free stars in the ONC implies that the cluster does not have a wide intrinsic age spread, but their result permit a spread of $\sim 3$~Myr. A variety of observational difficulties can also cause artificial age spreads \citep{Preibisch12}. And astrophysical calculations of stars decending the Hayashi tracks for different histories of accretion show that an artificial age spread can appear for coeval clusters under certain conditions \citep{Baraffe12}. A confusing element of this issue is that clusters often \citep[though not always;][]{Wang08} show mass segregation where massive OB stars concentrate in the cluster cores. The ages of massive stars are difficult to estimate as they quickly arrive on the main sequence while the PMS stars are on their Hayashi tracks. There is some evidence that massive stars in cluster cores are younger than more dispersed PMS stars in rich clusters (\S\ref{prev_evidence.section}). But it is not clear whether this reflects a general age gradient in cluster formation, or some special slow mode in the star formation process of massive stars, such as competitive accretion of core gas or stellar mergers \citep{Zinnecker07}. In this context, we present a new empirical finding: that PMS stars are younger in the core region than in the outer regions of two nearby rich clusters, the NGC~2024 (Flame Nebula) and Orion Nebula clusters in the Orion molecular cloud complex. This result is independent of the ages of massive stars in the core. The work rests on two foundations. The first is a new sample of cluster members developed by the MYStIX (Massive Young Star-Forming Complex Study in Infrared and X-ray) project for 20 star forming regions, including the Flame and Orion Nebulae \citep{Feigelson13}. The second is a new estimator of PMS stellar ages called $Age_{JX}$ that is derived from X-ray and near-infrared photometric data \citep[][hereafter G14]{Getman2014}. The spatial-age gradient we report here lies within the unified structure of a rich monolithic cluster on $< 1$~pc scales. Getman et al.\ report a separate result of spatial-age gradients across star forming regions on $\sim 2-20$~pc scales. We briefly review the methodology and samples from the MYStIX and $Age_{JX}$ studies (\S\ref{methods.section}), and present the results for the NGC~2024 and Orion Nebula clusters in \S\ref{results_section}. The implications for rich cluster formation are discussed in \S\ref{discussion.section}. | \label{conclusion_section} It has not been clearly known whether stellar cluster formation occurs within 1-few core free-fall times or over millions of years. The view of the slow mode of cluster formation is supported in part by empirical evidence of wide age spreads within rich stellar clusters. However, it has been unclear whether these age spreads are due to poor individual age estimates or to real extended star formation histories (\S \ref{intro_section}). In this work, we analyze age distributions of two nearby rich stellar clusters, the NGC 2024 (Flame Nebula) and Orion Nebula clusters in the Orion molecular cloud complex. Our analysis is based on a new estimator of PMS stellar ages, $Age_{JX}$, that is derived from X-ray and near-infrared photometric data (G14). To overcome the problem of uncertain individual ages, we compute median ages and their confidence intervals of stellar samples within annular subregions of the clusters. We find core-halo age gradients in both the NGC 2024 and Orion Nebula clusters: low-mass PMS stars in cluster cores appear younger, and thus formed later, than low-mass PMS stars in cluster peripheries (\S \ref{age_gradient_section}). Various selection effects were investigated (\S \ref{xlf_section}). In the ONC they turned out to be unimportant, but not in NGC 2024. Other considerations helped suggesting that these should not be a major bias in the result (\S \ref{ngc2024_core_section}). These findings are further supported by the independent discovery of the spatial gradients in the mid-infrared and near-infrared disk fractions (\S \ref{disk_fraction_section}). Based purely on PMS stellar data in a narrow mass range, our results give no information on the sequence of events that give rise to OB star formation and mass segregation. {\it An essential implication of our findings is that clusters do have true age spreads.} If clusters truly formed exceedingly rapidly, then our median $Age_{JX}$ estimates would be consistent with a single cluster age value. The ages shown in Figure~\ref{fig1} (panels c and f) invalidate rapid cluster formation for NGC~2024 and the ONC. We provide several theoretical star formation scenarios that alone, or in combination with each other, may lead to the observed core-halo age gradients (\S \ref{scenarios_section}). These include: exhaustion of gas in the periphery of a cloud, acceleration of star formation in the cloud core, late formation of massive stars with low-mass stellar siblings, kinematic outward drift of older stars, stellar dynamical heating with cluster relaxation, expansion of subclusters, infalling filaments nursing newly born stars, and subcluster mergers. | 14 | 3 | 1403.2742 |
1403 | 1403.2268_arXiv.txt | The galactic habitable zone is defined as the region with sufficient abundance of heavy elements to form planetary systems in which Earth-like planets could be born and might be capable of sustaining life, after surviving to close supernova explosion events. Galactic chemical evolution models can be useful for studying the galactic habitable zones in different systems. We apply detailed chemical evolution models including radial gas flows to study the galactic habitable zones in our Galaxy and M31. We compare the results to the relative galactic habitable zones found with ``classical'' (independent ring) models, where no gas inflows were included. For both the Milky Way and Andromeda, the main effect of the gas radial inflows is to enhance the number of stars hosting a habitable planet with respect to the ``classical'' model results, in the region of maximum probability for this occurrence, relative to the classical model results. These results are obtained by taking into account the supernova destruction processes. In particular, we find that in the Milky Way the maximum number of stars hosting habitable planets is at 8 kpc from the Galactic center, and the model with radial flows predicts a number which is 38\% larger than what predicted by the classical model. For Andromeda we find that the maximum number of stars with habitable planets is at 16 kpc from the center and that in the case of radial flows this number is larger by 10 \% relative to the stars predicted by the classical model. | The Circumstellar Habitable Zone (CHZ) has generally been defined to be that region around a star where liquid water can exist on the surface of a terrestrial (i.e., Earth-like) planet for an extended period of time (Huang 1959, Shklovsky \& Sagan 1966, Hart 1979). Kasting et al. (1993) presented the first one-dimensional climate model for the calculation of the width of the CHZ around the Sun and other main sequence stars. Later on, several authors improved that model: Underwood et al. (2003) computed the evolution of the CHZ during the evolution of the host star. Moreover, Selsis et al. (2007) considered the case of low mass stars, and Tarter et al. (2007) asserted that M dwarf stars can host planets in which the origin and evolution of life can occur. Recently, Vladilo et al. (2013) applied a one-dimensional energy balance model to investigate the surface habitability of planets with an Earth-like atmospheric composition but different levels of surface pressure. However what is most relevant to our paper is that it exists a well-established correlation between metallicity of the stars and the presence of giant planets: the host stars are more metallic than a normal sample ones (Gonzalez, 1997; Gonzalez et al., 2001; Santos et al., 2001, 2004; Fischer \& Valenti, 2005; Udry et al., 2006; Udry \& Santos, 2007). In particular, Fisher \& Valenti (2005) and Sousa at al. (2011) presented the probabilities of the formation of giant planets as a function of [Fe/H] values of the host star. In Sozzetti et al. 2009, Mortier et al. (2013a,b) these probabilities are reported for different samples of stars. The galactic chemical evolution can substantially influence the creation of habitable planets. In fact, the model of Johnson \& Li (2012) showed that the first Earth-like planets likely formed from circumstellar disks with metallicities $Z \geq 0.1 Z_{\odot}$. Moreover, Buchhave et al. (2012), analyzing the mission Kepler, found that the frequencies of the planets with earth-like sizes are almost independent of the metallicity, at least up to [Fe/H] values $\sim$ 0.6 dex. This is it was confirmed by Sousa et al. (2011) from the radial velocity data. Data from Kepler and from surveys of radial velocities from earth show that the frequencies of planets with masses and radii not so different from the Earth, and with habitable conditions are high: $\sim 20 \%$ for stars like the Sun (Petigura et al. 2013), between the 15 \% (Dressing \& Charbonneau 2013) and 50 \% for M dwarf stars (Bonfils et al. 2013). Habitability on a larger scale was considered for the first time by Gonzalez et al. ( 2001), who introduced the concept of the galactic habitable zone (GHZ). The GHZ is defined as the region with sufficient abundance of heavy elements to form planetary systems in which Earth- like planets could be found and might be capable of sustaining life. Therefore, a minimum metallicity is needed for planetary formation, which would include the formation of a planet with Earth-like characteristics (Gonzalez et al. 2001, Lineweaver 2001, Prantzos 2008). Gonzalez et al. (2001) estimated, very approximately, that a metallicity at least half that of the Sun is required to build a habitable terrestrial planet and the mass of a terrestrial planet has important consequences for interior heat loss, volatile inventory, and loss of atmosphere. On the other hand, various physical processes may favor the destruction of life on planets. For instance, the risk of a supernova (SN) explosion sufficiently close represents a serious risk for the life (Lineweaver et al. 2004, Prantzos 2008, Carigi et al. 2013). Lineweaver et al. (2004), following the prescription of Lineweaver et al. (2001) for the probability of earth-like planet formation, discussed the GHZ of our Galaxy. They modeled the evolution of the Milky Way in order to trace the distribution in space and time of four prerequisites for complex life: the presence of a host star, enough heavy elements to form terrestrial planets, sufficient time for biological evolution, and an environment free of life-extinguishing supernovae. They identified the GHZ as an annular region between 7 and 9 kpc from the Galactic center that widens with time. Prantzos (2008) discussed the GHZ for the Milky Way. The role of metallicity of the protostellar nebula in the formation and presence of Earth-like planets around solar-mass stars was treated with a new formulation, and a new probability of having Earths as a function of [Fe/H] was introduced. In particular, Prantzos (2008) criticized the modeling of GHZ based on the idea of destroying life permanently by SN explosions. Recently, Carigi et al. (2013) presented a model for the GHZ of M31. They found that the most probable GHZ is located between 3 and 7 kpc from the center of M31 for planets with ages between 6 and 7 Gyr. However, the highest number of stars with habitable planets was found to be located in a ring between 12 and 14 kpc with a mean age of 7 Gyr. 11\% and 6.5\% of all the formed stars in M31 may have planets capable of hosting basic and complex life, respectively. However, Carigi at al. (2013) results are obtained using a simple chemical evolution model built with the instantaneous recycling approximation which does not allow to follow the evolution of Fe, and where no inflows of gas are taken into account. In this work we investigate for the first time the effects of radial flows of gas on the galactic habitable zone for both our Galaxy and M31, using detailed chemical evolution models in which is relaxed the instantaneous recycle approximation, and the core collapse and Type Ia SN rates are computed in detail. For the GHZ calculations we use the Prantzos (2008) probability to have life around a star and the Carigi et al (2013) SN destruction effect prescriptions. In this work we do not take into account the possibility of stellar migration (Minchev et al. 2013, and Kybrik at al. 2013) and this will be considered in a forthcoming paper. The paper is organized as follows: in Sect. 2 we present our galactic habitable zone model, in Sect. 3 we describe our ``classical'' chemical evolution models for our Galaxy and M31, in Sects. 4 the reference chemical evolution models in presence of radial flows are shown. The results of the galactic habitable zones for the ``classical'' models are presented in Section. 5, whereas the ones in presence of radial gas flows in Section 6. Finally, our conclusions are summarized in Section 7. | In this paper we computed the habitable zones (GHZs) for our Galaxy and M31 systems, taking into account ``classical'' models and models with radial gas inflows. We summarize here our main results presented in the previous Sections. Concerning the ``classical'' models we obtained: \begin{itemize} \item The Milky Way model which is in agreement with the work of Lineweaver et al. (2004) assumes the case 2) for the SN destruction (the SN destruction is effective if the SN rate at any time and at any radius is higher than two times the average SN rate in the solar neighborhood during the last 4.5 Gyr of the Milky Way's life). With this assumption, we find that the Galactic region with the highest number of host stars of an Earth-like planet is between 7 and 9 kpc with the maximum localized at 8 kpc. \item For Andromeda, comparing our results with the ones of Carigi et al. (2013), with the same prescriptions for the SN destruction effects, we find substantial differences in the inner regions (R $\leq$ 14 kpc). In particular, in this region there is a high enough SN rate to annihilate life on formed planets at variance with Carigi et al. (2013). Nevertheless, we are in agreement for the external regions. It is important to stress the most important limit of the Carigi et al. (2013) model: Type Ia SN explosions were not considered. We have shown instead, that this quantity is important both for Andromeda and for the Galaxy. \end{itemize} In this work for the first time the effects of radial flows of gas were tested on the GHZ evolution, in the framework of chemical evolution models. \begin{itemize} \item Concerning the models with radial gas flows both for the Milky Way and M31 the effect of the gas radial inflows is to enhance the number of stars hosting a habitable planet with respect to the ``classical'' model results in the region of maximum probability for this occurrence, relative to the classical model results. In more details we found that: \item At the present time, for the Milky Way if we treat the SN destruction effect following the case 2) criteria, the total number of host stars as a function of the Galactic time and Galactocentric distance tell us that the maximum number of stars is centered at 8 kpc, and the total number of host stars is increased by 38 \% compared to the ``classical'' model results. \item In M31 the main effect of the gas radial inflow is to enhance at anytime the fraction of stars with habitable planets, described by the probability $P_{GHZ}$, in outer regions compared to the classical model results also for the models without SN destruction. This is due to the fact that: i) the M31R model has a fixed SFR efficiency throughout all the galactocentric distances, this means that in the external regions there is a higher SFR compared to the ``classical'' M31B model; ii) the radial inflow velocities are smaller in the outer part of the galaxy compared to the ones used for the Milky Way model RD, therefore not so much gas is removed from the outer shell. The galactocentric distance with the maximum number of host stars is 16 kpc. Presently, at this distance the total number of host stars is increased by 10 \% compared to the M31B model results. These values for the M31R model are always higher than the M31B ones. In spite of the fact that in in the future it will be very unlikely to observe habitable planets in M31, that could confirm these model results about the GHZ, our aim here was to test how GHZ models change in accordance with different types of spiral galaxies, and different chemical evolution prescriptions. \end{itemize} | 14 | 3 | 1403.2268 |
1403 | 1403.4079_arXiv.txt | GRB~130925A was an unusual GRB, consisting of 3 distinct episodes of high-energy emission spanning \til20 ks, making it a member of the proposed category of `ultra-long' bursts. It was also unusual in that its late-time X-ray emission observed by \swift\ was very soft, and showed a strong hard-to-soft spectral evolution with time. This evolution, rarely seen in GRB afterglows, can be well modelled as the dust-scattered echo of the prompt emission, with stringent limits on the contribution from the normal afterglow (i.e.\ external shock) emission. We consider and reject the possibility that GRB~130925A was some form of tidal disruption event, and instead show that if the circumburst density around GRB~130925A is low, the long duration of the burst and faint external shock emission are naturally explained. Indeed, we suggest that the ultra-long GRBs as a class can be explained as those with low circumburst densities, such that the deceleration time (at which point the material ejected from the nascent black hole is decelerated by the circumburst medium) is \til20 ks, as opposed to a few hundred seconds for the normal long GRBs. The increased deceleration radius means that more of the ejected shells can interact before reaching the external shock, naturally explaining both the increased duration of GRB 130925A, the duration of its prompt pulses, and the fainter-than-normal afterglow. | \label{sec:intro} Gamma-ray bursts (GRBs), discovered by \cite{Klebesadel73}, are the most powerful explosions in the universe. \cite{Mazets81} and \cite{Kouveliotou93} showed that GRBs can be divided into two classes based on their duration: long and short GRBs. These objects have different progenitors, with the short (\sqiglt2 s) GRBs believed to be the the mergers of binary neutron-star systems and long GRBs arising from the collapse of a massive star (see \citealt{Zhang09a} for a detailed discussion of GRB progenitors and classification). In both cases, it is generally believed that the prompt emission arises due to interactions within the outflow of material (see, e.g.\ \citealt{Zhang07Review}). Recently \cite{Gendre13}, \cite{Stratta13} and \cite{Levan14} have proposed an additional category of `ultra-long' bursts, GRBs with durations of kiloseconds. These authors consider tidal disruption of a white-dwarf star by a massive black hole, and a GRB with a blue supergiant progenitor (larger than those of normal long GRBs) as possible causes of these ultra-long bursts, with the latter being favoured. In contrast, \cite{Virgili13} suggest that the ultra-long GRBs simply represent the tail of the distribution of long GRBs. With the exception of GRB~101225A, the ultra-long GRBs show an X-ray afterglow, once the prompt emission is over. Such a feature is seen after most long GRBs, and is generally believed to occur when the material ejected by the GRB, which is travelling close to the speed of light, is decelerated by the circumburst medium (CBM). A shock forms and propagates into the medium, radiating by the synchrotron mechanism as it does so. This model is not uniformly accepted, with some authors (e.g.\ \citealt{Uhm07,Genet07,Leventis13}) arguing that the late-time emission is strongly affected by emission from a reverse shock, which propagates back into the out-flowing material once it is decelerated. Regardless of their physical origin, GRB X-ray afterglows show a range of different light curve behaviours \citep{Evans09}, perhaps the most curious of which is the so-called `plateau' phase \citep{Nousek06,Zhang06} -- a period during which the afterglow fades slowly, if at all. The most widely-accepted explanation for this plateau is that there is an ongoing injection of energy into the shocked CBM \citep[e.g][]{Liang07}. Such plateaux are not seen in all afterglows: \cite{Evans09} found them in $<70\%$ of bursts. In contrast to the light curves, the spectra of X-ray afterglows show little variation, with the photon index ($\Gamma$; $N(E) dE\propto E^{-\Gamma}$) distribution\footnote{The XRT catalogue quotes the spectral energy index, $\beta=\Gamma-1$} being approximately Gaussian, with a mean of 2.0 and a FWHM of 0.7 (\citealt{Evans09}, the live XRT GRB catalogue\footnote{http://www.swift.ac.uk/xrt\_live\_cat}). This spectrum is generally found not to evolve with time \citep[e.g.][]{Butler07a,Shen09}. In this paper we consider GRB~130925A, a GRB which triggered \swift, \fermi, \kw, \emph{INTEGRAL}, and \emph{MAXI}, and had a duration of $>5$ ks, making it a candidate ultra-long GRB. However, this burst is also unusual in that its late-time X-ray data showed a strong hard-to-soft spectral evolution with time. Recently, \cite{Bellm14} have analysed \swift, \emph{Chandra} and \emph{NuSTAR} data of this burst, and claim the presence of multiple afterglow components; however, we shall show that a simpler emission model can explain the data presented here. Throughout this paper we assume a cosmology with $H_0=71$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_m=0.27, \Omega_{\rm vac}=0.73$, and we made use of the online Cosmology Calculator\footnote{http://www.astro.ucla.edu/$\sim$wright/CosmoCalc.html} \citep{Wright06}. Errors are at the 90\%\ level unless otherwise stated. \begin{figure*} \begin{center} \psfig{file=fig1.eps,height=16cm,angle=-90} \caption{Multi-observatory light curves of the prompt and flaring emission. These were built assuming a constant spectral model, as fitted to the \emph{Episode 1} data (Section~\ref{sec:prompt}). The fluxes are given in each instrument's native band, and in the observer frame. This reveals the relative flux at different energies, for each pulse, illustrating the spectral variation from pulse to pulse. The data have been binned to a minimum signal-to-noise ratio per bin of 5, using the approach of \protect\cite{Evans10}. As \swift\ and \fermi\ are in low-Earth orbits, the times when the source was outside of their field of view are marked by the grey diagonal lines. For \swift-XRT whenever the source was in the field of view it was detected, so to keep the plot simple we do not mark the times when it was not in the field (although these will be similar to the BAT times). Similarly for {\emph MAXI\/} which could only observe the GRB for \til2 min of each \til93 min orbit (and only detected the GRB in one orbit) we do not include the observability intervals. } \label{fig:earlyCurve} \end{center} \end{figure*} | GRB~130925A was an extremely long GRB at $z=0.348$, with an observer-frame duration of around 20 ks, and three main episodes of emission at $E>15$ keV. Apart from its length, the properties of the prompt emission appear consistent with those of other bursts. However, the extreme duration of this burst is inconsistent with the general population, and we have ruled out observational bias as the cause of this incompatibility. The late-time X-ray data show a strong spectral evolution, which can be well modelled as dust scattering of the prompt emission. A systematic study of other GRBs shows evidence for such emission in at least 8 other objects. GRB~130925A is the most extreme example, because in addition to the dust echo, it shows no evidence for a contribution from a standard afterglow; we place a limit of $E_{\rm afterglow}<3.3\tim{50}$ erg, a factor of 1,000 lower than the energy released in the prompt phase. This faint (or missing) external shock is essential to the detection of a dust echo, because an external shock of normal brightness will otherwise outshine the echo. We have considered two possible scenarios to explain this object: a tidal disruption event, or a GRB. The former is difficult to reconcile with the observed timescales, although the disruption of a white dwarf may be permissible if the masses are finely tuned. The energetics, and the lack of emission detected from fallback accretion, appear to rule out a TDE origin for GRB 130925A. The lack of a standard, external-shock afterglow presents a challenge for the GRB interpretation, and even in a low density environment ($n\til10^{-3}$ cm$^{-3}$) the ratio of the prompt fluence to the limit on the afterglow fluence can only be explained if the prompt emission process converts more of its energy to radiation than is typical for GRBs. However, we argue that this is to be expected in a low density circumburst medium, in which the external shock forms at a greater distance from the GRB than normal, allowing more internal shocks to occur and dissipate energy which, in a typical GRB, would instead be injected into the external shock. The ultra-long GRBs detected so far show a lower ratio of afterglow to prompt fluence than the population of normal long GRBs, supporting the idea that they occur in a low-density environment. | 14 | 3 | 1403.4079 |
1403 | 1403.3974_arXiv.txt | {Carbon and oxygen isotope ratios are excellent measures of nuclear processing, but few such data have been taken toward extragalactic targets so far. Therefore, using the IRAM 30-m telescope, CN and CO isotopologues have been measured toward the nearby starburst galaxy NGC~253 and the prototypical ultraluminous infrared galaxy Mrk~231. Toward the center of NGC~253, the CN and $^{13}$CN $N$ = 1$\rightarrow$0 lines indicate no significant deviations from expected local thermodynamical equilibrium after accounting for moderate saturation effects (10 and 25\%) in the two detected spectral components of the main species. Also accounting for calibration uncertainties, which dominate the error budget, the $^{12}$C/$^{13}$C ratio becomes 40$\pm$10. This is larger than the ratio in the central molecular zone of the Galaxy, suggesting a higher infall rate of poorly processed gas toward the central region. Assuming that the ratio also holds for the CO emitting gas, this yields $^{16}$O/$^{18}$O = 145$\pm$36 and $^{16}$O/$^{17}$O = 1290$\pm$365 and a $^{32}$S/$^{34}$S ratio close to that measured for the local interstellar medium (20--25). No indication for vibrationally excited CN is found in the lower frequency fine structure components of the $N$ = 1$\rightarrow$0 and 2$\rightarrow$1 transitions at rms noise levels of 3 and 4\,mK (15 and 20\,mJy) in 8.5\,km\,s$^{-1}$ wide channels. Peak line intensity ratios between NGC~253 and Mrk~231 are $\sim$100 for $^{12}$C$^{16}$O and $^{12}$C$^{18}$O $J$ = 1$\rightarrow$0, while the ratio for $^{13}$C$^{16}$O $J$ = 1$\rightarrow$0 is $\sim$250. This and similar $^{13}$CO and C$^{18}$O line intensities in the $J$ = 1$\rightarrow$0 and 2$\rightarrow$1 transitions of Mrk~231 suggest $^{12}$C/$^{13}$C $\sim$ 100 and $^{16}$O/$^{18}$O $\sim$ 100, in agreement with values obtained for the less evolved ultraluminous merger Arp~220. Also accounting for other (scarcely available) extragalactic data, $^{12}$C/$^{13}$C ratios appear to vary over a full order of magnitude, from $>$100 in ultraluminous high redshift galaxies to $\sim$100 in more local such galaxies to $\sim$40 in weaker starbursts not undergoing a large scale merger to 25 in the Central Molecular Zone of the Milky Way. With $^{12}$C being predominantly synthesized in massive stars, while $^{13}$C is mostly ejected by longer lived lower mass stars at later times, this is qualitatively consistent with our results of decreasing carbon isotope ratios with time and rising metallicity. It is emphasized, however, that both infall of poorly processed material, initiating a nuclear starburst, as well as the ejecta from newly formed massive stars (in particular in case of a top-heavy stellar initial mass function) can raise the carbon isotope ratio for a limited amount of time.} | When studying stellar nucleosynthesis and chemical enrichment, it is difficult to optically distinguish between isotopes of a given element, since their atomic lines are blended. However, microwave lines from rare isotopic substitutions of a given molecular species, so-called ``isotopologues'', are well separated from their parent molecule, typically by a few percent of their rest frequency. Thus, the frequencies of the main and rare species are close enough to be observed with the same technical equipment but without the problem of blending. A few years ago, it became apparent (Wouterloot et al. 2008; Wang et al. 2009) that with respect to its composition, the metal poor outer Galaxy does not provide a ``bridge'' between the solar neighborhood and the even more metal poor Large Magellanic Cloud (LMC). This can be explained by the different age of the bulk of the stellar populations of the outer Galaxy and the LMC and can be exemplified by one of the most thoroughly studied isotope ratios, that of carbon. The two stable isotopes, $^{12}$C and $^{13}$C, have been measured throughout the Galaxy, in prominent star forming regions of the LMC, and in a large number of stellar objects (e.g., Milam et al. 2005; Wang et al. 2009; Abia et al. 2012; Mikolaitis et al. 2012). The $^{12}$C/$^{13}$C ratio is a measure of ``primary'' versus ``secondary'' processing. $^{12}$C is produced on rapid timescales primarily via He burning in massive stars. $^{13}$C is mainly produced via CNO processing of $^{12}$C seeds from earlier stellar generations. This occurs on a slower time scale during the red giant phase in low and intermediate mass stars or novae (for reviews, see Henkel et al. 1994; Wilson \& Rood 1994). Previous observations (e.g., Henkel et al. 1985; Stahl et al. 1989; Wouterloot \& Brand 1996; Milam et al. 2005; Sheffer et al. 2007) have demonstrated that the $^{12}$C/$^{13}$C ratio can vary strongly within the Galaxy. In the outer Galaxy very high ratios of $^{12}$C/$^{13}$C $>$100 are found; in the local interstellar medium $^{12}$C/$^{13}$C $\sim$ 70, while in the inner Galactic disk and Large Magellanic Cloud (LMC) $^{12}$C/$^{13}$C $\sim$ 50. The solar system ratio is 89. Within the framework of ``biased infall'' (e.g., Chiappini \& Matteucci 2001), the Galactic disk is slowly formed from inside out, which causes gradients in the abundances across the disk. The stellar $^{13}$C ejecta, reaching the interstellar medium with a time delay, are less dominant in the young stellar disk of the outer Galaxy than in the inner Galaxy and the old stellar body of the LMC (see, e.g., Hodge 1989 for the star formation history of the LMC). The solar system ratio, referring to a younger more $^{13}$C deficient disk, is therefore higher than that measured in the present local interstellar medium. Consistent with this idea, $^{12}$C/$^{13}$C ratios are particularly low ($\sim$25) in the Galactic center region with its old bulge (e.g., G{\"u}sten et al. 1985), while inflowing or infalling gas from outside appears to be characterized by higher ratios (Riquelme et al. 2010). We note that this scenario also explains other isotope ratios based on differences of primary and secondary nucleosynthesis, like that of $^{16}$O (a product of massive stars, $\ga$8\,M$_{\odot}$) and $^{17}$O (a product of lower mass stars), while $^{18}$O is apparently most efficiently synthesized in metal rich stars of large mass (e.g., Wouterloot et al. 2008). With respect to isotope ratios the extragalactic space beyond the Magellanic Clouds is almost unexplored and therefore very interesting to investigate (for previous pioneering efforts, see Aalto et al. 1991; Casoli et al. 1992; Henkel et al. 1993; Henkel \& Mauersberger 1993; Wang et al. 2004; Muller et al. 2006; Henkel et al. 2010; Mart\'{\i}n et al. 2010; Gonz{\'a}lez-Alfonso et al. 2012; Danielson et al. 2013). What ratios can be found when observing objects outside the Local Group of galaxies at low and high redshifts and in environments, which drastically differ from those in the Milky Way and the LMC? Is the Galaxy typical for its class or are its isotopic properties exceptional? And what kind of isotopic compositions can be expected in optical lines, when trying to determine high precision redshifts and to constrain variations in physical constants through time and space (e.g., Levshakov et al. 2006)? In the following we present and analyze new CN and CO data from the nearby prototypical starburst galaxy NGC~253 and the ultraluminous merger Mrk~231, in order to derive and to compare the carbon isotope ratios in these different environments. Sect.\,2 describes observations and data reduction. Sect.\,3 presents the CN and CO measurements and data analysis toward NGC253, including carbon and oxygen isotope ratios and CN excitation temperatures. In Sect.\,4 we discuss our data from Mrk~231 and provide a general overview over extragalactic carbon isotope determinations in targets beyond the Magellanic Clouds. Sect.\,5 summarizes the main results. | Using the IRAM 30-m telescope at Pico Veleta, we have detected two CN isotopologues toward the nearby starburst galaxy NGC~253 and four and three CO isotopologues toward NGC~253 and the ultraluminous merger galaxy Mrk~231, respectively. CN $N$=1$\rightarrow$0 and 2$\rightarrow$1 spectra from Mrk~231 are also presented. The main results of this study are: \begin{itemize} \item CN appears to be the best tracer to determine carbon isotope ratios in nearby external galaxies. \item Toward NGC~253, the measured $^{13}$CN $N$ = 1$\rightarrow$0 line intensities are compatible with local thermodynamical equilbrium (LTE) under optically thin conditions. The relative line intensities of the $^{12}$CN $N$ = 1$\rightarrow$0 features are best explained by LTE conditions modified by moderate saturation, affecting the peak intensity of the weaker component by $\sim$10\% and the stronger component by $\sim$25\%. For $^{12}$CN 2$\rightarrow$1, either the weakest of the three observed line components is enhanced or the feature of intermediate intensity is depleted relative to the expected LTE intensity under optically thin conditions. \item Accounting for calibration uncertainties and moderate saturation in the $^{12}$CN 1$\rightarrow$0 line, the $^{12}$C/$^{13}$C isotope ratio becomes 40$\pm$10 for the molecular core peaking some arcseconds south-west of the dynamical center of NGC~253. Combined with data from several CO isotopologues and adopting this $^{12}$C/$^{13}$C ratio also for the CO emitting gas (which is supported by results from Galactic CN and C$^{18}$O data), this yields $^{16}$O/$^{18}$O = 145$\pm$36 and $^{16}$O/$^{17}$O = 1290$\pm$365. \item CN and C$_2$H show both a number of hyperfine components, which allows us to determine optical depths even in extragalactic spectra covering a broad velocity range. A systematic survey of C$_2$H and its $^{13}$C bearing isotopologues in star forming clouds of the Galaxy would thus be essential to check whether resulting carbon isotope ratios are consistent with those already derived from H$_2$CO, C$^{18}$O, and CN. \item Toward NGC~253, there is no indication for vibrationally excited CN. The lower frequency fine structure components in the $v$ = 1 $N$ = 1$\rightarrow$0 and 2$\rightarrow$1 transitions are not seen down to rms levels of 3 and 4\,mK (15 and 20\,mJy) in 8.5\,km\,s$^{-1}$ wide channels. Those at higher frequency are blended by C$^{17}$O. \item The CN excitation temperature in NGC~253, derived from the $N$ = 1$\rightarrow$0 and 2$\rightarrow$1 lines is 3--11\,K, with a most likely value of $T_{\rm ex}$ $\sim$ 4\,K. With this value, the column density becomes $N$(CN) = 2 $\times$ 10$^{15}$\,cm$^{-2}$ and the density, assuming purely collisional excitation, becomes $n$(H$_2$) $\sim$ 2.5$\times$10$^4$\,cm$^{-3}$. \item CN data from the ultraluminous merger Mrk~231 indicate that the excitation temperature is enhanced by a factor of two with respect to NGC~253 and NGC~4945. In Mrk~231, relative CN line intensities within the $N$ = 1$\rightarrow$0 and 2$\rightarrow$1 transitions are compatible with local thermodynamical equilibrium. While the 1$\rightarrow$0 transitions appear to be optically thin, the 2$\rightarrow$1 lines show significant saturation effects. In view of the excitation temperature, which indicates a density of almost 10$^{5}$\,cm$^{-3}$ assuming exclusively collisional excitation, it would make sense to observe CN transitions with higher quantum numbers $N$ in Mrk~231 and other ultraluminous infrared galaxies (ULIRGs). \item A comparison between NGC~253 and Mrk~231 shows that $^{13}$C$^{16}$O is underabundant in Mrk~231 relative to $^{12}$C$^{16}$O and $^{12}$C$^{18}$O by almost a factor of three. This would yield $^{12}$C/$^{13}$C $\sim$ 100 and, because $^{13}$CO and C$^{18}$O show similar intensities in both the $J$ = 1$\rightarrow$0 and 2$\rightarrow$1 lines, also $^{16}$O/$^{18}$O $\sim$ 100. This is similar to the values determined for Arp~220, even though Arp~220 is a much less evolved ultraluminous merger. \item Obtaining a synthesis of so far obtained carbon isotope ratios from the central regions of actively star forming galaxies, the observed range of values appears to encompass a full order of magnitude. From ultraluminous galaxies at high redshift to local ULIRGs, to weaker local starbursting galaxies and to the central molecular zone of the Milky Way, ratios are $>$100, $\sim$100, $\sim$40, and 25, respectively. While this matches qualitative expectations of decreasing $^{12}$C/$^{13}$C values with time and metallicity, we note that (1) the extragalactic values are based on an extremely small data base and that (2) the ratios for the ULIRGs at high and low $z$ are still rather uncertain. Furthermore, it still has to be evaluated in how far $^{13}$C-deficient gas from the outer galactic regions and $^{12}$C-rich ejecta from massive stars in a nuclear starburst (the latter possibly enhanced by a top-heavy initial mass function), are contributing to raise the carbon isotope ratios during the lifetime of a starburst. \end{itemize} | 14 | 3 | 1403.3974 |
1403 | 1403.7524.txt | We present the discovery of two galaxy overdensities in the Hubble Space Telescope UDF: a proto--cluster, HUDFJ0332.4-2746.6 at $z = 1.84 \pm 0.01$, and a group, HUDFJ0332.5-2747.3 at $z =1.90 \pm 0.01$. Assuming viralization, the velocity dispersion of HUDFJ0332.4-2746.6 implies a mass of $M_{200}= (2.2 \pm 1.8) \times 10^{14} M_{\sun}$, consistent with the lack of extended X--ray emission. Neither overdensity shows evidence of a red sequence. About $50\%$ of their members show interactions and/or disturbed morphologies, which are signatures of merger remnants or disk instability. Most of their ETGs have blue colors and show recent star--formation. These observations reveal for the first time large fractions of spectroscopically confirmed star--forming blue ETGs in proto--clusters at $z\approx 2$. These star--forming ETGs are most likely among the progenitors of the quiescent population in clusters at more recent epochs. Their mass--size relation is consistent with that of passive ETGs in clusters at $z\sim0.7-1.5$. If these galaxies are the progenitors of cluster ETGs at these lower redshifts, their size would evolve according to a similar mass--size relation. It is noteworthy that quiescent ETGs in clusters at $z=1.8-2$ also do not show any significant size evolution over this redshift range, contrary to field ETGs. The ETG fraction is $\lesssim 50\%$, compared to the typical quiescent ETG fraction of $\approx 80\%$ in cluster cores at $z< 1$. The fraction, masses, and colors of the newly discovered ETGs imply that other cluster ETGs will be formed/accreted at a later time. | Galaxy clusters are the largest structures observed in the Universe. Their distribution and (baryonic and dark) matter content constrain the cosmological model, and the study of their galaxy properties reveals the influence of dense environments on galaxy evolution. Galaxies in clusters typically show a predominant early--type population and a red sequence (old stellar population) up to redshift z$\approx 1.5-2$ (e.g., Kodama et al. 2007; Mei et al. 2009; Andreon \& Huertas--Company 2011; Papovich et al. 2010; Snyder et al. 2012; Stanford et al. 2012; Zeimann et al. 2012; Gobat et al. 2013; Muzzin et al. 2013; Mantz et al. 2014). Most of the clusters observed in the local Universe have assembled their current early--type galaxy population at those redshifts (e.g., Cohn \& White 2005; Li et al. 2007; Chiang et al. 2013). The redshift range around $z\approx 1.5-2$, however, has remained largely unexplored until recently. The reason is that surveys based on cluster X--ray emission or the Sunyaev Zel'dovich effect (SZ) lack depth and/or area to reach detections of typical clusters at these redshifts, and ground--based optical spectroscopy would require excessive exposure times to confirm them spectroscopically when detected in the infrared/far--infrared bandpasses. In the past five years, cluster samples at $z>1.5$ have been significantly enlarged by the advent of deep and large enough surveys in the infrared and mid-infrared, such as GOODS-MUSIC (Castellano et al. 2007), the IRAC Distant Cluster Survey (IDCS; Eisenhardt et al. 2008; Stanford et al. 2012; Zeimann et al. 2012), the Spitzer Deep, Wide-Field Survey (SDWFS; Ashby et al. 2009), the Spitzer SPT Deep Field (SSDF; Ashby et al. 2013a), the Spitzer Adaptation of the Red-sequence Cluster Survey (SpARCS; Muzzin et al. 2013), Spitzer Wide-Area Infrared Extragalactic (SWIRE; Papovich et al. 2010), and the Clusters Around Radio-Loud AGN program (CARLA; Galametz et al. 2012; Wylezalek et al. 2013). Other cluster candidates have been identified around low luminosity radio sources (Chiaberge et al. 2010). Spectroscopic capability to confirm redshifts has been enhanced by optical and infrared grism spectroscopy with the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST), and infrared ground--based multi--object spectroscopy with the VLT/KMOS (Sharples et al. 2006), the Keck MOSFIRE (McLean et al. 2010; 2012) and the SUBARU MOIRCS (Ichikawa et al. 2006) instruments. Until now, most clusters detected at $z>1.5$ have been identified as overdensities of red galaxies (e.g., Gladders \& Yee 2000), then confirmed by the spectroscopic follow--up of at least five members within 2~Mpc (e.g., Castellano et al. 2007, 2011; Kurk et al. 2009; Papovich et al. 2010; Tanaka et al. 2010; Stanford et al. 2012; Zeimann et al. 2012; Muzzin et al. 2013), and/or by their X--ray emission (Andreon et al. 2009, 2011; Gobat et al. 2011; Santos et al. 2011). Four clusters have been spectroscopically confirmed at z$\sim 1.8-2$: JKCS~041 (Andreon et al. 2009; Newman et al. 2013), IDCS J1426+3508 (Stanford et al. 2012), IDCS J1433.2+3306 (Zeimann et al. 2012), and CL J1449+085 (Gobat et al. 2011; 2013). For all of the clusters with $z>1.8$, spectroscopic redshifts have been obtained with grism spectroscopy from HST/WFC3, after ground--based optical spectroscopy failed to obtain enough signal. These systems show large fractions ($\approx 50\%$) of star--forming galaxies, indicating that most of the quenching of star formation observed at lower redshift had not yet occurred (Tran et al. 2010; Fassbender et al. 2011; Hayashi et al. 2011; Tadaki et al. 2012; Zeimann et al. 2012; Brodwin et al. 2013). Recent observations at these redshifts also suggest that the specific star formation of galaxies in dense regions becomes higher than that in the field, although not all results are consistent with the supposed reversal of the star-formation density relation (Elbaz et al. 2007; Cooper et al. 2008; Gr{\"u}tzbauch et al. 2011; Hatch et al. 2011; Popesso et al. 2012; Andreon 2013; Gobat et al. 2013; Koyama et al. 2013; Strazzullo et al. 2013; Santos et al. 2014; Scoville et al. 2013; Tanaka et al. 2013; Ziparo et al. 2013). Current X--ray and SZ observations probe cluster virialization through the detection of the hot gas in the gravitational potential well, down to cluster masses of $\approx 10^{14} M_\odot$ and up to redshift of $z \approx 1$. At higher redshifts, only the extreme end of the cluster mass function can be detected by current instruments. A few objects at $1.5<z<2$ correspond to significant X--ray detections and were identified as already virialized (Andreon et al. 2009; Gobat et al. 2011; Santos et al. 2011; Stanford et al. 2012; Mantz et al. 2014). Two of them also show a significant SZ signal (Brodwin et al. 2012; Mantz et al. 2014). Their cluster masses cover the range of $M_{200}\approx (0.5 - 4) \times 10^{14} M_{\sun}$. The other detections (e.g., less massive objects) can only currently be identified as significant (passive or active) galaxy overdensities, without confirmation of virialization by the detection of hot gas. Depending on the presence, or not, of the red sequence and their richness, these objects have been identified as clusters or proto--clusters (e.g., Pentericci et al. 2000; Miley et al. 2004, 2006; Venemans 2007; Kuiper et al. 2010; Hatch et al. 2011). In this paper, we will use the term proto--cluster to mean a cluster in formation, in agreement with this literature. In our definition, a cluster in formation, or proto--cluster, is either (1) a cluster that has not yet formed a red sequence, and, as a consequence, is detected as an overdensity of star--forming galaxies, or (2) a cluster that has not yet assembled and whose galaxies are distributed in groups that eventually will collapse to form a cluster (e.g. Chiang et al. 2013). Depending on the object richness/mass a galaxy overdensity is defined as group or cluster. Numerical simulations show that 90$\%$ of dark matter halos with masses of $M_{200} \ge 10^{14} M_\odot$ are a very regular virialized population up to a redshift of $z\sim1.5$ (Evrard et al. 2008), and many works define as galaxy overdensities that have at least this mass as clusters. However, some other works define groups up to $ M \le few \ 10^{14} M_\odot $ (e.g. Yang et al. 2007), and the definition of galaxy overdensities as a group or a cluster varies in the literature. In this work, we will use the definition of clusters as overdensities with a mass of $M \ge 5 \times 10^{13} M_\odot$, because in previous studies of clusters at $z>1.5$ objects in this mass range have been defined as clusters in formation, or proto--clusters (e.g. Papovich et al. 2010). In fact, halos of this mass range at $z\sim1.5$ will be most probably accreted in clusters with masses of $M > 10^{14} M_\odot$ at $z<0.5$ (e.g. Chiang et al. 2013; Cautun et al. 2014). Concerning the build--up of their early--type population, various studies have focused on the evolution of galaxies in clusters/dense environments from $z\approx 2$ to the present, and compared it to the field (Rettura et al. 2010; Cooper et al. 2012; Mei et al. 2012; Papovich et al. 2012; Raichoor et al. 2012; Bassett et al. 2013; Huertas--Company et al. 2013ab; Lani et al. 2013; Newman et al. 2013; Poggianti et al. 2013; Shankar et al. 2013; Strazzullo et al. 2013; Vulcani et al. 2013; Delaye et al. 2014; Shankar et al. 2014). These results indicate that the median/average passive ETG sizes in clusters are larger (within $\sim 2\sigma$), and the analysis of the population with larger sizes suggests a different morphological type (E, S0) fractions and/or recently quenched faint galaxies. In this paper, we present the discovery of two galaxy overdensities at redshift of $z=1.84$ and $z=1.9$ in the HST Ultra--Deep Field (HUDF; Beckwith et al. 2006) with observations from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS; PI: S. Faber, H. Ferguson; Koekemoer et al. 2011; Grogin et al. 2011), and the 3D HST survey (PI: P. van Dokkum; van Dokkum et al. 2013; Brammer et al. 2012). In Sec.~2, we present the observations. In Sec.~3 we describe our spectroscopic sample selection. In Sec.~4 we present the newly discovered overdensities and estimate one structure's mass. In Sec.~5, we study the stellar population and structural properties of their galaxies. In Sec.~6 we conclude and in Sec.~7 we summarize our results. We adopt a $\Lambda CDM$ cosmology, with $\Omega_m =0.3$, $\Omega_{\Lambda} =0.7$, and $h=0.72$. All magnitudes are given in the AB system (Oke \& Gunn 1983; Sirianni et al. 2005). Stellar masses are estimated with a Chabrier initial mass function (Chabrier 2003). | Deep mid--infrared surveys, and space and ground--based infrared spectroscopy have enabled the discovery of clusters of galaxies at redshift $z=1.5-2$, an epoch largely unexplored until recently. Most of these discoveries have been based on the searches for star--forming galaxy overdensities around radio sources, and/or red galaxy overdensities in the mid--infrared with Spitzer IRAC. The advent of the HST WFC3 grism and ground--based infrared spectroscopy permits confirmation of these discoveries as real galaxy overdensities (Stanford et al. 2012; Zeimann et al. 2012; Gobat et al. 2013; Newman et al. 2013). Current X--ray and SZ observations probe cluster virialization through the detection of the hot gas in the gravitational potential well, down to cluster masses of $\approx 10^{14} M_\odot$ and up to redshift $z \approx 1$. At higher redshifts, only the extreme end of the cluster mass function can be detected by current instruments. A few objects at $1.5<z<2$ correspond to significant X--ray detections and were identified as already virialized (Andreon et al. 2009; Gobat et al. 2011; Santos et al. 2011; Stanford et al. 2012; Mantz et al. 2014). Two of them also show a significant SZ signal (Brodwin et al. 2012; Mantz et al. 2014). Their cluster masses cover the range of $M_{200}\approx (0.5 - 4) \times 10^{14} M_{\sun}$. The other detections (e.g., less massive objects) can only currently be identified as significant red galaxy overdensities, without confirmation of virialization by the detection of hot gas. Depending on the presence, or not, of the red sequence and their richness, these objects have been identified as clusters or proto--clusters (e.g., Pentericci et al. 2000; Miley et al. 2004, 2006; Venemans 2007; Kuiper et al. 2010; Hatch et al. 2011). In this paper, we presented the discovery of two star--forming galaxy overdensities in the HUDF using HST WFC3 grism spectroscopy and imaging observations from the CANDELS and 3D-HST Treasury programs. The richest overdensity, HUDFJ0332.4-2746.6, includes 18 spectroscopic members, of which 6 are ETGs. The other one, HUDFJ0332.5-2747.3, includes 7 spectroscopic members, of which 3 are ETGs. Our detections are mostly based on line emitter galaxy overdensities, similar to current proto--cluster discoveries at $z>2$, but different from current cluster detections at the same redshift that are based on red galaxy overdensities. We confirmed the grism redshifts using deep far-UV photometry from the UVUDF (Teplitz et al. 2013). \begin{table*} \begin{center} \caption{Comparison of HUDFJ0332.4-2746.6 and HUDFJ0332.5-2747.3 properties with those of already known clusters, proto--clusters and groups at $z=1.6-2$ \label{tab2}} \vspace{0.2cm} \resizebox{!}{2cm}{ \begin{tabular}{llccccccccccccccc} \tableline \tableline\\ Name &Identification &z&Overdensity&$\sigma_{disp}$&Mass&X--ray Lum./Detection&Reference\\ && &&(km/s)&($10^{14} \times M_\odot $)&($10^{43}$ erg s$^{-1}$)&\\ \tableline \tableline \\ CL J033211.67-274633.8 &Group&1.61&$\sim 5\sigma$&...&$M_{200}^{(a)} =0.32\pm0.08$&$1.8\pm0.6$&Tanaka et al. \\ IRC-0218A/XMM-LSS J02182-05102&Proto--cluster&1.62&$>20\sigma$&$860\pm490$&$M_{200}^{(b)} \sim 0.1-0.4$&$>4\sigma$ Detection&Papovich et al. 2010; 2012\\ SpARCS J022427-032354&Cluster&1.63&...&...&...&Detection&Muzzin et al. (2013)\\ IDCS J1426+3508&Cluster&1.75&...&...&$M_{200}^{(a)}\sim5.6\pm1.6$&$55\pm12$ &Stanford et al. 2012; Brodwin et al. 2012\\ JKCS~041&Cluster&1.80&...&...&$M_{200}^{(c)}\sim2$&$76\pm5$& Newman et al. 2013; Andreon et al. 2013\\ HUDFJ0332.4-2746.6 &Proto--cluster&1.84&$\sim 20\sigma$&$730\pm 260$&$M_{200}^{(b)} = 2.2 \pm 1.8 $&$<1-6$& This work\\ IDCS J1433.2+3306&Cluster&1.89&...&...&$M_{200}\sim 1$&...&Zeimann et al. 2012\\ HUDFJ0332.5-2747.3 &Group&1.90&$\sim 4-7\sigma$&...&...&...& This work\\ CL J1449+085&Cluster&1.99&$>20\sigma$&...&$M_{200}^{(a)} =0.53\pm0.09$&$6.4\pm1.8$&Gobat et al. 2013\\ \tableline \tableline\\ \end{tabular}} \end{center} \small{{\bf Note.} All estimates are given as they are from the references. For the overdensities, $\sigma$ is estimated with respect to the background, as given by the references. X--ray fluxes and mass estimates have not been homogenized. (a) and (b) indicate mass estimates derived from the X--ray flux and the velocity dispersion, respectively. (c) indicates that the mass estimate is derived from the X--ray flux and cluster richness.} \end{table*} Using a Nth-nearest neighbor distance estimator and the density contrast, we measure a galaxy overdensity at $\sim 20 \sigma$ and $\sim (4-7) \sigma$ above the background, for HUDFJ0332.4-2746.6 and HUDFJ0332.5-2747.3, respectively. Under the hypothesis of viralization, from HUDFJ0332.4-2746.6 velocity dispersion, we obtain a mass estimate of $M_{200}=(2.2 \pm 1.8) \times 10^{14} M_{\sun}$, consistent with the lack of extended X--ray emission. In Table~3, we compare our newly discovered structure to already known clusters, proto--clusters and groups at $z=1.6-2$. Within the uncertainties, HUDFJ0332.4-2746.6 has the properties characteristic of a proto--cluster, because of its overdensity and estimated mass, and HUDFJ0332.5-2747.3 those of a galaxy group, because of its overdensity. Predictions from numerical simulations (Cohn et White 2005; Li et al. 2007; Chiang et al. 2013; Cautun et al. 2014) suggest that HUDFJ0332.4-2746.6 is most probably a progenitor of $M_{200}\approx 10^{14} M_{\sun}$ galaxy clusters at $z\sim 1$ and of $M_{200}\approx few \times 10^{14} M_{\sun}$ galaxy clusters at the present. At $z\approx 1.8-1.9$ Chiang et al. (2013) predict the comoving effective sizes of clusters of mass $M_{200}\approx 10^{14} M_{\sun}$ to be $\approx 2-5$~Mpc. Their total mass extends beyond this spatial scale, based on the cosmological N--body simulation from the Millennium Run (Springel et al. 2005) and semi-analytic galaxy catalogs from Guo et al. (2011). Within the GOODS--CDFS area covered by the Guo et al. (2013) photometric redshift catalog, we searched for overdensities in photometric redshift ranges around the two overdensities and found several groups. Without extensive spectroscopic follow--up we cannot conclude that these groups are at the same spectroscopic redshift as our newly discovered structures. It would be interesting to follow them up spectroscopically and understand if our two overdensities are part of a larger structure at the same redshift. We estimate that at most $\approx 50\%$ of the proto--cluster members are ETGs, against the $80\%$ observed in clusters of galaxies at $z \approx 1-1.5$ (e.g., Postman et al. 2005; Mei et al. 2009; Mei et al. 2012). About $50\%$ of the structure members show possible interactions or disturbed morphologies (asymmetries, faint substructures, and tails), which are possible signatures of merger remnants or disk instability. This suggests mergers and possibly disk instabilities as the primary and ongoing mechanisms of assembly in at least half of the galaxies in dense environments at these redshifts. For galaxy clusters and proto--clusters at $z=1.6-1.9$, the ETG fractions can be quite different in different objects, going from $50\%$ (Gobat 2013; Zeimann et al. 2012; Muzzin et al. 2013) to $80\%$ (Papovich et al. 2012). The lower end of these estimated fractions and our results are close to the fractions of ETGs with mass of $M>10^{10} M_{\sun}$ obtained from Mortlock et al. (2013) in the CANDELS Ultra--Deep Survey (UDS). This suggests the existence of significant overdensities that have similar ETG fractions as the field. It is also interesting that Mortlock et al. found that $z\sim 1.85$ is a redshift of transition between an epoch in which irregular galaxy fractions dominate over disk galaxy fractions to an epoch in which the trend is inverted to the type fractions observed in the local Universe. Using multi--wavelength photometry from Guo et al. (2013), we study the two structures' galaxy colors, and find that their red sequence is not yet in place. All the confirmed ETG members, but two, show emission lines that indicate recent star formation activity. Only one ETG shows colors consistent with those characteristic of an old stellar population at these redshifts, e.g., all the others have active stellar populations. This is consistent with the fact that most of the ETGs in the two structures are star--forming and will be quenched only at a later time. From both of the two structures' ETG fractions and their colors, new ETGs would need to be formed (e.g., by transformations of LTGs by environmental effects; e.g., Boselli \& Gavazzi 2006) or accreted, to obtain the higher ETG fractions observed at lower redshifts. The progenitors of some of these newly transformed ETGs could have been observed as a passive bulge--dominated LTG population in clusters and dense regions at $z=1-1.3$ (Bundy et al. 2010; Mei et al. 2006ab, 2012; George et al. 2013). Current red sequence galaxies are predicted to form the bulk of their stars at an average formation redshift of $z_f=2-3$ from both the interpretation of their scaling relations and age and metallicity measurements (e.g., Thomas et al. 2005), and semianalytic models based on the Millennium simulation (e.g., De Lucia \& Blaizot 2007; Barro et al. 2013b; Shankar et al. 2013). This implies that part of their progenitors at $z\approx2$ are star--forming galaxies. Combined deep high resolution space imaging and grism spectroscopy permitted us to spectroscopically confirm star--forming blue ETG progenitors. At least part of the red sequence ETGs are already ETGs and are compact before quenching their star formation. Our results are consistent with recent observations in the HUDF and modeling by Barro et al. (2013a,b) that demonstrated how compact star--forming galaxies (all morphology selected) appear to be progressively quenched from $z=2-3$ to $z=1-2$. In this work, we spectroscopically confirm for the first time the presence of star--forming blue compact ETGs in significant galaxy overdensities, e.g. in a proto--cluster. Since star--forming ETGs are rare both in clusters and the field up to $z\approx 1.5$ (e.g., Mei et al. 2009; Huertas--Company et al. 2010; Brodwin et al. 2013; Barro et al. 2013ab, and references therein), the star--forming ETGs are most probably (at least part of) the progenitors of passive ETGs in galaxy clusters at $z\sim 1-1.5$. We compare the masses and the sizes of the structures' star--forming blue ETGs with those of passive ETGs in dense regions and galaxy clusters at $z=1-2$, and find that they lie on the same mass--size relation. Interestingly, quiescent ETGs in galaxy clusters at $z=1.8=2$ show a similar behavior as our structurer's blue star--forming ETGs, and the mass-normalized B--band rest-frame size, $\gamma$, does not significantly evolve in the redshift range $0.7<z<2$, contrary to field ETGs (Damjanov et al. 2011; Cimatti et al. 2012; Newman et al. 2013). This implies that, if these objects are the progenitors of quiescent ETGs in clusters at $z=1-1.5$, their mass--size relation did not evolve significantly even if their star--formation was quenched; galaxies could increase their mass, simultaneously increasing their size according to this relation. The diversity of these structures shows how overdensities at $z>1.5$ have less homogeneous galaxy populations than those at $z<1.5$. Large studies of clusters and proto--clusters at these higher redshift have to quantify how detection techniques impact their sample selection function, to obtain good statistics of their galaxy population. | 14 | 3 | 1403.7524 |
1403 | 1403.3003_arXiv.txt | {} {Eclipsing binary systems with pulsating components allow the determination of several physical parameters of the stars, such as mass and radius, that, when combined with the pulsation properties, can be used to constrain the modeling of stellar interiors and evolution. Hereby, we present the results of the study of CoRoT\,105906206, an eclipsing binary system with a pulsating component located in the CoRoT LRc02 field.} {The analysis of the CoRoT light curve was complemented by high-resolution spectra from the Sandiford at McDonald Observatory and FEROS at ESO spectrographs, which revealed a double-lined spectroscopic binary. We used an iterative procedure to separate the pulsation-induced photometric variations from the eclipse signals. First, a Fourier analysis was used to identify the significant frequencies and amplitudes due to pulsations. Second, after removing the contribution of the pulsations from the light curve we applied the PIKAIA genetic-algorithm approach to derive the best parameters that describe the orbital properties of the system.} {The light curve cleaned for pulsations contains the partial eclipse of the primary and the total eclipse of the secondary. The system has an orbital period of about 3.694~days and is formed by a primary star with mass $M_1$ = 2.25 $\pm$ 0.04~\Msun, radius $R_1$ = 4.24 $\pm$ 0.02~\Rsun, and effective temperature \teffp\ = 6750 $\pm$ 150~K, and a secondary with $M_2$ = 1.29 $\pm$ 0.03~\Msun, $R_2$ = 1.34 $\pm$ 0.01~\Rsun, and \teffs\ = 6152 $\pm$ 162~K. The best solution for the parameters was obtained by taking into account the asymmetric modulation observed in the light curve, known as the O'Connell effect, presumably caused by Doppler beaming. The analysis of the Fourier spectrum revealed that the primary component has p-mode pulsations in the range 5-13~d$^{-1}$, which are typical of $\delta$ Scuti type stars.} {} | \label{intro} The study of eclipsing binary systems has gained a new perspective since the beginning of the CoRoT space mission \citep{Baglinetal2006}. The superb photometry achievable from space, combined with ground-based spectroscopy, allows a precise and independent determination of mass and radius of the components, among other parameters. In particular, by studying pulsating stars in eclipsing binaries, such as the Classical $\gamma$~Dor and $\delta$~Sct type variables, one takes advantage of this parameter determination for the asteroseismic modeling of stellar structure and evolution. The CoRoT observations unveiled several targets suitable for this kind of research. $\delta$~Sct type variables are stars located in the classical instability strip on the H-R diagram with effective temperatures in the range 6300~$<$~\teff~$<$~9000~K, luminosities 0.6~$<$~\logL~$<$~2.0, and masses between 1.5 and 2.5~\Msun. Their evolutionary stages range from pre-main sequence to just evolved off the main sequence (about 2~mag above the ZAMS). They exhibit radial and/or non-radial pulsations, with low-order gravity (g) and/or pressure (p) modes with pulsation periods ranging from $\sim$15~min to $\sim$8~h \citep[see e.g.][and references therein]{RodriguezBreger2001, Buzasietal2005,Uytterhoevenetal2011}. Hence, $\delta$~Sct type stars are an interesting class of objects since they lie in the transition region between stars having a convective ($M < 2$~\Msun) or a radiative ($M > 2$~\Msun) envelope. Their masses are in a range where stars are developing a convective zone so they are useful for a better understanding of the mechanisms responsible for driving the pulsations. In this work we describe the analysis of CoRoT\,105906206, an eclipsing binary system showing properties typical of $\delta$~Sct type variables. Sections~\ref{phot} and \ref{spec} present the details of the photometric and the spectroscopic observations, respectively. Section~\ref{analysis} describes how we derive the parameters of the system through the analysis of the light and radial-velocity curves, and Sect.~\ref{phy_prop} provides additional physical properties. The resulting pulsation frequencies are discussed in Sect.~\ref{puls_prop}, and our final remarks and conclusions are in Sect.~\ref{remarks}. | \label{remarks} The study of CoRoT\,105906206 unveiled an eclipsing binary system in which the primary component pulsates in the range of frequencies typical $\delta$ Sct type variables, a result that agrees with the derived values of effective temperature, luminosity, mass, and stage of evolution. Moreover, from the theoretical point of view, a non-adiabatic analysis of a model matching the physical properties of the primary star gives excited frequencies of the most relevant modes ($\ell$ = 0, 1, and 2) in the same frequency range of the observed pulsations. By allowing the surface albedos and gravity darkening to vary as free parameters we have improved the solution for the binary model in comparison with the model found by keeping them fixed. In particular, our estimate of $\beta_1$ is in agreement with the calculations of \citet{Claret1999} for the gravity darkening as a function of the effective temperature for a 2~\Msun\ star. An interesting characteristic of this system is the presence of the O'Connell effect, an asymmetric photometric modulation pattern that we interpreted as due to the Doppler beaming of the emitted flux. We have quantified this effect by means of the beaming factor $B$, whose value depends on the passband of the photometric observations and on the physical properties of the stars. Using equations from \citet{MazehFaigler2010}, our Eq.~\ref{beam_eq}, and some of the parameters in Table~\ref{par_tab}, we obtain $B$ = 2.00 $\pm$ 0.05, which is in fair agreement with the beaming factor derived from the light curve model (see Table~\ref{par_tab}). The $\alpha_{\rm beam}$ factor used in those equations was set to unity. This factor accounts for the effect of the stellar light being shifted out or into the observed passband. According to \citet{FaiglerMazeh2011}, the value of $\alpha_{\rm beam}$ may range from 0.8 to 1.2 for F, G, and K stars observed with the CoRoT passband. The same beaming factor listed in Table~\ref{par_tab} is obtained setting $\alpha_{\rm beam}$ = 0.8. \begin{table*} \centering \caption[]{First 50 pulsation frequencies, amplitudes, and phases derived for CoRoT\,105906206 after subtracting the final binary model.} \label{freq} \begin{tabular}{l r@{}l c c c c} \hline\hline\noalign{\smallskip} & \multicolumn{2}{c}{frequency [d$^{-1}$]} & amplitude $\times$ 10$^3$ & phase [$2\pi$] & remark \\ \noalign{\smallskip}\hline\noalign{\smallskip} $F_{1}$ & 9.&4175 $\pm$ 0.0001 & 2.552 $\pm$ 0.012 & 0.559 $\pm$ 0.005 & \\ $F_{2}$ & 9.&0696 $\pm$ 0.0001 & 2.296 $\pm$ 0.012 & 0.491 $\pm$ 0.005 & \\ $F_{3}$ & 10.&7776 $\pm$ 0.0002 & 2.150 $\pm$ 0.012 & 0.995 $\pm$ 0.006 & \\ $F_{4}$ & 8.&9951 $\pm$ 0.0002 & 1.913 $\pm$ 0.012 & 0.384 $\pm$ 0.006 & 2$F_2$ $-$ $F_1$ + \Forb \\ $F_{5}$ & 5.&6119 $\pm$ 0.0003 & 1.160 $\pm$ 0.012 & 0.313 $\pm$ 0.010 & \\ $F_{6}$ & 9.&3471 $\pm$ 0.0003 & 1.179 $\pm$ 0.012 & 0.809 $\pm$ 0.010 & $F_2$ + \Forb \\ $F_{7}$ & 8.&8734 $\pm$ 0.0003 & 1.051 $\pm$ 0.012 & 0.019 $\pm$ 0.011 & $F_1$ $-$ 2\Forb \\ $F_{8}$ & 11.&3164 $\pm$ 0.0004 & 0.903 $\pm$ 0.012 & 0.221 $\pm$ 0.013 & $F_3$ + 2\Forb \\ $F_{9}$ & 12.&7668 $\pm$ 0.0004 & 0.976 $\pm$ 0.012 & 0.701 $\pm$ 0.012 & 2$F_3$ $-$ $F_2$ + \Forb \\ $F_{10}$ & 12.&2116 $\pm$ 0.0004 & 0.832 $\pm$ 0.012 & 0.405 $\pm$ 0.014 & 2$F_3$ $-$ $F_2$ $-$ \Forb \\ $F_{11}$ & 8.&9203 $\pm$ 0.0004 & 0.906 $\pm$ 0.012 & 0.800 $\pm$ 0.013 & \\ $F_{12}$ & 12.&4963 $\pm$ 0.0004 & 0.967 $\pm$ 0.012 & 0.684 $\pm$ 0.012 & 2$F_3$ $-$ $F_2$ \\ $F_{13}$ & 9.&6056 $\pm$ 0.0004 & 0.806 $\pm$ 0.012 & 0.229 $\pm$ 0.015 & $F_2$ + 2\Forb \\ $F_{14}$ & 11.&1236 $\pm$ 0.0005 & 0.723 $\pm$ 0.012 & 0.325 $\pm$ 0.016 & $F_1$ $-$ $F_2$ + $F_3$ \\ $F_{15}$ & 0.&1192 $\pm$ 0.0004 & 0.880 $\pm$ 0.012 & 0.686 $\pm$ 0.013 & \\ $F_{16}$ & 9.&4713 $\pm$ 0.0005 & 0.715 $\pm$ 0.012 & 0.427 $\pm$ 0.017 & \\ $F_{17}$ & 12.&4186 $\pm$ 0.0005 & 0.718 $\pm$ 0.012 & 0.810 $\pm$ 0.017 & 2$F_3$ $-$ $F_1$ + \Forb \\ $F_{18}$ & 12.&0733 $\pm$ 0.0005 & 0.721 $\pm$ 0.012 & 0.170 $\pm$ 0.016 & \\ $F_{19}$ & 8.&5391 $\pm$ 0.0005 & 0.647 $\pm$ 0.012 & 0.356 $\pm$ 0.018 & $F_2$ $-$ 2\Forb \\ $F_{20}$ & 9.&2153 $\pm$ 0.0005 & 0.688 $\pm$ 0.012 & 0.874 $\pm$ 0.017 & \\ $F_{21}$ & 5.&8385 $\pm$ 0.0006 & 0.581 $\pm$ 0.012 & 0.229 $\pm$ 0.020 & \\ $F_{22}$ & 5.&1446 $\pm$ 0.0006 & 0.548 $\pm$ 0.012 & 0.441 $\pm$ 0.022 & 19\Forb \\ $F_{23}$ & 10.&2152 $\pm$ 0.0006 & 0.530 $\pm$ 0.012 & 0.259 $\pm$ 0.022 & \\ $F_{24}$ & 0.&1467 $\pm$ 0.0004 & 0.772 $\pm$ 0.012 & 0.672 $\pm$ 0.015 & \\ $F_{25}$ & 7.&8192 $\pm$ 0.0007 & 0.476 $\pm$ 0.012 & 0.445 $\pm$ 0.025 & \\ $F_{26}$ & 8.&4036 $\pm$ 0.0006 & 0.606 $\pm$ 0.012 & 0.902 $\pm$ 0.020 & \\ $F_{27}$ & 10.&3200 $\pm$ 0.0007 & 0.473 $\pm$ 0.012 & 0.258 $\pm$ 0.025 & 2$F_1$ $-$ $F_2$ + 2\Forb \\ $F_{28}$ & 12.&3571 $\pm$ 0.0008 & 0.435 $\pm$ 0.012 & 0.378 $\pm$ 0.027 & \\ $F_{29}$ & 0.&5590 $\pm$ 0.0007 & 0.478 $\pm$ 0.012 & 0.116 $\pm$ 0.025 & 2\Forb \\ $F_{30}$ & 8.&6016 $\pm$ 0.0008 & 0.426 $\pm$ 0.012 & 0.487 $\pm$ 0.028 & $F_1$ $-$ 3\Forb \\ $F_{31}$ & 5.&4000 $\pm$ 0.0008 & 0.419 $\pm$ 0.012 & 0.989 $\pm$ 0.028 & \\ $F_{32}$ & 12.&1453 $\pm$ 0.0008 & 0.448 $\pm$ 0.012 & 0.452 $\pm$ 0.026 & 2$F_3$ $-$ $F_1$ \\ $F_{33}$ & 12.&6386 $\pm$ 0.0009 & 0.397 $\pm$ 0.012 & 0.383 $\pm$ 0.030 & \\ $F_{34}$ & 0.&2011 $\pm$ 0.0010 & 0.349 $\pm$ 0.012 & 0.676 $\pm$ 0.034 & $F_2$ $-$ $F_1$ + 2\Forb \\ $F_{35}$ & 9.&5168 $\pm$ 0.0006 & 0.609 $\pm$ 0.012 & 0.777 $\pm$ 0.019 & \\ $F_{36}$ & 6.&6930 $\pm$ 0.0009 & 0.369 $\pm$ 0.012 & 0.856 $\pm$ 0.032 & \\ $F_{37}$ & 5.&5582 $\pm$ 0.0010 & 0.351 $\pm$ 0.012 & 0.785 $\pm$ 0.034 & \\ $F_{38}$ & 14.&8369 $\pm$ 0.0010 & 0.341 $\pm$ 0.012 & 0.855 $\pm$ 0.035 & \\ $F_{39}$ & 6.&2852 $\pm$ 0.0011 & 0.321 $\pm$ 0.012 & 0.361 $\pm$ 0.037 & \\ $F_{40}$ & 12.&8082 $\pm$ 0.0009 & 0.399 $\pm$ 0.012 & 0.037 $\pm$ 0.030 & \\ $F_{41}$ & 11.&8103 $\pm$ 0.0009 & 0.379 $\pm$ 0.012 & 0.440 $\pm$ 0.031 & \\ $F_{42}$ & 5.&9771 $\pm$ 0.0010 & 0.347 $\pm$ 0.012 & 0.606 $\pm$ 0.034 & $F_3$ $-$ $F_5$ + 3\Forb \\ $F_{43}$ & 10.&5627 $\pm$ 0.0011 & 0.308 $\pm$ 0.012 & 0.771 $\pm$ 0.038 & \\ $F_{44}$ & 9.&3057 $\pm$ 0.0009 & 0.401 $\pm$ 0.012 & 0.201 $\pm$ 0.030 & \\ $F_{45}$ & 10.&5060 $\pm$ 0.0012 & 0.292 $\pm$ 0.012 & 0.673 $\pm$ 0.041 & \\ $F_{46}$ & 5.&6726 $\pm$ 0.0011 & 0.321 $\pm$ 0.012 & 0.447 $\pm$ 0.037 & \\ $F_{47}$ & 13.&0780 $\pm$ 0.0010 & 0.345 $\pm$ 0.012 & 0.836 $\pm$ 0.034 & \\ $F_{48}$ & 8.&6659 $\pm$ 0.0011 & 0.317 $\pm$ 0.012 & 0.352 $\pm$ 0.037 & \\ $F_{49}$ & 0.&2962 $\pm$ 0.0013 & 0.268 $\pm$ 0.012 & 0.925 $\pm$ 0.044 & \\ $F_{50}$ & 15.&2025 $\pm$ 0.0012 & 0.299 $\pm$ 0.012 & 0.655 $\pm$ 0.040 & \\ \hline \end{tabular} \tablefoot{The uncertainties are the formal values computed using equations from \citet{MontgomeryODonoghue1999}. The remark column shows the most relevant frequency combinations (\Forb\ = 0.270667~d$^{-1}$). The whole table containing the 220 pulsation frequencies is available in electronic form at the CDS.} \end{table*} The fact the primary star rotates with a sub-synchronous velocity may generate some doubt on our determination of the rotation period, and motivates us to provide some tentative explanations. A spin-orbit misalignment, for example, would lead to an overestimation of \Protp. However, using Eq. 22 of \citet{Hut1981} applied to the parameters derived for this system, and assuming that the primary component rotates as a rigid body, we can estimate the ratio of orbital to rotational angular momentum to be $\alpha \sim 30$. In Fig.~4 of that paper, for this value of $\alpha$ the time scale for circularization is much longer than the time for alignment. Therefore, if $e$ = 0, which is the case of our system, no misalignment is expected. Another explanation could be the loss of angular momentum due to mass transfer. However, the system components are both nearly spherical and far from filling the Roche lobe. The most plausible explanation seems to be the radius expansion of the primary component related to its stage of evolution. This star is passing through a region on the H-R diagram of roughly constant luminosity, decreasing effective temperature, and increasing radius. According to the grid of stellar models with rotation of \citet{Ekstrometal2012}, a star of about 2~\Msun\ that has just evolved off the main sequence will pass through a phase of decreasing equatorial velocity before reaching the base of the giant branch (see their Fig.~9). Though these models were computed for single stars, and not specifically for a star with the same parameters as the primary component of our system, they give us an indication that a decrease in the rotation rate is possibly taking place. The division of the light curve into 8 segments of about 20~days each was necessary to identify the bona fide pulsation frequencies. A shift of the frequency phases with time seems to disturb the identification of frequencies in the whole time series. We performed several tests in order to check the existence of phase shifts in the pulsation frequencies and to identify any periodical variation. However, even if phase shifts are indeed present, no clear periodical variation was found. We are not able to explain the origin of this variation, though we think that it is likely intrinsic to the star. The data reduction process and an instrument related effect could be the cause, but we have applied the same method to several other light curves of both CoRot and Kepler systems, and we did not see the same behavior before. We derived our results based on the first of the eight segments. We tested the others by proceeding with the prewhitening steps, which led to new solutions for the binary models, and to the identification of pulsation frequencies in each segment. A comparison of the fitted parameters shows very good agreement and low dispersion among the segments. The mean values are: $\langle$\teffs$\rangle$ = 6162 $\pm$ 13~K, $\langle{i}\rangle$ = 81.66 $\pm$ 0.15~\degr, $\langle{\Omega_1}\rangle$ = 4.27 $\pm$ 0.02, $\langle{\Omega_2}\rangle$ = 7.89 $\pm$ 0.05, $\langle{\beta_1}\rangle$ = 0.52 $\pm$ 0.02, $\langle{A_1}\rangle$ = 0.77 $\pm$ 0.11, $\langle{A_2}\rangle$ = 0.06 $\pm$ 0.08, and $\langle{B}\rangle$ = 1.48 $\pm$ 0.04. The dispersions are all smaller than the estimated uncertainties, and the values agree with those in Table~\ref{par_tab}. Regarding the analysis of the pulsation frequencies, the peaks with higher amplitudes in Fig.~\ref{freq_spec} ($> 1\times 10^{-3}$) were normally identified in all the eight segments of light curve, in particular the four genuine p-modes ($F_1$, $F_2$, $F_3$, and $F_5$) listed in Table~\ref{freq}. Small shifts in amplitude, probably related to the phase shifts, were also observed among the segments. We believe it would be useful to have more spectra collected during the eclipses in order to allow the modeling the Rossiter-McLaughlin effect. This would confirm whether the spin-orbit axes are indeed aligned, as we suspect, and reinforce the possibility of radius expansion of the primary star due to its stage of evolution. The gathering of more spectra, with higher S/N, would also improve the precision achieved in the spectroscopic analysis, yielding to an accurate abundance determination of elements other than iron. We also believe that the behavior of the amplitude and phase variations is still not well understood. The development of more robust programs and methods for the analysis of time series is required to properly deal with this kind of data, in which a large number of observation points and pulsation frequencies are present. | 14 | 3 | 1403.3003 |
1403 | 1403.3529_arXiv.txt | {Recently, the CoRoT target HD~175272 (F5V), which shows a weak signal of solar-like oscillations, was modelled by a differential asteroseismic analysis (Ozel et al. 2013) relative to a seismically similar star, HD~181420 (F2V), for which there is a clear signature of solar-like oscillations. The results provided by Ozel et al. (2013) indicate the possibility of HD~175272 having subsolar mass, while being of the order of 1000~K hotter than the Sun. This seems unphysical -- standard stellar evolution theory generally does not predict solar-metallicity stars of subsolar mass to be hotter than about 6000K -- and calls for a reanalysis of this star.} {We aim to compare the performance of differential asteroseismic analysis with that of grid-based modelling. } {We use two sets of stellar model grids and two grid-fitting methods to model HD~175272 and HD~181420 using their effective temperatures, metallicities, large frequency separations, and frequencies of maximum oscillation power as observational constraints.} {We find that we are able to model both stars with parameters that are both mutually compatible and comparable with other modelling efforts. Hence, with modest spectroscopic and asteroseismic inputs, we obtain reasonable estimates of stellar parameters. In the case of HD~175272, the uncertainties of the stellar parameters from our grid-based modelling are smaller, and hence more physical, than those reported in the differential analysis. For both stars, the models have significantly lower values of $\numax$ than the reported observed values. Furthermore, when using the asymptotic large frequency separation as opposed to the scaling relation to compute $\Dnu$, we find that our modelling results are significantly more self-consistent when $\numax$ is ignored. } {Grid-based modelling is a useful tool even in cases of weak solar-like oscillations. It provides more precise and more realistic results than obtained with differential seismology. The difference in the observed and modelled values of $\numax$ indicates that the four observational constraints are not fully consistent with the stellar models used here, with $\numax$ most likely to be the inconsistent constraint for these two stars. } | The CoRoT \citep{baglin2006,auvergne2009} and \textit{Kepler} \citep{borucki2008,borucki2010} missions have provided a wealth of high-quality, nearly-uninterrupted photometric time series, which are useful for investigations of stellar oscillations. From stellar oscillations in main-sequence stars, subgiants, and red giants it is possible to accurately derive stellar parameters such as mass, radius, mean density, and surface gravity, as well as more detailed knowledge about the internal stellar structure. For example, it has been possible to measure: whether \emph{helium is burning} in the cores of red giants \citep{beck2011,bedding2011,mosser2011mm}; how much (differential) rotation takes place \citep{beck2012,deheuvels2012,mosser2012rot}; the inclination angle and obliquity between the \emph{spin axes of a star and its companions} \citep{chaplin2013obl,huber2013}; the location of the second helium ionization zone \citep{miglio2010,mazumdar2012,mazumdar2014}. Solar-like oscillations -- oscillations stochastically excited in the turbulent outer convective zones of low mass main-sequence stars, subgiants, and red giants -- can be analysed to various levels of detail. Accurate measures of individual frequencies are important to study the internal structures of stars. However, it is not always possible to measure individual oscillation frequencies owing, for example, to a low signal-to-noise ratio of the oscillations. In such cases one can use so-called global oscillation parameters: the frequency separation between modes of the same degree and consecutive (acoustic) radial order $\Delta\nu$, which is roughly proportional to the square root of the mean density of the star; and the frequency of maximum oscillation power $\numax$, which scales with the surface gravity $g$ and square root of the effective temperature $\Teff$. These two parameters can be used to estimate the stellar mass and radius, when combined with effective temperature using well-known scaling relations \citep{kjeldsen1995}. The scaling relations are useful but should always be used with their limitations in mind. Firstly, they can be derived by assuming homology in stellar structures. This is clearly an approximation because structural features like the depths of convection zones and the presence (or absence) of convective cores change with mass, metallicity, and age. Comparisons with independently-derived radii and surface gravities have shown that the approximation is reasonably accurate for a wide range of stars, although with an increase in uncertainty for stars with different internal stellar structures compared to Sun-like stars \citep[e.g.][]{white2011,huber2012,silva2012,miglio2012}. Secondly, the $\Delta\nu$ scaling relation is derived in the asymptotic regime where the radial order $n$ is much larger than the degree $l$, i.e. $n\gg l$. This is usually true for oscillations of stars on the main sequence, but not necessarily for more evolved stars. Corrections to account for the non-asymptotic regime are currently being discussed \citep{mosser2013as,hekker2013as}. To constrain stellar age and composition, one can compare the observed global oscillation parameters with those of a large number of stellar models. This is often referred to as \emph{grid-based} modelling \citep[e.g.][]{basu2010,gai2011}. It has found wide application mostly in the analysis of large sets of data \citep[e.g.][]{chaplin2014,hekker2013}, but also of stars with weak signatures of oscillation \citep[e.g.][]{barclay2013}. Recently, \citet{ozel2013} proposed to derive stellar parameters for a star with a weak oscillation signal by computing linear differences with respect to the stellar parameters in a second star with a strong oscillation signal and similar observable parameters (e.g. $\Dnu$, $\numax$, $T_{\rm eff}$, [Fe/H]). \citet{ozel2013} referred to this method as \emph{differential seismology} and applied it to the seismically similar stars HD~175272 (F5V) and HD~181420 (F2V) \citep{bruntt2009,barban2009,huber2012} using CESAM models. HD~175272 was observed by CoRoT for 27 days and shows oscillations at a low signal-to-noise ratio. Though the individual oscillation frequencies cannot be identified for HD~175272, global seismic parameters can be determined and were found to be similar to the parameters of the well-studied star HD~181420. This star was therefore used as a reference to derive the parameters of HD~175272. In this work we present grid-based modelling for both HD~175272 and HD~181420, using two different sets of stellar models and two different grid-modelling methods. The observational constraints for HD~181420 and HD~175272 were taken from \citet{ozel2013} and are listed in Table \ref{input}. We compare our results with the results from differential asteroseismology.% \begin{table} \begin{minipage}{\linewidth} \caption{Observed parameters of HD~181420 (F2V) and HD~175272 (F5V) taken from \citet{ozel2013}.} \label{input} \centering \begin{tabular}{lcc} \toprule & HD~181420 & HD~175262 \\ \midrule $\Dnu/\uHz$ & 75.20 $\pm$ 0.04 & 74.9 $\pm$ 0.4 \\ $\numax/\uHz$ & 1610 $\pm$ 10 & 1600 $\pm$ 30 \\ $\Teff/{\rm K}$ & 6580 $\pm$ 100 & 6675 $\pm$ 120 \\ $\rm[Fe/H]$ & $-$0.05 $\pm$ 0.06 & +0.08 $\pm$ 0.11 \\ \bottomrule \end{tabular} \end{minipage} \end{table} \begin{table*} \caption{Grid-based modelling results.} \label{bigtab} \begin{tabular}{l@{\hskip1cm}cccc@{\hskip1cm}cccc} \toprule & \multicolumn{4}{c}{HD~181420} & \multicolumn{4}{c}{HD~175272} \\ Model grid & BASTI & BASTI & MESA\tablefootmark{a} & MESA\tablefootmark{b} & BASTI & BASTI & MESA\tablefootmark{a} & MESA\tablefootmark{b} \\ Method & LD & PySEEK & PySEEK & PySEEK & LD & PySEEK & PySEEK & PySEEK \\ \midrule $M/M_\sun$ & $1.40\pm0.04$ & $1.40^{+0.03}_{-0.03}$ & $1.41^{+0.04}_{-0.02}$ & $1.49^{+0.05}_{-0.02}$ & % $1.48\pm0.08$ & $1.48^{+0.06}_{-0.07}$ & $1.50^{+0.07}_{-0.07}$ & $1.59^{+0.05}_{-0.07}$ \\ [\tabspread] % $t/\text{Gyr}$ & $1.81^{+0.07}_{-0.07}$ & $1.8^{+0.5}_{-0.1}$& $2.0^{+0.2}_{-0.4}$& $1.3^{+0.2}_{-0.2}$ & $1.4^{+1.0}_{-0.6}$ & $1.3^{+0.5}_{-0.3}$& $1.4^{+0.4}_{-0.4}$& $1.0^{+0.4}_{-0.3}$\\ [\tabspread] $R/R_\sun$& $1.65\pm0.06$ & $1.65^{+0.01}_{-0.02}$& $1.66^{+0.02}_{-0.01}$ & $1.712^{+0.002}_{-0.002}$ & $1.68\pm0.06$ & $1.69^{+0.02}_{-0.03}$& $1.69^{+0.03}_{-0.03}$ & $1.74^{+0.01}_{-0.03}$\\ [\tabspread] $\Delta\nu/\uHz$& $75.24\pm0.01$& $75.26^{+0.05}_{-0.16}$& $75.20^{+0.19}_{-0.03}$& $75.16^{+0.04}_{-0.01}$ & $75.1\pm0.5$ & $75.1^{+0.4}_{-0.4}$& $75.1^{+0.4}_{-0.4}$& $75.1^{+0.4}_{-0.4}$\\ [\tabspread] $\numax/\uHz$& $1483.5\pm 0.4$ & $1484^{+2}_{-3}$ & $1490^{+4}_{-1}$ & $1449^{+30}_{-11}$ & $1496\pm25$ & $1500^{+17}_{-20}$& $1508^{+17}_{-24}$& $1484^{+27}_{-24}$\\ [\tabspread] $\Teff/{\rm K}$ & $6574^{+14}_{-14}$& $6583^{+7}_{-165}$ & $6552^{+124}_{-72}$ & $6780^{+175}_{-82}$ & $6662^{+147}_{-144}$ & $6648^{+153}_{-87}$ & $6661^{+125}_{-116}$ & $6810^{+116}_{-119}$ \\ [\tabspread] $\rm[Fe/H]$ & $-0.25 \pm 0.01$ & $0.06^{+0.09}_{-0.09}$ & $0.06^{+0.09}_{-0.09}$ & $0.06^{+0.09}_{-0.09}$ & $0.07 \pm 0.03$ & $0.22^{+0.11}_{-0.18}$ & $0.20^{+0.11}_{-0.18}$ & $0.25^{+0.09}_{-0.15}$ \\ \bottomrule \end{tabular} \tablefoot{\tablefoottext{a}{$\Delta\nu$ from scaling relations.} \tablefoottext{b}{$\Delta\nu$ from asymptotic large frequency spacing ($\Dnu\st{as}$, see Eq. \ref{nu_as})}.} \end{table*} \begin{table*} \caption{Parameters derived for HD~181420 in the literature.} \label{litHD18} \centering \begin{tabular}{lcccccc} \toprule \tiny{reference} & \tiny{\citet{bruntt2009}} & \tiny{\citet{mathur2010}}\tablefootmark{a} & \tiny{\citet{mathur2010}}\tablefootmark{b} & \tiny{\citet{huber2012}} & \tiny{\citet{ozel2013}}\tablefootmark{c} & \tiny{\citet{ozel2013}}\tablefootmark{d}\\ \midrule $M/\Msun$ & 1.31 $\pm$ 0.06 & 1.6 $\pm$ 0.3 & & 1.6 $\pm$ 0.2 & 1.3 $\pm$ 0.2 & 1.3 $\pm$ 0.2\\ $t/\Gyr$ & 2.7 $\pm$ 0.4 & & & & 2.1 $\pm$ 0.2 & 2.3 $\pm$ 0.3 \\ $R/R_\sun$ & 1.60 $\pm$ 0.03 & 1.7 $\pm$ 0.2 & 1.61 $\pm$ 0.03 & 1.73 $\pm$ 0.08 & 1.6 $\pm$ 0.1 & 1.6 $\pm$ 0.1\\ \bottomrule \end{tabular} \tablefoot{\tablefoottext{a}{scaling relations}\tablefoottext{b}{Radius Extractor \citep{creevey2013}}\tablefoottext{c}{GN93}\tablefoottext{d}{AGS05}} \end{table*} | We have successfully used grid-based modelling to derive consistent and realistic stellar parameters for both the high signal-to-noise target HD~181420 and the seismically similar star HD~175272. Our analysis employed two model-fitting methods and two sets of stellar models. For HD~181420 we derive values in the ranges of 1.30--1.45~M$_{\odot}$, 1.59--1.714~R$_{\odot}$ and 1.7--2.6~Gyr in mass, radius, and age, respectively. In the case of HD~175272, we derive smaller uncertainties than the differential analysis by \citet{ozel2013}, providing results in a physically expected regime, i.e., our results lie in the ranges 1.40--1.57 M$_{\odot}$, 1.62--1.73 R$_{\odot}$ and 1.27--1.64 Gyr for the mass, radius, and age, respectively. This demonstrates that grid-based modelling is useful even for low signal-to-noise targets. We also note that the modelled values of $\Dnu$, $\Teff$ and [Fe/H] are consistent with the observed values given by \citet{ozel2013}, but the frequencies of maximum oscillation power $\numax$ are significantly smaller in both stars. In one modelling case, we found that omitting $\numax$ greatly improves the consistency of the models with the other observables. We conclude that these observed values of $\numax$ are not consistent with the stellar models used here. | 14 | 3 | 1403.3529 |
1403 | 1403.1230_arXiv.txt | We present results of new three-dimensional (3D) general-relativistic magnetohydrodynamic simulations of rapidly rotating strongly magnetized core collapse. These simulations are the first of their kind and include a microphysical finite-temperature equation of state and a leakage scheme that captures the overall energetics and lepton number exchange due to postbounce neutrino emission. Our results show that the 3D dynamics of magnetorotational core-collapse supernovae are fundamentally different from what was anticipated on the basis of previous simulations in axisymmetry (2D). A strong bipolar jet that develops in a simulation constrained to 2D is crippled by a spiral instability and fizzles in full 3D. While multiple (magneto-)hydrodynamic instabilities may be present, our analysis suggests that the jet is disrupted by an $m=1$ kink instability of the ultra-strong toroidal field near the rotation axis. Instead of an axially symmetric jet, a completely new, previously unreported flow structure develops. Highly magnetized spiral plasma funnels expelled from the core push out the shock in polar regions, creating wide secularly expanding lobes. We observe no runaway explosion by the end of the full 3D simulation at $185\,\mathrm{ms}$ after bounce. At this time, the lobes have reached maximum radii of $\sim$$900\,\mathrm{km}$. | \begin{figure*}[t] \includegraphics[width=0.247125\textwidth]{Entropy_xz_TimeMarker_84966_oct.pdf} \includegraphics[width=0.247125\textwidth]{Entropy_xz_TimeMarker_84966.pdf} \includegraphics[width=0.247125\textwidth]{Entropy_xz_TimeMarker_95564.pdf} \includegraphics[width=0.247125\textwidth]{Entropy_xz_TimeMarker_109004.pdf} \caption{Meridional slices ($x-z$ plane; $z$ being the vertical) of the specific entropy at various postbounce times. The ``2D'' (octant 3D) simulation (leftmost panel) shows a clear bipolar jet, while in the full 3D simulation (3 panels to the right) the initial jet fails and the subsequent evolution results in large-scale asymmetric lobes.} \label{fig:octfullcmp} \vspace{0.5cm} \end{figure*} Stellar collapse liberates gravitational energy of order $10^{53}\,\mathrm{erg\,s}^{-1}$ ($100\, \mathrm{B}$). Most ($99\%$) of that energy is emitted in neutrinos, and the remainder ($\lesssim 1\, \mathrm{B}$) powers a core-collapse supernova (CCSN) explosion. However, a small fraction of CCSNe are hyper-energetic ($\sim 10\, \mathrm{B}$) and involve relativistic outflows (e.g., \citealt{soderberg:06,drout:11}). These \emph{hypernovae} come from stripped-envelope progenitors and are classified as Type Ic-bl (H/He deficient, broad spectral lines). Importantly, all SNe connected with long gamma-ray bursts (GRB) are of Type Ic-bl \citep{modjaz:11,hjorth:11}. Typical $\mathcal{O}(1) \mathrm{B}$ SNe may be driven by the {\it neutrino mechanism} \citep{bethe:85}, in which neutrinos emitted from the collapsed core deposit energy behind the stalled shock, eventually driving it outward (e.g., \citealt{mueller:12a,bruenn:13}). However, the neutrino mechanism appears to lack the efficiency needed to drive hyperenergetic explosions. One possible alternative is the \emph{magnetorotational} mechanism (e.g. \citealt{bisno:70,leblanc:70,meier:76,wheeler:02}). In its canonical form, rapid rotation of the collapsed core (Period $\mathcal{O}(1)\,\mathrm{ms}$, spin energy $\mathcal{O}(10)\,\mathrm{B}$) and magnetar-strength magnetic field with a dominant toroidal component drive a strong bipolar jet-like explosion that could result in a hypernova (\citealt{burrows:07b}). The magnetorotational mechanism requires rapid precollapse rotation ($P_0 \lesssim 4\,\mathrm{s}$; \citealt{ott:06spin,burrows:07b}) and an efficient process to rapidly amplify the likely weak seed magnetic field of the progenitor. The \emph{magnetorotational instability} (MRI,~\citealt{balbus:91,akiyama:03,obergaulinger:09}) is one possibility. The MRI operates on the free energy of differential rotation and, in combination with dynamo action, has been hypothesized to provide the necessary global field strength on an essentially dynamical timescale \citep{akiyama:03,thompson:05}. The wavelength of the fastest growing MRI mode in a postbounce CCSN core is much smaller than what can currently be resolved in global multi-dimensional CCSN simulations. Under the assumption that MRI and dynamo operate as envisioned, a common approach is to start with a likely unphysically strong precollapse field of $10^{12}-10^{13}\,\mathrm{G}$. During collapse and the early postbounce evolution, this field is amplified by flux compression and rotational winding to dynamically important field strength of $B_\mathrm{tor} \gtrsim 10^{15}-10^{16}\,\mathrm{G}$ \citep{burrows:07b}. In this way, a number of recent two-dimensional (2D) magnetohydrodynamic (MHD) simulations have found robust and strong jet-driven explosions (e.g., \citealt{shibata:06,burrows:07b,takiwaki:11}). Only a handful of 3D studies have been carried out with varying degrees of microphysical realism (\citealt{mikami:08,kuroda:10,scheidegger:10b,winteler:12}) and none have compared 2D and 3D dynamics directly. In this \emph{Letter}, we present new full 3D dynamical-spacetime general-relativistic MHD (GRMHD) simulations of rapidly rotating magnetized CCSNe. These are the first to employ a microphysical finite-temperature equation of state, a realistic progenitor model, and an approximate neutrino treatment for collapse and postbounce evolution. We carry out simulations in full unconstrained 3D and compare with simulations starting from identical initial conditions, but constrained to 2D. Our results for a model with initial poloidal $B$-field of $10^{12}\,\mathrm{G}$ indicate that 2D and 3D magnetorotational CCSNe are fundamentally different. In 2D, a strong jet-driven explosion obtains, while in unconstrained 3D, the developing jet is destroyed by nonaxisymmetric dynamics, caused most likely by an $m=1$ MHD kink instability. The subsequent CCSN evolution leads to two large asymmetric shocked lobes at high latitudes. Highly-magnetized tubes tangle, twist, and drive the global shock front steadily, but not dynamically outward. A runaway explosion does not occur during the $\sim$$185\,\mathrm{ms}$ of postbounce time covered by our full 3D simulation. | Our results show that 3D magnetorotational core-collapse supernovae are fundamentally different from what has been anticipated on the basis of axisymmetric simulations \citep{burrows:07b,dessart:08a,takiwaki:11}. A jet that develops in 2D is disrupted and fizzles in 3D. We suggest that the instability driving this is most likely an MHD kink ($m=1$) instability to which the toroidally-dominated postbounce magnetic-field configuration is prone. Instead of an axially symmetric jet, a completely new, previously unseen, wide double-lobed flow pattern develops, but we obtain no runaway explosion during the simulated time. The high precollapse field strength of $10^{12}\,\mathrm{G}$ yields $\sim$$10^{16}\,\mathrm{G}$ in toroidal field and $\beta = P_\mathrm{gas}/P_\mathrm{mag} < 1$ within only $\sim$$10-15\,\mathrm{ms}$ of bounce, creating conditions favorable for jet formation. Yet, the growth time of the kink instability is shorter than the time it takes for the jet to develop. In a short test simulation with an even more unrealistic, ten times stronger initial field, a successful jet is launched promptly after bounce (consistent with \citealt{winteler:12}), but subsequently experiences a spiral instability in its core. Realistic precollapse iron cores are not expected to have magnetic fields in excess of $\sim$$10^{8}-10^{9}\,\mathrm{G}$, which may be amplified to no more than $\sim$$10^{12}\,\mathrm{G}$ during collapse \citep{burrows:07b}. The $10^{15}-10^{16}\,\mathrm{G}$ of large-scale toroidal field required to drive a magnetorotational jet must be built up after bounce. This will likely require tens to hundreds of dynamical times, even if the magnetorotational instability operates in conjunction with a dynamo. The results of the present and previous full 3D rotating CCSN simulations \citep{ott:07prl,kuroda:13} suggest that MHD and also a variety of nonaxisymmetric hydrodynamic instabilities will grow to non-linear regimes on \emph{shorter timescales}, disrupting any possibly developing axial outflow. \emph{This is why we believe that the dynamics and flow structures seen in our full 3D simulation may be generic to the postbounce evolution of rapidly rotating magnetized core collapse that starts from realistic initial conditions}. If the polar lobes eventually accelerate, the resulting explosion will be asymmetric, though probably less so than a jet-driven explosion. The lobes carry neutron rich ($Y_e \sim 0.1-0.2$) material of moderate entropy ($s \sim 10-15\,k_B\,\mathrm{baryon}^{-1}$), which could lead to interesting $r$-process yields, similar to what \cite{winteler:12} found for their prompt jet-driven explosion. Even if the lobes continue to move outward, accretion in equatorial regions may continue, eventually (after $2-3\,\mathrm{s}$) leading to the collapse of the protoneutron star and black hole formation. In this case, the engine supplying the lobes with low-$\beta$ plasma is shut off. Unless their material has reached positive total energy, the lobes will fall back onto the black hole, which will subsequently hyperaccrete until material becomes centrifugally supported in an accretion disk. This would set the stage for a subsequent long GRB and an associated Type Ic-bl CCSN that would be driven by a collapsar central engine \citep{woosley:93} rather than by a protomagnetar \citep{metzger:11}. \vskip.2cm The results of the present study highlight the importance of studying magnetorotational CCSNe in 3D. Future work will be necessary to explore later postbounce dynamics, the sensitivity to initial conditions and numerical resolution, and possible nucleosynthetic yields. Animations and further details on our simulations are available at \url{http://stellarcollapse.org/cc3dgrmhd}. | 14 | 3 | 1403.1230 |
1403 | 1403.5249_arXiv.txt | \gro is a high-mass X-ray binary for which several claims of a cyclotron resonance scattering feature near 80\,keV have been reported. We use \nustarn, \suzakun, and \swift data from its giant outburst of November 2012 to confirm the existence of the 80\,keV feature and perform the most sensitive search to date for cyclotron scattering features at lower energies. We find evidence for a 78\spm{3}{2}\,keV line in the \nustar and \suzaku data at $> 4\sigma$ significance, confirming the detection using \suzaku alone by \citet{tmp_Yamamoto:14:GROCyc}. A search of both the time-integrated and phase-resolved data rules out a fundamental at lower energies with optical depth larger than 5\% of the 78\,keV line. These results indicate that \gro has a magnetic field of $6.7\times10^{12} (1+z)$\,G, the highest of known accreting pulsars. | \gro is a transient high-mass X-ray binary (HMXB) system with a neutron star primary and a Be companion. It was discovered by the Burst and Transient Source Experiment aboard the \textit{Compton Gamma-Ray Observatory} during a 1.4 Crab giant outburst in July 1993 \citep{Stollberg:93:GROJ1008Discovery,Wilson:1994:GROJ1008Discovery}. Optical followup identified its Be-type companion and suggested a distance to the source of 5\,kpc \citep{Coe:94:GROJ1008OptCounterpart}. Like other Be/X-ray binaries (Be/XRBs), \gro exhibits regular outbursts (Type I) due to accretion transfers during periastron passages as well as irregular giant (Type II) outbursts \citep[for a recent review of Be/XRB systems, see][]{Reig:2011:BeXRBReview}. Its Type I outbursts occur predictably at the 249.48 day orbital period \citep{Kuhnel:2013:GROJ1008,Levine:06:RXTEPeriodicities}. \citet{Kuhnel:2013:GROJ1008} found that the spectra of \gro during Type I outbursts are similarly regular: the continuum spectrum consists of an exponentially cutoff power-law and a low-energy black body component whose properties correlate strongly with source flux. Accreting pulsars, of which Be/XRBs are a subclass, characteristically exhibit cyclotron resonant scattering features (CRSFs) in the hard X-ray band due to Compton scattering off of electrons with orbits quantized by the $\sim10^{12}$\,G magnetic field of the neutron star. The observed line energy provides a direct probe of the magnetic field strength, with $E_{\rm cyc} = 11.6 B_{12}/(1+z)$~keV, where $B_{12}$ is the magnetic field strength in units of 10$^{12}$\,G and $z$ is the gravitational redshift at the emission radius \citep{Canuto:77:CRSF12B12}. Based on \textit{CGRO}/OSSE spectra, \citet{Grove:95:GROJ1008CRSF} and \citet{Shrader:99:GROJ1008CRSF} each reported indications for a possible CRSF at $\sim$88\,keV at low significance ($\sim2\sigma$) for \gron. Their data did not provide energy coverage below 50\,keV to search for a lower-energy fundamental CRSF at $\sim45$\,keV. If the 88\,keV feature were confirmed as the fundamental, it would imply that \gro has a magnetic field strength near 10$^{13}$\,G, the highest of any known accreting pulsar\footnote{\citet{LaBarbera:01:LMCX4Cyc} reported an extremely broad CRSF centered at 100\,keV for LMC X-4, but these measurements were not confirmed by \textit{INTEGRAL} \citep{Tsygankov:05:LMCX4NoCyc}.} \citep[e.g.,][]{Caballero:12:XRayPulsarReview}. Subsequent modeling of data taken over a broader energy band with \textit{RXTE}, \textit{INTEGRAL}, and \suzaku did not reveal a lower-energy fundamental line in the 40--50\,keV region \citep{Coe:07:GROJ1008Disk,Kuhnel:2013:GROJ1008}, and detection of the 88\,keV CRSF remained marginal. \citet{tmp_Wang:14:GROJ1008_INTEGRAL} reported a $\sim3\sigma$ detection of a CRSF at 74\,keV in a 2009 outburst with \textit{INTEGRAL}. The regular \gro Type I outburst of September 2012 was followed by several months of irregular flaring before the source brightened into a giant outburst in November 2012. The increased flux triggered \textit{MAXI} on November 9 \citep{Nakajima:2012:GROJ1008Brightening} and \textit{Swift}-BAT on November 13 \citep{Krimm:2012:GROJ1008Brightening}. Peak flux levels reached 1 Crab in the next week, providing an opportunity to obtain high-statistics observations of the system in outburst. \suzaku executed a Target-of-Opportunity (ToO) observation on November 20 and reported a detection of a cyclotron line at $E_{\rm cyc} =$74--80\,keV, with the exact energy depending on the continuum modeling \citep{Yamamoto:2012:GROSuzakuCyc,tmp_Yamamoto:14:GROCyc}. Thanks to its focusing hard X-ray telescopes, \nustar \citep{Harrison:2013:NuSTAR} provides unprecedented sensitivity in the broad 3--79\,keV band. \textit{NuSTAR}'s continuous energy coverage removes a major source of systematic errors when fitting broad-band models, while the large effective area and lack of pile-up enables high-statistics time-resolved spectroscopy for bright sources. \nustar is capable of executing ToO observations within 24\,hours of trigger and is thus an ideal instrument with which to study cyclotron lines across a wide range of magnetic field strengths in neutron star binary systems \citep[e.g.,][]{Fuerst:13:HerX1,Fuerst:14:VelaX1}. \nustar observed \gro on November 20, shortly after the peak of the outburst (Figure \ref{fig:lc}). \begin{figure} \includegraphics[width=\columnwidth]{batlc.pdf} \caption{ \swiftn-BAT light curve of the giant outburst of \gro with the \nustar and \suzaku observation times marked. The BAT count rate is in units of counts\,cm$^{-2}$\,s${-1}$. \label{fig:lc}} \end{figure} In this paper we combine \nustarn, \swift \citep{Gehrels:04:Swift}, and \suzaku \citep{Mitsuda:07:Suzaku} observations of the November 2012 giant outburst in order to obtain the best constraints on the existence of the putative cyclotron line. \S\ref{sec:observations} describes the observations and data reduction. In \S\ref{sec:fits}, we perform a series of spectral fits of the \nustarn, \suzakun, and \swift data. We fit continuum models (\S\ref{sec:cont_fits}) as well as the previously reported CRSF (\S\ref{sec:cyc_line}) to the data. Monte Carlo tests confirm the significance of the feature. We perform searches for generic CRSFs at lower energies in both the time-integrated (\S\ref{sec:fundamental_search}) and phase-resolved data (\S\ref{sec:phase_resolved}). We conclude in \S\ref{sec:discussion}. | 14 | 3 | 1403.5249 |
|
1403 | 1403.5555_arXiv.txt | {We investigate the potential of large X-ray-selected AGN samples for detecting baryonic acoustic oscillations (BAO). Though AGN selection in X-ray band is very clean and efficient, it does not provide redshift information, and thus needs to be complemented with an optical follow-up. The main focus of this study is (i) to find the requirements needed for the quality of the optical follow-up and (ii) to formulate the optimal strategy of the X-ray survey, in order to detect the BAO. We demonstrate that redshift accuracy of $\sigma_0=10^{-2}$ at $z=1$ and the catastrophic failure rate of $f_{\rm fail}\la 30\%$ are sufficient for a reliable detection of BAO in future X-ray surveys. Spectroscopic quality redshifts ($\sigma_0=10^{-3}$ and $f_{\rm fail}\sim 0$) will boost the confidence level of the BAO detection by a factor of $\sim 2$. For meaningful detection of BAO, X-ray surveys of moderate depth of $F_{\rm lim}\sim {\rm few~} 10^{-15}$ erg/s/cm$^2$ covering sky area from a few hundred to $\sim$ten thousand square degrees are required. The optimal strategy for the BAO detection does not necessarily require full sky coverage. For example, in a 1000-day long survey by an eROSITA type telescope, an optimal strategy would be to survey a sky area of $\sim 9000$ deg$^2$, yielding a $\sim 16\sigma$ BAO detection. A similar detection will be achieved by ATHENA+ or WFXT class telescopes in a survey with a duration of 100 days, covering a similar sky area. XMM-Newton can achieve a marginal BAO detection in a 100-day survey covering $\sim 400$ deg$^2$. These surveys would demand a moderate-to-high cost in terms the optical follow-ups, requiring determination of redshifts of $\sim 10^5$ (XMM-Newton) to $\sim 3\times 10^6$ objects (eROSITA, ATHENA+, and WFXT) in these sky areas.} | Mapping the large-scale structure (LSS) in the low redshift Universe with modern redshift surveys, together with cosmic microwave background (CMB) \citep{2000Natur.404..955D,2000ApJ...545L...5H,2013ApJS..208...19H,2013arXiv1303.5076P} and type Ia supernova \citep{1998AJ....116.1009R,1999ApJ...517..565P} measurements, has helped to establish the current standard cosmological model -- the $\Lambda$CDM model. The initial discovery of the baryonic acoustic oscillations (BAO) \citep{1970Ap&SS...7....3S,1970ApJ...162..815P} in the two-point clustering statistics of the blue-band 2dFGRS\footnote{\url{http://www2.aao.gov.au/2dfgrs/}} and r-band-selected SDSS\footnote{\url{http://www.sdss.org/}} luminous red galaxy (LRG) samples (redshifts $z\sim 0.2$ and $z\sim 0.35$, respectively) \citep{2005MNRAS.362..505C,2005ApJ...633..560E} has initiated significant efforts to try to measure this signal, which provides a theoretically well-understood standard ruler, at ever higher redshifts, this way mapping out the low redshift expansion history of the Universe in great detail.\footnote{For a recent review see \citet{2013PhR...530...87W}.} Detecting BAO demands major observational efforts because this relatively weak signal, $\sim 5\%$ modulation in the matter power spectrum, can only be detected by combining large survey volumes with high enough sampling density, to overcome cosmic variance and shot noise, respectively. This leads to the typical number of redshifts obtained in these surveys ranging from $\sim 10^5$ up to $\sim 10^6$. The measurements of BAO in the galaxy two-point function have been extended to redshifts of $z\sim 0.55$ and $z\sim 0.7$ by the BOSS\footnote{\url{http://www.sdss3.org/surveys/boss.php}} and WiggleZ\footnote{\url{http://wigglez.swin.edu.au/}} surveys, using LRGs and emission line galaxies (ELGs), respectively \citep{2012MNRAS.427.3435A,2011MNRAS.418.1707B}. By exploiting the correlations in quasar Lyman-{$\alpha$} forest fluctuations, the BAO detection has been pushed up to $z\sim 2.3$ \citep{2013A&A...552A..96B,2013JCAP...04..026S}. Even though at the moment there are no BAO detections in the redshift range $z\sim 1-2$, it will be covered by the upcoming eBOSS\footnote{\url{http://www.sdss3.org/future/eboss.php}} survey. The measurement at even higher redshifts, $z\sim 3$, will be achieved by the HETDEX\footnote{\url{http://hetdex.org/}} survey. The eBOSS will use ELGs up to redshifts $z\sim 1$ and beyond that $\sim 750\, 000$ quasars (QSOs) will be used to sample cosmic density field over $\sim 7500$ deg$^2$, i.e., with a sampling rate of $\sim 100$ deg$^{-2}$. This is a factor of $\sim 2$ higher than a predicted number density of the X-ray active galactic nuclei (AGN) with $z>1$ from the upcoming eROSITA\footnote{\url{http://www.mpe.mpg.de/erosita/}} \footnote{\url{http://hea.iki.rssi.ru/SRG/}} all-sky-survey (eRASS) \citep[e.g.,][]{2012arXiv1209.3114M,2013A&A...558A..89K}. Since the emission of X-rays is a generic feature accompanying AGN activity, the AGN selection in X-ray band is very effective \citetext{e.g., \citealp{2005ARA&A..43..827B}} and certainly much cleaner than the selection in other, lower energy wavebands. Since X-rays do not penetrate Earth's atmosphere, these observations have to be carried out in space, which severely limits the size of the achievable collective area. Despite that, as we know for example from the Chandra\footnote{\url{http://chandra.harvard.edu/}} deep field measurements \citep{2003AJ....126..539A,2011ApJS..195...10X}, the amazing AGN densities of $\sim 10^4$ deg$^{-2}$ should be achievable. However, to sample efficiently cosmic LSS, such high densities are completely unnecessary, and even modest AGN number densities, as achievable with eRASS in combination with large survey volumes, competitive measurements of two-point clustering statistics are possible. It is clear that to obtain distance information, X-ray surveys have to be complemented with optical spectroscopic follow-up. This is exactly analogous to the optical redshift surveys, only the imaging part is replaced with imaging in the X-ray band. In this paper we investigate the potential of the X-ray-selected AGN for probing the cosmic LSS in detail. For a clear benchmark of achievable quality, we focus on the ability to detect the BAO in the clustering power spectrum. Since the BAO represent a $\sim 5\%$ modulation on top of the smooth broad-band spectral component, the smooth part itself can be detected with an order-of-magnitude higher signal-to-noise ratio. One might wonder why attempt to use X-ray AGN for measuring the BAO. After all, almost all that matters for getting a BAO measurement is a large, uniformly covered survey volume combined with a large number of measured redshifts. Beyond the primary requirement for the redshifts to be obtained easily, the particular type of object used is only of secondary importance. Indeed, this is the way most of the upcoming BAO surveys are optimized; for example, for ELGs one only needs to detect the location of a few emission lines without needing to go down to the continuum level. In addition to a high enough sampling density of the LSS tracer objects, a second important factor is their clustering strength. Indeed, because the signal-to-noise per Fourier mode scales as a product of the power spectrum amplitude and comoving number density, an increase in the clustering bias by a factor of two leads to the same signal-to-noise even if the sampling density is reduced by a factor of four. This in fact is an advantage of the X-ray-selected AGN, since they are more strongly clustered than optically selected QSOs or ELGs. Also, as it turns out, X-ray-selected AGN are numerous enough to efficiently probe LSS at redshifts $z\sim 1$. In addition, it would be helpful if the cosmological BAO surveys could also be used for studying the astrophysics of the target objects. And this, we argue, is surely the case with X-ray-selected AGN. Indeed, the clean sample of AGN detected in X-ray band would certainly facilitate the study of accreting supermassive black holes (SMBHs) in the centers of galaxies, arguably one of the most remarkable discoveries of modern astrophysics. Also, additional synergetic effect might be expected from the fact that imaging and necessary spectroscopic follow-up are done in completely separate parts of the electromagnetic spectrum, this way helping to probe the physics of the AGN in a somewhat broader context. It is also important to realize that, no matter what, the prominence of the topic of AGN/SMBH evolution means that the optical follow-up of X-ray AGN samples detected by upcoming surveys like eROSITA \citep{2010SPIE.7732E..23P} will be done in one way or the other, and so using these AGN samples as probes of the LSS can at least be considered as an auxiliary research topic. One might think that, in contrast to cosmology, detailed AGN studies do not possibly need to follow up such a large number ($\sim 10^6$) of objects. But if one wishes to measure AGN clustering with any reasonable (e.g., $\sim 10\%$) accuracy in several luminosity and redshift bins, and maybe also slice the data according to some other measurables, one cannot do with much smaller sample sizes. Our ability to constrain galaxy evolution models has benefited enormously from the availability of huge numbers of spectra from the LSS surveys, often driven mostly by cosmological needs. Similar gains should also be expected for the AGN science. Owing to the importance of the optical follow-up for turning the X-ray selected AGN samples into genuine LSS probes, in this paper we aim to derive the necessary criteria for the quality of the spectroscopic/photometric redshifts. As stated above, we focus on the ability to detect the BAO; that is to say, the corresponding broad-band clustering signal is then detectable with an order of magnitude higher signal-to-noise. Our paper is organized as follows. In Section~\ref{sec2} we present an initial feasibility study, Section~\ref{sec3} provides a short description of the modeling details, followed by our main results in Section~\ref{sec4}. Our summary and conclusions are given in Section~\ref{sec5}. Throughout this paper we assume flat $\Lambda$CDM cosmology with $\Omega_m=0.3$, $\Omega_b=0.05$, $h=0.7$, and $\sigma_8=0.8$. | \label{sec5} We investigated the potential of large samples of X-ray-selected AGN to probe the large-scale structure of the Universe, in particular, to detect the BAO. For the X-ray-selected AGN, most of the BAO signal comes from redshifts $z\sim 1$, where the X-ray AGN population peaks. These redshifts are currently uncovered by any one of the existing dedicated BAO surveys. However, although X-ray surveys are very efficient in producing large samples of AGN, they do not provide any redshift information and so have to be complemented with an optical follow-up. The main goals of this study were (i) to find out the required quality criteria for the optical follow-up and (ii) to formulate the optimal strategy of the X-ray survey in order to facilitate accurate measurements of the clustering two-point function and detection of the BAO. Our main results are presented in Figs.~\ref{fig7} and \ref{fig8}, where the confidence levels for the BAO detection are shown as a function of X-ray survey parameters ($F_{\rm lim}$, $f_{\rm sky}$) and the parameters describing the quality of the optical follow-up ($\sigma_0$, $f_{\rm fail}$). In particular we demonstrated that redshift accuracy of $\sigma_0=10^{-2}$ at $z=1$ and the failure rate of $f_{\rm fail}\la 30\%$ are sufficient for a reliable detection of BAO in the future X-ray surveys. If spectroscopic quality redshifts ($\sigma_0=10^{-3}$ and $f_{\rm fail}\sim 0$) are available, the confidence level of the BAO detection will be boosted by a factor of $\sim 2$. For the meaningful detection of BAO, X-ray surveys of moderate depth of $F_{\rm lim}\sim {\rm a\,\,few~} 10^{-15}$ erg/s/cm$^2$ covering sky area from a few hundred to a few ten thousand square degrees are required. For the fixed survey duration, the optimal strategy for the BAO detection does not necessarily require full sky coverage. For example, in a $T=1000$ day survey by an eROSITA type telescope, an optimal strategy for BAO detection requires a survey of $\sim 9000$ deg$^2$ and would yield a $\sim 16\sigma$ BAO detection. A similar detection will be achieved by ATHENA+ or WFXT type telescopes in a survey with a duration of 100 days, covering similar sky area. XMM-Newton can achieve a marginal BAO detection in a 100-day survey covering $\sim 400$ deg$^2$. These surveys would impose moderate to high demands on the optical follow-ups requiring determination of redshifts of $\sim 10^5$ objects (XMM-Newton) to $\sim 3\times 10^6$ objects (eROSITA, ATHENA+ and WFXT) in the above-mentioned sky areas. Given the progress in the instrumentation for multi-object spectroscopy, these demands appear to be within the reach of modern and future ground-based optical facilities. Since the BAO is $\sim 5\%$ modulation on top of a smooth broad-band spectral shape, the amplitude of the power spectrum, hence the AGN clustering bias, can be determined with an order-of-magnitude higher signal-to-noise, and so can be done with much poorer quality photometric redshifts. \begin{appendix} | 14 | 3 | 1403.5555 |
1403 | 1403.2143_arXiv.txt | A variety of observational evidence demonstrates that brown dwarfs exhibit active atmospheric circulations. In this study we use a shallow-water model to investigate the global atmospheric dynamics in the stratified layer overlying the convective zone on these rapidly rotating objects. We show that the existence and properties of the atmospheric circulation crucially depend on key parameters including the energy injection rate and radiative timescale. Under conditions of strong internal heat flux and weak radiative dissipation, a banded flow pattern comprising east-west jet streams spontaneously emerges from the interaction of atmospheric turbulence with the planetary rotation. In contrast, when the internal heat flux is weak and/or radiative dissipation is strong, turbulence injected into the atmosphere damps before it can self-organize into jets, leading to a flow dominated by transient eddies and isotropic turbulence instead. The simulation results are not very sensitive to the form of the forcing. Based on the location of the transition between jet-dominated and eddy-dominated regimes, we suggest that many brown dwarfs may exhibit atmospheric circulations dominated by eddies and turbulence (rather than jets) due to the strong radiative damping on these worlds, but a jet structure is also possible under some realistic conditions. Our simulated light curves capture important features from observed infrared lightcurves of brown dwarfs, including amplitude variations of a few percent and shapes that fluctuate between single-peak and multi-peak structures. More broadly, our work shows that the shallow-water system provides a useful tool to illuminate fundamental aspects of the dynamics on these worlds. | Brown dwarfs are characterized by a vigorously convective interior overlain by a stratified weather layer (Burrows et al. 2006). Increasing observational evidence, including chemical disequilibrium (e.g., Saumon et al. 2006; Leggett et al. 2007), condensates and clouds (e.g., Tsuji 2002; Knapp et al. 2004), infrared flux variability (e.g., Artigau et al. 2009; Radigan et al. 2012; Apai et al. 2013), and surface patchiness (Crossfield et al.~2014) imply the existence of strong vertical mixing and large-scale atmospheric motion on brown dwarfs. To understand the atmospheric convection and circulation, several models have been put forward. A local-box simulation by Freytag et al. (2010) showed that convection could trigger gravity waves in the stratified layer, causing vertical mixing and helping maintain thin dust clouds. Showman \& Kaspi (2013) presented the first three-dimensional (3D) general circulation model of brown dwarfs and demonstrated that the atmosphere and interior dynamics are rotationally dominated. However, many aspects of the expected atmospheric dynamics remain uncertain. Especially, there is a lack of global simulations investigating the stratified layer on brown dwarfs. The surface patchiness suggested in the observations raises major questions about the nature of the atmospheric circulation on brown dwarfs. In particular, are the flows on brown dwarfs zonally banded, consisting of numerous east-west jet streams like those on Jupiter and Saturn? Or do they consist primarily of turbulence and eddies with no preferred directionality? The issue has major implications for interpretations of variability. To answer these questions, we introduce an idealized global shallow-water model to study the atmospheric circulation on brown dwarfs. The shallow water model has been extensively used in the atmospheric studies on Earth (e.g., Sadourny 1974), giant planets (e.g., Cho and Polvani 1996; Showman 2007) and exoplanets (Showman \& Polvani 2011). Ours are the first global numerical simulations of the dynamics in the stratified atmospheres of brown dwarfs. | We demonstrated using a global shallow-water model that zonal (east-west) jet streams and local vortices can form under conditions appropriate to brown dwarfs. The existence and properties of the jets crucially depend on the radiative damping timescale and the rate at which convection injects energy into the atmosphere. Strong internal heat flux (i.e., strong convective forcing) and weak radiative dissipation favors the formation of large-scale jets in the atmosphere, as shown in our simulations, whereas a weaker forcing and stronger dissipation will halt the formation of zonal jets and favor the generation of (horizontally) isotropic turbulence. The radiative timescale for most brown dwarfs above 1000 K is $\sim10^5$ s or less, and longer with colder atmospheres. The rate of energy injection at the RCB is less certain, which depends on the forcing mechanisms, either from the dry and moist convective processes, or from the upward propagating atmospheric waves. A crude estimate of a typical brown dwarf implies that its energy injection rate is several orders of magnitude larger than that on Jupiter. Our simulations suggest that many hot brown dwarfs may be eddy/turbulence dominated rather than jet dominated at typical IR photosphere levels. If a brown dwarf is cold enough, such as Y dwarfs, or the damping timescale is long, or the forcing is strong enough, zonal jets should form, as seen on Jupiter. Nevertheless, it is difficult to precisely relate our forcing and damping parameters to the brown dwarf spectral sequence, as $\epsilon$ and $\tau_{\rm rad}$ will depend on the detailed nature of the convection, the thickness of the layer communicating with the photosphere (which may include the top portion of the convection zone), and other factors. While our finding of a regime transition is robust and should carry over to the full 3D system, these uncertainties imply that more realistic three-dimensional models will be necessary to pin down precisely where the transition falls in the brown dwarf spectral sequence. Despite these uncertainties, it is clear that Jupiter is in the jet-dominated regime, providing some confirmation of our findings. The long-time integration of the shallow water system provides a new tool to understand the observed light curve variations. We found that our simulated brown dwarf atmospheres are dominated by the rotational modulation in short-term light curves, with lightcurve shapes that vary from single to multi-peaked periodic structures and amplitudes of a few percent, qualitatively consistent with recent observed infrared flux variations. | 14 | 3 | 1403.2143 |
1403 | 1403.4373_arXiv.txt | {A precise characterisation of the red giants in the seismology fields of the CoRoT satellite is a prerequisite for further in-depth seismic modelling. High-resolution FEROS and HARPS spectra were obtained as part of the ground-based follow-up campaigns for 19 targets holding great asteroseismic potential. These data are used to accurately estimate their fundamental parameters and the abundances of 16 chemical species in a self-consistent manner. Some powerful probes of mixing are investigated (the Li and CNO abundances, as well as the carbon isotopic ratio in a few cases). The information provided by the spectroscopic and seismic data is combined to provide more accurate physical parameters and abundances. The stars in our sample follow the general abundance trends as a function of the metallicity observed in stars of the Galactic disk. After an allowance is made for the chemical evolution of the interstellar medium, the observational signature of internal mixing phenomena is revealed through the detection at the stellar surface of the products of the CN cycle. A contamination by NeNa-cycled material in the most massive stars is also discussed. With the asteroseismic constraints, these data will pave the way for a detailed theoretical investigation of the physical processes responsible for the transport of chemical elements in evolved, low- and intermediate-mass stars.} | \label{sect_introduction} Early observations by the MOST (e.g., Kallinger \etal \cite{kallinger08}) and WIRE (e.g., Stello \etal \cite{stello08}) satellites have demonstrated the tremendous potential of extremely precise and quasi-uninterrupted photometric observations from space for studies of red-giant stars. Breakthrough results are currently being made from observations collected by \c \ (Michel \etal \cite{michel08}) and {\it Kepler} (Borucki \etal \cite{borucki10}), which offer the opportunity for the first time to derive some fundamental properties of a vast number of red giants from the modelling of their solar-like oscillations (see the reviews by Christensen-Dalsgaard \cite{christensen_dalsgaard11}, Chaplin \& Miglio \cite{chaplin13}, and Hekker \cite{hekker13}). Amongst the most exciting results achievable by asteroseismology of red-giant stars are the possibility of inferring their evolutionary status (e.g., Montalb\'an \etal \cite{montalban10}; Bedding \etal \cite{bedding11}; Mosser \etal \cite{mosser11}), constraining their rotation profile (e.g., Beck \etal \cite{beck12}; Deheuvels \etal \cite{deheuvels12}), or determining the detailed properties of the core in He-burning stars (Mosser \etal \cite{mosser12}, Montalb\'an \etal \cite{montalban13}). In addition, their global seismic properties can provide a high level of accuracy of their fundamental properties, such as masses, radii, and distances, which may then be used to map and date stellar populations in our Galaxy (e.g., Miglio \etal \cite{miglio09}, \cite{miglio13}). Carrying out an abundance analysis of red-giant pulsators is relevant for two closely related reasons. The most obvious one is that only accurate values of the effective temperature and chemical composition are independently derived from ground-based observations that permit a robust modelling of the seismic data (e.g., Gai \etal \cite{gai11}; Creevey \etal \cite{creevey12}). Conversely, asteroseismology can provide the fundamental quantities (e.g., mass, evolutionary status) that are needed to best interpret the abundance data. This would allow us, for instance, to better understand the physical processes controlling the amount of internal mixing in red giants. One issue of particular interest and is currently actively debated -- and this is one of the objectives of this project -- is to investigate the nature of the transport phenomena that are known to occur for low-mass stars after the first dredge-up but before the onset of the He-core flash (e.g., Gilroy \& Brown \cite{gilroy91}). Thanks to their brightness, a comprehensive study of the chemical properties of the red giants lying in the \c \ seismology fields is relatively easy to achieve. This can be compared with the case of the fainter stars observed in the exofields of \c \ (Gazzano \etal \cite{gazzano10}; Valentini \etal \cite{valentini13}) or in the {\it Kepler} field (Bruntt \etal \cite{bruntt11}; Thygesen \etal \cite{thygesen12}), for which the abundances of the key indicators of mixing (C, N, Li, and \iso) have not been systematically investigated to our knowledge. The most noticeable attempts in the case of the {\it Kepler} red giants are the low-precision (uncertainties of the order of 0.5 dex) carbon abundances derived for a dozen stars by Thygesen \etal (\cite{thygesen12}) and the study of lithium in the open cluster \object{NGC 6819} by Anthony-Twarog \etal (\cite{anthony_twarog13}). This paper is organised as follows: Sect.~\ref{sect_targets} presents the targets observed, while Sect.~\ref{sect_observations} discusses the observations and data reduction. The determination of the seismic gravities is described in Sect.~\ref{sect_seismic_constraints}. The methodology implemented to derive the chemical abundances and stellar parameters is detailed in Sects.~\ref{sect_chemical_abundances} and \ref{sect_parameters}, respectively. The uncertainties and reliability of our results are examined in Sects.~\ref{sect_errors} and \ref{sect_validation}, respectively. We present the procedure used to correct the abundances of the mixing indicators from the effect of the chemical evolution of the interstellar medium (ISM) in Sect.~\ref{sect_correction_chemical_evolution}. Section \ref{sect_key_results} is devoted to a qualitative discussion of some key results. Finally, some future prospects are mentioned in Sect.~\ref{sect_conclusion}. | \label{sect_conclusion} We are entering a new era where spectroscopic and asteroseismic data of superb quality can be combined to provide a global view of red giants in unprecedented detail. Astrometric data from the {\it Gaia} space mission and new long-baseline interferometric facilities will soon also open new perspectives. On the other hand, major advances are being made on various theoretical aspects (e.g., Charbonnel \& Lagarde \cite{charbonnel_lagarde10}; Ludwig \& Ku\v{c}inskas \cite{ludwig12}). Our study is an effort to ultimately fully characterise the stars in our sample. This may be achieved for those for which detailed seismic information is available, such as HD 50890 (Baudin \etal \cite{baudin12}) or HD 181907 (Carrier \etal \cite{carrier10}; Miglio \etal \cite{miglio10}). The modelling of the \c \ data for other stars in the seismology fields is underway (e.g., Barban \etal \cite{barban14}). The extent of mixing experienced by each of our targets results from the combined action of different physical processes (convective and rotational mixing, as well as thermohaline instabilities) whose relative efficiency (or merely occurrence) is a complex function of their evolutionary status, mass, metallicity, and rotational history. A preliminary comparison with evolutionary models supports the widespread occurrence of mixing processes other than convection in our sample. We will take advantage of the asteroseismic constraints to provide in a forthcoming paper (Lagarde et al., in preparation) a thorough interpretation of our abundance data based on theoretical models incorporating the three mechanisms mentioned above (Charbonnel \& Lagarde \cite{charbonnel_lagarde10}). Finally, dramatic advances may be expected from the analysis of the large population of red-giant stars monitored by the {\it Kepler} satellite. The various evolutionary sequences can clearly be distinguished from asteroseismic diagnostics (e.g., Stello \etal \cite{stello13}; Montalb\'an \etal \cite{montalban13}), which opens up the possibility of mapping out the evolution of the mixing indicators during the shell-hydrogen and core-helium burning phases for a very large number of stars. An inspection of the spectra obtained by Thygesen \etal (\cite{thygesen12}) for 82 red giants in the {\it Kepler} field (mostly obtained with FIES installed on the Nordic Optical Telescope; NOT) shows that these data are not of sufficient quality to confidently measure the generally very weak Li and $^{13}$CN features. Although demanding in terms of telescope time, such a study is amenable for the brightest targets, which can be observed on larger facilities, and may be particularly rewarding. | 14 | 3 | 1403.4373 |
1403 | 1403.2892.txt | % context heading (optional) % {} leave it empty if necessary {Asymptotic giant branch (AGB) stars lose their envelopes by means of a stellar wind whose driving mechanism is not understood well. Characterizing the composition and thermal and dynamical structure of the outflow provides constraints that are essential for understanding AGB evolution, including the rate of mass loss and isotopic ratios.} % aims heading (mandatory) {We characterize the CO emission from the wind of the low mass-loss rate oxygen-rich AGB star W\,Hya using data obtained by the HIFI, PACS, and SPIRE instruments onboard the Herschel Space Observatory and ground-based telescopes. $^{12}$CO and $^{13}$CO lines are used to constrain the intrinsic $^{12}$C/$^{13}$C ratio from resolved HIFI lines.} % methods heading (mandatory) { We combined a state-of-the-art molecular line emission code and a dust continuum radiative transfer code to model the CO lines and the thermal dust continuum. } % results heading (mandatory) {The acceleration of the outflow up to about 5.5 km/s is quite slow and can be represented by a $\beta$-type velocity law with index $\beta = 5$. Beyond this point, acceleration up the terminal velocity of 7 km/s is faster. Using the $J$= 10--9, 9--8, and 6--5 transitions, we find an intrinsic $^{12}$C/$^{13}$C ratio of $18 \pm 10$ for W\,Hya, where the error bar is mostly due to uncertainties in the $^{12}$CO abundance and the stellar flux around 4.6 $\mu$m. To match the low-excitation CO lines, these molecules need to be photo-dissociated at $\sim$\,500 stellar radii. The radial dust emission intensity profile of our stellar wind model matches PACS images at 70 $\mu$m out to 20$\arcsec$ (or 800 stellar radii). For larger radii the observed emission is substantially stronger than our model predicts, indicating that at these locations there is extra material present. } % conclusions heading (optional), leave it empty if necessary {The initial slow acceleration of the wind may imply inefficient dust formation or dust driving in the lower part of the envelope. The final injection of momentum in the wind might be the result of an increase in the opacity thanks to the late condensation of dust species. % The derived intrinsic isotopologue ratio for W\,Hya is consistent with values set by the first dredge-up and suggestive of an initial mass of 2 M$_\odot$ or more. However, the uncertainty in the isotopologic ratio is large, which makes it difficult to set reliable limits on W\,Hya's main-sequence mass. } | The asymptotic giant branch (AGB) represents one of the final evolutionary stages of low and intermediate mass stars. AGB objects are luminous and have very extended, weakly gravitationally bound and cool atmospheres. Their outermost layers are expelled by means of a dusty stellar wind \citep[e.g.][]{Habing2003}. The high mass-loss rate during the AGB phase prevents stars with masses between 2 M$_{\odot}$ and 9 M$_{\odot}$ from evolving to the supernova stage. During their lives, low and intermediate mass stars may undergo three distinct surface enrichment episodes. Those are referred to as dredge-ups, and they happen when the convective streams from the outer layers reach deep into the interior. Elements synthesized by nuclear fusion or by slow-neutron capture in the interior of AGB stars are brought to the surface and eventually ejected in the wind \citep[e.g.][]{Habing2003}. In this way, AGB stars contribute to the chemical enrichment of the interstellar medium and, in a bigger context, to the chemical evolution of galaxies. First and second dredge-up processes occur when these stars ascend the giant branch \citep{Iben1983}. The third dredge-up is in fact a series of mixing events during the AGB phase, induced by thermal pulses \citep[TPs,][]{Iben1975}. Evolutionary models predict by how much the surface abundance of each element is enriched for a star with a given initial mass and metallicity \citep[][and references therein]{Ventura2009, Karakas2010, Cristallo2011}. These models, however, need to be compared with observations. In particular, the change in surface chemical composition of AGB stars depends on initial mass and the assumed mass loss as a function of time. A very powerful diagnostic for the enrichment processes are surface isotopic ratios. From evolutionary model calculations, these ratios are found to vary strongly depending on the dredge-up events the star has experienced, and, therefore, evolutionary phase, and on the main sequence mass of the star \citep[e.g.][and references therein]{Boothroyd1999,Busso1999,Charbonnel2010,Karakas2011}. Since the outflowing gas is molecular up to large distances from the star (typically up to $\approx$ 1000 R$_{\star}$), the isotopic ratios must be retrieved from isotopologic abundance ratios. In this paper, we use an unparalleled number of $^{12}$CO and $^{13}$CO emission lines and the thermal infrared continuum to constrain the structure of the outflowing envelope of the oxygen-rich AGB star W Hya and, specifically, the isotopic ratio $^{12}$C/$^{13}$C. W\,Hya was observed by the three instruments onboard the Herschel Space Observatory \citep[hereafter {\it Herschel};][]{Pilbratt2010}. These are the Heterodyne Instrument for the Far Infrared, HIFI, \citep{deGraauw2010}, the Spectral and Photometric Imaging Receiver Fourier-Transform Spectrometer, SPIRE FTS, \citep{Griffin2010}, and the Photodetector Array Camera and Spectrometer, PACS, \citep{Poglitsch2010}. We supplemented these data with earlier observations from ground-based telescopes and the Infrared Space Observatory \citep[ISO;][]{Kessler1996}. The observations carried out by {\it Herschel} span an unprecedented range in excitation energies for the ground vibrational level and cover, in the case of W\,Hya, CO lines from an upper rotational level $J_{\rm up}$= 4 to 30. When complemented with ground-based observations of lower excitation transitions, this dataset offers an unique picture of the outflowing molecular envelope of W\,Hya. This allows us to reconstruct the flow from the onset of wind acceleration out to the region where CO is dissociated, which is essential for understanding the poorly understood wind-driving mechanism. Specifically, the velocity information contained in the line shapes of the HIFI high-excitation lines of $^{12}$CO, $J$=16-15 and 10-9 probe the acceleration in the inner part of the flow; the integrated line fluxes from $J$=4-3 to $J$=11-10 measured by SPIRE and the highest $J$ transitions observed by PACS give a very complete picture of the CO excitation throughout the wind. Finally, the low-$J$ transitions secured from the ground probe the outer regions of the flow. The availability of multiple $^{13}$CO transitions, in principle, permits constraints to be placed on the intrinsic $^{13}$CO/$^{12}$CO isotopologic ratio. A robust determination of this ratio is sensitive to stellar parameters and envelope properties, and for this reason is not easy to obtain. We modelled the CO envelope of W\,Hya in detail and discuss the effect of uncertainties on the parameters adopted to the derived $^{12}$CO/$^{13}$CO ratio. Together with the gas, we simultaneously and consistently model the solid state component in the outflow and constrain the abundance and chemical properties of the dust grains by fitting the ISO spectrum of W\,Hya. In this way we can constrain the dust-to-gas ratio. In Sect. \ref{sec:WHya}, the target, W\,Hya, and the available dataset are introduced, and the envelope model assumptions are presented. Section \ref{sec:radiation_field} is devoted to discussing radiative transfer effects that hamper determinations of isotopic ratios from line strength ratios, especially for low mass-loss rate objects. We present and discuss the results of our models in Sects. \ref{sec:CO_WHya} and \ref{sec:disc}. Finally, we present a summary of the points addressed in this work in Sect. \ref{sec:summary}. %__________________________________________________________________ | \label{sec:disc} \subsection{The outer CO envelope} The modelling of W\,Hya suggests a wind structure that is atypical of oxygen-rich AGB sources, both in terms of the behaviour of the CO gas and of the dust, particularly so near the CO photodissociation zone. Using maps of $^{12}$CO $J$=2-1 and $^{12}$CO $J$=1-0 for other sources, \citet{Castro-Carrizo2010} show that the location of this zone matches, or is larger than, the photodissociation radius predicted by \cite{Mamon1988}. The strengths and shapes of low-excitation lines ($J_{\rm up} \le 4$) in W\,Hya, however, clearly indicate that the size of the CO envelope is significantly smaller than predicted by \cite{Mamon1988}. That the situation is complex may be discerned from the $^{12}$CO $J$=1-0 and $^{13}$CO $J$=2-1 pure rotational lines. Weak emission is observed for these lines, but no emission is predicted when we adopt r$_{1/2}$ = 0.4 r$_{1/2}^{\rm \,m}$. These lines are, however, mainly excited in the outer parts of the CO envelope (r $\gtrsim$ 600 R$_{\star}$, or 15$\arcsec$ for the adopted stellar parameters and distance), a region where the PACS images show that the envelope of W\,Hya is not predicted well by our constant mass-loss rate model. \subsection{The $^{12}$CO/$^{13}$CO ratio} For the first time, we have multiple isotopic transitions in $^{12}$CO and $^{13}$CO available to constrain the $^{12}$CO/$^{13}$CO isotopologic ratio. Three of the four lines for which we have data for the $^{13}$CO isotopologue, i.e. $J$=10-9, 9-8, and 6-5, point to an intrinsic $^{12}$CO/$^{13}$CO ratio of 18. For comparison, the line ratios between the two isotopologues observed by HIFI are around 8 and 8.7 for transitions $J$=10-9 and $J$=6-5, respectively. The only previous attempt to constrain the intrinsic ratio is by \cite{Milam2009}, who found a value of 35 using the $J$=2-1 of $^{13}$CO transition. We could not use this particular transition, since it is poorly reproduced by our model. We note that \citeauthor{Milam2009} considered a mass loss that is an order of magnitude greater than was found by us and \cite{Justtanont2005}, and a three times lower $^{12}$CO abundance. They also assumed W\,Hya to be at a distance of 115 pc, which implies a twice higher luminosity than we have adopted. Given the intricacies in forming the $^{12}$CO and $^{13}$CO lines, especially in the case of the outer envelope of W\,Hya, it is hard to assess the meaning of the factor-of-two difference in the intrinsic $^{12}$C/$^{13}$C. We therefore discuss the uncertainties in this ratio in more detail. This discussion is also important in view of a comparison with theoretical predictions, this ratio being a very useful tool for constraining AGB evolution models. \subsubsection{The uncertainty of the determined $^{12}$CO/$^{13}$CO ratio} In order to quantify the robustness of the derived $^{12}$CO/$^{13}$CO ratio, we carried out a test in which we vary parameters that so far were held fixed in our model grid and studied the effect. First, we investigate the impact of varying the assumed $^{12}$CO abundance relative to H (standard at $2.0 \times 10^{-4}$) and the stellar luminosity considered (5400\,$L_{\odot}$). We calculated models in which we changed each of these parameters, but only one at a time, by a factor of two -- both toward higher and lower values. When these parameters are varied, the $^{12}$CO line fluxes and shapes also change. We scaled the mass-loss rate in order to fit the line flux observed by SPIRE, since the $^{12}$CO lines observed by this instrument are excited in the same region as $^{13}$CO transitions used to determine the isotopic ratio. We did not attempt a fine-tuning to match the strengths and shapes of the profiles. The factor-of-two changes in each of the two parameters affect the line fluxes of $^{13}$CO by typically 20 to 25 percent and at most 30 percent. Second, we studied the effect of changes in the input stellar spectrum. As pointed out in Sect. \ref{sec:radiation_field}, the stellar flux in the near infrared may have an important effect on the CO line strengths as photons of these wavelengths can efficiently pump molecules to higher rotational levels. In our models, the spectral emission of W\,Hya is approximated by a black body of 2500 K. However, the stellar spectrum is much more complex, and its intensity changes considerably even for small differences in wavelength. Specifically, molecules in the stellar atmosphere can absorb photons, thereby reducing the amount available for exciting $^{12}$CO and $^{13}$CO further out in the envelope. Figure \ref{fig:fit_ISO} indicates that the molecular absorption at 4.7 $\mu$m is less than a factor of two. We assume a factor-of-two decrease in the stellar flux in the 4.7 $\mu$m region to assess the impact of the near-IR flux on the modelled lines. The change in the integrated line flux of $^{12}$CO lines is only about five percent. The $^{13}$CO lines respond more strongly, varying by typically 25\%. The combined impact of these three sources of uncertainties on the derived isotopic ratio would be $\sim$\,40\% in this simple approach. Also accounting for uncertainties due to the flux calibration and noise (which are about 25\% uncertain) and the actual model fitting (25\% uncertain), we conclude that the intrinsic isotopic ratio determined here is uncertain by 50\% to 60\%. This implies that W\,Hya has a $^{12}$CO/$^{13}$CO ratio of $18 \pm 10$. Better signal-to-noise observations of, particularly, $^{13}$CO, in combination with spatial maps of both $^{12}$CO and $^{13}$CO lines, are required to constrain this value better. \subsubsection{Connecting the $^{12}$C/$^{13}$C ratio to stellar evolution} From evolutionary model calculations, the surface $^{12}$C/$^{13}$C ratio is expected to change in dredge-up events. It is found to decrease by a factor of a few after the first dredge-up, taking place during the ascent on the red giant branch (RGB) and reaching a value of typically 20 for stars more massive than 2 M$_\odot$. For stars with masses lower than 2 M$_\odot$, it is found to increase with decreasing mass, reaching about 30 at 0.8 M$_\odot$. In stars that experience the second dredge-up (M$_\star \gtrsim$ 4.5 M$_\odot$), this ratio is found to decrease further by a few tens of percent during the ascent on the AGB \citep{Busso1999,Karakas2011}. Stars with masses higher than 1.5 M$_\odot$ experience the third dredge-up, a continuous process that occurs during the thermally pulsing AGB phase. Evolutionary models show that this ratio is steadily increasing thanks to the surface enrichment of $^{12}$C or is not changing significantly if the star is massive enough, M$_\star \gtrsim 4.0$ M$_\odot$, for hot bottom burning to operate. Recent calculations include extra-mixing processes to explain the low values of the $^{12}$C/$^{13}$C ratio observed in low mass RGB stars \citep{Tsuji2007,Smiljanic2009,Mikolaitis2012}. Extra-mixing processes are thought to occur also during the AGB phase \citep{Busso2010}, but its causes and consequences are more uncertain. Models that include extra mixing in the RGB predict lower isotopic ratios ($\sim$\,10) for low mass stars ($\sim$\,1\,M$_\odot$). When compared to model predictions, a value of 18 for the $^{12}$C/$^{13}$C ratio would be consistent with W\,Hya having an isotopic ratio that reflects the value set by the first dredge-up \citep{Boothroyd1999,Charbonnel2010} for star with masses higher than about 2 M$_\odot$. If W\,Hya's mass lies between 1.5 M$_\odot$ and 4.0 M$_\odot$, the value found by us further suggests that the star has experienced few or none of these third dredge-up events. Our intrinsic isotopic ratio, however, is not very constraining, since it agrees within the uncertainties with three very different scenarios for W\,Hya's evolutionary stage: first, having a low value of this ratio ($\sim$\,8), hence having suffered extra mixing in the first dredge-up, characteristic of low mass stars; second, having a ratio of indeed 18, which implies a higher mass; or, third, having a higher ratio ($\sim$\,28) and being on its way to becoming a carbon star. Decreasing the error bars by a factor of three or four would allow one to draw stronger conclusions on this matter. Such accuracy may be achieved with the Atacama Large Millimeter/submillimeter Array. \subsection{The wind acceleration} The wind acceleration in W\,Hya is quite slow. The highest excitation line for which we have an observed line shape, $^{12}$CO $J$=16-15, has an excitation of its upper level that peaks at eight stellar radii, decreasing to one-fifth of this peak value at 30\,$R_{\star}$. The triangular shape and the width of this profile indicate that it is formed in the accelerating part of the flow. The $^{12}$CO $J$=10-9 line is still explained well by a $\beta$ = 5.0 model, but the region where this line is excited seems to be where the wind starts to be accelerated faster than our model with $\beta$ = 5.0. Interestingly, this effect is noted mainly in the blue-shifted part of the flow. The population of level $J$=10 of $^{12}$CO reaches a maximum at 25 $R_{\star}$, decreasing to one-fifth of this peak value at 70 $R_{\star}$. This shows that the wind approaches the terminal velocity indeed much later than expected, somewhere around 50 stellar radii. Furthermore, transition $J$=6-5 of $^{12}$CO is formed in a region where the wind has already reached maximum expansion velocity, contrary to what a model with $\beta$=5.0 predicts. This indicates that, although the wind has a slow start until 5.5 - 6.0 km/s, the last injection of momentum happens quite fast. Other authors have also concluded that the wind of W\,Hya is accelerated slower than expected \citep{Lucas1992,Szymczak1998}, in agreement with our results. The shapes of $^{13}$CO $J$=10-9 and $J$=9-8 lines are also asymmetric, as is that of $^{12}$CO $J$=10-9 line. The reason for this is not clear but may be connected to large scale inhomogeneities that damp out, or smooth out, at large distances. A direction-dependent acceleration law, for example, or direction-dependent excitation structures of the higher levels of these two transitions might be the reason we see this asymmetry. The higher optical depth in the $^{12}$CO lines might be able to make this feature less pronounced in the $J$=10-9 of this isotopologue. We note that these two $^{13}$CO lines do not have a high signal-to-noise ratio, therefore, no firm conclusion can be drawn based on this apparent asymmetry. We have constrained the wind structure of W\,Hya using an unprecedented number of $^{12}$CO and $^{13}$CO emission lines. We were especially interested in understanding the excitation of $^{12}$CO and $^{13}$CO for this source. The envelope structure derived in this study will enable analysis of other molecular abundances in the outflow, such as ortho- and para-water and its isotopologues, SiO and its isotopologues, SO, SO$_2,$ and even carbon-based molecules such as HCN. Specifically, we may thus obtain excitation conditions of these molecules and the heating and cooling rates -- mainly thanks to water transitions -- associated to it. These species too will add to our understanding of the physical and chemical processes in the wind. The main conclusions obtained from modelling $^{12}$CO and $^{13}$CO are \begin{itemize} \item{The model that best fits the data has a mass-loss rate of $1.3 \times 10^{-7}\ M_{\odot}$yr$^{-1}$, an expansion velocity of $7.5$ km/s, a temperature power-law exponent of $0.65$, a CO dissociation radius 2.5 times smaller than what is predicted by theory, and an exponent of the $\beta$-type velocity law of 5.0. We note that the wind has a slow start that is better reproduced by a high value of this exponent, but that the envelope reaches its final expansion velocity sooner than such a model would predict.} \item{The smaller outer CO radius is supported mainly by the line strengths of the low-$J$ lines. Introducing a broken temperature law does not fix this problem, and a varying mass-loss rate, lower in the outer envelope, seems to contradict what is seen in the PACS dust maps.} \item{By comparing our constant mass-loss rate dust model with recently published PACS images of W\,Hya, we note that our dust model does not reproduce the observations beyond 20$\arcsec$, corresponding to 800 R$_\star$ for the adopted parameters and distance. This extra emission may originate in material expelled in a phase of higher mass loss or be the result of a build up of material from interaction with previously ejected gas or interstellar medium gas.} \item{We derive a $^{12}$CO to $^{13}$CO isotopic ratio of 18 $\pm$10. The accuracy is not sufficient to draw firm conclusions on the evolutionary stage or main-sequence mass of W\,Hya, but a ratio of 20 would be expected for an AGB star with mass higher than 2 M$_\odot$ that did not experience $^{12}$C enrichment due to the third dredge-up phase. Spatially resolved observations may help constrain the $^{12}$CO abundance and the $^{13}$CO excitation region and allow for a more precise estimate of this ratio.} \end{itemize} | 14 | 3 | 1403.2892 |
1403 | 1403.7000_arXiv.txt | { CO observations in active galactic nuclei and star-bursts reveal high kinetic temperatures. Those environments are thought to be very turbulent due to dynamic phenomena such as outflows and high supernova rates.\\ We investigate the effect of mechanical heating on atomic fine-structure and molecular lines, and their ratios. We try to use those ratios as a diagnostic to constrain the amount of mechanical heating in an object and also study its significance on estimating the H$_2$ mass.\\ Equilibrium photo-dissociation models (PDRs hereafter) were used to compute the thermal and chemical balance for the clouds. The equilibria were solved for numerically using the optimized version of the Leiden PDR-XDR code. Large velocity gradient calculations were done as post-processing on the output of the PDR models using RADEX.\\ High-$J$ CO line ratios are very sensitive to mechanical heating (\gm~hereafter). Emission becomes at least one order of magnitude brighter in clouds with $n \sim 10^5$~\cmt~and a star formation rate of 1~\modotyr~(corresponding to \gm~$ = 2 \times 10^{-19}$~\ecs). Emission of low-$J$ CO lines is not as sensitive to \gm, but they do become brighter in response to \gm. Generally, for all of the lines we considered, \gm~increases excitation temperatures and decreases the optical depth at the line centre. Hence line ratios are also affected, strongly in some cases. Ratios involving HCN are a good diagnostic for \gm, where the HCN(1-0)/CO(1-0) increases from 0.06 to 0.25 and the HCN(1-0)/HCO$^+$(1-0) increase from 0.15 to 0.5 for amounts of {\gm~equivelent to 5\% of the surface heating rate}. Both ratios increase to more than 1 for higher \gm, as opposed to being much less than unity in pure PDRs.\\ The first major conclusion is that low-$J$ to high-$J$ intensity ratios will yield a good estimate of the mechanical heating rate (as opposed to only low-$J$ ratios). The second one is that the mechanical heating rate should be taken into account when determing $A_V$ or equivalently $N_{\rm H}$, and consequently the cloud mass. Ignoring \gm~will also lead to large errors in density and radiation field estimates. } | The study of molecular gas in external galaxies dates back to the mid-seventies, with the detection of ground-state emission from CO (the most abundant {molecules} after hydrogen) in {a small number of bright nearby galaxies. At present observations CO and many other molecules exist for a very large number of galaxies, near and far. It is important to be able to interpret the emission in the various lines from those galaxies, since that gives us insight in the physics dominating the interstellar medium in the star forming regions of these extra-galactic sources.} For decades, line observations had to be done from the ground in a frequency range limited by atmospheric opacity, so that for most molecular species only the {low} transitions were accessible. {Level transitions at higher rest frame frequencies, were only possible for distant galaxies for which the high-frequency lines were red-shifted into atmospheric windows accessible from the ground. In the past few years the {\it Herschel} Space Observatory \citep{Pilbratt2010} operating outside the Earth's atmosphere has provided direct observations of spectral lines at frequencies hitherto impossible or hard to access. By way of example we mention the determination of extensive $^{12}$CO rotational transitions ladder in galaxies such as M82 \citep{loenen10, panuzzo2010, kamentzky2012} and Mrk231 \citep{vanderwerf10, gozalez12}. {\it Herschel} ran out of coolant in April 2013, but at about the same time, the Atacama Large Millimeter Array (ALMA) became operational. With ALMA, a large fraction of the important submillimeter spectrum is still accessible, at vastly superior resolution and sensitivity, allowing detection and measurement of diagnostic molecular line transitions largely out of reach until then.} {Conducting} detailed studies of the physical properties of the molecular gas {of close-by star-forming galaxies} involves a challenging inversion problem, where resultant line intensities are used to constrain gas densities, molecular content, kinetic temperatures and the nature and strengths of the radiation field exciting the gas. {In order to solve} this problem, it is necessary to get a clearer understanding of the underlying physics and phenomena characterizing specific regions such as galaxy centres, including our own. A good starting point to analyze molecular gas emission is the application of the so-called large-velocity-gradient (LVG) models { \citep{sobolev1960}. This assumes an escape probability formalism for photons in different geometries which simplifies solving for the radiative transfer significantly. LVG models have been widely used by the ISM community with some other basic assumptions to estimate the molecular density of the gas, species abundances and the kinetic temperature \citep[][among others]{henkel83, Jansen1994, Hogerheijde2000, radex, despotic}. These models provide only an insight for the physical and chemical properties of the clouds; the actual nature of the source of energy cannot be determined using those LVG models, see for example \cite{Israel2009a,Israel2009b}. The next level of sophistication over LVG modelling involves the application of photon-dominated region (PDR) models \citep{cloudy, Hollenbach1999, petit06, rolling07, bisbas12}. These models self-consistently solve for the thermal and chemical structure of clouds irradiated by UV photons. In PDRs, energy sources other than UV photons could dominate the thermal and chemical balance. In the vicinity of an active galactic nucleus (AGN), PDR models can be augmented by models for X-ray dominated region \citep[XDRs][]{Maloney1996,bradford03,meijerink2005-1,Papadopoulos2011, bayet11-1, meijerink11}.} In both these models, the underlying assumption is that the thermal balance is dominated by radiation. The physical situation in galaxy centers, star-bursts and dense cores \citep{pineda10} is, however, more complicated. There are other processes, such as mechanical feedback that may also excite the gas mechanically \citep{loenen2008, Ossenkopf02-a, Ossenkopf02-b, mvk12}. {Although these models are much more sophisticated than LVG models, a simplified comparison of many PDR codes\footnote{In the comparison benchmark the chemistry involved 4 elements (H, He, O and C) and 30 species. For more details on the benchmarks and the codes used see \texttt{http://goo.gl/7Hf6mD}} \citep{rolling07} has shown that they shed a statistical view on the underlying processes. This is particularly true in the transition zone from atomic to molecular gas, where an order of magnitude difference between the various quantities compared in the models is not uncommon. Such discrepancies are mainly due to the uncertainties in the chemical reaction constants, which in turn influence the reaction rates, abundances and thermal balance \citep{vasyunin04}. In addition to those uncertainties observations of extra-galactic sources have spatial resolution limitations. For example the resolution of {\it Herschel} for the nucleus of NGC 253 is on the order of 1 kpc. The surface area covered by such a beam size contains a large number of clouds. In modelling the nucleus of such galaxies one might need to consider two or more PDRs simultaneously. Although considering more than one PDR component improves the fits significantly, the increased number of free parameters usually has a negative impact on to the statistical significance of those fits. This is particularly valid whenever the number of lines being fitted is low. Here we follow the modelling of paper I \citep{mvk12} where we studied the effect of mechanical heating (\gm) by considering its impact on the thermal and chemical structure (abundances, column densities and column density ratios of species) of PDRs. Hence our basic modelling premise will be the same in this paper. Namely, an 1D semi-infinite plane-parallel geometry is adopted. It is assumed that the slab is illuminated with a FUV source from one side. Another major assumption is that the clouds are in an equilibrium state. Since equilibrium is assumed, we consider a simplified recipe in accounting for mechanical feedback. For simplicity the contribution of mechanical heating to the total heating budget, is added in an ad-hoc fashion uniformly throughout the cloud. Our approximation of the effect of mechanical heating by a single homogeneous heating term is a simplification. In practice, the mechanical energy which could be liberated by supernova events or gas outflows, is deposited locally in shock fronts. In these fronts, which are the interaction surfaces between high speed flows and the ambient medium, the energy is not necessarily distributed uniformly throughout the cloud volume. On the other hand, this energy will eventually cascade to smaller spatial scales and thermalize en route to equilibrium. The efficiency of the ``thermalization'' is conservatively taken to be 10\%. Consequently the approximation we adopt may be less applicable to systems where the dynamical time-scales are comparable to the thermal and chemical time-scales; this occurs for example in clouds in the inner kpc of galaxy centres. Our choice for the ranges in mechanical heating explored is based primarily on estimates by \cite{loenen2008}. They found that fits for the line ratios of the first rotational transition ($J = 1-0$) of the molecules HCN, HNC and HCO$^+$ are greatly enhanced by using PDR models which included ``additional'' heating. They attributed this extra heating to dissipated turbulence and provided an estimates for it. The major conclusion of Paper I was that even small amounts of mechanical heating, as low as 1\% of the surface UV heating, has significant effects on the molecular abundances and column densities. Those effects are mainly manifested as enhanced CO abundances which could increase by up to a factor of two. Although this might not seem a significant effect, the column densities of the high density tracers such as HCN and HNC increase (or decrease) by an order of magnitude depending on the amount of \gm.} The aim of this paper is to understand both the ground-state and the more highly excited states of molecular gas in galaxy centers and to determine whether turbulence or shocks can make a major contribution to the molecular emission. {In other words, we thus extend the work done in Paper I, which focused on the chemical abundances and column densities only, by studying the signature of mechanical feedback on selected atomic and molecular emission lines.} The models presented in this paper also apply to other regions where the gas is, e.g., (1) heated by young stellar objects (YSO's), (2) stirred up turbulently by the fast motions of stars, or (3) violently heated by supernovae. {Since we assume equilibrium, applying our models to those regions is of course an approximation}. In all cases, non-negligible amounts of mechanical energy may be {eventually} injected into the ISM \citep{sb99}. Part of this energy is then converted to {mechanical} heating, particularly important in so-called star-burst galaxies. Since the amount of turbulent energy absorbed by the ISM is a priori unknown, we explore a wide range of possibilities of turbulent heating {contributions} to PDRs. In our approach, the additional heating self-consistently modifies the emission. {In this paper we provide two new estimates of mechanical heating rates and re-enforce our assumptions of Paper I (see the methods section below).} Although we introduce an extra free parameter (the amount of absorbed turbulent energy), the basic molecular {abundances and} gas parameters are self-consistently determined by the equilibria that we solve for in the PDR models. In the following we explore, {using those 1D equilibrium PDR models}, the effect of mechanical heating (\gm) on atomic and molecular line intensities for a range of : densities, FUV flux (\go), metallicities and column densities. {In doing so we} aim to find good diagnostics for \gm~{and to check for the usefulness of such PDR models with an additional ``ad-hoc'' heating term in constraining mechanical heating.} | We have studied the effect of \gm~on a wide range of parameter space in $n$ and \go~ covering six order of magnitude in both ( $1 < n < 10^6$~ \cmt~ and $1 < G_0 < 10^6$). Throughout this parameter space we investigated the the most important and commonly observed molecular emission and atomic fine-structure lines and their ratios. The explored range in mechanical heating (\gm) covers {quiescent regions}, with almost no star-formation, as well as violently turbulent star-bursts. The star-formation rates for those range from 0.001 \modotyr~ to $\sim 100$ \modotyr~ respectively. The two fundamental questions we try to answer in this paper are: {\bf(a)} is it possibile to constrain the mechanical heating rate in a {star-forming region} by using molecular line ratios as a diagnostic? {(b)} how important is \gm~in recovering the molecular H$_2$ mass of a {star-forming region} using observed molecular line emission such as those of CO? Before discussing these questions, we {state the main characteristics of mechanically heated PDRs we observed in our grids: } \begin{itemize} \item The most significant contribution of \gm~to the atomic fine-structure line intensities results from enhanced temperatures in the molecular zone. This is especially the case for the [CI] lines. {For clouds whose density is below the critical density of those lines}, half of the emission {intensity emanates from} the molecular zone. FS line ratios, such as [CII] 158\mum/[CI] 369\mum, [OI] 63\mum/[CI] 369\mum~ and [CI] 369\mum/[CI] 609\mum, are good diagnostics for \gm~in low-density PDRs ($n <10^3$~\cmt). \item High-$J$ to low-$J$ transitional ratios of $^{12}$CO and $^{13}$CO, such as CO(16-15)/CO(1-0), are good diagnostics for \gm~over the whole density range considered. In cotrast low-$J$ CO line ratios, such as CO(2-1)/CO(1-0) or CO(4-3)/CO(1-0), are useful as diagnostics\footnote{We refer the reader to the end of this section for a small discussion on the difference about regions dominated by cosmic-rays in comparison to ones dominated by \gm.} only for clouds with $n < 10^3$ \cmt. \item The line ratios of \thco/$^{12}$CO (in both low-$J$ and high-$J$ transitions) have a strong dependence on \gm. They decrease as \gm~ increases. This complements the range in density where low-$J$ transitions of $^{12}$CO (and $^{13}$CO) can be used as diagnostics for \gm. \item At high metallicities ($Z = 2$~\zsun), HCN and HNC are very good diagnostics for \gm~{when \go~$\gtrsim 10^5$, such sources include} star-bursts in galaxy centers. \item {Line ratios such as} HCN(1-0)/CO(1-0), HCN(1-0)/HCO$^+$(1-0), CN(1$_{1/2}$-0$_{1/2}$)/HCN(1-0), CN(2$_{3/2}$-1$_{3/2}$)/HCN(1-0), CS(1-0)/HCO$^+$(1-0) {show a strong dependance of \gm, hence they are a good diagnostic of it.} \end{itemize} The major conclusions of the paper, which we demonstrated in the application section is: low-$J$~ transitions alone are not good enough to constrain mechanical heating; ratios involving high-$J$~ to low-$J$ transitions do a much better at that. Another major conclusion is the importance of \gm~in constraining $A_V$ or, equivalently, the hydrogen column density $N_{\rm H}$, which can be used to determine the molecular mass of the cloud. In comparing Figure-\ref{fig:constraining} to the ones of higher $A_V$ in the appendix, one can see that if \gm~is ignored, it is easy to under- or over-estimate the $A_V$ by a factor of five (or more). Ignoring \gm~also results in more than an order of magnitude error in estimating the $n$ and \go. For instance in looking at the last row of Figure-\ref{fig:constraining}, one can see that when \gm~is ignored, an error up to two orders of magnitude can be done in constraining the ranges of $n$ and \go. We emphasis that our approach in constraining the physical parameters of clouds using the observed line ratios, is just a proof of concept demonstration. Ultimately one must use more elaborate minimization methods to attempt to constrain the physical parameters. However, it is most likely that the parameters {which best fit} the observations, will be very close to the ones obtained using the method adopted in the application section. We leave it to the interested reader to make use of the grids which are published as well with this paper (see Figures-\ref{HCN-HCO+-grid-grids}, \ref{HNC-HCO+-grid-grids}, \ref{HCN-HNC-grid-grids} in the appendix). We finalize our discussion by touching on the effect of cosmic rays (CR). Although it is outside the scope of this paper, we explored the effect of enhanced CR rates. Diagnostic line ratio grids for HCN, HNC and HCO$^+$ are fundamentally different from those which are dominated by \gm~(see Figure-\ref{CR-grid-grids}). Hence, we expect that in using diagnostics presented in this paper, {clouds which are embedded in environments where the CR rate is enhanced}, would not be mistaken with {clouds whose heating budget is dominated by \gm.} | 14 | 3 | 1403.7000 |
1403 | 1403.0882_arXiv.txt | Quantifying how the baryonic matter traces the underlying dark matter distribution is key to both understanding galaxy formation and our ability to constrain the cosmological model. Using the cross-correlation function of radio and near-infrared galaxies, we present a large-scale clustering analysis of radio galaxies to $z\sim2.2$. We measure the angular auto-correlation function of $K_\textrm{s}<23.5$ galaxies in the VIDEO-XMM3 field with photometric redshifts out to $z=4$ using VIDEO and CFHTLS photometry in the near-infrared and optical. We then use the cross-correlation function of these sources with 766 radio sources at $S_{1.4} > 90$ $\mu$Jy to infer linear bias of radio galaxies in four redshift bins. We find that the bias evolves from $b = 0.57\pm0.06$ at $z\sim0.3$ to $8.55\pm3.11$ at $z\sim2.2$. Furthermore, we separate the radio sources into subsamples to determine how the bias is dependent on the radio luminosity, and find a bias which is significantly higher than predicted by the simulations of Wilman et al., and consistent with the lower luminosity but more abundant FR-\textsc{I} population having a similar bias to the highly luminous but rare FR-\textsc{II}s. Our results are suggestive of a higher mass, particularly for FR-\textsc{I} sources than assumed in simulations, especially towards higher redshift. | The observed distributions of galaxies and clusters today are far removed from the homogeneous picture we have of the early Universe using the cosmic microwave background (CMB; e.g. \citealt{komatsu11}), and we require large numbers of them to piece together a statistical understanding of clustering on cosmological scales. Cosmological applications of large-scale clustering measurements require information about the gravitating mass distribution in the Universe, which in a $\Lambda$CDM cosmology is strongly tied to the dark matter distribution. Direct observations tell us only about the baryonic matter, from which we must infer the dark matter distribution. Various tools exist for measuring the clustering signal of observed sources, such as nearest neighbour measures (e.g. \citealt{bahcall83}), counts-in-cells (e.g. \citealt{magliocchetti99,blake02b,yang11}), correlation functions (e.g. \citealt{groth77,bahcall83,blake02a,blake02b,croom05}) and power spectra (e.g. \citealt{cole05,percival07,komatsu11}). Due to its relative simplicity to calculate, and relation to its Fourier transform (the power spectrum), the two-point spatial correlation function has become a standard in quantifying cosmological structure. A means by which we can quantify the extent to which the observable and dark matter are tied using the correlation function is through the linear bias parameter $b(z)$, the ratio of the galaxy correlation function to that of the dark matter. The bias quantifies the difference in the clustering of the dark matter haloes acting solely under gravity and of galaxies inhabiting those haloes with other effects making their structure more or less diffuse. This has a heavy dependence on the galaxy masses and the epoch under consideration (e.g. \citealt{seljak04}). Extragalactic radio sources make useful probes of large-scale structure, being readily detectable up to high redshifts ($z\sim6$). Being unaffected by dust extinction, radio surveys are able to provide unbiased samples of larger volumes than would be available to an optical survey. Unfortunately many radio sources, particularly at higher redshifts, have very faint optical counterparts, which combines with the often extended nature of radio emission from active galactic nuclei (AGN) to make it difficult to optically identify and obtain redshifts for these individual sources \citep[see e.g.][]{mcalpine12}. Without knowing the distance to a given radio source, clustering analyses are confined to two dimensions with the angular correlation function measuring any excess of source pairs as a function of their angular separation. The broad redshift distribution typical of radio surveys can make detection of this clustering difficult as the majority of close pairs of sources are widely separated in the line of sight direction, diluting any genuine clustering signal. Strong detections of this clustering signal over a range of angular separations were made possible with the advent of large area radio surveys observing to depths of a few mJy: e.g. Faint Images of the Radio Sky at Twenty-cm (FIRST; \citealt{becker95}), the Westerbork Northern Sky Survey (WENSS; \citealt{rengelink97}), the NRAO VLA Sky Survey (NVSS; \citealt{condon98}) and the Sydney University Molonglo Sky Survey (SUMSS; \citealt{bock99}). A positive correlation function is measured with high significance using these surveys extending to separations of several degrees (see work by \citet{cress96} and \citet{magliocchetti98,magliocchetti99} with FIRST, \citet{blake02a,blake02b} and \citet{overzier03} with NVSS, \citet{rengelink98} with WENSS, and \citet{blake04} with SUMSS). Angular clustering studies (such as those above) assume a power law form for the spatial correlation function (also a common assumption for direct spatial clustering measurements; e.g. \citealt{magliocchetti04,brand05}), which is also preserved in angular projection \citep{limber53}. Inferring the spatial clustering properties of a galaxy sample from this projected form requires a knowledge of the redshift distribution of the sample, itself subject to uncertainty in addition to that resulting from the diluted signal arising from a sample with a broad redshift distribution. Photometric redshift surveys, while lacking the precision obtained from galaxy spectra necessary for a full 3D clustering analysis, provide a more accurate redshift distribution for a given sample of radio sources than assumed models or luminosity functions. Furthermore, they allow a sample to be divided into redshift bins, each with a well known distribution (given large enough numbers to account for small photometric errors). \citet{lindsay14} use a combination of spectroscopic and photometric redshifts to investigate the clustering of FIRST radio sources to $z\sim 1.5$ and provide some comparison between spatial and angular correlation function results (with and without the precision of spectroscopic redshifts, respectively). However, redshift measurements are lacking at high redshift where the clustering is stronger but poorly constrained over such large areas. While sky coverage alone, with surveys such as NVSS, provides the statistical power required to measure the strength of the clustering of radio sources over large scales to depths of a few mJy, the depths of similarly large-area optical surveys, spectroscopic or otherwise, do not allow for optical identification of the radio sources with any significant completeness. However, small-area surveys have been carried out at the $\mu$Jy level, which also have potential uses for cosmology and large-scale structure measurements. At the $\mu$Jy level, the radio population becomes less dominated by FR-\textsc{I} and FR-\textsc{II} type active galactic nuclei (AGN), and we observe a greater fraction of star-forming galaxies. However, the lower flux-density limit also extends the range at which we can detect AGN, reaching beyond $z\sim1$ where the bias of radio sources is poorly understood. It is important to measure the bias of the radio sources to these high redshifts, and to know how it evolves, in order to inform cosmological experiments dependent on disentangling the observed galaxy clustering from other effects, such as cosmic magnification (e.g. \citealt{scranton05, wang11}) and the integrated Sachs-Wolfe effect (ISW; \citealt{mcewen07, giannantonio08, raccanelli08}). In particular the large volume of the Universe that will be opened up by the SKA and its precursors may provide important information on the very largest scales \citep[e.g.][]{raccanelli12,camera12}. The aim of this paper is to investigate the bias of a sample of faint radio sources, extending to $z>2$ where observational measurements are lacking. We use 1.4 GHz radio data from the VLA-VIRMOS Deep Field \citep{bondi03} covering an area of 1 square degree to $S_{1.4} > 90$ $\mu$Jy, overlapping with optical photometry from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) Deep-1 field (D1) and near-infrared photometry from the VISTA Deep Extragalactic Observations (VIDEO; \citealt{jarvis13}) survey with a depth of $K_\textrm{s} < 23.5$. We overcome the signal-to-noise issue of having a far smaller sample than a wider, shallower NVSS-like survey by inferring the properties of the radio sources by the combined use of the angular correlation function of $K_\textrm{s}$-selected VIDEO sources (with sufficiently large numbers to keep uncertainties small) and the angular cross-correlation of these VIDEO sources with the radio sample \citep[see e.g.][for similar use of this technique]{guo11,hartley13}. With reliable photometric redshifts out to $z\sim4$ for all of the galaxies used, we have a good knowledge of the redshift distributions of our samples as well as estimates of their radio luminosity. Even when coarsely binning by redshift, this gives us valuable constraints on the bias of these radio sources in bins up to a median redshift of $z=2.15$, and an insight into the clustering specifically of typical radio AGN at high redshift. This paper is organized as follows: Section \ref{data} describes the multi-wavelength surveys from which we construct our galaxy samples. Section \ref{methods} details the correlation function methods used to calculate the galaxy bias and Sections \ref{results} and \ref{discussion}, respectively, show our results and present our discussion of them. The results are summarized in Section \ref{conclusions}. The cosmological model used throughout this paper is the flat, $\Lambda$CDM concordance cosmology where $\Omega_m = 0.3$, $\Omega_\Lambda = 0.7$ and $\sigma_8 = 0.8$. All distances are kept in units of $h^{-1}$Mpc where $H_0 = 100 h$ km s$^{-1}$Mpc$^{-1}$ and $h$ is not explicitly assumed. | 14 | 3 | 1403.0882 |
|
1403 | 1403.0544_arXiv.txt | Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binary's nature and inspiral kinematics. Using the \texttt{lalinference\_mcmc} Markov-chain Monte Carlo parameter estimation code, we use two fiducial examples to illustrate how the geometry and kinematics are encoded into the modulated gravitational wave signal, using coordinates well-adapted to precession. Extending previous work, we demonstrate the performance of detailed parameter estimation studies can often be estimated by ``effective'' studies: comparisons of a prototype signal with its nearest neighbors, adopting a fixed sky location and idealized two-detector network. Using a concrete example, we show higher harmonics provide nonzero but small \emph{local} improvement when estimating the parameters of precessing BH-NS binaries. We also show higher harmonics can improve parameter estimation accuracy for precessing binaries by breaking leading-order discrete symmetries and thus ruling out approximately-degenerate source orientations. Our work illustrates quantities gravitational wave measurements can provide, such as the orientation of a precessing short gamma ray burst progenitor relative to the line of sight. More broadly, ``effective'' estimates may provide a simple way to \emph{estimate trends} in the performance of parameter estimation for generic precessing BH-NS binaries in next-generation detectors. For example, our results suggest that the orbital chirp rate, precession rate, and precession geometry are roughly-independent observables, defining natural variables to organize correlations in the high-dimensional BH-NS binary parameter space. | Ground based gravitational wave detector networks (notably LIGO \cite{gw-detectors-LIGO-original-preferred} and Virgo \cite{gw-detectors-VIRGO-original-preferred}) are sensitive to the relatively well understood signal from the lowest-mass compact binaries $M=m_1+m_2\le 16 M_\odot$ \cite{2003PhRvD..67j4025B,2004PhRvD..70j4003B,2004PhRvD..70f4028D,BCV:PTF,2005PhRvD..71b4039K,2005PhRvD..72h4027B,2006PhRvD..73l4012K,2007MNRAS.374..721T,2008PhRvD..78j4007H,gr-astro-eccentric-NR-2008,gw-astro-mergers-approximations-SpinningPNHigherHarmonics,gw-astro-PN-Comparison-AlessandraSathya2009}. Strong signals permit high-precision constraints on binary parameters, particularly when the binary precesses. Precession arises only from spin-orbit misalignment; occurs on a distinctive timescale between the inspiral and orbit; and produces distinctive polarization and phase modulations \cite{ACST,gw-astro-SpinAlignedLundgren-FragmentA-Theory,gwastro-SpinTaylorF2-2013}. As a result, the complicated gravitational wave signal from precessing binaries is unusually rich, allowing high-precision constraints on multiple parameters, notably the (misaligned) spin \cite{LIGO-CBC-S6-PE,gwastro-mergers-HeeSuk-FisherMatrixWithAmplitudeCorrections}. Measurements of the spin orientations alone could provide insight into processes that misalign spins and orbits, such as supernova kicks \cite{2013MNRAS.434.1355J,2012MNRAS.423.1805N}, or realign them, such as tides and post-Newtonian resonances \cite{2013PhRvD..87j4028G}. More broadly, gravitational waves constrain the pre-merger orbital plane and total angular momentum direction, both of which may correlate with the presence, beaming, and light curve \cite{2010ApJ...722..235V,2011ApJ...733L..37V,2013ApJ...767..141V} of any post-merger ultrarelativistic blastwave (e.g, short GRB) \cite{2009ARAA..47..567G}. Moreover, spin-orbit coupling strongly influences orbital decay and hence the overall gravitational wave phase: the accuracy with which most other parameters can be determined is limited by knowledge of BH spins \cite{1995PhRvD..52..848P,2013PhRvD..87b4035B,gwastro-mergers-HeeSuk-FisherMatrixWithAmplitudeCorrections,gwastro-mergers-HeeSuk-CompareToPE-Aligned}. Precession is known to break this degeneracy \cite{2006PhRvD..74l2001L,2009PhRvD..80f4027K,2011PhRvD..84b2002L,gwastro-mergers-HeeSuk-FisherMatrixWithAmplitudeCorrections,2007CQGra..24..155V,LIGO-CBC-S6-PE}. In sum, the rich gravitational waves emitted from a precessing binary allow higher-precision measurements of individual neutron star masses, black hole masses, and and black hole spins, enabling constraints on their distribution across multiple events. In conjunction with electromagnetic measurements, the complexity of a fully precessing gravitational wave signal may enable correlated electromagnetic and gravitational wave measurements to much more tightly constrain the central engine of short gamma ray bursts. Interpreting gravitational wave data requires systematically comparing all possible candidate signals to the data, constructing a Bayesian posterior probability distribution for candidate binary parameters \citeMCMC{}. Owing to the complexity and multimodality of these posteriors, successful strategies adopt two elements: a well-tested generic algorithm for parameter estimation, such as variants of Markov Chain Monte Carlo or nested sampling; and deep insight into the structure of possible gravitational wave signals, to ensure efficient and complete coverage of all possible options \cite{gw-astro-PE-Raymond-JumpProposals,gw-astro-PE-systemframe}. Owing both to the relatively large number of parameters needed to specify a precessing binary's orbit and to the seemingly-complicated evolution, Bayesian parameter estimation methods have only recently able to efficiently draw inferences about gravitational waves from precessing sources \cite{gw-astro-PE-systemframe}. These improvements mirror and draw upon a greater theoretical appreciation of the surprisingly simple dynamics and gravitational waves from precessing binaries, both in the post-Newtonian limit \cite{ACST,2012PhRvD..86h4017B,gwastro-mergers-nr-Alignment-ROS-PN,gwastro-SpinTaylorF2-2013,2013PhRvD..88l4015K} and strong field \cite{gwastro-mergers-nr-Alignment-ROS-Polarization,gwastro-mergers-nr-Alignment-ROS-CorotatingWaveforms,gwastro-mergers-nr-Alignment-BoyleHarald-2011,gwastro-mergers-nr-ComovingFrameExpansion-TransitionalHybrid-Schmidt2012,gwastro-mergers-nr-ComovingFrameExpansionSchmidt2010,gwastro-nr-imrphenomP}. For our purposes, these insights have suggested particularly well-adapted coordinates with which to express the dynamics and gravitational waves from precessing BH-NS binaries, enabling more efficient and easily understood calculations. In particular, these coordinates have been previously applied to estimate how well BH-NS parameters can be measured by ground-based detectors \cite{gwastro-mergers-HeeSuk-FisherMatrixWithAmplitudeCorrections}. In this work, we will present the first detailed parameter estimation calculations which fully benefit from these insights into precessing dynamics. In short, we will review the natural parameters to describe the gravitational wave signal; demonstrate how well they can be measured, for a handful of selected examples; and interpret our posteriors using simple, easily-generalized analytic and geometric arguments. As a concrete objective, following prior work \cite{gwastro-mergers-HeeSuk-FisherMatrixWithAmplitudeCorrections,gwastro-mergers-HeeSuk-CompareToPE-Aligned} we will explore whether higher harmonics break degeneracies and provide additional information about black hole-neutron star binaries. In the absence of precession, higher harmonics are known to break degeneracies and improve sky localization, particularly for LISA \cite{2006PhRvD..74l2001L,2009PhRvD..80f4027K,2011PhRvD..84b2002L}. That said, these and other studies also suggest that higher harmonics provide relatively little additional information about generic precessing binaries, over and above the leading-order quadrupole radiation \cite{gwastro-mergers-HeeSuk-FisherMatrixWithAmplitudeCorrections,2011PhRvD..84b2002L}. For example, for two fiducial nonprecessing and two fiducial precessing signals, \citet{gwastro-mergers-HeeSuk-FisherMatrixWithAmplitudeCorrections}, henceforth denoted \abbrvEFM{}, provide concrete predictions for how well detailed parameter estimation strategies should perform, for a specific waveform model. A previous work \cite{gwastro-mergers-HeeSuk-CompareToPE-Aligned}, henceforth denoted \abbrvAlignedPE{}, demonstrated these simple predictions accurately reproduced the results of detailed parameter estimation strategies. In this work, we report on detailed parameter estimation for the two fiducial precessing signals described in \abbrvEFM{}. As with nonprecessing binaries, we find higher harmonics seem to provide significant insight into geometric parameters, in this case the projection of the orbital angular momentum direction on the plane of the sky. As this orientation could conceivably correlate with properties of associated electromagnetic counterparts, higher harmonics may have a nontrivial role in the interpretation of coordinated electromagnetic and gravitational wave observations. This paper is organized as follows. In Section \ref{sec:Review} we describe the gravitational wave signal from precessing BH-NS binaries, emphasizing suitable coordinates for the spins (i.e., defined at $100\unit{Hz}$, relative to the total angular momentum direction) and the waveform (i.e., exploiting the corotating frame to decompose the signal into three timescales: orbit, precession, and inspiral). Our description of gravitational waves from precessing BH-NS binaries follows \citet{gw-astro-SpinAlignedLundgren-FragmentA-Theory}, henceforth denoted \abbrvBLO, and \cite{gwastro-SpinTaylorF2-2013}, henceforth denoted \abbrvLO. Next, in Section \ref{sec:Results} we describe how we created synthetic data consistent with the two fiducial precessing signals described in \abbrvEFM{} in gaussian noise; reconstructed a best estimate (``posterior distribution'') for the possible precessing source parameters consistent with that signal; and compared those predictions with semianalytic estimates. These semianalytic estimates generalize work by \abbrvEFM{}, approximating the full response of a multidetector network with a simpler but more easily understood expression. Using simple analytic arguments, we describe how to reproduce our full numerical and semianalytic results using a simple separation of scales and physics: orbital cycles, precession cycles, and geometry. The success of these arguments can be extrapolated to regimes well outside its limited scope, allowing simple predictions for the performance of precessing parameter estimation. We conclude in Section \ref{sec:Conclusions}. For the benefit of experts, in Appendix \ref{ap:RevisedEffectiveFisher} we discuss the numerical stability and separability of our effective Fisher matrix. | \label{sec:Conclusions} In this work we performed detailed parameter estimation for two selected BH-NS binaries, explained several features in terms of the binary's kinematics and geometry, and compared our results against analytic predictions using the methods of \cite{gwastro-mergers-HeeSuk-FisherMatrixWithAmplitudeCorrections,gwastro-mergers-HeeSuk-CompareToPE-Aligned}. First, despite adopting a relatively low-sensitivity initial-detector network for consistency with prior work, we find by example that parameter estimation of precessing binaries can draw astrophysically interesting conclusions. Since our study adopted relatively band-limited initial detector noise spectra, we expect advanced interferometers \cite{LIGO-Inspiral-Rates,2010CQGra..27h4006H} will perform at least as well (if not better) at fixed SNR. For our fiducial binaries, the mass parameters are constrained well enough to definitively say if it is a BH-NS binary (as opposed to BH-BH); the mass parameters are constrained better than similar non-precessing binaries; and several parameters related to the spin and orientation of the binary can be measured with reasonable accuracy. Second and more importantly, we were able to explain our results qualitatively and often quantitatively using far simpler, often analytic calculations. Building on prior work by \abbrvBLO, \abbrvLO, and others \cite{gwastro-mergers-nr-Alignment-ROS-Polarization}, we argued precession introduced distinctive amplitude, phase, and polarization modulations on a precession timescale, effectively providing another information channel independent from the usual inspiral-scale channel found in non-precessing binaries. Though our study targeted only two specific configurations, we anticipate many of our arguments explaining the measurement accuracy of various parameters can be extrapolated to other binary configurations and advanced detectors. The effective Fisher matrix approach of \abbrvEFM{} and \abbrvAlignedPE{} provides a computationally-efficient means to undertake such extrapolations. Third and finally, we demonstrated that for this mass range and orientation, higher harmonics have minimal local but significant global impact. For our systems, we found higher harmonics broke a degeneracy in the orientation of $\hat{L}$ at our reference frequency (100 Hz), but otherwise had negligible impact on the estimation of any other parameters. Due to the relatively limited calculations of spin effects in post-Newtonian theory, all inferences regarding black hole spin necessarily come with significant systematic limitations. For example, \citet{gwastro-mergers-pn-spinterms-Nitz2013} imply that poorly-constrained spin-dependent contributions to the orbital phase versus time could significantly impact parameter estimation of nonprecessing black hole-neutron star binaries. Fortunately, the leading-order precession equations and physics are relatively well-determined. For example, the amplitude of precession-induced modulations is set by the relative magnitude and misalignment of $\vec{L}$ and $\vec{S}_1$. In our opinion, the leading-order symmetry-breaking effects of precession are less likely to be susceptible to systematic error than high-order corrections to the orbital phase. Significantly more study would be needed to validate this hypothesis. Robust though these correlations may be, the quantities gravitational wave measurements naturally provide (chirp mass; precession rate; geometry) rarely correspond to astrophysical questions. We have demonstrated by example that measurements of relatively strong gravitational wave signals can distinguish individual component masses and spins to astrophysical interesting accuracy [Fig. \ref{fig:Results:Intrinsic}]. Given the accuracy and number of measurements gravitational waves will provide, compared to existing astrophysical experience \cite{PSconstraints3-MassDistributionMethods-NearbyUniverse,2010CQGra..27k4007M,2010ApJ...725.1918O,2012ApJ...757...55O,2013ApJ...778...66K}, these measurements should transform our understanding of the lives and deaths of massive stars. Ignoring correlations, gravitational wave measurements seem to only relatively weakly constrain spin-orbit misalignent [Fig. \ref{fig:Results:Intrinsic}], a proxy for several processes including supernova kicks and stellar dynamics. That said, gravitational wave measurements should strongly constrain the precession rate, a known expression of spins, masses, and spin-orbit misalignment. Formation models which make nontrivial predictions about both spin magnitude and misalignment might therefore be put to a strong test with gravitational wave measurements. | 14 | 3 | 1403.0544 |
1403 | 1403.7687_arXiv.txt | {Though \lyalp\ emission is one of the most used tracers of massive star formation at high redshift, it is strongly affected by neutral gas radiation transfer effects. A correct understanding of these effects is required to properly quantify the star formation rate along the history of the Universe.} {We aim to parameterize the escape of \lyalp\ photons as a function of the galaxy properties, in order to properly calibrate the \lyalp\ luminosity as a tracer of star formation intensity at any age of the Universe.} {We are embarked in a program to study the properties of the \lyalp\ emission (spectral profile, spatial distribution, relation to Balmer lines intensity,...) in a number of starburst galaxies in the Local Universe. The study is based on HST spectroscopic and imaging observations at various wavelengths, X-ray data and ground-based spectroscopy, complemented with the use of evolutionary population synthesis models.} {We present here the results obtained for one of those sources, IRAS~08339+6517, a strong \lyalp\ emitter in the Local Universe which is undergoing an intense episode of massive star formation. We have characterized the properties of the starburst, which transformed $1.4\times10^{8}$ \msun\ of gas into stars around $5-6$ Myr ago. The mechanical energy released by the central Super Stellar Cluster (SSC) located in the core of the starburst has created a cavity devoid of gas and dust around it, leaving a clean path through which the UV continuum of the SSC is observed, with almost no extinction. While the average extinction affecting the stellar continuum is significantly larger out of the cavity, with \ebv=0.15 in average, we have not found any evidence for regions with very large extinctions, which could be hiding some young, massive stars not contributing to the global UV continuum. The observed soft and hard X-ray emissions are consistent with this scenario, being originated by the interstellar medium heated by the release of mechanical energy in the first case, and by a large number of active High Mass X-ray Binaries (HMXBs) in the second. In addition to the central compact emission blob, we have identified a diffuse \lyalp\ emission component smoothly distributed over the whole central area of IRAS~08339+6517. This diffuse emission is spatially decoupled from the UV continuum, the \hal\ emission or the \hal/\hb\ ratio. Both locally and globally, the \lyalp/\hal\ ratio is lower than the Case B predictions, even after reddening correction, with an overall \lyalp\ escape fraction of only 4\%.} {We conclude that in IRAS~08339+6517 the \lyalp\ photons resonantly scattered by an outflowing shell of neutral gas are being smoothly redistributed over the whole central area of the galaxy. Their increased probabibility of being destroyed by dust would explain the low \lyalp\ escape fraction measured. In any case, in the regions where the diffuse \lyalp\ emission shows the largest \lyalp/\hal\ ratios, no additional sources of \lyalp\ emission are required, like ionization by hot plasma as proposed for Haro~2, another galaxy in our sample. These results stress again the importance of a proper correction of scattering and transfer effects when using \lyalp\ to derive the star formation rate in high-redshift galaxies.} | The \lyalp\ emission is one of the most useful tracers of massive star formation in the early Universe, since at high redshift it becomes visible in the optical-infrared range. Moreover, for redshifts above $z\sim4$ it becomes the only emission line easily acccesible from ground--based telescopes. But the study of \lyalp\ emission in starburst galaxies in the Local Universe has shown that radiation transfer through neutral hydrogen can completely distort its properties, affecting its profile and intensity, and even transforming the emission into a damped absorption when the column density of neutral gas is high enough \citep{MasHesse03}. In order to investigate further the properties of the \lyalp\ emission, and its correlation with other characteristics of the starbursts originating it, we are embarked in a program to study in detail \lyalp\ emitting galaxies in the Local Universe \citep{Ostlin09,Oti12,Hayes13a}. The final aim of this program is the proper calibration of \lyalp\ as a tracer of star formation, which could be used to derive the star formation intensity along the history of the Universe. In this work we present a detailed multiwavelength analysis of the \lyalp\ emitting galaxy IRAS~08339+6517, complementing previous partial results by \citet{MasHesse03} and \citet{Ostlin09}. IRAS~08339+6517 (hereinafter IRAS~0833) is a face-on spiral galaxy at $80.2$ Mpc, which is undergoing a starburst episode and shows a prominent \lyalp\ emission line. The brightest UV knots are aligned along an internal bar oriented close to the $N-S$ direction \citep{Ostlin09}. \citet{LopezSanchez06} derived an age of $4-6$ Myr for the most recent burst using \hal\ spectroscopic data. They also estimated that there exist two older underlying stellar populations with ages $100-200$ Myr and $1-2$ Gyr. \citet{Cannon04} reported from NRAO VLA data that IRAS~0833 harbours $1.1 \times 10^{9}$ \msun\ of neutral hydrogen. They also detected a tidal stream between IRAS~0833 and its minor companion 2MASX J08380769+6508579, estimating for the stream material a mass of $3.8 \times 10^{9}$ \msun. The \lyalp\ emission of IRAS~0833 was first reported by \citet{Kunth97} from the analysis of HST/GHRS high-resolution spectrum of its nuclear region. They found that the \lyalp\ line shows a P~Cyg profile, as well as the presence of a blueshifted secondary \lyalp\ emission component, on top of the spectral P~Cyg trough. From the same data, \citet{Kunth98} measured the flux of the line, as well as the column density of the neutral hydrogen which produces the observed P~Cyg absorption. Later, HST/STIS long-slit observations with high spectral resolution led \citet{MasHesse03} to confirm that \lyalp\ photons can actually escape from IRAS~0833 because most of the neutral gas surrounding the source is being pushed out by the starburst activity. The velocity shift causes that, whereas the blue photons of the line are actually resonantly scattered by H~I, the red wing eventually escapes, leading to the observed P~Cyg profile. They measured the velocity of expansion of the superbubble deriving $\sim$$300$ km s$^{-1}$. They argued that the secondary \lyalp\ emission could be produced at the leading front of the superbubble with no neutral hydrogen ahead, explaining why this minor component is detected blueshifted by $\sim$$300$ km s$^{-1}$ on top of the absorption trough caused by the outflowing medium. Table~\ref{irastable} summarizes the basic properties of the starburst galaxy IRAS~0833. In this work we have analyzed HST, XMM-Newton, IUE and ground-based observations aiming to characterize the properties of the starburst in IRAS~0833, and in order to check whether the conclusions from the study of Haro~2 (also known as Mrk~33 and IRAS~10293+5439) by \citet{Oti12} about the nature of the diffuse, extended \lyalp\ emission, could be extended to another \lyalp\ emitting starburst galaxy with very different morphology and global properties. We describe the observational data in Sect.~\ref{obsdatairas}, the results are presented in Sect.~\ref{resultsiras}, and they are discussed in Sect.~\ref{discussioniras}. Finally, conclusions are outlined in Sect.~\ref{conclusions}. \begin{table*} \caption[IRAS~0833 summary]{IRAS~0833 coordinates, redshift, distance, scale, Galactic H~I, color excess toward the source, and oxygen abundance.} \label{irastable} \centering \begin{tabular}{cccccccc} \hline\hline\\ \multicolumn{1}{c}{R. A.} & \multicolumn{1}{c}{Decl.} & Redshift$^{\mathrm{a}}$ & \multicolumn{1}{c}{Distance$^{\mathrm{a}}$} & \multicolumn{1}{c}{Scale$^{\mathrm{a}}$} & \multicolumn{1}{c}{$N($H\,I$)^{\mathrm{b}}_{\rm{Gal}}$} & \ebv$_{\rm{Gal}}$ & $12+\rm{log}(\rm{O}/\rm{H})^{\mathrm{c}}$ \\ (J2000.0) & (J2000.0) & & (Mpc) & (pc arcsec$^{-1}$) & (cm$^{-2}$) & & \\ \hline\\ $08$ $38$ $23.18$ & $+65$ $07$ $15.20$ & $0.0191$ & $80.2$ & $390$ & $4.5\times10^{20}$ & $0.094$ & $8.45$ \\ \hline \end{tabular} \begin{flushleft} $^{\mathrm{a}}$ From NED (the NASA/IPAC Extragalactic Database).\\ $^{\mathrm{b}}$ Average value from \citet{Dickey90} and \citet{Kalberla05}.\\ $^{\mathrm{c}}$ Value from \citet{LopezSanchez06}. \end{flushleft} \end{table*} | \label{conclusions} We have carried out a multiwavelength spectral and photometric analysis of the face-on, spiral, star-forming galaxy IRAS~0833. The properties of its starburst episode and associated X-ray emission have been defined, and the morphology of the \lyalp\ emission has been discussed, together with its relation to the UV continuum from the massive stars, the \hal\ line and the \hal/\hb\ ratio. \begin{itemize} \item The properties of the starburst in IRAS~0833 have been defined by comparison to evolutionary population synthesis models. We conclude that a single stellar population with an age $5.5$ Myr, a mass of $M \sim 1.4\times10^{8}$ \msun, and average stellar and nebular extinctions of \ebv=$0.15$ and \ebv=$0.06$, respectively, can account for the integrated UV, \hal\ and FIR photometry, as well as for the spectral profile of the photospheric Si~IV and C~IV lines. The integrated UV spectrum shows the $2175$ \AA\ feature, consistent with an LMC-like extinction law. \item An underlying stellar population, some hundreds of Myrs old, dominates the IR-optical continuum in IRAS~0833, as well as the observed Ca~II triplet and Mg$_{2}$ absorption lines. \item The nucleus of IRAS~0833 shows a massive cluster whose stellar continuum is barely attenuated (\ebv=$0.01$). We have estimated that it accounts for $20$\% of the observed integrated UV flux and $5$\% of the total mass of the starburst. The images of the nucleus show a very weak \hal\ emission co-spatial to the central cluster. In fact, the synthesis models overestimate by a factor $1.5$ the \hal\ luminosity emitted within a central circular region of {\em radius}~$=0.5\arcsec$ ($\sim$$200$ pc). We argue that the low \hal\ emission observed in this core region is due to the lack of nebular gas around the massive central cluster, which has cleaned its surroundings after pushing out the nearby gas, producing an expanding \hal-emitting shell. \item The X-ray image does not provide any spatial information on the morphology of the emission. The starburst episode can account for the thermal soft X-ray emission detected assuming an efficiency in the conversion of mechanical energy into X-rays of $\sim$$1-4$\%, within the typical range for starburst galaxies. The non-thermal component, which dominates the hard X-ray emission, is consistent with the number of active HMXBs expected for an evolved starburst with the properties derived for IRAS~0833. \item Two spectral \lyalp\ components are observed. The main \lyalp\ is detected along $16\arcsec$ ($\sim$$6$ kpc) and shows a P~Cyg profile originated by resonant scattering by neutral hydrogen outflowing at $\sim$$300$ km s$^{-1}$. The velocity structure extends all along the slit. The secondary emission is $\sim$$10$ times weaker, extends over $6\arcsec$ ($\sim$$2.3$ kpc) and is detected over the spectral trough caused by the outflowing neutral material. All this indicates that the starburst activity has accelerated the sourrounding neutral gas which no longer scatters the whole line, but only its bluest photons. In the leading front of the superbubble the gas seems to have undergone recombination, producing the secondary \lyalp\ emission, with probably scarce neutral material ahead, so that it is detected blueshifted by $\sim$$300$ km s$^{-1}$. \item \lyalp\ is observed in emission along $16\arcsec$ ($\sim$$6$ kpc), without regions of total \lyalp\ absorption. It does not show any spatial matching with the UV continuum, \hal\ line or Balmer decrement whatsoever. \lyalp\ photons escape mostly from two compact areas associated to, but not coincident with, the \hal-emitting shell, with a size of $1\arcsec$ ($\sim$$400$ pc, north) and $1.5\arcsec$ ($\sim$$600$ pc, south). In addition, there is a diffuse \lyalp\ component which extends northward $6\arcsec$ ($\sim$$2.3$ kpc). \item Similarly as found in other starburst galaxies, like Haro~2 \citep{Oti12}, the diffuse \lyalp\ emission shows the highest \lyalp/\hal\ ratios, as well as the highest values of the \lyalp\ escape fraction, \fesclya. The globally integrated \lyalp/\hal\ ratio is well below the Case B predictions (even after dereddening using the \ebvneb\ average value derived from the \hal/\hb\ ratio), indicating an enhanced destruction of \lyalp\ photons with respect to the extinction extrapolated from the Balmer lines. \item We conclude that the outflowing neutral gas in front of the IRAS~0833 starburst area is resonantly scattering most of the \lyalp\ photons, producing the observed P~Cyg profile. These scattered photons are smoothly redistributed over the whole central area until either they are destroyed by interaction with dust, or escape from an extended region. Multiple scattering enhances the probability of interaction with dust, explaining why the \lyalp/\hal\ ratio values are much lower than expected for Case B conditions and the average extinction. We do not find any evidence in IRAS~0833 of any other further source of \lyalp\ photons, like ionization by a hot plasma as proposed for Haro~2. If present, its contribution should be negligible when compared to the ionization by massive stars. \item The star formation rate in galaxies, e.g. high-redshift sources, may be severly underestimated when it is derived only from integrated fluxes of the \lyalp\ line without a proper correction of transfer effects in the interstellar medium. \end{itemize} | 14 | 3 | 1403.7687 |
1403 | 1403.0128_arXiv.txt | The crystalline color superconducting phase is believed to be the ground state of deconfined quark matter for sufficiently large values of the strange quark mass. This phase has the remarkable property of being more rigid than any known material. It can therefore sustain large shear stresses, supporting torsional oscillations of large amplitude. The torsional oscillations could lead to observable electromagnetic signals if strange stars have a crystalline color superconducting crust. Indeed, considering a simple model of strange star with a bare quark matter surface, it turns out that a positive charge is localized in a narrow shell about ten Fermi thick beneath the star surface. The electrons needed to neutralize the positive charge of quarks spill in the star exterior forming an electromagnetically bounded atmosphere hundreds of Fermi thick. When a torsional oscillation is excited, for example by a stellar glitch, the positive charge oscillates with typical kHz frequencies, for a crust thickness of about one-tenth of the stellar radius, to hundreds of Hz, for a crust thickness of about nine-tenths of the stellar radius. Higher frequencies, of the order of few GHz, can be reached if the star crust is of the order of few centimeters thick. We estimate the emitted power considering emission by an oscillating magnetic dipole, finding that it can be quite large, of the order of $10^{45}$ erg/s for a thin crust. The associated relaxation times are very uncertain, with values ranging between microseconds and minutes, depending on the crust thickness. The radiated photons will be in part absorbed by the electronic atmosphere, but a sizable fraction of them should be emitted by the star. | One of the routes for studying the properties of matter at very high densities is by the inspection of the properties of compact stellar objects (CSOs). These are stars having a mass of $1-2 M_\odot$ and a radius of about $10$ km, typically observed as pulsars. Baryonic matter inside a CSO is squeezed at densities about a factor $3$-$5$ larger than in heavy nuclei. From a simple geometrical reasoning one can argue that in these conditions baryons are likely to lose their identity~\cite{Weber-book} and a new form of matter should be realized. One possibility is that the extremely high densities and low temperatures may favor the transition from nuclear matter to deconfined quark matter in the core of the CSO~\cite{Ivanenko1965, Ivanenko:1969gs, Collins, Baym:1976yu}. In this case compact (hybrid) stars featuring quark cores and a crust of standard nuclear matter would exist. A second possibility is that strange matter is the ground state of the hadrons~\cite{Witten:1984rs}. In this case at high densities there should exist the possibility of converting nuclear matter to deconfined matter. The resulting CSO would be a strange star~\cite{Alcock:1986hz, Haensel:1986qb}, {\it i.e} a CSO completely constituted of deconfined matter, see~\cite{Madsen:1998uh} for a review. Unfortunately these two possibilities cannot be checked by first principle calculations. Indeed at the densities relevant for CSOs, quantum chromodynamics (QCD) is nonperturbative, because the typical energy scale is about $\Lambda_\text{QCD}$. Moreover, lattice QCD simulations at large baryonic densities are unfeasible because of the so-called sign problem~\cite{Barbour:1986jf}, see~\cite{Aarts:2013naa} for a recent review and~\cite{Yamamoto:2014lia} for a study of an inhomogeneous phase. Although not firmly established by first principles, it is reasonable to expect that if deconfined quark matter is present, it should be in a color superconducting (CSC) phase~\cite{Rajagopal:2000wf, Alford:2007xm, Anglani:2013gfu}. The reason is that the critical temperature of color superconductors is large, $T_{c} \simeq 0.57 \Delta$, where $\Delta\sim 5 -100$ MeV is the gap parameter. For the greatest part of the CSO lifetime, the temperature is much lower than this critical temperature and the CSC phase is thermodynamically favored. It is widely accepted that at asymptotic densities, when the up, down and strange quarks can be treated as massless, the color-flavor locked (CFL) phase~\cite{Alford:1998mk} is the ground state of matter. This phase is energetically favored because quarks of all flavors and of all colors form standard Cooper pairs, thus maximizing the free energy gain. However, considering realistic conditions realizable within CSOs a different CSC phase could be realized. The reason is that the nonzero and possibly large value of the strange quark mass, $M_s$, combined with the requirement of beta equilibrium, electromagnetic and color neutrality, tends to pull apart the Fermi spheres of quarks with different flavors~\cite{Alford:2002kj}. The mismatch between the Fermi spheres is proportional to $M_s^2/\mu$, where \be\label{eq:muaverage} \mu = \frac{\mu_u+\mu_d+\mu_s}3\,, \ee is the average quark chemical potential. The free energy price of having simultaneous pairing of three-flavor quark matter increases with increasing values of $M_s^2/\mu$. Since the free energy gain is proportional to the CFL gap parameter, $\Delta_{\text{CFL}}$, if $M_s^2/\mu > c \Delta_{\text{CFL}}$, with $c$ a number of order $1$~\cite{Alford:2003fq}, a different and less symmetric CSC phase should be favored. One possibility is that the crystalline color superconducting (CCSC) phase is realized~\cite{Alford:2000ze, Rajagopal:2006ig,Anglani:2013gfu, Mannarelli:2014jsa}. In this phase quarks form Cooper pairs with nonzero total momentum, and there is no free energy cost proportional to $M_s^2/\mu$. The only free energy cost is due to the formation of counterpropagating currents; see for example the qualitative discussion in~\cite{Mannarelli:2014jsa}. Actually, with increasing values of $M_s^2/\mu$ various inhomogeneous CSC phases can be realized, because the system has many degrees of freedom~\cite{Anglani:2013gfu}. The CCSC phase should be favored for certain values of the chemical potential mismatch. In reality, the CCSC phase is not one single phase but a collection of phases, characterized by their crystalline arrangements, which are favored for different values of $M_s^2/\mu$. The Ginzburg-Landau (GL) analysis of~\cite{Rajagopal:2006ig} has shown that in three-flavor quark matter there are two good candidate structures that are energetically favored for \be 2.9 \Delta_{\text{CFL}} \lesssim \frac{M_s^2}{\mu} \lesssim 10.4 \Delta_{\text{CFL}}\,. \ee This range of values is certainly model dependent, moreover the GL expansion is under poor quantitative control~\cite{Anglani:2013gfu}. For this reason we shall consider strange star models in which both the CFL phase and the CCSC phase are realized. Since the CFL phase is expected to be favored at high densities, we shall assume that it is realized in the core of the CSO. The CCSC phase is favored at smaller densities and constitutes the crust of the CSO. The radius, $R_{\it c}$, at which the CFL core turns into the CCSC crust will be used as a free parameter. We shall restrict our analysis to bare strange stars~\cite{Alcock:1986hz}, meaning that we shall assume that on the top of the strange star surface there is no other layer of baryonic matter. Our model of strange star resembles the typical onion structure of a standard neutron star with a solid crust and a superfluid core. It is similar to the model discussed in~\cite{Rupak:2012wk} for studying $r-$mode oscillations. In that work the core radius was determined using a microscopic approach; instead we treat $R_{\it c}$ as a free parameter. One quantitative difference between our model and standard neutron star models, is that the CCSC phase is extremely rigid, much more rigid than the ironlike crust. The shear modulus of the energetically favored phase can be obtained studying the low energy oscillations of the condensate modulation~\cite{Casalbuoni:2001gt,Casalbuoni:2002pa,Casalbuoni:2002my,Mannarelli:2007bs}. In particular, the low energy expansion of the GL Lagrangian of~\cite{Mannarelli:2007bs} leads to a shear modulus \be\label{eq:nu} \nu \simeq \nu_0\left(\frac{\Delta}{10 \text{ MeV}}\right)^2\left(\frac{\mu}{400 \text{ MeV}}\right)^2\,, \ee where \be \label{eq:nu0} \nu_0= 2.47 \frac{\text{MeV}}{\text{fm}^3}\,, \ee will be our reference value. The reader is warned that the actual value of the shear modulus might differ from $\nu_0$ by a large amount because of the various approximations used in~\cite{Mannarelli:2007bs}. The value of $\Delta$ is also uncertain, with reasonable values ranging between $5$ MeV and $25$ MeV, see the discussions in~\cite{Mannarelli:2007bs,Anglani:2013gfu}. Regarding the quark chemical potential, we shall consider the values obtained in the construction of hydrodynamically stable strange stars. The shear modulus of different crystalline structures is proportional to $\nu$, with corrections of the order unity. Since in our treatment we shall only exploit the rigidness of the CCSC phase giving the order of magnitude estimates for the various computed quantities, the actual crystalline pattern is irrelevant for our purposes. Taking into account the uncertainty in the gap parameter and in the quark chemical potential, it can be estimated that the value of $\nu$ is larger than in conventional neutron star crust (see for example~\cite{Strohmayer}), by at least a factor of $20-1000$~\cite{Mannarelli:2007bs}. This large value of the shear modulus is due to the fact that the typical energy density associated with the oscillations of the condensate modulation is $\mu^2 \Delta^2$, where $\Delta$ is determined by the strong interaction in the antitriplet channel. Instead, in conventional neutron star the associated energy is at the electromagnetic scale. Given the large shear modulus, one immediate consequence is that CCSC matter can sustain large deformations. In Refs.~\cite{Lin:2007rz, Haskell:2007sh, Lin:2013nza, Knippel:2009st, Rupak:2012wk} it has been studied the emission of gravitational waves by various mechanisms that induce a quadrupole deformation of the CCSC structure. See also~\cite{Andersson:2001ev} for a discussion of a different mechanism of gravitational wave emission from strange stars. In the present paper we shall instead consider the electromagnetic (EM) emission by strange stars with a CCSC crust. Since the strange star surface confines baryonic matter but allows the leakage of electrons, it follows that at the star surface there is a charge separation at the hundreds of Fermi scale~\cite{Alcock:1986hz}. Because of the large shear modulus, our model of bare strange star can sustain large and fast torsional oscillations, leading to a periodic displacement of the surface charge. We shall see that the frequencies of torsional oscillations are of the order of MHz if the crust is hundreds of meters thick. Lower frequencies are reached if the crust is a few kilometers thick; GHz frequencies are reached if the crust is few centimeters thick. The amplitude of the oscillations at the star surface is in any case of the order of centimeters, leading to an enormous emitted radiation, of the order of $10^{41}$ erg/s, steeply increasing for thin crusts. Thus the oscillation energy should be radiated away very efficiently, on time scales of milliseconds or even microseconds for a thin crust and of the order of hundreds of seconds for a thick crust. More in detail, we shall determine the frequency, the amplitude, the damping times and the emitted power as a function of the various parameters that characterize the strange star. This paper is organized as follows. In Sec.~\ref{sec:equilibrium} we discuss spherically symmetric strange stars in hydrodynamical equilibrium. In Sec.~\ref{sec:charge} we determine the charge distribution close to the surface of the strange star. In Sec.~\ref{sec:nonradial} we study the torsional oscillations of the strange star, estimating the frequencies, the emitted power and the decay time as a function of the various parameters of the model. We draw our conclusions and a possible connection with astronomical observations in Sec.~\ref{sec:conclusions}. | \label{sec:conclusions} We have discussed two very simple strange star models entirely composed of deconfined color superconducting matter. Our star models are very similar to those proposed in~\cite{Rupak:2012wk} for the discussion of $r-$mode oscillations. We assume that the star core is composed by CFL matter and there is a crust of rigid CCSC quark matter. The size of the star crust is unknown, because it depends on the detailed values of the strange quark mass and of the gap parameters, which are very uncertain. For this reason we have treated the ratio between the core radius and the star radius as a free parameter. In our treatment of the crust we have determined the equilibrium charge configuration, in Sec.~\ref{sec:charge}, using the free Fermi gas distributions but at the same time we have considered CCSC matter, in Sec.~\ref{sec:nonradial}, as a rigid crystalline structure. These two facts may seem to be in contradiction. However, in the relevant crystalline phases, quarks close to the Fermi sphere have a linear dispersion law~\cite{Casalbuoni:2003sa, Anglani:2013gfu}, which indeed mimics the behavior of free quarks. The effect of the condensate is to induce a direction dependent Fermi velocity. Moreover, not all quarks on the top of the Fermi sphere are paired. For these reasons we have assumed that the EM properties of the CCSC phase are similar to those of unpaired quark matter. What is rigid is the modulation of the underlying quark condensate that can be seen as the structure on the top of which quarks propagate. This treatment of the EM properties of the CCSC phase is in our opinion an educated assumption. A detailed study of the EM properties of the CCSC phase is necessary to substantiate this approach. The discussion of the quark matter surface can certainly be improved including condensation effects, following for example the discussion in~\cite{Alford:2001zr}, or viscous damping below the star crust as in~\cite{Lindblom:2000gu}. Moreover it would be interesting to study whether strangelet crystals could form on the star surface~\cite{Jaikumar:2005ne}. One should investigate whether these strangelet nuggets might coexist with the CCSC phase, presumably assuming that the surface tension of quark matter is not too large, eventually leading to a drastic reduction of the surface charge density. In our simple treatment, we estimate the emitted energy of the torsional oscillations using an oscillating magnetic dipole. The emitted power is extremely large, for stars with a small CFL core it is of the order of $10^{41} \eta$ erg/s, where $\eta$ is a screening factor due to the presence of the electrosphere, estimated in Eq.~\eqref{eq:etaeff}. The emitted power steeply increases with increasing values of $a$, see Fig.~\ref{fig:radiated power}, meaning that stars with a large CFL core and a thin CCSC crust would probably emit all the oscillation energy in milliseconds. For a sufficiently thin crust, say hundreds of meters thick, we expect that the emission is at the MHz frequency. Given the large emitted power, it is tempting to compare our results with the most powerful observed EM emissions. The radio bursts observed from Rotating Radio Transients have a duration of few milliseconds and the associated flux energy is extremely large~\cite{McLaughlin:2005eq}. However, the observed frequencies are of the order of GHz, see~\cite{Lorimer:2007qn, Thornton:2013iua, 2013Sci...341...40C}, whereas we found that the frequencies associated with the $n=1, l=1$ mode of a star with a $1$ km CCSC crust are of the order of tens of kHz. If the crust is thinner, say a few centimeters thick, then GHz frequencies can be attained, but in this case the emitted power, estimated by Eq.~\eqref{eq:Pa}, is extremely large and the damping time should be much less than the observed milliseconds. A loophole might be that by Eq.~\eqref{eq:Pa} we are overestimating the emitted power by orders of magnitude. The reason is that in Eq.~\eqref{eq:Pa} we are using the coherent emission approximation, which conceivably breaks down at such large frequencies. Moreover, we are assuming the presence of a net positive charge, with electrons only providing a screen for the emitted power. A more refined treatment should include the effect of the star magnetic field which might strongly couple the oscillation of the star and of the electrosphere. Therefore, future work in this direction is needed to clarify how the presented discussion of the emitted EM power changes in the presence of strong magnetic fields, see for example \cite{Glampedakis:2006apa, Levin:2006qd}. A different possibility is that there exists a mechanism for exciting predominantly modes with higher angular momentum and/or higher principal quantum numbers. In this case, frequencies larger than tens of kHz could be reached for stars with a thick crust, as well. Different powerful phenomena of great interest are giant magnetar x-rays flares~\cite{Strohmayer:2005ks}. The observation of these flares has posed a challenge to strange stars with no crust~\cite{Watts:2006hk}. The standard explanation of these flares is indeed related with the seismic vibrations of the crust triggered by a starquake. Typical frequencies are of the order of hundreds of Hz at most and the emitted luminosities is of the order of $10^{44} - 10^{46}$ erg/s. The measured decaying time is of order of minutes. In our model, oscillations of hundreds of Hz can be reached only if the shear modulus is sufficiently small, of the order of $\nu_0 10^{-4}$, making it comparable with standard nuclear crusts, and if the CCSC crust is sufficiently thick, say of the order of a few kilometers, meaning that $a \sim 0.1$. For these small values of $a$ the damping time can be of the order of hundreds of seconds, see the last column in Table~\ref{table:damping}. Basically, our bare strange star model has frequency and decay times compatible with magnetar flares only if it has the same structure of a standard neutron star. The caveat is that these flares are observed in magnetars, which are CSOs expected to have a large magnetic field. In our simple treatment we have neglected the effect of the background magnetic field, which however in the case of magnetars could be sizable. We have neglected the effect of the temperature, as well. Although temperature effects are negligible for strange stars older than $\sim10$ s \cite{Page:2002bj}, when the temperature has dropped below the MeV scale, it would be interesting to see what is the effect of a large, say $\sim 10$ MeV temperature, see for example the discussion in \cite{Cheng:2003hv, Usov:2004kj}. Unfortunately, the shear modulus has only been computed at vanishing temperature~\cite{Mannarelli:2007bs}. A detailed study of the temperature dependence of the shear modulus and of the response of the CCSC structure to the temperature is needed to ascertain the correct temperature dependence of the torsional oscillations. However, let us assume that the CCSC structure has already formed when the temperature is of the order of few MeV, and that it responds to the temperature as a standard material, meaning that with increasing temperature the shear modulus decreases. From Eq.~\eqref{eq:w1} it follows that the frequency of the torsional oscillation decreases, and, from Eq.~\eqref{eq:W11}, that the amplitude increases. Moreover, an increasing temperature should lead to an increase of the number densities of the light quarks and electrons, leading to a larger $Q_+$. The overall effect on the radiated power is not obvious, because in Eq.~\eqref{eq:P} we have that $\omega_{11}$ decreases, but $W_{11}$ and $Q_+$ increase; therefore a careful study of the various contributions is necessary. Regarding the emission mechanisms of the electrosphere, one should consider the various processes that become relevant at nonvanishing temperature. In particular, $e^+e^-$ production is believed to be the dominant process at high temperature~\cite{Usov:1997ff, Usov:2001sw, Aksenov:2003kh, Aksenov:2003vy}. Finally, note that in the evaluation of the horizontal displacement one should include the radial dependence of the shear modulus and of the matter densities as well as GR corrections, which are expected to be small, but should nevertheless be considered for a more refined study. | 14 | 3 | 1403.0128 |
1403 | 1403.5011_arXiv.txt | Here we report observations of the two lowest inversion transitions of ammonia (\ammonia) with the 70-m Tidbinbilla radio telescope. The aim of the observations is to determine the kinetic temperatures in the dense clumps of the G333 giant molecular cloud associated with RCW~106 (hereafter known as the G333 GMC) and to examine the effect that accurate measures of temperature have on the calculation of derived quantities such as mass. This project is part of a larger investigation to understand the timescales and evolutionary sequence associated with high-mass star formation, particularly its earliest stages. Assuming that the initial chemical composition of a giant molecular cloud is uniform, any abundance variations within will be due to evolutionary state. We have identified 63 clumps using SIMBA 1.2-mm dust continuum maps and have calculated gas temperatures for most (78 per cent) of these dense clumps. After using \textit{Spitzer} GLIMPSE 8.0\,\um\ emission to separate the sample into IR-bright and IR-faint clumps, we use statistical tests to examine whether our classification shows different populations in terms of mass and temperature. We find that in terms of log clump mass (2.44~--~4.12\,\msun) and log column density (15.3~--~16.6 cm$^{-2}$), that there is no significant population difference between IR-bright and IR-faint clumps, and that kinetic temperature is the best parameter to distinguish between the gravitationally bound state of each clump. The kinetic temperature was the only parameter found to have a significantly low probability of being drawn from the same population. This suggests that clump radii does not have a large effect on the temperature of a clump, so clumps of similar radii may have different internal heating mechanisms. We also find that while the IR-bright clumps have a higher median log virial mass than the IR-faint clumps (IR-bright:~2.88\,\msun; IR-faint:~2.73\,\msun), both samples have a similar range for both virial mass and FWHM (IR-bright:~log virial mass~=~2.03~--~3.68\,\msun, FWHM~=~1.17~--~4.50\,\kms; IR-faint:~log virial~mass~=~2.09~--~3.35\,\msun, FWHM~=~1.05~--~4.41\,\kms). There are 87~per~cent (40~of~46) of the clumps with masses larger than the virial mass, suggesting that they will form stars or are already undergoing star formation. | \begin{figure*} \centering \includegraphics[trim=20 60 85 97,clip,width=0.99\textwidth]{FIGURES/Fig1} \caption{\label{fig:overview} The G333 giant molecular cloud as seen in the infrared. The shocked gas (\textit{Spitzer} 4.5\,\um), PAH$^+$ emission (\textit{Spitzer} 8.0\,\um) and cool dust (\textit{Herschel} 160\,\um) are shown in blue, green and red, respectively. The contours are from the SIMBA 1.2\,mm dust continuum emission at 0.1, 0.2, 0.5, 1, 1.5, 2.5, 5, 10 and 12\,Jy/beam (as per the contours of fig. 4 of \citealt{Mookerjea2004}). The position of the peak emission within SIMBA dust clumps identified with {\sc clumpfind} are overlaid with pink plus signs. The positions associated with RCW~106 have been overlaid with white stars \citep{Rodgers1960}.} \end{figure*} The life cycles of high-mass ($\ge$8\,\msun) stars have a major impact on the evolution of galaxies, while in turn, the position of a molecular cloud in the Galaxy has a major impact on the efficiency and type of star formation which occurs therein \citep{Luna2006}. However, exactly how these stars form, on what timescales and how they shape their environments during this active and energetic phase is poorly understood (see the review by \citealt{Zinnecker2007}). The G333 giant molecular cloud (GMC), centred at~$l$~=~333.$^{\circ}$2, $b$~=~-0.$^{\circ}$4, is a 1.2\degr\ $\times$ 0.6\degr\ region of the southern Galactic Plane located at a distance of 3.6 kpc \citep{Lockman1979} and is the fourth most active star forming region in the Galaxy \citep{Urquhart2014}. The complex forms part of the Galactic Ring of molecular clouds at a Galactocentric radius of 3-5 kpc, it contains the bright \HII~regions RCW~106 (G332.9-0.6; Rodgers, Campbell \& Whiteoak 1960) and G333.6-0.2 \citep{Manchester1969}, as well as high-mass star forming clumps, MSX infrared sources and \textit{Spitzer} ``Extended Green Objects'' \citep{Cyganowski2008}. This cloud also contains the very young, high-mass star forming core G333.125$-$0.567 \citep{Becklin1973,Garay2004,Lo2007,Lo2011} which is an isolated core at an evolutionary stage without any radio continuum or near-infrared detection. We have used the Mopra radio telescope to study the G333~GMC extensively in 20 molecular tracers including $^{13}$CO \citep{Bains2006}, C$^{18}$O \citep{Wong2008}, HCN, HCO$^+$, and N$_2$H$^+$ \citep{Lo2009}. In order to investigate a large sample of star forming clumps at different stages of evolution, we are conducting a multi-wavelength study of the G333~GMC. This region is within the area of the \textit{Spitzer} GLIMPSE (3.6, 4.5, 5.8, 8.0\,\um; \citealt{Benjamin2003,Churchwell2009}) and MIPSGAL (24, 70\,\um; \citealt{Carey2009}), and the \textit{Herschel} Hi-GAL (70, 160, 250, 350, 500\,\um; \citealt{Molinari2010}) surveys. \citet{Mookerjea2004} have defined multiple millimetre continuum clumps within this one molecular cloud, some associated with maser emission (e.g. \citealt{Breen2007}), as well as obvious polycyclic aromatic hydrocarbon (PAH) emission. We expect to have a range of evolutionary states within our clumps. The ammonia (\ammonia) molecule can be used to probe the physical conditions within dense molecular gas. It has a large number of transitions that are sensitive to a variety of excitation conditions and can be detectable in both warm molecular gas and quiescent dark clouds. The rotational temperature and optical depth for each clump can be calculated from multiple (\Jm,\Km) inversion transitions and their hyperfine components, respectively \citep{Ungerechts1983}. Hence the kinetic temperature can be calculated \citep{Tafalla2004}; however the lower \one\ and \two\ transitions are only useful for constraining temperatures lower than 30\,K \citep{Danby1988,Hill2010}. In this paper we report on the selection of dense clumps based on SIMBA dust emission and pointed \ammonia~\one\ and \two\ observations towards these clumps. Although finding the kinetic temperature is our main concern there are also several other physical parameters that can be determined from our measurements, including virial mass and column density. This is so we will have a sample of clumps within the G333~GMC, with clear selection criteria which will be used to compare the 3-mm molecular transitions and infrared \textit{Herschel} and \textit{Spitzer} dust surveys. We have chosen to study a single molecular cloud as the initial chemical composition of each clump should be very similar. Obtaining a reliable temperature measurement of each clump will allow us, in future papers, to calculate accurate molecular abundances for comparison between clumps. | \label{sect:conclusion} In this paper we have presented data from the two lowest inversion transitions of \ammonia\ in the G333 giant molecular cloud with the 70-m Tidbinbilla radio telescope. Our main conclusions are as follows: (1) There were 63 SIMBA 1.2-mm dust clumps identified with {\sc clumpfind} and pointed \ammonia\ observations were conducted towards the peak of each clump. The peak of each clump was offset from the clump centroid by between 1.6 and 39.5 arcsec. (2) A variety of environments were identified within the G333~GMC and the sample was separated into 30 IR-bright and 33 IR-faint clumps. One clump from each category was identified via \ammonia~\two\ emission, to not be associated with the \vlsr\ of the G333~GMC, and one clump was identified to have an inaccurate \Tkin; resulting in 29 IR-bright and 31 IR-faint clumps. The \ammonia~\one\ and \two\ were fitted for 20 IR-bright and 26 IR-faint clumps, with mean \Tkin\ values of 24.2\,K and 19.3\,K, respectively. (3) We found that the clumps appeared to cluster into three regions. The IR-bright clumps were found predominately towards the centre of each region, especially for Regions B and C. This may indicate sequentially triggered star formation in the vicinity around IR-faint clumps. (4) Using \ammonia~\one\ and \two, the clump masses were found to be between 278 and 13036 \msun. The dust temperature is often assumed: 20\,K for isolated clumps and 40\,K for \HII~regions; however this assumption can significantly shift the masses of the clumps (e.g. for 20\,K the masses of our clumps were 251--23723\,\msun, and for 40\,K the masses of our clumps were 105--9951\,\msun) and can affect whether the clump is determined to be bound and will collapse onto itself, or if it is unbound and remains a starless core. Hence accurate measurements of kinetic temperatures are needed for studies of the gravitationally bound state of clumps. (5) The largest clumps are also the most unstable. We find that the clumps with signs of star formation are predominately associated with the least stable clumps. This may be due to feedback from an internal heating source. We found that 70~per~cent of the clumps had masses larger than the virial mass (187--6848\,\msun), suggesting that they will form stars or are already undergoing star formation. (6) A K-S test showed that the \Tkin\ for IR-bright and IR-faint clumps have a much smaller probability of being drawn from the same population. A tentative difference between the two populations in terms of FWHM could indicate a contribution due to feedback. No difference was seen for the other physical parameters. We conclude that IR-bright and IR-faint clumps can have the same masses but that the warmer regions are more evolved. This is the fourth paper in a series of papers utilising molecular line observations of the G333 giant molecular cloud associated with RCW~106 (G333~GMC). In this paper we reported on the selection of dense clumps based on SIMBA dust emission and pointed \ammonia~\one\ and \two\ observations towards these clumps. Future papers in the series will analyse the individual clumps and combine the information presented in this paper with the molecular 3-mm tracers presented in \citet{Bains2006}, \citet{Wong2008} and \citet{Lo2009}, and dust from the \textit{Spitzer} Space Telescope and the \textit{Herschel} Space Observatory. | 14 | 3 | 1403.5011 |
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