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1808 | 1808.01325_arXiv.txt | Constant-roll inflation was recently introduced by Motohashi, Starobinsky and Yokoyama as a phenomenological way to parametrize deviations from the slow-roll scenarios. In this paper, we investigate the dynamics of both the background and the perturbations in this model, without making any slow-roll assumptions. The perturbation spectra are computed with an efficient and accurate novel method that allowed us to quickly scan the parameter space of constant-roll inflation. We derive the constraints on the model parameters from the cosmic microwave background anisotropy measurements provided by the joint analysis of the Planck Collaboration and the BICEP2/Keck Array data. | \label{sec:Introduction} The inflationary paradigm has been one of the most successful developments since its very first appearance in \citep{Starobinsky:1980te, Sato:1981, PhysRevD.23.347, Linde:1982, Albrecht:1982}, as its characteristic accelerated expansion solves most of the caveats of standard big bang cosmology. In its most common form, inflation is driven by a scalar degree of freedom rolling slowly down a not very steep potential. Quantum fluctuations of the inflaton source the primordial inhomogeneities from which the actual large scale structure of the Universe emerges. Throughout the years, a multitude of inflationary models were proposed where the dynamics of the background field is highly overdamped, and the production of scalar and tensor fluctuations can be completely characterized by the so-called slow-roll parameters. Slow roll by itself is not a necessary condition for an inflationary model to be viable, and it is interesting to also explore models which break away from the slow-roll restrictions. Motohashi \textit{et.\ al.}\ recently introduced a constant-roll inflation \citep{Motohashi:2014ppa,Motohashi:2017aob} which replaces the usual slow-roll condition with an ansatz that the field rolls at a constant rate, be it slow or not. The model is rather neat as it characterizes the deviation from a slow roll by a single parameter and allows analytic integration of the expansion history and the full scalar field potential reconstruction. The potential driving constant-roll inflation only differs from the one in natural inflation \citep{PhysRevLett.65.3233} by the addition of a negative cosmological constant (with specially chosen value). The constant-roll rate can be tuned by the period of the potential, which corresponds to the global symmetry breaking scale in natural inflation. In this paper, we derive constraints on constant-roll inflation from the cosmic microwave background (CMB) anisotropies data \citep{Adam:2015rua, Ade:2015xua, Ade:2015lrj, Ade:2015tva}. In previous efforts \citep{Motohashi:2017aob}, the confrontation of this model with observational data used the well-known consistency relations between slow-roll and fluctuation spectra parameters \citep{Liddle:1994dx, Gong:2001he}, which assumes that using the exact background solutions, one can describe certain features of the perturbations spectra by using slow-roll approximation while this holds accurately in the parameter range to be explored. Even though this assumption is not inconsistent with the data, we find that there are small but noticeable differences if one computes the fluctuation spectra exactly. In our approach we do not impose any slow-roll assumptions and instead just directly evaluate the scalar and tensor power spectra of primordial fluctuations in a sufficiently large sector of the parameter space by numerical integration. This procedure allows us to evaluate deviations from the standard slow-roll approximation of the spectral index $n_s$ and the tensor-to-scalar ratio $r$. Achieving this with adequate parameter sampling and high precision throughout the mode evolution can be computationally expensive. We use a single-field version of our general method \citep{Ghersi:2016gee} which separates the fast and slow scales in the mode evolution to exponentially increase efficiency of sub-horizon integration. Our computational method allows us to scan a significant portion of the parameter space quickly and extremely accurately on a personal computer with minimal specifications. Constant-roll inflation has an uncertainty on the field value where inflation ends, as the potential needs to be cut at some value $\phi_0$ to get an exit from inflation. This introduces a third parameter to the model in addition to the mass scale and the roll rate, which fortunately turns out to be entirely degenerate as far as fluctuation spectra are concerned. This allows us to set tight constraints on two combinations of the model parameters for constant-roll inflation: one that determines the amplitude of scalar and tensor perturbations (along with the characteristic energy scale where inflation occurs), and the second one which sets the roll rate (and quantifies the deviations from the slow-roll approximation). We also compare constant-roll inflation with other models via estimation of the allowed region on the $r$ versus $n_s$ diagram, where each point can be identified with (at least) one choice of the model parameters after the spectrum is evaluated at the pivot scale. \begin{figure*} \centering \subfigure{ \includegraphics[width=.45\textwidth]{figures/Potential.pdf}} \, \subfigure{ \includegraphics[width=.5\textwidth]{figures/CR_inflatingmap.pdf}} \caption{\label{fig:background} Left panel: constant-roll inflation potential \eqref{eq:CR_potential} for the model parameters $M^2=2.0\times10^{-9}M_{\mathrm{Pl}}^2$ and different values of $\beta$. The region of interest is in the range $\phi\in (0;\phi_0]$, shown for the specific value of $\beta=0.02$. Right panel: Map of initial conditions in the phase space for $M^2=2.0\times10^{-9}M_{\mathrm{Pl}}^2$, $N_*=55$ and $\beta=0.02$. The color map represents the number of e-folds before reaching $\pm\phi_0$. Phase space trajectories converge as a power law towards the attractor (instead of exponentially, as is usually the case in slow-roll inflation) as in the case of power law inflation, which is a particular scenario of the constant-roll model. } \end{figure*} The layout of this paper is as follows: In section \ref{sec:Model_Background}, we present the model and scan a representative subset of the background phase space in order to determine the expansion history due to each choice of initial conditions. Our exploration of the phase space also includes the attractor formed by converging field trajectories. We describe the dynamics of the scalar and tensor fluctuations in section \ref{sec:Perturbations}, where we discuss the separation technique of scalar and tensor modes into fast and slow components, a mode injection scheme to calculate the spectra numerically, and compute the representative spectra given a set of arbitrary model parameters. We show that both the scalar and tensor spectra are featureless, and, as a consistency check, we also explicitly show that none of the modes evolve on super-horizon scales. In section \ref{sec:Observational_Constraints}, we use the joint likelihood data from Planck 2015 \citep{Adam:2015rua, Ade:2015xua, Ade:2015lrj} and BICEP2/Keck Array \cite{Ade:2015tva} to constrain the constant-roll inflation model parameters\footnote{We are profoundly aware of the Planck 2018 release \cite{Akrami:2018vks, Aghanim:2018eyx, Akrami:2018odb}, however the joint likelihood with BICEP/Keck is not available yet at the time of this writing.}. Finally, in section \ref{sec:Discussions}, we discuss the results and conclude. | \label{sec:Discussions} In this paper, we provide constraints of the model parameters in constant-roll inflation, as proposed in \citep{Motohashi:2017aob,Motohashi:2014ppa}. These are not the only efforts regarding models with similar features, for instance see \citep{Tzirakis:2007bf, PhysRevD.52.5486, Anguelova:2017djf, Cai:2017bxr, Yi:2017mxs, Nojiri:2017qvx, Motohashi:2017vdc, Karam:2017rpw, Morse:2018kda} for further examples. Our numerical procedure is optimized for an efficient evaluation of the scalar and tensor power spectra of primordial fluctuations, and can scan more than 8000 different choices of model parameters in a reasonable time on minimal computing hardware. It does not require assuming the slow-roll approximation as it is based on the direct computation of the cosmological parameters ($n_s,r,A_s,n_T$) from the featureless power spectra shown in Fig.~\ref{fig:power_spectra}. The code passes numerous accuracy tests and long-time integration of the mode evolution confirms that there is no spurious evolution on super-horizon scales. In order to provide tight constraints of the model parameters, we needed to address the degeneracy between $M$ and $N_*$. We found $M_{\star}$ defined in \eqref{eq:new_parameter} to be a good auxiliary parameter that leaves the spectra almost invariant under different choices of $N_*$ for any fixed value of $M_{\star}$. After using the CMB measurements from the Planck Collaboration \citep{Adam:2015rua, Ade:2015xua, Ade:2015lrj} and their joint likelihood with the BICEP2/Keck Array \citep{Ade:2015tva}, we estimated $\log_{10} \beta =-1.77^{+0.17}_{-0.35}$ and $\log_{10} (M_{\star}/M_{\rm {Pl}})^2 = -9.98_{-0.6}^{+0.7}$ at 95\% C.L. for $N_*=0$, as shown in Fig.~\ref{fig:ModelParameters_Sampling}. The constraints for $\beta$ are not significantly modified by any different choice of $N_*$, however, due to the parameter degeneracy the same cannot be said about the constraints for $M$. The parameter range on $r$ versus $n_s$ diagram covered by constant-roll inflation in Fig.~\ref{fig:TiltVSRatio} does not appear to overlap with any of the regions covered by the other inflationary models considered in \citep{Ade:2015xua, Ade:2015lrj}, making this model observationally interesting for the next generations of CMB experiments. \appendix | 18 | 8 | 1808.01325 |
1808 | 1808.08204_arXiv.txt | Ultrafast outflows (UFOs) have recently been found in the spectra of a number of active galactic nuclei (AGN) and are strong candidates for driving AGN feedback. 1H0707-495 is a highly accreting narrow line Seyfert 1 and the second most X-ray variable bright AGN. Previous studies found evidence of blueshifted absorption at 0.1-0.2c in its spectrum. We perform a flux-resolved analysis of the full \xmm\ dataset on this AGN using both CCD and grating data, focusing on the low flux spectrum. We find strong evidence for an ultrafast outflow in absorption at $\sim$0.13c, with an ionisation parameter $\log(\xi$/erg~cm~s$^{-1})=4.3$. Surprisingly, we also detect blueshifted photoionised emission, with the velocity increasing at higher ionisation states, consistent with a trend that has been observed in the UV spectrum of this object. The bulk of the X-ray emitting material is moving at a velocity of 8000 km/s, with ionisation parameter $\log(\xi$/erg~cm~s$^{-1})=2.4$. The wind kinetic power inferred from the UFO absorption is comparable to that of the UV and X-ray emission features despite their different velocities and ionisation states, suggesting that we are viewing an energy-conserving wind slowing down and cooling at larger distances from the AGN. | Ultrafast outflows (UFOs) are thought to be powerful winds from active galactic nuclei (AGN) with outflow velocities greater than 10000 km/s. They are most commonly identified through high-energy absorption features from \ion{Fe} {XXV/XXVI} in the 7-10 keV energy band \citep[e.g.][]{Tombesi+10}, consistent with highly ionized gas blueshifted at significant fractions of the speed of light. These features are generally thought to originate in winds magnetically or radiatively driven off the AGN accretion disc at high Eddington rates \citep{Pounds+03, Reeves+03, Fukumura+15}. If this scenario is correct, these winds are of great interest because they are very strong candidates for driving AGN feedback, as they couple with galactic gas much more efficiently than jets. Narrow line Seyfert 1s (NLS1s) are a subclass of highly variable AGN that usually host lower-mass supermassive black holes ($10^{6}-10^{7} M_{\odot}$). They are thought to accrete at high Eddington fractions \citep[possibly super-Eddington,][]{Jin+12}. IRAS 13224-3809 (hereafter IRAS 13224) and 1H0707-495 (hereafter 1H0707) are the most X-ray variable objects from this class, varying by factors of tens within hours. These two objects share many similarities, including their broadband X-ray spectra, timing behaviour \citep{Zoghbi+10, Kara+13} and UV emission features \citep{Leighly+04a}. \citet{Parker+16, Parker+17} recently found a variable $\sim$0.2c UFO in the spectrum of IRAS 13224. It is observed most clearly in the 7-10 keV band, but is also visible in the 0.4-2 keV Reflection Grating Spectrometer (RGS) data \citep{Pinto+18}. The UFO absorption is strongest when the flux of the AGN is low, and almost disappears in high flux states, varying on time-scales of ks. Given all the similarities between IRAS 13224 and 1H0707, it is reasonable to expect 1H0707 to also possess powerful winds. Early studies of 1H0707 with \xmm\ already noticed a sharp drop in flux at 7 keV, which was interpreted as the blue wing of relativistically broadened iron K emission, or alternatively as blueshifted ionised iron absorption or the blue wing of a P Cygni wind profile \citep{Boller+02, Fabian+02, Done+07}. With larger datasets, it was possible to show that a major component of the continuum emission is indeed iron K and L reflection \citep{Fabian+09, Zoghbi+10}. \citet{Dauser+12} found absorption features, on top of smeared reflection, consistent with the Si, S, Ar and Ca Ly$\alpha$ lines in the long 2008 and 2010 XMM-Newton observing campaigns, with outflow velocities of 0.11c and 0.18c, respectively. \citet{Blustin+09} found double-peaked emission lines consistent with a broad-line region origin, but no signs of a UFO in the high-spectral resolution RGS data using the full 2008 campaign dataset. More recently, \citet{Hagino+16} re-analysed the archival \xmm\ data, finding clear evidence of an absorption feature at 8 keV, likely from blueshifted ionised iron. Here, we perform a flux-resolved analysis of the full \xmm\ dataset including high spectral-resolution RGS data aiming to confirm the presence of absorption features from a UFO. We report the detection of blueshifted photoionized gas in emission with velocity increasing with ionisation state (in agreement with UV data) in the low flux 1H0707-495 spectrum. We also show strong evidence for the presence of an ultrafast outflow at 0.14c in the same spectrum. This work will be followed by a more technical paper describing the full dataset in detail showing the full flux and time resolved dataset. | Our results show that using flux-resolved high-resolution X-ray spectroscopy to obtain a low-flux spectrum of the NLS1 1H0707-495 reveals blueshifted emission as well as strong evidence for an ultrafast outflow in absorption. We find reasonable agreement between the different models used to describe the emission features. It is especially reassuring that the models agree on the velocity of about 8000 km/s and the ionisation parameter of $\log\xi\sim2.1-2.4$, from which the physical properties of the wind can be inferred. The turbulent velocity of gas is 3000-6000 km/s, and the column density is several times $10^{21}$ \pcm. The UFO material is much more ionised with $\log\xi\sim4.3$, column density of $3 \times 10^{23}$ \pcm, turbulent velocity of 10000-12000 km/s and systematic speed of 39000-42000 km/s (0.13-0.14c). The parameters of the UFO do not stand out if compared to other AGN, where velocities between 0.1 and 0.3c are commonly observed \citep{Tombesi+10,Parker+18}. The ionisation parameter and column density are very similar to the UFO observed in IRAS 13224, although the velocity is smaller \citep[0.2-0.25c in IRAS 13224, see][]{Parker+17}. \citet{Dauser+12} analysed the 2010 and 2012 campaigns on 1H0707 separately and found evidence for a UFO velocity shift from 0.11c to 0.18c. Our result of 0.14c using the low flux state of the full dataset (2000 to 2011) therefore averages over this possible shift (however the full dataset is necessary to analyse the emission features). This is likely captured in the rather high velocity width of the UFO lines ($\sim$10000 km/s). A velocity shift would also decrease the UFO detection significance, which is nevertheless still very high with \delcstat$=85-115$ for 4 D.o.F. \citep[see][to see how Monte Carlo simulations can be used to determine the precise statistical significance]{Kosec+18a,Kosec+18b}. In each case, it is encouraging that including the absorber raises the rest-frame energy of the smeared iron K emission line from an unphysically low value of $\sim$5.6 keV to $\sim$6.6 keV, regardless of the absorption model used. With this discovery, we are adding 1H0707 to a list of known AGN with strong evidence for multiphase outflows. Detection of two UFOs in absorption at 0.06c and 0.13c was reported using hard X-ray, soft X-ray and also UV data in the spectrum of another NLS1 PG 1211+143 \citep{Pounds+16a,Pounds+16b,Kriss+18}. Similarly, the spectrum of PDS 456 shows evidence for two very fast UFOs at 0.25c and at 0.46c \citep{Nardini+15,Reeves+18}. Other examples are IRAS 17020+4544, with evidence for up to 5 UFO phases \citep{Longinotti+15}, and IRAS F11119+3257, where X-ray UFO absorption as well as a kpc-scale molecular outflow (with comparable energetics) is observed \citep{Tombesi+15}. However, we note two important differences between these objects and 1H0707. First, all the aforementioned outflows were detected in absorption only. To our knowledge, 1H0707 is currently the only known object to show significantly blueshifted X-ray absorption and emission at the same time. NGC 4051 shows evidence for some blueshifted X-ray emission \citep{Pounds+11}, but much slower at $\sim$750 km/s. The second difference is in the outflow velocities - while most UFOs in absorption achieve sub-relativistic speeds of 0.05-0.5c, here the blueshifted emission is significantly slower at <10000 km/s. It is useful to estimate the total kinetic power of the outflowing gas. Here we estimate the power separately for both absorbing and emitting gas and compare them, following the steps of \citet{Pinto+17} and \citet{Kosec+18a}. The wind power is $\dot{E}_{\textrm{kin}}=\frac{1}{2}\dot{M}u^{2}$ where $u$ is the wind velocity. The outflow rate $\dot{M}$ is then determined using the ionisation parameter $\xi$: $\dot{M}=4\pi\Omega C_{\textrm{V}} m_{\textrm{H}} \mu L_{\textrm{ion}} u/\xi$ where $\Omega$ is the solid angle of the outflow as a fraction of $4\pi$, $C_{\textrm{V}}$ is the volume filling factor defining how clumpy the wind is and $L_{\textrm{ion}}$ is the ionising luminosity. $m_{\textrm{H}}$ is the hydrogen (proton) mass and $\mu$ the mean atomic weight ($\sim$1.2 if the abundances are solar). The mechanical power of the outflow is therefore: $\dot{E}_{\textrm{kin}}=2\pi\Omega C_{\textrm{V}} L_{\textrm{ion}} m_{\textrm{H}} \mu u^{3}/\xi$. For the ultrafast absorber, using the best-fitting values from the \textsc{pion} + \textsc{pion} fit, we obtain $\dot{E}_{\textrm{kin}}=~34^{+4}_{-5}~\Omega C_{\textrm{V}} L_{\textrm{ion}}$. Repeating the same calculation for the photoionised emitter (from the same spectral fit) gives $\dot{E}_{\textrm{kin}}=~27_{-7}^{+6}~\Omega C_{\textrm{V}} L_{\textrm{ion}}$. If the ionising luminosity, solid angle and filling factor of the outflows are comparable, these are two strikingly similar estimates despite completely different velocities and ionisation parameters. However, we note that the volume filling factor, C$_{\textrm{V}}$, of both gas phases is highly uncertain. If for instance the lower ionisation wind component is in form of compact clumps, its C$_{\textrm{V}}$ could be much smaller than the one of the UFO absorbing gas. Then the kinetic power of the soft X-ray emitting material could be significantly lower than estimated above. \begin{figure} \includegraphics[width=\columnwidth]{Emission_lines_revised.pdf} \caption{The outflow velocity of different ions versus the ionisation parameter at which the abundance of each partially ionised ion in a photoionised plasma peaks \citep[the SPEX value from][]{Mehdipour+16}. Values for the low-ionisation transitions were taken from \citet{Leighly+04a,Leighly+04b}. The blue curve is the best fit function to ions with non-zero velocity, in form $v=b\times(\xi$/erg~cm~s$^{-1})^{a}$, where $a=0.36 \pm 0.04$ and $b=(1800 \pm 300)$ km~s$^{-1}$.} \label{Ion_velocities} \end{figure} \citet{Leighly+04a} performed a UV spectral study of 1H0707 and IRAS 13224 and found that while low ionisation lines such as \ion{Mg}{II} and \ion{C}{III} appear to be rest-frame and of disc origin, higher ionisation lines \ion{Si}{IV}, \ion{O}{IV]} and \ion{C}{IV} are blueshifted at up to $\sim2000$ km/s. Here we have discovered an extension of the same trend in X-rays with 2 high ionisation transitions, \ion{N}{VII} and \ion{O}{VIII}, at much higher velocities (see Fig. \ref{Ion_velocities}). Curiously, no \ion{O}{VII} emission is seen, which could be due to imperfectly modelled absorption. If we fit the ions with non-zero velocity with a function in form $v=b\times\xi^{a}$, where $v$ is velocity, $\xi$ is the ionisation parameter and $a$ and $b$ are constants, the best-fitting powerlaw slope is $a=0.36 \pm 0.04$ \citep[we note that we choose arbitrary 500 km/s errorbars on UV ion velocities due to a lack of uncertainties in][]{Leighly+04a}. This suggests that $\frac{v^{3}}{\xi}$ is consistent with being constant and hence that energy is being conserved if the ion emission comes from the same wind which produces the UFO absorption and the soft X-ray emission. In conclusion, we present strong evidence of ultrafast absorption as well as slower blueshifted emission in the X-ray spectrum of 1H0707. The trend of increasing velocities of higher ionised ions and the possible similar kinetic powers of UV, soft X-ray emitters and UFO absorbers suggest that we are witnessing the evolution of a stratified, kinetic energy-conserving wind. It would likely be launched close to the central accretor by radiation pressure, especially if the mass accretion rate is around or above the Eddington limit \citep[which is probably the case for 1H0707,][]{Jin+12}, and leave an imprint in form of UFO absorption. During the expansion, the wind would cool and slow down upon interaction with surrounding material, imprint the soft X-ray and UV spectra, and eventually deposit its kinetic energy at much larger (kpc) scales to produce AGN feedback. We note that this is not to be confused with the energy conserving feedback, which occurs on much larger (kpc) scales when the outflowing gas is no longer Compton-cooled by the AGN radiation and it expands adiabatically. An alternative solution is that the blueshifted soft X-ray lines are the extension of an accelerating line-driven wind, proposed by \citep{Leighly+04b} based on the UV features only. The UFO absorption could then be completely unrelated, its kinetic power only coincidentally similar to that of the remaining features. It is also possible that the observed UFO absorption is not in fact signature of a real outflow, but rather blueshifted absorption of the relativistic reflection spectrum by an extended corotating atmosphere of small clouds above the disk (Fabian et al. 2018, submitted). | 18 | 8 | 1808.08204 |
1808 | 1808.01780_arXiv.txt | Luminous and ultra-luminous infrared galaxies ((U)LIRGs) are rare today but are increasingly abundant at high redshifts. They are believed to be dusty starbursts, and hence should have high rates of supernovae (multiple events per year). Due to their extremely dusty environment, however, such supernovae could only be detected in rest-frame infrared and longer wavelengths, where our current facilities lack the capability of finding them individually beyond the local universe. We propose a new technique for higher redshifts, which is to search for the presence of supernovae through the variability of the integrated rest-frame infrared light of the entire hosts. We present a pilot study to assess the feasibility of this technique. We exploit a unique region, the ``IRAC Dark Field'' (IDF), that the {\it Spitzer Space Telescope} has observed for more than 14 years in 3--5~\micron. The IDF also has deep far-infrared data (200--550~\micron) from the {\it Herschel Space Observatory} that allow us to select high-redshift (U)LIRGs. We obtain a sample of (U)LIRGs that have secure optical counterparts, and examine their light curves in 3--5~\micron. While the variabilities could also be caused by AGNs, we show that such contaminations can be identified. We present two cases where the distinct features in their light curves are consistent with multiple supernovae overlapping in time. Searching for supernovae this way will be relevant to the James Webb Space Telescope (\JWST) to probe high-redshift (U)LIRGs into their nuclear regions where \JWST\, will be limited by its resolution. | Luminous and ultra-luminous infrared galaxies (LIRGs and ULIRGs; hereafter ``(U)LIRGs'') have high IR luminosity (integrated over rest-frame 8--1000~\micron) of $L_{IR}>10^{11}$ and $>10^{12}L_\odot$, respectively. It is widely believed that (U)LIRGs are starbursts, and that their strong IR emissions are mostly due to the dust-reprocessed UV photons from their large numbers of young stars. On the other hand, (U)LIRGs usually also harbor AGNs, which often makes it difficult to attribute their major IR power source solely to starbursts \citep[see][]{Lonsdale2006}. It is important to distinguish these hypotheses or, more likely, to determine their fractional contributions to the (U)LIRG power and how those may change with redshift. Although (U)LIRGs are rare today, they are more common at high redshifts \citep[e.g.,][]{LeFloch2005, Magnelli2013}, which make them relevant to the global picture of galaxy evolution across cosmic time. A decisive way to determine the fraction of (U)LIRGs' power supplied by starbursts would be to measure their rates of supernovae (SNe). If they are indeed dominantly powered by starbursts, (U)LIRGs should have high star formation rates (SFRs; $>10$ and $>100M_\odot$~yr$^{-1}$ for LIRGs and ULIRGs, respectively), and hence should also have high rates of SNe. For ULIRGs, the rate $r_{SN}$ is estimated to be $\gtrsim 2$--3 events yr$^{-1}$ \citep[][]{vanBuren1994, Mattila2001}. However, due to the severe dust obscuration, such SNe would have to be searched for in the radio or IR. VLBI detections of radio SNe and SN remnants in the ULIRG Arp 220 and the LIRG Arp 299 \citep[e.g.,][and references therein] {Lonsdale2006b, PerezTorres2009, RomeroCanizales2011, RomeroCanizales2014, Bondi2012, Varenius2017} lend strong support to high $r_{SN}$ in (U)LIRGs. For example, \citet[][]{Lonsdale2006b} derive $r_{SN} \sim 4$ events yr$^{-1}$ for Arp 220, which implies a sufficient SFR to account for its $L_{IR}$ without resorting to AGN. VLBI imaging, however, still cannot be applied to (U)LIRGs beyond the local universe. IR surveys have also discovered a few tens of SNe in local (U)LIRGs \cite[e.g.,][]{Maiolino2002, Cresci2007, Mattila2007, Kankare2008, Miluzio2013, Kool2018}, including multiple SNe in the same galaxies \citep[e.g.,][]{Kankare2012, Kankare2014}. Two main conclusions have been drawn from these results: (1) (U)LIRGs indeed have a high rate of SNe embedded by dust, which are not visible to optical surveys. (2) The current IR surveys must still be missing a large fraction of dusty SNe close to the nuclear region of the host galaxies due to both the extreme dust extinctions and the much decreased survey sensitivities when working against the bright background. Unfortunately, these IR surveys also do not go beyond the local universe. As an alternative to discovering SNe individually, we propose to reveal them through the variability of the integrated IR light of the host. This method can be easily applied to high-$z$, because it requires only high-precision differential photometry. As far as we are aware, no search of this type has been performed, and a pilot study is needed to assess the prospects for present instruments and especially for the {\it James Webb Space Telescope} (\JWST). To set the scale required, a supernova peaking at $M\sim -19$~mag within a host of $M\sim -21$~mag (i.e., $m\sim 22.4$~mag at $z\approx 1$) would increase the host brightness by $\sim 0.16$~mag, which should be detectable by current facilities. If a (U)LIRG has multiple SNe per year, they could overlap in time and result in even larger variability. Admittedly, finding evidence of dust-embedded SNe in this way is inferior to resolving them individually in terms of the follow-up applications of the SNe; nevertheless, it is still a powerful means to probe the nuclear regions that the activities are expected to be the most violent and yet are the most difficult to penetrate. The only major contaminations would be AGNs, which are known to vary with typical amplitudes of a few tenths of magnitude \citep[e.g.,][]{Peterson2001}. In this paper, we exploit a unique field known as the ``IRAC Dark Field'' \citep[hereafter ``IDF''; see][]{Krick2009}. Since its launch in 2003, the {\it Spitzer Space Telescope} has been observing this area for the calibration of its InfraRed Array Camera (IRAC; \citet[][]{Fazio2004}), producing a deep field of $\sim 13$\arcmin\, in radius. The IDF (R.A. $=17^{\rm h}40^{\rm m}$, decl. $=68^{\rm o}40^{\prime}$, J2000) is close to the North Ecliptic Pole, and is in a region of the lowest zodiacal background (hence ``dark''). During the cryogenic phase (2003 October to 2009 May), all four IRAC channels (3.6, 4.5, 5.8, and 8.0~\micron) were used. After the coolant depletion (``warm-mission'' phase), the 3.6 and 4.5~\micron\, channels (hereafter ``Ch1'' and ``Ch2,'' or ``Ch1/2'') have continued observations without any significant loss of sensitivity. The IDF is the only region on the sky with long-duration ($>14$ years) monitoring data in 3--5~\micron\, (sampling rest-frame near-IR up to $z\approx 3.5$), and its early data ($\sim 2$ years) were already of unprecedented time baseline such that it inspired a search for Population III supernovae, albeit with null results \citep[][]{Frost2009}. The IDF is ideal for our purpose here because of two additional reasons: it has (1) hundreds of (U)LIRGs revealed by the far-IR (FIR) observations from the {\it Herschel Space Observatory} and (2) medium-deep \Chandra\, X-ray observations for AGN diagnostics. Our paper is organized as follows. We present the data in \S 2, and describe the selection of variable objects in \S 3. The analysis of these variable objects is given in \S 4, which is followed by a discussion in \S 5. A brief summary is given in \S 6. We use AB magnitudes throughout the paper, and adopt $\Omega_M=0.27$, $\Omega_\Lambda=0.73$ and $H_0=71$~km s$^{-1}$ Mpc$^{-1}$. | Strictly speaking, the analysis in \S 4 only shows that the variabilities in M21355 and M26166 are consistent with the SNe interpretation but does not definitely prove it, the latter of which probably could only be claimed if the SNe were detected individually. However, we are able to rule out the AGN variability as their cause based on the Ch1/2 color of the hosts and the light curve behaviors, and hence leave the SNe explanation as the likely alternative. Multiple SNe have been detected individually in at least two local LIRGs (Arp 299 and IC 833; see the references in \S 1), and thus it should not be surprising that we find evidence of similar events at high redshifts. One might question why such variabilities cannot be due to other types of transients. Among all other populations, only tidal disruption events \citep[TDEs; see][,for a review]{Komossa2015}, which are thought to be due to the disruption of a star falling into the supermassive black hole at a galaxy center, could possibly have IR amplitude and varying time scale comparable to SNe. TDEs emit most strongly in the X-ray to optical wavelengths, and these energetic photons could be absorbed by the dusty ISM around the black hole and re-emit in IR \citep[see, e.g.][]{Lu2016}. Such IR ``echoes'' have been found for a few TDEs \citep[][]{Dou2016, Dou2017, Jiang2016, Jiang2017, vanVelzen2016} by using the {\it Wide-field Infrared Survey Explorer} ({\it WISE}) data \citep[][]{Wright2010} in $W1$ (3.4~\micron) and $W2$ (4.6~\micron) bands, which are close to the Ch1/2 bands used in our study. \citet[][]{Wang2018} further present a sample of {\it WISE} sources that have similar variability and suggest that they could also be the IR echoes of TDEs (but see also \citet[][]{Assef2018}). More energetic TDEs have also been suggested, such as the very luminous transient in Arp 299 recently discovered by \citet[][]{Mattila2018}. However, invoking TDEs for M21355 and M26166 is problematic, because both objects would certainly require multiple TDEs to explain the features in their light curves. This would imply several events over ten years, which is orders-of-magnitude higher than the expected rate of $\sim$10$^{-5}$~yr$^{-1}$ per galaxy \citep[][]{Wang2004, Wang2012, vanVelzen2014, Holoien2016}. \footnote{While there are now suggestions that TDEs could occur at a much higher rate in (U)LIRGs \citep[][]{Tadhunter2017}, such a connection is yet to be established.} Therefore, we believe that TDEs are unlikely the cause. In contrast, the multiple SNe interpretation comes naturally, as it meets the expectation that (U)LIRGs should have a high rate of SNe because of their high SFR. We emphasize that our pilot study here is the first one using variability of integrated IR light to reveal dust-embedded SNe in (U)LIRGs beyond the local universe. There have been other IR variability studies in the literature, some of which also utilize IRAC Ch1/2. A significant example is that of \citet[][]{Kozlowski2010b}, who investigated the IRAC variability of objects in the 8.1~deg$^2$ \Spitzer\, Deep Wide-Field Survey in the Bo\"{o}tes field over four epochs spanning four years. Aiming at variability in general, however, they do not target (U)LIRGs, and most of their variable objects are due to AGNs. While this work has led to the serendipitous discovery of a self-obscured SN at $z\approx 0.2$ \citep[][]{Kozlowski2010c}, the SN is not related to a (U)LIRG and its obscuration is due to its dusty circumstellar medium but not the environment. Another example is the ongoing SPitzer InfraRed Intensive Transients Survey (SPIRITS; \citet[][]{Kasliwal2017}), which searches for Ch1/2 transients in 190 nearby galaxies. SPIRITS has also led to the discovery of new SNe: \citet[][]{Jencson2017} report two SNe in IC 2163 (not a LIRG) separated by less than two years. This survey, which does not include (U)LIRGS, is confined to the local universe ($< 15$~Mpc) and only aims to discover transients that can be individually resolved. The implication of our study can be understood in two-fold. First, we present strong supporting evidence that high-z (U)LIRGs, like their local counterparts, have high rate of SNe. While determining $r_{SN}$ is beyond the scope of this paper, it is obvious that the two cases \footnote{We note that the other objects in the FIR sample also have hints of variabilities but are at lower levels; however we have to differ the discussion to a forthcoming paper because our current analysis does not yet allow us to confidently assess these more subtle features in the light curves.} shown in Figure 4 require multiple SNe per year over the active periods. This makes (U)LIRGs ideal targets to search for high-z SNe in the rest-frame IR, which will become feasible when the \JWST\, comes online in the near future. The unprecedented IR resolution and sensitivity offered by the \JWST\, will easily enable us to detect such SNe individually out to any redshifts where (U)LIRGs are seen and to assemble large samples that can lead to many applications. Second, using the integrated light variability as the indicator of SNe in high-z (U)LIRGs will remain relevant in the \JWST\, era because it will still be difficult for \JWST\, to probe close to the nuclear regions. For example, \JWST's resolution at 4.4~\micron\, (the reddest band of its NIRCam instrument) is $\sim $ 0\arcsec.17, which corresponds to $\sim 1.4$~kpc at $z\approx 1$--2. ULIRGs have now been found out to $z\approx 6$--7 \citep[][]{Riechers2013, Fudamoto2017, Strandet2017}, and to sample the rest-frame $K$-band at such redshifts \JWST\, will need to observe at 18--20\micron\, using its MIRI instrument at the resolution of $\sim $ 0\arcsec.75, which corresponds to $\sim 4.2$~kpc. In such cases, our method will be the only option. Of course, one would not be able to obtain \JWST\, time baseline or cadence comparable to the IDF IRAC observations, and the ``quiet phase'' argument presented in \S 4 would not be applicable. However, if the \JWST\, monitoring is done in at least two bands, the color information can always be used to judge if the observed variability is more likely due to SNe or AGN. In addition, contemporary observations in one optical band can also greatly help the judgment, because the variability caused by dusty SNe should not be seen in optical due to the large extinction in (U)LIRGs. Lastly, we point out that the very field of IDF is of great interest for the \JWST. By design, the IDF is close to the North Ecliptic Pole and thus is in the continuous viewing zone (CVZ) of \JWST, which is the narrow region within $\pm 5^{\circ}$ from the Ecliptic Poles \footnote{See ``James Webb Space Telescope User Documentation'', \url{https://jwst-docs.stsci.edu/display/JTI/JWST+Observatory+Coordinate+System+and+Field+of+Regard} }. For this reason, the IDF can be visited by the \JWST\, at any time of the year. It will be ideal for a \JWST\, monitoring program, especially when considering the fact it is the only region in the CVZ that has deep \Herschel\, data revealing a large sample of high-z (U)LIRGs. | 18 | 8 | 1808.01780 |
1808 | 1808.03099_arXiv.txt | We present an analysis of the impact of spiral density waves (DWs) on the radial and surface density distributions of supernovae (SNe) in host galaxies with different arm classes. We use a well-defined sample of 269 relatively nearby, low-inclination, morphologically non-disturbed and unbarred Sa--Sc galaxies from the Sloan Digital Sky Survey, hosting 333 SNe. Only for core-collapse (CC) SNe, a significant difference appears when comparing their $R_{25}$-normalized radial distributions in long-armed grand-design (LGD) versus non-GD (NGD) hosts, with that in LGD galaxies being marginally inconsistent with an exponential profile, while SNe~Ia exhibit exponential surface density profiles regardless of the arm class. Using a smaller sample of LGD galaxies with estimated corotation radii ($R_{\rm C}$), we show that the $R_{\rm C}$-normalized surface density distribution of CC~SNe indicates a dip at corotation. Although not statistically significant, the high CC~SNe surface density just inside and outside corotation may be the sign of triggered massive star formation by the DWs. Our results may, if confirmed with larger samples, support the large-scale shock scenario induced by spiral DWs in LGD galaxies, which predicts a higher star formation efficiency around the shock fronts, avoiding the corotation region. | \label{intro} The spiral arm structure of star-forming disc galaxies was explained in the framework of density wave (DW) theory by the pioneering work of \citet[][]{1964ApJ...140..646L}. According to this theory, semi-permanent spiral patterns especially in grand-design (GD) galaxies, i.e. spiral galaxies with prominent and well-defined spiral arms, are created by long-lived quasi-stationary DWs. Despite an excellent progress of the theory \citep[for recent comprehensive reviews, see][]{2014PASA...31...35D,2016ARA&A..54..667S}, there are many disputes on the lifetime of spiral patterns, and the ability of DWs to generate large-scale shocks and trigger star formation, as originally proposed by \citet[][]{1969ApJ...158..123R}. For example, the simulations by \citet[][]{2011MNRAS.410.1637S} manifest short-lived patterns. In another example, using a multiband analysis for some GD galaxies, \citet{2010ApJ...725..534F} found that there is no shock trigger, and that the spiral arms just reorganize the material from the disc out of which stars form \citep[see also][]{2012A&A...542A..39G}. Nevertheless, the results of many other studies are consistent with the picture where the DWs cause massive star formation to occur by compressing gas clouds as they pass through the spiral arms of GD galaxies \citep[e.g.][]{1990ApJ...349..497C,1996A&A...308...27K,2002MNRAS.337.1113S,2009A&A...499L..21G, 2009ApJ...694..512M}. For example, using H$\alpha$ direct imaging accompanied with broad-band images in $R$ and $I$ bands, \citet{2013AA...560A..59C} studied the distribution of H~{\footnotesize II} regions of spiral arms and found clear evidence for the triggering of star formation in the sense of a high density of H~{\footnotesize II} regions at the fixed radial ranges in some GD galaxies. Recently, \citet{2016ApJ...827L...2P} showed that pitch angle of galaxies is statistically more tightly wound, i.e. smaller, when viewed in the light from the evolved/older stellar populations. Both the results, complementing each other, are in excellent agreement with the prediction of theory that stars are not only born in the DW but also move out of it as they age \citep[see also most recent results by][]{2018MNRAS.478.3590S}. An alternative to the DW theory is the idea of reorganization of the distribution of H~{\footnotesize II} regions in multiple arms of differentially rotating disc with star formation processes generated by the stochastic self-propagating method developed by \citet[][]{1976ApJ...210..670M} and \citet[][]{1978ApJ...223..129G}. This mechanism is supposed to work in non-GD (NGD) galaxies, producing flocculent spiral arms. In the context of above-mentioned scenarios, the main goal of this article is to study the possible impact of spiral DWs (triggering effect) on the distribution of supernovae (SNe) in discs of host galaxies, when viewing in the light of different nature of Type Ia and core-collapse (CC) SNe progenitors. Recall that Type Ia SNe result from stars with masses lower than $\sim7.5~M_{\odot}$ \citep[ages from $\sim0.5$~Gyr up to $\sim10$~Gyr, see][]{2012PASA...29..447M} in close binary systems, while the progenitors of Types Ibc and II SNe,\footnote{{\footnotesize Traditionally, SNe of Types Ib and Ic, including uncertain spectroscopic Type Ib/c, are denoted as SNe Ibc. All these and other subtypes of CC~SNe, i.e. Ibc, II, IIb (transitional objects with observed properties close to SNe II and Ib), and IIn (dominated by emission lines with narrow components) SNe, arise from young massive stars with possible differences in their masses, metallicities, and ages \citep[see e.g.][for more details]{2011MNRAS.412.1522S}.}} collectively called CC~SNe, are massive \citep[$M\gtrsim7.5~M_{\odot}$, see e.g.][]{2018ApJ...860...39W} young short-lived stars \citep[from a few up to $\sim100$~Myr, see][]{2015PASA...32...19A,2018MNRAS.476.2629M,2018arXiv180501213X}. The first attempt to study the distribution of SNe within the framework of DW theory was performed by \citet{1973PASP...85..564M}. Using the locations of 19 SNe, he suggested that stars in a spiral galaxy are formed in a shock front on the inner edge of a spiral arm, then drift across the arm as they age, predicting for SN progenitors (more likely for SNe II) a short lifetime (a few million years) and high masses (a few tens of solar masses). However, using the fractions of GD and flocculent galaxies in a sample of 111 hosts with 144 SNe, \citet{1986ApJ...311..548M} suggested that DWs do not greatly enhance the massive star formation rate per unit luminosity of a galaxy, mentioning that star formation in most galaxies may be dominated by stochastic processes. Results similar to those in \citet{1973PASP...85..564M} were obtained also by \citet{1996ApJ...473..707M} and \citet{2007AstL...33..715M} for Types II and Ibc SNe, respectively. In other studies, different authors \citep[e.g.][]{1976ApJ...204..519M,1994PASP..106.1276B,2005AJ....129.1369P} investigated the distribution of SNe relative to spiral arms of galaxies. Such studies did not interpret their results within the DW theory nor did they distinguish among various spiral arm classes \citep[ACs;][]{1987ApJ...314....3E} of SNe host galaxies. Indeed, in our recent paper \citep{2016MNRAS.459.3130A}, we already studied the distribution of SNe relative to the spiral arms of their GD and NGD host galaxies, using the Sloan Digital Sky Survey (SDSS) images from the $g$, $r$, and $i$ bands. We found that the distribution of CC~SNe (i.e. tracers of recent star formation) is affected by the spiral DWs in their host GD galaxies, being distributed closer to the corresponding edges of spiral arms where large-scale shocks, thus star formation triggering, are expected (see also farther in the text of Section~\ref{DWTInt}). Such an effect was not observed for Type Ia SNe (less-massive and longer-lived progenitors) in GD galaxies, as well as for both types of SNe in NGD hosts. In this paper, we expand our previous work, and for the first time study the differences between the radial distributions of SNe in unbarred Sa--Sc host galaxies with various spiral ACs. In parallel, to check the triggering effect at different galactocentric radii, we study the consistency of the surface density distribution of SNe (normalized to the optical radii, and for a smaller sample also to corotation radii of hosts) with an exponential profile in GD and NGD galaxies. The layout of this article is the following. In Section~\ref{sample}, we present sample selection and reduction, and determination approach of spiral ACs. The results and their interpretation within the framework of DW theory are presented in Sections~\ref{resdiscus} and \ref{DWTInt}, respectively. Section~\ref{concl} summarizes our conclusions. To conform the values used in databases of our recent papers \citep[][]{2012A&A...544A..81H,2014MNRAS.444.2428H,2016MNRAS.456.2848H,2016MNRAS.459.3130A}, a cosmological model with $\Omega_{\rm m}=0.27$, $\Omega_{\rm \Lambda}=0.73$, and $H_0=73 \,\rm km \,s^{-1} \,Mpc^{-1}$ Hubble constant \citep{2007ApJS..170..377S} are adopted in this article. | \label{concl} In this study, using a well-defined and homogeneous sample of SN host galaxies from the coverage of SDSS DR13, we analyse the radial and surface density distributions of Type Ia and CC~SNe in host galaxies with different ACs to find the possible impact of spiral DWs as triggers for star formation. Our sample consists of 269 relatively nearby (${\leq {\rm 150~Mpc}}$, the mean distance is 82~Mpc), low-inclination ($i \leq 60^\circ$), morphologically non-disturbed and unbarred Sa--Sc galaxies, hosting 333 SNe in total. In addition, we perform an extensive literature search for corotation radii, collecting data for 30 host galaxies with 56 SNe. The main results concerning the deprojected and inner-truncated ($\tilde{r} \geq 0.2$) distributions of SNe in host galactic discs are the following: \begin{enumerate} \item We find no statistical differences between the pairs of the $R_{25}$-normalized radial distributions of Type Ia and CC~SNe in discs of host galaxies with different spiral ACs, with only one significant exception: CC~SNe in LGD and NGD galaxies have significantly different radius distributions (Table~\ref{RSNR25_KS_AD}). The radial distribution of CC~SNe in NGDs is concentrated to the centre of galaxies with relatively narrow peak and fast exponential decline at the outer region, while the distribution of CC~SNe in LGD galaxies has a broader peak, shifted to the outer region of the discs (upper panel of Fig.~\ref{HistSDFSurfd}). \item The surface density distributions of Type Ia and CC~SNe in most of the subsamples are consistent with the exponential profiles. Only the distribution of CC~SNe in LGD galaxies appears to be inconsistent with an exponential profile (Table~\ref{tableGDNGDexp} for the AD statistic but only very marginally so for the KS statistic), being marginally higher at $0.4\lesssim R_{\rm SN}/R_{25} \lesssim0.7$. The inconsistency becomes more evident when comparing the same distribution with the scaled exponential profile of CC~SNe in NGD galaxies (middle panel of Fig.~\ref{HistSDFSurfd}). \item Using a smaller sample of LGD galaxies with estimated corotation radii, we show, for the first time, that the surface density distribution of CC~SNe shows a dip at corotation, and enhancements at $^{+0.5}_{-0.2}$ corotation radii around it (Fig.~\ref{surfdens}). However, these features are not statistically significant (Fig.~\ref{distCorot}). The CC~SNe enhancements around corotation may, if confirmed with larger samples, indicate that massive star formation is triggered by the DWs in LGD host galaxies. Considering that the different LGD host galaxies have various corotation radii (Table~\ref{dataRcorGal} and Fig.~\ref{RcR25}) distributed around the mean value of $\langle R_{\rm C}/R_{25}\rangle=0.42\pm0.18$ (Fig.~\ref{RCR25histcum}), the radii of triggered star formation by DWs are most probably blurred within a radial region including $\sim0.4$ to $\sim0.7$ range in units of $R_{25}$, without a prominent drop in the mean corotation region (middle panel of Fig.~\ref{HistSDFSurfd}). \end{enumerate} These results for CC~SNe in LGD galaxies may, if confirmed with larger samples and better corotation estimates, support the large-scale shock scenario \citep[e.g.][]{1973PASP...85..564M}, originally proposed by \citet[][]{1969ApJ...158..123R}, which predicts a higher star formation efficiency, avoiding the corotation region \citep[e.g.][]{1990ApJ...349..497C,2002MNRAS.337.1113S,2013AA...560A..59C,2016MNRAS.459.3130A}. When more information will become available on corotation radii of SN host galaxies, it would be worthwhile to extend our study, by comparing the $R_{\rm C}$-normalized radial and surface density distributions of Type Ia and CC~SNe in LGD galaxies. This will also allow to check the impact of spiral DWs on the distribution of less-massive and longer-lived progenitors of Type Ia SNe. Moreover, similar analysis of SNe in SGD galaxies can help to understand the role of DWs in star formation triggering, if any. | 18 | 8 | 1808.03099 |
1808 | 1808.07445_arXiv.txt | The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. SO will measure the temperature and polarization anisotropy of the cosmic microwave background in six frequency bands centered at: 27, 39, 93, 145, 225 and 280 GHz. The initial configuration of SO will have three small-aperture 0.5-m telescopes and one large-aperture 6-m telescope, with a total of 60,000 cryogenic bolometers. Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The small aperture telescopes will target the largest angular scales observable from Chile, mapping $\approx 10\%$ of the sky to a white noise level of 2~$\mu$K-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, $r$, at a target level of $\sigma(r)=0.003$. The large aperture telescope will map $\approx 40\%$ of the sky at arcminute angular resolution to an expected white noise level of 6 $\mu$K-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the Large Synoptic Survey Telescope sky region and partially with the Dark Energy Spectroscopic Instrument. With up to an order of magnitude lower polarization noise than maps from the \planck{} satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev--Zel'dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources\footnote{A supplement describing author contributions to this paper can be found at \url{https://simonsobservatory.org/publications.php}}. | \label{sec:intro} \input intro.tex | \label{sec:summary} \input summary.tex | 18 | 8 | 1808.07445 |
1808 | 1808.02867_arXiv.txt | Approaches used in modern numerical simulations of the dynamics of dust and gas in circumstellar disks are tested. The gas and dust are treated like interpenetrating continuous media that can exchange momentum. A stiff coupling between the gas and dust phases is typical for such disks, with the dust stopping time much less than the characteristic dynamical time scale. This imposes high demands on the methods used to simulate the dust dynamics. A grid, piecewise-parabolic method is used as the basic algorithm for solving the gas-dynamical equations. Numerical solutions obtained using various methods to compute the momentum exchanges are presented for the case of monodisperse dust. Numerical solutions are obtained for shock tube problem and the propagation of sound waves in a gas-dust medium. The studied methods are compared in terms of their ability to model media with (a) an arbitrary (short or long) dust stopping time, and (b) an arbitrary dust concentration in the gas (varying the dust to gas mass ratio from 0.01 to 1). A method for computing the momentum exchange with infinite-order accuracy in time is identified, which makes it possible to satisfy the conditions (a) and (b) with minimal computational costs. A first-order method that shows similar results in the test computations is also presented. It is shown that the proposed first-order method for monodisperse dust can be extended to a regime when the dust is polydisperse; i.e., a regime represented by several fractions with different stopping times. Formulas for computing the gas and dust velocities for polydisperse dust with each fraction exchanging momentum with the gas are presented. | Simulating the dynamics of gas–dust circumstellar disks is a topical problem in modern computational astrophysics (see, e.g., \cite{HaworthEtAl2016}). The dust and solid bodies in a circumstellar disk are represented by objects with various sizes, from submicron dust particles to planetary cores. For dust particles whose sizes are less than the mean free path of the gas molecules in the circumstellar disk, the ratio of the typical dust stopping time to the local gas velocity (the so-called Epstein\cite{Weidenschilling1977} regime for gas flowing around a rigid body) is given by \footnote{The commonly used term for this ratio, the ``stopping time'', can lead to confusion, since, in the approximation considered here, a particle does not acquire the velocity of the gas, but instead a constant velocity relative to the gas velocity.}: \begin{equation} \label{eq:t_stop_rho} t_{\rm stop}=\frac{s \rho_{\rm s}}{c_{\rm s} \rho_{\rm g}}, \end{equation} where $s$ is the radius of a dust particle (assumed to be spherical), $\rho_{\rm s}$ the density (intrinsic density) of the dust material, $\rho_{\rm g}$ the density of the gas in the circumstellar disk, and $c_{\rm s}$ the sound speed in the gas. For dust particles with sizes of about 1~$\mu$m the dust stopping time $t_{\rm stop}$ in the disk is of order 100~s (see, e.g., \cite{StoyanovskayaDust,LaibePrice2011Test}), while the dynamics of the disk require simulations covering $10^{11}$~s ($\approx 10^4$~yrs) or more. This means that numerical solutions of the non-stationary equations for a multiphase gas–dust medium with the application of explicit integration schemes lead to unacceptably high computational costs. This raises the question of searching for numerical methods enabling exact integration of the dust trajectories with a time step $\tau$ determined purely by the Courant condition for the gas-dynamical part of the system. A number of approaches have been used to solve this problem (see, e.g., \cite{BaiStone2010ApJS,ZhuDust,ChaNayakshinDust2011,RiceEtAl2004,FranceDustCode,Pignatale2016}), which were systematically analyzed in \cite{StoyanovskayaDust}. In addition to the difficulties associated with taking into account the influence of the gas on the dust when integrating the equations for the dust, the correct computation of momentum transfer from the dust to the gas is also problematic (see, e.g., \cite{BateDust2014,LaibePrice2014OneFluidDust,Ishiki2017,YangJohansen2016}). Averaged over the disk, the ratio of the volume density of dust to the gas density does not exceed $\varepsilon=\displaystyle \frac{\rho_{\rm d}}{\rho_{\rm g}}=0.01$, and the influence of the dust on the gas dynamics is therefore often neglected. On the other hand, the results of simulations show that dust particles can be concentrated in certain areas in the disk (e.g., in spiral arms \cite{RiceEtAl2004}, the inner part of the disk \cite{VorobyovEtAl2017}, or self-gravitating gaseous clumps \cite{ChaNayakshinDust2011}), enhancing the local dust-to-gas mass ratio to values of $\varepsilon\approx 1$ or more. Laibe and Price \cite{LaibePrice2011Test} solved test problem of the propagation of sound waves in a two-phase medium applying smoothed-particle hydrodynamics. In their numerical model, the gas and dust were described as separate groups of model particles. They found that, in the case of a high drag coefficient between the gas and dust and with a high concentration of dust in the gas (i.e., when $\varepsilon\approx1$), correct computation of the perturbation amplitude requires that \begin{equation} \label{eq:sparesSPH} h<c_{\rm s} t_{\rm stop}. \end{equation} This condition probably arises in smoothed-particle computations involving convective transport that exceeds the decay of the wave. Vorobyov et al. \cite{VorobyovEtAl2017} solved test problems of the propagation of sound waves and the shock tube problem but applying the finite-difference, finite-volume grid method described in detail in \cite{StoneNorman1992} to model the dynamics of the gas and dust components of the disk. The semi-implicit scheme presented by Cha and Nayakshin \cite{ChaNayakshinDust2011} was used to compute the mutual drag between the dust and gas. It was established that such computations for a medium with a high drag coefficient between the gas and dust and with a high concentration of dust in the gas encountered problems. Applying the scheme of \cite{ChaNayakshinDust2011} required that the time step $\tau$ be much smaller than the velocity relaxation time $t_{\rm stop}$. However, when only the influence of the gas on the dust dynamics is taken into account (not the ``back reaction'' of the dust on the gas dynamics), this scheme gives good results for test problems, without a stiff limitation on the time step. This raises the question of creating a universal numerical scheme that is free from these limitations on the spatial and temporal steps. The need for a universal numerical scheme is motivated by the following factors. The ``frozen'' solid phase approximation is often used to compute the dynamics of disks with submicron dust (see, e.g., \cite{Drozdovskaya2015, Drozdovskaya2016, DemidovaGrininDust2017}). If it is important to take into account the dust drift, one computationally effective approach to this is a transition to an asymptotic approximation, or to the short-friction-time approximation \cite{JohansenKlahr2005, Akimkin2015SFTA, Akimkin2017SFTA}.In this approximation, the velocities of the bodies and of the gas are related by a simple algebraic expression that yields correct results for the dust drift in circumstellar disks only for grains of a limited size (see \cite{StoyanovskayaDust} or more detail, and see \cite{PriceLaibeSFTA} for smoothed-particle hydrodynamics). On the other hand, the results of the numerical simulations \cite{BrauerDullemondHenning2008} and of observations show that the dust grains in circumstellar disks grow from 1~$\mu$m to 1-10~cm or more over the first 10 million years of the disk’s evolution. Therefore, simulations of the disk dynamics over long time scales impose requirements on the algorithms used, which must enable computation of momentum exchange between the gas and dust for a wide range of sizes for the solid bodies, from 1~$mu$m to tens of meters, with corresponding variations in the frictional force. Furthermore, it is important that these algorithms can be included in models for gas disks that have already been developed, and do not require fundamental changes in the method used to compute the gas dynamics, for example the transition to a conservative form of the equations (the scheme for the equations of a two-phase medium in conservative form developed by Miniati \cite{Miniati2010}). In our current study, we have analyzed numerical schemes for the computation of the mutual drag between the gas and dust, and present approaches that make it possible to develop fast methods for the computation of this force in circumstellar gas-dust disks. The finite-difference and finite-volume method \cite{StoneNorman1992} with piecewise-parabolic interpolation \cite{ColellaWoodward1984} for the gas-dynamical part of the equations is used as an example. We have shown the possibility of computing the rapid exchange of momentum between the gas and dust in a circumstellar disk for an arbitrary dust concentration. We have also verified the necessity of the condition (\ref{eq:sparesSPH}) when using grid methods to solve the gas-dynamical equations. Section \ref{sec:discnummodel} presents a brief description of the numerical method used to solve the gas-dynamical equations, which is used as a basis to test various methods for computing the drag between the gas and the solid phase. The tested schemes for the computation of the momentum exchange between the gas and moodisperse dust (with first-order and infinite-order approximations in time) are described in Section \ref{sec:schemes1}. Sections \ref{sec:DustyWave} and \ref{sec:DustyShock} describe one-dimensional test problems for a gas-monodisperse dust system, and Sections \ref{sec:NumDustyWave} and \ref{sec:NumDustyShock} present the results of these test computations. In Section \ref{sec:schemesN} we generalize the scheme with first-order approximation in time to the case of polydisperse dust and present direct computational formulas. Our conclusions are presented in Section \ref{sec:Resume}. | \label{sec:Resume} We have presented and compared approaches that are used in modern numerical models applied to the computation of the dynamics of gas-dust circumstellar disks. Circumstellar disks consist of gas and solid bodies ranging from submicron dust to meter-sized bodies. The stopping time for small dust grains is much less than the dynamical time scale; i.e., it comprises a small fraction of an orbit of the disk around the central protostar. We have limited our consideration to models in which the gas and dust are treated like interpenetrating continuous media that can exchange momentum. We have focused on the suitability of various methods for modeling a medium with (a) arbitrary (short or long) stopping times for the dust and (b) arbitrary dust concentration in the gas (the dust to gas mass ratio varied from 0.01 to 1). We will now summarize our main results. The method for computing the momentum exchange based on analytical solutions have infinite-order accuracy in time. Applying this method to a two-phase medium makes it possible to satisfy conditions (a) and (b) with minimal computational costs making it an optimal approach for the solution of non-stationary problems. The semi-implicit scheme with operator splitting applied to a two-phase medium is stable, that is, it enables computations with $\tau>t_{\rm stop}$, but its actual accuracy becomes unacceptably low for time steps $\tau>\displaystyle\frac{t_{\rm stop}}{\varepsilon}$. This scheme is not recommended, since it requires time steps as small as an explicit scheme when $t_{\rm stop} \ll 1$ and $\varepsilon \approx 1$. Our proposed semi-implicit scheme for the barycentric and relative velocities with first-order accuracy in time for a two-phase medium enables satisfaction of the conditions (a) and (b) with computational costs comparable to the method with infinite-order accuracy. An advantage of this method is that it can be extended to a regime where the dust is polydisperse, in other words, it is represented by several dust fractions with different stopping times. We have presented formulas for the computation of the gas and dust velocities when the dust has $N$ fractions, each of which exchanges momentum with the gas; these formulas require $O(N^2)$ arithmetic operations at each time step. | 18 | 8 | 1808.02867 |
1808 | 1808.05992_arXiv.txt | It has been suggested that the accretion-induced collapse (AIC) of an oxygen-neon white dwarf (ONe WD) to a neutron star is a theoretically predicted outcome in stellar evolution, likely relating to the formation of some neutron star systems. However, the progenitor models of AIC events are still not well studied, and recent studies indicated that CO WD+He star systems may also contribute to the formation of neutron star systems through AIC process when off-centre carbon ignition happens on the surface of the CO WD. In this work, I studied the single-degenerate (SD) model of AIC events in a systematic way, including the contribution of the CO WD+He star channel and the ONe WD+MS/RG/He star channels. Firstly, I gave the initial parameter space of these SD channels for producing AIC events in the orbital period--secondary mass plane based on detailed binary evolution computations. Then, according to a binary population synthesis approach, I gave the rates and delay times of AIC events for these SD channels based on their initial parameter space. I found that the rates of AIC events in our galaxy are in the range of $\sim0.3-0.9\times10^{-3}$\,yr$^{-1}$, and that their delay times are $>$30\,Myr. I also found that the ONe WD+He star channel is the main way to produce AIC events, and that the CO WD+He star channel cannot be ignored when studying the progenitors of AIC events. | Carbon-oxygen white dwarfs (CO WDs) in binaries are thought to produce type Ia supernovae (SNe) when they grow in mass close to the Chandrasekhar limit (${M}_{\rm Ch}$; e.g. Hachisu, Kato \& Nomoto 1996; Langer et al. 2000; Podsiadlowski 2010; Wang \& Han 2012; Maoz, Mannucci \& Nelemans 2014). However, oxygen-neon (ONe) WDs are expected to collapse into neutron stars through electron-capture reactions once they increase their masses to ${M}_{\rm Ch}$, in which the transformation from ONe WDs to neutron stars is referred as the process of accretion-induced collapse (AIC; see, e.g. Miyaji et al. 1980; Canal et al. 1990; Nomoto \& Kondo 1991). AIC events are a kind of electron-capture SNe, the remnants of which are neutron star systems (e.g. Miyaji et al. 1980). They are predicted to be very faint and fast, and thus difficult to observe; a small amount ($\sim$$10^{-3}\,{M}_\odot$) of $^{56}{\rm Ni}$ synthesized during collapse indicates that AIC events are relatively dim optical transients (e.g. Woosley \& Baron 1992; Dessart et al. 2006). Piro \& Thompson (2014) suggested that the resulting optical transient is considerably fainter than that of a typical type Ia SN (by 5 mag or more) and lasts for a few days to a week. AIC may be a viable and promising way to form some troublesome neutron star systems that are difficult to be explained by type II core-collapse SNe (see Canal, Isern \& Labay 1990 for a review). For example, low-/intermediate-mass X-ray binaries (e.g. van den Heuvel 1984; Podsiadlowski, Rappaport \& Pfahl 2002), low-/intermediate-mass binary pulsars (e.g. Nomoto \& Kondo 1991; Tauris, Langer \& Kramer 2012; Liu et al. 2018a), and millisecond binary pulsars if they are later spun up by mass accretion (e.g. van den Heuvel 1984; Bailyn \& Grindlay 1990; Bhattacharya \& Van den Heuvel 1991; Chen et al. 2011; Tauris et al. 2013; Freire \& Tauris 2014). AIC events have been proposed as a possible source of r-process elements (e.g. Wheeler, Cowan \& Hillebrandt 1998; Fryer et al. 1999; Qian \& Wasserburg 2007) and a source of gravitational wave emission (e.g. Abdikamalov et al. 2010). They might also relate to the formation of rapidly spinning magnetars, fast radio bursts and ultra high-energy cosmic rays like gamma-ray bursts (e.g. Dar et al. 1992; Usov 1992; Piro \& Kollmeier 2016; Lyutikov \& Toonen 2017; Cao, Yu \& Zhou 2018). Moriya (2016) recently argued that gravitational waves from AIC events may be accompanied by radio-bright optically faint (possibly X-ray-bright) transients, which can be used to verify the AIC origin of the observed gravitational waves. Although the potential importance of AIC, there has been no reported direct detection for such events and it is still unclear about their progenitor models. Over the past few decades, two classic kinds of progenitor models of AIC events have been proposed, that is, the single-degenerate (SD) model and the double-degenerate (DD) model. For the SD model, an ONe WD accretes H-/He-rich material from its non-degenerate companion that could be a main-sequence or a slightly evolved star (the ONe WD+MS channel), a red-giant star (the ONe WD+RG channel), or a He star (the ONe WD+He star channel). The accreted material will burn into O and Ne, and accumulate onto the surface of the ONe WD. AIC may occur when the ONe WD increases its mass close to ${M}_{\rm Ch}$ (e.g. Nomoto \& Kondo 1991; Tauris et al. 2013; Brooks et al. 2017; Wu \& Wang 2018; Ruiter et al. 2018). For the DD model, it involves the merger of two WDs with a combined mass larger than ${M}_{\rm Ch}$, the merging of which results from the gravitational wave emission (e.g. Webbink 1984; Iben \& Tutukov 1984; Yoon, Podsiadlowski \& Rosswog 2007; Ruiter et al. 2018). Previous studies on the SD model of AIC events mainly involve the ONe WD accretors. Yungelson \& Livio (1998) suggested that the expected AIC rate is no more than 1\% of that of SNe Ia. Tauris et al. (2013) investigated the binary computations of ONe WD+MS/RG/He star systems that may experience AIC and then be recycled to produce binary pulsars. Although these ONe WD binary systems have been investigated by Tauris et al. (2013), they only considered the case with the initial ONe WD mass of $1.2\,M_{\odot}$. Additionally, recent studies suggested that CO WD+He star systems may also contribute to the formation of neutron star systems through AIC process when the off-centre carbon ignition occurs on the surface of the CO WD (e.g. Brooks et al. 2016; Wang, Podsiadlowski \& Han 2017).\footnote{The CO WD accretors with He donor stars are thought to be one of the promising ways to form the observed type Ia SNe in young populations (e.g. Wang et al. 2009; Ruiter, Belczynski \& Fryer 2009).} Wang, Podsiadlowski \& Han (2017) recently found that off-centre carbon burning happens on the surface of the WD if the mass-accretion rate is above a critical value ($\sim$$2.05\times 10^{-6}\,{M}_\odot\,\mbox{yr}^{-1}$). Off-centre carbon burning will convert CO WDs to ONe WDs through an inward-propagating carbon flame, resulting in the formation of neutron stars through AIC process if the mass-transfer continues (e.g. Saio \& Nomoto 1985, 1998; Nomoto \& Iben 1985; Schwab, Quataert \& Kasen 2016; Brooks et al. 2016, 2017). Note that off-centre carbon burning provides an alternative way to form neutron stars, which will increase the rates of AIC events (see also Brooks et al. 2017). Studies of the AIC event rate using binary population synthesis (BPS) should include all of these SD channels, especially the CO WD+He star channel that has been previously neglected. In this work, I will study the SD model of AIC events in a systematic way, including the contribution of the CO WD+He star channel and the ONe WD+MS/RG/He star channels. I introduce the basic assumptions and methods for binary evolution computations, and give the initial parameter space of AIC events for the CO WD+He star channel in Section 2 and the ONe WD+MS/RG/He star channels in Section 3. In Section 4, I show the BPS methods and the corresponding results. Finally, a discussion is given in Section 5 and a summary in Section 6. | AIC has been suggested as a natural theoretical final fate for ONe WDs once their masses approach ${M}_{\rm Ch}$. However, the final outcome of accreting ONe WDs is sill under debate. Jones et al. (2016) found that the deflagration of oxygen could happen in the degenerate ONe cores, leading to the formation of a subpopulation of type Ia SNe (see also Miyaji et al. 1980; Isern, Canal \& Labay 1991). However, Wu \& Wang (2018) recently found that the final outcome of accreting ONe WDs is electron-capture induced collapse rather than thermonuclear explosion though different initial ONe WD masses and mass-accretion rates could affect the evolution of central density and temperature; the central temperature of the accreting ONe WDs cannot reach the explosive oxygen or neon ignition temperature due to neutrino cooling, resulting in the formation of neutron stars finally (see also Schwab, Quataert \& Bildsten 2015; Brooks et al. 2017). Tauris et al. (2013) studied the binary evolution of ONe WD$+$MS/RG/He star systems that may experience AIC and then be recycled to form binary pulsars. However, they only provided a parameter space of these ONe WD binary systems for producing AIC events with $M^{\rm i}_{\rm ONe}=1.2\,\rm M_{\odot}$. Compared with the results of Tauris et al. (2013), the initial parameter space in the present work has more massive donor stars and longer orbital periods. In the work of Tauris et al. (2013), they assumed that CE will be formed if $\dot{M}_{\rm 2}$ is larger than a critical value (i.e. three times of Eddington mass-accretion rate). As Tauris et al. (2013) pointed out, the critical value they adopted may be the largest uncertainties in their calculations. In the SD model, the progenitors of AIC events could be CO WD+He star systems or ONe WD binary systems. CO WD+He star systems could produce neutron star+He star systems if AIC happens, in which neutron stars may be recycled when the He stars refill their Roche lobe, resulting in the formation of intermediate-mass binary pulsars finally. ONe WD binary systems will evolve to some different neutron star systems if AIC occurs, depending on star types of their mass donors, as follows: (1) The ONe WD$+$MS systems may experience AIC and evolve to form fully recycled millisecond binary pulsars with He WD companions (e.g. Tauris et al. 2013; Ablimit \& Li 2015). (2) The ONe WD$+$RG systems are more likely to form intermediate-mass binary pulsars, including mildly recycled pulsars and CO/ONe WD companions with long orbital periods (e.g. Tauris et al. 2013). (3) The ONe WD$+$He star systems may experience AIC and eventually form intermediate-mass binary pulsars with short orbital periods (e.g. Liu et al. 2018a). A number of WD binaries are known to be possible candidates for the SD progenitors of AIC events. The most relevant known binary system to the present work is perhaps HD 49798 with its WD companion. HD 49798 is a hydrogen stripped subdwarf O6 star (1.50$\pm$0.05$\,M_{\odot}$) that has an X-ray pulsating companion RX J0648.0$-$4418 (1.28$\pm$0.05$\,M_{\odot}$) with an orbital period of 1.548\,d, but the nature of the compact companion is still under debate (e.g. Thackeray 1970; Bisscheroux et al. 1997; Mereghetti et al. 2009, 2016; Liu et al. 2015, 2018a; Popov et al. 2018). By analyzing the angular momentum and magnetic field, Mereghetti et al. (2016) argued that the X-ray pulsating companion of HD 49798 is likely a neutron star (see also Brooks, Kupfer \& Bildsten 2017). However, the large emitting radius ($\sim$40\,km) obtained from the black body spectral is still puzzling. Popov et al. (2018) recently suggested that the contraction of a young WD can well explain the continuous stable spin-up of the compact companion. Liu et al. (2018a) also suggested that the companion of HD 49798 may be a WD but not a neutron star based on binary evolution computations. Assuming the companion of HD 49798 is a CO WD, Wang \& Han (2010b) found that the massive WD can grow in mass to ${M}_{\rm Ch}$ after about $6\times10^{4}$\,yr based on detailed binary evolution computations. In this binary, off-centre carbon burning will happen when the WD increases its mass close to ${M}_{\rm Ch}$ due to the high $\dot{M}_{\rm 2}$ ($>$$2.05\times 10^{-6}\,{M}_\odot\,\mbox{yr}^{-1}$; see Wang \& Han 2010b). Thus, I speculate that the massive WD in this binary may eventually form a neutron star through AIC and but not a type Ia SN. In addition, U Sco, TCrB and RS Oph contain massive WDs that are already close to ${M}_{\rm Ch}$, which are possible progenitor candidates of AIC events (e.g. Hachisu, Kato \& Nomoto 1999; Parthasarathy et al. 2007). U Sco is a recurrent nova, including a $1.55\pm0.24\,M_{\odot}$ WD and a $0.88\pm0.17\,M_{\odot}$ MS donor with an orbital period of $\sim1.23$\,d (e.g. Thoroughgood et al. 2001). Mason (2011) suggested that the WD in U Sco may be an ONe WD based on spectroscopic observations, and thus its final fate may collapse into a neutron star but not a type Ia SN. Note that Mason (2013) rectified her conclusion in the erratum and concluded that there is no evidence on neon overabundance in the ejecta of U Sco (see also Miko\l{}ajewska \& Shara 2017). T CrB is a symbiotic system, including a $\sim$$1.2\,M_\odot$ WD and a $\sim$$0.7\,M_\odot$ RG star with an orbital period of $\sim$227\,d (e.g. Belczy$\acute{\rm n}$ski \& Miko\l{}ajewska 1998). RS Oph is a symbiotic system, including a 1.2$-$$1.4\,M_\odot$ WD and a 0.68$-$$0.8\,M_\odot$ RG star with an orbital period of $\sim$454\,d (e.g. Brandi et al. 2009). However, it is still unclear whether the WD in T CrB and RS Oph is a CO WD or an ONe WD. Miko\l{}ajewska \& Shara (2017) recently argued that the WD in RS Oph may be a CO WD by analyzing its spectra, making it a likely progenitor candidate of type Ia SNe. In order to confirm the existence of AIC process, it is important to understand electromagnetic signatures of AIC events and to identify them in transient surveys. Piro \& Thompson (2014) suggested that a particularly strong signature of an AIC event would occur for an ONe WD that accretes material from a RG star. In such cases, the $\sim$$10^{50}$\,erg explosion from the AIC collides with the surface of the RG companion, creating an X-ray flash lasting $\sim$1\,hr followed by an optical signature of AIC. Piro \& Thompson (2014) argued that the strongest signal of the optical and X-ray emission will come directly from the shocked region though the strength of the signal would be strongly dependent on the viewing angle. Moriya (2016) suggested that the AIC radio transients originated from SD systems may be detected in future radio transient surveys such as the Square Kilometer Array transient survey and the Very Large Array Sky Survey. Future observational surveys may finally detect such events like AIC events with low luminosities (e.g. Piro \& Thompson 2014). | 18 | 8 | 1808.05992 |
1808 | 1808.00579_arXiv.txt | One-dimensional (vertical) models of planetary atmospheres typically balance the net solar and internal energy fluxes against the net thermal radiative and convective heat fluxes to determine an equilibrium thermal structure. Thus, simple models of shortwave and longwave radiative transport can provide insight into key processes operating within planetary atmospheres. Here, we develop a simple, analytic expression for both the downwelling thermal and net thermal radiative fluxes in a planetary troposphere. We assume that the atmosphere is non-scattering at thermal wavelengths and that opacities are grey at these same wavelengths. Additionally, we adopt an atmospheric thermal structure that follows a modified dry adiabat as well as a physically-motivated power-law relationship between grey thermal optical depth and atmospheric pressure. To verify the accuracy of our analytic treatment, we compare our model to more sophisticated ``full physics'' tools as applied to Venus, Earth, and a cloudfree Jupiter, thereby exploring a diversity of atmospheric conditions conditions. Next, we seek to better understand our analytic model by exploring how thermal radiative flux profiles respond to variations in key physical parameters, such as the total grey thermal optical depth of the atmosphere. Using energy balance arguments, we derive convective flux profiles for the tropospheres of all Solar System worlds with thick atmospheres, and propose a scaling that enables inter-comparison of these profiles. Lastly, we use our analytic treatment to discuss the validity of other simple models of convective fluxes in planetary atmospheres. Our new expressions build on decades of analytic modeling exercises in planetary atmospheres, and further prove the utility of simple, generalized tools in comparative planetology studies. | The thermal structure of a planetary atmosphere is determined via complex energy and mass exchanges in radiative, advective, and diffusive processes. One-dimensional (vertical) models of planetary atmospheres seek to explain how radiative processes and the vertical convective transport of heat and condensible species combine to establish the average atmospheric structure of a world. In these one-dimensional planetary climate models, treatments of radiative transport vary in complexity. The most sophisticated radiation tools operate at high spectral resolution \citep{wordsworthetal2017} with full physics treatments of scattering processes \citep{robinson&crisp2018}, or may adopt lower-resolution correlated-$k$ techniques \citep{goodyetal1989,lacis&oinas1991}. Alternatively, the simplest models may use a semi-grey two-stream approach \citep[e.g.,][]{mckayetal99}. Similarly, sophisticated treatments of convective transport can range from applications of planetary boundary layer physics \citep{mellor&yamada1974} to mixing length models \citep[e.g.,][]{gierasch&goody1968}. Less-complex tools apply the relatively straightforward ``convective adjustment'' approach \citep{manabe&strickler1964}. Many of these topics are discussed in a recent review by \citet{marley&robinson2015}. Semi-grey, windowed-grey, and banded-grey radiative transfer techniques have a long history of application to planetary atmospheres \citep{robinson2015}. Semi-grey or windowed-grey radiative transfer models have been used to explore the climate of modern and ancient Earth \citep{hart78,weaver&ramanathan1995,friersonetal2006,pelkowskietal2008}. Similar semi-grey radiative approaches have been applied to studies of both the one-dimensional and three-dimensional structure of Titan's atmosphere \citep{mckayetal99,mitchelletal2006}, as well as to runaway greenhouse worlds \citep{nakajimaetal1992}. Beyond the Solar System, the limited atmospheric data available combined with the explosion of interest in exoplanets has driven the need for simple parameterized \citep{madhusudhan&seager2009} or physically-based \citep{hubenyetal2003,hansen2008} atmospheric thermal structure models. Building on the semi-grey radiative equilibrium solution applied to hot Jupiter exoplanets in \citet{guillot2010}, \citet{parmentier&guillot2014} developed a banded-grey ``picket fence'' radiative equilibrium model that can better reproduce the structure of hot Jupiter stratospheres \citep{parmentieretal2015}, where semi-grey radiative equilibrium models tend to overestimate atmospheric temperatures \citep[see explanation in][their Section 4.7]{pierrehumbert2011}. \citet{hengetal2012} extensively investigated the application of semi-grey radiative equilibrium models to hot Jupiter atmospheres, and these concepts have subsequently been adapted to include scattering \citep{hengetal2014} and ``picket fence'' thermal opacities \citep{mohandasetal2018}. Markedly fewer studies have combined grey radiative transfer techniques with treatments of convection. This may seem striking as convection is known to be critical to driving vertical transport, and can be related to effective upwelling windspeeds in planetary tropospheres \citep{gierasch&conrath1985}. In a pair of early examples, \citet{sagan1969} and \citet{weaver&ramanathan1995} investigated the onset of convective instability in semi-grey and windowed-grey atmospheres. More recently, \citet{ozawa&ohmura1997} \citep[and also][]{wu&liu2010,herbertetal2013} used a semi-grey radiative transfer model to derive convective fluxes for Earth-like conditions under the ``maximum entropy production'' principle, wherein convective energy transport is postulated to maximize the local entropy production rate. Indeed, \citet{ozawa&ohmura1997} showed that temperature profiles computed using the maximum entropy production principle were less steep and had lower surface temperatures than pure radiative equilibrium solutions, thus reproducing behaviors seen in models that adopt other treatments of convection \citep[e.g.,][]{manabe&strickler1964}. \citet{lorenz&mckay2003} used semi-grey radiative transport expressions to heuristically arrive at an analytic expression for the convective flux at a planetary surface, and showed that this expression could reproduce the convective fluxes computed by more complex models. Finally, \citet{robinson&catling2012} produced analytic expressions for the thermal structure of a planetary atmosphere with a semi-grey radiative stratosphere overlying a convective troposphere whose structure follows a modified dry adiabat. These authors used this tool to understand the physics behind a common 0.1~bar tropopause pressure seen throughout the Solar System \citep{robinson&catling2014}. In what follows, we extend the \citet{robinson&catling2012} model to include an analytic treatment of downwelling thermal radiative fluxes in a semi-grey atmosphere that includes a convective troposphere, and also introduce more realistic lower boundary conditions to a previous solution for the upwelling thermal radiative flux. Taken together, these expressions for the upwelling and downwelling thermal radiative fluxes yield straightforward, physically-based expressions for both the net thermal flux and the convective heat flux in planetary tropospheres. We validate our net thermal flux treatment against more sophisticated climate and radiative transfer models, and we apply our derived convective heat flux profiles to compare Solar System worlds. Finally, we use our new model to comment on the maximum entropy production approach explored by \citet{ozawa&ohmura1997} and on the heuristic convective flux expression given by \citet{lorenz&mckay2003}. | Net thermal and convective energy fluxes are critically important to determining atmospheric thermal structure, especially in one-dimensional (vertical) planetary climate models. We derive a simple expression for the net downwelling thermal radiative flux in a planetary troposphere where the relationships between temperature, pressure, and optical depth are all expressed as power-laws. When combined with previous results, our new treatment yields an analytic expression for the net thermal radiative flux in a convective planetary troposphere. For appropriate, physically-based input parameters, our analytic net thermal radiative flux expression reproduces results from more-sophisticated, spectrally-resolved models applied to Earth, Venus, and a cloudfree Jupiter. Application of our model across the Solar System demonstrates common shapes and scalings in the convective flux profiles of Earth, Jupiter, Saturn, Uranus, and Neptune. Further applications of our model sheds new light on both ``maximum entropy production'' principles as well as other simple treatments of convection. Simple models remain an excellent tool for inter-comparing processes in planetary atmospheres both within and beyond the Solar System. \ack TDR is supported by an award from the NASA Exoplanets Research Program (\#80NSSC18K0349) and by the NASA Astrobiology Institute's Virtual Planetary Laboratory under Cooperative Agreement \#NNA13AA93A. JPT is supported by the National Science Foundation's Research Experience for Undergraduates program through the CAMPARE program directed out of California State Polytechnic University, Pomona. \label{lastpage} | 18 | 8 | 1808.00579 |
1808 | 1808.09458_arXiv.txt | {First-ascent red giants in the approximate mass range $0.7\lesssim M/M_\odot\lesssim 2$ ignite helium in their degenerate core as a flash. Stellar evolution codes predict that the He flash consists of a series of consecutive subflashes. Observational evidence of the existence of the He flash and subflashes is lacking. The detection of mixed modes in red giants from space missions \corot\ and \kepler\ has opened new opportunities to search for such evidence.} {During a subflash, the He burning shell is convective, which splits the cavity of gravity modes in two. We here investigate how this additional cavity modifies the oscillation spectrum of the star. We also address the question of the detectability of the modes, to determine whether they could be used to seismically identify red giants passing through the He flash.} {We calculate the asymptotic mode frequencies of stellar models going through a He subflash using the JWKB approximation. To predict the detectability of the modes, we estimate their expected heights, taking into account the effects of radiative damping in the core. Our results are then compared to the oscillation spectra obtained by calculating numerically the mode frequencies during a He subflash.} {We show that during a He subflash, the detectable oscillation spectrum mainly consists of modes trapped in the acoustic cavity and in the outer g-mode cavity. The spectrum should thus at first sight resemble that of a core-helium-burning giant. However, we find a list of clear, detectable features that could enable us to identify red giants passing through a He subflash. In particular, during a He subflash, several modes that are trapped in the innermost g-mode cavity are expected to be detectable. We show that these modes could be identified by their frequencies or by their rotational splittings. Other features, such as the measured period spacing of gravity modes or the location of the H-burning shell within the g-mode cavity could also be used to identify stars going through a He subflash.} {The features derived in this study can now be searched for in the large datasets provided by the \corot\ and \kepler\ missions.} | } Stars in the mass range $0.7\lesssim M/M_\odot\lesssim 2$ ignite He in their core under conditions of strong electron degeneracy, which results in a thermal runaway known as the He core flash. The basic features of the He core flash have been known since numerical models of stellar evolution were followed from the tip of the red giant branch to the core He burning phase (\citealt{harm64}, \citealt{thomas67}). It is well established that He is ignited off-center, in the layers of maximal temperature, because of the energy carried away by neutrinos in the center of the star. Instead of expanding and cooling, these layers are further heated owing to the degeneracy of electrons, which results in a thermal runaway. The localized heating leads to superadiabatic gradients and to the onset of convection in the He-burning layers. The rapid increase in temperature eventually removes the electron degeneracy. Initial hydrodynamic calculations of the He core flash found that it should induce a disruption of the star (\citealt{edwards69}, \citealt{deupree84}), while more modern 2D- and 3D-simulations have shown that the flash does not produce a hydrodynamical event (\citealt{deupree96}, \citealt{mocak08}, \citealt{mocak09}). One critical question is the time it takes for He burning to reach the center of the star. 1D evolutionary models predict that after the peak of the He flash, electron degeneracy is locally removed in the shell where He was ignited. The layers below remain inert and degenerate until the heat produced by the first He flash diffuses inward. Electron degeneracy is then removed in the inner layers through a series of weaker secondary He flashes occurring closer and closer to the stellar center (\citealt{thomas67}, \citealt{iben84}, \citealt{bildsten12}). The duration of the phase of successive He subflashes is determined by the timescale over which thermal diffusion operates inward after each subflash. It was found to be of the order of 2 Myr (\citealt{bildsten12}), which represents a non-negligible fraction of the duration of the phase of quiet He core burning ($\sim$ 100 Myr). The existence of these subflashes has been questioned by 2D- and 3D-simulations of the He core flash (\citealt{mocak08}, \citealt{mocak09}). These studies suggest that the convective region that develops as a result of He burning rapidly extends inward, potentially reaching the center of the star on a timescale of about a month. Degeneracy would then be lifted in the core without the occurrence of He subflashes. So far, no observational evidence was obtained of any star going through the He-flash or the subsequent subflashes. If the He flash consists in a series of subflashes, the odds of observing a star in this phase are much higher than if it is a single event, as suggested by 2D- and 3D-simulations. Asteroseismology could then be very helpful to identify stars during the He flash. Indeed, red giants are known to stochastically excite non-radial mixed modes in their convective envelopes. These modes behave as gravity (g) modes in the core, and as pressure (p) modes in the envelope. The exceptional diagnostic potential of these modes has been known since they were found in stellar models (\citealt{dziembowski71}, \citealt{scuflaire74}, \citealt{osaki75}). With the advent of space missions \corot\ (\citealt{baglin06}) and \kepler\ (\citealt{borucki10}), mixed modes were detected in thousands of subgiants (\citealt{deheuvels10}, \citealt{deheuvels11}, \citealt{campante11}) and red giants (\citealt{bedding11}, \citealt{mosser11}). Among other applications, mixed modes can be used to measure the nearly constant period spacing $\Delta\Pi$ of high-radial-order dipolar g modes (\citealt{bedding11}, \citealt{mosser11}, \citealt{vrard16}), which depends on the fine structure of the deep core. It has been shown that He core burning giants (belonging to the so-called red clump), which have convective cores, have distinctly larger $\Delta\Pi$ than H-shell burning giants (first-ascent red giants), whose cores are radiative. This has been used as a powerful tool to distinguish the two populations (\citealt{bedding11}, \citealt{mosser11}). \cite{bildsten12} argued that the period spacings of g modes could also be used to identify red giants in the phases between He subflashes. Indeed, in the aftermath of a He subflash, the core structure is close to that of a star on the red giant branch (RGB), but the subflash leaves an imprint that significantly modifies the period spacing of g modes. \cite{bildsten12} thus found that stars between two subflashes have values of $\Delta\Pi$ intermediate between those of RGB stars and those of He core burning giants. In this paper, we investigate the oscillation spectrum of red giants \textit{during} the He subflashes. As mentioned above, during a subflash, the layers in which He is ignited become convective, owing to the heating that the nuclear reactions produce. Consequently, gravity waves become evanescent in the He-burning layers. The g-mode cavity is thus split into two distinct cavities that are separated by the He-burning shell. During a subflash, the star has three different cavities: two internal g-mode cavities and the external p-mode cavity. The oscillation spectrum is thus expected to be altered compared to other phases (i) because the shape of the cavities is modified, and (ii) because of the additional g-mode cavity. We here investigate whether this can be used to identify red giants undergoing a He subflash. Detecting a star in this phase would provide direct evidence of the existence of He subflashes and give us valuable insight on this poorly known event of stellar evolution. In Sect. \ref{sect_1Dmodel}, we show that if He subflashes exist, several tens of red giants are expected to be in the process of a subflash among the $\sim$ 15,000 red giants for which the \kepler\ satellite (\citealt{borucki10}) has detected oscillations. The special case of three mode cavities inside a star has not been addressed so far. One can expect that it leads to complex oscillation spectra, whose interpretation can be complicated. In Sect. \ref{sect_JWKB}, we calculate the asymptotic mode frequencies in the case of three cavities using the JWKB approximation. We use these analytic calculations to predict the oscillation spectrum of red giants undergoing a He subflash. In Sect. \ref{sect_numerical}, we calculate numerically the oscillation spectra of stellar models during a He subflash and we compare the results to the predictions of the asymptotic mode frequencies. This leads us to propose ways of seismically identify red giants going through a He subflash in Sect. \ref{sect_discussion}. | } In this paper, we showed that red giants undergoing He core subflashes could be identified using the properties of their oscillation mode frequencies. During a He subflash, red giants have three propagating cavities because the convective He-burning shell splits the g-mode cavity in two. We calculated the expected mode frequencies in this case using both an asymptotic analysis and full numerical computations. We further estimated the expected mode heights taking into account the effects of radiative damping in order to determine which oscillation modes could be detected in \kepler\ seismic data. If the \kepler\ sample does contain red giants that are undergoing a He subflash, these stars must have been so far identified as core-helium burning giants, considering the resemblance of their oscillation spectra. However, we have obtained in this study a list of clear, detectable features that could enable us to identify red giants passing through a He subflash. These features can be summarized as follows \paragraph{Asymptotic period spacing between He subflashes} \cite{bildsten12} showed that the asymptotic period spacings of g modes in the aftermath of a He subflash are significantly larger than those of RGB stars and much smaller than those of red clump stars (see also Fig. \ref{fig_deltapi_q}, top panel). \paragraph{Asymptotic period spacing of the \gdeux-cavity during a He subflash} We showed in Sect. \ref{sect_deltapi_JWKB} that during the first part of a He subflash, the asymptotic period spacing of the \gdeux-cavity also lies in the ``period spacing desert'' between RGB and red clump stars. As we have shown, most of the \gdeux-dominated modes should have detectable heights in the oscillation spectra of red giants going through a subflash, so that the asymptotic period spacing $\Delta\Pi_2$ should be easy to measure observationally. This could therefore constitute a way of identifying red giants undergoing a He subflash. However, the shortness of the period during which $\Delta\Pi_2$ is significantly below the lowest period spacings of red clump stars makes this type of detection rather unlikely. \paragraph{Buoyancy radius of the H-burning shell} We have shown that the signature of the glitch produced by the H-burning shell in the \gdeux-cavity should be clearly detectable in the oscillation spectrum of red giants undergoing a He subflash (see Sect. \ref{sect_glitch}). It causes the periods of \gdeux-dominated modes to oscillate as a function of the radial order (see Fig. \ref{fig_echelle_adipls} and \ref{echelle_stretch_adipls}), and the period of this oscillation can be used to estimate the buoyancy radius of the H-burning shell in the \gdeux-cavity (see Eq. \ref{eq_period_osc}). During the He subflash, we found that the buoyancy radius of the H-burning shell corresponds to 82\% of the total buoyancy radius of the \gdeux-cavity, which results in an oscillation with a period of $\Delta n \sim 6$. By contrast, during the clump phase, the buoyancy radius of the H-burning shell amounts to about 70\% of the buoyancy radius of the g-mode cavity. This corresponds to an oscillation with a period of $\Delta n \sim 3$ for the g modes, which is significantly different from what was obtained during a He subflash. We thus conclude that the period of the oscillation produced by the H-burning shell could be used as a means to separate red giants undergoing a He subflash from regular clump stars. \paragraph{Detection of additional modes trapped in the \gun-cavity} Based on our study, we expect to detect mostly \gdeux- and p-dominated modes during a He subflash. Consequently, the oscillation spectrum of a red giant going through a He subflash should be quite similar to that of a regular clump star with an asymptotic period spacing corresponding to $\Delta\Pi_2$. However, during the most part of the subflash, several \gun-dominated mixed modes are also expected to have detectable heights in the power spectrum. These modes could appear as anomalies in the oscillation spectrum of red giants identified as belonging to the red clump. If the coupling $q_1$ between the g-mode cavities is large enough, the frequencies of the detectable \gun-dominated modes significantly deviate from the pattern of the \gdeux- and p-dominated modes. In this case, representing the oscillation modes in a stretched \'echelle diagram would enable us to directly spot these additional modes (see bottom right panel of Fig. \ref{fig_echelle_ratio} and right panel of Fig. \ref{echelle_stretch_adipls}). This seems to be an efficient way of identifying stars in a He subflash. However, we found that $q_1$ becomes strong enough to make this type of detection possible only at the end of a He subflash. The probability of detecting a red giant in this specific phase remains low. We should also mention the caveat that additional modes can also be produced by structural glitches in certain conditions (\citealt{cunha15}). Although we did not find such effects in the stellar models that were computed in this study, this should be kept in mind when searching for red giants going through the He flash using seismology. \paragraph{Detection of anomalous rotational splittings} In the case of weaker coupling intensities $q_1$, the detectable \gun-dominated modes are not expected to show significant deviations from the pattern of the \gdeux- and p-dominated modes (see middle panels of Fig. \ref{echelle_stretch_adipls}). However, for several of the detectable mixed modes, the \gun-cavity contributes to more than half of the inertia. One important consequence is that these modes are predominantly sensitive to the rotation in the \gun-cavity. Predicting the rotation profile of red giants during the He-core flash would require to determine (i) the internal rotation profile of red giants at the tip of the RGB (which is unknown because seismology has brought measurements of the rotation of RGB stars no further than the luminosity bump), (ii) the structural changes during the He-flash (expansion of the layers below the H-burning shell by about a factor of 10 and contraction of the layers above), and (iii) the internal transport of angular momentum during this phase, which is completely unknown. The structural changes during the flash induce a strong forcing of radial differential rotation between the layers below the H-burning shell and those above. Unless the redistribution of angular momentum is efficient enough to enforce a solid-body rotation during the flash despite the shortness of this phase, one expects to have a different rotation rate below and above the H-burning shell. If it is indeed the case, then the average rotation in the \gdeux-mode cavity (which includes the H-burning shell) is expected to be different from the rotation in the \gun-cavity, which lies well below the H-burning shell. It is thus plausible that \gun-dominated modes have rotational splittings that differ from those of the \gdeux-dominated modes. This could be used to identify \gun-dominated modes in the oscillation spectra. As mentioned above, the internal rotation profiles of red giants during the He flash are completely unknown. We only know from \cite{mosser12b} that the core of primary clump stars spins with an average frequency of about 100 nHz. In order to roughly assess the sensitivity of the diagnostic that we propose here, we considered a piecewise-constant rotation profile with the \gdeux-cavity spinning at a rotation rate $\Omega_{\rm g_2} = 100$ nHz, the p-mode cavity rotating at $\Omega_{\rm p} = 10$ nHz (this value is completely arbitrary, but it does not impact our conclusions), and the \gun-cavity rotating only 50\% faster than the \gdeux-cavity, i.e. $\Omega_{\rm g_1} = 150$ nHz. We calculated the rotational kernels of model 1ov and combined them with the chosen rotation profile to calculate theoretical rotational splittings, which are shown in Fig. \ref{fig_splitting}. As can be seen in Fig. \ref{fig_splitting}, the splittings of \gdeux- and p-dominated modes vary smoothly with frequency\footnote{In the case of two mode cavities, it has been shown that the variations in the rotational splittings with frequency correspond to the so-called $\zeta$ function (see \citealt{mosser15} for more details).}, while modes that have a non-negligible contribution of the \gun-cavity to their inertia have rotational splittings that clearly deviate from this relation. With the chosen rotation profile, the splittings of pure \gun\ modes would be approximately $\Omega_{\rm g_1}/2 = 75$ nHz (see e.g. \citealt{goupil13}), a value which is nearly reached by the most \gun-dominated modes (see Fig. \ref{fig_splitting}). This represents a 25-nHz difference with the splittings of \gdeux-dominated modes. With four years of \kepler\ data, the expected precision on the measured splittings is about 10 nHz, so that \gun-dominated would have significantly larger rotational splittings in the observed spectrum. Red giants going through a He subflash could thus be characterized by the detection of mixed dipolar modes with rotational splittings that are significantly different from those of the \gdeux- and p-dominated modes, which follow a well-understood pattern (\citealt{mosser15}). \\ \begin{figure} \begin{center} \includegraphics[width=9cm]{splitting_1.7M_flash2_diff.ps} \end{center} \caption{Rotational splittings obtained for model 1ov, assuming a piecewise-constant rotation profile with $\Omega_{\rm g_1} = 150$ nHz, $\Omega_{\rm g_2} = 100$ nHz, and $\Omega_{\rm p} = 10$ nHz (see text). Modes that are trapped mainly in the \gun-cavity (resp. \gdeux-cavity) are shown as red (resp. blue) filled circles. The size of the circles indicates the expected height of each mode in the observed spectrum. Only the modes with a height corresponding to at least 10\% of the height of a pure p mode are shown. The vertical dashed lines indicate the location of theoretical pure p modes. \label{fig_splitting}} \end{figure} These features can already be searched for within the catalog of about 15,000 \kepler\ red giants for which oscillations have been detected. The seismic detection of He flashing giants would nicely confirm the existence of the He-core subflashes predicted by 1D evolutionary models and exclude the picture based on 2D- and 3D-simulations claiming no occurence of a series of subflashes (\citealt{mocak08}, \citealt{mocak09}). If rotational splittings can be detected for mixed modes trapped mainly in the inner g-mode cavity during a He-subflash, we could also measure the differential rotation within the core of the star. This would place precious constraints on the transport of angular momentum in red giants. Finally, we stress that the detection of the seismic features of the He subflashes depends a lot on the intensity of the coupling between the two g-mode cavities, which remains uncertain. Consequently, even if these features fail to be detected with \kepler\ data, it would not necessarily exclude the picture of the He flash based on 1D evolutionary models. | 18 | 8 | 1808.09458 |
1808 | 1808.00053_arXiv.txt | The search for exoplanets has encompassed a broad range of stellar environments, from single stars in the solar neighborhood to multiple stars and various open clusters. The stellar environment has a profound effect on planet formation and stability evolution and is thus a key component of exoplanetary studies. Dense stellar environments, such as those found in globular clusters, provide particularly strong constraints on sustainability of habitable planetary conditions. Here, we use Hubble Space Telescope observations of the core of the Omega Centauri cluster to derive fundamental parameters for the core stars. These parameters are used to calculate the extent of the Habitable Zone of the observed stars. We describe the distribution of Habitable Zones in the cluster and compare them with the stellar density and expected stellar encounter rate and cluster dynamics. We thus determine the effect of the stellar environment within the Omega Centauri core on the habitability of planets that reside within the cluster. Our results show that the distribution of Habitable Zone outer boundaries generally lie within 0.5~AU of the host stars, but that this small cross-sectional area is counter-balanced by a relatively high rate of stellar close encounters that would disrupt planetary orbits within the Habitable Zone of typical Omega Centauri stars. | \label{intro} Thus far, searches for exoplanets have primarily occurred around field stars, such as the exoplanet survey undertaken by the {\it Kepler} mission \citep{bor10}. The prospect of exoplanet detection in globular cluster environments is particularly enticing since they represent a relatively old stellar population and allow studies of how cluster dynamics influences planet formation and evolution \citep{fre06,sok07,spu09,dej12,por15,cai17}. A survey for transiting exoplanets among lower main-sequence (MS) stars in the globular cluster NGC~6397 by \citet{nas12} did not detect any significant exoplanet signatures. The primary target of exoplanet searches in globular clusters has been 47 Tucanae (47~Tuc). Observations of 34,000 stars in the 47~Tuc core by \citet{gil00} using the Hubble Space Telescope (HST) did not detect any transiting planets, despite predictions of almost 20 planet detections. Follow-up grand-based observations by \citet{wel05} in the uncrowded outer regions of 47~Tuc also did not detect transiting planets, indicating that the apparent lack of planets in the core may not be solely due to cluster dynamics. However, a recalculation by \citet{mas17} of the expected planet occurrence rates in 47~Tuc based on {\it Kepler} results determined that only a handful of planets detections should be expected, thus potentially reducing the statistical significance of the initial null result. Omega Centauri ($\omega$~Cen, NGC~5139) is a globular cluster that is also the possible remnant of a disrupted dwarf galaxy \citep{gne02,noy08}. As the largest globular cluster in the Milky Way galaxy, $\omega$~Cen provides an ideal stellar population for investigations concerning the interaction of radiation environments and stellar dynamics \citep{mer97,rei06,van06}. An additional advantage of studying cluster stars in the context of exoplanets is that they tend to have measured luminosities that enable the calculation of the Habitable Zone (HZ) for each of the stars \citep{kop13,kop14}. Such calculations in turn allow for the quantification of habitability within these dense cluster environments and thus direct the motivation of terrestrial exoplanet searches in globular clusters. Here we present an analysis of {\it HST} observations of the core of $\omega$~Cen and a calculation of HZs for the observed stars. In Section~\ref{hst} we outline the {\it HST} observations, including the calibration, passbands, and quantity of stars. Section~\ref{stellar} describes the methodology used to select MS stars and the derivation of stellar parameters. Section~\ref{hz} presents the calculations of the HZ for the stellar sample and discusses their distribution. The convolution of the HZ boundaries and the stellar dynamics is addressed in Section~\ref{dynamics}, taking into account the mean distance between stars and the rate of close stellar encounters. Section~\ref{implications} discusses the implications of the HZ calculations for potential habitability within $\omega$~Cen and how this is balanced by planetary orbit disruptions from the close encounter rate between stars. We finally provide concluding remarks in Section~\ref{conclusions}. | \label{conclusions} The $\omega$~Cen cluster is amongst the most studied objects in the sky and provides a unique opportunity to study large globular cluster dynamics as well as the effect on the local group. The {\it HST} observations of the core have been utilized here to fully explore the HZ distribution of the stars in that region and we have presented the first such calculations of HZs in an extremely high stellar density environment. The peak of the HZ distribution within 0.5~AU of the host stars is a consequence of the relatively aged population of stars in the cluster and is a positive aspect of the overall habitability environment in the $\omega$~Cen core. However, the compact nature of the HZ regions is more than offset by the potential disruption of planetary systems, where close encounters of only 0.5~AU are expected to occur on average every $1.65 \times 10^6$~years. Though the large resulting population of free-floating terrestrial planets are intrinsically interesting from formation and dynamical points of view, the potential for habitability in the $\omega$~Cen core environment is significantly reduced by such scattering events. The primary lesson that can be extracted from this analysis is the underlining of the importance of quantifying the long-term dynamical stability of orbits inside HZ regions taking into account both internal (planetary) dynamics and external (stellar) interactions. | 18 | 8 | 1808.00053 |
1808 | 1808.07673_arXiv.txt | Accurate and robust wavefront reconstruction methods for pyramid wavefront sensors are in high demand as these sensors are planned to be part of many instruments currently under development for ground based telescopes. The pyramid sensor relates the incoming wavefront and its measurements in a non-linear way. Nevertheless, almost all existing reconstruction algorithms are based on a linearization of the model. The assumption of a linear pyramid sensor response is justifiable in closed loop AO when the measured phase information is small but may not be reasonable in reality due to unpreventable errors depending on the system such as non common path aberrations. In order to solve the non-linear inverse problem of wavefront reconstruction from pyramid sensor data we introduce two new methods based on the non-linear Landweber and Landweber-Kaczmarz iteration. Using these algorithms we experience high-quality wavefront estimation especially for the non-modulated sensor by still keeping the numerical effort feasible for large-scale AO systems. | Time-varying optical perturbations introduced by the atmosphere severely degrade the image quality of ground based telescopes. Adaptive Optics (AO) systems correct these atmospheric aberrations in real-time \cite{Ha98,Roddier,Tyson00}: The facilities have devices incorporated that sense the incoming wavefronts and cancel the originated perturbations with a deformable mirror. Suitable mirror configurations are based on an accurate estimation of the shape of the incoming wavefront and can be calculated from wavefront sensor measurements. Reconstruction of the wavefront from sensor data is an inverse problem for which the underlying mathematical forward model depends on the type of the wavefront sensor (WFS). This paper is concerned with solving the inverse problem of wavefront reconstruction using a pyramid wavefront sensor. \bigskip More than twenty years ago, the pyramid wavefront sensor (PWFS) was proposed for the first time as a promising alternative to other types of wavefront measuring devices \cite{Raga96}. For the next generation of ground based Extremely Large Telescopes (ELTs), the pyramid sensor has been gaining attention from the scientific community by setting new standards for AO correction quality. Due to outstanding results recorded on existing observing facilities, the sensor is included as baseline for many instruments on ELTs such as ESO's Extremely Large Telescope, the Thirty Meter Telescope (TMT), and the Giant Magellan Telescope (GMT). Particularly for segmented ELT pupils, the pyramid sensor seems to be the wavefront sensor of choice \cite{Esposito_2003_SPIE_pwfs_cophasing, Esposito_2012_pwfs_NGS_SCAO_GMT,Hippler_2018,Surdej_Thesis}. \bigskip A focus lies in the development of wavefront reconstruction algorithms for the pyramid sensor based on theoretical investigations of the model as, e.g., in \cite{HuSha18_1,KoVe07,Shatokhina_PhDThesis,Veri04} accompanied by numerical simulations or laboratory studies on optical test benches \cite{Bond_2016,EsRiFe00,Martin_ao4elt4_pwfs_bench_on-sky,Pinna_2008_HOT_bench,RaFa99,Turbide_ao4elt3_pwfs_bench,Veran_ao4elt4_pwfs_vs_sh, Verinaud_2005_pwfs_vs_sh,Ragazzoni_ao4elt3_pwfs_lab}. On sky, the first single star AO loop was closed on AdOpt@TNG \cite{raga2000a} at the Telescopio Nazionale Galileo with a PWFS. In recent years, remarkable operational results have been reported at the $8$~m Large Binocular Telescope (LBT) \cite{Esposito2010_AO_for_LBT,Esposito_2011_pwfs_onsky,Pedichini_2016_XAO_pwfs_LBT}. In addition to the LBT, the pyramid sensor is integrated in the AO systems of the Subaru Telescope (SCexAO), the Magellan Telescope (MagAO), the Mont Megantic Telescope (INO Demonstrator), and the Calar Alto Telescope (PYRAMIR). \bigskip Aside from astronomical applications, the pyramid sensor is used in adaptive loops in ophthalmology \cite{Chamot06,Daly_2010,Iglesias02} and microscopy \cite{Ig11, Ig13}. The underlying concepts are comparable to atmosphere induced perturbations sensing for adaptive optics in astronomy. In microscopy, the pyramid sensor is introduced for direct phase detection. Unstained cellular media sometimes appear transparent. Hence, measuring the imprinted phase changes induced by variations in the index of refraction is necessary for the observation of biological structures. For adaptive optics systems in the eye, the pyramid sensor is used to perform high efficient and flexible wavefront sensing to compensate ocular aberrations. \bigskip From a mathematical perspective, the relation between the incoming, unknown wavefront and the measured pyramid wavefront sensor response is non-linear. Basically, the pyramid sensor signal can be modeled as the incoming wave convolved with the point spread function of the sensor. Due to the sinusoidal nature of the measurements, the model has a suitable linear approximation depending on the amplitude of the incoming wavefront \cite{HuSha18_1}. In closed loop AO, already corrected wavefronts are measured by the wavefront sensor. Thus, the existence of small incident wavefronts allows to assume a linear response of the PWFS. However, for open loop data or larger wavefront errors, for instance induced by non common path aberrations (NCPAs), this assumption is not fulfilled. Non common path errors appear in AO systems when the wavefront sensor does not belong to the same light path as the science camera. Then, the AO system suffers from aberration differences between the wavefront sensor and the science camera. Additionally, optical elements may be incorporated in the non common path as, for instance, in the case of Multi Conjugate AO systems. In these cases the assumption of small residual wavefronts being measured by the wavefront sensor, and further the linearity of the pyramid sensor may be violated. Non-linear wavefront reconstructors are considered as one possibility to handle the non-linearity effects of the pyramid sensor introduced by influences such as NCPAs. Currently, there still exist only a few attempts, e.g., \cite{Clare_2004,Frazin_18,Fauv16,Fauv17,korkiakoski_nonlinear_08,Korkiakoski_08,KoVe07,Viotto16} for handling the non-linearity of pyramid sensors with applications in astronomical AO. We introduce a new idea of non-linear wavefront reconstruction and propose to apply the non-linear Landweber/Landweber-Kaczmarz method. Both iterative algorithms have already been studied in-depth by the mathematical community with multiple applications in the field of inverse problems. \bigskip The paper is organized as follows: The non-linear inverse problem of wavefront reconstruction from pyramid sensor data is introduced in Section \ref{chap_invProb}. We also consider the mathematical models of the underlying wavefront sensor as well as its approximations. In Section \ref{chap_landweber}, we adapt the Landweber and Landweber-Kaczmarz iteration to the problem of non-linear wavefront reconstruction using pyramid sensors and introduce two new methods for wavefront reconstruction, namely the non-linear LIPS (Landweber Iteration for Pyramid Sensors) and the non-linear KLIPS (Kaczmarz Landweber Iteration for Pyramid Sensors). The evaluation of the Fr\'{e}chet derivatives and the corresponding adjoints which are needed for the application of the algorithms is done in Section \ref{chap_frechet}. In Section \ref{chap_complexity}, we mention some details on the discretization of the problem and the computational complexity of the proposed methods, and we show the performance of the reconstructors using closed loop end-to-end simulations in Section \ref{chap_numerics}. | We have established two methods, namely Landweber and Landweber-Kaczmarz iteration for pyramid sensors, for accurate and stable non-linear wavefront reconstruction. The theoretical background was accompanied by a first numerical evaluation of the reconstruction quality. Especially for the non-modulated sensor, the two algorithms provided outstanding performance, with the Landweber iteration being outmatched by its Kaczmarz version. Although, the Landweber method is known to converge slowly, we experienced accelerated convergence for AO closed loop simulations using only a small amount of Landweber or Landweber-Kaczmarz iterations per time step. For the sensor having no modulation applied, the warm restart technique additionally sped up the convergence. The low number of necessary iterations positively impacts the computational load of the algorithms whose complexity is given by roughly $\mathcal{O}\left(N_a^{3/2}\right)$. According to the results obtained when using linear and non-linear reconstruction methods in end-to-end simulations, we propose choosing the way of reconstruction, i.e., linear or non-linear, dependent on the modulation of the pyramid sensor. For the modulated sensor, we recorded higher reconstruction quality for linear reconstructors while for the non-modulated sensor we experienced better correction for the non-linear methods. However, note that this conclusion was drawn from a limited number of closed loop simulations without critical effects perturbing the linearity of the sensor such as NCPAs. As already mentioned, the assumption of small residual wavefronts being measured by the wavefront sensor and on account of this the linearity of the pyramid sensor may be violated by non common path errors of the system. Thus, the ability of existing linear and non-linear reconstruction strategies to deliver high quality wavefront corrections even under the impact of large NCPAs is of great interest. We plan to come back to this topic including a detailed investigation of the reconstruction performance for the proposed non-linear algorithms LIPS and KLIPS in the presence of realistic NCPAs in a subsequent paper. Generally, the influence of the magnitude of the incoming phase distortions on the reconstruction quality needs to be analyzed for both linear and non-linear reconstruction methods. Obstruction effects induced by wide telescope spiders (secondary mirror support structures) were omitted in the simulations. The non-linear LIPS and KLIPS both offer the possibility to be combined with direct segment piston reconstructors according to the so called Split Approach described in \cite{HuShaOb18,ObRafShaHu18_proc}. Nevertheless, the stability of the algorithms for segmented pupils needs to be examined in detail. Proper choices for the basis representations~\eqref{eq:im.1}~-~\eqref{eq:im.2}, e.g., using wavelets, may significantly improve the reconstruction quality and will be analyzed in future work. However, the representation using the characteristic functions of the subapertures as basis functions allows for offline precomputations, an advantage which may not exist for different choices of basis representations. The two wavefront reconstruction methods presented in this paper are based on the roof wavefront sensor forward model while data are obtained from pyramid sensors. The derivation of the Fr\'{e}chet derivatives and their adjoint operators for the full pyramid sensor model are planned. Since the latter more precisely describes the pyramid wavefront sensor, we may gain in reconstruction performance. We will come back to this topic including detailed comparisons of pyramid and roof sensor models as basis in the reconstruction approach in an upcoming paper. At present, there already exist several methods that allow for accurate wavefront reconstruction such as MVM based approaches or the P-CuReD algorithm \cite{Shat13} with LE Strehl ratios around $0.89$ as summarized in, e.g., \cite{HuShaOb18}. Nevertheless, we want to emphasize the importance of the development of new algorithms since the high reconstruction performance with the linear methods is obtained in undisturbed closed loop AO systems. As recently as extensive studies on the behavior of the linear and non-linear algorithms in the presence of realistic ELT effects such as NCPAs, telescope spiders or the low wind effect have been performed, further conclusions on preferences can be drawn. Due to the non-linearity of the pyramid sensor, degradation of the image quality may appear for reconstructors which are based on the linearity assumption. Furthermore, the LIPS and KLIPS can easier be adapted to more precise pyramid sensor models or segmented telescope pupils as, for instance, the P-CuReD algorithm. The non-linear algorithms are in an early stage of development and improvements for future investigations are expected. | 18 | 8 | 1808.07673 |
1808 | 1808.02260_arXiv.txt | % {The stellar wind in high-mass microquasars should interact with the jet. This interaction, coupled with orbital motion, is expected to make the jet follow a helical, nonballistic trajectory. The jet energy dissipated by this interaction, through shocks for example, could lead to nonthermal activity on scales significantly larger than the system size.} {We calculate the broadband emission from a jet affected by the impact of the stellar wind and orbital motion in a high-mass microquasar.} {We employ a prescription for the helical trajectory of a jet in a system with a circular orbit. Subsequently, assuming electron acceleration at the onset of the helical jet region, we compute the spatial and energy distribution of these electrons, and their synchrotron and inverse Compton emission including gamma-ray absorption effects.} {For typical source parameters, significant radio, X- and gamma-ray luminosities are predicted. The scales on which the emission is produced may reduce, but not erase, orbital variability of the inverse Compton emission. The wind and orbital effects on the radio emission morphology could be studied using very long baseline interferometric techniques.} {We predict significant broadband emission, modulated by orbital motion, from a helical jet in a high-mass microquasar. This emission may be hard to disentangle from radiation of the binary itself, although the light curve features, extended radio emission, and a moderate opacity to very high-energy gamma rays, could help to identify the contribution from an extended (helical) jet region.} | High-mass microquasars (HMMQ) are X-ray binaries that host a massive star and a compact object (CO) from which jets are produced. The stellar wind can strongly influence the jet propagation, both because the jet has to propagate surrounded by wind material, and because the wind lateral impact may significantly bend the jet away from the star. Several authors have used numerical and analytical methods to study, on the scales of the binary, the interaction of HMMQ jets with stellar winds and their radiative consequences \citep[e.g.,][]{romero03,romero05,perucho08,owocki09,araudo09,perucho10,perucho12,yoon15,bosch16,yoon16}. On scales larger than the binary system, orbital motion should also affect the dynamics of the jet, making it follow a helical trajectory \citep[e.g.,][]{bosch13,bosch16}. There are a few well-established microquasars in which evidence of a helical jet has been observed; for example, SS 433, 1E~1740.7$-$2942 and Cygnus~X-3 (\citealt{abell79,mioduszewski01,stirling02,miller04,luque15}; see also \citealt{sell10} for the possible case of Circinus~X-1). In the case of SS 433, the jet helical geometry likely originates in the accretion disk \citep[e.g.,][]{begelman06}; in the case of 1E~1740.7$-$2942, the system likely hosts a low-mass star and the role of its wind could be minor; in the case of Cygnus~X-3, the apparent jet helical shape has an unclear origin. \cite{bosch16} proposed that Cygnus~X-1 and Cygnus~X-3 could be affected by orbital motion and the stellar wind, although the uncertainties on the jet and wind properties make quantitative predictions difficult. Unlike the case of Cygnus~X-3, no clear evidence of a helical or bent jet has yet been found for Cygnus~X-1 \citep{stirling01}. In this work we study the implications of the impact of the stellar wind and orbital motion for the nonthermal emission of a HMMQ, from radio to gamma rays. Using an analytical prescription for the jet dynamics based on the results of \cite{bosch16}, the nonthermal radiation from a helical jet (spectra, light curves, and morphology) is computed numerically, considering a leptonic model with synchrotron and inverse Compton (IC) emission. The paper is organized as follows: In Sect.~\ref{windjet}, the interaction between the stellar wind and the jet is described. The technical aspects of the model are explained in Sect.~\ref{model}. The results of the calculations are presented in Sect.~\ref{results} and a discussion is provided in Sect.~\ref{discussion}. Unless stated otherwise, the convention $Q_{\rm x} = Q/10^{\rm x}$ is used throughout the paper, with $Q$ in cgs units. | \label{discussion} As argued by \cite{bosch16}, a nonballistic helical jet region is the likely outcome of a HMMQ jet interacting with the stellar wind under the effect of orbital motion. In the present work, we have shown that such a region is predicted to produce significant fluxes from radio to gamma rays if $L_{\rm NT}\sim \eta_{\rm NT}L_{\rm j}\gtrsim 10^{34}\eta_{\rm NT,-2}$~erg~s$^{-1}$, for a source at a few kiloparsecs. These significant fluxes are explained by the high synchrotron and IC efficiencies at the helical jet onset location, $\boldsymbol{r_0}$, for typical HMMQ $L_\star$-values. Since realistic $\eta_B$-values are expected to be well below equipartition with the radiation field, the IC component is likely to dominate the nonthermal emission, peaking around 10~GeV. Specific gamma-ray light curve features are also predicted: a non-negligible impact of gamma-ray absorption, combined with angular effects for this process and IC. Peculiar changing radio morphologies, which can trace the jet helical structure, are expected as well. We note that hydrodynamical instabilities and wind-jet mixing make our results mostly valid for the inner helical jet region, say up to a few $D_\star$. Beyond that point, the jet helical geometry is likely to become blurred, eventually turning into a bipolar, relatively wide, and collimated supersonic outflow; a mixture of jet and wind material. Although the flow may still be mildly relativistic for very energetic ejections, in general the resulting "jet" is expected to be much faster than the stellar wind, but nonrelativistic. Our results are based on a number of strong simplifications, in particular regarding the stability of the helical jet. Therefore, detailed numerical simulations of the jet-wind interaction on middle to large scales are necessary for more accurate predictions. Nevertheless, despite the simplifications adopted, the main features of the scenario are expected to be rather robust, at least at a semi-quantitative level. These are: non-negligible fluxes; specific light curves characterized by the value of $\boldsymbol{r_0}$, the interplay of jet and counter-jet emission, and angular IC and gamma-ray absorption effects; and curved jet radio morphologies with characteristic orbital evolution. This is so because the first- or even zeroth-order level of the dynamical, radiative, and geometrical effects involved are taken into account in our calculations. Two important system parameters, eccentricity and $d_{\rm O}$, have been assumed constant in our calculations. Despite being difficult to ascertain the impact of eccentricity in a high-mass microquasar without numerical calculations, simulations of pulsar-star wind colliding in eccentric binaries \citep{barkov16,bosch17} suggest that the effect of eccentricity should be important only for rather eccentric binaries. In that case, the nature of the interaction structure may not be helical at all, being not only strongly asymmetric, and inclined towards the apastron side of the orbit, but also likely much more sensitive to disruption. The value of $d_{\rm O}$, and thus $P$, may also change. This would leave the helical jet geometry unaffected: both the helical vertical step and $x_{\rm turn}$ are $\propto P\propto d_{\rm O}^{3/2}$. On the other hand, the luminosity would change as $\propto P^{-1}\propto d_{\rm O}^{-3/2}$ except for emission produced under the fast radiative cooling regime of electrons (in our setup the highest-energy end of the synchrotron and IC emission), which is independent of $d_{\rm O}$. The helical jet radiation in a very wide system would be hardly detectable unless the flow is slow, which allows electrons to radiate more energy. On the other hand, in a very compact system, radio emission would be hard to resolve for a slow helical jet flow, as the source would be too small. The emission on the scales of the binary, produced for instance by jet internal shocks or by the first wind-induced recollimation shock in the jet (stage 2), could be important. In which case: (i) assuming that the same nonthermal luminosity is injected in both regions, the radio emission from the binary scales would be strongly absorbed via synchrotron self-absorption and wind free-free absorption; and (ii) the X- and gamma-ray emission would be at a similar level if produced in the fast radiation cooling regime, and at a higher level otherwise because of the higher $B$-value and IC-target density. Gamma-ray absorption could however strongly attenuate the gamma-ray luminosity $>100$~GeV for most of the orbit. Therefore, the helical jet could contribute significantly to the overall nonthermal radiation of HMMQ, and particularly in radio and $>100$~GeV, even if electrons are also accelerated closer to the jet base. This was the main motivation for this work: to perform a first exploration of specific radiation features of the helical jet region, so that it could be disentangled from the other emitting sites. For the HMMQ Cygnus~X-1 and Cygnus~X-3, their uncertain wind and jet parameters make it difficult to make concrete predictions; for example, a non-ballistic jet region may not form at all \citep[see][and references therein]{yoon16,bosch16}, and an individual detailed source analysis is out of the scope of this work. In spite of this, our findings are not in contradiction with the radio morphology and the gamma-ray light curves of these sources \citep[e.g.,][]{stirling01,mioduszewski01,miller04,zanin16,zdziarski18}. Future detailed modeling together with deep, high-resolution radio observations and the high-energy light curves could provide hints of helical jet emission. The wind-jet interaction in HMMQ resembles, to a significant extent, the wind-wind interaction in high-mass binaries hosting young pulsars. The latter sources are probably extended mostly on the orbital plane and along the orbit semi-major axis, whereas the bipolar helical-jet structure is focused mostly in a direction perpendicular to the orbit plane \citep{bosch15,bosch16,bosch17}. Nevertheless, the interactions of the stellar wind with a relativistic pulsar wind or jet, on binary, middle, and large scales, share many qualitative properties, and this may mask a fundamentally different engine (accretion vs. a pulsar wind) when observing sources of yet unknown CO. These similarities are: extended radio structures with orbital evolution found at mas scales; strong radio absorption on the binary scales; similar hydrodynamics, and therefore impact of instabilities, adiabatic losses, and Doppler boosting effects\footnote{The much higher energy per particle of shocked pulsar winds can lead to stronger Doppler boosting effects than in a HMMQ jet, although mass-loading smoothens this difference.}, for the shocked flows outside the binary region; and gamma-ray light curves strongly affected by IC and gamma-ray absorption angular effects, in a likely extended/multi-zone emitter. Radio observations, high-quality multiwavelength data, numerical simulations, and realistic radiation calculations \citep[e.g.,][]{hess06,perucho08,magic09,fermi09,perucho10,moldon11a,moldon11b,moldon12,perucho12,bosch15,dubus15,zanin16,yoon15,yoon16,delacita17,bosch17,wu18,barkov18} are therefore needed to characterize radiation scenarios in high-mass binaries with unknown CO, such that empirical observables can help to disentangle the CO nature. | 18 | 8 | 1808.02260 |
1808 | 1808.07029_arXiv.txt | A stellar flare can brighten a planet in orbit around its host star, producing a light curve with a faint echo. This echo, and others from subsequent flares, can lead to the planet's discovery, revealing its orbital configuration and physical characteristics. A challenge is that an echo is faint relative to the flare and measurement noise. Here we use a method, based on autocorrelation function estimation, to extract faint planetary echoes from stellar flare light curves. A key component of our approach is that we compensate for planetary motion; measures of echo strength are then co-added into a strong signal. Using simple flare models in simulations, we explore the feasibility of this method with current technology for detecting planets around nearby M dwarfs. We also illustrate how our method can tightly constrain a planet's orbital elements and the mass of its host star. This technique is most sensitive to giant planets within 0.1~au of active flare stars and offers new opportunities for planet discovery in orientations and configurations that are inaccessible with other planet search methods. | \label{intro} Like a radar chirp or a sonar ping, a pulse of light from an astrophysical object allows us to glimpse the surrounding darkness. By tracking the light curve of a time-varying astrophysical source, we can extract the echo of such a pulse, looking for scattered light from things otherwise hidden \citep[e.g.,][]{rest2012}. Examples include the discovery of rings and other features following supernova explosions \citep[e.g.,][]{crotts1989}, and reverberation mapping of protoplanetary accretion disks around stars and gas in the vicinity of supermassive black holes \citep[e.g.,][]{horne1991, peterson2004, huan2016}. Light echoes of stellar flares may potentially reveal the presence of planetary disks of dust/debris \citep{gaidos1994, sugerman2003} and planets \citep{argyle1974, matloff1976, bromley1992, clark2009, mann2017, sparks2018}. Recently, Sparks et al evaluated additional discriminants of the scattered light, including fluorescence signatures and Doppler effects, thus bolstering the case for detecting echoes around M dwarfs.\citep{sparks2018} Echoes from multiple flare events from the same star change with the orbit of a planet and its physical properties, thus providing a new avenue for extracting orbital parameters\citep{argyle1974, mann2017}. Detection of planetary echoes is challenging. However, if it can be accomplished, it nicely complements other planet detection methods. Transit surveys, although limited to edge-on systems, can provide planetary and stellar radii and estimates of orbital elements \citep[e.g.,][]{borucki2010, mullally2015}. Radial velocity studies \citep[e.g.,][]{mayor2011} also constrain planetary masses; when combined with transits, they set a gold standard for planet confirmation. Other methods, including microlensing \citep[see][]{sumi2011} and direct detections \citep[e.g.,][]{marois2008, janson2013}, are sensitive to planets on distant orbits. Planetary echoes provide a direct detection method for close-in planets that works irrespective of a viewer's orientation, made possible only by the time-variability of their host. Figure~\ref{fig:wedge} illustrates the sensitivity of these detection methods to planet size, orbital distance, and orientation relative to an observer. A key to using planetary echoes for new detections, or as follow-up to known planetary systems, is repeat events. Like transits and radial velocity measurements, sampling a planet at various points along its orbit allows for reconstruction of orbital elements. In echo detection, differences in the arrival time of echoes can provide tight constraints on orbital elements and viewing angles. Because sets of echo delay times depend on physical distance and orbital period, the mass of the host star can also be accurately estimated. That echoes are photons reflected from the planet itself means that their strength depends on planet radius and albedo (atmospheric and surface composition) and orbital phase. Echo sets can arise from any viewing angle, but echo strengths fall off quickly with distance. Thus the method is most sensitive to giant planets inside 0.1~au for typical flare stars (Fig.~\ref{fig:wedge}). If combined with transits and radial velocity measurements, which provide separate constraints on stellar and planetary radii and masses, the possibility of using echoes to constrain the planet's surface composition is greatly enhanced. The ideal star for planetary echo detection has many strong, short outbursts. As a class, M dwarfs seem particularly well suited. A subset of these stars (the dMe) have tens of flares per day \citep[e.g.,][]{pettersen1986, hawley2014, davenport2016, yang2017}, and the contrast between the flare emission and the quiescent stellar light can be as high as $10^{4}$--$10^{5}$ \citep[e.g.,][]{schmidt2014, schmidt2016}. This combination --- high flare frequency and strong flare contrast --- make these stars, including AD Leonis \citep{bromley1992} and Proxima Cen \citep{sparks2018}, excellent preliminary candidates for light echo detection. Furthermore, M dwarfs are the most common type of star in the galaxy\citep{ledrew2001}, providing a very large number of potential observation targets. \begin{figure} \centerline{% \includegraphics[width=4.0in]{f1.pdf}} \caption{\label{fig:wedge}Detection regimes for each leading exoplanet detection method, plotted in a cylindrical coordinate system with the semi-major axis as the radial coordinate, system orientation as the azimuthal coordinate, and planet size/mass as the depth coordinate (adapted from \citep{mann2017}). Transit is shown in green, radial velocity in yellow, direct imaging in red, and echo detection in blue. Echoes allow probing into inner solar systems viewed from any angle, which were previously very difficult to detect.} \end{figure} The detection of faint echoes is an extraordinary challenge, calling for a commitment of both collecting area and observing time. Observation of echoes from an exoplanet requires (i) analyzing a signal that is typically buried in the measurement noise, (ii) isolating the echo from the possibly complex flare tail and post-flare brightening activity, (iii) accounting for the probability that the exoplanet is in a favorable position relative to both the flare and Earth, and (iv) developing detection significance criteria. While the concepts motivating this `interstellar lidar' are straightforward, there is no generalized approach available to enable demonstration. Here, we propose a framework for exoplanet echo detection by statistical analysis of the autocorrelation signals of multiple high-contrast flare events measured at high cadence (typically 10~s or faster). Through simulations, we show that we are able to extract echoes and orbital and other parameters by additively building up a signal using data from a sufficiently large number of flares and, in most cases, can place confidence intervals on the data by using statistical analysis and resampling techniques. As we show here, even if echoes are not individually resolved in light curves, their signatures can rise above noise when combined together using assumptions about a planet's orbit to account for variations in the echo delay time. In practice, confirmation of the presence of faint echoes and estimates of the planet's orbital elements go hand in hand. We organize this paper as follows. In \S\ref{sect:method}, we review echo detection and describe the algorithms we use for selecting and processing flare light curves. Toward understanding the feasibility of our method, we also provide examples of successful planet detection and parameter extraction from mock flares. Then, in \S\ref{sect:framework}, we provide a framework for using faint echoes for planet discovery, with details for how to explore the inner regions of planetary systems by tracking flare activity. We consider the prospects of using this method for planet discovery or follow-up observations in \S\ref{sect:prospects} and we conclude in \S\ref{sect:conclude}. \needspace{6em} | \label{sect:conclude} Here we introduce a framework for extracting and interpreting faint planetary echoes of stellar flares. It opens up a new detection regime for planet hunting, namely the very inner region of any planetary system, not just those that happen to be viewed edge on. This method complements existing detection techniques well, and is feasible with existing instrumentation. Many observed flare-like events are required for detection, but by prioritizing active stars, we can reduce the observation time needed to demonstrate the feasibility. Additionally, because our approach only requires photometry, multiple stars can be monitored simultaneously with a single focal plane array---an echo detection survey can piggyback on the hardware of transit and asteroseismology surveys if they provide support for $\lesssim$10~s cadence data products. With simple simulations, we also show that it is possible for echoes to reveal information about a planet and its stellar host. In our examples we cover orbital orientations that are close to the host star, viewed face-on or approximately so, to exemplify the strength of this method for discovering new planets in a previously undetectable regime of orbits. Our statistical echo detection method is effective for all bright close-in planets, whether observed face-on, edge-on or somewhere in between. Given enough events, we are able to extract the complete set of orbital parameters for an exoplanet. The main difficulty with our method is that the echoes are drowned out by noise in most situations. To maximize the strength of an echo against the noise of a variability event and prevent scintillation-induced false positives, space observation is strongly beneficial. Another host of difficulties may come from complex flare structures that can mimic or mask echoes. Other complications come from non-idealities of the flares, including the change in light travel time associated with where they the occur on the star's surface and their potential spatial extent. Ways to obviate this problem include downweighting, rejecting flares with multiple large peaks, more detailed detection algorithms that can accommodate more complex parameters such as a maximum likelihood model, or developing different detection algorithms based on deconvolution. Future work will consider this problem using observed flare light curves. While echo detection requires large data sets and extensive multi-parameter searches to produce convincing results, we are emboldened by the success of Kepler and other persistent observatories that provide years of data. Furthermore, the capacity to extract orbital parameters provides a major benefit to other exoplanet endeavors, including studies of habitability and validating solar system formation models. And echoes rely on different phenomena from other planet hunting techniques, providing the opportunity for an independent confirmation of a discovery. In light of the unique advantages of echo detection, we believe that the challenges are worth overcoming. | 18 | 8 | 1808.07029 |
1808 | 1808.00609_arXiv.txt | The main asteroid belt (MB) is low in mass but dynamically excited. Here we propose a new mechanism to excite the MB during the giant planet ('Nice model') instability, which is expected to have featured repeated close encounters between Jupiter and one or more ice giants ('Jumping Jupiter' -- JJ). We show that, when Jupiter temporarily reaches a high enough level of excitation, both in eccentricity and inclination it induces strong forced vectors of eccentricity and inclination across the MB region. Because during the JJ instability Jupiter's orbit `jumps' around, the forced vectors keep changing both in magnitude and phase throughout the whole MB region. The entire cold primordial MB is thus excited as a natural outcome of the JJ instability. The level of such an excitation, however, is typically larger than the current orbital excitation observed in the MB. We show that the subsequent evolution of the Solar System is capable of reshaping the resultant over-excited MB to its present day orbital state, and that a strong mass depletion ($\sim$90$\%$) is associated to the JJ instability phase and its subsequent evolution throughout the age of the Solar System. | The present-day asteroid main belt (MB) presents a challenge for theories of planet formation. Orbits within the MB have eccentricities ranging from 0 to $\sim$0.4 and orbital inclinations from 0 to more than 20 degrees. This high level of excitation is hard to reconcile with the presumably cold initial orbits of all planetesimals in the proto-planetary disk (including the MB asteroids and primordial trans-Neptunian objects) -- with eccentricities and inclinations near zero -- as well as the cold orbits of the terrestrial and giant planets. The MB is low in mass, containing a total of just $\sim 5 \times 10^{-4} \mearth$~\citep{demeo2013}. This is far less (100--1000 times less) than the few Earth-masses expected if the MB region were part of a disk with a smooth radial surface density gradient \citep[e.g.,][]{hayashi1981,bitsch15}. Finally, the belt shows broad compositional diversity but is dominated by two prominent classes: the S-types in the inner MB and C-types in the outer MB, albeit with significant overlap~\citep{gradie82,demeo2013,demeo2014}. Addressing these constraints within a self-consistent framework of terrestrial- and giant-planet formation is an imposing theoretical challenge \citep[e.g.,][]{morbidelli2007,hansen2009,walsh2011,izidoro2015,levison2015a,levison2015b,walsh2016,raymond2017a,raymond2017b}. Some theories succeeded in matching the MB's level of excitation but presented other major problems. The `classical model' of terrestrial planet formation includes a distribution of planetary embryos extending out into the asteroid belt~\citep{chambers98,chambers01,raymond06,obrien06}, which naturally excited the surviving asteroids~\citep{petit01,chambers01b,obrien2007}. However, the classical model has a well-known Achilles heel: it systematically results in the formation of Mars analogs almost as massive as Earth~\citep{wetherill91,raymond2009,morishima10}, and very often leaves planetary embryos surviving in the belt, which is not consistent with the current observations of the MB \citep{raymond2009}. Sweeping secular resonances during planetesimal-driven migration of Jupiter and Saturn was also proposed to excite the MB \citep{minton2011,lykawka2013}. However, this model requires a fast migration for Saturn ($\dot{a}\sim$ 4 au/Myr in the case of an initially cold MB or $\dot{a}\sim$ 0.8 au/Myr for an initially hot MB) with Jupiter fixed at $\sim$5.2 au \citep{minton2011}. According to \citet{morbidelli2010}, a more realistic time scale of migration for Jupiter and Saturn embedded in a planetesimal disk should be $\tau \sim$ 5 My. Planet migration on this timescale would result in a MB incompatible with that currently observed, where one would obtain an inner belt with a larger fractional number of asteroids in high inclined orbits than is observed today \citep{morbidelli2010,walshmorby2011,toliou2016}. Rather than a smooth giant planet migration, an early 'Nice model' planetary instability has the potential to explain the asteroid belt's orbital structure. In the Nice model, the giant planets formed in a more compact and more circular/coplanar configuration than their current one, and achieved their current configuration after a phase of dynamical instability after gas dispersal. \citet{clement2018} showed that the instability can produce sufficient excitation and mass depletion exterior to $\sim$1.5 au to explain the small mass of Mars. While promising in terms of solving the small Mars problem, the simulations of \citet{clement2018} did not have high enough resolution to fully populate the MB. Rather, while they did provide a decent match to the MB they were forced to co-add many simulations to produce a model belt \citep[Figure 6 in][]{clement2018}. The Grand Tack model \citep[GT;][]{walsh2011} was the first model to match the inner Solar System in a single evolutionary scenario. In the GT, Jupiter is assumed to have formed beyond the snow line and migrated inward via planet-gas disk interactions~\citep[e.g.][]{kley12,baruteau14}. Meanwhile, Saturn grew and migrated inward towards Jupiter~\citep{masset03}. When Saturn caught up with Jupiter the planets became locked in either mutual 3:2 or 2:1 mean motion resonance~\citep[MMR;][]{masset01,morby07b,pierens08,pierens11,pierens14}. At this point the planets' direction of migration was reversed \citep[this happened when Jupiter was at around 1.5--2 au,][]{brasser2016} and both planets migrated outwards until the gas in the disk dissipated, reaching their pre-instability location \citep{nesvorny2012,deienno2017}. Within the framework of the GT model, Jupiter and Saturn's excursion into the terrestrial and MB region has several implications. It confines the distribution of most solid material within $\sim$1 au from the Sun, explaining why Mars accretion stopped and the planet remained small \citep{wetherill1978,hansen2009}. The excursion of Jupiter through the asteroid belt can also explain how the S-type and C-type asteroids were implanted into the MB region, with S-types originating interior to Jupiter's original orbit and the C-types farther out~\citep{walsh12}. The resulting MB population is dynamically excited, the two asteroid types are partially mixed and the total mass, is just a few times the current one. In fact, the MB after the GT is over-excited compared with the present-day belt, but \citet{deienno2016} showed that the subsequent $\sim$4.5 Gy evolution of the Solar System naturally erodes the over-excited component so that the final distribution matches the present-day MB. A caveat, however is that the inclination distribution out of the GT simulations should be confined within $\sim$20$\degr$ in order to reproduce the current ratio in the number of asteroids above and below the $\nu_6$ secular resonance. Despite the GT's success the scenario remains controversial \citep[see][for a critical review]{raymond2014}. The key uncertainty is related to the outward migration mechanism of the planets, which has not been validated when gas accretion onto the giant planets is taken into account in a self-consistent way \citep{dangelo2012}. Indeed, in an isothermal disk with Jupiter and Saturn in 3:2 MMR the planets only migrate outward for Jupiter-to-Saturn mass ratios between roughly 2 and 4~\citep{morby07b}. Of course, this ratio was evolving while the planets were accreting gas, with a direct feedback between the giant planets' growth and migration. Another class of models invokes that the asteroid belt had a low mass from the very beginning \citep{izidoro2015,levison2015b,ogihara2015,moriaty2015,drazkowska16}. These models argue that the drift of small particles due to aerodynamics drag could have concentrated material near 1 au, leaving little mass in the asteroid belt. Starting from a steep enough radial surface density distribution of solid material, \citet{izidoro2015} was indeed able to build terrestrail planets similar to the real one, with a large Earth/Mars mass-ratio, but, they could not explain the orbital excitation of the MB (which remained too dynamically cold) nor its taxonomical mixture. However, additional mechanisms have been proposed that could reconcile the low-mass asteroid belt model with the present-day MB and provide a viable alternative to the GT model. \citet{raymond2017a,raymond2017b} showed that even if the MB was originally empty or almost empty (compatible with the Low Mass Asteroid Belt scenario), the growth of Jupiter and Saturn during the gas disk phase naturally implants scattered primordial planetesimals into the MB region. Planetesimals from the Jupiter-Saturn region and beyond are scattered inward during the giant planets' growth and implanted into the belt under the action of aerodynamic gas-drag \citep{raymond2017a}. They could correspond to the C-type asteroids that we observe today. In addition, planetesimals scattered outward from the terrestrial planet-forming region, due to their interaction with rogue planetary embryos, can be implanted onto main belt orbits by resonant interactions with Jupiter \citep{bottke06,raymond2017b}. They could correspond to the S-type asteroids. While this may solve the problem of the MB's taxonomical mixture, a problem persists. The dynamical state of the MB is still cold, mainly because the implantation of C-type asteroid occur via gas-drag damping, such that all but the largest ones (D $= 1000 ~\rm km$) end up with orbital eccentricity and inclinations near zero \citep[see Fig. 3 in][]{raymond2017a}. One proposed solution is the chaotic excitation model described by \citet{izidoro2016}. In this model, Jupiter and Saturn are initially in mean motion resonance (as predicted by migration models) but are not very close to the resonance center, so that they have some chaotic motion on secular timescales. It remains to be demonstrated whether such a specific configuration is consistent with migration models of resonant capture. Indeed, the chaotic excitation has only been demonstrated when Jupiter and Saturn are initially locked in their mutual 2:1 MMR and for specific configurations inside this resonance. However, according to \cite{nesvorny2012} and \citet{deienno2017}, it is more likely to reconstruct the orbital architecture of the outer Solar System with a giant planet instability if Jupiter and Saturn were initialy in the 3:2 MMR. The goal of this paper is to better understand the evolution and dynamical excitation of a cold primordial MB during the giant planet dynamical instability. Our study starts from a best guess for the initial configuration of the giant planets proposed by \citet{deienno2017}\footnote{Similar results could be expected from the evolution proposed by \citet{gomes2018}, due to the fact that what matters is the evolution of Jupiter durring the JJ-instability phase and not the one of Neptune as in \citet{nesvorny2015}.}, with Jupiter and Saturn initially locked in their 3:2 MMR. We show how the evolution of Jupiter is the key for the understanding of both the excitation of the MB and the chaotic evolution by \citet{izidoro2016}, when starting from a resonant configuration of the giant planets. Our approach is similar to that of \citet{clement2018} but with two main differences. First, we start with a low-mass asteroid belt with the goal of demonstrating dynamical excitation with little focus on mass depletion. Second, we consider enough particles in order to assess the final orbital distribution in the asteroid belt with good statistics. This study is not meant to disprove neither the GT nor the chaotic excitation model. Rather, we describe a new mechanism for exciting the asteroid belt starting from a dynamically cold, low-mass setup. Our mechanism is a by-product of the giant planet instability and, even though the belt may be temporarily over-excited, subsequent dynamical evolution brings it a state consistent with the present-day belt. It is also out of the scope of the present paper to try to provide an exact match of the present day MB, which would demand a prohibitive number of simulations and testing over a too large number of parameters. Our paper is structured as follows. In section \ref{sec2} we present our instability model and the effects that it has on a primordial cold MB. In section \ref{sec3} we discuss the direct effect that each planet has upon the MB. Section \ref{sec4} is devoted to understanding the mechanism of excitation working behind our results. In section \ref{sec5} we discuss the implications of our results for the time of the planetary instability, by considering the effects on the excitation of terrestrial planets. We compare the MB from our simulations with the present day asteroid main belt in section \ref{sec6}, where we also discuss the constraint on the initial mass of the asteroid belt. Lastly, section \ref{sec7} concludes the paper. | \label{sec7} We have shown that a jumping-Jupiter (JJ) evolution during the giant planet instability can excite a dynamically cold primordial main asteroid belt (MB) to an over-excited state (comparable to those obtained in both the Grand Tack model \citep[GT --][]{walsh2011} and in the chaotic excitation \citep{izidoro2016}), which subsequently evolves to the current level of excitation due to the preferential removal of the most dynamically excited asteroids over the Solar System age. We started by performing instability simulations of the giant planets starting from an initially 5 planet multi-resonant configuration \citep[with resonant period ratios of 3:2, 3:2, 2:1, 3:2 --][]{deienno2017}, as suggested by hydrodynamical simulations of planet migration in a gas-dominated disk. We selected a ``nominal'' simulation, which satisfies all constraints already considered for the JJ instability scenario \citep{nesvorny2012,deienno2017}. Then, we restricted our attention to the JJ instability period and recorded for every 1 year output the orbits of Jupiter, Saturn, and $pl5$ \citep[the ejected extra ice giant planet predicted by][and \citet{nesvorny2012}]{nesvorny2011,batygin2012}. We interpolated the recorded orbits of the planets to simulate their effect over an initially dynamically cold MB. We found that Jupiter is dynamically responsible for exciting the entire MB. The other planets, Saturn and $pl5$, have only minor direct effects upon the MB, but play an important role in the excitation mechanism by making Jupiter acquire a rapidly varying non-negligible orbital inclination during the instability phase. The mechanism that excites the MB from a cold initially state to a very excited one is the presence of large and rapidly evolving forced vectors of eccentricity ($e_{forced}$) and inclination ($I_{forced}$) due to the eccentric, inclined and rapidly changing orbit of Jupiter. Because the secular phases of the asteroids are rapidly randomized, different asteroids achieve different amplitudes of oscillation during the JJ instability phase. Thus, asteroids spread all over the parameter space of orbital eccentricity and inclination. Once the instability has ended and Jupiter and Saturn reach their present regular orbits, the ($e_{forced}$) and ($I_{forced}$) forced vectors' reduce in amplitude and evolve regularly. Consequently, the asteroids are frozen with their acquired proper eccentricities and inclinations. Our mechanism is similar to that presented by \citet{izidoro2016} but in our case we do not require that Jupiter and Saturn remain in the 2:1 MMR for long time. Our scenario is consistent with Jupiter and Saturn being originally in the 3:2 MMR \citep{masset01}. Our results also suggest that the kind of evolution that Jupiter has to have during the JJ instability to excite the MB is more consistent with an early instability in the Solar System rather than a late instability, although new constraints \citep{marty2017} indicate that the instability nevertheless postdated terrestrial planet formation. Finally, we showed that the subsequent evolution of the excited MB throughout the age of the Solar System makes the final distribution of the asteroids quite consistent with the present day asteroid main belt orbital configuration. We find that if the asteroid belt had originally comprised a large mass, as assumed in \citet{clement2018} from the minimum-mass solar nebula model, the giant planet instability alone would not have removed enough mass from the MB region. In this case, an additional depletion mechanism as the Grand Tack or with some temporary embedded embryos within the MB \citep{raymond2009,clement2018} should be invoked. Still, it remains to be demonstrated whether a combination of \citet{clement2018} model with temporary embedded embryos in the MB and self-stirring from a massive disc with an early JJ instability like shown in this work can provide the required depletion. On the other hand, our results support the Low Mass Asteroid Belt model \citep{izidoro2015,drazkowska16,izidoro2016,raymond2017a,raymond2017b}, which may provide a coherent alternative to the Grand Tack model for the evolution of the inner Solar System. | 18 | 8 | 1808.00609 |
1808 | 1808.02618_arXiv.txt | The migration of Neptune's resonances through the proto-Kuiper belt has been imprinted in the distribution of small bodies in the outer Solar System. Here we analyze five published Neptune migration models in detail, focusing on the high pericenter distance (high-$q$) trans-Neptunian Objects (TNOs) near Neptune's 5:2 and 3:1 mean-motion resonances, because they have large resonant populations, are outside the main classical belt, and are relatively isolated from other strong resonances. We compare the observationally biased output from these dynamical models with the detected TNOs from the Outer Solar System Origins Survey, via its Survey Simulator. All of the four new OSSOS detections of high-$q$ non-resonant TNOs are on the Sunward side of the 5:2 and 3:1 resonances. We show that even after accounting for observation biases, this asymmetric distribution cannot be drawn from a uniform distribution of TNOs at 2$\sigma$ confidence. As shown by previous work, our analysis here tentatively confirms that the dynamical model that uses grainy slow Neptune migration provides the best match to the real high-$q$ TNO orbital data. However, due to extreme observational biases, we have very few high-$q$ TNO discoveries with which to statistically constrain the models. Thus, this analysis provides a framework for future comparison between the output from detailed, dynamically classified Neptune migration simulations and the TNO discoveries from future well-characterized surveys. We show that a deeper survey (to a limiting $r$-magnitude of 26.0) with a similar survey area to OSSOS could statistically distinguish between these five Neptune migration models. | The Kuiper Belt as observed today looks very different from the dynamically cold, flat disk of leftover planetesimals originally hypothesized to exist beyond Neptune's orbit \citep{Edgeworth1949}. Several dynamically distinct components have been detected in the Kuiper belt, some of which are highly excited, i.e.\ on very eccentric, inclined orbits \citep[e.g.,][]{Gladmanetal2008}. The largest fraction of trans-Neptunian objects (TNOs) do indeed reside within the main classical belt on dynamically cold orbits. The Kuiper Belt also contains a large fraction ($\sim$20\%) of TNOs on orbits that are in mean-motion resonances with Neptune \citep{Gladmanetal2012,Adamsetal2014}, and a significant scattering component that is on highly excited, dynamically unstable orbits \citep{Gladman2005,Shankmanetal2013}. Of interest in this work are the population of non-resonant TNOs with pericenters outside the gravitational scattering influence of Neptune: the ``detached'' population \citep{Gladmanetal2002}. Increasingly detailed dynamical simulations over the years have shown that much of the observed orbital structure of the Kuiper Belt can be caused by the outward migration of Neptune's orbit, with incrementally powerful constraints on the exact timing and mode of Neptune's migration \citep[e.g.,][]{Malhotra1993,Thommesetal1999,Tsiganisetal2005,BrasserMorbidelli2013,NesvornyVokrouhlicky2016}. In order to compare these detailed simulations to observations of the distribution of TNO orbits, it is vital that observational biases are understood and accounted for. Particularly for the high pericenter distance (high-$q$) TNOs, the observational biases are severe and can have unintuitive consequences for the detected orbital distributions \citep[for a detailed discussion of these observational bias effects, see][]{Shankmanetal2017}. A thorough and well-tested way to account for observing biases is to carefully record a survey's depth, pointing direction and area on the sky, tracking fraction, and detection efficiency. These biases can then be applied to the output from a detailed dynamical simulation by Survey Simulator software, and the simulated detections can then be directly compared with the real survey detections in a statistically significant way, effectively ``debiasing'' the survey \citep{Jonesetal2006}. This technique can only be applied to TNOs discovered in surveys that carefully record their biases; TNOs pulled from the Minor Planet Center Database without regard for discovery survey cannot be debiased because most surveys do not publish their biases and survey characteristics. In this paper we take the results from five recently published, detailed Neptune migration simulations and compare them to the detected TNOs from the Outer Solar System Origins Survey \citep[OSSOS;][]{Bannisteretal2016,Bannisteretal2018}, making use of the OSSOS Survey Simulator \citep{LawlerSurveySimulator,Petitetal2018}. We particularly focus on the high-pericenter TNOs as a powerful ``fossilized'' tracer of Neptune's migration. In Section~\ref{sec:highq} we discuss the dynamics of high-$q$ TNOs, as well as review in detail the properties of the migration simulations that we analyze (Section~\ref{sec:sims}) and the structure of the near-resonant orbital element distributions for the different models (Section~\ref{sec:5231}). In Section~\ref{sec:comparing} we use the OSSOS Survey simulator (Section~\ref{sec:surveysim}) to apply the survey biases to the models, starting with a simple uniform distribution (Section~\ref{sec:uniform}), then observationally biasing the dynamical models (Section~\ref{sec:surveysimsetup}) and comparing them with the real OSSOS detections. While so few real detections provide little statistical constraint on the models, we conclude that overall, grainy slow Neptune migration provides the best match (Section~\ref{sec:gsbest}), and this analysis provides a framework for how to compare these future TNO detections with the dynamical model output. We conclude with a comparison to the MPC database (Section~\ref{sec:mpc}) and a discussion of how resonant sticking may be important to explain high-$q$ TNOs on larger semimajor orbits (Section~\ref{sec:dropouts}). In the Appendix, we provide detailed properties and analysis of a future, deeper survey that would be able to statistically distinguish between these migration models. | The current observations of the outer Solar System show that the distribution of high-$q$ particles near the 5:2 and 3:1 resonances are not uniform. The analysis here has shown that more high-$q$ TNOs on the Sunward side of these two resonances is not an observational bias effect, and the structure is likely due to resonant dropouts during Neptune migration. The distribution of these near-resonant particles provides a powerful discriminating tool for assessing how well different models of planetary migration reproduce the outer Solar System. The current four characterized near-resonant TNO detections, all on the Sunward side of nearby resonances, provide a statistically significant rejection of a uniform distribution, and indicate that Grainy Slow Neptune migration \citep[as in][]{KaibSheppard2016} provides the closest match to the observed near-resonant TNO distribution. Out of the five Neptune migration simulations analyzed, the simulation which used {\bf grainy Neptune migration with slower timescales} and a scattering jump that keeps Neptune at $e<0.1$ best reproduces the relative number and distribution of near-resonant high-$q$ TNOs observed by OSSOS, but there simply aren't yet enough high-$q$ TNOs to provide statistically robust support for any of the models we tested above the others. We hope this paper has provided a framework to rigorously test future observational datasets against upcoming dynamical models. The Large Synoptic Survey Telescope is expected to detect hundreds of new TNOs because of its incredible sky coverage and cadence. The LSST main survey of 18,000 square degrees has a single-image limiting magnitude of $m_r=24.5$ \citep{Ivezicetal2008,Jonesetal2016}, shallower than much of OSSOS. It will thus provide comparatively few high-q TNOs, due to the steep TNO size distribution. However, a Deep Drilling Survey of only a few suitably sited pointings, with a comparatively sparse cadence, may also be able to differentiate between these models. The most powerful way to test migration models will be through a deeper targeted TNO survey, such as the proposed survey we modeled for Subaru HSC (see Appendix), which would detect enough high-$q$ TNOs to distinguish between these five migration models at high statistical significance. Additionally, larger-scale Neptune migration simulations with more scattering particles can test the effectiveness of resonant sticking by scattering TNOs during Neptune's migration phase for producing very high-$q$ TNOs at large semimajor axes, such as Sedna. Due to the extreme biases against observing these extremely high-$q$ TNOs and the low number of detections, the best way to understand their population is through dynamical modelling in combination with a Survey Simulator to fully account for these severe observation biases. By reconstructing the details of Neptune's migration through detailed study of the Kuiper Belt's orbital structure, we learn about possible additional, now-ejected giant planets \citep[as suggested by the Jumping Jupiter model;][]{Nesvorny2015b}, and the size and number of planetesimals that had formed at this distance, since grainy migration requires a large number of relatively large ($\sim$1000~km) planetesimals \citep{NesvornyVokrouhlicky2016}. The large OSSOS dataset and Survey Simulator, which are both publicly available, provide the most powerful way to test these and future dynamical evolution models of the Solar System. Using a Survey Simulator is the best way to take into account the complicated observational biases in the outer Solar System, particularly in the high-$q$ and resonant TNO populations, and we hope that this will become the standard for testing the validity of dynamical models. | 18 | 8 | 1808.02618 |
1808 | 1808.05724_arXiv.txt | We present the distance priors from the finally released $Planck~ \textrm{TT,TE,EE}+\textrm{lowE}$ data in 2018. The uncertainties are around $40\%$ smaller than those from $Planck$ 2015 TT$+$lowP. In order to check the validity of these new distance priors, we adopt the distance priors to constrain the cosmological parameters in different dark energy models, including the $\Lambda$CDM model, the $w$CDM model and the CPL model, and conclude that the distance priors provide consistent constraints on the relevant cosmological parameters compared to those from the full $Planck$ 2018 data release. | \label{introduction} Since two supernova surveys reported the discovery of cosmic acceleration independently in 1998 \cite{Riess:1998cb,Perlmutter:1998np}, a new component except from matter and radiation, named dark enenrgy (DE) \cite{Peebles:2002gy}, is required assuming the general relativity (GR) remains correct for our universe. DE is the mathematically simplest explanation to the accelerating expansion of the universe, but its nature is still a puzzle. Several methods can be used to give constraints on the properties of DE. A straight-forward method is the distance measurement, such as the direct determination of $H_0$ \cite{Riess:2016jrr}, surveys on Type Ia Supernovae (SNe) \cite{Conley:2011ku,Suzuki:2011hu} and the baryon acoustic oscillation (BAO) measurements \cite{Cole:2005sx}. They provide absolute or relative distance measurements in a narrow range of redshift with percent level uncertainties. Obviously, the narrow detecting range of redshift restricts the validity of exploring the evolution of DE in full range of redshift. Moreover, the uncertainties increase as the redshift gets higher. DE is a component with negative pressure, which produces a force of repulsion, and affects the galaxy clustering. Then we can explore it using gravitational lensing \cite{Sanchez:2006nj}, clusters of galaxies \cite{Neveu:2017jkg}, redshift-space distortions (RSD) \cite{Gil-Marin:2015sqa} and the Alcock-Paczynksi (AP) effect \cite{Alcock:1979mp}. However, our limited knowledge about the structure formation bring a big challenge in the specific processing. We can also use the cosmic microwave background (CMB) \cite{Komatsu:2008hk,Aghanim:2018eyx} to constrain DE properties because DE plays an important role in the matter constitution and leaves footprints on the late-time power spectra of CMB. This method breaks the limitation of redshifts and possesses high-accuracy. Combining other measurements, a spatially flat $\Lambda$CDM model remains a convincing model. But it also has limitations that it requires the full Boltzmann analysis \cite{Bean:2003fb,Weller:2003hw,Li:2008cj}, which is really a very time-consuming process. More importantly, equations for linear density perturbations in some DE models are difficult to build \cite{Dvali:2000xg,Koyama:2006ef}. As a result, the method of distance priors \cite{Bond:1997wr,Efstathiou:1998xx,Wang:2007mza} are proposed to be a compressed likelihood to substitute the full Boltzmann analysis of CMB. Since the first data release in 2013 \cite{Ade:2013zuv}, Planck satellite provides CMB data with high accuracy. Although the preliminary observations of $TE, EE$ power spectrum at high multipoles were released in $Planck$ 2015 \cite{Ade:2015xua}, this data release laid emphasis on the temperature power spectrum. Recently, Planck Collaboration release the final data of the CMB anisotropies (hereafter $Planck$ 2018) \cite{Aghanim:2018eyx}. Since improved measurements of low-$l$ polarization allow the reionization optical depth to be determined with higher precision compared to $Planck$ 2015, there are significant gains in the precision of some parameters which are correlated with the reionization optical depth. Due to improved modelling of the high-$l$ polarization, moreover, there are more robust constraints on many parameters which will be affacted by residual modelling uncertainties only at the $0.5\sigma$ level. The constraints on the distance priors given in ``Planck Blue Book" \cite{Planck:2006aa} are about $50\%$ smaller than those given by $Planck$ 2015 TT$+$lowP \cite{Ade:2015rim}. All in all, it is meaningful to update the distance priors with the full-mission $Planck$ measurement of CMB. Following the previous work in \cite{Huang:2015vpa}, we update the distance priors with $Planck$ 2018 and present the constraints on several DE models with these new distance priors. This paper is organized as follows. In Sec.\ref{method}, we show our methodology to reconstruct the distance priors from $Planck$ 2018 chains. Then the new distance priors are presented in Sec.\ref{results}. In Sec.\ref{de}, we check our results in several different DE models. Concretely, we constrain the equation of state of DE from distance priors and compare our results with those by fitting the full data of $Planck$ 2018 release. A brief summary is given in Sec.\ref{sum}. In addition, we provide a note on how to use the distance priors in the CosmoMC package in the appendix which should be quite useful for the readers. | \label{sum} In this work, we update the distance priors from the final release of the Planck Collaboration in the base $\Lambda$CDM model, the $w$CDM model, the $\Lambda$CDM$+\Omega_k$ model and the $\Lambda$CDM$+A_\textrm{L}$ model. We give their mean values and the correlation matrices. Our new constraints on the distance priors are about $40\%$ tighter than those from $Planck$ 2015 TT$+$lowP \cite{Ade:2015rim}. Compared to our previous work \cite{Huang:2015vpa} based on the $Planck$ data release in 2015, our new results are slightly improved and $R$ in the base $\Lambda$CDM model gives the best improvement about $8\%$. We also check our results in the base $\Lambda$CDM model with the distance priors and constrain the related parameters in the $w$CDM model and the CPL model combining the low redshift BAO measurements. In all of these three DE models, we obtain quite similar constraints compared to $Planck$ 2018 release. It indicates that the distance priors derived from the base $\Lambda$CDM model can be used to replace the global fitting of full data released by $Planck$ in 2018 for the other DE models. \vspace{5mm} \noindent {\bf Acknowledgments} We acknowledge the use of HPC Cluster of ITP-CAS. This work is supported by grants from NSFC (grant NO. 11335012, 11575271, 11690021, 11747601), Top-Notch Young Talents Program of China, and partly supported by the Strategic Priority Research Program of CAS and Key Research Program of Frontier Sciences of CAS. \newpage \begin{appendix} | 18 | 8 | 1808.05724 |
1808 | 1808.09020_arXiv.txt | In this paper we identify and study the properties of low mass dwarf satellites of a nearby Local Group analogue - the NGC-3175 galaxy group with the goal of investigating the nature of the lowest mass galaxies and the `Missing Satellites' problem. Deep imaging of nearby groups such as NGC-3175 are one of the only ways to probe these low mass galaxies which are important for problems in cosmology, dark matter and galaxy formation. We discover 553 candidate dwarf galaxies in the group, the vast majority of which have never been studied before. We obtained R and B band imaging, with the ESO 2.2m, around the central $\sim$500kpc region of NGC-3175, allowing us to detect galaxies down to $\sim$23 mag (M\textsubscript{B}$\sim$-7.7 mag) in the B band. In the absence of spectroscopic information, dwarf members and likely background galaxies are separated using colour, morphology and surface brightness criteria. We compare the observed size, surface brightness and mass scaling relations to literature data. The luminosity function with a faint end slope of $\alpha$ = -1.31, is steeper than that observed in the Local Group. In comparison with simulations, we find that our observations are between a pure $\Lambda$CDM model and one involving baryonic effects, removing the apparent problem of finding too few satellites as seen around the Milky Way. | \label{chap:introduction} The $\Lambda$ cold dark matter ($\Lambda$CDM) model has enjoyed considerable success in explaining the observed properties of structure formation and growth. This model matches with the observed fluctuations in the cosmic microwave background power spectrum \citep{hinshaw2013nine,planck2014cosmology}, the growth of large scale structure, quasar absorption lines and the Lyman $\alpha$ forest \citep{springel2006large}. Because of this, one main focus over the past two decades has been to constrain or modify $\Lambda$CDM by searching for deviations from observations at small scales, such as within galaxy groups. In a hierarchical scenario, galaxies assemble via mergers of smaller dark matter (DM) haloes where the merging process is not entirely smooth, i.e. substructures (haloes) are not always destroyed. Numerical simulations of pure dark matter particles indeed predict thousands of DM haloes orbiting the Milky Way (MW) and the Local Group (LG) compared to the few tens and hundreds, respectively, of observed satellite galaxies \citep{kauffmann1993formation,moore1999dark,klypin1999missing,springel2008Aquarius} - this is known as the ``missing satellites problem''. In particular, it was found by \citet{klypin1999missing} that the discrepancy in the abundance of satellites between the hierarchical models and observations occurs below v\textsubscript{circ} $\sim$ 50kms\textsuperscript{-1}, corresponding to the faint end of the luminosity function. The study of dwarf galaxy population is therefore an important probe of the hierarchical $\Lambda$CDM model at small scales. Since it was first shown that substructure would likely survive in galactic haloes, there has been considerable effort towards trying to reconcile $\Lambda$CDM with observations. Theories have been focused on producing realistic MW halo simulations by invoking various baryonic physics including winds and, stellar and supernova feedback effects all of which, suppress star formation in low mass galaxies (e.g., \citealt{scanna2009discsdata,wadepuhl2011satellite,scanna2012aquila}). In addition, feedback from active galactic nuclei (AGN) has also been suggested to suppress star formation, even in the most massive dwarf galaxies \citep{dashyan2018agn}. Although the most recent generation of cosmological simulations (e.g., EAGLE project: \citealt{schaye2015eagle,crain2015eagle-issues} and APOSTLE: \citealt{fattahi2016apostle}) benefit from the increase in computational power, higher resolution and the incorporation of feedback effects, there remains a need to implement the uncertain subgrid physics. For example, \cite{scanna2012aquila} compare the formation of a MW analogue using 13 different cosmological simulation codes in a $\Lambda$CDM structure formation scenario. Each code is run with the same initial conditions, but the outputs exhibit large variations in stellar mass, size, morphology and gas content. Observationally, the census of Local Group satellites has been largely complete at the bright end, and thus the focus over the past decade has shifted to detecting ever fainter satellites (M\textsubscript{B} $>$ -9). Systematic searches of the Local Group have revealed such faint satellites around both M31 \citep{2007ApJ...671.1591I,2007ApJ...659L..21Z,2008ApJ...676L..17I} and a population of ultra faint and ultra diffuse galaxies around the Milky Way \citep{belakurov2006bootes,zucker2006canes,koposov2015beasts,kim2016pegasus3,torrealba2016giant,torrealba2016aquarius2}, with now $>$ 100 known satellites of the LG. Whilst other possible solutions to the missing satellites problem have been proposed, using for example, Warm dark matter cosmologies, which can suppress the number of low mass haloes that form galaxies, it is possible that the satellites of the Milky Way and the Local Group may not be representative of their mass scale. Additionally, observations have shown that the Magellanic Clouds may have a satellite system of their own (e.g., \cite{koposov2015beasts, 2018MNRAS.475.5085T}) which has introduced debate on the membership of some newly discovered satellites to the LMC or the Milky Way. Proper motions from Gaia data release 2 find some of the newly discovered dwarf galaxies to be inconsistent with being associated to the Magellanic Clouds \citep{2018arXiv180501448K}. This ongoing debate in the literature suggests a need to study abundance and properties of satellites around analogues, beyond the Local Group. In the nearby universe, studies of satellite properties of hosts with different masses to the Milky Way have already begun (e.g., NGC 253: \citealt{sand2014discovery}; NGC 3109: \citealt{sand2015antlia}; NGC 6503: \citealt{koda2015discovery}; NGC 2403: \citealt{carlin2016first}; M101: \citealt{merritt2014m101,bennet2017m101dw}; M81: {\citealt{2013AJ....146..126C}}; Centaurus A: {\citealt{2016ApJ...823...19C}}). A large survey is also being led to study the satellite population around 100 Milky Way analogues - the SAGA survey \citep{geha2017saga_arXiv}. Initial results from 8 such analogue hosts find the existence of the missing satellites problem. However, this survey has a magnitude limit of M\textsubscript{r} $\sim$ -12.3, whereas many satellites fainter than this limit have been found around the Milky Way, where the differences between models and observations is the most acute. In this study, we focus on the NGC-3175 group - a nearby LG analogue. This group was chosen based on both the similarity of K-band luminosities of the two large galaxies to the Local Group, and the group's local environment. The group consists of two large spiral galaxies, NGC-3137 (M\textsubscript{K} = -22.2) and NGC-3175 (M\textsubscript{K} = -22.9) \citep{skrutskie2006_2mass}. In comparison, the M31 has M\textsubscript{K} = -23.4, which is computed using $m_{K}$ = 1.1 mag \citep{2003AJ....125..525J} and a distance of 784kpc \citep{1998ApJ...503L.131S}. The MW has M\textsubscript{K} = -24.0 \citep{1996ApJ...473..687M, 2001ApJ...556..181D}. In addition, the group also contains other low mass spiral galaxies, comparable to the LG. Our aim is to identify the satellite population, study their properties and carry out an initial comparison with the predictions from $\Lambda$CDM. This paper is organised as follows: Section 2 provides an overview of the imaging data from the ESO WFI telescope. Section~\ref{sec:3} describes the SExtractor configuration used for object detection and star-galaxy separation to generate a sample of potential dwarf candidates. Section~\ref{sec:4} describes the implementation of GALFIT, using GALAPAGOS-2 to fit surface brightness profiles of the sample, and examines the model fitting quality through comparisons with simulated objects. We also determine here the criteria for defining group membership of the dwarf galaxy sample. We analyse the properties of the dwarf candidates, in comparison with observations from literature data in Section~\ref{sec:5}. The cosmological implications of our findings are explored in Section~\ref{sec:6} by the way of comparisons to various $\Lambda$CDM simulations of the Local Group. We provide our conclusions in Section~\ref{sec:7}. In this paper, we use a $\Lambda$CDM cosmology with $\Omega_{m} = 0.3$, $\Omega_{\Lambda} = 0.7$ and $H_{0}=70$ h kms\textsuperscript{-1} Mpc\textsuperscript{-1}. We use a distance of 14Mpc to NGC-3175 \citep{sorce2014dist} in order to compute absolute magnitudes of the dwarf candidates. The distance modulus uncertainty of 0.43 mag \citep{sorce2014dist} from the Tully-Fischer distance estimate corresponds to an 18\% uncertainty in the quoted distance. This does not affect our background selection, instead only shifts the range of the parameters that are derived in this paper based on the assumed distance, such as absolute magnitude, physical size and luminosity/mass. | 18 | 8 | 1808.09020 |
|
1808 | 1808.00271_arXiv.txt | The mass--velocity--size relation of late-type galaxies decouples into independent correlations between mass and velocity (the Tully--Fisher relation), and between mass and size. This behaviour is different to early-type galaxies which lie on a Fundamental Plane. We study the coupling of the Tully--Fisher and mass--size relations in observations (the SPARC sample), empirical galaxy formation models based on halo abundance matching, and rotation curve fits with a hydrodynamically motivated halo profile. We systematically investigate the correlation coefficient between the Tully--Fisher residuals $\Delta V_r$ and mass--size residuals $\Delta R$ as a function of the radius $r$ at which the velocity is measured, and thus present the $\Delta V_r-\Delta R$ relation across rotation curves. We find no significant correlation in the data at any $r$, aside from $r \ll R_\text{eff}$ where baryonic mass dominates. We show that this implies an anticorrelation between galaxy size and halo concentration (or halo mass) at fixed baryonic mass, and provides evidence against the hypothesis that galaxy and halo specific angular momentum are proportional. Finally, we study the $\Delta V_r-\Delta R$ relations produced by the baryons and dark matter separately by fitting halo profiles to the rotation curves. The balance between these components illustrates the ``disk--halo conspiracy'' required for no overall correlation. | \label{sec:intro} Dynamically, to first order, a galaxy is described by a mass, $M$, a size, $R$, and a characteristic velocity, $V$. Understanding the relations between these properties as a function of cosmic time is a major goal of galaxy astrophysics, with ramifications not only for the connection between galaxies of various types and their host dark matter halos, but also for the processes that drive galaxy formation and evolution. The $M$--$R$--$V$ relation of early-type galaxies forms a \emph{Fundamental Plane} (FP;~\citealt{Djorgovski, Dressler}), implying a single constraint between these variables. In contrast, late-type galaxies follow two separate relations, the \emph{Tully--Fisher} relation $M-V$ (TFR;~\citealt{TF}) and \emph{mass--size} relation (MSR). These are decoupled, in that their residuals $\Delta V \equiv \log(V)-\langle \log(V)|\log(M) \rangle$ and $\Delta R \equiv \log(R)-\langle \log(R)|\log(M) \rangle$ are uncorrelated (\citealt{McGaugh_res, Pizagno, Reyes, Lelli_BTFR}). While the FP may be understood as arising from virial equilibrium (for suitable choices of stellar initial mass function (IMF), dark matter fraction and radial orbit anisotropy;~\citealt{Dutton_2013, Desmond_FJR}), the independence of the TFR and MSR has been used to argue for an additional constraint between the properties of late-type galaxies that reduces the dimensionality of the effective parameter space (e.g.~\citealt{Famaey_McGaugh}). It may be surprising that $\Delta V$ and $\Delta R$ are independent because a larger galaxy at fixed mass has a less concentrated baryonic mass profile and should therefore rotate more slowly by Kepler's laws. The baryon-only prediction $\Delta V \propto -0.5 \: \Delta R$ is amply ruled out by the data (e.g.~\citealt{McGaugh_res}). However, this neglects the effect of both the shape of the halo velocity profile (which larger galaxies sample at larger radii) and the dependence of the galaxy--halo connection on galaxy size. These effects have been modelled in different ways generating disagreement among literature studies, whose conclusions range from assertions of incompatibility between the observations and predictions of standard galaxy formation models (e.g.~\citealt{McGaugh_TTP, Lelli_BTFR}) to assertions of complete compatibility (e.g.~\citealt{Courteau_Rix, Dutton_2007}). If the independence of the TFR and the MSR is not due to an additional constraint then it must arise ``by chance'' from the interrelation of the density profiles of baryonic and dark matter: our work explores how this may come about. There is confusion in the literature for three reasons: \begin{enumerate} \item{} Summarising the rotation curve (RC) of a galaxy by a single velocity, $V$, introduces a degree of arbitrariness since measuring $V$ at different radii may be expected to yield different results. Thus, while standard galaxy formation naturally predicts negligible $\Delta V-\Delta R$ correlation where RCs plateau, far beyond where most of the baryonic mass resides~\citep{Desmond_BTFR}, it may fail to do so if measured within the stellar disk (\citealt{DW15}, hereafter DW15). Different Tully--Fisher studies tend to use various definitions of radii to measure $V$ (see \citealt{Yegorova} for a comparison of different choices). The relation between these different TFRs depends on the shape of the RCs and hence on the total mass profiles. \item{} Model $M$--$R$--$V$ relations depend crucially on the correlation between the baryonic mass profiles of late-type galaxies and the masses, $M_\text{vir}$, and concentrations, $c$, of their host haloes, which are largely responsible for setting $V$. While the $M_*-M_\text{vir},c$ relation is well known from abundance matching (AM) studies, as well as more direct observations (see~\citealt{ghc_review} and references therein), the $R-M_\text{vir},c$ relation remains mostly unconstrained. Populating more massive or more concentrated haloes with larger galaxies at fixed baryonic mass will clearly induce a positive $\Delta V-\Delta R$ correlation. Most authors impose no correlation between $R$ and halo properties at fixed $M_*$ (e.g.~\citealt{Dutton_2011, Dutton_2013, DC}), a strong assumption that neglects any potential correlation between the galaxy and halo angular momentum. Other authors impose an anticorrelation between $R$ and $c$ by assuming that the specific angular momenta of galaxies and halos are proportional (e.g. \citealt{MMW}, DW15). One can also use results from hydrodynamical simulations of galaxy formation~\citep{Desmond_EAGLE}, apply prescriptions for converting gas to stars as a function of baryonic surface density (e.g.~\citealt{Dutton_2007}), or employ tunable toy models (\citealt{Desmond_MDAR, Desmond_BTFR} and here). Given the sensitivity of the $\Delta V-\Delta R$ relation to correlation between $R$ and halo properties, it is not surprising that these studies reach apparently contradictory conclusions. \item{} Velocity and size residuals are sensitive to the baryonic mass distributions of galaxies as well as the radii at which the RCs are sampled. It is difficult to ascertain the bias introduced by comparing model galaxies to observed ones with different mass profiles, or in cases where the mock and real observations are not made in the same way. While the use of simplistic functional forms for mass components is common, baryonic density profiles may be matched exactly between real and mock galaxies where high-quality photometry is available. \end{enumerate} We construct a semi-empirical $\Lambda$CDM model for galaxies in the \textit{Spitzer} Photometry and Accurate Rotation Curves (SPARC;~\citealt{SPARC}) sample by adapting and expanding previous work in~\citet{Desmond_BTFR}. Our particular interest is in comparing predicted and observed $\Delta V-\Delta R$ correlations when $V$ is measured at a range of radii across the RCs of galaxies. Besides clarifying the relative importance of various factors in setting the agreement of data and theory, we will show that this information brings new constraining power to the dependence of galaxy size on halo properties as well as the inner density profiles of haloes. We identify models in approximate agreement with the measured $\Delta V-\Delta R$ relation for all velocity choices, and hence show how the decoupling of the TFR and MSR may come about in $\Lambda$CDM. | \label{sec:conc} Using $153$ late-type galaxies from the SPARC sample, we investigate the correlation between the residuals of the mass--size and baryonic Tully--Fisher relations with velocities measured at a range of radii. Our main findings are the following: \begin{itemize} \item{} The correlation between the velocities and sizes of galaxies at fixed baryonic mass is a weak function of the radius $r$ at which the velocity is measured, with Spearman's rank coefficient $\rho_\text{sr}$ rising from $\sim-0.5$ in the baryon-dominated inner regions ($r \ll R_\text{eff}$) to $\sim-0.2$ further out where the dark matter is more important. The full radial dependence of this relation provides new information about the dependence of galaxy size on halo properties. \item{} Models that set $M_*$ by abundance matching and assume that $R_\text{eff}$ is uncorrelated with halo properties at fixed galaxy mass overpredict the strength of the $\Delta V_r-\Delta R$ relation by $1-5\sigma$, depending on $r$. This suggests an anticorrelation of galaxy size with halo concentration (or mass) at fixed baryonic mass, in line with previous inferences from the $M$--$R$--$V$ relations of late-type galaxies. We show agreement within $3\sigma$ for all $r$ using a model in which $\Delta c \simeq -0.4\:\Delta R_\text{eff}$. \item{} The $\rho_\text{sr}-r$ relation may also be matched by fitting the RCs with a partly cored DC14 halo profile. We show explicitly the $\Delta V_r-\Delta R$ correlation produced by the dark matter and anticorrelation produced by the baryons, thus quantifying the ``baryon--halo conspiracy'' required for no overall correlation at any $r \gtrsim R_\text{eff}$. \item{} The $\rho_\text{sr}-r$ relation provides further evidence against the hypothesis that galaxy and halo specific angular momentum are proportional. We conclude that, under standard assumptions for halo density profiles and the galaxy--halo connection, this putative proportionality cannot be responsible for setting galaxy size at low redshift. \end{itemize} | 18 | 8 | 1808.00271 |
1808 | 1808.02042_arXiv.txt | Astrophysical searches for new long-range interactions complement collider searches for new short-range interactions. Conveniently, neutrino flavor oscillations are keenly sensitive to the existence of long-ranged flavored interactions between neutrinos and electrons, motivated by lepton-number symmetries of the Standard Model. For the first time, we probe them using TeV--PeV astrophysical neutrinos and accounting for all large electron repositories in the local and distant Universe. The high energies and colossal number of electrons grant us unprecedented sensitivity to the new interaction, even if it is extraordinarily feeble. Based on IceCube results for the flavor composition of astrophysical neutrinos, we set the ultimate bounds on long-range neutrino flavored interactions. | \label{appendix:potential_derivation} Due to the $L_e-L_\beta$ ($\beta = \mu, \tau$) symmetry, an electron sources a Yukawa potential \begin{equation}\label{equ:potential_one_electron} V_{e\beta} = - \frac{ g_{e\beta}^{\prime 2} } { 4\pi d } e^{-m_{e\beta}^\prime d} \end{equation} at a distance $d$ from it, where $g_{e\beta}^\prime$ is the new coupling between electrons and neutrinos, and $m_{e\beta}^\prime$ is the mass of the $Z_{e\beta}^\prime$ that acts as mediator. For a given value of the mass, the range of the interaction is $1/m_{e\beta}^\prime$; beyond that, the potential is exponentially suppressed. Because we focus on tiny mediator masses, the interaction range is between meters and thousands of Gpc. Below, we compute the most important contributions to the potential, coming from electrons in the Earth, Moon, Sun, Milky Way, and cosmological electrons. When calculating the number of electrons $N_e$ in a concentration of matter, we assume that the matter is isoscalar --- it has roughly equal number of protons $N_p$ and neutrons $N_n$ --- and electrically neutral, so that the electron fraction in them is $Y_e \equiv N_e / (N_p + N_n) = 0.5$. With this, we convert from baryon density to electron density. \subsection{Electrons in the Earth} To calculate the potential due to the $N_{e,\oplus} \sim 4 \cdot 10^{51}$ electrons inside the Earth, we compute the electron column densities traversed by neutrinos inside the Earth prior to arriving at IceCube. To do this, we use the profile of electron number density $n_{e,\oplus}$ built from the matter density profile of the Preliminary Reference Earth Model (PREM)\ \cite{Dziewonski:1981xy}. The profile, constructed from seismic data, consists in concentric layers of increasing density towards the center of the Earth. At the position of IceCube, the net potential acting on neutrinos arriving from all directions is \begin{eqnarray} V_{e\beta}^\oplus &=& 2 \pi \frac{g_{e\beta}^{\prime 2}}{4\pi} \int_0^\pi d\theta \int_0^{r_{\max}(\theta)} dr ~r ~\langle n_{e,\oplus}(r,\theta) \rangle_\theta \nonumber \\ && \qquad\qquad\qquad\qquad\qquad \times \sin \theta ~e^{-m_{e\beta}^\prime r} \;, \end{eqnarray} where $R_\oplus = 6371$~km is the radius of the Earth, $\langle n_{e,\oplus} \rangle_\theta$ is the average electron density along the direction given by $\theta$, and $r_{\max}(\theta) = (R_\oplus-d_{\rm IC}) \cos \theta + \left[ (R_\oplus-d_{\rm IC})^2 \cos^2 \theta + (2R_\oplus-d_{\rm IC}) d_{\rm IC} \right]^{1/2}$ is the length of the chord traversed by the neutrino inside the Earth, with $d_{\rm IC} = 1.5$~km the approximate depth of IceCube. To compute the potential due to standard matter effects inside the Earth, we adopt a simpler prescription: $V_{\rm mat}^\oplus = \sqrt{2} G_F \langle n_e^\oplus \rangle$, where $\langle n_e^\oplus \rangle \equiv Y_e \langle n_N \rangle / (2 m_p)$ is the average electron density and $\langle n_N \rangle \approx 5.5$~g~cm$^{-3}$ is the average nucleon density according to the PREM. We do this because, in the regime where standard matter effects become important --- when the interaction range is smaller than $R_\oplus$ --- other limits on $g_{e\beta}^\prime$ are stronger, as shown in \figu{limits_emu}, avoiding the need for a more sophisticated calculation. \subsection{Electrons in the Moon and the Sun} We treat the Moon and the Sun as point sources of electrons. The potential $V_{e\beta}^{\leftmoon}$ due to electrons in the Moon is obtained by evaluating \equ{potential_one_electron} at $d = d_{\leftmoon} \approx 4 \cdot 10^5$~km --- the distance between the Earth and the Moon --- and multiplying it by $N_{e,\leftmoon} \sim 5 \cdot 10^{49}$ --- the number of electrons in the Moon. Similarly, the potential $V_{e\beta}^{\astrosun}$ due to electrons in the Sun is obtained by evaluating \equ{potential_one_electron} at $d = d_{\astrosun} =1$~A.U. --- the distance between the Earth and the Sun --- and multiplying it by $N_{e,\astrosun} \sim 10^{57}$ --- the number of electrons in the Sun. \subsection{Electrons in the Milky Way} \setcounter{figure}{0} \renewcommand{\thefigure}{A\arabic{figure}} \begin{figure}[t!] \centering \includegraphics[width=\columnwidth]{mw_electron_number_density_total.png} \caption{\label{fig:mw_electron_number_density}Density of electrons in the Milky Way, in Galactocentric coordinates. Electrons are distributed in the central bulge, thin disc, and thick disc of stars and cold gas\ \cite{McMillan:2011wd}, and in the diffuse halo of hot gas\ \cite{Miller:2013nza}.} \end{figure} The baryonic content of the Milky Way consists of stars and cold gas --- distributed in a central bulge, a thick disc, and a thin disc --- and hot gas --- distributed in a diffuse halo. We compute the potential due to the total $N_{e,{\rm MW}} \sim 10^{67}$ electrons, assuming, as before, $Y_e = 0.5$. Figure \ref{fig:mw_electron_number_density} shows the density of electrons in the Milky Way. For the central bulge, thick disc, and thin disc, we assume the simplified profiles of matter density from \Ref\ \cite{McMillan:2011wd}. These were obtained via a Bayesian fit to photometric and kinematic data. Each of the three components is modeled as a flat cylinder centered on the Galactic Center, with the matter density exponentially falling away from the axis and from the Galactic Plane. We adopt the parameter values from the ``convenient model'' of \Ref\ \cite{McMillan:2011wd}. For the diffuse halo of hot gas, we assume the spherical saturated matter density profile from \Ref\ \cite{Miller:2013nza}, obtained from measurements of O VII K$\alpha$ x-ray absorption lines using XMM-Newton. The density is highest at the Galactic Center and falls exponentially outwards. We calculate the potential due to Milky Way electrons by integrating the electron column density along all incoming neutrino directions, \ie, \begin{eqnarray}\label{equ:potential_mw} V_{e\beta}^{\rm MW} &=& \frac{g_{e\beta}^{\prime 2}}{4\pi} \int_0^\infty dr \int_0^\pi d\theta \int_0^{2\pi} d\phi ~r ~n_{e, {\rm MW}}(r,\theta,\phi) \nonumber \\ && \qquad\qquad\qquad\qquad\qquad \times \sin\theta ~e^{-m_{e\beta}^\prime r} \;, \end{eqnarray} with the coordinate system centered at the position of the Earth, which is located 8.33~kpc away from the Galactic Center\ \cite{McMillan:2011wd}. The potential is dominated by electrons in stars and cold gas. Though the halo of hot gas accounts for a significant fraction of the baryonic content of the Milky Way, its density is low, so halo electrons are only a tiny contribution to the total potential in \equ{potential_mw}. \subsection{Cosmological electrons} \renewcommand{\thefigure}{A\arabic{figure}} \begin{figure}[t!] \centering \includegraphics[width=0.49\textwidth]{suppression_vs_mass.pdf} \caption{\label{fig:yukawa_suppression}Yukawa suppression $\mathcal{Y}_{e\beta}$ of the potential due to cosmological electrons, as a function of mediator mass $m_{e\beta}^\prime$, for two fixed values of redshift: $z=0$ and $z=6$. For comparison, we show the causal horizon for the two choices.} \end{figure} In addition to the electron repositories in the local Universe, there is, at all redshifts, a cosmological distribution of electrons. The huge number of cosmological electrons --- $N_{e,{\rm cos}} \sim 10^{79}$ --- is what allows us to set the best bounds on the coupling $g_{e\beta}^\prime$ at the lowest values of mediator mass, where the interaction range is of the order of the size of Universe, or larger. Below, we calculate the potential due to cosmological electrons. Consider a neutrino that sits at the center of a sphere of radius $R$ that is homogeneously filled with a constant number density $n_e$ of electrons. The integrated long-range potential at the position of the neutrino is then \begin{equation}\label{equ:potential_def_general} V_{e\beta} = g_{e\beta}^{\prime 2} n_e \left[ \frac { 1-e^{-m_{e\beta}^\prime R}(1+m_{e\beta}^\prime R) } { m_{e\beta}^{\prime 2} } \right] \;. \end{equation} IceCube neutrinos are predominantly extragalactic, and presumably generated in sources at different redshifts. Because of the cosmological expansion, the density of cosmological electrons and the potential that they source varies with redshift. We take into account these effects as follows. The causal horizon defines the largest possible region within which events can be causally connected to each other\ \cite{Weinberg:2008zzc}. At redshift $z$, the comoving size of the causal horizon centered around the neutrino is \begin{equation} d_{\rm H} \left( z \right) = H_0^{-1} \int_0^{\left(1+z\right)^{-1}} \frac{dx}{h\left(x\right)} \;, \end{equation} where $H_0 = 100 h$ km s$^{-1}$ Mpc$^{-1}$ is the Hubble constant, with $h = 0.673$~\cite{Agashe:2014kda}, $x \equiv \left( 1+z \right)^{-1}$, and $h\left(x\right) \equiv H\left(x\right) / H_0$, with the Hubble parameter $H\left(x\right) = H_0 x \sqrt{ \Omega_\Lambda^0 x^2 + \Omega_\text{M}^0 x^{-1} }$. We adopt a $\Lambda$CDM cosmology with vacuum energy density $\Omega_\Lambda = 0.692$ and matter density $\Omega_{\rm M} = 0.308$\ \cite{Ade:2015xua}. The causal horizon changes from about 14.5 Gpc at $z=0$ to about 0.9 Gpc at $z=6$. \setcounter{figure}{0} \renewcommand{\thefigure}{B\arabic{figure}} \begin{figure*}[t!] \centering \includegraphics[width=0.49\textwidth]{eff_mix_angles_vs_v_em_enu_0100_tev_no_z_000_nu_nubar.pdf} \includegraphics[width=0.49\textwidth]{prob_vs_v_em_enu_0100_tev_no_z_000_init_e_nu_nubar.pdf} \caption{\label{fig:mixing_prob_lrp}Effective neutrino mixing parameters ({\it left}) and modified probabilities $P_{ee}$, $P_{e\mu}$, and $P_{e\tau}$ ({\it right}), in the presence of the new long-range interaction from the $L_e-L_\mu$ symmetry, at neutrino energy $E_\nu = 100$~TeV, as a function of the potential $V_{e\mu}$. For comparison, we show the value of the $ee$ element of $\matr{H}_{\rm vac}$ at this energy. Standard mixing parameters are fixed to their best-fit values under normal mass ordering from \Ref\ \cite{deSalas:2017kay}. Dashed lines show the standard values of the quantities, \ie, for $V_{e\mu} = 0$. Top panels are for neutrinos; bottom panels are for anti-neutrinos. When computing limits, we consider equal fluxes of $\nu$ and $\bar{\nu}$.} \end{figure*} The content of baryonic matter inside the causal horizon (see \eq~(16.105) in \Ref~\cite{Giunti:2007ry}) is \begin{equation} M_{\rm H} \left( z \right) = \frac{H_0^2}{16 G_N} d_{\rm H}^3 \left( z \right) \Omega_b^0 \;, \end{equation} where $\Omega_b^0 \approx 0.02207 h^{-2} \approx 0.05$~\cite{Agashe:2014kda} is the density of baryons in the local Universe. The total mass is predominantly made up of protons, neutrons, and electrons, \ie, $M_{\rm H} \left( z \right) \simeq N_p \left( z \right) m_p + N_n \left( z \right) m_n + N_e \left( z \right) m_e$, where $m_p$, $m_n$, and $m_e$ are the masses of one proton, neutron, and electron. We estimate the number of electrons by assuming that the number of protons and neutrons is roughly equal ($N_p \approx N_n$) and the net electric charge is zero ($N_p \approx N_e$). Taking $m_n \approx m_p$, this results in \begin{equation} N_e \left( z \right) \simeq M_{\rm H} \left( z \right) / \left( 2 m_p + m_e \right) \;. \end{equation} By evaluating \equ{potential_def_general} with $R = d_{\rm H}(z)$ and $n_e = N_e(z) / V_{\rm H}(z)$, with $V_{\rm H}(z) \equiv (4/3) \pi d_{\rm H}^3(z)$ the causal volume, the potential acting on a neutrino at redshift $z$ is \begin{equation}\label{equ:potential_def} V_{e\beta}^{\rm cos}(z) = \mathcal{C}_{e\beta}(z) \cdot \mathcal{Y}_{e\beta}(z) \;. \end{equation} The term due to the Coulomb part of the potential, \begin{equation}\label{equ:potential_def_coulomb} \mathcal{C}_{e\beta}(z) = \frac{3}{2} \frac{g_{e\beta}^{\prime 2}}{4\pi} \frac{N_e(z)}{d_{\rm H}(z)} \;, \end{equation} describes a potential with infinite range, mediated by a massless mediator. The Yukawa suppression, \begin{equation}\label{equ:potential_def_yukawa} \mathcal{Y}_{e\beta}(z) = \frac{2}{[m_{e\beta}^\prime d_{\rm H}(z)]^2} \left\{ 1 - e^{-m_{e\beta}^\prime d_{\rm H}(z)} [1+m_{e\beta}^\prime d_{\rm H}(z)] \right\} \;. \end{equation} reflects the reduced interaction range due to the mediator being massive and the finite size of the causal horizon. Smaller values of $\mathcal{Y}_{e\beta}$ represent stronger suppression. Figure \ref{fig:yukawa_suppression} illustrates the behavior of the Yukawa suppression. For a fixed redshift, the suppression is important --- \ie, $\mathcal{Y}_{e\beta} \ll 1$ --- as long as the interaction range $1/m_{e\beta}^\prime$ is small compared to the causal horizon. This means that the contribution of electrons located far from the neutrino is exponentially suppressed. This occurs for $m_{e\beta}^\prime \gtrsim 10^{-31}$~eV at $z=6$ and $m_{e\beta}^\prime \gtrsim 10^{-33}$~eV at $z=0$. On the other hand, if the range is comparable to or larger than the causal horizon, there is no Yukawa suppression, \ie, $\mathcal{Y}_{e\beta} \approx 1$. In this case, the interaction range is effectively infinite, that is, larger than the size of the causally connected Universe. | 18 | 8 | 1808.02042 |
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1808 | 1808.10461_arXiv.txt | In order to explain unusually high luminosity and spectral nature of ultra-luminous X-ray sources (ULXs), some of the underlying black holes are argued to be of intermediate mass, between several tens to million solar masses. Indeed, there is a long standing question of missing mass of intermediate range of black holes. However, as some ULXs are argued to be neutron stars too, often their unusual high luminosity is argued by super-Eddington accretions. Nevertheless, all the models are based on non-magnetized or weakly magnetized accretion. There are, however, evidences that magnetic fields in accretion discs/flows around a stellar mass black hole could be million Gauss. Such a magnetically arrested accretion flow plausibly plays a key role to power many combined disc-jet/outflow systems. Here we show that flow energetics of a 2.5-dimensional advective magnetized accretion disc/outflow system around a stellar mass black hole are sufficient to explain power of ULXs in their hard states. Hence, they are neither expected to have intermediate mass black holes nor super-Eddington accretors. We suggest that at least some ULXs are magnetically powered sub-Eddington accretors around a stellar mass black hole. | Ultra-luminous X-ray sources (ULXs) are very bright, point-like, non-nuclear X-ray emitters found in nearby galaxies. Their apparent luminosities, assuming isotropic emission, are in the range of $3 \times 10^{39}-10^{41}\ ergs \ s^{-1}$, which exceed the Eddington luminosity limit of a neutron star or even that of the heaviest stellar-mass black hole $(\sim 20M_{\odot})$ \citep{2006ARA&A..44..323F}. Here, the Eddington limit is defined as \begin{equation} L_{Edd}=\frac{4\pi c G M m_{p}}{\sigma_{T}}\simeq 1.3\times 10^{38} \left(\frac{M}{M_{\odot}} \right) \text{erg s$^{-1}$}, \end{equation} where $M$ is the mass of the accretor, $m_{p}$ the proton mass, $\sigma_{T}$ the Thomson scattering cross-section, $G$ the Newton's gravitation constant and $c$ the speed of light. Three alternate physical scenarios have been proposed to explain the large apparent luminosities of ULXs. One possibility is that they might be powered by accretion on to intermediate-mass black holes (IMBHs) with masses in the range of $10^{2}-10^{4}\ M_{\odot}$. Second, they can be stellar-mass black holes, achieved super-Eddington luminosities through slim-disc model \citep{2003ApJ...597..780E} or radiation pressure dominated geometrically thin accretion disc model \citep{2002ApJ...568L..97B} as a result of the nonlinear development of ``photon-bubble instability" \citep{1998MNRAS.297..929G}. A third scenario is beamed emission from a stellar mass black hole system, either through relativistic boosting along our line of sight \citep{2002A&A...382L..13K} or through geometric beaming effect \citep{2001ApJ...552L.109K}. A combination of supper-Eddington and mild beamed emission from stellar mass black hole can also be a plausible mechanism to explain their large apparent luminosities \citep{2007MNRAS.377.1187P}. Indeed in some rare cases, dodging of this Eddington limit is possible. In highly magnetized neutron stars, the presence of large magnetic fields $B\gtrsim 10^{12} \ G$ suppresses the electron scattering cross-section \citep{1979PhRvD..19.2868H} and, hence, reduces the effect of radiation pressure and increases the effective Eddington luminosity. In addition, the strong magnetic fields of the neutron star disrupt the accretion flow at the Alfven radius, and the matter is funneled along the field lines onto the magnetic poles. This geometry also provides apparent super-Eddington luminosity, as radiation can escape from the sides of the column \citep{1976MNRAS.175..395B}, perpendicular to the magnetic field in a ``fan beam" pattern. The important evidence supporting IMBHs scenario is the presence of soft excesses in the energy spectra of some ULXs. X-ray spectra in a number of ULXs are shown to be well fitted with the combined multicolour disc blackbody and power-law continuum model, similar to Galactic black hole binaries. The key difference is that the derived disc temperatures for ULX spectra are $0.1-0.3$ keV \citep{2004ApJ...614L.117M}, much lower than that for stellar mass black holes in their high state (at around $1$ keV). The cool accretion disc suggests a missing population of high-state of IMBHs. However, this cool accretion disc model has been disputed extensively. \cite{2006MNRAS.371..673G} argued that the soft excess could be a soft deficit depending on the energy range over which the power-law continuum is modeled. They showed that the spectra could be fitted equally well with a combination of smeared emission and absorption lines from highly ionized, fast outflow surrounding the primary X-ray source. Hence, they suggested that those components should not be taken as evidence for accretion disc emission, nor provided reliable measure of black hole masses. \cite{2006MNRAS.371.1216D} explained this cool disc by ``disc-corona coupling" model, where the optically thick Comptonizing corona over the inner disc drains power from the hot disc material. In the context of searching for the true physical nature of ULXs, one or two ULXs might be intermediate mass black holes \citep{2009Natur.460...73F}. The more recent argument (see \citealt{2007MNRAS.377.1187P}; \citealt{2011NewAR..55..166F} for reviews, \citealt{2002ApJ...568L..97B}; \citealt{2014Natur.514..198M} for theoretical disputes) is that the majority of ULXs are stellar mass black holes. Recent identification of coherent pulsations in three sources (M82 X-2, \citealt{2014Natur.514..202B}; NGC 7793 P13, \citealt{2016ApJ...831L..14F}; and, NGC 5907 ULX-1, \citealt{2017Sci...355..817I}) has brought support to the perspective that some ULXs likely host a neutron star. Most ULXs with steep power law, soft excess and/or high energy downturn can well be explained by different models. Nevertheless the interpretation of a significant fraction of ULXs with a hard power-law spectrum remains mysterious. \cite{2011AN....332..330S} already pointed out regarding this long-standing issue (see also \citealt{2006ApJ...649..730W}). In this letter, we propose a magnetized disc-outflow coupled model to address a plausible mechanism of finding the hidden nature of hard-state ULXs. The disc threaded by ordered magnetic fields provides the most efficient way of tapping the gravitational potential energy of black hole liberated through accretion to power jets/outflows \citep{1982MNRAS.199..883B}. As the pseudo-Newtonian framework considered here does not capture full general relativistic effect, the present model is inefficient of tapping the rotational energy of black hole \citep{1977MNRAS.179..433B}, unlike magnetically arrested disc (MAD) model \citep{2011MNRAS.418L..79T}. The magneto-centrifugally driven outflows are more plausible to emerge from the hot puffed up region of the advective accretion flow. Also, vertically inflated strong toroidal fields can enhance the outflow power in the form of ``magnetic tower" \citep{2004ApJ...605..307K}. We suggest that the observed hard-state ULXs are actually geometrically thick, highly magnetized, advective but sub-Eddington accretion flows orbiting stellar mass black holes and hence no need to incorporate the existence of the missing class of IMBHs, nor super-Eddington accretions. The letter is organised as follows. In Section 2, we recall the spectral classifications of ULXs along with some hard-state sources, the heart of interest of this letter. In Section 3, we model the coupled disc-outflow symbiosis for magnetized advective accretion flows. Subsequently, we discuss our results, in particular focusing on the energetics of the accretion induced outflows, in Section 4. Finally we end with discussions and conclusions in Sections 5 and 6 respectively. | Actual source of energy in ULXs is still under debate. On the other hand, the dynamics and energetics of the outflow of underlying systems are intrinsically coupled to the disc flow behaviors through the fundamental conservation laws (mass, momentum and energy). In this advective paradigm, the presence of large scale strong magnetic field provides a generic explanation of powerful unbound matters. The unbounded matter in the form of outflow is more plausible to emerge from the hot, puffed up region of the accretion flow. Most of the energy released by accreting matter is available to drive an outflow. The maximum possible outflow power in our model is $\sim 7.5\times 10^{39}$ erg s$^{-1}$ for a non-rotating stellar mass black holes accreting at sub-Eddington accretion flow. Hence, this scenario can give a plausible indication to visualise the unclear nature of hard-state ULXs without incorporating the existence of the missing class of intermediate mass black holes, nor with the super-Eddington accretion. | 18 | 8 | 1808.10461 |
1808 | 1808.01088_arXiv.txt | We present a detailed analysis of post-correlation beamforming (i.e. beamforming which involves only phased sums of the correlation of the voltages of different antennas in an array), and compare it with the traditionally used incoherent and phased beamforming techniques. Using data from the GMRT we show that post-correlation beamformation results in a many-folds increase in the signal-to-noise for periodic signals from pulsars and several order of magnitude reduction in the number of false triggers from single pulse events like fast radio bursts (FRBs). This difference arises primarily because the post-correlation beam contains less red-noise, as well as less radio frequency interference. The post-correlation beam can also be more easily calibrated than the incoherent or phased array beams. We also discuss two different modes of post-correlation beamformation, viz. (1) by subtracting the incoherent beam from the coherent beam and (2) by phased addition of the visibilities. The computational costs for both these beamformation techniques as well as their suitability for studies of pulsars and FRBs are discussed. Techniques discussed here would be of interest for all upcoming surveys with interferometric arrays. Finally, we describe a time-domain survey with the GMRT using the post-correlation beamformation as a case study. We find that post-correlation beamforming will improve the current GMRT time-domain survey sensitivity by $\sim$ 2 times for pulsars with periods of few 100s of millisecond and by many-folds for even slower pulsars, making it one of the most sensitive surveys for pulsars and FRBs at low and mid radio frequencies. | \label{sec:intro} Despite over five decades of pulsar surveys there are only $\sim$ 2600 pulsars that have been discovered so far\footnote{\url{http://www.atnf.csiro.au/people/pulsar/psrcat/}}. This is 5\% or less of the total Galactic population of pulsars (estimates of the Galactic population range from 40,000 to 90,000 objects, see e.g. \cite{Lorimer08}) and a large population of pulsars remains to be discovered by current and future surveys. Even though there has been an accelerating rate of discovery over the last decade, this has not been uniform across the entire parameter space occupied by pulsars. For example, even though the population of known Galactic field millisecond pulsars (MSPs) has increased approximately 4 fold over the last decade\footnote{\url{http://astro.phys.wvu.edu/GalacticMSPs/GalacticMSPs.txt}}, there has only been a $\sim$ 40\% increase in the number of known slow pulsars (i.e. pulsars with period, P $>$ 30~ms). This very modest increase in the number of known slow pulsars is particularly unfortunate, since the already known population of relatively slow pulsars contains several interesting objects, such as double neutron stars ($\sim$ 15 known, \cite{Tauris17}), which enable tests of strong field gravity, energetic young pulsars with significant spin-down noise, normal pulsars showing intermittency, drifting, and nulling, probing hitherto unknown emission physics, magnetars with extraordinary high magnetic fields ($\sim$ 29 known\footnote{\url{http://www.physics.mcgill.ca/~pulsar/magnetar/main.html}}), ultra slow pulsars (only 2 known) with period $>$ 10s which graze the theoretical death-line. One of the major reasons for the relatively slow increase in the number of such known pulsars is that the detection of these objects via periodicity searches can be severely affected by both instrumental red-noise and radio frequency interference (RFI). Both of these phenomena particularly reduce the search sensitivity at the low frequency end of the power spectrum of the detected time series, which is where the signal from these objects is strongest. In addition to pulsars, the population of time-domain radio transients consists of Rotating Radio Transients (\cite{McLaughlin06}; 112 known\footnote{\url{http://astro.phys.wvu.edu/rratalog/}}) and Fast Radio Bursts (\cite{Lorimer07}, \cite{Thornton13}; 33 known\footnote{\url{http://www.frbcat.org/}}). All the Fast Radio Bursts (FRBs) discovered to date are single events (except for one repeating FRB) of millisecond duration with dispersion measure (DM) values generally higher than the possible Galactic contribution. The non-repeating nature of these sources warrants real-time time-domain detections aided by simultaneous millisecond time-scale imaging to localize these events in order to maximise the science returns. Rotating Radio Transients (RRATs) show occasional flashes of dispersed radio bursts of typically a few milliseconds duration. The cause of their sporadic emission as well as their connection to other neutron star populations are not fully understood. Detection of a large number of FRBs and RRATs is essential in order for us to gain a better understanding of the nature of these sources. However, detection of such single pulse events with millisecond duration in dedispersed time-series data is severely hindered by the presence of RFI. Time-domain surveys are generally sensitivity limited, hence surveys with more sensitive instruments should lead to a higher discovery rate. Many of the existing as well as future high sensitivity radio telescopes are interferometric arrays. Planned surveys with telescopes like MeerKAT (e.g. TRAPUM\footnote{\url{http://www.trapum.org/}}), SKA Phase1 \citep[e.g.][]{Levin17} also need to optimally combine signals from many small telescopes (i.e. do ``beamformation''). The GMRT was one of the first interferometric instruments to be systematically used for pulsar searches. The high discovery rate of the GMRT High Resolution Southern Sky (GHRSS\footnote{\url{http://www.ncra.tifr.res.in/ncra/research/research-at-ncra-tifr/research-areas/pulsarSurveys/GHRSS}}; \cite{Bhattacharyya16,Bhattacharyya17}) as well as the Fermi-directed survey \citep{Bhattacharyya13} demonstrate the capabilities of the GMRT for low frequency pulsar searches. The recent upgrade of the GMRT allowing much larger instantaneous bandwidths (uGMRT; \cite{Gupta17}) brings a significant increase in its theoretical survey sensitivity for pulsars and FRBs at low and mid radio frequencies. With the uGMRT, phase-2 of the GHRSS survey \citep{Roy18} is expected to achieve a sensitivity better than all existing and ongoing off-galactic plane surveys. Most of the existing and planned surveys however use one of the two traditionally used methods of beamformation, viz. Incoherent Array (IA) or Phased Array (PA) beams, which are described in more detail below. In this paper we explore the possibility of significantly improving the observed time-domain sensitivity using yet another kind of beamformation, viz. ``post-correlation beamforming''. We show that in this kind of beamforming, the contribution of instrumental red-noise to the power spectrum is significantly reduced, thus greatly improving the sensitivity towards low and mid spin frequency pulsars. We also show that post-correlation beamformation can be used to significantly reduce the effect of RFI, thus improving the time-domain sensitivity for periodicity and single pulse search. Both of these factors lead to reduction of the number of false detections by several orders of magnitude. This not only allows one to lower the candidate detection threshold (i.e. probe fainter flux levels) but also greatly eases the problem of carrying out on-the-fly imaging and other follow-up of these events to maximize the science returns. | The improvements seen in time-domain processing using post-correlation beamformation aided with the enhanced sensitivity of the uGMRT for the GHRSS phase-2 survey, provide the motivation to develop a time-domain survey with a post-correlation beamformer. We compute here the estimated parameters for such a survey. To benchmark, we consider the uGMRT 300$-$500~MHz band with 30 antennas, 200~MHz bandwidth, 2048 spectral channels, visibility beamformation at 1~ms time-resolution with about 128 beams covering $\sim$ 10\arcmin~FoV. We note that covering the entire field of view with PC beams would require $\sim$ 1600 beams. We estimate a survey sensitivity of $\sim$ 0.1~mJy at 400~MHz (considering the radiometer equation \ref{eqn2} with a 2\% loss for ignoring the auto-correlation power), for a 10$\sigma$ detection for a 10\% duty cycle, a post-correlation beam gain of 7 K/Jy for 200~MHz bandwidth, 10~mins of dwell time, and a system temperature of 106~K. We also calculate a sensitivity of 0.05~Jy as the 5$\sigma$ detection limit for 5~ms transient millisecond bursts, which would correspond to weak scattering \citep{Thornton13}. Fig. \ref{fig:FRB_survey} shows the components required for such time-domain survey with the post-correlation beamformer as specified above. The required components are shown in four different colours. Visibilities computed in the uGMRT backend (GWB; marked in blue) at 1~ms time resolution are transferred to the the post-correlation beamformer nodes (marked in orange) with an aggregate data rate of $\sim$ 3 GB/s. We aim to implement in-field phasing (\cite{Kudale17}) using a sky model derived from the time-averaged visibilities in order to improve the coherence in phasing up to baseline length of several kilometers. This optimises the GMRT phased array sensitivity beyond central compact core (most current phased array observations use only the antennas in the central square). In addition of deriving the phasing model, a baseline based flag masking the bad baselines will also be generated in real-time from these time-averaged visibilities. Coherent additions of these visibilities will result in 128 of such visibility beams. The multi-DM search for single pulses (colored in yellow) on each of these visibility beams would need to be executed on a separate FRB cluster followed by coincidence filtering to remove spurious events \citep{Bhat13}. It is also proposed to record these 128 beams with 1~ms time-resolution giving a total data rate of 200 MB/s into disk for quasi-realtime search for pulsars using the same cluster. We note that the proposed 1~ms time-resolution is sufficient to detect double neutron star systems, young pulsars, normal pulsars as well as object like radio magnetars. Visibility buffers corresponding to candidate single pulse events will be recorded at 1~ms time resolution covering the full DM sweep time-range. For a event at a DM of 2000 pc cm$^{-3}$, the total DM sweep time over 200~MHz band in uGMRT 300$-$500~MHz band is $\sim$ 50~seconds, which results in 40 GB buffer size on each of the post-correlation beam nodes. This means one can easily hold few buffers for accommodating the pipeline delay and flush them to a storage based on the real-time triggers. These visibilities will be processed through the processing blocks (marked in green) for millisecond imaging localization at quasi real-time. This block includes removal of dispersion delay followed by a flagging and calibration pipeline and snapshot imaging. We note that part of this imaging pipeline to localise time-domain events has already been demonstrated for the GHRSS phase-1 survey \citep{Bhattacharyya16}. In this paper, we demonstrate that use of post-correlation beamformer for radio interferometric array results in a many-fold increase of the detection significance of time domain events compared to the conventional incoherent and coherent array beamformer. This increase in sensitivity is driven by the lower red-noise and RFI contamination of the post-correlation beam. Post-correlation beamformation also allows one to use standard interferometric calibration techniques for calibrating the beam. We compare two different modes of post-correlation beamformation, viz. (1) PA-IA beamformation, which does not require computation of the visibilities and (2) visibility beamformation where the beam is formed from the computed visibilities. We also show that the PA-IA beamformation is computationally economical for a small number of high time resolution beams. At low time resolutions, the visibility based beamformation is computationally cheaper. Visibility based beamformation also allows for better control in flagging/suppressing RFI. For multi-element feed system (e.g. Parkes multibeam system) or for phased array feed, the PC beam can also be used to subtract RFIs (correlated within the feed elements) from feed element response \citep{Kocz10}. These new beamforming techniques could significantly improve the sensitivity of time-domain studies with both existing (e.g. uGMRT, JVLA) and upcoming (e.g. CHIME, \cite{Amiri18}; OWFA, \cite{Subrahmanya17}) radio interferometric arrays. As a specific example, we have presented a proposed time-domain survey with the uGMRT. | 18 | 8 | 1808.01088 |
1808 | 1808.08160_arXiv.txt | We present a study of 7 southern open clusters based on UBVRI CCD photomety (Johnsons-Cousins system) and Gaia DR2 data. Dias 4, Dias 6 and four other clusters had UBVRI photometric observations determined for the first time. From the observational UBVRI data we obtained photometric membership probability estimates and, using the proper motions from the UCAC5 catalog, we also determined the kinematic membership. From Gaia DR2 astrometric data we determine the stellar membership using proper motions and parallaxes, taking into account the full covariance matrix. For both independent sets of data and membership we apply our non subjective multidimensional global optimization tool to fit theoretical isochrones to determine the distance, age, reddening, metallicity and binary fraction of the clusters. The results of the mean proper motions, distances and ages are in agreement, but the ones obtained from Gaia DR2 data are more precise in both membership selection and estimated parameters. In the case of NGC 6087, the Cepheid S Nor, member of the open cluster, was used to obtain an independent distance estimate, confirming the one determined by our fitting method. We also report a serendipitous discovery of two new clusters in the extended field near what was originally Dias 4. | This paper is part of a series motivated by the need for a homogeneous set of open cluster parameters such as distances and ages, to improve the New catalog of Optically Visible Open Clusters and Candidates published by \cite{Dias2002} (hereafter DAML02\footnote{The latest version (3.5) can be accessed on line at \url{https://wilton.unifei.edu.br/ocdb/}.}) which is widely used in different astrophysical researches and specially by our group, to investigate the spiral arms structure \citep{Dias2005} and evolution of the galactic disk \citep{Lepine2011}. A major problem in studies of open clusters is the determination of the membership probabilities of stars. Clearly with more accurate determination of cluster membership it is possible to better constrain estimates of distances, ages, and velocities (proper motion and radial velocity). Our team has contributed in this topic through membership probability estimates from both photometric \citep{Monteiro2017} and proper motion data \citep{Dias2014,Dias2018}. In this study we show how the solution of this question evolved in the era of the Gaia mission \citep{GAIA-DR22018}. The open clusters investigated in the present study were selected from DAML02 with the aim to provide a set of homogeneous UBVRI data and parameters determined from them in a non subjective isochrone-fitting approach. For all the clusters studied here, except for NGC 6087, these are the first results based on UBVRI data. The cluster NGC 6087 was observed in this run because the Cepheid S Nor, member of the cluster, allows us to obtain an independent check of the distance estimate by our isochrone fit method. Despite the fact that several of the clusters investigated in the present work had previous determinations of distances and ages, important corrections were needed given the discrepancies between results obtained by different works using different methods, as discussed by \citet{Netopil2015}. There are several reasons that may explain the differences in the parameters of the clusters published in the literature. However, the most important reasons are: 1) characteristics and quality of the data, 2) determination of the membership probabilities of the stars and 3) the isochrone-fitting method used. In our previous works we emphasized some important points in determining accurately the parameters of open clusters. Two of the most important ones are the relevance of the U filter to correctly estimate the extinction (which is limited by the spectral-type/reddening degeneracy of the color-color diagram) and the subjectivity in the visual isochrone fits, which are still used in many works. With the publication of the Gaia DR2 catalog, with its unprecedented astrometric precision, we can give answers to relevant questions in the study of open clusters, such as: how does data quality improve membership determination? What is the confidence and precision of the cluster parameters determined by the isochrone fits from Gaia DR2 photometric data alone? The objects studied in this work, which were observed in our photometric Survey of Southern Open Clusters, are briefly presented in the next Section. In general, since the survey is a long period project, the clusters observed are selected based mainly on their visibility (given the allocated telescope time) as well as the most up to date information on the availability of good quality CCD UBVRI photometry for each object. This requirement is justified given our goal to work towards an homogeneous sample of objects. Some objects are re-observed if additional information can be gained, as in the case of the cluster NGC 6087 described below. The available data is described in two main Sections, 3 and 4. Section 3 refers to UBVRI data, providing details of the observation and membership determination, and in Section 4 we present the Gaia DR2 data and astrometric membership. In Sec. 5 we describe the isochrone fitting method used. In Sec. 6 we present a discussion of the results obtained for each cluster. In Sec. 7 we compare the results with those published by different studies and discuss results obtained from UBVRI and Gaia DR2 data. In Sec. 8 we give our final conclusions. | We presented fundamental parameters of seven open clusters studied which except for one, had UBVRI photometry obtained for the first time. It is surprising that for some open clusters there were photometric data for only a reduced number of stars, as in the case of the NGC 5138 studied in this work. Although in general photoelectric data are more accurate, the number of observed stars is typically much smaller, which can lead to problems in the distance and age determination due to the poor sampling of the main sequence in the CMD. The results of the parameters and mean proper motions obtained in this work agree with previous ones from the literature. In this work we have also used the Gaia DR2 data to estimate membership from astrometric data which, due to its superior quality, better define the main sequence and turn-off of the clusters in the CMD. It helps to constrain the isochrone to fit the clusters providing more reliable and precise results. From the isochrone fit performed by our global optimization tool we conclude is possible determine the E(B-V) from the Gaia photometric data and estimate values of [Fe/H] with uncertainty of about 0.1 dex. An interesting point in this work is the consistency between the UBVRI and Gaia results. We also point out the agreement between the distance determined by parallax, period-luminosity relation and the isochrone fit for the Cepheid S Nor, member of the cluster NGC 6087. This external check shows the results obtained by the global optimization tool developed in our previous papers, to fit theoretical isochrones to open cluster photometric data is reliable. Finally, based on the Gaia data we also report a discovery of two new clusters (Dias 4a and Dias4b) in the extended field near what was originally Dias 4. | 18 | 8 | 1808.08160 |
1808 | 1808.03272_arXiv.txt | Son of X-Shooter (SOXS) will be a high-efficiency spectrograph with a mean Resolution-Slit product of $\sim 4500$ (goal 5000) over the entire band capable of simultaneously observing the complete spectral range 350-2000 nm. It consists of three scientific arms (the UV-VIS Spectrograph, the NIR Spectrograph and the Acquisition Camera) connected by the Common Path system to the NTT and the Calibration Unit. The Common Path is the backbone of the instrument and the interface to the NTT Nasmyth focus flange. The light coming from the focus of the telescope is split by the common path optics into the two different optical paths in order to feed the two spectrographs and the acquisition camera. The instrument project went through the Preliminary Design Review in 2017 and is currently in Final Design Phase (with FDR in July 2018). This paper outlines the status of the Common Path system and is accompanied by a series of contributions describing the SOXS design and properties after the instrument Preliminary Design Review. | \label{sec:intro} % The research on transients has expanded significantly in the past two decades, leading to some of the most recognized discoveries in astrophysics (e.g. gravitational wave events, gamma-ray bursts, super-luminous supernovae, accelerating universe). Nevertheless, so far most of the transient discoveries still lack an adequate spectroscopic follow-up. Thus, it is generally acknowledged that with the availability of so many transient imaging surveys in the next future, the scientific bottleneck is the spectroscopic follow-up observations of transients. Within this context, SOXS aims to significantly contribute bridging this gap. It will be one of the few spectrographs on a dedicated telescope with a significant amount of observing time to characterize astrophysical transients. It is based on the concept of X-Shooter \cite{vernetetal2011} at the VLT but, unlike its “father”, the SOXS science case is heavily focused on transient events. Foremost, it will contribute to the classifications of transients, i.e. supernovae, electromagnetic counterparts of gravitational wave events, neutrino events, tidal disruptions of stars in the gravitational field of supermassive black holes, gamma-ray bursts and fast radio bursts, X-ray binaries and novae, magnetars, but also asteroids and comets, activity in young stellar objects, and blazars and AGN. SOXS\cite{schipanietal2018} will simultaneously cover the electromagnetic spectrum from 0.35 to 2.0\ $\mu$m using two arms (UV--VIS and NIR) with a product slit--resolution of $\sim 4500$. The throughput should enable to reach a S/N$\sim 10$ in a 1-hour exposure of an R=20 mag point source. SOXS, that will see its first light at the end of 2020, will be mounted at the Nasmyth focus of NTT replacing SOFI. The whole system (see Figure\ \ref{fig:soxs1}) is constituted by the three main scientific arms: the UV--VIS spectrograph\cite{rubinetal2018, cosentinoetal2018}, the NIR Spectrograph\cite{vitalietal2018} and the acquisition camera\cite{brucalassietal2018}. The three main arms, the calibration box\cite{kuncarayaktietal2018} and the NTT are connected together\cite{biondietal2018} by the Common Path (CP). \begin{figure} [ht] \begin{center} \begin{tabular}{c} % \includegraphics[height=10cm]{SOXS_CP_fig1.jpg} \end{tabular} \end{center} \caption[example] { \label{fig:soxs1} SOXS: front and side view of the instrument with the identification of the two spectrographs and the common path.} \end{figure} The main characteristics of the three scientific arms are listed in Table\ \ref{tab:subsy}. \begin{table}[ht] \caption{Main characteristics of the SOXS sub systems connected to the SOXS common path.} \label{tab:subsy} \begin{center} \begin{tabular}{|l|c|c|c|} \hline \rule[-1ex]{0pt}{3.5ex} & AG Camera & UV--VIS& NIR \\ \hline \rule[-1ex]{0pt}{3.5ex} F/\# & 3.6 & 6.5 & 6.5 \\ \hline \rule[-1ex]{0pt}{3.5ex} Spectral Range& ugrizY $+$ V& 350--850 nm& 800 -- 2000 nm \\ \hline \rule[-1ex]{0pt}{3.5ex} Resolution& $-$ & $3500 - 7000$ & 5000 \\ \hline \rule[-1ex]{0pt}{3.5ex} Pixel Scale (arcsec/px)& 0.205 & 0.139 & 0.164 \\ \hline \rule[-1ex]{0pt}{3.5ex} Detector & Andor& e2v CCD44--82 2k$\times$ 4k& H2RG\ 2k $\times$ 2k \\ \hline \rule[-1ex]{0pt}{3.5ex} Pixel Size ($\mu$m) & 13.0& 15.0& H2RG\ 18.0 \\ \hline \end{tabular} \end{center} \end{table} | \label{sec:conclusion} % The SOXS Common Path is the backbone of this instrument connecting the telescope unit (NTT) with all the SOXS scientific arms (UV-VIS and NIR spectrographs and the acquisition camera) and the scientific arms with the calibration units. We have outlined the main aspects of the SOXS common path, highlighting the optical characteristics, the mechanical interfaces with the other SOXS subsystems and the CP motorized function and service function to be controlled by control electronics and instrument software. | 18 | 8 | 1808.03272 |
1808 | 1808.04514_arXiv.txt | The dense environment of globular clusters (GCs) can facilitate the formation of binary black holes (BBHs), some of which can merge with gravitational waves (GW) within the age of the Universe. We have performed a survey of Monte-Carlo simulations following the dynamical evolution of GCs with different masses, sizes and binary fractions and explored the impact of the host GC properties on the formation of BBH mergers. We find that the number of BBH mergers from GCs is determined by the GC's initial mass, size and primordial binary fraction. We identify two groups of BBH mergers: a primordial group whose formation does not depend on cluster's dynamics and a dynamical group whose formation is driven by the cluster's dynamical evolution. We show how the BBH origin affects the BBH mergers' main properties such as the chirp mass and merging time distributions. We provide analytic expressions for the dependence of the number of BBH mergers from individual GCs on the main cluster's structural properties and the time evolution of the merger rates of these BBHs. These expressions provide an essential ingredient for a general framework allowing to estimate the merger rate density. Using the relations found in our study, we find a local merger rate density of 0.18--1.8 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ for primordial BBH mergers and 0.6--18 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ for dynamical BBH mergers, depending on the GC mass and size distributions, initial binary fraction and the number density of GCs in the Universe. | } Recently, Advanced LIGO has made the first detection of gravitational waves (GWs) and opened a new window to explore very energetic events \citep{2016PhRvL.116f1102A}. The event responsible for the GWs revealed by this first detection, GW150914, was the merger of black holes (BHs) in a binary system and it has been followed by four more detections of merging binary BHs \citep[BBHs,][]{2016PhRvL.116x1103A,2016PhRvX...6d1015A,2017PhRvL.118v1101A,2017PhRvL.119n1101A} and one merging binary neutron stars \citep{2017PhRvL.119p1101A}. A number of different scenarios for the formation of these merging compact binaries have been proposed so far; the different formation mechanisms proposed have invoked isolated binary evolution \citep[e.g.][]{2002ApJ...572..407B,2007ApJ...662..504B,2012ApJ...759...52D}, three-body interactions in dense stellar systems \citep[e.g.][]{2000ApJ...528L..17P,2006ApJ...637..937O,2016ApJ...824L...8R,2018ApJ...855..124S}, the orbital evolution of hierarchical systems \citep[e.g.][]{2012MNRAS.422..841A,2014ApJ...781...45A,2016ApJ...816...65A,2018ApJ...856..140H,2018arXiv180508212R}, relativistic captures \citep[e.g.][]{2009MNRAS.395.2127O,2015MNRAS.448..754H,2017PhRvD..96h4009B,2018ApJ...860....5G}. As for the environment in which these compact binaries might form, the scenarios proposed include globular clusters \citep[GCs,][]{2010MNRAS.402..371B,2011MNRAS.416..133D,2013MNRAS.435.1358T,2014MNRAS.440.2714B,2015PhRvL.115e1101R,2016PhRvD..93h4029R,2017ApJ...834...68C,2017PASJ...69...94F,2017MNRAS.464L..36A,2017MNRAS.469.4665P,2017arXiv170607053B,2018A&A...615A..91B,2018PhRvD..97j3014S}, young/open clusters \citep[e.g.][]{2014MNRAS.441.3703Z,2017MNRAS.467..524B,2018MNRAS.473..909B} and galactic nuclei \citep[e.g.][]{2009MNRAS.395.2127O,2012ApJ...757...27A,2018MNRAS.474.5672L}. An important aspect concerning the formation of BHs is the mass fall-back after the supernova explosions. As discussed by \citet{2002ApJ...572..407B}, this fall-back (i.e., failed supernovae) mechanism can increase the remnant BH masses and reduce the natal kicks, which, in turn, can lead to a larger fraction of BHs retained inside the host stellar system \citep{2015ApJ...800....9M,2016MNRAS.458.1450W, 2016MNRAS.463.2109R,2018MNRAS.478.1844A,2018MNRAS.479.4652A}. The retention of a large number of BHs can significantly influence not only the internal dynamics \citep[e.g.][]{2013MNRAS.432.2779B} but also the observational properties of star clusters \citep[e.g.][]{2008MNRAS.386...65M,2017ApJ...834...68C,2017arXiv171203979W,2018ApJ...855L..15K,2018MNRAS.476.5274L,2018MNRAS.479.4652A,2018MNRAS.478.1844A}. The retained BHs in a dense stellar system rapidly sink to the centre of the system due to the effects of dynamical friction and form a compact subsystem predominantly composed of BHs, on a timescale of few hundreds Myr \citep{2013ApJ...763L..15M}. Due to its short relaxation timescale, a BH subsystem quickly undergoes core collapse and generate energy through the formation and dynamical interactions of BBHs \citep{2013MNRAS.432.2779B}. Recoil velocities acquired during binary-single and binary-binary interactions can result in BHs ejection from GCs, and some numerical studies \citep[e.g.][]{2015ApJ...800....9M,2017MNRAS.469.4665P} suggested that $\sim$30\% of dynamically escaping BHs are in binary systems, some of which are expected to merge within the age of the Universe. Moreover, \citet{2018MNRAS.478.1844A} suggested that some massive Galactic GCs (GGCs) are still harbouring a large number of BHs and that the formation and ejection of BBHs can still be ongoing in those GGCs. The BBHs' properties as well as the merger and detection rates of these BBHs are significantly affected not only by the global properties of host GCs such as the initial mass, size and the metallicity \citep[e.g.][]{2016PhRvD..93h4029R,2017MNRAS.464L..36A,2017ApJ...836L..26C} but also by the GC's stellar initial mass function and the prescriptions for the mass fall-back and the stellar wind \citep[see e.g.][and the references therein]{2017ApJ...834...68C}. In this paper, we present an analysis of the survey of Monte-Carlo simulations of GCs evolution from \citet{2017MNRAS.464.2511H} and of another set of simulations performed specifically for this paper aimed at a detailed characterization of the link between the properties of BBHs formed in GCs and the structure of the host GCs. Understanding the connection between the properties of the BBHs and those of their host GCs is an important step for more realistic estimates of the merger rate of BBHs. We extracted the information of all escaping BBHs from our GC simulations and found some empirical relations between the properties of merging BBHs and those of the host GCs. These relations provide an essential ingredient to estimate the merger and detection rates of BBHs for any assumed GC system properties and GC formation rate. We also provided examples of estimates of the local merger rate density for various assumptions concerning the properties of GC systems. The structure of this paper is as follows. We briefly describe the numerical method, the initial conditions and assumptions of our GC simulations in Section \ref{S2}. The relations between the properties of merging BBHs and those of the host GC are presented in Section \ref{S3}. In Section \ref{S4}, we then estimate the local merger rate density based on these relations. We conclude with a summary of our results in Section \ref{S5}. | } In this paper we have studied the formation of binary black holes (BBHs) in globular clusters (GCs) and explored the relation between the number and properties of merging BBHs and the structural properties of their host GCs. Our study is based on a large survey of Monte Carlo simulations following the dynamical evolution of GCs with a broad range of different initial masses, sizes and primordial binary properties. Our results have revealed a close correlation between the number of BBH mergers escaping from GCs and the properties of host GCs such as the initial mass, half-mass radius and the fraction of primordial binaries (Figs. \ref{F1} and \ref{F4}). We identified two groups of BBH mergers; one group is composed of primordial BBH mergers forming simply as a result of binary stellar evolution and escaping from GCs due to the natal kicks by supernova explosions. The second group is composed of dynamical BBH mergers forming as a result of binary-binary and binary-single interactions in the GC dense environments and ejected from GCs through the dynamical interactions. The number of primordial BBH mergers is correlated with the GC's initial mass and binary fraction (see Eq. \ref{E3}), while we found that the number of dynamical BBH mergers produced in 12 Gyr is correlated with a parameter $\gamma_{\rm dyn}$ (see Eq. \ref{E2}) depending on the GC's initial mass and half-mass density (Figs. \ref{F2} and \ref{F3}). Interestingly we have shown that the number of dynamical BBH mergers correlates also with the same $\gamma_{\rm dyn}$ parameter but defined in terms of the GC's current properties (Figs. \ref{F5} and \ref{F6}). We provide analytic expressions describing the correlations between the number of BBH mergers and the host GC's properties and apply them to estimate the BBH merger rate for a few different models of GC populations but the expression provided in our study can be used more in general for GC populations with initial conditions different from those adopted in our calculations. The specific properties of primordial and dynamical BBH mergers such as the merging time and the chirp mass distribution are very important for the estimate of the local merger rate and the detection rate. In general, we find that the merger rate decreases with time due to the continuous ejection of single and binary BHs from GCs (Fig. \ref{F7}). We showed that the time evolution of the merger rate for primordial BBH mergers decreases more rapidly than that for dynamical BBH mergers; this difference is due to differences between the formation and ejection timescales of the two groups of BBH mergers (Fig. \ref{F8}). The two groups of BBH mergers are characterized also by differences in the chirp masses. The dynamical BBH mergers contribute more massive BBH mergers compared to the primordial BBH mergers (Figs. \ref{F9} and \ref{F10}). Based on the analytic expressions obtained from study, we estimated the local merger rates of BBHs escaping from GCs. The local merger rate for primordial BBHs depends only on the cosmological GC formation rate and we obtained a rate of 0.18--1.8 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ (Section \ref{S4.1}) depending on the primordial binary fraction. To estimate the local merger rate for dynamical BBHs, on the other hand, it is necessary make an assumption on the initial distribution of GC masses and size. As pointed out above, the analytic expressions obtained in this paper allow to calculate the local merger rate for any assumption concerning these initial distributions. We estimated a local merger rate for dynamical BBHs of 1.3--18 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ depending on a variety of combinations of the initial GC mass function and size distribution (Section \ref{S4.2}). We also estimated a local rate for dynamical BBH mergers from the current properties of surviving GCs equal to 0.6--9.3 ${\rm Gpc}^{-3}{\rm yr}^{-1}$ (Section \ref{S4.3}; see also Table \ref{T2}), assuming all GCs have the same age and metallicity. The production of BBH mergers from GCs also can be influenced by the formation and the presence of intermediate mass black holes (IMBHs) in GCs. \citet{2015MNRAS.454.3150G} suggested that a seed BH for an IMBH can be formed by the runaway collisions of massive main-sequence (MS) stars \citep[see also][]{2002ApJ...576..899P,2017MNRAS.472.1677S}. This process will preferentially deplete the massive MS progenitors for stellar-mass BHs. Moreover, \citet{2007MNRAS.374..857T} have found that hard binaries can be disrupted by the interactions with the IMBH. These interactions between the IMBH and BBHs might result in the capture of one BH to the IMBH and the ejection of the companion BH \citep[this IMBH-BH binary can deplete the stellar-mass BH population by ejection; see][]{2014MNRAS.444...29L}, which is the possible source of intermediate mass ratio inspirals (IMRIs) for space-based GW detectors \citep[e.g.][]{2002ApJ...581..438M,2009ApJ...698L.129S}. Detailed investigations for the effects of the formation of IMBHs in GCs on the merger rate of stellar-mass BBHs will be studied in our forthcoming papers. | 18 | 8 | 1808.04514 |
1808 | 1808.05332_arXiv.txt | We explore effects of random non-axisymmetric perturbations of kinetic helicity (the $\alpha$ effect) and diffusive decay of bipolar magnetic regions on generation and evolution of large-scale non-axisymmetric magnetic fields on the Sun. Using a reduced 2D nonlinear mean-field dynamo model and assuming that bipolar regions emerge due to magnetic buoyancy in situ of the large-scale dynamo action, we show that fluctuations of the $\alpha$ effect can maintain the non-axisymmetric magnetic fields through a solar-type $\alpha^{2}\Omega$ dynamo process. It is found that diffusive decay of bipolar active regions is likely to be the primary source of non-axisymmetric magnetic fields observed on the Sun. Our results show that non-axisymmetric dynamo models with stochastic perturbations of the $\alpha$ effect can explain periods of extremely high activity (`super-cycle' events) as well as periods of deep decline of magnetic activity. We compare the models with synoptic observations of solar magnetic fields for the last four activity cycles, and discuss implications of our results for interpretation of observations of stellar magnetic activity. | Since the seminal papers of \citet{choud92} and \citet{h93}, random variations of kinetic helicity in dynamo processes (the so-called $\alpha$ effect) are often considered as the main source of long-term variations of solar activity cycles \citep{oss-h96a,moss-sok08,uetal09,pipea2012AA,2014AA563A18P}. In the standard mean-field framework, turbulent generation of magnetic fields results from reflection-symmetry breaking of helical convection motions \citep{KR80}. In the mean-field theory, the effect is described by the mean-electromotive force, \[ \mathbf{\mathcal{E}}=\left\langle \mathbf{u}\times\mathbf{b}\right\rangle ={\alpha}\circ\left\langle \mathbf{B}\right\rangle +\dots, \] where $\mathbf{u}$ is the turbulent velocity, $\mathbf{b}$ is the turbulent magnetic field, $\left\langle \mathbf{B}\right\rangle $ is the large-scale magnetic field, and coefficient $\alpha=-\frac{1}{3}\left\langle\mathbf{u}\cdot\nabla\times\mathbf{u}\right\rangle\tau_{{\rm cor}}$ is a pseudo-scalar proportional to the kinetic helicity, $\mathbf{u}\cdot\nabla\times\mathbf{u}$, and turbulent correlation times, $\tau_{{\rm cor}}$. The amount of convective energy, which can be spent on turbulent generation of the large-scale magnetic field by the $\alpha$ effect, is only few percents of the total convective energy \citep{park}. Taking this constraint into account, it was shown that magnitude of the $\alpha$ effect can randomly vary in each hemisphere in the range from 10 to 20 percent (see, \citealt{choud92,h93,moss-sok08}). However, the results of \citet{choud92} and \citet{oss-h96a} showed that in order to explain the Grand cycles of solar magnetic activity the random fluctuations should be of the same order as the mean magnitude of the $\alpha$-effect. Results of \citet{moss-sok08} showed that the time scale of fluctuations should also be taken into account. They found that if the correlation time is comparable to the cycle duration then the fluctuations with amplitude of few dozen percents are sufficient to explain the Grand minima of solar activity. The current paradigm assumes that sunspots are formed from large-scale axisymmetric toroidal magnetic field emerging from the solar convection zone where the field is regenerated by hydromagnetic dynamo. Results of \citet{KR80} and \citet{rad86AN} showed that, because of the differential rotation, the solar dynamo can not maintain a regular non-axisymmetric large-scale magnetic field. Nevertheless, large-scale non-axisymmetric magnetic fields are commonly observed on the Sun, for example, in the form of coronal holes \citep{1974Natur250.717G}, which represent regions of open magnetic flux \citep{stix77}. The surface flux-transport models successfully simulate the process of formation of coronal holes from decaying active regions \citep{1990ApJ355.726W,2017ApJ843.111C}. These models assume that influence of surface non-axisymmetric magnetic fields on the dynamo action in the deep convection zone is negligible. {\citet{moss99} and \citet{bigruz} showed that weak large-scale non-axisymmetric field structures may be consistent with non-linear mean field models of the solar dynamo, in which non-axisymmetric dynamo modes are maintained by either non-linearity of $\alpha$-effect quenching, or non-axisymmetric distribution of $\alpha$. It was suggested that the excitation of the non-axisymmetric modes can be sensitive to the radial dependence of the rotation law \citep{moss99,2017MNRAS.466.3007P}. \citet{pk15} studied response of a nonlinear non-axisymmetric mean-field solar dynamo model to non-axisymmetric perturbations and showed that the effect can depend on the root depth of the non-axisymmetric magnetic fields. The non-axisymmetric dynamo models may be relevant to the problem of solar active longitudes \citep{berd06}.} Observational results of \citet{2012AA547A93S} showed that the presence of background (basal) magnetic flux observed on the surface of the Sun does not depend on the magnetic cycle. From this consideration it seems that much of the basal flux may well originate from the global dynamo. This flux may persists during the solar minima because diffusion of solar bipolar regions could take long time. In this paper we explore additional possibility which stems from non-axisymmetric dynamo action. Longitudinal fluctuations of the $\alpha$ effect are usually ignored in mean-field stellar dynamo models. Using nonlinear mean-field dynamo models we show that such non-axisymmetric random perturbations can maintain large-scale non-axisymmetric magnetic fields in a solar-type $\alpha^{2}\Omega$ dynamo. Our goal is to investigate the process of stochastic excitation of large-scale non-axisymmetric magnetic field and estimate how it affects the large-scale basal magnetic flux. To compare this mechanism with diffusive decay of bipolar active regions, we simulate active region emergence using the Parker's magnetic buoyancy effect. To demonstrate the difference between the two competitive mechanisms we employ a reduced 2D non-linear and non-axisymmetric dynamo model which describes the dynamo wave propagation on the spherical surface. The modeling results are compared with synoptic observations of large-scale solar magnetic fields on the Sun. The paper is organized as follows. Section 2 describes the dynamo model and its parameters. Section 3 presents results of numerical simulations for various model conditions. Section 4 gives an outline of observational data and comparison with the model. The final section summarizes and discusses the main results of our analysis. | We used a relatively simple 2D mean-field dynamo model to understand whether non-axisymmetric dynamo modes can be generated and maintained in the presence of random non-axisymmetric perturbations of the $\alpha$-effect and due to diffusive decay of emerging bipolar regions. Without such perturbations the non-axisymmetric dynamo modes do not develop, and the dynamo solutions are axisymmetric. Here, for the first time, we demonstrate that the non-axisymmetric dynamo can happen even for the solar conditions, {\bf despite the strong differential rotation.} The reduced 2D non-linear non-axisymmetric dynamo models considered in this paper allow us to investigate influence of the perturbations on properties of the dynamo cycles, including the degree of non-axisymmetry of the dynamo-generated magnetic field and the hemispheric asymmetry in different phases of the magnetic cycles. Despite the simplicity, the models give insight on how large-scale non-axisymmetric magnetic structures observed on the Sun may develop, as well as directions for development of more realistic non-axisymmetric dynamo models. Our model of emerging bipolar regions was based on parameterization of the Parker's buoyancy instability of the axisymmetric toroidal magnetic field. Short- and long-term stochastic large-scale (up to octupole) perturbations of the $\alpha$-effect of various amplitude were considered separately and in combination with the bipolar regions. It is found that large-scale non-axisymmetric dynamo modes can be excited and maintain because of diffusion of emerging bipolar magnetic regions. Without perturbations of the $\alpha$-effect the non-axisymmetric magnetic field evolution affects evolution of the axisymmetric toroidal magnetic field via magnetic buoyancy. This kind of coupling was discussed previously by \citet{pk15}. In general, formation of large-scale non-axisymmetric magnetic field due to active region decay is usually accepted for granted \citep{2012LRSP96M}. Yet, the origin of the large-scale non-axisymmetric component during the solar minima is poorly understood. Our results show that remnants of decaying bipolar regions can persists during the solar minima when the cycle duration is determined by the turbulent diffusion scale. It is found that short-term stochastic non-axisymmetric fluctuations of the $\alpha$-effect with the standard deviation of 25\% relative to the axisymmetric level ($\sigma_{\xi}=0.25$) ) can generate weak non-axisymmetric magnetic field. Its strength is two orders of magnitude smaller than the strength of magnetic field in magnetic bipolar regions. The magnitude of turbulent $\alpha$-effect fluctuations is unknown. \citet{h93,oss-h96a} suggested that a high level short-term fluctuations with $\sigma_{\xi}=1$ can explain the Grand minima events. The results of \citet{moss-sok08} showed that a low level ($\sigma_{\xi}=0.1$) of long-term $\alpha$ fluctuations is another option. Our model with strong non-axisymmetric fluctuations of the $\alpha$-effect ($\sigma_{\xi}=1$) shows super-cycle events caused by a non-linear interaction of the non-axisymmetric dynamo and the process of formation of bipolar regions. The super-cycle magnitude is more than two times greater than the mean maximum of the magnetic cycles. The model run lasted 250 cycles (Fig.~\ref{fig:m2cd}a,b) shows a few other prolonged cycles of somewhat smaller magnitudes, as well as periods of low magnetic activity, but the super-cycle events are rare. Comparison the mean spectra of the latitudinally averaged strength of large-scale radial magnetic field with synoptic observations of solar magnetic fields during the last four cycles showed that the short-term non-axisymmetric perturbations of the $\alpha$-effect with $\sigma_{\xi}=0.5-1$ can be an option to explain the low azimuthal order part of the spectrum. Our simulations show that without the non-axisymmetric dynamo the magnetic field strength in this part of spectrum would be factor 2-3 lower than it is seen in the observational data. In comparison of our results with solar observations, we have to keep in mind that in our model the toroidal magnetic field generation and the bipolar region formation occur in the same place. {Taking into account the strong effect of the differential rotation in our models and the dominant role of the axisymmetric toroidal magnetic field, the shallow surface tachocline could be considered as a relevant place for our models. This can be different from the solar case \citep{b05}. Also, our results can be applied to stars with shallow convection zones (late-F and early-G spectral classes).} Young solar analogs often show a combination of the `inactive' and `active' branches of the cyclic activity \citet{2009AA_strassm}. The active branch shows long cycles \citep{1999ApJ_sa_br,2007ApJ_bohm}. \citet{2016ApJ823.133P} conjectured that the active branch can be due to the non-axisymmetric dynamo. This conclusion is supported by results of \citet{2016MNRAS1129S}. Here, for the first time we demonstrate the non-axisymmetric dynamo for a solar-type model. | 18 | 8 | 1808.05332 |
1808 | 1808.05618_arXiv.txt | In young circumstellar disks, accretion---the inspiral of disk material onto the central star---is important for both the buildup of stellar masses and the outcome of planet formation. Although the existence of accretion is well documented, understanding the angular momentum transport mechanism that enables disk accretion has proven to be an enduring challenge. The leading theory to date, the magnetorotational instability, which redistributes angular momentum within the disk, is increasingly questioned, and magnetothermal disk winds, which remove angular momentum from the disk, have emerged as an alternative theoretical solution. Here we investigate whether measurements of disk radii can provide useful insights into which, if either, of these mechanisms drive disk accretion, by searching for evidence of viscous spreading in gaseous disks, a potential signature of ``in disk'' angular momentum transport. We find that the large sizes of most Class II (T Tauri) gas disks compared to those of their earlier evolutionary counterparts, Class I gas disks, are consistent with expectations for viscous spreading in the Class II phase. There is, however, a large spread in the sizes of Class II gas disks at any age, including a population of very small Class II gas disks. Their small sizes may result from processes such as photoevaporation, disk winds, or truncation by orbiting low mass companions. | Circumstellar disks play a starring role in the formation of stars and planets. Stars accrete a significant fraction of their mass through disks and planets form from the dust and gas in disks. Disks surround all stars at birth because the material from which stars form, molecular cloud cores, possesses more angular momentum than can be contained in the star alone. As the disk evolves, the disk material spirals inward toward the star, is channeled onto stellar magnetic field lines, and eventually crashes onto the stellar surface, producing bright ultraviolet (UV) emission. From the luminosity of the UV excess, typical (few Myr old) T Tauri stars are inferred to accrete at a rate of $\sim 10^{-8}-10^{-7}\Msunpery$ (Hartmann et al.\ 1998, 2016), and a $\sim 1\Msun$ star is inferred to grow in mass by a few percent to a few tens of percent during the T Tauri phase, the initial few Myr of its life. Stellar accretion rates are well documented and characterized. With measurements now available for hundreds of young stars over a range of ages and masses, stellar accretion rates are found to decrease with stellar age (Sicilia-Aguilar et al.\ 2010; Manara et al.\ 2012; Antoniucci et al.\ 2014; Venuti et al.\ 2014), increase with stellar mass (Muzerolle et al.\ 2003; Calvet 2004; Herczeg \& Hillenbrand 2008; Fang et al.\ 2009; Alcala et al.\ 2014; Antoniucci et al.\ 2014; Manara et al.\ 2015; Natta et al.\ 2006), and are systematically reduced in transition objects, i.e., in disks with large central optically thin regions that may be forming giant planets (Kim et al.\ 2016; Najita et al.\ 2007, 2015). The inspiral of the accreting disk gas is expected to affect the outcome of planet formation. Giant planets are expected to couple strongly to their gaseous disks and migrate inward from their formation distances along with the accretion of the disk toward the star. The resulting inward Type II migration is thought to explain the large number of giant exoplanets that are found much closer to their stars than Jupiter is in our solar system (e.g., Lin et al.\ 1996). Despite the theoretical importance and documented existence of accretion, understanding exactly how disk accretion occurs, i.e., the mechanism that is responsible for disk angular momentum transport, has proven to be an enduring challenge. While the magnetorotational instability (MRI; Balbus \& Hawley 1991) had been hailed as the answer to this question for a couple decades, recent work finds that non-ideal MHD effects suppress the instability in the planet formation region (1--10\,AU), even in the upper disk layers, a consequence of the low ionization of T Tauri disks. With such ``in disk'' angular momentum transport thus apparently suppressed, magnetothermal disk winds launched from the disk surface have emerged as an alternative angular momentum removal mechanism (Bai \& Stone 2013; Kunz \& Lesur 2013; Gressel et al.\ 2015; Bai et al.\ 2016; see Turner et al.\ 2014 for a review). Angular momentum transport occurs quite differently through disk winds and the MRI. The MRI redistributes angular momentum within the disk, so that a small fraction of the disk mass acquires most of the angular momentum, which allows the rest of the disk to accrete. The disk wind removes angular momentum from the disk in order to accomplish the same objective. Neither mechanism has a verified observational signature thus far, making it difficult to determine which of these, if either, drive disk accretion. Here we investigate whether measurements of disk radii can provide useful insights. If angular momentum transport within the disk is important, disks will spread with time as the fraction of the disk that takes up the excess angular momentum moves to larger radii and the remainder accretes (Lynden-Bell \& Pringle 1974; Hartmann et al.\ 1998). If disk winds remove the excess angular momentum, disks need not grow in size with time. Previous commentary on this topic has largely focused on the possible change in size with age of the {\it dust} component of Class II disks. In star-forming regions separated by a few Myr in age, the dust component of disks, as measured from submillimeter continuum emission, is found to be slightly larger for older disks in Lupus than those associated with the younger Taurus and Ophiuchus populations (Tazzari et al.\ 2017). While one might hope to detect more obvious evolution in disk size by comparing disk size measurements at 1--3 Myr to those of even older populations ($\sim 10$ Myr), disk photoevaporation induced by stellar FUV irradiation has been argued to significantly reduce the size of a gaseous disk on few Myr timescales (e.g., Gorti et al.\ 2015). Photoevaporation will also strip away small grains that are coupled to the gas, potentially making the effect of viscous spreading difficult to detect at late times. Moreover, the likelihood that the large grains responsible for disk submillimeter emission migrate inward early in the evolution of disks (Takeuchi \& Lin 2002, 2005; Birnstiel \& Andrews 2014) suggests that submillimeter continuum measurements will underestimate the radii of Class II gas disks (e.g., Ansdell et al.\ 2018). To sidestep these difficulties, here we compare the evolution in the size of {\it gaseous} disks, focusing on the evolution at earlier times, between the Class I and Class II phases. Section 2 describes the observational data that we use to address this issue. Sections 3 and 4 describe our result and its implications. | As shown in the previous section, most Class II disks in Taurus are larger in radius than the Class I disks that have been studied to date, consistent with expectations for disk spreading, i.e., angular momentum transport within the disk in the Class II phase. Disks might spread as a consequence of angular momentum transport through gravitational instability (e.g., review by Kratter \& Lodato 2016) or viscous transport (e.g., review by Hartmann et al.\ 2016). Processes other than such ``in-disk'' angular momentum transport tend to reduce the sizes of gas disks. Photoevaporation by stellar FUV irradiation acts to truncate the disk at large radii and cause it to shrink with time, even in the presence of viscous spreading (Gorti et al.\ 2015). If magnetothermal winds (Bai \& Stone 2013; Bai et al.\ 2016) remove angular momentum efficiently from disks, disks could accrete without needing to spread with time. The formation of giant planets at large radii can also truncate disks. Our result complements observational and theoretical studies of angular momentum transport in disks. While the MRI (Balbus \& Hawley 1991; Gammie 1996) has long been the favored mechanism for disk accretion in the T Tauri phase, recent theoretical studies that explore the impact of non-ideal MHD effects have seriously questioned whether the MRI can operate in T Tauri disks, especially at radii relevant to planet formation $\sim 1$--10\,AU. Winds launched by a combination of magnetic and thermal effects have been proposed as an alternative transport mechanism (Bai \& Stone 2013; Kunz \& Lesur 2013; Simon et al.\ 2013a, 2013b, 2015; Lesur et al.\ 2014; Gressel et al.\ 2015; Bai et al.\ 2016; Bai \& Stone 2017; see Turner et al.\ 2014 for a review). Neither mechanism (MRI or magnetothermal winds) has a verified observational signature thus far at these distances. Disk turbulence possibly driven by the MRI has been detected both within 1\,AU and beyond 40\,AU. At disk radii within 0.3 AU, high resolution spectroscopy of CO overtone emission has uncovered evidence for non-thermal velocities comparable to the sound speed in the disk atmospheres of a few young stars (e.g., Carr et al.\ 2004; Najita et al.\ 1996; 2009; Doppmann et al.\ 2008), consistent with the non-thermal motions expected for MRI-driven turbulence. High resolution ALMA observations of outer disks appear to favor low levels of non-thermal broadening, at only $\sim 5$--10\% of the sound speed (HD163296 and TW Hya--Flaherty et al.\ 2015, 2018; de Gregorio-Monsalvo et al.\ 2013). However, turbulence at a larger fraction of the sound speed ($\sim 20$\%) has recently been detected in the outer disk of DM Tau (K.\ Flaherty 2018, private communication). No signature of turbulence has yet been reported at the disk radii where non-ideal MHD effects are expected to strongly suppress the MRI (1--10\,AU). The existence and character of magnetothermal winds are also uncertain. Theoretical studies predict that winds capable of driving disk accretion at the observed stellar accretion rates will be massive, with mass loss rates comparable to disk accretion rates. It has been suggested that the low velocity component of the OI 6300A line emission from T Tauri stars provides evidence for magnetothermal winds (Simon et al.\ 2016). However, the decomposition of a complex OI 6300A profile into multiple components potentially introduces uncertainty in the interpretation. More detailed studies of this and other diagnostics, combined with quantitative theoretical predictions of observable wind signatures can potentially verify the existence and angular momentum transport properties of magnetothermal winds. In the meantime, the larger sizes of most Taurus Class II disks compared to Class I disks strongly suggest that angular momentum redistribution within the disk, by some mechanism, plays a large enough role in disk evolution that a large fraction of disks spread significantly from the Class I to Class II phases. The data do not comment on whether the mechanism responsible is the MRI or other processes. Disk winds may also remove angular momentum but not enough to prevent the spreading of these disks. These results complement earlier commentary on the evolution of (primarily dust) disk sizes that found tentative, sometimes conflicting, results. Although Andrews et al.\ (2007) seemed to find no trend of dust disk size with age among Class II objects (their Fig.~15), subsequent studies found tentative evidence that dust disk sizes do increase with age (Isella et al.\ 2009, their Figure 10; Guilloteau et al.\ 2011, their Figure 13). More recently, Tazzari et al.\ (2017) found that in star-forming regions separated by 1--2 Myr in age, the sizes of Class II disks, as measured from submillimeter {\it continuum} emission, are slightly larger for disks in Lupus (1--3\,Myr) than those in the slightly younger Taurus and Ophiuchus (1--2\,Myr) populations. They tentatively attributed the size difference to viscous evolution. Thus, the evidence for increasing {\it dust} disk size with age during the Class II phase is modest to uncertain, consistent with the picture from Figure 2. Of the 22 Lupus Class II disks in the recent study by Ansdell et al.\ (2018), which range in size from $\sim 100$\,AU to $\sim 500$\,AU, approximately half have gas disk radii $>200$\,AU, a smaller fraction than in the Taurus sample studied here but still quite large. Although the authors did not compare the sizes of Class I gas disks with their Class II gas disk sizes, it seems clear that if the Class I disks from Table 1 are typical of the evolutionary precursors of the Lupus Class II disks, the large gas disks ($> 200$\,AU) among the Lupus population also suggest that viscous spreading occurs in the T Tauri phase (Figure 4). For the purpose of this study, the Lupus disks are less ideal than the Taurus disks for two reasons. Firstly, the binarity of sources in Lupus is not as completely characterized as that of Taurus sources. As a result, some Lupus disks may possess unknown stellar companions that have dynamically truncated their gaseous disks. Secondly, Lupus is an older star forming region ($\sim 3$\,Myr) than Taurus (1--2\,Myr). As a result, photoevaporation has had more time to evaporate away outer disks (Gorti et al.\ 2015). Giant planets, which have had more time to form in older systems, can also truncate disks dynamically. Despite these possible effects, the Lupus Class II disks still appear larger than the Class I disks. More extensive measurements of gas disk sizes are needed to understand the timing and extent of ``in-disk'' angular momentum transport. Among the Class II disks studied here, there is a likely bias toward larger disks which are brighter and easier to study and resolve. Measurements of disk radii for a larger number of disks would illuminate the full range and frequency of gas disk sizes as a function of age. At the present time, the existence of a large number of disks that are larger than Class I gas sizes (Fig.\ 3) strongly suggests that at least some disks spread in the Class II phase. One of the limitations of this study is the small number of Class I sources with reported gas disk radii. The presence of an infalling envelope also makes it challenging to measure Class I gas disk sizes; future work may find a way around this difficulty. If future studies of a larger population of Class I sources find disks systematically much larger than those studied to date, our conclusion will need to be revised. Further measurements of Class I disks can also reveal when disk spreading occurs. One might argue that the larger sizes of Class II disks are an outcome of viscous spreading in the Class I phase rather than the Class II phase. If true, surveys of a larger number of Class I disks should encounter Class I disks with larger sizes. Interestingly there is, in addition to the majority of large disks ($> 200$\,AU), a population of very small gas disks over a range of ages ($< 100$\,AU). The small disks shown in Figure 3 come primarily from the sample studied by Simon et al.\ (2017). These authors suggested that the small gas disk sizes they measured were due in part to to the cooler effective temperatures of the stars in their sample. However, we did not find a strong trend between stellar luminosity and gas disk size in the sample studied here. Such small disks are not anticipated at ages of several Myr if all disks spread with an effective viscosity of $\alpha >0.001$. These systems may be disks that are trucated from the outside by photoevaporation, disk winds, or planetary companions. Further observations of these systems, to search for winds or companions, can test these ideas. | 18 | 8 | 1808.05618 |
1808 | 1808.07101_arXiv.txt | The \emph{Fermi} $\gamma$-ray source 1FGL J1417.7--4407 (J1417) is a compact X-ray binary with a neutron star primary and a red giant companion in a $\sim$5.4 day orbit. This initial conclusion, based on optical and X-ray data, was confirmed when a 2.66 ms radio pulsar was found at the same location (and with the same orbital properties) as the optical/X-ray source. However, these initial studies found conflicting evidence about the accretion state and other properties of the binary. We present new optical, radio, and X-ray observations of J1417 that allow us to better understand this unusual system. We show that one of the main pieces of evidence previously put forward for an accretion disk---the complex morphology of the persistent H$\alpha$ emission line---can be better explained by the presence of a strong, magnetically driven stellar wind from the secondary and its interaction with the pulsar wind. The radio spectral index derived from VLA/ATCA observations is broadly consistent with that expected from a millisecond pulsar, further disfavoring an accretion disk scenario. X-ray observations show evidence for a double-peaked orbital light curve, similar to that observed in some redback millisecond pulsar binaries and likely due to an intrabinary shock. Refined optical light curve fitting gives a distance of 3.1$\pm$0.6 kpc, confirmed by a \emph{Gaia} DR2 parallax measurement. At this distance the X-ray luminosity of J1417 is (1.0$^{+0.4}_{-0.3}$) $\times 10^{33}$ erg s$^{-1}$, which is more luminous than all known redback systems in the rotational-powered pulsar state, perhaps due to the wind from the giant companion. The unusual phenomenology of this system and its differing evolutionary path from redback millisecond pulsar binaries points to a new eclipsing pulsar ``spider" subclass that is a possible progenitor of normal field millisecond pulsar binaries. | \label{sec:intro} Millisecond pulsars (MSPs) form when matter and angular momentum are accreted onto a neutron star from a non-degenerate companion, recycling them to very rapid spin periods. These systems are generally observable as low-mass X-ray binaries (LMXBs). The typical MSP recycling process involves accretion from a giant donor star overfilling its Roche-lobe, and ends as the orbital period grows and accretion onto the neutron star eventually stops. The resulting system has a rotationally-powered pulsar primary and a low-mass (0.2--0.3 \Msun) white dwarf companion, with orbital periods ranging from days to weeks \citep{Tauris06}. These types of systems constitute the bulk of the known MSPs in the Galactic field. The most important advance in expanding the known population of MSP binaries has been multi-wavelength (X-ray, optical, and radio) follow-up observations of \emph{Fermi}-LAT GeV $\gamma$-ray sources, which have led to the discovery of many MSPs in binaries with non-white dwarf companions. With improved statistics, these systems have been categorized based on their companion mass: black widows have very light ($M_{c}\lesssim0.10M_{\odot}$), highly ablated companions, while redbacks have non-degenerate, main sequence-like companions ($M_{c}\gtrsim0.2M_{\odot}$) that typically fill a substantial fraction of their Roche lobe \citep{Roberts11}. These systems frequently show lengthy, irregular radio eclipses, making them challenging to discover in normal radio pulsar surveys. These new binaries show interesting phenomenology, but have also drawn extensive interest as the long sought-after links between MSPs and their LMXB progenitors. In particular, three redbacks have been observed to undergo transitions between an accretion-powered ``disk state'' and a rotationally-powered ``pulsar state'' on timescales of days to months \citep{Archibald09, Papitto13, Bassa14, Roy15, Bogdanov15, Johnson15}. These systems, known as transitional millisecond pulsars (tMSPs), give one view of the end of the MSP recycling process, but also provide essential insights into the physics of low-level accretion onto magnetized compact objects and the interactions between MSPs and their stellar and gaseous environment. One challenge in extending these insights to understanding the formation of all MSPs is that all the known tMSPs have short orbital periods ($\lesssim 0.5$ days), and hence will likely not end their lives as the \emph{typical} field MSP binaries, which have degenerate companions and longer orbital periods. The progenitors to such systems are thought to be red giant--neutron star binaries with $> 1$ day periods \citep[e.g.,][]{Tauris99}. One of the few known systems fitting the latter description is a recent discovery. 1FGL J1417.7--4407 / 3FGL J1417.5--4402 (hereafter J1417) is a Galactic compact binary whose stellar counterpart was first discovered by \citet{Strader15} in an optical survey of unassociated \emph{Fermi}-LAT $\gamma$-ray sources. A variable X-ray source near the center of the \emph{Fermi} error ellipse matches a bright optical source. Optical photometry and spectroscopy revealed that the optical source is a red giant, and modeling its ellipsoidal variations, radial velocities, and rotational velocity showed that the system is an evolved $\sim$0.35 \Msun~late-G/early-K giant in a 5.37 day orbit with a $\sim$2 \Msun, suspected neutron star primary. This compact object interpretation was confirmed when \citet{Camilo16} found a 2.66 ms radio pulsar at the same location and with the same orbital period and phase as the optical binary discovered by \citet{Strader15}. The long orbital period, giant secondary, and short spin period suggest this system is likely in the late stages of the standard MSP recycling process that will end with a white dwarf companion in a $\gtrsim 8$ day orbit \citep{Podsiadlowski02}, making it the first \emph{typical} MSP binary progenitor identified in the Galaxy. The associated $\gamma$-ray emission, non-degenerate secondary, and MSP primary make J1417 similar to other redbacks, while its wider orbit, giant companion, and inferred evolutionary track are unique, leading us to suggest it as the first member of the ``huntsman" subclass of MSP binaries. Furthermore, despite the fact that J1417 hosts an MSP, this system shows phenomenology dissimilar to redbacks/tMSPs in their pulsar states: in particular, the optical spectra show double-peaked H$\alpha$ emission lines at nearly all epochs \citep{Strader15}, which is a classic signature of an accretion disk. This emission was observed even during times when the system was observed by \citet{Camilo16} as a radio pulsar, precluding the possibility that a pulsar to disk state change had occurred. Another peculiarity is that, at the distance inferred by \citet[][4.4 kpc]{Strader15}, the implied X-ray luminosity was $\sim 1.4\times10^{33}$ erg s$^{-1}$, typical for a redback/tMSP in the disk state but higher than usually observed for a system in the pulsar state. \citet{Camilo16} suggest a nearer distance, which would produce a more typical X-ray luminosity of $\sim 10^{32}$ erg s$^{-1}$, but which still leaves the spectroscopic evidence for an accretion disk unexplained. To better constrain the properties of J1417 and its connection to redbacks/tMSPs, here we report on new multi-wavelength observations of the system. We describe our newly acquired X-ray, radio, and optical/near-IR observations of the source in \S\ref{sec:xrayobservations}, \S\ref{sec:radioobs}, and \S\ref{sec:optobs}, respectively. In \S\ref{sec:optLCs} we perform detailed modeling of the ellipsoidal light curve, while we attempt to explain the source of the complex H$\alpha$ structures in \S\ref{sec:Halpha}. Concluding remarks are presented in \S\ref{sec:discussion}. | \label{sec:discussion} We have presented multiwavelength follow-up observations of the MSP binary J1417, a system likely in the late stages of the standard MSP recycling process that began after the secondary evolved off the main sequence and filled its Roche Lobe. Recently, \citet{Swihart17} reported on the discovery of a compact binary assocated with the unidentified \emph{Fermi} source 2FGL J0846.0+2820. This system, similar to J1417, also has an inferred heavy neutron star primary with a giant secondary in a wide 8.1 d orbit. Although no radio pulsations have yet been discovered in 2FGL J0846.0+2820, given the clear differences between these systems and the ``redback" and ``black widow" subclasses of MSP binaries, we have termed these systems with giant companions \emph{huntsman} binaries after the large huntsman spider. From the perspective of the pulsar, the solid angle subtended by the secondary in J1417 is 1.3--1.4\%, comparable to the value for typical redback systems with unevolved donors \citep{Roberts15}. However, if some of the X-ray emission comes from a shock close to the secondary, then the effective solid angle is larger. While the light curve itself shows no evidence for irradiation (\S~\ref{sec:optLCs}), consistent with the high luminosity of the evolved secondary, the evidence for a wind from the optical spectroscopy shows that a substantial amount of material is leaving the system. This material is likely responsible for the difficulty in detecting pulsations from the MSP, even compared to typical redbacks \citep{Camilo16}. It is possible that similar huntsman systems remain undetected for this same reason. The radio flux densities for J1417 are consistent with those expected for a MSP with modest scintillation, excepting the few VLA epochs where the pulsar is not detected. As it happens, these epochs were at superior or inferior conjunction, which is when the pulsar was also not detected in timing observations \citep{Camilo16}. This would be consistent with a scenario in which the radio emission was absorbed rather than scattered by the material in the system. On the other hand, both ATCA detections were obtained at or just after inferior conjunction. Hence there may be both stochastic and orbital components to the variations in eclipsing material, consistent with the conclusions we draw for the H$\alpha$ variations in \S\ref{sec:Halpha}. \citet{Strader15} pointed out that the 3FGL \emph{Fermi}-LAT spectrum of J1417 was a power-law with no evidence for curvature. This is unusual among MSPs, and is more similar to the $\gamma$-ray bright low-mass X-ray binaries 3FGL J1544.6--1125 and 3FGL J0427.9--6704 \citep{Acero15, Bogdanov16, Strader16}. If this power-law spectrum is confirmed in the forthcoming 4FGL \emph{Fermi}-LAT catalog, then it could suggest another source of high-energy emission in the system beyond simply the pulsar magnetosphere. The new X-ray observations have allowed a better comparison of the X-ray properties of J1417 to known redbacks and tMSPs. At our new optically inferred distance (3.1 $\pm$ 0.6 kpc), $L_X = 0.7-1.4 \times 10^{33}$ erg s$^{-1}$, which is more typical of tMSPs in their accretion-powered state and brighter than all known redbacks in their pulsar state. If there is no accretion disk, as we suspect, it is likely that the bulk of this X-ray emission is coming from a strong intrabinary shock near the surface of the secondary. The tidally locked giant could generate a substantial magnetic field that may facilitate the formation of a luminous shock. The most important new data to interpret J1417 would be an X-ray light curve complete in orbital phase, elucidating the nature of an intrabinary shock and allowing modeling of the H$\alpha$ emission in this context. Forthcoming \emph{Gaia} data releases should address systematics in the parallax measurements and definitively confirm the unusually high X-ray luminosity of the system. The unusual properties of this huntsman binary motivate ongoing searches for similar pulsar binaries. | 18 | 8 | 1808.07101 |
1808 | 1808.07271_arXiv.txt | \herschel\ observations of far infrared N$^+$ emission lines have demonstrated that dense plasma, with $n_e\sim30\,{\rm cm^{-3}}$, is ubiquitous in the inner Galactic plane. By combining the information from \herschel\ with other tracers of ionised gas, we build a picture of this dense plasma. We adopt a collisional ionisation model, so the analysis is not tied to a specific energisation mechanism. We find that the dense plasma is concentrated in a disk that is $130\;{\rm pc}$ thick, and makes a significant contribution to radio pulsar dispersion measures in the inner Galactic plane. The strength of the far infrared N$^+$ emission requires high temperatures in the plasma, with $T \simeq 19{,}000\,{\rm K}$ indicated both by the ratio of N$^+$ to C$^+$, and by the ratio of N$^+$ to microwave bremsstrahlung in the inner Galactic plane. This parallels the situation at high Galactic latitudes, where strong optical emission is observed from N$^+$ (and S$^+$), relative to both \ha\ and microwave bremsstrahlung, and suggests a common origin. If so, the same gas provides a natural explanation for the extreme radio-wave scattering phenomena that are sometimes observed in pulsars and quasars. We therefore propose a new picture of the warm ionised medium as seen in emission, in which the plasma is dense, hot, and localised in numerous structures of size $\sim 10^2\,{\rm AU}$ that are clustered around stars. | Amongst the many interesting results flowing from the far-infrared (FIR) {\it Herschel\/} observatory, one of the most remarkable is the discovery that N$^+$ line emission arises predominantly from dense, ionised gas ($n_e=30\pm 20\,{\rm cm^{-3}}$), throughout the inner Galactic plane \citep[][G15, henceforth]{goldsmith2015}. The physical context for this result is not completely clear, but the emission appears to be diffuse and widespread so the interstellar medium (ISM) seems to be implicated. Although the {\it Herschel\/} data are largely consistent with earlier findings from the COBE satellite \citep{bennett1994}, the dense plasma that is required does not yet have a place in our contemporary picture of the warm ionised medium (WIM) of the Galaxy \citep[e.g.][]{haffner2009}. Optical line emission from the ionised ISM has been studied since the early 1970's \citep{reynolds1973}, and is dominated by the WIM. By comparing emission measures (${\rm EM}=\int n_e^2\, {\rm d}s$) from optical line studies, with dispersion measures (${\rm DM}=\int n_e\, {\rm d}s$) from radio pulsars, along particular lines of sight, \citet{reynolds1991} concluded that the WIM has a low density ($n_e\sim0.1\,{\rm cm^{-3}}$) and a high filling fraction ($f\ga0.2$). Subsequent studies have reinforced those findings \citep[e.g.][]{berkhuisenmuller2008,gaensler2008}. However, these conclusions rest on the assumption that both integrals are dominated by the same regions of space. That might not be true if the ISM manifests a broad range in $n_e$: DM might arise mainly from low-density plasma that has a high filling fraction, while simultaneously most of the observed EM could be due to dense plasma that has a low filling fraction. An additional reason for caution is that optical studies of the WIM are strongly affected by dust -- via absorption and scattering -- which complicates the interpretation of the spectra, and censors our view of the distant WIM, particularly at low Galactic latitudes. The WIM that is remote from the Sun might be different to that seen locally. Models of the Galactic distribution of free electrons typically use several, structurally distinct components in order to approximate the observed distribution of pulsar DMs \citep{taylorcordes1993,cordeslazio2002,yao2017} (henceforth TC93, NE2001 and YMW16, respectively). In these models the DM at high Galactic latitudes is ascribed primarily to a thick disk component of free electrons that has a scale-height of order $1\,{\rm kpc}$. At low latitudes a thin disk component (scale-height of order $0.1\,{\rm kpc}$) dominates the observed DMs towards the inner Galaxy. The models also incorporate ionised gas that is associated with the Galactic spiral arms, and some additional, smaller-scale structures (e.g. the Gum Nebula). It is possible, in principle, that one or more of these components is something other than warm plasma, but usually they are all assumed to be WIM. The possibility that these various components of the WIM might differ greatly in character is underlined by the fact that the thin disk is known to be much more effective in scattering radio waves than the thick disk (TC93). Notionally, each of the free electron models (TC93, NE2001, YMW16) provides a unique prescription for the plasma density at every point in the Galaxy. However, as those models are designed to match pulsar DMs, primarily, they provide strong constraints on the average electron density, but the point-to-point density fluctuations are not directly constrained. In other words: where the free-electron models have a notional electron density $\bar{n}_e$, it is possible instead to have plasma of density $n_e\gg \bar{n}_e$ and filling fraction $f=\bar{n}_e/n_e\ll1$, so that the same DM results. Constraints on high density fluctuations are possible if measured EMs are simultaneously considered, but to date that approach has relied on optical emission lines and therefore relates primarily to the local WIM. To study the emission from the thin disk and spiral arm components of the WIM, it is best to observe at wavelengths that are unaffected by dust --- the FIR and radio bands. Radio recombination line (RRL) studies of the ISM have been pursued for many years \citep[e.g.][]{anantha1985,alves2015} and have often targeted the bright, inner disk of the Galaxy. In principle, RRL studies yield powerful diagnostic information on the plasma conditions (density, temperature, velocity field), and they provided some early indications of widespread, dense ($n_e\sim{\rm few\;cm^{-3}}$) plasma in the inner disk \citep[e.g.][]{anantha1985}. However, at the plasma densities of interest to us RRLs are maser lines \citep{draine2011}, which makes them difficult to interpret. More recently, multi-frequency surveys of the radio sky by the {\it WMAP\/} and \planck\ satellites have yielded high signal-to-noise ratio, well sampled, all-sky maps of Galactic radio emissions, including the bremsstrahlung from ionised gas \citep{bennett2003,adam2016}. These bremsstrahlung maps immediately place strong constraints on the large-scale distribution of the WIM. They also yield information about the microphysics. It was shown by \citet{davies2006} and \citet{dobler2008} that the ratio of WMAP bremsstrahlung \citep{bennett2003} to \ha\ \citep{finkbeiner2003} is lower than expected for photoionised plasma at $8{,}000\,{\rm K}$. This situation led to suggestions that the plasma temperature might be very low \citep[$3{,}000\,{\rm K}$,][]{dobler2009}, or that time-dependence might be playing a role \citep{dong2011}. The FIR studies of G15 have provided fresh insight into the physics of the ionised ISM. They sampled the full range of Galactic longitudes, with 149 pointings distributed over the Galactic plane, targeting the two N$^+$ lines at $122\,{\rm\mu m}$ and $205\,{\rm\mu m}$. The resulting picture is dominated by the inner Galaxy, with positive detections coming almost exclusively from longitudes $|l|\la60^\circ$. The intensity ratio of the two N$^+$ transitions is sensitive to the electron density in the emitting regions over the range $3\la n_e({\rm cm^{-3}})\la3{,}000$. Although the densities derived by G15 do vary from position to position, the variations are modest and a key feature of the data is that the density is high across all the various sight lines where N$^+$ emission is detected. High density plasma is therefore the dominant contributor to N$^+$ FIR emission for the inner Galactic plane. Henceforth we refer to this dense gas as dense-WIM (D-WIM) without prejudice to the specific physical environment in which it arises (e.g. near massive stars, perhaps), or what fraction of the WIM is in this form. The FIR perspective on the WIM is fundamentally challenging because the diffuse ISM is characterised, in part, by a typical pressure of $n\times T\sim3{,}000\;{\rm K\, cm^{-3}}$ \citep{jenkinstripp2011}, so that $n_e\sim0.15\,{\rm cm^{-3}}$ is expected in a diffuse, fully ionised region. If the WIM density is actually $200\times$ larger, one immediately faces difficult questions about the dynamics --- e.g. what confines the gas? Or, if it is not confined, why does it not simply expand until it reaches pressure equilibrium with the ambient medium? Similar problems have been encountered for decades in studies of radio-wave propagation in the ISM, where electron densities $n_e\sim10^{2\pm1}\,{\rm cm^{-3}}$ have been inferred from large radio-wave scattering angles and their associated flux modulations \citep{rickett1990,rickett2011}. Various extreme radio-wave scattering (ERS) phenomena have been reported, depending on the nature of the radio source. For pulsars: multiple imaging \citep{cordeswolszczan1986,rickett1997}, and parabolic arcs in the ``secondary spectrum'' \citep{stinebring2001,cordes2006}. For quasars: extreme scattering events \citep{fiedler1987,fiedler1994,bannister2016}, and intra-day variability \citep{kedziora1997,dennettthorpedebruyn2000,bignall2003}. In some cases the effects are known to be transient, implying that the regions of high plasma density are quite limited in their spatial extent \citep{kedziora2006,lovell2008,debruynmacquart2015}. Estimated sizes range from $\sim1\;{\rm AU}$ to $\sim100\;{\rm AU}$. The incidence of ERS in compact radio quasars is low, e.g. $\sim10^{-3}$ for the most extreme cases of intra-day variability \citep{lovell2003}, but the small size of the individual scattering regions means that they must nevertheless be very common --- much more numerous than stars, for example. Thus, although the ERS phenomena are rare, the plasma structures that cause them are not. This paper considers the properties of the Galactic D-WIM, with particular reference to the constraints that follow by combining the FIR spectroscopic information with other astrophysical data. Our aim is to answer basic questions such as: can the observed emission lines -- both optical and FIR -- all arise from D-WIM? If so, what is the likely temperature of the plasma? Can the D-WIM also explain the ERS phenomena? and the dispersion of radio pulses? Previous studies of the properties of the WIM have often assumed that the plasma is photoionised \citep[e.g.][]{mathis1986}. We did not make that assumption, partly because there are other possibilities -- low-energy cosmic-rays, for example, are an attractive option \citep{walker2016} -- and partly because it is already known that the optical spectra of the WIM observed at high latitude \citep{haffner1999,reynolds1999} are difficult to explain using photoionised plasmas. The difficulty is that the WIM appears to be hotter than can be explained by UV photoionisation alone, so that additional heating processes must be invoked. Lacking a clear picture of the physics giving rise to the WIM, we chose a route which does not require us to specify those processes. Instead we simply characterise the plasma by its density and temperature and require that it be in collisional ionisation equilibrium. This is a logical progression from previous studies: if UV photoionisation models of the WIM require additional heating processes, why not simplify the picture by dropping the photoionisation and leave everything to the heating process? The resulting model is a new approach to describing the WIM which, even if it is not entirely satisfactory as it stands, provides a useful point of reference. To compute the ionisation equilibria for our model, and the resulting emission line characteristics, we employ the {\it CHIANTI\/} atomic database and the associated Python scripts provided in the {\it ChiantiPy\/} software package \citep{dere1997,delzanna2015}. This paper is organised as follows. In the next section we describe the model of the D-WIM used in this paper. In section 3 we consider constraints that can be obtained directly from the \herschel\ data themselves. Sections 4 and 5 combine the information from \herschel\ with \planck\ data and with radio pulsar dispersion measures, respectively. We then consider the local D-WIM in \S6, using observations of microwave bremsstrahlung and optical line emission, and highlighting the connection to extreme radio-wave scattering phenomena. Discussion and conclusions follow in \S\S7,8. | The ionised gas discovered by \citet{goldsmith2015} is so dense and highly pressured that it makes sense to identify it as a distinct component in its own right --- the D-WIM. It forms a geometrically thin disk in the inner Galaxy, and that disk probably exhibits strong spiral structure. D-WIM makes a substantial contribution to the observed pulsar dispersion measures in the inner Galactic plane, albeit with large point-to-point variations, and may dominate the DMs on some of these lines-of-sight. At high Galactic latitude, by contrast, it makes a negligible contribution to pulse dispersion. The D-WIM dominates the scattering measure and the emission measure towards the inner Galactic plane, and probably contributes substantially to the observed emissions all over the sky. It is also a natural candidate to explain the extreme radio-wave scattering phenomena that are sometimes seen in pulsars and quasars. Drawing on what is known about the scattering material then leads to a picture of the D-WIM in which large numbers of tiny ($100\,{\rm AU}$) clouds are clustered in parsec-sized regions around stars. The velocity dispersion of the stars themselves provides vertical support against the gravitational potential of the disk. Several pieces of evidence suggest that the D-WIM is too hot for a pure UV photoionisation model, and within a collisional ionisation equilibrium model we prefer a temperature of $19{,}000\,{\rm K}$ (inclusion of charge transfer reactions in the model would likely lower our preferred temperature, see Appendix A). In the context of a circumstellar interpretation of the D-WIM, an important heat source for the plasma may be UV pumping of H$_2$. This would mean that hotter plasma would be associated with cooler photospheres, leading to a correlation between the D-WIM temperature and height above the Galactic plane. | 18 | 8 | 1808.07271 |
1808 | 1808.02381_arXiv.txt | We study a theory of massive tensor gravitons which predicts blue-tilted and largely amplified primordial gravitational waves. After inflation, while their mass is significant until it diminishes to a small value, gravitons are diluted as non-relativistic matter and hence their amplitude can be substantially amplified compared to the massless gravitons which decay as radiation. We show that such gravitational waves can be detected by interferometer experiments, even if their signal is not observed on the CMB scales. | Cosmic inflation became a standard paradigm in primordial cosmology, while it is still the subject of intensive researches for its unknown nature. A major prediction of the inflation theory is the production of primordial gravitational waves (GWs) which is scale-invariant and whose amplitude is proportional to the inflationary Hubble scale. Thus, by measuring the amplitude, we can reveal the energy scale of inflation. A number of different experiments such as Planck~\cite{Akrami:2018odb}, SKA~\cite{Janssen:2014dka}, LISA~\cite{AmaroSeoane:2012je}, Advanced-LIGO (A-LIGO)~ \cite{TheLIGOScientific:2016dpb} and DECIGO~\cite{Seto:2001qf,Kawamura:2011zz} put bounds on or aim to detect it. Nevertheless, it should be stressed that even if inflation occurred, the primordial GWs may be different from the conventional prediction based on general relativity. Among various possibilities to generalize the gravity theory, massive gravity attracts conspicuous attention and has been applied to the study on the primordial GWs~\cite{Dubovsky:2009xk, Gumrukcuoglu:2012wt,Fasiello:2015csa, Kuroyanagi:2017kfx}. The study of massive gravity stemmed from one of fundamental questions in classical field theory, ``Can a spin-$2$ field have a non-vanishing mass or not?'' This led Fierz and Pauli in 1939~\cite{Fierz:1939ix} to find a unique Lorentz-invariant mass term for a linearized spin-$2$ field, for which a nonlinear completion was found in 2010~\cite{deRham:2010ik,deRham:2010kj}. Another motivation is the accelerated expansion of the universe today: a graviton mass term may lead to acceleration without a need for dark energy. From this point of view, the assumption of Lorentz-invariance does not seem to have a firm justification since the graviton mass as an alternative to dark energy is supposed to be of the cosmological scale today and the expansion of the universe anyway breaks the Lorentz-invariance at the cosmological scale. Once the assumption of Lorentz-invariance is relaxed at the cosmological scale, new possibilities open up~\cite{ArkaniHamed:2003uy,Rubakov:2004eb,Dubovsky:2004sg,Blas:2009my,Comelli:2013txa,Langlois:2014jba}. In particular, a massive graviton forms a representation of the three-dimensional rotation group instead of four-dimensional Lorentz group, and therefore the number of physical degrees freedom in the gravity sector does not have to be five. The minimal theory of massive gravity (MTMG) introduced in \cite{DeFelice:2015hla,DeFelice:2015moy} is one of such possibilities and propagates only two physical degrees of freedom in the gravity sector, allowing for self-accelerating, homogeneous and isotropic cosmological solutions without pathologies such as strong coupling and ghosts, that are usually unavoidable in Lorentz-invariant massive gravity~\cite{DeFelice:2012mx}. The recently developed positivity bounds that significantly shrink the viable parameter space of the Lorentz-invariant massive gravity theory \cite{Cheung:2016yqr,Bonifacio:2016wcb,Bellazzini:2017fep,deRham:2017xox} also do not apply to those Lorentz-violating theories, including MTMG, since those bounds rely on Lorentz invariance at all scales. Moreover, because of the absence of extra degrees of freedom, MTMG completely evades the so called Higuchi bound, which states that the mass of a Lorentz-invariant massive graviton should be greater than the Hubble expansion rate up to a factor of order unity in order to avoid turning extra degrees of freedom into ghosts in cosmological backgrounds~\cite{Higuchi:1986py}. From the viewpoint of effective field theories, it is plausible to expect that there should be other Lorentz-violating massive gravity theories with similar properties and MTMG is just one concrete example of such theories. \footnote{ A generalization of solid inflation~\cite{Gruzinov:2004ty, Endlich:2012pz} dubbed supersolid inflation~\cite{Nicolis:2013lma} is classified into these theories and the primordial GWs in supersolid inflation are studied in \cite{Cannone:2014uqa, Bartolo:2015qvr, Ricciardone:2016lym, Ricciardone:2017kre}.} As we shall see in the rest of the present paper, those properties stated here open up a new observational window to GWs produced in the early universe. | In this letter, we have investigated the primordial GWs in the theory of massive tensor gravitons \eqref{Lh}. Contrary to the massless graviton case, the massive gravitons with a mass comparable to the inflationary Hubble scale $m=\mathcal{O}(H_{\inf})$ generate a blue-tilted tensor spectrum during inflation. Moreover, while their mass is significant after inflation, the dilution of the energy density of the massive gravitons becomes slower $\rho_h^{\rm massive}\propto a^{-3}$ than the massless ones $\rho_h^{\rm massless} \propto a^{-4}$. Thus, $\Omega_{\rm GW,0}$ in the massive case can be substantially amplified compared to the massless case. Consequently, we have obtained the blue-tilted and largely amplified primordial GWs which are suitable for the detection by the interferometers and to avoid the CMB constraint at the same time. We have derived the analytic expression for $\Omega_{\rm GW,0}$ \eqref{OGW estimate} and illustrated its detectability in Fig.~\ref{fig_spectrum} and \ref{fig_contour}. We have found that it is even possible to generate primordial GWs detectable for all of SKA, LISA and advanced-LIGO. Our findings further motivate the theoretical works on massive gravitons and the experimental efforts to detect stochastic GWs. | 18 | 8 | 1808.02381 |
1808 | 1808.02454_arXiv.txt | As astronomers, we are living an exciting time for what concerns the search for other worlds. Recent discoveries have already deeply impacted our vision of planetary formation and architectures. Future bio-signature discoveries will probably deeply impact our scientific and philosophical understanding of life formation and evolution. In that unique perspective, the role of observation is crucial to extend our understanding of the formation and physics of giant planets shaping planetary systems. With the development of high contrast imaging techniques and instruments over more than two decades, vast efforts have been devoted to detect and characterize lighter, cooler and closer companions to nearby stars, and ultimately image new planetary systems. Complementary to other planet-hunting techniques, this approach has opened a new astrophysical window to study the physical properties and the formation mechanisms of brown dwarfs and planets. I will briefly review the different observing techniques and strategies used, the main samples of targeted stars, the key discoveries and surveys, to finally address the main results obtained so far about the physics and the mechanisms of formation and evolution of young giant planets and planetary system architectures. | \label{sec:intro} % Today's heritage in direct imaging (DI) of exoplanets is intimately connected to the pioneer work in the late 80's and early 90's for the development of Adaptive Optics (AO) system, infrared (IR) detectors, and coronographic techniques for the instrumentation of ground-based telescopes. The COME-ON AO prototype\cite{kern1989,rousset1990} (that will later become the ESO3.6m/ADONIS instrument\cite{beuzit1993}), the Johns Hopkins University AO Coronagraph\cite{golimowski1992}, or the CFHT CIRCUS coronographic camera at CFHT\cite{beuzit1991}, were precursor instruments that soon motivated the research and development of more sophisticated AO high-contrast imagers on 10m-class telescopes (PALAO-PHARO at Palomar, CIAO at Subaru, NIRC2 at Keck, NaCo at VLT, and NIRI and NICI at Gemini), confirming that ground-based instrumentation had demonstrated performances that could compete with space and \textit{HST}. Already at that time, following the discovery of the first brown dwarf GD\,165\,B\cite{zuckerman1992}, the power of combining high-angular resolution and high-contrast techniques was well envisioned for the discovery and characterization of substellar companions, including exoplanets, and protoplanetary and debris disks \cite{nakajima1994}. The emblematic discoveries and images of Gl\,229\,B\cite{nakajima1995} and $\beta$ Pictoris\cite{mouillet1997} shown in Fig.~\ref{fig:precursors} simply supported it, and motivated it even more. Later-on, with the dawn of exoplanet discoveries in radial velocity in 1995, DI started to routinely exploit 10m-class telescopes in the early 2000s to slowly joined the small family of planet hunting techniques known nowadays with radial velocity, transit, $\mu$-lensing and astrometry. Nowadays, DI currently brings a unique opportunity to explore the outer part of exoplanetary systems at more than 5-10~au to complete our view of planetary architectures, and to explore the properties of relatively cool giant planets. The exoplanet's photons can indeed be spatially resolved and dispersed to probe the atmospheric properties of exoplanets (and brown dwarf companions). As today's imaged exoplanets are young (because they are hotter, brighter, thus easier to detect than their older counterparts), their atmospheres show low-gravity features, as well as the presence of clouds, and non-equilibrium chemistry processes. These physical conditions are very different and complementary to the ones observed in the atmospheres of field brown dwarfs or irradiated inflated Hot Jupiters (studied in spectroscopy or with transit techniques like transmission and secondary-eclipse, respectively). Finally, DI enables to directly probe the presence of planets in their birth environment. Planet characteristics and disk spatial structures can then be linked to study the planet -- disk interactions and the planetary system's formation, evolution, and stability, which is a fundamental and inevitable path to understand the formation of smaller telluric planets with suitable conditions to host life. \begin{figure}[t] \begin{center} \includegraphics[height=5cm]{web_print.jpg}\hspace{0.5cm} \includegraphics[height= 5cm]{eso9714a.jpg} \caption{\textit{Left,} Discovery image of the cool brown dwarf companion Gliese 299\,B with the Johns Hopkins University AO Coronagraph at Palomar with the \textit{HST}/WFPC2 follow-up observation\cite{nakajima1995}. \textit{Right,} ESO3.6m/ADONIS coronographic observation of the edged-on debris disk around $\beta$ Pictoris\cite{mouillet1997}.} \label{fig:precursors} \end{center} \end{figure} | \label{sec:conclu} % Today's success of DI relies on a sophisticated instrumentation designed to detect a faint planetary signal, angularly close to a bright host star. It also relies on a fine target selection of young, nearby stars sharing common kinematics, photometric and spectroscopic properties. This combination enabled the discovery of the first exoplanets and/or planetary mass companions at large physical separations ($>100$\,au) or with small mass ratio with their primaries. This success was followed by breakthrough discoveries of closer and/or lighter exoplanets. Each one of these discoveries has proven to be rich in terms of scientific exploitation and characterization to directly probe the presence of planets in their birth environment, to explore the orbital, physical and spectral characterization of young Jupiters, or more globally explore the young planetary system architectures. Vast efforts are now devoted to systematic searches of exoplanets in DI with an increasing number of large scale surveys. With bigger samples and enhanced detection performances, new large surveys of 100+ nights with the second generation of planet finders will offer unprecedented statistical constraints on the occurrence of giant planets at wide orbits. With the rich perspective of new/upgraded instruments from the ground (VLT/ESPRESSO, CFHT/SPIROU, ESO3.6/NIRPS, LBT/iLocater, SCExAO/CHARIS, Keck/KPIC, VLT/ERIS, LBT/SHARK(S), MagAO-X, Gemini/GPI+, VLT/SPHERE+...) and space missions (\textit{GAIA, TESS, CHEOPS, JWST, PLATO, WFIRST, ARIEL...}), devoted to the study of exoplanets, we can hope to obtain a complete census of nearby planetary systems within a decade from now. This will end the era of exoplanet surveys and will open a characterization phase for the extremely large telescopes (ELT, TMT, GMT) or the dedicated space missions from space (LUVOIR, HABEX...) that might exploit the synergy of various planet hunting techniques including DI with the ultimate objective to detect and characterize the first bio-signatures at the horizon 2030--2040. | 18 | 8 | 1808.02454 |
1808 | 1808.06794_arXiv.txt | Earlier studies on Coronal Mass Ejections (CMEs), using remote sensing and in situ observations, have attempted to determine some of the internal properties of CMEs, which were limited to a certain position or a certain time. For understanding the evolution of the internal thermodynamic state of CMEs during their heliospheric propagation, we improve the self-similar flux rope internal state (FRIS) model, which is constrained by measured propagation and expansion speed profiles of a CME. We implement the model to a CME erupted on 2008 December 12 and probe the internal state of the CME. It is found that the polytropic index of the CME plasma decreased continuously from 1.8 to 1.35 as the CME moved away from the Sun, implying that the CME released heat before it reached adiabatic state and then absorbed heat. We further estimate the entropy changing and heating rate of the CME. We also find that the thermal force inside the CME is the internal driver of CME expansion while Lorentz force prevented the CME from expanding. It is noted that centrifugal force due to poloidal motion decreased with the fastest rate and Lorentz force decreased slightly faster than thermal pressure force as CME moved away from the Sun. We also discuss the limitations of the model and approximations made in the study. | } Coronal mass ejections (CMEs) are the large-scale structures containing mass, kinetic energy and magnetic flux that are expelled from the Sun into the heliosphere \citep{Tousey1973,Hundhausen1984,Chen2011,Webb2012}. The CMEs in the heliosphere are referred as interplanetary coronal mass ejections (ICMEs) which are often understood as flux-ropes maintaining their magnetic connection to the Sun while propagating in the solar wind \citep{Larson1997}. They are of interest to scientific community because studying them we can enhance our understanding of (i) physical process responsible for removal of built-up magnetic energy and plasma from the solar corona (ii) kinematic and thermodynamic evolution of an expanding magnetized plasma blob in an ambient magneto-fluid medium and (iii) mechanism for exchange of energy and plasma dynamics between different plasma regions \citep{Low2001,Howard2007,Lopez2000}. They are also of interest to the technical community because they are the main drivers of severe space weather leading to disruption to a range of technologies such as communications systems, electronic circuits and power grids at the Earth, and thus our technology is vulnerable to them \citep{Schwenn2006,Pulkkinen2007,Baker2009}. CMEs have been detected by remote sensing and in-situ spacecraft observations for decades. Until a decade back, CMEs were routinely imaged only near the Sun primarily by coronagraphs onboard spacecraft. The launch of \textit{Solar TErrestrial RElations Observatory} (STEREO) in 2006 \citep{Kaiser2008} provided us the opportunity to track CMEs continuously between the Sun and Earth from multiple viewpoints. Most of the studies have focused on the signatures of origins for CMEs, their dynamic evolutions, masses, arrival times, induced radio bursts, geo-effectiveness, and connection between magnetic flux ropes measured in-situ and CME structures observed by coronagraphs and heliospheric imagers \citep{Munro1979,Webb2000,Wang2002,Cliver2002,Schwenn2005,Forsyth2006,Gopalswamy2009,Kilpua2012,Deforest2013,Mishra2015b,Shen2017,Mishra2017,Harrison2018}. There have been a few studies exploiting the radio, X-ray, and EUV imaging as well as in-situ observations for understanding the thermodynamic properties of the CMEs. EUV spectral observations from the ultraviolet coronagraph spectrometers (UVCS), coronal Diagnostic Spectrometer (CDS), and solar ultraviolet measurements of emitted radiation (SUMER) instruments on \textit{SOlar and Heliospheric Observatory} (SOHO) \citep{Domingo1995} have helped us to infer the density, temperature, ionization state and Doppler velocity of CMEs \citep{Raymond2002,Kohl2006}. They have also suggested that CMEs be a loop like structure with helical magnetic field, and probably have higher temperature than the inner corona \citep{Antonucci1997,Ciaravella2000}. The heating rates of CMEs inferred from UVCS observations show that heating of the CME material continues out to 3.5 \textit{R}$_\sun$ and is comparable to the kinetic and gravitational potential energies gained by the CMEs \citep{Akmal2001,Ciaravella2003}. Recently, \citet{Bemporad2010} estimated the physical parameters of plasma (temperature and magnetic field) in pre- and post-shock region using white-light, EUV and radio observations of a fast CME. The combination of density, temperature and ionization state of CMEs constrains their thermal history and have been used to understand the physical processes within CME plasma. Some internal properties of CMEs is also measured at near and beyond 1 AU from their in-situ observations by instruments onboard Voyagers, Ulysses, Helios, Wind, ACE, and STEREO spacecraft. For example, CMEs in in-situ observations show structure of a spiral magnetic field, low plasma beta, and low temperature than that in the ambient solar wind \citep{Burlaga1981,Richardson1993}. The reason for lower temperature is expansion of CMEs during their propagation as their leading edges usually move faster than the trailing edges and/or pressures inside CMEs are higher than that in the ambient solar wind. Measuring the properties of an individual ICME through the heliosphere is not always possible due to sparse distribution of in situ spacecraft which are rarely radially aligned and further due to difficulty in identification of ICMEs in the solar wind. The ion charge states in ICMEs are often higher implying high temperature (several million K) at their solar source \citep{Lepri2001,Zurbuchen2003}. The thermodynamic evolution of ICMEs have been statistically studied using in-situ observations taken over a range of radial distance from 0.3 to 30 AU in the heliosphere \citep{Wang2004a,Wang2005a,Liu2005,Liu2006}. These studies have demonstrated the coulomb collision within ICMEs and their moderate expansion compared with theoretical predictions. They also showed that magnetic field decreases faster in ICMEs than in the solar wind, but the density and temperature decreases slower in ICMEs than in the solar wind. This implied that the plasma in the ICMEs must be heated. The radial expansion speed of ICMEs is found to be of the order of the Alfven speed \citep{Jian2008}. Global MHD modeling of ICMEs based on a polytropic approximation to the energy equation has also been done for interpreting the observations \citep{Riley2003,Manchester2004}. However, the polytropic process and turbulence dissipation \citep{Goldstein1995} are intrinsically different and therefore modeling the thermodynamic state of CMEs is difficult. Although there are few studies addressing the internal states of CMEs, but most of them provide thermodynamics of CMEs only at a certain heliocentric distance and/or at a certain time. Based on a statistical surveys using multi-spacecraft measurements, the polytropic index of CME plasmas was suggested to be around 1.1 to 1.3 from 0.3 AU to 20 AU which is about constant over solar cycle \citep{Liu2005,Liu2006} while the polytropic index for solar wind is noted as 1.46 \citep{Totten1995}. Thus, the expansion of an ICME behaves more like an isothermal than adiabatic process which has polytropic index as 1.66. However, the understanding of the continuous evolution of internal state of an individual CME during its heliospheric propagation is still limited. So far the only attempt to figure out the internal state of an individual CME during its propagation in the outer corona was done by \citet{Wang2009}, (hereafter Paper I), in which a model to reveal the Flux Rope Internal State (FRIS) was developed. Using the model, one could infer the internal forces and thermodynamic properties of CMEs from the coronagraph and heliospheric imagers observations. In their study, they estimated the polytropic index of CME plasma and suggested that there is continuous heat injection into the CME plasma. They also found that thermal pressure caused the CME expansion while the magnetic force prevented the CME from expansion, and both the forces decrease continuously as CME move away from the Sun. However, there was a mistake in deriving equation 10 in Paper I though it did not affect the final results of their work, and the use of polytropic equation of state (Equation 12 in Paper I) was not proper. Generally, a polytropic process is a thermodynamic process that obeys the relation between fluid's thermal pressure ($p$) and density ($\rho$) by means of an index ($\Gamma$) described as \begin{eqnarray} p=b\rho^\Gamma \label{polytropic} \end{eqnarray} \\ where both $\Gamma$ and $b$ are not constants and change with time. It describes the change of state of any fluid. We emphasize that the value of $b$ was kept constant in Paper I which was incorrect. This is because $b$ should change when a thermodynamic system evolve from one polytropic process to another. Further, we use the equation of thermodynamics and derive a few additional parameters, such as absorbed heat, entropy, heating rate and entropy changing rate of the CME. Thus, in the present study, we improve the Flux Rope Internal State (FRIS) model (Section~\ref{fris}), and apply it to the CME of 2008 December 12 to demonstrate what we can learn from the observations with the aid of the model (Section~\ref{appmodel}). A summary and discussion on our study are presented in Section~\ref{Resdis}. \textbf{ | \label{Resdis}} \begin{table} \caption{List of the derived internal thermodynamic parameters, constants and coefficients from FRIS model} \begin{center} \hrule \vspace{0.1cm} \hrule {\small \begin{tabular}{cccc} \multicolumn{4}{c}{\textit{Internal thermodynamic parameters derived from the model}} \\ \hline Quantities & Factors & Values & SI units \\ \hline Lorentz force ($\overline{f}_{em}$) & $\frac{k_2 M}{k_7}$ & $c_2 R^{-5} + c_3 L^{-2} R^{-3}$ & Pa m$^{-1}$ \\ Thermal pressure force ($\overline{f}_{th}$) & $\frac{k_2 M}{k_7}$ & $\lambda L^{-\gamma} R^{-\gamma-1}$ & Pa m$^{-1}$ \\ Centrifugal force ($\overline{f}_{p}$) & $\frac{k_2 M}{k_7}$ & $c_1 R^{-5} L^{-1}$ & Pa m$^{-1}$ \\ Proton number Density ($\overline{n}_p$) & $\frac{M}{k_7}$ & $\frac{1}{\pi m_{p}}$ $(L R^2)$$^{-1}$ & kg m$^{-3}$ \\ Thermal pressure ($\overline{p}$) & $\frac{k_2 k_8 M}{k_4 k_7}$ & $\lambda (L R^2)^{-\gamma}$ & Pa \\ Temperature ($\overline{T}$) & $\frac{k_2 k_8}{k_4}$ & $\frac{\pi \sigma}{\gamma-1} \lambda (LR^2)^{1-\gamma}$ & K \\ Changing rate of entropy ($\frac{ds}{dt}$) & & $\frac{1}{\sigma \lambda} \frac{d\lambda}{dt}$ & J K$^{-1}$ kg$^{-1}$ s$^{-1}$ \\ Heating rate ($\overline{\kappa}$) & $\frac{k_2 k_8}{k_4}$ & $\frac{\pi}{\gamma-1}(LR^2)^{1-\gamma} \frac{d\lambda}{dt}$ & J kg$^{-1}$ s$^{-1}$ \\ Thermal energy ($E_i$) & $\frac{k_2 k_8 M}{k_4}$ & $\frac{\pi }{\gamma-1} \lambda (L R^2)^{1-\gamma}$ & J \\ Magnetic energy ($E_m$) & & $E_{m1}$ + $E_{m2}$ & J \\ $E_{m1}$ & $\frac{k_9}{k_7}$ & $\frac{\pi}{\mu_0} L^{-1}$ & J \\ $E_{m2}$ & $k_7 k_{10}$ & $\frac{\pi}{\mu_0} L R^{-2}$ & J \\ Polytropic index ($\Gamma$) & & $\gamma+\frac {\ln \frac{\lambda(t)}{\lambda(t+\Delta t)}} {\ln \left\{\frac{L (t+\Delta t)}{L (t)} \Big[ \frac{R(t+\Delta t)}{R (t)} \Big]^2 \right\}}$ & \\ \end{tabular} \hrule \begin{tabular}{cc} \multicolumn{2}{c}{\textit{All the constants ($k_{1-12}$) introduced in the model}} \\ \hline Constants & Interpretations \\ \hline $k_1$ & Scale the magnitude of the poloidal motion \\ $k_{2-6, 8-10}$ & Integrals of distributions of density, poloidal speed and magnetic vector potential \\ $k_7$ & Ratio of the length of the flux rope $l$ to the distance $L$ \\ $k_{11}$ & Coefficient of equivalent conductivity \\ $k_{12}$ & Aspect ratio, i.e., the ratio of the radius of the flux rope $R$ to the distance $L$ \\ \end{tabular} \hrule \begin{tabular}{lc} \multicolumn{2}{c}{\textit{All the coefficients ($c_{0-5}$) introduced in the model}} \\ \hline Coefficients & Expressions \\ \hline $c_0$ & $\frac{k_4 M^{\gamma-1}}{k_2 k_7^{\gamma-1}}$ \\ \noalign{\vskip 0.1cm} $c_1$ & $\frac{k_1^2 k_3 L_A^2}{k_2 M^2} \ge 0$ \\ \noalign{\vskip 0.1cm} $c_2$ & $\frac{- k_5 k_7}{\mu_0 k_2 M}$ \\ \noalign{\vskip 0.1cm} $c_3$ & $\frac{- k_6}{\mu_0 k_2 k_7 M} \le 0$ \\ \noalign{\vskip 0.1cm} $c_4$ & $\frac{k_2 k_8 M}{(\gamma-1) k_4 k_7 k_{11} T_a}$ \\ \noalign{\vskip 0.1cm} $c_5$ & $\frac{\pi \sigma k_2 k_8}{(\gamma-1) k_4 T_a}$ \\ \noalign{\vskip 0.1cm} \end{tabular}} \hrule \vspace{0.1cm} \hrule \label{summ} \end{center} \tablecomments{\scriptsize Top panel: Quantity=Factor $\times$ Value. The factors are unknown constants that can not be inferred from FRIS model. The distance ($L$) of the center of flux rope CME from the solar surface and its radius ($R$) can be derived from the observations. The variable $\lambda$ is given by equation~\ref{govern_n2}. The $\gamma$ is the heat capacity ratio (adiabatic index) and $\mu_{0}$ is the magnetic permeability of free space. The $\sigma$=$\frac{(\gamma-1)m_p}{2k}$, where $m_p$ is the proton mass and $k$ is the Boltzmann constant, $M$ is the total mass of a CME. Middle panel: Among the constants, $k_{2,7,8,11} > 0$ and $k_{3,6,9,10} \ge 0$. Bottom panel: The coefficients ($c_{0-5}$) are also constants and can be derived from the model. $L_A$ is the total angular momentum of a flux rope CME and $T_a$ is the equivalent temperature of the ambient solar wind around the CME base. \normalsize} \end{table} In the present study, we have improved the analytical flux rope internal state (FRIS) model for investigating the evolution of the internal thermodynamic state of a CME. The model is constrained by the observed propagation and expansion behavior of a CME. The internal thermodynamic parameters derived from the model and the details of the constants introduced in the model are summarized in the Table~\ref{summ}. We have applied the FRIS model to the CME of 2008 December 12 and determined the evolution of its internal properties. We find that the polytropic index of the CME plasma decreased from initially 1.8 to 1.66 slowly and further quickly decreased down to around 1.35. It suggests that initially there be heat released out from the CME before reaching to an adiabatic state and then a continuous injection of heat into the CME plasma. The value of polytropic index obtained in our study is not in good agreement with that obtained in \citet{Liu2005,Liu2006} using combined surveys of ICMEs in in situ observations. However, their estimated polytropic index of 1.1 to 1.3 was for the distance between 0.3 and 20 AU while the CME we have studied was within 15 solar radii from the Sun. We also find that the Lorentz force is directed inward while the thermal pressure force and centrifugal force is directed outward from the center of the CME. All these three forces decreased as the CME propagated away from the Sun. The time-variation in resultant direction of the net force is consistent with the expansion acceleration which reveals that the thermal pressure force is the internal driver of the CME expansion, whereas the Lorentz force prevented the CME from expansion. We emphasize that, in general, the direction of Lorentz force may be both inward or outward, i.e., the Lorentz force can cause both expansion and contraction of the flux-rope. As it is obvious from equation~\ref{lorentz_n2} that the constant $k_6$ is always larger than or equal to zero, while the sign of the constant $k_5$ is determined by the $B_z^2 (R) - B_z^2 (0)$. It implies that $J_\phi$ $\times$ $B_z$ could contribute in contraction or expansion depending on the distribution of $B_z$ in the cross-section of the flux rope. Also, it can be noted from equation~\ref{emforce} that the direction of Lorentz force depends on the unknowns $c_2$ and $c_3$. The coefficient $c_3$ is always less or equal to zero while the sign of the coefficient $c_2$ depends on the constant $k_5$. For the CME under study, on fitting equation~\ref{govern_n1n2}, the value of $c_2$ was estimated to be less than zero. This implies that the sign of $k_5$ was positive. Therefore, the direction of Lorentz force was inward which prevented the CME from expansion. Based on the obtained results, we note that the negative expansion acceleration, Lorentz force dominating the thermal force and release of heat happen together. Moreover, we find that among the three forces, the centrifugal force decreased with fastest rate and Lorentz force decreased slightly faster than the thermal pressure force. We note that even a small difference between the Lorentz and thermal forces can drive the expansion acceleration of the CME at the order of 1 m s$^{-2}$. As a consequence of the release and absorption of heat by the CME, a decrease in the entropy during initial phase and an increase in the entropy at latter phase of the CME propagation is found. Our analysis find that rate of heat release and entropy loss of the CME is slowing down with time, and gradually turning into increasing rate of heat absorption and entropy gain. Thus, the CME studied here is found to go through an isentropic (adiabatic and reversible, no heat transfer) point around 9 \textit{R}$_\odot$ after which the expansion acceleration of the CME is positive. Since, heat is disorganized form of energy, the direction of entropy transfer is the same of the direction of heat transfer. This CME launched with hot temperature from lower corona of the Sun through a rapid magnetic energy release process and then cooled down during expansion. The heat release out of the CME in its initial propagation phase before around 9 \textit{R}$_\odot$ is probably due to that the CME structure was not expanded sufficiently and therefore still hotter enough than ambient coronal medium. However, the CME is found to be heated in the latter phase of its propagation. The heating could be possibly due to the conduction of heat from the solar surface, solar wind or due to dissipation of magnetic energy into thermal energy. \citet{Kumar1996} suggested that the heating may result from the local magnetic dissipation as they have shown that around 58\% of magnetic energy lost in the expansion is available for the heating. In our study, we attempted to apply FRIS model to the complete measurements from COR1 and COR2 observations. However, we faced difficulty in fitting the governing equation~\ref{govern_n2} for the CME measurements in COR1 FOV, for which the model was not reliable. We think that the rising and declining phase of the CME acceleration in COR1 FOV and then a gap of measurements between COR1 and COR2 FOVs, could be the reasons for the unreliability. We also tried to separate the observations of acceleration and deceleration phase and then fit the each phase with the model. This also could not improve the fitting as the number of data points were not sufficient enough. Based on these trials, we decided not to include the COR1 measurements in the present study. This is logical as the CME may not follow the self-similar expansion, which is one of the basic assumptions of the FRIS model, during its impulsive acceleration phase near the Sun. Moreover, the gravitational forces and the equivalent fictitious force in a non-inertial frame are not considered in FRIS model. Although these forces are very small for most CMEs beyond outer corona, however they may significantly distort the model results for some CMEs which have slow expansion acceleration in the inner corona near the Sun. Further, there have been studies on the solar wind stretching effect caused by the divergent radial expansion of solar wind flow, which is of a kinematic effect, on the expansion of CMEs \citep{Newkirk1981,Suess1988,Crooker1996,Riley2003,Riley2004}. Due to this effect, a flux rope CME in the solar wind does not remain in cylindrical shape but rather becomes a convex-outward, ``pancake'' shape. These studies confirm that the self-similar assumption is broken gradually as CME moves away from the Sun. Earlier studies have suggested that self-similar assumption is a valid approximation when the CME is nearly force-free and not too far away from the Sun \citep{Low1982,Burlaga1988,Chen1997,Demoulin2009,Shapakidze2010,Subramanian2014}. We expect that the FRIS model would be suitable to apply on the CME observations from couple of solar radii (i.e, COR2 FOV) to within tens of solar radii from the Sun. In another study, we plan to estimate the internal parameters of the CME beyond coronagraphic FOV using CME measurements from HI1 observations. In the FRIS model, some effects of coupling between the ambient solar wind and the CMEs have been implicitly included. The drag interaction between the CMEs and the solar wind, causing momentum exchange between them, has effect on the propagation speed (i.e., $v_c$) of the CMEs \citep{Cargill2004,Manoharan2006,Vrsnak2010,Subramanian2012,Mishra2013,Liu2016}. Further, the pressure in ambient solar wind has effect of preventing the free expansion (i.e., $v_e$) of CMEs \citep{DalLago2003,Demoulin2009,Gulisano2010}. These effects of solar wind on a CME give different time-variation of $L$ and $R$, which can be measured from imaging data, and therefore are included in the model. Moreover, the distortion of the circular cross section of the flux rope is not considered mainly because the difficulty of the derivation of the model. Following the discussion in Paper I, another limitation of the model is due to the assumption of an axisymmetric cylindrical flux rope, and thus the curvature of the axis of the flux rope is not considered in the model. The axial curvature causes the Lorentz force to have an additional component for driving the CME in the heliosphere. The neglect of the axial curvature generally would cause an underestimation of Lorentz force from the model. We emphasize that distortion of the circular cross-section of the flux rope would cause an overestimation of the its radius ($R$) and underestimation of its distance ($L$) from the solar surface. Therefore, it is expected that from our measurements the expansion speed is overestimated and the propagation speed is underestimated. Thus we find that in our study, the density, thermal pressure force and Lorentz force is underestimated than its actual values. However, the extent of underestimation would be different at different distances from the Sun. We expect that errors in the derived internal thermodynamic parameters would not be significant at smaller distances, i.e., within COR2 FOV, where the distortion in the circular cross-section is not much. The FRIS model described in this study is an improved version of the earlier developed flux rope model in Paper I. In Paper I, the authors have made a comparison of their model with \citet{Kumar1996}, and the differences described there would also be valid for the improved version of the model. It would be interesting to extrapolate the estimated internal thermodynamic properties of the CMEs to far away from the Sun up to around 1 AU. This can be done by extrapolating the observed kinematics using drag based model \citep{Vrsnak2013} of the CMEs or directly measuring the kinematics from imaging observations. The uncertainty from the model can further be examined based on the CME measurements from in situ observations. In a separate study, we would focus on the quantification of errors due to breakdown of some of the assumptions taken in the model. Further, it would be worth examining if other CMEs also show a similar evolution of their thermodynamic parameters as 2008 December 12 CME studied here. \newpage \textbf{ | 18 | 8 | 1808.06794 |
1808 | 1808.04428_arXiv.txt | This is a guide for preparing papers for \textit{Monthly Notices of the Royal Astronomical Society} using the \verb'mnras' \LaTeX\ package. It provides instructions for using the additional features in the document class. This is not a general guide on how to use \LaTeX, and nor does it replace the journal's instructions to authors. See \texttt{mnras\_template.tex} for a simple template. The abstract of the paper. | The journal \textit{Monthly Notices of the Royal Astronomical Society} (MNRAS) encourages authors to prepare their papers using \LaTeX. The style file \verb'mnras.cls' can be used to approximate the final appearance of the journal, and provides numerous features to simplify the preparation of papers. This document, \verb'mnras_guide.tex', provides guidance on using that style file and the features it enables. This is not a general guide on how to use \LaTeX, of which many excellent examples already exist. We particularly recommend \textit{Wikibooks \LaTeX}\footnote{\url{https://en.wikibooks.org/wiki/LaTeX}}, a collaborative online textbook which is of use to both beginners and experts. Alternatively there are several other online resources, and most academic libraries also hold suitable beginner's guides. For guidance on the contents of papers, journal style, and how to submit a paper, see the MNRAS Instructions to Authors\footnote{\label{foot:itas}\url{http://www.oxfordjournals.org/our_journals/mnras/for_authors/}}. Only technical issues with the \LaTeX\ class are considered here. Sections and lists are generally the same as in the standard \LaTeX\ classes. \subsection{Sections} \label{sec:sections} Sections are entered in the usual way, using \verb' | 18 | 8 | 1808.04428 |
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1808 | 1808.03722_arXiv.txt | We present a long-term light curve of the precataclysmic variable (CV) V1082\,Sgr obtained by the $K2$-mission over the course of 81 days. We analyze the entire complex light curve as well as explore several sections in detail with a sliding periodogram. The long dataset allows the first detection of the orbital period in the light curve, as well as the confirmation of cyclical variability on a longer timescale of about a month. A portion of the light curve in deep minimum reveals a clean, near-sinusoidal variability attributed to the rotation of the spotted surface of the donor star. We model that portion of the light curve assuming that the donor star grossly under-fills its Roche lobe, has cool spots similar to a chromospherically active, slightly evolved early K-star, and might be irradiated by the X-ray beam from the magnetically accreting white dwarf. The fast variability of the object in the active phases resembles the light curves of magnetic CVs (polars). | Cataclysmic Variables (CVs) are interacting close binary systems consisting of a red star filling its corresponding Roche lobe and losing matter to a white dwarf (WD) companion \citep{1995CASSS...5.....H}. In systems with a strongly magnetic WD the matter falling into the potential well of the WD is captured and channeled onto the magnetic pole(s). There are also a handful of binaries known as prepolars, which are considered as part of the CV family, as there is evidence of accretion onto the WD in these systems \citep{2005ASPC..330..137W,2005ApJ...630.1037S}. All of them contain late M dwarfs, and the orbital periods of the systems are comparable to typical orbital periods for CVs (i.e. less than 6 hr). However, where the prepolars differ dramatically from CVs is in their accretion rates. Prepolars have been observed to accrete at a rate that is two orders of magnitude less than the typical rate in CVs. In fact, prepolars are technically not CVs, since the accretion geometry in CVs typically requires the secondary to be overflowing its Roche lobe, while prepolars are detached binaries. Instead, accretion in prepolars is assumed to arise from a coupling of the magnetic fields of both stars in the binary that draws matter lost by the wind from the donor star to accrete onto the magnetic pole of the WD \citep{2012ApJ...758..123W,2015SSRv..191..111F}. There should be counterparts of prepolars with donors of earlier spectral types. So far, only two or three candidates have been proposed and the jury is still out as to whether these systems are truly prepolars \citep{1988ApJ...331L..29R,2017ASPC..509..489T}. The $K2$ mission commenced after the original {\sl Kepler} mission was terminated for technical reasons \citep{2014PASP..126..398H}. It provides precision photometry of fields concentrated around the ecliptic plane. $K2$ provides data at long 30\,m and short 1\,m cadences over $\sim$80 day intervals with precision close to that of the original {\sl Kepler} mission. We proposed observations of \sgr, an object that demonstrates a large amplitude variability on very different time scales \citep{2016ApJ...819...75T}. Previous long-term photometry revealed that the system is active, or bright most of the time with occasional deep minima. The variability appears to be quasiperiodic with cycles roughly 29 days long. No definite periodicities were found at that or shorter periods. The orbital period of 20.82\,hr was determined from the spectroscopic analysis of radial velocity (RV) variations \citep{2010PASP..122.1285T}. The orbital period is well above the 0.4\,day upper limit at which a zero age main sequence red dwarf would be filling its corresponding Roche lobe in a binary with an average mass WD primary. The donor star is clearly visible at $ 50-100\%$ of the total flux around 5000\AA\ depending on the accretion activity state. Although the object often shows strong emission lines resembling a CV, only a spectrum of a K\,2 star is visible in the optical range during the times of minima with a lack of additional radiation in the continuum or spectral lines. This further supports the idea that the companion is underfilling its Roche lobe, as these minima are difficult to explain with a Roche lobe overfilling scenario. However, the precise determination of spectral and particularly the luminosity class of the donor star based on the low-resolution and highly variable spectra was inconclusive. The secondary is chromosperically active as can be inferred from the presence of narrow H$_\alpha$ and \ion{Ca}{2} emission lines \citep{2016ApJ...819...75T} when the accretion is halted. When the accretion turns on, the emerging strong emission lines are symmetric and of low RV suggesting that they are not formed in an accretion stream characteristic to ordinary polars. Hence, \citet{2016ApJ...819...75T,2017ASPC..509..489T} suggest that V1082\,Sgr is a prime candidate for one of the hard sought detached binaries with a magnetic WD and a magnetically active K-star. V1082 Sgr has also been studied at X-ray wavelengths by \citet{2013MNRAS.435.2822B} who showed that \sgr\ is highly variable in X-rays, with variations on a wide range of time scales from hours to months. The length of the observation was not sufficient to cover the unusually long orbital period of the system. However, \citet{2016ApJ...819...75T} showed that the observed X-ray flare may be related to a changing viewing angle of the accretion column over the orbital period during one of the system's accretion driven stages. A complex fit to the X-ray spectrum reinforces the proposition that the plasma reaches typical temperatures achieved in a magnetically confined accretion flow, where a standing shock is formed at the poles of a compact star. Here we present the analysis of $K2$ observations of \sgr, which provides new information on the accretion process in this system and adds to the evidence for the magnetic nature of the binary. Some parallels with the X-ray results can be drawn. \clearpage \section[]{Observations} \begin{figure}[t] \centering \includegraphics[width=8.5cm, clip]{k2_lc} \caption{ Light curve of \sgr. Bottom panel: the individual measurements are plotted as tiny dots, connected by thin line. The thick line is a cubic polynomial fit to the data. Top panel: the residual light curve after subtraction of the fit and converted to a logarithmic scale. } \label{fig:lc} \end{figure} \sgr\ was observed by the {\sl Kepler} spacecraft as part of Campaign 7 of the $K2$ mission from 2015 October 4 to December 26 (BJD =245\,57301.4 -- 57382.8; MJD 2467.2 -- 2549.8 ). The integration time of the {\sl Kepler} spacecraft is 6.02\,s. Since it is unfeasible to save every single data point taken of an object with this short an integration time (due to the limitations of bandwidth when downloading data from the spacecraft), {\sl Kepler} data are averaged over two different time spans -- short cadence and long cadence. For short cadence data, exposures are averaged over approximately 1 minute, while long cadence data correspond to 30 minutes of data. As such, the short cadence data can be treated as a subset of long cadence data, since they are both derived from the same set of 6\,s exposures. We obtained both long and short cadence data (exposures of 29.4\,m and 58.8\,s respectively) for \sgr. The data are in the form of integrated photoelectrons collected during either a one or 30\,m observation. Each data point in the time series is the direct sum of counts within a predefined aperture. The apertures are constructed to maximize the signal-to-noise ratio of the light curves and take into account the varying pixel response function across the focal plane \citep{2010ApJ...713L..97B}. The light curves obtained by the in-house pipeline reduction were downloaded from the Mikulski Archive for Space Telescopes. For the short cadence light curve we acquired data processed by the Everest pipeline \citep{2016AJ....152..100L} which aims to increase the precision of the photometry designed for exoplanet detection. However we found that the procedure misinterpreted the overall variability of the object and treated them as undesirable trends, removing features which we believe are part of the intrinsic variability of this peculiar binary. Hence, we use in the following analysis the raw fluxes corresponding to the {\scshape{sap\_\,flux}} in the long cadence dataset. In general, the variability demonstrated by this object far exceeds the stringent precision limits of the {\sl Kepler/K2} mission, designed to detect microvariability produced by transient extra-solar planets. The initial 1.2 days of data, as well as outliers found upon visual inspection as not belonging to the intrinsic variability of the object, were removed. \begin{figure}[t] \includegraphics[width=8cm, bb=20 160 580 700, clip]{power_k2} \caption{ Power spectra of the polynomial fit to the light curve (red curve) and to the residual light curve (blue curve) are presented in the bottom panel. The zoomed-in portions of the power spectra with prominent peaks are presented in upper panels. The arrow in the upper left panel indicates 29\,days cyclical variability of the object. The arrow in the upper right panel corresponds to the spectroscopic orbital period of the binary. The gray curve on both of the top panels represents a power spectrum of the original observed light curve. The frequency is in days$^{-1}$. } \label{fig:pws} \end{figure} Additional 40 day monitoring of the object was obtained with the 1.5\,m telescope of Observatorio Astron\'omico Nacional at San Pedro M\'artir (OAN SPM) equipped with the RATIR instrument \citep{2012SPIE.8446E..10B,2012SPIE.8444E..5LW} and operating robotically. The data were acquired in Bessel-V and near-IR $J$ and $H$ bands and differential photometry was used to obtain the final magnitudes. An automatic pipeline procedure implemented in python was used to perform preliminary tasks of bias subtraction, flat-fielding, and cosmic-ray removal. The pipeline also conducts astrometric calibration and sky subtraction for infrared (IR) images. Aperture photometry was done using IRAF {\sl aphot} package \citep{1986SPIE..627..733T}. For more detailed information on these and simultaneous spectroscopic observations see \citet[][hereafter Paper\,II]{paper2} | We explored an unprecedented 80-day-long uninterrupted light curve of the enigmatic binary \sgr\ with high time resolution obtained by the $K2$ mission. This is impossible using ground-based telescopes, with the long 0.867\,d orbital period of the binary and $\sim29$\,days cyclical variability. We identified the orbital variability in the light curve known previously from spectroscopy. We also observe cyclical, quasiperiodic minima in the light curve in the $K2$ data, as well as in the follow-up ground based photometry. The minima usually are brief, lasting two or three orbital periods, followed by a sudden and strong increase of the brightness. When the system is active it exhibits fast, large amplitude variability resembling ordinary magnetic CVs or polars. Some transient periods are seen in the active phase, for which there are no ready explanations. The $\sim2$\,hr transient period that has been observed in X-rays is marginally detected in the optical light curve. The only persistent, and strictly periodic signal is the orbital one, revealed in both active accretion and accretion-shutdown states. In the active state the signal at the orbital frequency is strong, indicating modulation of the accretion process similar to polars. The period is coherent throughout the entire 80 day dataset. In the low brightness state the orbital period persists and is clearly visible. Spectroscopic and photometric observations and the spectral energy distribution show that during this interval nearly all of the light comes from the K\,2 star. Detection of a smooth orbital variability during the deep minimum confirms the absence of accretion, as the latter is usually accompanied with fast spikes in the light curve. The form of the light curve suggests that the K-star is not ellipsoidally shaped. The duration of this nonaccreting state is not long and has not been observed repetitively with sufficient time resolution in order to provide an observational base for serious modeling. However, we demonstrate qualitatively that it can simply be a result of a large cool spot on the surface of a chromospheric K-star. The orbital variability could also be produced by a hot spot formed as a result of irradiation. The reality can be more complex with both hot and cool spots present. Regardless of the origin of spot(s), the light from the K-star modulated with the orbital period means that the K-star rotates synchronously with the binary system. The form of the variability indicates an absence of deformation associated with the star filling its Roche lobe. These are the two the most important results from our analysis of the $K2$ observations. Paper\,II pairs these conclusions with the mass of the WD determined from the X-ray observations and the results of the high-resolution spectroscopy to further the interpretation of this interesting system. | 18 | 8 | 1808.03722 |
1808 | 1808.04806.txt | When a neutron star cools to below the critical temperature for the onset of superfluidity, nucleon pair breaking and formation (PBF) processes become the dominant mechanism for neutrino emission, while the modified URCA and the nuclear bremsstrahlung processes are suppressed. The PBF processes in neutron stars have also been used to set upper limits on the properties of axions, which are comparable to those set by supernova SN 1987A. We apply this constraint on Weinberg's Higgs portal model, in which the dark radiation particles (the Goldstone bosons) and the dark matter candidate (a Majorana fermion) interact with the Standard Model (SM) fields solely through the mixing of the SM Higgs boson and a light Higgs boson. We compare the Goldstone boson emissivity with that of the neutrinos by considering several superfluid gap models for the neutron singlet-state pairing in the neutron star inner crust, as well as in the core region. We find that the PBF processes in the superfluid neutron star interior can indeed probe Weinberg's Higgs portal model in a new parameter space region. Together with our previous works on the constraints from supernovae and gamma-ray bursts, this study demonstrates further the competitiveness and complementarity of astrophysics to laboratory particle physics experiments. | \label{sec:intro} After its birth, a neutron star with an initial core temperature of $\sim 10^{11}~{\rm K}$ cools via neutrino emission from the interior during the first $10^5$ years, and subsequently by photon thermal emission from the surface~\cite{Yakovlev:2000jp,Yakovlev:2004iq,Page:2005fq,Potekhin:2015qsa,Schmitt:2017efp,Potekhin:2017ufy,Ozel:2012wu}. The basic neutrino production mechanisms are the modified URCA and the nuclear bremsstrahlung processes. The direct URCA processes are possible only if the proton fraction in the degenerate nuclear matter exceeds a certain threshold value (see e.g. Ref.~\cite{Brown:2017gxd}.) Analytical approximations of neutrino luminosities for those three processes have also been derived~\cite{Ofengeim:2016rkq,Ofengeim:2017xxr}, which can be used to simplify the comparison of theoretical modelling with the observations of neutron star cooling. However, as the neutron star interior cools to below the critical temperature for the onset of nucleon superfluidity, theoretical calculation is much complicated. Superfluidity and superconductivity have two important effects on neutron star cooling via neutrino emission. On the one hand the modified URCA emission rate is reduced due to the appearance of an energy gap at the Fermi surface, which suppresses single particle excitations of the paired nucleons. On the other hand, the nucleon pair breaking and formation (PBF) processes are switched on and become the dominant neutrino emission mechanism at this stage~\cite{Flowers:1976ux,Voskresensky:1987hm,Yakovlev:1998wr,Leinson:2006gh,Kolomeitsev:2008mc,Steiner:2008qz,Page:2009fu,Kolomeitsev:2010hr,Kolomeitsev:2010pm,Leinson:2014cja,Leinson:2017dlo}. It is generally assumed that neutrons undergo singlet-state Cooper pairing in the neutron star inner crust, and triplet-state pairing in the core~\cite{Tamagaki:1970}. Protons are expected to undergo singlet-state pairing in the core. The NASA Chandra X-ray observatory has recorded a steady decline of the effective surface temperature of the supernova remnant Cassiopeia A. This finding is interpreted as the evidence for the existence of superfluidity in its core~\cite{Shternin:2010qi,Elshamouty:2013nfa}. Neutron star superfluidity may also be studied using pulsar glitches, as shown by Refs.~\cite{Ho:2015vza,Ho:2017ipg}. For recent reviews on the superfluidity in neutron stars, we refer to Refs.~\cite{Potekhin:2015qsa,Gezerlis:2014efa,Pethick:2015jma,Haskell:2017lkl,Sedrakian:2018ydt}. Beyond the Standard Model (SM) of particle physics, axion emission from nucleon PBF processes in neutron stars has been studied in Refs.~\cite{Sedrakian:2018ydt,Keller:2012yr,Leinson:2014ioa,Sedrakian:2015krq}. Simulation of neutron star cooling by axions in addition to neutrinos performed in Ref.~\cite{Sedrakian:2015krq} determined an upper bound on the axion mass of $m_a \lesssim (0.06 - 0.12)~{\rm eV}$, comparable to those set by supernovae (SN 1987A) and white dwarfs. See Ref.~\cite{Sedrakian:2018ydt} for a most recent summary of this topic. In this work we show that another interesting example to study in the context of neutron cooling is provided by Weinberg's Higgs portal model~\cite{Weinberg:2013kea}, which was proposed to account for the dark radiation in the early universe~\cite{Riess:2016jrr} (see, however, also Ref.~\cite{Heavens:2017hkr}.) In this model, Weinberg considered a global $U (1)$ continuous symmetry associated with the conservation of some quantum number, and introduced a complex scalar field to break it spontaneously. The radial field of the complex scalar field acquires a vacuum expectation value (vev), and mixes with the SM Higgs field. The Goldstone bosons arising from the symmetry breaking would be massless and very weakly-interacting. Thus they can decouple from the early universe thermal bath at the right moment, and be a good dark radiation candidate. Previously we have examined energy losses due to the resonant emission of Weinberg's Goldstone bosons in a post-collapse supernova core~\cite{Keung:2013mfa,Tu:2017dhl}, as well as in the initial fireballs of gamma-ray bursts~\cite{Tu:2015lwv}. In this work we focus on the Goldstone boson resonance production when the neutron star cools to just below the critical temperature for the onset of the superfluidity. In section~\ref{sec:neutrino} we briefly summarise current attempts to study neutrino emission from the nucleon PBF processes using the Green function approach in the Nambu-Gor'kov formalism. Section~\ref{sec:model} contains a short review on Weinberg's Higgs portal model. In Section~\ref{sec:goldstone} we describe our method for estimating the Goldstone boson emissivity from the nucleon PBF processes. In section~\ref{sec:emissivity} we first determine the profiles of the neutron superfluid gap energy and the critical temperature in the neutron star inner crust and core region. Based on this information we compare the Goldstone boson and neutrino emissivities by adopting different gap models, and at different radii inside the neutron star. Variations of our neutron PBF bounds on Weinberg's Higgs portal model are discussed, and the bounds are confronted with those set by laboratory experiments and by high-energy astrophysics. In section~\ref{sec:summary} we summarise this work. | \label{sec:summary} Weinberg's Higgs portal model is another good example to elucidate that high-energy astrophysical objects such as the supernovae and gamma-ray bursts are excellent laboratory for probing particle physics. In this model, massless Goldstone bosons arising from the spontaneous breaking of a $U (1)$ symmetry play the role of the dark radiation in the early universe. They couple to the Standard Model fields solely through the mixing of the $\varphi$ and $r$ fields, which give rise to the SM Higgs boson and a light Higgs boson $h$. Goldstone boson production in the hot proto-neutron star core formed in stellar collapse is dominated by the emission of a real light Higgs boson in nuclear bremsstrahlung processes and its subsequent decay. After the neutron star cools to below the critical temperature for the onset of superfluidity, resonant production of Goldstone bosons becomes possible again through the neutron Cooper pair breaking and formation processes. Theoretical calculation of the neutrino emissivity due to neutron PBF processes is a difficult task. So far all estimates by various approaches agree well, although we note that this problem is not settled yet. In this work we assume that in the superfluid phase, the scalar vertex is modified to the same extent by the nuclear medium effects as the vector vertex, and neglect the unknown shift present in the dressed scalar vertex. We compare the Goldstone boson emissivity with that of the neutrinos by considering several superfluid gap models for the neutron singlet-state pairing in the neutron star inner crust, as well as in the core region. For a typical gap energy of $1~\Mev$, resonance production of Goldstone boson pairs is efficient when the light Higgs boson is lighter than about $15~\Mev$, in which case useful constraints can be obtained. Assuming a larger gap energy increases the Goldstone boson emissivity, but does not improve the PBF constraints. In gap models which predict higher critical temperatures, the PBF bound can be improved and its applicability covers larger light Higgs boson mass $m_h$. In those neutron singlet-state pairing gap models which extend to the neutron star core, the Goldstone boson emissivity is less suppressed due to the larger neutron Fermi momentum therein, so the PBF bounds are strengthened. Overall we found that the neutron PBF processes in the superfluid neutron star interior offer the unique possibility to explore the low light Higgs boson mass ($m_h \simeq \mathcal{O} (1)~\Mev$), small $\varphi$--$r$ mixing ($\theta_H \approx 0.0157\, g_H (\vevr / 1~\Gev) \lesssim 1.6 \cdot 10^{-5}$) region in the parameter space of Weinberg's Higgs portal model. Together with our previous works on supernovae and gamma-ray bursts constraints, this study demonstrates further the competitiveness and complementarity of astrophysics to laboratory particle physics experiments. \begin{center} \begin{figure}[t!] \includegraphics[width=0.6\textwidth,angle=-90]{NSPBF_gvevr.eps} \caption{Neutron star PBF upper limits on $g_H \vevr$, the product of the Higgs portal coupling with the vacuum expectation value of the radial field $r$, for various light Higgs boson mass $m_h$. Several gap models of the neutron singlet-state ($^1 S_0$) pairing superfluid are considered at two different radii of the neutron star interior, as described in section~\ref{sec:GBPBFbound}. Case {\it i}): bound derived by invoking Eq.~(\ref{eq:Qcriterion}) at the neutron star radius $r \simeq 10.2~{\rm km}$ where the Fermi momentum is $p_F = 0.77~{\rm fm}^{-1}$, and assuming the gap energy $\Delta_p = 1~\Mev$, so that the corresponding critical temperature is $T_{cns} \approx 7 \cdot 10^9~{\rm K}$. The emissivity comparison is made at the crust temperature $T = 6.85 \cdot 10^9~{\rm K}$ (red solid line). Case {\it ii}): at $p_F = 0.77~{\rm fm}^{-1}$, assuming $\Delta_p = 1.75~\Mev$, $T_{cns} \approx 7 \cdot 10^9~{\rm K}$, at $T = 6.85 \cdot 10^9~{\rm K}$ (blue dashed). Case {\it iia}): same as case {\it ii}), but the emissivity comparison is made at a higher crust temperature $T = 9.8 \cdot 10^9~{\rm K}$ (pink dotted). Case {\it iii}): same as case {\it i}), but the comparison is made at the radius $r \simeq 9.7~{\rm km}$ where $p_F = 1.37~{\rm fm}^{-1}$ (green dot-dashed). Also shown are the upper limits set by laboratory experiments (dash-double dotted lines, from top to bottom), such as radiative Upsilon decays $\Upsilon (n S) \rightarrow \gamma + h$, $B$ meson invisible decay $B^+ \rightarrow K^+ + h$, as well as $K$ meson invisible decay $K^+ \rightarrow \pi^+ + h$. } \label{fig:NSPBF_gvevr} \end{figure} \end{center} \begin{center} \begin{figure}[ht!] \includegraphics[width=0.6\textwidth,angle=-90]{NSGRBSN_gvevr.eps} \caption{Same as Fig.~\ref{fig:NSPBF_gvevr}, here including the upper limits set by considering other astrophysical objects, as well as by dark matter detection when the extended version of Weinberg's Higgs portal model is considered. Solid lines in red, blue, pink, and green are the neutron PBF bounds derived assuming case {\it i}), {\it ii}), {\it iia}), and {\it iii}), respectively. The two dashed brown lines below the "SN 1987A" label are those we derived in Ref.~\cite{Tu:2017dhl} by applying Raffelt's criterion on the energy loss rate of an exotic particle species in the proto-neutron star core. Two distinct estimates were adopted for the amplitudes of the nuclear bremsstrahlung processes $N N \rightarrow N N \al \al$: the global fits for the nucleon-nucleon elastic scattering cross section data (upper), and the one-pion exchange (OPE) approximation (lower). The two dotted orange lines with the "GRB" label between them are those we derived in Ref.~\cite{Tu:2015lwv} by invoking energy loss argument on the initial fireballs of gamma-ray bursts. Two GRB initial fireball temperature values $T_0 = 18~\Mev$ (lower) and $8~\Mev$ (upper) were assumed, and the Higgs portal coupling $g_H$ was taken to saturate the current collider bound in Eq.~(\ref{eq:gcolliderbound}). The two dot-dashed yellow-green lines with the "DM" label between them are the upper limits set by the dark matter direct search experiment LUX, for WIMP mass $M_\chi = 10~\Gev$ (upper) and $100~\Gev$ (lower), respectively.} \label{fig:NSGRBSN_gvevr} \end{figure} \end{center} | 18 | 8 | 1808.04806 |
1808 | 1808.04564_arXiv.txt | Near-Earth asteroid (3200) Phaethon is notable for its association to a strong annual meteor shower, the Geminids, indicative of one or more episodes of mass ejection in the past. The mechanism of Phaethon's past activity is not yet understood. Here we present a Hubble Space Telescope (HST) search of meter-sized fragments in the vicinity of Phaethon, carried out during Phaethon's historic approach to the Earth in mid-December of 2017. Numerical simulation conducted to guide HST's pointing also show that the dynamical evolution of Phaethon-originated particles is quick, as ejected materials take no longer than $\sim250$~yr to spread to the entire orbit of Phaethon. Our search was completed down to 4-meter-class limit (assuming Phaethon-like albedo) and was expected to detect 0.035\% particles ejected by Phaethon in the last several decades. The negative result of our search capped the total mass loss of Phaethon over the past few dozen orbits to be $10^{12}$~kg at $3\sigma$ level, taking the best estimates of size power-law from meteor observations and spacecraft data. Our result also implies a millimeter-sized dust flux of $<10^{-12}~\mathrm{m^{-2}~s^{-1}}$ within 0.1~au of Phaethon, suggesting that any Phaethon-bound mission is unlikely to encounter dense dust clouds. | \label{sec:intro} Near-Earth asteroid (3200) Phaethon is dynamically associated with the strong Geminid meteor shower \citep{Whipple1983,Williams1993}, as well as several other asteroids \citep{Ohtsuka2006,Kasuga2009}, collectively known as the Phaethon-Geminid Complex (PGC). It has long been known that strong meteor showers are typically associated with unambiguous comets which activities are driven by sublimation of cometary water ice. However, numerous observations of Phaethon taken in the past several decades have so far rejected Phaethon as a typical comet \citep[e.g.][]{Cochran1984,Chamberlin1996,Hsieh2005,Licandro2007,Wiegert2008,Jewitt2010,Jewitt2013,Li2013,Hui2017}. The formation mechanism of PGC remains an intriguing question. One peculiar aspect of Phaethon is its orbit: Phaethon has an orbital period of 1.4~yr and a perihelion distance of $q=0.14$~au. This leads to its frequent exposure to extreme solar heating. Recent work by \citep{Granvik2016} suggested that asteroids with small perihelion distances such as Phaethon are prone to catastrophic disruptions due to the extensive thermal stress they experience. Curiously, the behavior of the PGC system -- several asteroids and a dense meteoroid stream being dynamically related to each other -- is in line with a disintegrative origin. To examine this hypothesis, it is important to know how materials got ejected and how they evolve. Phaethon has been selected as the target for the DESTINY$^+$ mission (abbreviation of ``Demonstration and Experiment of Space Technology for INterplanetary voYage, Phaethon fLyby and dUst Science Phaethon fLyby with reUSable probe''), currently being considered by the Japan Aerospace Exploration Agency (JAXA). One of the mission goals is to understand the dust environment in Phaethon's vicinity \citep[e.g.][]{Krueger2017, Arai2018}. Since dust grains in Phaethon's vicinity will predominately be young ejecta from Phaethon, it is useful to understand Phaethon's recent activity. However, this is a challenging task as Phaethon's current activity is confined to the perihelion, which only become accessible after the launch and operation of the Solar and Terrestrial Relations Observatory (STEREO) in 2006. Despite on an Earth-approaching orbit, Phaethon does not approach the Earth often, with the last close ($<0.1$~au) approach in 1974, making it difficult to study anything in its vicinity. On 2017 December 16, Phaethon passed only 0.07~au from the Earth, the closest since 1974 and also until 2093. This close approach provides an excellent and rare opportunity to study young ejecta in Phaethon's vicinity. Here we report our modeling and observational investigation of such ejecta, as well as its implication on the recent behavior of Phaethon. | \label{sec:conc} We present a guided HST search of meter-sized fragments in the vicinity of Phaethon, with the goal of looking for evidence of recent disruption of this object. We first numerically simulated the motion of a number of virtual particles in order to decide the best pointing for HST. We found that the dynamical evolution of Phaethon-originated particles is quick, possibly due to stronger radiation differentiation resulting from the small perihelion distance of Phaethon. Particles ejected just above escape speed take $\sim250$~yr to encircle the entire orbit, while those ejected via sublimation-driven activities common in typical comets take only $\sim30$~yr. Our HST search was completed down to 4-meter-class limit assuming Phaethon-like albedo, and was expected to detect 0.035\% particles ejected by Phaethon in the past $\sim4$ decades. The negative result suggests that the total mass loss of Phaethon over the past a few dozen orbits is $<10^{12}$~kg at $3\sigma$ level, a small fraction of the Geminid meteoroid stream, taking the best estimates of size power-law from meteor observations and spacecraft data. Our result also implies a mm-sized dust flux of $<10^{-12}~\mathrm{m^{-2}~s^{-1}}$ within 0.1~au of Phaethon, a level that is comparable to background meteoroid flux. This suggests that any Phaethon-bound spacecraft, such as the DESTINY$^+$ mission, is unlikely to encounter dense dust clouds. Our work is admittedly limited by the small searched volume restricted by the short observing window. Future facilities with wider field-of-view, such as the Large Synoptic Survey Telescope (LSST) and James Webb Space Telescope (JWST), will enable wider searches over a short period of time and could potentially provide more stringent constraints. | 18 | 8 | 1808.04564 |
1808 | 1808.00492_arXiv.txt | We disclose remarkable features of the scalar-tensor theory with the derivative coupling of the scalar field to the curvature in the Palatini formalism. Using disformal transformations, we show that this theory is free from Otrogradski ghosts. For a special relation between two coupling constants, it is disformally dual to the Einstein gravity minimally coupled to the scalar, which opens the way to constructing several exact solutions. The disformal transformation degenerates at the boundary of the physical region, near which the desingularization properties are revealed, illustrated by exact solutions: non-singular accelerating cosmology and a static spherically symmetric geon. We also construct the exact pp-waves of this theory propagating at the speed of light. | 18 | 8 | 1808.00492 |
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1808 | 1808.05562_arXiv.txt | It has been observationally well established that the magnetic configurations most favorable for producing energetic flaring events reside in \dss, a class of sunspots defined as having opposite polarity umbrae sharing a common penumbra. They are frequently characterized by extreme compactness, strong rotation and anti-Hale orientation. Numerous studies have shown that nearly all of the largest solar flares originate in \dss, making the understanding of these structures a fundamental step in predicting space weather. Despite their important influence on the space environment, surprisingly little is understood about the origin and behavior of \dss. {\color{black} In this paper, we perform a systematic study of the behavior of emerging flux ropes to test a theoretical model for the formation of \dss: the kink instability of emerging flux ropes. We simulated the emergence of highly twisted, kink-unstable flux ropes from the convection zone into the corona, and compared their photospheric properties to those of emerged weakly twisted, kink-stable flux ropes. We show that the photospheric manifestations of the emergence of highly twisted flux ropes closely match the observed properties of \dss, and we discuss the resulting implications for observations. Our results strongly support and extend previous theoretical work that suggested} that the kink instability of emerging flux ropes is a promising candidate to explain \ds formation, as it reproduces their key characteristics very well. | \label{sec:intro} One of the most important features of the solar atmosphere, from the standpoint of space weather forecasting, is the subset of sunspots known as \dss. Classified as having opposite polarity umbrae that share a common penumbra \citep{Kunzel65}, \dss exhibit, by definition, extremely compact photospheric flux distributions. They are often observed to rotate rapidly after emergence \citep{Kurokawa87,Kurokawa91,Tanaka91,LF00,LF03}, contain highly twisted magnetic fields \citep{LF00,LF03,Holder04}, and violate Hale's law \citep{Smith68,Zirin87}. Hale's law states that for a given 11-year solar cycle, the majority of sunspot pairs observed in the Northern (Southern) solar hemisphere will be oriented with the negative (positive) polarity spot to the East (West). This ordering flips with each successive solar cycle. \dss are overwhelmingly associated with explosive flares, being responsible for $>90\%$ of X-class flares during the last two solar cycles \citep{Tanaka91,Shi94,Sammis00,Guo14}. Conversely, over 90\% of the \dss studied by \citet{Tanaka91} were flare active. The details of why \dss manifest their unique properties, however, are poorly understood. Understanding the observed behavior of \dss is critical for predicting their explosive flares. \par Numerical studies explaining \ds formation have typically come in four varieties: 1) The kink instability of emerging flux ropes \citep{Linton98,Linton99,Fan99,Takasao15,Toriumi17,Toriumi17b}, in which a highly twisted flux rope emerges with a deformed axis, producing a complex active region (AR) that manifests a strongly sheared polarity inversion line across the entire AR. \citet{Takasao15} simulated one such region, NOAA 11429, and found that it was likely formed through the emergence of a kink-unstable flux rope. 2) The splitting off of a portion of a subsurface flux rope to create small parasitic polarities \citep{Jaeggli16,Toriumi17,Toriumi17b}. 3) The emergence of multiple buoyant sections along a single emerging flux rope \citep{Toriumi14, Fang15, Prior16c,Toriumi17b}, and 4) the interaction of two emerging flux ropes, each containing a single buoyant section {\color{black}\citep{Toriumi14, Jouve18}}. \par In this paper, we will focus on the first mechanism, i.e., the generation of \dss via the kink instability of emerging flux ropes. Much of the theoretical underpinning of the theory of the kink instability of twisted flux ropes was developed for applications in tokamak physics by \citet{Shafranov57} and \citet{Kruskal58}, and then in solar physics \citep{Gold60,Anzer68,Hood80, Mikic90}. In highly twisted flux ropes, the kink instability converts twist (rotation of field lines about the flux rope's central axis) into writhe \citep[a deformation of the axis itself;][]{Moffatt92}. The kink instability sets in when the destabilizing magnetic pressure of the azimuthal field encircling the flux rope overwhelms the stabilizing magnetic tension in the central axial field. This occurs when flux ropes are highly twisted \citep[e.g.,][]{Shafranov57,Kruskal58}, and, crucially for interpreting observations and predictive modeling, the helical sense of the kink will have the same sense as that of the flux rope twist \citep{Linton96}.\par \citet{Linton99} modeled the kinking of a twisted flux rope and argued that, if such a flux rope were to emerge through the photosphere, the kink would cause it to emerge with a significantly tilted configuration (suggestive of anti-Haleness), then rotate and reorient itself into a Hale configuration, in agreement with observed evolution of \dss \citep{LF03}. Taken together, simulations of highly twisted flux ropes and the analytical work of \citet{Linton96,Linton98,Linton99} suggest that the kink instability of emerging flux ropes is a promising mechanism to explain the formation and behavior of a significant proportion of \dss. \par {\color{black} An open question is: what is the initial twist on these emerging flux ropes? One way to estimate flux rope twist is by measuring the twist parameter $\alpha=(\nabla\times\vecB)/\vecB$. At the photospheric level, $\alpha$ can either be measured directly through its normal component, $\alpha_n=J_n/B_n$, with $n$ denoting the component normal to the photosphere, $J$ the current density and $B$ the magnetic field \citep[e.g.,][]{Leka96} or indirectly by fitting a coronal constant-$\alpha$ force free model to the observations \citep[often denoted $\alpha_{best}$, e.g.,][]{Pevtsov94,Pevtsov95,Longcope98,Longcope99,Holder04}. Observations of $\alpha_n$ averaged over each individual AR area find that $\alpha_n$ ranges from $\pm 1\times10^{-10}$ to$\pm1\times10^{-7} \;\mathrm{m}^{-1}$ \citep{Leka96,Otsuji15}, while linear force free fits of $\alpha_{best}$ find a similar range of $0$ to $5\times10^{-8}\;\mathrm{m}^{-1}$ \citep{Pevtsov94,Pevtsov95}. \par Analytical arguments suggest that the twist must be large enough for the flux ropes to maintain coherence inside the convection zone \citep{Emonet98}. \citet{Longcope99} found that if this minimum twist were transferred from the convection zone directly to the photosphere, the corresponding peak value of $\alpha$ should be larger than the observed average ranges of $\alpha_n$ or $\alpha_{best}$. % Numerical models of emerging flux ropes have typically used initial twists larger than that required to survive the convection zone, and the twist needed for a kink is yet higher still. The question, therefore, is how to explain the relatively low observed values of photospheric $\alpha_n$. \par Several theoretical arguments can help resolve this difficulty. First, both $\alpha$ and $\alpha_n$ vary significantly across the initial subsurface flux rope, with $\alpha$ peaking at the center and vanishing at the edges, and $\alpha_n$ even reversing sign beyond a certain radius. Thus, taking the average of either quantity will lead to values much smaller than the peak value. Second, the assumption that $\alpha$ (or $\alpha_n$) is transferred directly from the convection zone to the photosphere is unlikely to hold up during the dynamic emergence of the flux rope, as significant reconnection, diffusion, and kinking are expected to reduce the twist on the emerging flux rope. It has also been demonstrated in several flux emergence simulations \citep[e.g.,][]{Fan09,Leake13}, that a significant fraction of the twist, in the form of $\alpha$, is trapped below the photosphere, so that the observed local $\alpha$ at the photosphere is about an order of magnitude lower than the local $\alpha$ in the convection zone portion of that same field line. \par One consequence of this reasoning is that it implies that it may not be possible to infer the flux rope's initial twist directly from $\alpha_n$ or $\alpha_{best}$. Nevertheless, it is clear that some ARs do have significantly larger values of $\alpha_{best}$ or $\alpha_n$ than others \citep{Pevtsov94,Pevtsov95,Longcope98,Holder04}. The ARs showing the largest values of either $\alpha_n$ or $\alpha_{best}$ have not been systematically studied in observations, but an individual study found $\alpha_{best}=2.5\times10^{-8}\;\mathrm{m}^{-1}$ in \dss as compared to $1.1\times10^{-8}\;\mathrm{m}^{-1}$ in typical ARs \citep{Holder04}. This suggests that the flux ropes that form \dss are more twisted than typical emerging flux ropes, and may explain these higher values of $\alpha_{best}$. In addition, due to the kink instability, highly twisted flux ropes are expected to manifest several other features at the photospheric level that suggest they may be the source of \dss on the photosphere.} \par The kink-instability model of \ds formation predicts four testable consequences for the photospheric and coronal properties of the resulting ARs. \par First, since the kink instability occurs only for highly twisted flux ropes, the emerging AR should exhibit high twist. Thus, the kink-instability model naturally explains the high twists observed in \dss \citep{Holder04}.\par Second, the conversion of twist into writhe manifests as a strong rotation of the flux distribution on the photosphere. Crucially, the sense of this rotation will be determined by the sign of the flux rope twist \citep{Linton99}, wherein a right (left) handed twist will give a right (left) handed kink, which, upon passing through the photosphere, will translate into a counter-clockwise (clockwise) rotation. This provides a testable prediction for \ds formation. Thus, the kink of the emerging flux rope is a promising mechanism for explaining the observed rotation of \dss on the photosphere \citep{Kazachenko10,Vemareddy16,Wang16}.\par Third, the kinking motion should break the cylindrical symmetry of the flux rope about its initial axis, moving the flux rope legs off of the initial axis. In its nonlinear phase, the kink instability should cause the rising loop to fold over on itself, causing the legs of the rising flux rope to be held very close to each other, or even, in extreme cases, to form a knot \citep{Linton98}. The predicted result is that, on the photospheric level, opposite polarity regions of the emerging AR would not separate to any appreciable distance. As a result, the `compactness' of the photospheric flux distribution in \dss may readily explained by the kink instability model of \ds formation \citep{Howard96,LF00,LF03}. \par Finally, at the coronal level, the highly twisted field in the kinked structure should contain a tremendous amount of free magnetic energy, making it susceptible to intense energy release. This would then explain the association of \dss with X-class flares \citep{Tanaka91,Shi94,Sammis00,Guo14}. \par The picture that emerges, therefore, is that at the photosphere, kinked flux ropes are expected to be compact (if they have kinked enough to bring the legs of the flux rope close together), to be twisted (since kinking requires high twist), to rotate (with the kinking motion manifesting itself as a rotation on the photosphere) and, at the coronal level, to flare (due to high levels of twist, which corresponds to free energy, and knots, which represents topological complexity). This is consistent with the observed properties of \dss, which are known to be compact, twisted, and strongly rotating and flaring. Thus, several predictions of the kinking flux rope model are eminently testable via numerical simulations. But although this is strong theoretical support for the kink instability model of \ds formation, very few numerical studies have tested this idea. With the exception of a few simulations \citep{Matsumoto98, Fan99, Takasao15, Toriumi17b}, the overwhelming majority of flux emergence studies have focused on non-kinking, weakly twisted flux ropes. Furthermore, very few authors \citep{Fan99,Murray06,Sturrock16} have performed parameter studies to investigate how varying the initial flux rope parameters affects the photospheric flux distribution in emerging flux ropes. Of these, only one \citep{Fan99} used a kink-unstable flux rope, and this study did not model the actual emergence. Thus, although significant theoretical work has argued that \dss are the photospheric manifestations of the emergence of kinked flux ropes rising from the convection zone into the corona, no systematic numerical study of the emergence of such kinked flux ropes has been undertaken.\par In this paper, we perform a parameter study of the emergence of twisted flux ropes from the convection zone into the corona. We vary only a single parameter: the flux rope's initial dimensionless twist, which determines the stability of the flux rope. We study twists ranging from kink-stable to marginally stable to unstable and explore the consequences of the emergence of these flux ropes at the photospheric level. | \label{sec:implications} The lack of understanding of the formation of \dss is one of the most important impediments preventing proper prediction of solar energetic events. The emergence of highly twisted, kink unstable flux ropes has been hypothesized to be the source of a large percentage of \dss \citep{Fan99,Linton96,Toriumi17}. In this work, we test this model using numerical simulations of the emergence of both initially kink-stable and -unstable flux ropes from the convection zone, through the photosphere, into the corona. We focused mainly on AR properties that can be measured using line-of-sight and vector magnetogram observations and related them to the subsurface properties of emerging flux ropes.\par By calculating the flux weighted centers of mass of each polarity, we demonstrated that initially highly twisted flux ropes remain much more compact, and rotate much more than, their lower twist, kink-stable counterparts. We also showed that while low twist flux ropes obey Hale's law, kink unstable flux ropes appear to violate it. Our results demonstrate that at the photosphere, emerging kinked flux ropes behave in a manner that is both qualitatively and quantitatively similar to the most well-documented behavior of \dss \citep{Kunzel65,Smith68, Kurokawa87,Zirin87,Tanaka91,LF00,LF03}. However, quantitative statements of exactly what is meant by `compactness' and `rotation' are sparse, so it is difficult to compare with observations. \par On the other hand, our work also indicates that quantitative measurements of many \ds properties are unlikely to produce results which are vastly different than those measured in simple sunspot groups. Parameters like $\alpha_x$, $J_x$, $\mathcal{R}$, all of which are measurable from photospheric observations, without recourse to models of the coronal field, do not reveal major consistent differences for highly twisted versus weakly twisted flux ropes. Photospheric measurements of these parameters may reveal higher values for \dss, but it is also possible that they may reveal lower values, depending on the instant at which the measurement was taken. Plotting the time evolution of these parameters may also reveal differences, but the results presented here suggest that, with the exceptions of the separation distance between opposite polarities and rotation angle of the opposite polarities, there is no simple dependence of many measurables on the flux rope's initial twist. Even the free energy in the coronal volume, thought to be a proxy for energetic flaring events, does not show an obvious dependence on the initial flux rope twist, despite the much more complicated coronal topology evident in the higher twist simulations. {\color{black} In contrast, Figure 8 in \citet{Toriumi11} shows that, for initially weakly twisted flux ropes, there appears to be a dependence of magnetic energy on initial twist. However, the differences in the numerical setups between those simulations and the ones presented here make a direct comparison challenging. \par The lack of dependence of our results on the initial twist arises due to several effects. First, the nature of the kink instability is to reduce the field line twist by converting twist to write \citep{Berger84, Linton96}, so that once a flux rope has kinked, its effective twist, and therefore $\alpha$, is smaller than its initial value, and may turn out to be comparable to that in a lower twist flux rope. Indeed, it is possible that the lower twist flux rope need not, itself, be kink stable for this result to hold. Since it started out with a smaller value of $\alpha$, the lower twist flux rope may, as a result of a kink, experience a smaller decrease in $\alpha$ than the higher twist flux rope, resulting in the two flux ropes having comparable values of $\alpha$. Regardless, it is clear that $\alpha$ is not simply transferred directly from the convection zone to the photosphere, but instead evolves dynamically during the emergence process, explaining its decrease from convection zone to photospheric values. Second, the rapid expansion of the magnetic field once it reaches the coronal level causes a significant decrease in the value of $\alpha$ at the photospheric level, since the expansion of the field into the corona occurs faster than Alfv\'en waves can spread the twist along the field line, creating a gradient in $\alpha$ along the expanding field line. This effect has also been observed in previous high twist simulations \citep{Fan09, Leake13}. Finally, reconnection inside the flux rope itself could destroy a lot of the initial twist structure, perhaps through an inverse cascade of magnetic helicity \citep{Antiochos13,Knizhnik15,Knizhnik17,Knizhnik17b}, leaving a relatively weakly twisted internal structure, forming active regions that have lost much of the information about the structure of the initial flux rope. \par The simulations presented here show that the dynamics of emerging highly twisted flux ropes cause copious internal reconnection to occur, as evidenced by the formation of concave up loops and knots during the emergence process. Such complicated topological structures can only be formed, in the absence of an external magnetic field, by internal reconnection. This internal reconnection would likely manifest itself as flaring behavior on the Sun. We conclude that flaring internal to an emerging kinking active region can be strong, independent of the state (or even absence) of external fields around it, in agreement with observations showing that \dss can produce X-class flares within themselves \citep{Zirin73, Zirin87, Wang91, Schmieder94}. } | 18 | 8 | 1808.05562 |
1808 | 1808.02497_arXiv.txt | The Fermi Gamma-Ray Space Telescope has provided evidence for diffuse gamma-ray emission in the central parts of the Milky Way and the Andromeda galaxy. This excess has been interpreted either as dark matter annihilation emission or as emission from thousands of millisecond pulsars (MSPs). We have recently shown that old massive globular clusters may move towards the center of the Galaxy by dynamical friction and carry within them enough MSPs to account for the observed gamma-ray excess. In this paper we revisit the MSP scenario for the Andromeda galaxy, by modeling the formation and disruption of its globular cluster system. We find that our model predicts gamma-ray emission $\sim 2-3$ times larger than for the Milky Way, but still nearly an order of magnitude smaller than the observed Fermi excess in the Andromeda. Our MSP model can reproduce the observed excess only by assuming $\sim 8$ times larger number of old clusters than inferred from galaxy scaling relations. To explain the observations we require either that Andromeda deviates significantly from the scaling relations, or that a large part of its high-energy emission comes from additional sources. | \label{sect:intro} The gamma-ray luminosity of star-forming galaxies has been under scrutiny for a long time since its study may provide important clues to the acceleration mechanisms of cosmic rays and their transport through the interstellar medium, and constrain the star formation rate as well as the gas and metallicity content of a galaxy. Thanks to the Large Area Telescope instrument on board of the Fermi Gamma-Ray Space Telescope (Fermi-LAT), new high-quality data from $20$~MeV to over $300$~GeV have been available to study the high-energy physics \citep{atw09}. These data have revealed peculiarities of the gamma-ray emission from the inner region of our Galaxy, the so-called Fermi Bubbles -- large structures extending up to 8 kpc away from the Galactic plane \citep{ack14}. Analyses of the diffuse gamma-ray emission also found a spherically-symmetric excess around the Galactic Centre, peaking at $\sim 2$~GeV and extending out to $\sim 3\,$kpc from the centre \citep{aba14,cal15,lee15,ajel16}. Two main explanations have been proposed for the observed excess, based mainly on similarity with the radial distribution and energy spectrum of the emission. A possibility is that the excess is a product of dark matter annihilation \citep{cal15}. Alternatively, the emission could be due to thousands of unresolved MSPs \citep*{bra15,bar16,arc17,fao18,fpb18}. Besides the Milky Way, seven external star-forming galaxies have been observed by Fermi in gamma rays, including the Small and Large Magellanic Cloud and the Andromeda galaxy \citep{acker12}. The latter is of particular interest since it is the only other large spiral with a prominent bulge which is close enough that the disk and bulge can be resolved as separate components. Its galactic nucleus harbors a supermassive black hole and a central blue cluster (P3) surrounded by two overdensities of stars (P1 and P2), which reside on either side of P3 with a separation of $\sim 1.8$ pc \citep{bender2005,lauer2012}. \citet{acker17} reported the detection of diffuse gamma-ray emission on the order $\sim 2.8 \times 10^{38}$ erg s$^{-1}$, that extends up to $\sim 5$ kpc from Andromeda's center, with the significance of spatial extent at the $4\sigma$ level. Its morphology is not well constrained and can be described either by a uniform disk or a Gaussian distribution. Compared to the Milky Way's excess, the Andromeda excess is about one order of magnitude larger. Moreover, this emission does not correlate with regions rich in gas, and its spectrum is consistent with a simple power law or with a truncated power-law with an exponential cut-off in the GeV range. The latter closely resembles the MSP spectral templates. As in the Galactic case, there have been claims for both the MSP and dark matter-annihilation origin of the Andromeda's diffuse emission \citep{mcdaniel18}. \citet{acker17} suggested that, if MSPs are responsible for the emission, the $\sim 4-10$ times higher flux in Andromeda could be attributed to the correspondingly higher number of globular clusters in that galaxy \citep{barm01,gall07}. Recently, \citet{eckn17} proposed that the emission comes from an unresolved population of MSPs formed \textit{in situ}. In this paper, we revisit the MSP scenario in the Andromeda galaxy. We model the formation and disruption of Andromeda globular clusters across all cosmic time, starting from redshift $z=3$ to the present time, and calculate the amount of MSPs deposited in the Andromeda bulge as a consequence of cluster disruption, while accounting also for the spin-down of the MSPs due to magnetic-dipole braking. This paper is organized as follows. In Section 2, we describe the semi-analytical model we used to generate and evolve the primordial population of globular clusters. In Section 3, we show that our fiducial model underestimates the measured Andromeda excess. Finally, in Section 4, we discuss the implications of our findings and summarize our conclusions. | \label{sect:conclusions} The \textit{Fermi} Telescope has revealed a gamma-ray excess around our Galactic Center (out to $\sim 3\,$kpc) of the order of $\sim 10^{37}$ erg s$^{-1}$, which has been interpreted either as dark matter annihilation emission or as emission of thousands of MSPs. \textit{Fermi} also showed evidence of a diffuse gamma-ray emission ($\sim 2.8 \times 10^{38}$ erg s$^{-1}$) also in the centre (up to $\sim 5$ kpc) of the Andromeda galaxy. As in the case of the Galactic Centre, there have been suggestions for both a MSP and for a dark matter-annihilation emission. In this letter, we have revisited the MSP scenario in the Andromeda galaxy, by modeling the formation and disruption of GCs, that can deliver thousands of MSPs in the bulge. We have modeled the MSP gamma-ray emission by taking into account also the spin-down due to magnetic-dipole braking, and found that the total gamma-ray luminosity is $\sim 1.6$-$3.5\times 10^{37}$, i.e., nearly one order of magnitude smaller than the observed excess. Our MSP model can reproduce the \textit{Fermi} excess only by assuming a number of primordial clusters that is $\sim 8$ times larger than that inferred from the galactic scaling relations. Recently, \citet{eckn17} proposed that the emission from an unresolved population of MSPs formed \textit{in situ} can account for $\sim 7 \times 10^{37}$ erg s$^{-1}$ of the excess. While both our model and the \citet{eckn17} model cannot account for all the observed excess, they can explain nearly half of it when taken together. We also note that M31 likely had a burst of star formation $\sim 1-2$ Gyr ago, which could boost both the abundance of close binaries and massive star clusters up to a factor of $\sim 2$ \citep{dong2018}. A combination of all these factors could provide the astrophysical origin of the gamma-ray emission in the Andromeda galaxy. Finally, we note that some of the neutron stars delivered by the GCs may mass-segregate to some extent and also be successfully exchanged in few-body interactions in binaries that later could lead to the formation of MSPs, which could enhance our predicted rate \citep{leiant2016}. This would give a maximum contribution roughly comparable to the \textit{in situ} formation scenario, which can account only for $\sim 1/4$ of the excess \citep{eckn17}, being the mass in GCs of the order of the mass of the nuclear star cluster. However, the details of binary modeling would be the same for Andromeda and our Galaxy, while the observed gamma-ray fluxes are very different. Hence, MSPs delivered by GCs cannot explain both the Milky Way and Andromeda fluxes, and therefore other sources of gamma-rays in M31 center are required. | 18 | 8 | 1808.02497 |
1808 | 1808.05424_arXiv.txt | Searches for millisecond-duration, dispersed single pulses have become a standard tool used during radio pulsar surveys in the last decade. They have enabled the discovery of two new classes of sources: rotating radio transients and fast radio bursts. However, we are now in a regime where the sensitivity to single pulses in radio surveys is often limited more by the strong background of radio frequency interference (RFI, which can greatly increase the false-positive rate) than by the sensitivity of the telescope itself. To mitigate this problem, we introduce the Single-pulse Searcher (\textsc{SpS}). This is a new machine-learning classifier designed to identify astrophysical signals in a strong RFI environment, and optimized to process the large data volumes produced by the new generation of aperture array telescopes. It has been specifically developed for the LOFAR Tied-Array All-Sky Survey (LOTAAS), an ongoing survey for pulsars and fast radio transients in the northern hemisphere. During its development, \textsc{SpS} discovered 7 new pulsars and blindly identified $\sim$80 known sources. The modular design of the software offers the possibility to easily adapt it to other studies with different instruments and characteristics. Indeed, \textsc{SpS} has already been used in other projects, e.g.\ to identify pulses from the fast radio burst source FRB~121102. The software development is complete and \textsc{SpS} is now being used to re-process all LOTAAS data collected to date. | \label{sec:introduction} The first pulsar was discovered by recording its single pulses at $\sim80$\,MHz using an aperture array \citep{Hew68}. In later studies, folding and Fourier-based techniques were used to take advantage of the pulsar periodicity. Many pulsar observations shifted to higher observing frequencies around $1.4$\,GHz, where the separation between pulsar signals and sky brightness is maximum for most of the pulsar population \citep{Cli86}. Furthermore, phased arrays were generally replaced by large single dishes, which remove the complexity of signal correlation permitting an increase in telescope sensitivity and bandwidth \citep{Gar12}. However, in recent years the increase in available computing power makes it possible to build phased aperture array telescopes with sensitivities and bandwidths that outperform traditional single dishes at low radio frequencies, offering a larger field-of-view (FoV) and more flexible instruments \citep[][]{Haa13,Tay12,Tin13}. This enables an exploration of a parameter space that is complementary to other searches: e.g., it is possible to detect sources having a spectrum steeper than the sky background \citep[spectral index $\alpha \sim -2.5$,][]{Moz17}, which are likely too faint to be detected at higher frequencies. In addition, the larger FoV improves survey speed, and makes all-sky searches tractable. The most sensitive phased aperture array telescope to date is the LOw Frequency ARray \citep[LOFAR,][]{Haa13,Sta11}. For example, its large collecting area already enabled detailed studies of archetypal sources, and the properties of the known pulsar population. The former is exemplified by the discovery of radio/X-ray mode switching in PSR~B0943+10 \citep{Her13}. Examples of the latter are the pulsar census results presented by \citet{Kon16} and \citet{Bil16}. Beyond these known sources, many pulsars in our Galaxy remain undetected. It was recognised early on that LOFAR has great potential for discovering these \citep{Lee10}. Pilot surveys placed limits on the occurrence of fast transients at low frequencies, and discovered the first two radio pulsars with LOFAR \citep{Coe14}. We are now performing a full, sensitive survey of the northern hemisphere called the LOFAR Tied-Array All-Sky Survey \citep[LOTAAS,][]{Coe14,San18}\fnurl{http://www.astron.nl/lotaas}. LOTAAS has already demonstrated its ability to find new pulsars using periodicity searches (with over 80 discoveries to date) and in this paper we focus on discoveries made through single pulses. The long dwell time (1\,hr) and large FoV ($\sim 10$\,sq.\,deg. per pointing) of LOTAAS also make the survey potentially well placed to discover fast radio transients, as long as they are not strongly affected by scattering or dispersive smearing. \subsection{Signal classification} An increasing issue for pulsar surveys is the presence of radio-frequency interference (RFI) produced by several devices, which can mimic the behaviour of astrophysical signals and limit survey sensitivities \citep[e.g.][]{Lyo16}. The large number of RFI detections makes it impractical to visually inspect and follow-up all the detected signals. This is a worsening problem caused by the increasing number of devices emitting radio waves and the improvements in telescope characteristics, such as sensitivity, dwell time and bandwidth. Therefore, this is a major challenge for next-generation radio telescopes and in particular the Square Kilometre Array \citep[SKA,][]{Ell04}. An improvement is obtained by building telescopes in RFI-free zones, areas where the human presence is minimal. However, the radio emissions of air planes and satellites are still present. In order to lower the number of detections to be inspected by eye, many automated classifiers have been developed for pulsar surveys (see \citealt{Lyo16} and references therein for a summary). These automatic classifiers evolved from simple heuristics and thresholds on S/N \citep[e.g.][]{Cli86} to semi-automated ranking algorithms \citep[e.g.][]{Lee13}. Also the graphical representation of the detected signals evolved, visualizing increasing information describing their parameters \citep[e.g.][]{Bur06}. Machine learning (ML) techniques began to be used to evaluate heuristic performance, set threshold values and perform the classification \citep[e.g.][]{Eat10}. Most recently, significant efforts are being spent in the selection of pulsar signals to deal with the large number of detections from new, sensitive radio telescopes \citep[e.g.][]{Yao16,For17,Bet17}. Here a branch of ML called statistical classification \citep{Mit97} is used to filter to select astrophysical signals. This requires first acquiring a large set of candidate examples for which the ground truth origin or `class' is known. When there are two classes under consideration, the classification task is termed `binary'. In binary problems the targets, i.e. astrophysical signals, belong to the positive class. The negative class describes all other examples (e.g.\ RFI or noise). In either case the examples must be characterised via one or more variables commonly known as `features'. Features are numerical or textual descriptors that summarise a candidate in some relevant way (e.g.\ S/N, pulse width, etc.). Features must be extracted by algorithms for each candidate, and linked to their true class `labels'. When combined, this information forms what is known as a `training set'. Using supervised learning it is possible to `learn' a mathematical function from this training set, that can automatically perform a similar mapping on new data. This process is known as `training'. The training process aims to split the training data into their respective classes, by using the inherent differences in the feature distributions to separate them. The learning process is guided via a heuristic, most often error minimisation, that quantifies how many errors are made. Each correct positive classification is known as a True Positive (TP), whilst an incorrect positive classification is known as a False Positive (FP). Similarly, negative classifications can be described in terms of True Negative (TN) and False Negative (FN) predictions. Together, these four outcomes form the so-called confusion matrix, used to assess how successfully an algorithm has learned the mapping. For a good classification, it is essential to have features that permit to separate the data into positive and negative classes. Therefore, specific algorithms must be designed to extract such features. Moreover, these algorithms need to be fast and efficient in order to keep the computing time low. These algorithms can be designed by looking at the different properties of the members of the positive and negative classes. The classification success is usually determined during a `testing' phase, conducted on an independent sample of candidate examples. If the model learned during training performs well during testing (produces few FPs and FNs) it can be used to derive predictions for new previously unseen data. An algorithm will usually be successful if trained on a large representative sample of data. Different heuristics can be used to evaluate single features, such as the information gain \citep[also known as mutual information,][]{Bro12}, a measure of the correlation between a feature and the target variable \citep{Lyo16}. Also, several metrics exist to evaluate the performance of the whole set of features in classifying the data. In this study, we made use of standard metrics such as the false negative rate (FNR) and the false positive rate (FPR), which must be as low as possible for a good classification, the true positive rate (TPR, also known as recall), the positive predictive value (PPV, also known as precision), the accuracy (ACC), the G-Measure (G-M, the geometric mean of recall and precision) and the F-Measure (F-M, the harmonic mean of recall and precision), which must be as high as possible for a good classification \citep[e.g.][]{Pow11}. All these metrics assume values between zero and one. \subsection{Single-pulse searches} Soon after the initial discovery of pulsars, surveys began taking advantage of the inherent periodicity of pulsar signals to improve search sensitivity \citep{Lor04}. This is usually achieved by performing a Fourier transform of the time-series. However, this technique greatly decreases the sensitivity to sources whose emission is not regular over time \citep{Mcl06}. Therefore, it has become standard procedure to include single-pulse searches in pulsar surveys to avoid missing sources with large pulse amplitude variations or a large null fraction \citep{Lor04}. Moreover, two new classes of sources discovered in recent years have created new interest in single-pulse searches: rotating radio transients \citep[RRATs,][]{Mcl06} and fast radio bursts \citep[FRBs,][]{Lor07}. The former class is composed of pulsars whose emission is so sporadic in time that they are missed by periodicity searches. Typical RRAT pulse rates range from as many as one per few seconds, up to one per several hours\fnurl{http://astro.phys.wvu.edu/rratalog}. The FRB class \citep{Tho13} is composed of extra-galactic radio flashes \citep{Ten17}. To date, only one has been observed to repeat \citep{Spi16} and no periodicity has been detected \citep{Sch16}. A typical search for single pulses is performed after de-dispersing the data collected by the telescope. This aims to correct for the frequency-dependent delay induced by the interaction of the radio waves from the source with free electrons present along the line of sight. The amount of dispersive delay exhibited by a signal is proportional to the dispersion measure (DM, which is the column density of free electrons). Since the DM of the source is unknown {\it a priori}, it is necessary to de-disperse the signal at many trial values. The time-series resulting from the addition of all frequency channels is then searched for single pulses. This is usually achieved by convolving each de-dispersed time-series with a top-hat function of variable width $W$. The properties of the function and the convolution are recorded every time the resulting signal-to-noise ratio (S/N) is above a certain threshold (see \citealt{Lor04} for a detailed discussion). \subsection{LOTAAS Single-pulse Searcher} The number of signal detections arising from RFI is particularly large for LOTAAS because the LOFAR Core is in a region of high population density. In addition, the high sensitivity and long dwell time offered by the survey and the large parameter space necessary to be searched at these low frequencies increase the number of false detections. For these reasons, an automated classifier has been developed to classify the periodic signals of LOTAAS \citep[][]{Lyo16,Tan18}. It uses the advantages of statistical classification to build a solid statistical framework for rejecting RFI. The presence of RFI is particularly problematic for single-pulse searches. In fact, as opposed to periodicity searches, it is not possible here to filter out aperiodic signals. Usually, single-pulse classifiers take advantage of pulse shape in the frequency-time domain where, as opposed to RFI, astrophysical signals are expected to typically be broadband and dispersed \citep{Lor04}. As opposed to periodicity searches discussed earlier, only a few classifiers have been reported to specifically sift single-pulse detections. \citet{Kea10} subtracted the non-dispersed signal from their data \citep{Eat09} and used spatial information from a multi-beam survey to discover ten new RRATs. \citet{Spi12} developed a multi-moment technique useful for quantifying the deviation present in the pulse intensity at different frequencies. \citet{Kar15} presented \textsc{RRATtrap}, which uses manually-set thresholds to discriminate astrophysical signals based on their S/N behaviour as a function of DM. Similarly, \citet{Den16} developed \textsc{Clusterrank}, which rejects RFI instances that deviate from the theoretical relation between signal strength, width and DM \citep{Cor03}. \citet{Dev16} studied different ML algorithms applied to their single-pulse classifier. For binary classification, a Random Forest (RF) trained on an oversampled set (RF$^2_\text{over}$) performed the best in their case. Here we present a new single-pulse classifier, Single-pulse Searcher \citep[\textsc{SpS},][]{mic18}, which is able to discriminate astrophysical signals from RFI with high speed and accuracy. In its current implementation (LOTAAS Single-pulse Searcher, \textsc{L-SpS}), it has been specifically designed to process LOTAAS data. LOTAAS observations and data processing are presented in \textsection\ref{sec:observations}; the \textsc{SpS} classifier is presented in \textsection\ref{sec:L-SpS}; first discoveries are presented in \textsection\ref{sec:results}; and conclusions and future developments are discussed in \textsection\ref{sec:conclusions}. | \label{sec:conclusions} We have presented \textsc{L-SpS}, a new classifier for searches of single radio pulses in the LOTAAS survey. It employs a ML algorithm to discriminate astrophysical signals from RFI, with high accuracy. During its development, the algorithm has discovered 7 new pulsars and blindly identified $\sim$80 known sources. A full reprocessing of the LOTAAS data with the latest version of \textsc{L-SpS}, as presented here, is under way. Future improvements to the software include testing of multimoment analysis and development of additional features. Also, we only made use of binary classification, i.e. instances were divided into astrophysical and RFI. The use of multiclass classification (e.g.\ distinguishing broad-band and narrow-band RFI) could improve the performance \citep{Tan18}. In addition, a larger training set with positive instances better distributed (e.g.\ more high-DM pulsars) will be used in future. Finally, deep learning techniques could significantly improve the classification performance \citep{Den14}. However, deep learning algorithms typically require larger training sets. Therefore, they could possibly be used to reprocess the survey data when a sufficient number of discoveries and re-detections is achieved. \subsection{Portability} Although \textsc{L-SpS} has been designed specifically for the LOTAAS survey, efforts are ongoing to produce a more general software \citep[\textsc{SpS},][]{mic18} that can be readily adapted to other projects. The aim is to create a program that is user-friendly, simple to customize and robust to different observation characteristics, in order to be easily used in a generic study. This is achieved by designing a modular software where the different tasks discussed in \textsection\ref{sec:L-SpS} are performed by different modules executed in sequence by a main script. Therefore, the sequence can be easily modified and each of the modules can be tailored to a specific study. A first release of this software is freely available on github\fnurl{https://github.com/danielemichilli/SpS}. At the time of writing, while the correct operation of \textsc{SpS} has been extensively tested, some of the features developed specifically for the LOTAAS survey still need to be included, such as the capability to process multiple telescope beams in parallel over different computer cores. Arguably the most critical part of the program is the final selection of astrophysical signals. In fact, due to the need for a large data set of labelled detections, an ML analysis can be difficult or impossible to perform in the case of small studies. Therefore, a set of filters that do not rely on ML techniques was created for these situations. While such filters have been designed to keep the false negative rate low, the false positive rate will be higher than in the ML approach, though still manageable for small projects. It is difficult to assess the general performance of these filters since they depend on the characteristics of the specific observations. A rough estimate is obtained from the study of FRB~121102 with Arecibo. The features used typically reduce the number of candidates by $\sim 80$-$90$\%. Of the remaining candidates, typically $\sim$25\% were found to be real after visual inspection, though this fraction varied between 1\% and 64\% in different observations (depending on the severity of RFI). | 18 | 8 | 1808.05424 |
1808 | 1808.02204_arXiv.txt | Globular clusters (GCs) in the Milky Way exhibit a well-observed bimodal distribution in core radii separating the so-called ``core-collapsed" and ``non-core-collapsed" clusters. Here, we use our H\'{e}non-type Monte Carlo code, \texttt{CMC}, to explore initial cluster parameters that map into this bimodality. Remarkably, we find that by varying the initial size of clusters (specified in our initial conditions in terms of the initial virial radius, $r_v$) within a relatively narrow range consistent with the measured radii of young star clusters in the local universe ($r_v \approx 0.5-5$ pc), our models reproduce the variety of present-day cluster properties. Furthermore, we show that stellar-mass black holes (BHs) play an intimate role in this mapping from initial conditions to the present-day structural features of GCs. We identify ``best-fit" models for three GCs with known observed BH candidates, NGC 3201, M22, and M10, and show that these clusters harbor populations of $\sim 50-100$ stellar-mass BHs at present. As an alternative case, we also compare our models to the core-collapsed cluster NGC 6752 and show that this cluster likely contains few BHs at present. Additionally, we explore the formation of BH binaries in GCs and demonstrate that these systems form naturally in our models in both detached and mass-transferring configurations with a variety of companion stellar types, including low-mass main sequence stars, white dwarfs, and sub-subgiants. | \label{sec:intro} \subsection{Globular Cluster Evolution} \label{sec:evolution} The study of the evolution of dense star clusters is motivated by the application of these systems to a variety of areas in astrophysics. As high density environments, star clusters, in particular the old globular clusters (GCs), are expected to facilitate high rates of dynamical encounters, which can lead to the formation of various stellar exotica, including low-mass X-ray binaries, millisecond pulsars, blue stragglers, and cataclysmic variables. Observations of the spatial distribution of GCs in their host galaxies provide constraints on the formation and evolution of galaxies, making GCs valuable tools for extragalactic astronomy. Additionally, over the past several years, GCs have been shown to be efficient factories of the merging binary black hole (BH) systems that may be observed as gravitational-wave sources by LIGO, Virgo, and LISA \citep[e.g.,][]{Moody2009,Banerjee2010,Ziosi2014,Rodriguez2015,Rodriguez2016a,Hurley2016,Chatterjee2017a,Chatterjee2017b, Breivik2016,Askar2017, Kremer2018c}. This, in addition to the discovery of gravitational waves emitted from merging BH binaries by LIGO \citep{Abbott2016a,Abbott2016b,Abbott2016c,Abbott2016d,Abbott2016e, Abbott2017}, has sparked renewed interest in understanding the formation and evolution of BHs in GCs. The old GCs observed in the Milky Way feature a clear bimodality in observed core radius \citep[e.g.,][]{Harris1996,McLaughlin2005}, separating the so-called ``core-collapsed'' clusters from their relatively puffy counterparts. Our understanding of the evolution of dense star clusters, and in particular, the dynamical processes that may lead to or prevent core-collapse has a long and varied history that has been guided by the complementary efforts of numerical simulations and observations over the past several decades (see, e.g., \citet{Heggie2003} for a thorough review). Because star clusters are self-gravitating systems with negative heat capacities, dynamical perturbations in a cluster naturally lead to a flow of energy from the strongly self-gravitating core to the relatively sparse halo. The negative heat capacity means that the core becomes even hotter as the result of these perturbations, increasing the flow of energy to the halo in a runaway process that leads to core-contraction and ultimately collapse. % This ``core-collapse" can be halted by an energy source in the core, which is expected to arise from binaries. For some time, these binaries were thought to exclusively form dynamically through three-body binary formation \citep[e.g.,][]{Heggie2003}; however, since the early 1990s, when primordial binary populations began to be observationally motivated, theoretical analyses have focused on studying properties of clusters with primordial binary populations as they pass through the so-called ``binary-burning'' phase, where the cluster core is supported against collapse by super-elastic dynamical scattering interactions of binary stars \citep[e.g.,][]{Vesperini1994,Fregeau2007,Chatterjee2013a}. Arguably, the most important recent shift in our understanding of how GCs evolve came from the observational and theoretical confirmation that GCs contain dynamically important populations of stellar-mass BHs up to the present time. % Being the most massive objects in a GC, the BH population ``collapses" quickly and generates energy through dynamical binary formation, binary-burning, and dynamical ejections (see Section \ref{sec:BHs} for details and references). However, it is important to distinguish this BH collapse from the traditional observational definition of core-collapse in GCs. In particular, this BH collapse leaves little signature on the shape of the light profile of the GC which is sensitive only to the luminous stars \citep[e.g.,][]{Chatterjee2017a}. The only effect on the surface brightness profile is indirect: through strong dynamical encounters in the inner, BH-dominated region, BHs are frequently ejected to higher orbits in the cluster potential, leading to interactions with luminous stars in the outer parts of the cluster. Through these interactions, the BHs deposit energy into the GC's stellar bulk, leading to ``puffier" surface brightness profiles \citep[e.g.,][]{Mackey2007,Mackey2008,Kremer2018d}. Thus, this BH collapse is very different from the formation of a cusp in the surface brightness profile which is the traditional observational definition of core-collapsed GCs. Most recently, several analyses have shown that only after the stellar-mass BH population is significantly depleted, can the surface brightness profile of a GC reach a traditional core-collapse architecture \citep[e.g.,][]{Mackey2008,Kremer2018d}. At this stage, in absence of a large number of BHs, the luminous binaries become the dominant source of energy at the GC's center. In this study, we use the term ``core-collapsed'' to simply denote clusters (and cluster models) that are relatively centrally concentrated and have surface brightness profiles with prominent central cusps. Observations of young massive clusters \citep[e.g.,][]{Holtzman1992,Whitmore1995,Miller1997,Bastian2005,Fall2005,Gieles2006,Scheepmaker2007,Scheepmaker2009,PortegiesZwart2010}, the expected progenitors of GCs, can provide insight into the various initial cluster properties that may determine the eventual outcome of the cluster, in particular, whether the GC has undergone core-collapse by the present day. Remarkably, observations indicate that although the masses of such young clusters can span several orders of magnitude, their sizes (e.g., core or half-light radii) span a relatively narrow range. In this paper, we demonstrate that by exploring the small range in initial cluster size motivated by observations of young massive clusters, % we produce a large spectrum of GC types at the present-day, ranging from core-collapsed clusters to puffy clusters with large core radii. We parameterize the cluster size in terms of the cluster virial radius, $r_v$, a theoretical quantity defined as \begin{equation} r_v = \frac{GM^2}{2\lvert U \rvert} \end{equation} where $M$ is the total cluster mass and $U$ is the total cluster potential energy, which can be calculated from the masses and positions of particles in our Monte Carlo calculation (Section \ref{sec:method}). The initial relaxation timescale is directly related to the initial cluster size. Thus, the initial $r_v$ sets the dynamical clock of each cluster and controls how dynamically old a particular cluster is at a fixed physical time window, which, in turn, determines how close or far the cluster is from undergoing core-collapse. The half-mass relaxation time is given by \begin{equation} \label{eq:relaxation_time} t_{\rm{rh}} = 0.138 \frac{M^{1/2}R_{\rm{h}}^{3/2}}{\langle m \rangle G^{1/2}\ln \Lambda} \end{equation} \citep[Equation 2-63 of][]{Spitzer1987}, where $M$ is the total cluster mass, $R_{\rm{h}}$ is the half-mass radius, $\langle m \rangle$ is the mean stellar mass, and $\ln \Lambda$ is the Coloumb logarithm where $\Lambda \simeq 0.4 N$, where $N$ is the total number of particles. We demonstrate here that the evolution of stellar-mass BH populations in GCs, which is discussed at length in Section \ref{sec:BHs}, is intimately related to the contraction or expansion of the GC's core radius. In particular, since the initial $r_v$ of a cluster determines the initial relaxation timescale, the initial $r_v$ also controls how dynamically processed the BHs are at any given late physical time. \subsection{Black Holes in Globular Clusters} \label{sec:BHs} Thousands of BHs are likely to form in GCs as the result of the evolution of massive stars. The number of these BHs that are \textit{retained} in GCs today is less certain. BHs are expected to be ejected from their host GCs through one of two primary mechanisms: ejection due to sufficiently large natal kicks or ejection via recoil as a result of strong dynamical encounters with other remaining BHs. BH natal kicks, which are caused by asymmetric mass loss of supernova ejecta are poorly constrained \citep[e.g.,][]{Belczynski2002,Belczynski2010,Repetto2012,Fryer2012,Mandel2016,Repetto2017}. If BH natal kicks are comparable in magnitude to the high speeds % expected for the natal kicks of core-collapse NSs \citep[e.g.,][]{Hobbs2005}, the vast majority % of BHs are likely to be ejected from GCs immediately upon formation because of the low escape speeds % of typical GC cores. However, in the case of weaker BH natal kicks, a potentially large fraction of BHs may be retained post supernova. The long-term retention of BHs that are not ejected promptly from natal kicks has long been a subject of debate. Until relatively recently, it was argued that BHs retained after formation would quickly mass-segregate and form a dense sub-cluster dynamically decoupled from the rest of the GC \citep[e.g.,][]{Spitzer1967,Kulkarni1993,Sigurdsson1993}. The BH members of this compact sub-cluster would then undergo strong dynamical encounters, ultimately ejecting all but a few BHs from the cluster on sub-Gyr timescales. However, more recently, several theoretical and computational analyses have demonstrated that this argument of rapid BH evaporation is not correct, and in fact, many BHs may be retained at present \citep[e.g.,][]{Merritt2004,Hurley2007,Mackey2007,Mackey2008,Morscher2015,Chatterjee2017a}. The topic of retained BHs in GCs has been further motivated observationally. In the past decade, several stellar-mass BH candidates have been identified in both Galactic \citep{Strader2012,Chomiuk2013,Miller-Jones2014,Shishkovsky2018} and extragalactic \citep{Maccarone2007,Irwin2010} GCs. Most recently, the first stellar-mass BH to be identified through radial velocity measurements was found in the MW GC NGC 3201 \citep{Giesers2018}. The observations of these stellar-mass BH candidates suggest that at least some GCs do indeed retain populations of BHs at present and given that these host GCs do not show any particular trends in their observable properties, it appears that BH retention to present day may be common to most GCs. Several recent papers have used numerical simulations of GCs with large numbers of retained BHs to examine possible observational signatures that may indicate the presence of BH populations in GCs. \citet{Askar2018} predicted 29 MW GCs likely to have large BH subsystems, including two clusters considered here (M22 and NGC 3201) using a combination of numerical GC models and observations of MW GCs. \citet{Weatherford2017} demonstrated that a measure of mass segregation can be a robust observational tool to constrain unseen retained BH populations in GCs and predicted the number of BHs in three MW GCs (47 Tuc, M10, and M22) by correlating the size of BH populations with observational measurements of mass segregation. Additionally, several previous analyses have used numerical simulations to model specific MW clusters known to harbor stellar-mass BH candidates. For example, \citet{Sippel2013} used N-body methods to model the MW GC M22 (known to contain \textit{two} stellar-mass BHs) and demonstrated that M22-like models can retain moderate numbers of BHs at late times. Shortly thereafter, \citet{Heggie2014} modeled M22 using Monte Carlo methods, and demonstrated similar results. More recently, \citet{Kremer2018d} used Monte Carlo methods to model NGC 3201 and showed that $\gtrsim 200$ BHs are necessary to produce models with observational features matching this cluster. \citet{Kremer2018d} showed that BHs are readily found in binaries with luminous companions (LCs) in BH-retaining clusters, although, \citet{Chatterjee2017a} and \citet{Kremer2018a} demonstrated that the presence of BH--LC binaries in a GC is uncorrelated with the total retained population of BHs. In general, the natal kick strengths determine the fraction of BHs retained immediately post formation. Subsequently, the cluster ejects BHs via dynamical processing including mass segregation and strong scattering over several relaxation times. In \citet{Kremer2018d}, we used the highly uncertain magnitudes of BH natal kicks to vary the number of BHs retained post supernova to ultimately control the retention fraction in GC models today. In this work, we vary the initial virial radius of the models to control the initial relaxation timescale to ultimately control how dynamically processed the BHs are at any given late physical time. We present a new grid of Monte Carlo GC models with varying initial virial radii and identify the models that best match three MW GCs in which stellar-mass BH candidates have been identified: NGC 3201 \citep{Giesers2018}, M22 \citep[two BH candidates; ][]{Strader2012}, and M10 \citep{Shishkovsky2018}. We demonstrate that the number of BHs retained in a GC has a significant effect upon the long-term evolution of the cluster. We show that both M22 and M10 likely contain $\sim 40-50$ stellar-mass BHs at present, in agreement with the predictions made be other recent studies, in particular \citet{Weatherford2017} and \citet{ArcaSedda2018}. In agreement with \citet{Kremer2018d}, we also show that NGC 3201 contains $>100$ BHs. Additionally, we show that accreting BH binaries similar to the observed systems are naturally produced in our models that are most similar to these three clusters. We also compare our models to the core-collapsed MW GC NGC 6752, which has similar total mass to NGC 3201, M10, and M22. We demonstrate that NGC 6752 likely contains few BHs at present.% In Section \ref{sec:method}, we briefly describe our numerical techniques and discuss our grid of GC models. In Section \ref{sec:results} we show our results and discuss the best-fit models for the MW GCs considered in this study. In Section \ref{sec:BHMTB}, we explore the dynamical formation of accreting BH binaries in our models through several possible formation channels and discuss our results in the context of several of the observed accreting BH binaries identified to date. We conclude and discuss our results in Section \ref{sec:conclusion}. | \label{sec:conclusion} We have demonstrated that by exploring a small range in initial cluster size (parameterized in terms of the initial cluster virial radius) motivated by observations of young massive clusters, we can produce a spectrum of cluster types, ranging from core-collapsed to puffy. Furthermore, we have shown that the initial $r_v$ of a GC model has a substantial effect upon the total number of BHs retained in the cluster at late times. Within the range of virial radii considered in this study ($r_v=0.5-5$ pc), our models retain BH populations ranging in size from just a couple to over 600 BHs at $t=12$ Gyr. In particular, we have shown that the set of 11 GC models computed for this study span the observational features of four different Milky Way GCs: NGC 3201, M10, M22, and NGC 6752, the former three of which contain observed stellar-mass BH candidates. By identifying those cluster models that most accurately match the observed surface brightness profiles and velocity dispersion profiles of specific Milky Way GCs, we predict the total number of BHs retained in these clusters. At the present-day, we predict M10 retains $39 \pm 9$ BHs, M22 retains $40 \pm 9$ BHs, and NGC 6752 retains $16 \pm 7$ BHs. As a follow-up to the results of \citet{Kremer2018d}, in which we used the magnitude of BH natal kicks to adjust the number of BHs retained at late times, we predict with our new set of models that NGC 3201 retains $121 \pm 10$ BHs. The numbers of BHs predicted here are consistent with the predictions of other recent analyses that have used alternative methods to constrain BH numbers \citep[e.g.,][]{Weatherford2017,Askar2018}. The post-birth retention fraction of BHs in this analysis is very different compared to that of \citet{Kremer2018d}. In the present analysis, dynamical encounters are the primary mechanism through which BHs are ejected (the retention fraction at birth is fixed between different models), as opposed to \citet{Kremer2018d}, where the BH retention is determined through a combination of dynamical interactions \textit{and} natal kicks, which, in that analysis, are varied between models. Nonetheless, we demonstrate a similar correlation to that shown in \citet{Kremer2018d} between present-day structural parameters and the total number of BHs retained. Additionally, for NGC 3201, we estimate a similar total number of BHs retained in the cluster at present. This indicates that for GCs that are sufficiently dynamically evolved, the specific way that BHs are removed may matter less in shaping the present-day structure of the host GC than the number of BHs retained at present. Additionally, we have explored the formation of BH--LC binaries in our models through several possible formation channels. We demonstrated that BH binaries are readily produced in our models in both mass-transferring and detached configurations. Furthermore, these BH binaries are found with MS, WD, and SSG companions, in line with the companion types identified for observed GC BH candidates. % Note that, as discussed in \citet{Shishkovsky2018}, the identification of the primary star in the M10 binary as a BH is uncertain. In fact, several other possible options are consistent with the observations. A neutron star--red straggler binary, a RS CVn, a WD--red straggler/SSG binary, and even an isolated red straggler/SSG may all be viable alternative options (see Section 4 of \citet{Shishkovsky2018} for further details). We note that we identify 73 WD--SSG binaries in our models at late times (using the channels described in \citet{Geller2017c} to identify SSGs), 23 of which are found in mass-transferring configurations. Thus, from a dynamical-formation perspective, a WD--SSG/red straggler may indeed be a viable explanation for the binary of interest in M10. As discussed in \citet{Shishkovsky2018}, follow-up observations of this binary are necessary to more precisely constrain the true nature of the system. Additionally, we note that \citet{Ivanova2017} explored the formation of BH--red straggler binaries in GCs through the grazing tidal capture of giants by BHs and estimated a formation rate of $\sim 1$ BH--red straggler binary per 50 BHs per Gyr in a typical cluster. Treatment of this grazing capture process is beyond the scope of \texttt{CMC}, therefore, we neglect this channel here and simply note that consideration of this channel may lead to an increase in the number of BH--red straggler binaries. % Indeed, many details pertaining to the formation and evolution of exotic stellar sources such as SSGs and red stragglers remain uncertain. More thorough study of the formation of such objects (and the ways these objects may interact with BH populations in GCs) is needed to more precisely constrain their nature. As described in Section \ref{sec:method}, we fix all initial cluster parameters for our grid of models with the exception of the initial virial radius. This allows us to isolate the effect that the initial virial radius has upon the long-term retention of BHs and its effect upon the structural properties of the cluster at late times. However, in fixing other initial parameters, in particular the initial $N$ and Galactocentric distance, we must address several caveats. First, although the clusters considered in this study all have approximately similar total cluster masses at the present day, they are not identical. In this case, fixing the initial $N$ in our models limits our ability to produce best-fit models that capture the range in total cluster mass of the GCs considered here. As discussed in Section \ref{sec:method}, by allowing for $10\%$ uncertainties in the heliocentric distances of each cluster, the SBPs for our models can be shifted slightly to the right or left, which effectively allows us to compensate for the limited range in total cluster mass of our fixed-$N$ grid. For example, the published heliocentric distance of M22 is 3.2 kpc \citep{Harris1996}. To attain the SBP for our best-fit model, we adopt a value of $d=2.9$ kpc, which shifts the SBP slightly to the right relative to a choice of $d=3.2$ kpc. If the value of 3.2 kpc is assumed to be precise, this suggests that our models may be slightly undermassive relative to M22. To test this, we also ran a single additional model with initial $N=10^6$ and $r_v=0.9$ pc, which, at late times, has a SBP and velocity dispersion profile that also effectively match M22, but for a heliocentric distance of $3.2$ kpc. The final mass of this model is $\sim 20 \%$ higher than in the best-fit M22 model discussed in Section \ref{sec:m22}. As expected, more BHs are produced initially in the $N=10^6$ model ($\sim 2000$ versus $\sim 1500$ in the $N=8\times 10^5$ model). As a result, the $N=10^6$ model retains 79 BHs at $t=12$ Gyr, slightly higher than the $N_{\rm{BH}}=49$ value given for our best-fit M22 model. We conclude that although a slightly more massive model may more accurately match the published heliocentric distance of M22, the number of BHs will likely not change significantly, at least within the uncertainties of this analysis. Secondly, by fixing the initial Galactocentric distance of our models and by assuming circular orbits in the Galactic potential, we neglect possible close passages ($d < 8$ kpc) to the Galactic center which may arise from eccentric cluster orbits. For a summary of the dynamical evolution of GCs on eccentric orbits about the Galactic potential see, for example, \citet{Baumgardt2003}. As noted in that analysis, M10, M22, and NGC 6752 may all have eccentric cluster orbits, with estimated pericenter distances of 3.4, 2.9, and 4.8 kpc, respectively. However, as also noted in \citet{Baumgardt2003}, the dissolution timescales for these three clusters due to close passages near the Galactic center are all $\gtrsim 3$ Hubble times \citep[see Table 2 of][]{Baumgardt2003}, so our treatment of circular orbits at a fixed Galactocentric distance of 8 kpc is likely a reasonable approximation. % Nonetheless, we note that more precise modeling of the GCs considered in this study may incorporate better constrained Galactocentric distances and cluster orbits in the Galactic potential attained from, for example, \textit{Gaia}. In reality, the process through which GCs are formed is likely more complex than considered in this analysis. The first few to 10s of Myrs of cluster evolution likely feature various complex processes such as hierarchical mergers and residual gas expulsion. Indeed, such processes are hinted at from observations of several young massive clusters \citep[e.g.,][]{Kuhn2014,Gennaro2017}. In particular, residual gas expulsion could lead to significant cluster expansion at early times, attenuating the long-term dynamical processing of BHs and thus altering the structural features of the clusters at late times. However, several recent analyses \citep[e.g.,][]{Banerjee2017,Brinkmann2017,Banerjee2018} have shown that the early stages of formation of some clusters may feature a substantially more compact embedded phase of sub-pc length scale, comparable to the thickest molecular-cloud filaments, from which a substantial gas dispersal would result in sizes comparable to those of the initial configurations considered here and also of the observed gas-free young massive clusters, as demonstrated in Figure \ref{fig:rc_obs}. While such processes may be important, they are beyond the scope of this analysis. The assumption here is that such formation processes are absorbed into the definition of initial conditions of our models. Finally, we note that one notable feature of the core-collapsed cluster NGC 6752 is the presence of five observed millisecond pulsars (MSPs), which display unusual locations and/or accelerations compared to other pulsars observed in GCs \citep{Damico2002}. This suggests the occurrence of uncommon dynamics in NGC 6752. In particular, one of these pulsars, PSR A, is observed at a distance of 6.39 arcmin from the gravitational center of NGC 6752 \citep{Damico2002}, the largest radial offset for any GC MSP observed to date. \citet{Colpi2003} argues that a four body-scattering event involving a stellar-mass BH--BH binary may be able to provide sufficient energy to eject PSR A to its current position in the cluster. Although a detailed examination of the formation and dynamical evolution of MSPs is beyond the scope of this paper, we note that our model most-closely matching NGC 6752 does contain 0--3 stellar-mass BH binaries at late times, which are similar to those invoked in \citet{Colpi2003} to describe the peculiar location of PSR A. A more detailed study of the interaction between BHs and MSPs in GCs will be presented in a forthcoming study \citep{Ye2018}. As discussed in \citet{Colpi2003}, although the presence of stellar-mass BH--BH binaries may be sufficient to explain the anomalously high position of PSR A in NGC 6752, it may be difficult for a stellar-mass BH binary to also explain the anomalously high accelerations of PSR B and PSR E. Instead, as discussed in, e.g., \citet{Ferraro2003} an intermediate-mass BH ($M\sim100-200\,M_{\odot}$) may be necessary. A more detailed study of the formation of intermediate-mass BHs and the role that such objects play in the evolution of their host cluster is beyond the scope of this paper, and we defer such analysis to a future study. | 18 | 8 | 1808.02204 |
1808 | 1808.03278_arXiv.txt | It has long been known that the vertical motions of Galactic disk stars increase with stellar age, commonly interpreted as vertical heating through orbit scattering. Here we map the vertical actions of disk stars as a function of age ($\tau\le 8$~Gyrs) and across a large range of Galactocentric radii, $\overline{R}_{\rm GC}$, drawing on APOGEE and Gaia data. We fit $\widehat{J_z}(\overline{R}_{\rm GC},\tau )$ as a combination of the vertical action at birth, $\widehat{J_{z,0}}$, and subsequent heating $\DJz(\overline{R}_{\rm GC})$ that scales as $\tau^{\gamma(\overline{R}_{\rm GC})}$. The inferred birth temperature, $\widehat{J_{z,0}}(\overline{R}_{\rm GC})$ is $1 \;{\rm kpc}\;{\rm km/s}$ for $3~{\rm kpc}< \overline{R}_{\rm GC}<10~{\rm kpc}$, consistent with the ISM velocity dispersion; but it rapidly rises outward, to $8\;{\rm kpc}\;{\rm km/s}$ for $\overline{R}_{\rm GC} = 14~{\rm kpc}$, likely reflecting the stars' birth in a warped or flared gas disk. We find the heating rate $\DJz$ to be modest and nearly constant across all radii, $1.6\;{\rm kpc}\;{\rm km/s}\;{\rm Gyr}^{-1}$. The stellar age dependence $\gamma$ gently grows with Galactocentric radius, from $\gamma \simeq 1$ for $\overline{R}_{\rm GC}\lesssim R_\odot$ to $\gamma \simeq 1.3$ at $\overline{R}_{\rm GC} =14\,$kpc. The observed $J_z - \tau$ relation at all radii is considerably steeper ($\gamma\gtrsim 1$) than the time dependence theoretically expected from orbit scattering, $J_z\propto t^{0.5}$. We illustrate how this conundrum can be resolved if we also account for the fact that at earlier epochs the scatterers were more common, and the restoring force from the stellar disk surface mass density was low. Our analysis may re-instate gradual orbital scattering as a plausible and viable mechanism to explain the age-dependent vertical motions of disk stars. | \label{sec:introduction} In the context of $\Lambda$CDM hierarchical cosmogony, galaxy formation started out vigorously, with a rapid gas inflow and frequent mergers \citep[e.g.,][]{whi78,bro04,bro12,vog14}. During this period, stars formed from highly turbulent, clumpy ISM with large velocity dispersion and were born with kinematically hot orbits \citep{bou09,for12}, as also borne out by high redshift observations \citep[e.g.,][]{for09,win15}. For the Milky Way, this early phase of vigorous evolution faded 8--10 Gyrs ago, giving way to more gradual gas acquisition and an extended period without any major mergers. Since then, gas increasingly settled into a thin disk before forming stars, resulting in ``upside-down'' formation of the main, extended\footnote{This component is loosely referred to as the low-$\alpha$ or ``thin'' disk; it is this disk ``component'' that is the subject of this work.} stellar disk \citep{bir13,sti13,gra16}. At present, the star-forming molecular gas in the Milky Way disk has a small velocity dispersion \citep{sta89,sta05,sta06,aum09,mar14,aum16}, and so do the stars that form from it. Subsequently, stars are bound to acquire more vertical motion over time through a variety of dynamical processes. Indeed, vertical thickening of spiral disks seems prevalent throughout the cosmos \citep[e.g.,][]{yoa06,jur08}. The present day distribution of vertical motions, e.g., characterized by their velocity dispersion, $\sigma_z$ in stars of different ages and Galactocentric radii therefore reflects a combination of their birth ``temperature'' and subsequent heating. Constraining and understanding the vertical motions of Galactic disk stars therefore provides a key test of the processes presumed to set the vertical structure of disks in general. Several different physical processes may have contributed to the vertical heating of the Galactic stellar disk, causing either rapid ``non-adiabatic heating'', or more gradual ``adiabatic heating''. Cosmological simulations have shown that galaxies of the Milky Way's size are frequently experiencing minor mergers \citep{qui93,wal96,vel99,kaz09,hou11,gom13,don16,moe16}, external perturbations that can heat up the disk. But there are also more gradual internal heating mechanism: classically, giant molecular clouds (GMCs) act as scatterers that could heat up the disk either directly or by redirecting some of the in-plane heating (e.g., through transient spiral arms or the Galactic bar) to the vertical direction \citep{spi53,bar67,lac84,car85,car87,jen90}. In-plane random motions can also be converted to vertical motions in the stellar disk through bending waves \citep[e.g.,][]{sha10,fau14,deb14,wid14}. But the interpretation of disk stars' vertical velocity dispersion, $\sigma_z$ as disk heating is often complicated by the overall secular evolution of the disk. For instance, the gradual, adiabatic increase in the mid-plane baryon density will cause an increase in $\sigma_z$ \citep[e.g.,][]{bah84,van88,jen92,vil10}. And radial migration of stars \citep{sel02,sch09b,min10} also affects the vertical disk structure: it should cause more extended vertical motion at reduced velocity dispersion for stars that move outward, and the opposite effect for stars that move inward \citep{loe11,min12,ros13,mar14,ver14,aum17}. Traditionally, studies have characterized the effects of vertical disk heating through the age-velocity dispersion relation (AVR) \citep[e.g.,][]{str46,wie77,qui01,sea07,sou08,aum09,san18}. The Geneva-Copenhagen Survey (GCS) provides the current state-of-the-art for such a relation in the solar neighborhood \citep{nor04,hol07,hol09,aum09,cas11}. Solar neighborhood studies basically agree that the present-day vertical velocity dispersion among stars of age $\tau$ scales approximately as $\sigma_z \sim \tau^{0.5}$. But the interpretation of this scaling is still under debate, as the simplest models of heating through a time-independent population of scatterers would imply a different evolution of vertical motions $\sigma_z \sim \tau^{0.25}$ \citep{lac84,han02}. And with only local information at hand, the various heating mechanisms, when combined with the effects of radial migration, may have degenerate observational signatures. The combination of Gaia DR2 \citep{gai18,lin18}, of the on-going large-scale spectroscopic surveys, such as APOGEE \citep{maj17}, Galah \citep{des15} and Gaia-ESO \citep{smi14}, and of consistent stellar age estimates across a wide range of Galactocentric radii \citep[e.g.,][]{mar15,nes16} make it now possible to characterize and interpret the history of vertical motions among (low-$\alpha$) disk stars throughout the Galaxy. This is what we set out to do in this paper. It seems sensible to characterize the vertical motions of stars by their vertical actions, $J_z$, rather than their vertical velocities $v_z$ or velocity dispersion, $\sigma_z$. This is mainly because the vertical action is an adiabatic invariant under any gradual changes of the potential reflecting the growth of the Galaxy, and an approximate invariant under radial migration through churning \citep{car87,sel13}, as the vertical motions are only weakly coupled to in-plane resonances. In contrast, $\sigma_z$ will change in a growing potential and under radial migration, with the scale-height h$_z$ changing in compensation such as to conserve $J_z$. Note that for the simple case of harmonic vertical oscillations, $\sigma_z\propto \tau^{0.25}$ corresponds to $J_z\propto \tau^{0.5}$. Therefore, mapping the present-day $J_z$ as a function of stellar age $\tau$ and current Galactocentric radius, may make it easier to interpret this distribution in terms of: (a) with what ``vertical birth temperature'' did star start out, and (b) what subsequent heating (defined as an increase in $J_z$) did they incur subsequently. Specifically, we combine here a red clump sample derived from APOGEE in \citet{tin18a} with their Gaia DR2 proper motions \citep{lin18}, which yield a large number of stars across the Milky Way disk with precise 6D phase space coordinates, from which their vertical actions can be reliably estimated. Furthermore, precise stellar ages ($25\%$) can be derived for this sample as we will show. A global ($3~{\rm kpc}<\overline{R}_{\rm GC}<14~{\rm kpc}$) study of the vertical structure of the Milky Way main stellar disk\footnote{In this study, we use the term main, extended or thin stellar disk to describe the low-$\alpha$ sequence of the Galactic disk \citep[e.g.,][]{rix13,hay15}, and will use these terms interchangeably. Similarly, the thick disk in this study describes the $\alpha$-enhanced disk and does not necessarily mean the geometrical thick disk.} also requires careful modeling of the selection function. The paper is organized as follows. In Section~\ref{sec:data}, we present and derive precise distances and actions for the red clump sample, as well as precise ages, inferred from a data-driven model drawing asteroseismic training data. In Section~\ref{sec:model}, we introduce a physical model of vertical action which capture the full distribution of vertical action at different radii and ages. We also describe the derivation of the selection function in vertical action, which turns out to be important in the subsequent Bayesian inference. In Section~\ref{sec:results}, we will discuss the inference posterior of our models and study how the vertical heating and birth temperature of stars depends on the Galactocentric radii. We will discuss the results in the context of a simple epoch-dependent but analytic scattering model in Section~\ref{sec:discussion} and conclude in Section~\ref{sec:conclusion}. Throughout this paper, we will assume the following units: velocity [km/s], distance [kpc], age/time [Gyr], and vertical action [kpc km/s]. | \label{sec:conclusion} We have quantified the global vertical temperature of the Milky Way's stellar disk as a function of stellar age, $J_z (\Rbar, \tau)$, spanning the Galactocentric radii from 3$\,$kpc to 14$\,$kpc and ages $\tau < 8$~Gyr. To this end, we combined a pristine subset of APOGEE red clump stars previously derived in \citet{tin18a} and proper motions from the recent Gaia DR2 \citep{gai18}, yielding a sample of $\sim 20,000$ stars with the precision of $7\%$ in distance, $25\%$ in stellar age and $15\%$ vertical action across the Milky Way. We chose to model the vertical action, $J_z(\Rbar,\tau)$ instead of the classical age-velocity dispersion relation, as $J_z$'s adiabatic invariance makes the results more interpretable. Our finding can be summarized as followed: \begin{itemize} \item The full distribution of $J_z$ at any given $(\Rbar,\tau)$, can be very well approximated by an isothermal distribution $p(J_z) \sim \exp(-J_z/\widehat{J_z})$. \item The best-fitted $\widehat{J_z} (\overline{R}_{\rm GC},\tau)$ then informs about the evolution of $J_z$ at different radius and time. But, importantly, $\widehat{J_z} (\overline{R}_{\rm GC},\tau)$ does not reflect the evolutionary paths of any stellar population {\it per se}. We parametrize $\widehat{J_z}(\overline{R}_{\rm GC},\tau) \equiv \widehat{J_{z,0}} (\overline{R}_{\rm GC})\ +\ \DJz(\overline{R}_{\rm GC})\cdot (\tau/1\,{\rm Gyr})^{\gammRC}$. \item In fitting this parameterized model to the data, we account for the selection function in $J_z$, $S(J_z)$, well approximated by a broken power-law. We also find that accounting for the observational uncertainties in this fitting matters. \item We find the birth actions $\widehat{J_{z,0}}$ to be consistent with the expectation from the ISM or star cluster velocity dispersion, for $\overline{R}_{\rm GC} < 10\,$kpc: $\widehat{J_{z,0}} = 1\,$kpc km/s. At larger radii, the birth action increases to $\widehat{J_{z,0}} = 8\,$kpc km/s at $R_{\rm GC} = 14\,$kpc, which might indicate that stars were formed under Galactic warp or flare beyond $10\,$kpc, enabled by the lower disk self-gravity at these radii. \item The increase of $J_z$ with stellar age for the last Gyr, traditionally interpreted as the ``heating rate'' $\DJz$, shows a constant value $\sim 1.6\;{\rm kpc}\;{\rm km/s}\;{\rm Gyr}^{-1}$, with only mild dependence with radius. But its power law scaling with age increases with Galactocentric radius, from $\gamma \simeq 1$ at $\overline{R}_{\rm GC} = 3\,$kpc to $\gamma \simeq 1.3$ at $\overline{R}_{\rm GC} = 14\,$kpc. \item Our constraint on $\gamma$ in the Solar neighborhood is consistent with the GCS \citep{hol09} value $\sigma \sim \tau^{0.53}$ (or, $\gamma \sim 1.06$). \item To cast the global empirical constraint on $\widehat{J_z} (\overline{R}_{\rm GC},\tau)$ we derived, in terms of actual heating scenarios, we present a simple analytic model: we assume that the vertical heating of all stellar populations is dominated by orbit scattering (e.g., from GMCs), with $J_z\propto t^{0.5}$. But we account for changes in the scattering amplitude with epoch, due to an exponential decrease of SFR in the Milky Way and an inside-out growth of the Milky Way stellar disk. We show that such a model can reproduce the range of power-law indices $\gamma$ in observed present-day age-action relation $\widehat{J_z} (\tau)$, despite $\gamma > 0.5$ at all radii. The result suggests that orbit scattering (from GMCs) might be the dominant source of disk vertical heating for much of the low-alpha disk over the last 8$\,$Gyrs. The thin disk is unlikely to have gone through any dramatic major merger, although we could not rule out indirect influence from the spiral arms, the Galactic bar and the impact from minor mergers. \end{itemize} While the unique data from Gaia and APOGEE allows for the measurement of the global heating rate in the form of vertical action across the Milky Way disk, this study undoubtedly only explored a small part of what could potentially be attained by combining Gaia with large spectroscopic surveys like APOGEE, Galah, Gaia-ESO, and LAMOST. The full potential can only be realized if we incorporate the vertical heating model into a complete description of the Milky Way where more aspects of the Milky Way are studied and constrained simultaneously. And with only that, we might finally do justice to the data, and a fuller understanding of the formation of the Milky Way might eventually come to focus. | 18 | 8 | 1808.03278 |
1808 | 1808.08676_arXiv.txt | We analyze the impact of a proposed tidal instability coupling $p$-modes and $g$-modes within neutron stars on GW170817. This non-resonant instability transfers energy from the orbit of the binary to internal modes of the stars, accelerating the gravitational-wave driven inspiral. We model the impact of this instability on the phasing of the gravitational wave signal using three parameters per star: an overall amplitude, a saturation frequency, and a spectral index. Incorporating these additional parameters, we compute the Bayes Factor (\lnB) comparing our \pg~model to a standard one. We find that the observed signal is consistent with waveform models that neglect \pg~effects, with $\lnB = \lnBAbstract$. By injecting simulated signals that do not include \pg~effects and recovering them with the \pg~model, we show that there is a $\simeq \FAPlogU$ probability of obtaining similar \lnB~even when \pg~effects are absent. We find that the \pg~amplitude for 1.4 $M_\odot$ neutron stars is constrained to $\lesssim \AupperAbstract$, with maxima a posteriori near $\sim \AestAbstract$ and \pg~saturation frequency $\sim \FestAbstract$. This suggests that there are less than a few hundred excited modes, assuming they all saturate by wave breaking. For comparison, theoretical upper bounds suggest a \pg~amplitude $\lesssim 10^{-6}$ and $\lesssim 10^{3}$ modes saturating by wave breaking. Thus, the measured constraints only rule out extreme values of the \pg~parameters. They also imply that the instability dissipates $\lesssim \EnlupperAbstract$ over the entire inspiral, i.e., less than $\EnlEgrratio$~of the energy radiated as gravitational waves. | \label{section:introduction} Detailed analysis of the gravitational-wave (GW) signal received from the first binary neutron star (NS) coalescence event (GW170817 \cite{GW170817}) constrains the tidal deformability of NSs and thus the equation of state (EOS) above nuclear saturation density \cite{GW170817SourceProperties, EOS, De2018}. Studies of NS tidal deformation typically focus on the linear, quasi-static tidal bulge induced in each NS by its companion. Such deformations modify the system's binding energy and GW luminosity and thereby alter its orbital dynamics. The degree of deformation is often expressed in terms of the tidal deformability $\Lambda_i \propto (R_i/m_i)^5$ of each component \cite{Flanagan2008}, or a particular mass-weighted average thereof ($\tilde{\Lambda}$) \cite{GW170817SourceProperties}. The strong dependence on compactness $R/m$ means that a stiffer EOS, which has larger $R$ for the same $m$, imprints a larger tidal signals than a softer EOS. Current analyses of GW data from the LIGO \cite{LIGO} and Virgo \cite{Virgo} detectors favor a soft EOS \cite{EOS, GW170817GRB}. Specifically, \cite{GW170817SourceProperties} finds $\tilde{\Lambda} \lesssim \lambdamax$ at the 90\% credible level for all waveform models considered, allowing for the components to spin rapidly. The pressure at twice nuclear saturation density is also constrained to $P = \pressure$ (median and 90\% credible region) \cite{EOS} assuming small component spins. In addition to GW phasing, the EOS-dependence of $\tilde{\Lambda}$ should correlate with post-merger signals \cite{gw170817postmerger}, possible tidal disruptions, and kilonova observations \cite{gw170817kilonova}. Observed light-curves for the kilonova suggest a lower bound of $ \tilde{\Lambda}\gtrsim \lambdamin $ \cite{Radice2018, Coughlin2018}. Although some dynamical tidal effects are incorporated in these analyses (see, e.g., \cite{Hinderer2016, GW170817SourceProperties}), the impact of several types of dynamical tidal effects are neglected because they are assumed to be small or have large theoretical uncertainties. These effects arise because tidal fields, in addition to raising a quasi-static bulge, excite stellar normal modes. Three such excitation mechanisms are (i) resonant linear excitation, (ii) resonant nonlinear excitation, and (iii) non-resonant nonlinear excitation (see, e.g., \cite{Andersson2018}). The first occurs when the GW frequency (the oscillation frequency of the tidal field) sweeps through a mode's natural frequency (see, e.g., \cite{Lai1994, Reisenegger:94, Ho1999, Lai:06, Flanagan:07, Yu2017a, Yu2017b, Xu2017}). However, since the GW frequency increases rapidly during the late inspiral, the time spent near resonance is too short to excite modes to large amplitudes. As a result, for modes with natural frequencies within the sensitive bands of ground-based GW detectors, the change in orbital phasing is expected to be small ($\Delta \Psi \lesssim 10^{-2}\textrm{ rad}$) unless the stars are rapidly rotating \cite{Ho1999, Lai:06, Flanagan:07}. The impact of resonant nonlinear mode excitation (i.e., the parametric subharmonic instability) is likewise limited by the swiftness of the inspiral \cite{Weinberg2013}. The proposed \pg~tidal instability is a non-resonant, nonlinear instability in which the tidal bulge excites a low-frequency buoyancy-supported $g$-mode and a high-frequency pressure-supported $p$-mode \cite{Weinberg2013, Venumadhav2014, Weinberg2016, Zhou2017}. It occurs in the inner core of the NS, where the stratification is weak and the shear due to the tidal bulge is especially susceptible to instability. Unlike resonantly excited modes, an unstable \pg~pair continuously drains energy from the orbit once excited, even after the orbital frequency changes significantly. There are many potentially unstable \pg~pairs, each becoming unstable at a different frequency and growing at a different rate. Although there is considerable uncertainty about the number of unstable pairs, their exact growth rates, and how they saturate, estimates suggest that the impact could be measurable with current detectors \cite{Essick2016}. In this letter, we investigate the possible impact of the \pg~instability on GW170817 using the phenomenological model developed in \cite{Essick2016}. The model describes the energy dissipated by the instability within each NS, indexed by $i$, in terms of three parameters: (i) an overall amplitude $A_i$, which is related to the number of modes participating in the instability, their growth rates, and their saturation energies, (ii) a frequency $f_i$ corresponding to when the instability saturates, and (iii) a spectral index $n_i$ describing how the saturation energy evolves with frequency. In Section \ref{section:phenomenologlical model}, we describe our models in detail. In Section \ref{section:model selection}, we compare the statistical evidence for models that include the \pg~instability relative to those that do not. In Section \ref{section:parameter exclusion}, we investigate the constraints on the \pg~parameters from GW170817, and in Section \ref{section:discussion} we conclude. | \label{section:discussion} While GW170817 is consistent with models that neglect \pg~effects, it is also consistent with a broad range of \pg~parameters. The constraints from GW170817 imply that there are $\lesssim\Nmodeguestimate$ excited modes at $f=100\,\mathrm{Hz}$, assuming all modes grow as rapidly as possible and saturate at their breaking amplitudes ($\lambda=\beta=1$ in Eq.~(7) of \cite{Essick2016}) and that the frequency at which modes become unstable is well approximated by $f_0$. For comparison, theoretical arguments suggest an upper bound of $\sim 10^{3}$ modes saturating by wave breaking \cite{Essick2016}. More modes may be excited if they grow more slowly or saturate below their wave breaking energy. We can also use the measured constraints to place upper limits on the amount of energy dissipated by the \pg~instability. As Fig.~\ref{figure:energy} shows, \pg~effects dissipate $\lesssim \EnlupperNinetylogU$ throughout the entire inspiral at 90\% confidence. In comparison, GWs carry away $\gtrsim \EgrupperNinetylogU$. This implies time-domain phase shifts $|\Delta \phi| \lesssim \deltaPhihundredlowerNinetylogU$ (\deltaOrbitshundredlowerNinetylogU~orbits) at $100\textrm{ Hz}$ and $|\Delta \phi| \lesssim \deltaPhithousandlowerNinetylogU$ (\deltaOrbitsthousandlowerNinetylogU~orbits) at $1000\textrm{ Hz}$ after accounting for the joint uncertainty in component masses, spins, linear tides, and \pg~effects. A $g$-mode with natural frequency $f_g$ is predicted to become unstable at a frequency $f_{\rm crit}\simeq 45\, \mathrm{Hz} (f_g/10^{-4}\lambda f_{\rm dyn})^{1/2}$, where $f_{\rm dyn}$ is the dynamical frequency of the NS and $\lambda$ is a slowly varying function typically between $0.1-1$ \cite{Weinberg2016,Essick2016}. Since the modes grow quickly, the frequency at which the instability saturates is likely close to the frequency at which the modes become unstable ($f_0\simeq f_{\rm crit}$). If we assume that the observed peak near $f_0\sim\FestAbstract$ is not due to noise alone, then the maximum a posteriori estimate for $f_0$ along with approximate values for the masses (1.4 $M_\odot$) and radii (11 km) of the components \cite{EOS} imply $f_g \simeq \fgguestimate$. \begin{figure} \includegraphics[width=\columnwidth]{prl-intenergy-logU.pdf} \caption{ Upper limits on the cumulative enegy dissipated by the \pg~instability as a function of frequency. We note the relatively strong constraints at lower frequencies, where \pg~effects are more pronounced. } \label{figure:energy} \end{figure} With several more signals comparable to GW170817, it should be possible to improve the amplitude constraint to $A_0 \lesssim 10^{-7}$. Obtaining even tighter constraints will likely require many more detections, especially since most events will have smaller SNR. Future measurements will also benefit from a better understanding of how the instability saturates. To date, there have only been detailed theoretical studies of the instability's threshold and growth rate \cite{Weinberg2013, Venumadhav2014, Weinberg2016, Zhou2017}, not its saturation. As a result, we cannot be certain of the fidelity of our phenomenological model. While this letter was in final internal review, related work was posted \cite{Reyes2018} with, in particular, the conclusion that the \Hgr~model is strongly favored over the \Hnl~model by a factor of at least $10^4$. We are investigating possible reasons for the differences between our conclusions. The authors gratefully acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, the Department of Science and Technology, India, the Science \& Engineering Research Board (SERB), India, the Ministry of Human Resource Development, India, the Spanish Agencia Estatal de Investigaci\'on, the Vicepresid\`encia i Conselleria d'Innovaci\'o, Recerca i Turisme and the Conselleria d'Educaci\'o i Universitat del Govern de les Illes Balears, the Conselleria d'Educaci\'o, Investigaci\'o, Cultura i Esport de la Generalitat Valenciana, the National Science Centre of Poland, the Swiss National Science Foundation (SNSF), the Russian Foundation for Basic Research, the Russian Science Foundation, the European Commission, the European Regional Development Funds (ERDF), the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the Paris \^{I}le-de-France Region, the National Research, Development and Innovation Office Hungary (NKFI), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Science and Engineering Research Council Canada, the Canadian Institute for Advanced Research, the Brazilian Ministry of Science, Technology, Innovations, and Communications, the International Center for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR), the Research Grants Council of Hong Kong, the National Natural Science Foundation of China (NSFC), the Leverhulme Trust, the Research Corporation, the Ministry of Science and Technology (MOST), Taiwan and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS and the State of Niedersachsen/Germany for provision of computational resources. N. Weinberg was supported in part by NASA grant NNX14AB40G. | 18 | 8 | 1808.08676 |
1808 | 1808.04491_arXiv.txt | We present a SALT-RSS spectroscopic study of a sample of S0 galaxies established by \citet{Vaghmare2015} as having pseudobulges using a combination of photometric criteria. We extract the spectra of various regions along the galaxy major axis using standard long-slit spectroscopic reduction procedures and model the spectra using STARLIGHT to derive detailed star formation histories. The central spectra of galaxies without bars in our sample reveal a complex star formation history, which is consistent with the belief that pseudobulges have a history of star formation distributed over extended periods of time. The spectra of the unbarred galaxies contain strong emission lines such as $H\alpha$, indicating active star formation, which appears to be in contradiction with the expectation that S0 galaxies have been stripped of gas. In the case of the two barred galaxies in the sample, the spectrum is dominated by light from a much older stellar population. This seems to suggest an accelerated formation of the pseudobulge made possible by the action of the bar. One of these galaxies appears to have exhausted its reservoir of gas and thus has no signature of a recently formed population of stars while the other galaxy has managed to give rise to new stars through a recent funnelling action. We have also confirmed the influence of bars on the nature of the stellar population in a pseudobulge using an alternate sample based on the SDSS. | \label{sec:intro} There are several ways by which one can approach the study of galaxy evolution. One approach is to classify the galaxies in the nearby Universe into different morphological types and study their properties. In such an approach, the study of S0 galaxies has received considerable attention in the last decade. S0 galaxies are characterised by the presence of, what appears to be, an elliptical-like bulge and a smooth outer disk devoid of any apparent spiral arms. Indeed, the study of these galaxies is important because hidden within their inter-relationship with galaxies of other types are clues to the varied processes that play important roles in the overall picture of galaxy evolution (See \citet{Aguerri2012} and references therein). For example, observational studies suggest that the central components of S0 galaxies viz. bulges resemble elliptical galaxies \citep{Renzini99}. They have thus likely formed in a similar manner to ellipticals, i.e. through hierarchical clustering and mergers. However, the observation that the fraction of S0 galaxies within a cluster of galaxies grows at the cost of spirals \citep{Dressler1980}, suggests that S0s originate from spirals. Gas stripping via ram pressure is often considered a viable process for such a transformation in dense cluster environments \citep{Gunn1972, Aragon-Salamanca2006, Laurikainen2010, Maltby2015}. However, we know that S0's are equally common in groups \citep{Wilman2009, Just2010, Bekki2011}. These observations suggest that the processes such as ram pressure stripping are not responsible for the formation of the majority of S0s in groups where minor mergers and tidal effects can control their evolution \citep{Mazzei2014, Mapelli2015}. Simulations too suggest that there are multiple methods for forming S0s - they can arise in major mergers, can grow through slow/secular processes and can also form through gas stripping of spirals \citep{Querejeta2015, Tapia2017}. Traces of past merger events which impact the observed kinematics have been observed in some S0s \citep{Falcon-Barroso2004}. The observed star formation (SF) and SF history (SFH) characteristics of S0s can be complex (e.g. \citet{Barway2013} and references therein). \citet{Barway2007, Barway2009} suggest that the dominant formation process in case of S0s is a function of luminosity, with brighter S0s forming in a manner similar to ellipticals and fainter S0s forming through secular processes or perhaps by gas stripping of spirals \citep{Rizzo2018}, which in turn may have formed through secular evolution. \citet{Vaghmare2013} used archival deep mid-infrared images from the Spitzer Infrared Array Camera to systematically study the bulges of S0 galaxies. Bulges, as defined photometrically, are excesses of light over an inward extrapolation of an exponential profile fitted to the outer disk. They are known to occur in two varieties - classical, resembling ellipticals in almost every aspect including morphology, colour, nature of stellar populations and kinematics, and pseudo, resembling disks and believed to have formed through secular evolution \citep{Kormendy2004}. \citet{Vaghmare2013} point out that pseudobulges do exist in S0 galaxies and preferentially occur in fainter S0s. But what is perhaps a more interesting result is that disks of pseudobulge hosting S0s have a lower scale length than those hosting classical bulges. In \citet{Vaghmare2013}, the authors speculate that the lower scale length could imply either (i) that the population of disks with lower scale length on average preferentially host pseudobulges or (ii) that the lowered scale length is a result of some process responsible for either the bulge's or the overall galaxy's growth. In a follow-up study, \citet{Vaghmare2015} compare the disk properties of spirals and S0s and find that pseudobulge hosting S0s have a lower scale length than the pseudobulge hosting spirals. The authors explain this as being due to lowered disk luminosity in case of S0s hosting pseudobulges. They further compare bulge luminosities to demonstrate that only the early-type spirals may transform into S0s with pseudobulges through disk fading via gas stripping, while late-type spirals will need additional processes, especially to aid the growth of bulges to observed luminosities. The conclusions reached by \citet{Vaghmare2013, Vaghmare2015} and by Barway et al. rely on statistical arguments. Correlations are derived between various parameters, which in turn are derived from imaging data. While such studies indeed offer insights into broad trends among galaxies in a given class, they cannot provide information on individual galaxies and their star formation / assembly histories. For this, one requires data from multiple wavebands. \citet{Barway2013} use broad band photometry from multiple surveys spanning UV, optical and infrared wavelengths but again use statistical arguments to point out broad trends among S0 galaxies. In order to truly constrain the formation histories of S0s, one needs to have spectroscopic data. Using stellar population synthesis techniques, one can then derive very detailed star formation histories for these galaxies and confront the conclusions reached by the photometric studies. To this effect, we have been using the Southern African Large Telescope's (SALT) Robert Stoby Spectrograph (RSS) to observe a select sample of S0 galaxies. The work presented in this paper focusses on a subset of the galaxies - those shown to host pseudobulges by \citet{Vaghmare2015}, whose photometric properties and their implications were summarised earlier. The aim here is to check for consistency between star formation histories and the conclusions based on the photometric observations. This paper is organised as follows - the data and the reduction methods are described in section \ref{sec:data}, section \ref{sec:specmod} explains the process of modelling the spectra using \textsc{starlight} while sections \ref{sec:result}, \ref{sec:discussion} and \ref{sec:bar_dn4000} present the detailed results and possible interpretations. Throughout this paper, we use the standard concordance cosmology with $\Omega_M= 0.3$, $\Omega_\Lambda= 0.7$ and $h_{100}=0.7$. Also, magnitudes used in this work are in the AB system. \begin{figure*} \centering \includegraphics[width=0.8\textwidth]{figure1.pdf} \caption{The 3.6 micron images obtained using the Spitzer IRAC, for the eight galaxies studied in the present paper.} \label{fig:spitzer_images} \end{figure*} | \label{sec:discussion} We have seen above that the barred galaxies in our sample have largely similar stellar population properties and so is the case with the unbarred galaxies taken as a group but there are important differences between these groups. \subsection{The unbarred group} \label{subsec:unbarred_group} Recall that the parent sample of this study is the sample of 25 pseudobulge hosting S0 galaxies, as described in \citet{Vaghmare2013}. The authors classified pseudobulges using a very conservative criterion. Typically, studies aimed at bulge classification adopt a very simple criterion where all bulges with S\'{e}rsic index $n<2$ are classified as pseudobulges and others as classical. But as \citet{Vaghmare2013} argue, the parameter $n$ is not easy to constrain and thus there is scope for misclassification. \citet{Gadotti2009} proposed an alternate criterion based on the Kormendy diagram and argued on the merits of such an approach. \citet{Vaghmare2013} adopted a combination of the two criteria to ensure that a secure classification is obtained. The chances of misclassifying a galaxy as a pseudobulge host is thus quite low. \citet{Vaghmare2015} suggested that the pseudobulge hosting S0s have a lower disk luminosity with respect to their spiral counterparts, which the authors interpret as a disk that has faded while undergoing a transformation in morphology from spiral to S0. The authors argue that this transformation involves stripping of gas which is needed for sustaining active star formation. The signs of active star formation in these galaxies, as indicated by their spectra is in contradiction with this conclusion. Further to confirm if the gas stripping process is a viable scenario, we investigated the environment of these unbarred galaxies. We found that excluding IC\,2085, the galaxies in the unbarred group are in an isolated environment. One possible resolution is that these isolated galaxies are not gas stripped spirals. In this case, we have to conclude that these disks are inherently less luminous and somehow such disks have an affinity to be a part of pseudobulge hosting S0 galaxies. Another explanation is that these objects are gas stripped spirals but have had their gas replenished through numerous gas rich minor mergers which in turn led to complex star formation \citep{Penoyre2017}. \subsection{The barred group} \label{subsec:barred_group} An interesting commonality in the two galaxies in this group, apart from the stellar population, is that these galaxies are barred. With the usual caveat of lack of robustness due to small numbers, this common observation allows for some speculation on why, despite such a conservative classification criterion, the bulges of these galaxies are found not to be consistent with pseudobulges. Recall that the photometric parameters of the bulges as derived by performing 2-d bulge-disk decomposition, have been used for classifying them. One may thus argue that the presence of a bar has a systematic effect on the derived bulge properties \citep{Laurikainen2005, Gadotti2009}. But \citet{Vaghmare2013} recognize this problem and take care to fit a bar component as well. Thus the unaccounting of a bar component cannot explain this observation. Another explanation for the old stellar population in these galaxies is as follows. The presence of the bar led to an amplified funnelling of gas towards the centre of the galaxies in the past. This allowed the pseudobulge to form much earlier than the rest of the galaxies where there was no bar component to aid the quick formation of a pseudobulge. As a result the pseudobulges in both these galaxies contain a very old population as can be seen in the Figure \ref{fig:sfh_all}. In the case of NGC 1533, there does not seem to have been any gas available to lead to recent star formation while in the case of NGC 5750, there is some evidence of recent star formation. A confirmation of whether the bar action can explain the older age could be obtained from a high spatial resolution rotation curve for these galaxies. The relative domination of a random component of stellar velocities vs systematic rotation may be able to shed light on whether there is funnelling of gas taking place. However, such a study is not possible using the present data. \label{sec:summary} In this paper, we have studied eight S0 galaxies established by \citet{Vaghmare2015} to host pseudobulges, using long-slit spectra obtained from the SALT-RSS. We have modelled the spectra using \textsc{starlight} to derive detailed star formation histories of these galaxies as well as age and metallicity gradients. The present study focusses primarily on the spectra of the central regions of the galaxy and, using the spectral information, confronts the conclusions drawn by \citet{Vaghmare2015}. The most important conclusion is that these eight galaxies are not all similar in terms of their star formation histories. This means that objects grouped in one class using photometric criteria (the class here being pseudobulge hosting S0s) can exhibit diverse properties. The present study brings out the need for further studies that are based on spectral analysis to truly constrain the formation mechanisms at work in the formation of these objects. We discovered that six of these eight galaxies, which are unbarred, exhibit a complex star formation history with active star formation. We attempt reconciling the observed ongoing star formation with the conclusion reached by \citet{Vaghmare2015} that these are gas stripped spirals. It has been suggested by \citet{Poggianti2017} that the process of ram pressure stripping in galaxies can cause initial fuelling of gas inwards, which could lead to star formation in the central regions. Once the gas is stripped, the disk can fade, but residual gas in the central region could be responsible for the observed star formation. This would make fading due to stripping consistent with our observations. But since most of the galaxies are in an isolated environment the question would remain as to what caused the stripping. In the other two galaxies, which are barred, we find a population similar to those expected in elliptical galaxies. We have detected a trace of recent star formation in one of these galaxies which likely indicates that the bar is funnelling / has funnelled gas towards the center leading to a formation of a younger group of stars. We have also used a sample of SDSS galaxies to show that the preferential occurrence of older populations in barred S0 galaxies, suggested by the spectral data, is likely a real phenomenon. The study of this SDSS sample also suggests that there are unbarred pseudobulge hosting S0s with very old populations \citep{Mishra2017}. However, no such object has been found in the present study. Using the data obtained from the SALT-RSS, it is possible to perform a very detailed analysis of the star formation history of the off-center regions of the galaxy. This can lead to new insights into how galaxies formed. We defer such a detailed study to a future paper. | 18 | 8 | 1808.04491 |
1808 | 1808.06177_arXiv.txt | A search for dark matter (DM) with mass in the sub-GeV region (0.32--1 GeV) was conducted by looking for an annual modulation signal in XMASS, a single-phase liquid xenon detector. Inelastic nuclear scattering accompanied by bremsstrahlung emission was used to search down to an electron equivalent energy of 1 keV. The data used had a live time of 2.8 years (3.5 years in calendar time), resulting in a total exposure of 2.38 ton-years. % No significant modulation signal was observed and 90\% confidence level upper limits of $1.6 \times 10^{-33}$ cm$^2$ at 0.5 GeV was set for the DM-nucleon cross section. This is the first experimental result of a search for DM mediated by the bremsstrahlung effect. In addition, a search for DM with mass in the multi-GeV region (4--20 GeV) was conducted with a lower energy threshold than previous analysis of XMASS. Elastic nuclear scattering was used to search down to a nuclear recoil equivalent energy of 2.3 keV, and upper limits of 2.9 $\times$10$^{-42}$ cm$^2$ at 8 GeV was obtained. | The nature of dark matter (DM) is a key mystery in cosmology, and detecting it via any force other than gravity is essential for advancing particle physics beyond the standard model. Weakly interacting massive particles (WIMPs) at $O$(100 GeV) are predicted by theoretical extensions of the standard model, such as the constrained minimal supersymmetric standard model and are strong DM candidates {\cite{WIMPs}. They have been investigated extensively via nuclear recoil \cite{XENON1T,LUX,PANDA}; however, no significant detections of WIMPs have been confirmed. Other theories predict a myriad of different DM types, light-mass WIMPs \cite{DUAN2018296}, asymmetric DM \cite{AsymmDM1,AsymmDM2,AsymmDM3}, or hidden sector DM {\cite{hiddenDM} and many others; the mass of these DM candidates ranges from sub-GeV to a few GeV. Semi-conductor and crystal detectors have searched for these light DM candidates by lowering their nuclear recoil energy thresholds \cite{CDMSLitePaper, CRESSTSurPaper}. A search via DM-electron scattering by existing detectors have also been performed {\cite{DM_elec, DM_elec_SLAC}. In addition to these detectors, conventional xenon detectors should also be sensitive to DM with sub-GeV mass \cite{subGeV, subGeV2}, due to the irreducible contribution of the bremsstrahlung effect accompanying nuclear recoils \cite{subGeV}. The bremsstrahlung effect can occur when DM collides with a nucleus causing it to recoil and accelerate. In the case that a mass of DM particle is 1 GeV, the energy deposited by the bremsstrahlung photon is at most 3 keV. This energy is considerably more than that deposited by elastic nuclear recoil ($\sim$0.1 keV). In addition to this bremsstrahlung effect, another inelastic effect called the Migdal effect} has also been suggested \cite{Migdal}. This effect leads to the emission of an electron from the atomic shell and causes subsequent radiation through the inelastic recoil of DM and nuclei.} Although the bremsstrahlung and Migdal effects need both be calibrated experimentally in xenon and cross sections are smaller than that of elastic nuclear recoil ($\sim$$10^{-6}$ for Migdal, $\sim$$10^{-8}$ for Bremsstrahlung at 1 GeV), because these inelastic effects lead to larger energy deposition than elastic nuclear recoil, it should be possible to detect sub-GeV DM through these effects. Moreover, searching for a spin-dependent (SD) interaction utilising these effects is an attractive possibility, since xenon has a larger fraction of odd isotopes than that of other isotopes, such as oxygen \cite{CRESSTSurPaper}. Xenon has two stable odd isotopes, namely $^{129}$Xe and $^{131}$Xe which account for 26.4\% and 21.2\% of the natural xenon abundance, respectively; oxygen has only 0.04\% of odd isotopes. Further theoretical studies are expected to enable the quantitative interpretation of the SD interaction by sub-GeV DM. This letter reports on the first experimental search for sub-GeV DM (0.32--1.0 GeV) utilizing the bremsstrahlung effect. In the case of xenon, the Migdal effect is accompanied by M-shell electron emission, and the most likely de-excitation energy is 0.66 keV from the 3d orbit. As discussed in Section 4, since our understanding of detector responses is limited to those greater than 1 keV, we focus only on for the signal from the bremsstrahlung effect in this analysis. On the other hand, the search for multi-GeV DM (4--20 GeV) via conventional elastic nuclear recoils \cite{XMASS_MOD, XMASS_MOD2017} was performed. For multi-GeV DM search, data with lower energy threshold than in previous studies \cite{XMASS_MOD, XMASS_MOD2017} were used to improve sensitivity in the low mass range. These searches were conducted by looking for the annual modulation of the event rate in the XMASS data. | We carried out the annual modulation analysis for XMASS-I data to search for the sub-GeV and multi-GeV DM via the bremsstrahlung effect and elastic nuclear recoil, respectively. The former search limits the parameter space of DM with a mass of 0.5 GeV to below 1.6 $\times$ $10^{-33}$ cm$^2$ at 90\% CL. This is the first experimental result for a sub-GeV DM search focused on annual modulation and bremsstrahlung photons emitted by inelastic nuclear recoils. The additional search for the multi-GeV DM with the lower threshold data obtained a limit for the parameter space of DM with a mass of 8 GeV to below 2.9 $\times$ $10^{-42}$ cm $^2$ at 90\% CL. | 18 | 8 | 1808.06177 |
1808 | 1808.08489_arXiv.txt | The Next Generation Balloon-borne Large Aperture Submillimeter Telescope (BLAST-TNG) is a submillimeter mapping experiment planned for a 28 day long-duration balloon (LDB) flight from McMurdo Station, Antarctica during the 2018-2019 season. BLAST-TNG will detect submillimeter polarized interstellar dust emission, tracing magnetic fields in galactic molecular clouds. BLAST-TNG will be the first polarimeter with the sensitivity and resolution to probe the $\sim$0.1 parsec-scale features that are critical to understanding the origin of structures in the interstellar medium. BLAST-TNG features three detector arrays operating at wavelengths of 250, 350, and 500 \um (1200, 857, and 600 GHz) comprised of 918, 469, and 272 dual-polarization pixels, respectively. Each pixel is made up of two crossed microwave kinetic inductance detectors (MKIDs). These arrays are cooled to 275 mK in a cryogenic receiver. Each MKID has a different resonant frequency, allowing hundreds of resonators to be read out on a single transmission line. This inherent ability to be frequency-domain multiplexed simplifies the cryogenic readout hardware, but requires careful optical testing to map out the physical location of each resonator on the focal plane. Receiver-level optical testing was carried out using both a cryogenic source mounted to a movable xy-stage with a shutter, and a beam-filling, heated blackbody source able to provide a 10-50 $^\circ$C temperature chop. The focal plane array noise properties, responsivity, polarization efficiency, instrumental polarization were measured. We present the preflight characterization of the BLAST-TNG cryogenic system and array-level optical testing of the MKID detector arrays in the flight receiver. | 18 | 8 | 1808.08489 |
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1808 | 1808.02048_arXiv.txt | {Motivated by the $\sim7\%$ dipole anisotropy in the distribution of ultra-high energy cosmic-rays (UHECRs) above 8 EeV, we explore the anisotropy induced by the large scale structure, using constrained simulations of the local Universe and taking into account the effect of magnetic fields. The value of the intergalactic magnetic field (IGMF) is critical as it determines the UHECR cosmic horizon. { We calculate the UHECR sky maps for different values of the IGMF variance and show the effect of the UHECR horizon on the observed anisotropy.} The footprint of the local ($\lesssim350$ Mpc) Universe on the UHECR background, a small angular scale enhancement in the Northern Hemisphere, is seen.} At 11.5 EeV (the median value of the energy bin at which the dipole has been reported), the LSS-induced dipole amplitude is $A_1\sim10\%$, for IGMF in the range [0.3-3] nG for protons, helium and nitrogen, compatible with the rms value derived from the cosmic power spectrum. { However at these energies the UHECRs are also influenced by the Galactic Magnetic Field (GMF) and we discuss its effect on the LSS-induced anisotropy. } | The origin of the ultra-high energy cosmic-rays (UHECRs) is still unknown. To identify a source we need to know the arrival direction of the UHECRs. However, UHECRs are deflected on their way to the Earth by the intervening Galactic and { intergalactic} magnetic fields (GMF and IGMF, respectively). % The only observed statistically significant deviation from isotropy is a large scale dipole anisotropy \citep[][{\color{black}hereafter PAO17}]{2017Sci...357.1266P}, { of the order of a few percent}, reported at $\sim$5$\sigma$ significance level for UHECR energies $E>$8 EeV. % { We can expect that extragalactic UHECR sources follow, up to a biasing factor, } the large scale structure (LSS) of the Universe. Both the energy and composition of the cosmic-rays change during the extragalactic propagation because of their interaction with the cosmological photons backgrounds (GZK effect). % Moreover, contrarily to the photons, neutrinos and gravitational waves, UHECRs are deflected by the IGMF, and enter a diffusion regime after a time of a few $D/c^2$ ($D$ is the diffusion coefficient). % The observed UHECR dipole anisotropy is set by the size of the UHECR observable Universe. The "cosmic-ray horizon", the largest distance that the UHECR can propagate {\it at a given energy}, depends on their diffusion coefficient in the IGMF and on their mean free path in the photons backgrounds {\color{black}\citep{2000PhRvL..84.3527F,2004NuPhS.136..169P, 2010arXiv1005.3311P, 2014PhRvD..89l3001H,2015PhRvD..92f3014H}}. Different nuclei don't experience the same energy losses, and therefore, even if they have the same rigidity $\sim E/Z$ (i.e. they behave the same way in the IGMF), they have different horizons. This situation is unique to UHECRs: different energy and nuclei species probe different distances. Therefore, it has been suggested that, at a given energy and composition, the anisotropy in the UHECR background probes the {source} distribution within the cosmic-ray horizon \citep{Waxman+97}. We investigate this possibility, assuming that the distribution of UHECR sources follow the LSS. We calculate the UHECR dipole anisotropy induced by the matter distribution, taking into account the diffusive propagation of the UHECRs in the IGMF. We derive the amplitude and direction of the % UHECR dipole, for different IGMF values and different compositions. { We then estimate the effect of the GMF on the LSS-induced UHECR anisotropy, for proton and nitrogen at 11.5 EeV.} \begin{figure*} \centering \includegraphics[scale=0.5]{horizons2.pdf} \caption{UHECR horizons as a function of the energy for different values of the IGMF.} \label{horizons} \end{figure*} In a previous study \citep[][hereafter GP17]{2017ApJ...850L..25G}, we derived the expected UHECR extragalactic dipole from the observed LSS density power spectrum. We found a maximum value for the rms dipole amplitude of $\sim8b$\% for IGMF strength $\gtrsim1$ nG, for helium and nitrogen at energies greater than 8 EeV. Here $b$ is the bias factor. It is larger than unity if the UHECR sources are more clustered than the dark matter. {\color{black} We showed that the energy dependence of the dipolar amplitude increases as a function of the energy. This is consistent with the findings by \citet{2014PhRvD..89l3001H,2018ApJ...854L...3W}.} The novelty of our approach here is the reconstructed density field of the local Universe \citep{2018NatAs.tmp...91H} based on the {\it CosmicFlow-2} catalog of peculiar velocities to calculate sky maps of the UHECR anisotropy induced by the LSS for different UHECR horizons. {\color{black} Previous studies used either the 2 Micron All-Sky Redshift Survey (2MRS) galaxy catalog for the source distribution \citep{2014PhRvD..89l3001H,2015PhRvD..92f3014H} or the local large-scale mass structure model of \citet{2005JCAP...01..009D} \citep{2018ApJ...854L...3W} in which the data on the source distribution extent only to $\sim 110$ Mpc. The simulations that we use allow to extrapolate the LSS to regions that are poorly observed because of Galactic foregrounds, and also to probe larger distances, up to $\sim 350$ Mpc. } A 3D view of the density field used in our calculations {\color{black}from \citet{2018NatAs.tmp...91H}} can be explored at this link \href{https://skfb.ly/6AFxT}{[https://skfb.ly/6AFxT]}. All the major overdensities of the Local Universe are shown as isosurfaces of different colors. { To derive the LSS-induced anisotropy, we consider different cosmic-ray horizons that are determined by the diffusion of UHECRs of different compositions in different IGMFs .} { In this work we assume a homogeneous and purely turbulent IGMF, {\color{black} and we vary its strength to probe different magnetic horizons}. In reality the IGMF variance is expected to be correlated with the different structures, clusters, filaments, voids \citep[e.g.][]{2008PhRvD..77l3003K}. This may change the propagation of the UHECRs in the field with stronger deflections within regions of stronger magnetic field and weaker ones. The overall effect might be mimicked by varying the coherence length or by more detailed simulations. However, as we are mostly interested in the dipole this would probably won't have a significant effect, as already shown by \citet{2018MNRAS.475.2519H} who tested different magnetogenesis models and obtain similar UHECR anisotropy for the different models. Note, however, that these authors didn't consider the GMF which, as we show later, has a significant effect on the dipole and hence must be taken it into account. Note also that these authors {\color{black} chose a finite number of source positions up to 140 Mpc, and these positions (as well as the magnetic field structure) then were periodically repeated, which lead to a rather isotropic distribution} beyond 140 Mpc, reducing the dipole for UHECRs whose horizon is larger than this distance.} { The plan of the paper is as follow.} We present the { observations} in section \ref{observations}. We discuss the effects of the intergalactic magnetic fields on the UHECR horizons in section \ref{magnetic}. { In section \ref{Method} we discuss the reconstruction of the density field and the calculations of the UHECR propagation in the IGMF. } We present the results in section \ref{results}. { We show the effect of the GMF in section \ref{Galactic}} and discuss our results in \ref{discussion}. | \label{discussion} { We calculated the LSS-induced UHECR anisotropy, assuming that the source density is proportional to the matter density $\rho$. The novelty is to use constrained simulations from \citet{2018NatAs.tmp...91H} which provide an estimate of the local cosmic { density field up to $\sim350$ Mpc}. We developed an original approach to be able to calculate the sky maps for different IGMFs and discussed the effect of magnetic horizons on the UHECR anisotropy. } With the density field of the local Universe, we recover a dipole amplitude of the same order as the rms value (GP17), $A_1\sim0.1$, for IGMF in the range [0.3-3] nG for 11.5 EeV protons, helium and nitrogen. We recall that this energy is the median value of the energy bin at which the dipole has been reported. \citet{2018NatAs.tmp...91H} calculated the bias relation between the matter and the density field, $\rho_g=(\rho/\bar{\rho})^{b}$, { with $b = 1.74 \pm 0.13$ for the luminosity density density field derived from the compilation of the 2M++ redshift survey of galaxies \citep{2015MNRAS.450..317C}. We opted here to make the simplest assumption that the intensity of the UHECR sources follows the mass distribution. Relaxing this assumption and allowing for a linear bias factor implies that the results quoted here about the anisotropy need to be multiplied by this bias factor. }% {\color{black} A significant bias between the matter density and the sources would increase the dipole amplitude.} The anisotropy induced by the LSS presents small-scale structures. If protons were dominating at 11.5 EeV, a proton anisotropy would not be significantly altered by the GMF \citep[e.g.][]{2016IAUFM..29B.723F}. It is interesting to note that the LSS-induced anisotropy presents an enhancement which is not far from the Cen A direction ($l=310$\degree, $b=20$\degree), and that a clustering was already reported in that direction by Auger \citep{Aab15}. If nitrogen is dominating at 11.5 EeV, then the rigidity is smaller. For an IGMF of a few nG, we obtain a large scale angular anisotropy (well represented by a dipole) in the Virgo direction. Our preliminary considerations of the GMF suggest that it deflects the LSS-induced dipole towards the direction observed by Auger. While we have presented here calculations only for a single value of the energy, a full parametric analysis is planned in a further paper to better understand the effect of varying the IGMF and GMF parameters for a given evolution of the composition with energy. \\ NG and TP were supported by the I-CORE Program of the Planning and Budgeting Committee, the Israel Science Foundation (grant 1829/12), and an advanced ERC grant TReX. YH was supported by an ISF grant 1013/12. We thank the Red Espa\~nola de Supercomputaci\'on for granting us computing time in the Marenostrum Supercomputer at the BSC-CNS where the simulations used for this paper have been performed. | 18 | 8 | 1808.02048 |
1808 | 1808.00567_arXiv.txt | \bicep3 is a 520mm aperture on-axis refracting telescope observing the polarization of the cosmic microwave background (CMB) at 95GHz in search of the B-mode signal originating from inflationary gravitational waves. \bicep3's focal plane is populated with modularized tiles of antenna-coupled transition edge sensor (TES) bolometers. \bicep3 was deployed to the South Pole during 2014-15 austral summer and has been operational since. During the 2016-17 austral summer, we implemented changes to optical elements that lead to better noise performance. We discuss this upgrade and show the performance of \bicep3 at its full mapping speed from the 2017 and 2018 observing seasons. \bicep3 achieves an order-of-magnitude improvement in mapping speed compared to a Keck 95GHz receiver. We demonstrate 6.6\ukrts\, noise performance of the \bicep3 receiver. | \label{sec:intro} % The cosmic microwave background (CMB) has been observed extensively to probe the early history and evolution of the Universe, bolstering the standard \lcdm cosmology. However, the standard \lcdm cosmology fails to provide an explanation for the homogeneity, isotropy, and flatness of the observable Universe. Inflation is the leading framework that resolves these problems by assuming an epoch of exponential expansion prior to the standard Big Bang expansion. Inflation stretches the tensor perturbations of the metric and produces a stochastic gravitational wave background. Since the inflationary gravitational wave (IGW) background is the only source known to produce the curly pattern in polarization, so-called `B-mode' polarization, on the CMB at the last scattering surface, the detection of B-modes at degree angular scales is a valid test for this framework\cite{Kamionkowski2016}. The level of the B-mode power from IGW is related to the energy scale of the inflation, and it is characterized by the ratio of the amplitude of the tensor perturbation to the amplitude of the scalar perturbation, called the tensor-to-scalar ratio `$r$'. The predicted level of the B-mode power is very small and requires deep CMB polarization maps. The \bicep/Keck Collaboration has deployed a series of telescopes to the South Pole in search of the B-mode signal potentially originating from the IGW. With these small aperture telescopes, we focus on scanning a small patch of the sky to obtain deep polarization maps at degree angular scales. Since the detection of the B-mode at degree angular scales by \bicep2 which had operated at 150GHz\cite{BKI}, we have continued to observe the same patch at multiple frequency bands to separate CMB polarization from foreground components that can also contribute to the B-mode power. Keck Array has been equipped with five \bicep2-size telescopes at different frequencies and operational since 2012. Utilizing the capacity to house five receivers on the Keck mount, we have deployed and replaced receivers at frequencies of 95, 150, 220, and 270GHz. \bicep3 is the third generation of the family with a larger aperture and faster optics, hosting more detectors on its focal plane than \bicep2 or Keck Array receivers. With 2400 optically coupled transition edge sensor (TES) bolometers at its full capacity, \bicep3 was designed to achieve ten times the throughput of a single Keck 95GHz receiver. The design of \bicep3 was discussed in detail in Ref.~\citenum{Ahmed14}. The initial performance from the engineering season in 2015 was presented in Ref.~\citenum{wu15}. There were significant upgrades and fixes based on what we investigated from the engineering season, and the preliminary performance from the first science season in 2016 was presented in Refs.~\citenum{Grayson16},\citenum{Hui16},\citenum{Karkare16} including further details of \bicep3 design and operation schemes. The first science season still exhibited an elevated level of per-detector noise compared to Keck 95GHz receivers. This proceeding discusses the upgrades and fixes we implemented for the second science season in 2017 and presents \bicep3 performing at its full stable capacity. | In this proceeding, we present the upgrades we performed on \bicep3 during the 2016-17 austral summer. We have evaluated the noise performance of the detectors from the full season data in 2016 and 2017 as well as the preliminary performance from 2018 season. We confirm the improved performance in 2017 continues to hold in 2018. The major upgrades include the replacement of the IR filter stack formed of reflective metal-mesh filters with absorptive foam filters, replacing delaminated edge-filters and replacing four tile modules. Comparing the full season data in 2016 and 2017, we show improvement in the timestream-based median per-detector NET from 312\ukrts\, to 265\ukrts\, and the array NET from 8.68\ukrts\, to 6.64\ukrts. \bicep3 performs better than Ref.~\citenum{wu15}'s projected receiver NET of 6.9\ukrts. \bicep3 continues to make the deepest CMB polarization map made to date at 95 GHz. \bicep3 still has room for improvement. Ref.\citenum{Barkats18} suggests the usage of ultra-thin window design would further reduce the in-band loss and may improve NET. The change from \bicep3's 1.25-inch thick window to 0.01-inch thick window may reduce NET by 20\% at 95GHz. \bicep3 has demonstrated stable performance and serves as a stepping stone for the upgrade of the Keck Array to the \bicep Array, an array of four \bicep3-size receivers observing at 30/40, 95, 150, and 220/270 GHz\cite{Grayson16,Hui18}. Research and development is ongoing, including the window design\cite{Barkats18}, cryostat and mount design\cite{Crumrine18}, module design\cite{Soliman18}, and readout technology\cite{Henderson18,obrient2018tkid}, which are included in this volume of proceedings. | 18 | 8 | 1808.00567 |
1808 | 1808.00751_arXiv.txt | Sparse Aperture Masking (SAM) allows for high-contrast imaging at small inner working angles, however the performance is limited by the small throughput and the number of baselines. We present the concept and first lab results of Holographic Aperture Masking (HAM) with extreme liquid-crystal geometric phase patterns. We multiplex subapertures using holographic techniques to combine the same subaperture in multiple non-redundant PSFs in combination with a non-interferometric reference spot. This way arbitrary subaperture combinations and PSF configurations can be realized, giving HAM more uv-coverage, better throughput and improved calibration as compared to SAM, at the cost of detector space. | \label{sec:intro} % Sparse aperture masking (SAM) is a technique that turns a single dish telescope into an interferometer by masking out a large fraction of the pupil. The opaque mask consists of a sparse combination of holes such that the point-spread function (PSF) is a combination of interferometric fringes from each baseline. Because SAM is an interferometric method it is possible to measure down to half the diffraction limit of a single dish telescope. More importantly, with SAM it is possible to measure closure phases, an observable that is independent of the incoming wavefront aberration. Both advantages make SAM a good option for high contrast imaging and with the improved calibration that came with adaptive optics systems, sparse aperture masking has been extremely successful in imaging asymmetric structures around stars at small separations unreachable by other techniques like coronagraphy. SAM has been used to measure the shape and grain sizes of dust shells around stars \cite{Norris2012}, discovering substellar companions around young stars \cite{Kraus2012,Huelamo2011} and measure stellar multiplicity in star-forming regions \cite{Ireland2008,Martinache2009,Cheetham2015}. \\ Non-redundant masking is a subtechnique of SAM and requires the holes to be places in non-redundant patterns. Only a limited amount of holes can be combined in a non-redundant way and non-redundant masks therefore have a low throughput. Techniques like segment tilting and pupil remapping are ways to improve the throughput by making different non-redundant combinations of the aperture. Both techniques are complex to implement for a given telescope compared to the simplicity of sparse aperture masking where only one mask with holes is needed. Holographic aperture masking (HAM) uses a single phase plate to combine non-redundant subapertures at different focal plane locations, maintaining the simplicity of SAM. The possibilities with HAM go beyond the segment tilting as holographic techniques can be used to make multiple copies of each subaperture, enabled by liquid-crystal technology. A comparison between SAM and HAM is given in Fig. \ref{fig:HAMSAM}. HAM can incorporate SAM while adding more baselines by interfering additional subapertures with PSF copies at a separate location in the focal plane. While more detector space is required, HAM has more baselines and closure phases, uses more subapertures, allows for broadband operation and can be used to generate amplitude reference spots. \\ In this paper, we present the theory for blazed gratings and liquid-crystal technology in section \ref{sect:theory}, the design of holographic aperture masks in section \ref{sect:design}, lab results in section \ref{sect:lab} and conclusions are presented in section \ref{sect:conclusion}. \begin{figure}[ht] \center \includegraphics[width = \textwidth]{HAMSAM.pdf} \caption{Comparison of sparse aperture masking (left) and holographic aperture masking (right). Holographic aperture masking uses a phase plate to combine otherwise redundant subapertures at separate locations in the pupil plane. A non-redundant mask is shown on top left with the resulting PSF on the bottom left. Top right is a schematic of the HAM combinations, where each subaperture with the same color is combined at the PSF encircled in that color. Subapertures are multiplexed to make multiple PSF copies. Combinations can be one dimensional at the same location (red) or in triangles at a different location for each baseline (blue). In green are the two subapertures that have non-interferometric PSFs used for amplitude monitoring. Two copies of each PSF are created with opposite circular polarization state. \label{fig:HAMSAM}} \end{figure} | \label{sect:conclusion} \itemize{ \item Liquid-crystal technology enables the use of holographic techniques for masking interferometry. \item A standalone holographic aperture mask (HAM) with one dimensional subaperture combinations can operate up to more than $30\%$ bandwidth, however the number of closure phases is limited. \item We spectrally resolve fringes with HAM using these one dimensional subaperture combinations with large bandwidths. \item Multiplexing subapertures not used by sparse aperture masking (SAM) increases the number of baselines, closure phases and throughput at the cost of detector space. \item Leakage from deviations of half-wave retardance interfere with the SAM point-spread function but can be controlled using a double grating technique. \item Holographic aperture masking works in the lab and will be on sky soon. \item Liquid-crystal technology also can be used for broadband achromatic nullers. } | 18 | 8 | 1808.00751 |
1808 | 1808.10225_arXiv.txt | Quantum reduced loop gravity is designed to consistently study symmetry reduced systems within the loop quantum gravity framework. In particular, it bridges the gap between the effective cosmological models of loop quantum cosmology and the full theory, addressing the dynamics before the minisuperspace reduction. This mostly preserves the graph structure and SU(2) quantum numbers. In this article, we study the phenomenological consequences of the isotropic sector of the theory, the so-called emergent bouncing universe model. In particular, the parameter space is scanned and we show that the number of inflationary e-folds is almost always higher than the observational lower bound. We also compute the primordial tensor power spectrum and study its sensitivity upon the fundamental parameters used in the model. | The Higgs boson discovery \cite{Aad:2012tfa} and the direct observation of gravitational waves \cite{Abbott:2016blz} have strengthened the reliability of well corroborated theories: the standard model of particle physics (based on quantum field theory) on the one hand, and general relativity (GR) on the other hand. Beside these recent observations, the long-standing issue of quantizing gravity still calls for a solution. All physical theories must make contact with experiments or observations and this often constitutes one of the main difficulties for quantum gravity. Loop quantum gravity \cite{Ashtekar:2004eh,Rovelli:2004tv,Thiemann:2007zz} (LQG) is a consistent attempt in this direction, as witnessed by the recent effort on dealing with the black hole quantum dynamics (both within the canonical \cite{Alesci:2018loi, Ashtekar:2018cay} and covariant formulations \cite{Christodoulou:2016vny}), together with the prediction of the big bang singularity resolution \cite{Bojowald:2001xe, Ashtekar:2006uz,Ashtekar:2006wn} and the power spectrum calculation \cite{Agullo:2013ai,Ashtekar:2015dja,Agullo:2017eyh} made possible by loop quantum cosmology (LQC).\\ This article is about the observable consequences of LQG in cosmology, when the full theory structure is taken into account. This can be done using a suitable gauge fixed version of the theory called quantum reduced loop gravity (QRLG) \cite{Alesci:2012md, Alesci:2013xd, Alesci:2014uha, Alesci:2014rra, Alesci:2015nja, Alesci:2016gub}. Differences between LQC and QRLG are both in the philosophy and the methodology. The former is a LQG-inspired, polymerlike \cite{Agullo:2016tjh,Corichi:2007tf} quantization of a classically symmetry reduced system, while the latter is a subsector of LQG adapted to the symmetry of the system one is interested in. In the two approaches, quantization and symmetry reduction are in reverse order: LQC quantizes a classical reduced system, QRLG selects a symmetric subsector from the full quantum theory. If LQC can be seen as the simplest and most straightforward application of LQG ideas, starting from the beginning with less degrees of freedom to quantize, from the QRLG perspective it can be trusted as a first order quantum correction to the classical dynamics, since relevant structures of LQG are lost and have to be ``injected" in the process. On the contrary, QRLG retains all the features of the full theory and, moreover, does indeed recover LQC at first order \cite{Alesci:2016rmn,Alesci:2017kzc}.\\ In this article we extend the study of QRLG addressing inflation and discussing features of the power spectrum for cosmological perturbations. In isotropic QRLG, the Friedman Lemaitre Robertson Walker (FLRW) background is replaced by an emergent bouncing universe \cite{Alesci:2016xqa}. Here we focus on observable signatures of this scenario and compare them to the ones provided by LQC. As shown in \cite{Alesci:2016rmn,Alesci:2017kzc}, the corrections are subleading only up to the (first) bounce -- when going backward in time -- and, for earlier times, they grow and lead to a complete different dynamics. Thus, the observational consequences of the QRLG scenario have to be studied as they may differ from LQC ones. Before introducing our model, we briefly review LQG in order to make possible the understanding of our results also to the reader unfamiliar with the full theory.\\ LQG is a background free, nonperturbative Hamiltonian quantization of gravity whose starting point is the 3+1 foliation of the GR first order tetradic formulation. It is a modern canonical quantization that takes advantage of a new set of phase space variables -- the Ashtekar variables \cite{PhysRevLett.57.2244} -- in order to cast the classical theory in a form close to the one of a local SU(2) gauge theory. The Ashtekar variables $A_{a}^i(x;t)\,,E^a_i(x;t)$ are an $su(2)$ connection and a (densitized) triad field, which are canonically conjugate, $\{A_{a}^i(x),E^b_j(y)\}=8\pi G\gamma\,\delta^b_a\delta^i_j\delta^3(x-y)$, and read $A_{a}^i:=\omega^i_a +\gamma K_a^i\,,E^a_i:=\frac{1}{2}\epsilon_{ijk}\epsilon^{abc}e_b^je_c^k\,,$ where $i,j,k$ are $su(2)$ algebra indices, $a,b,c$ space ones, $\omega^i_a$ is the spin-connection compatible with the triad $e^b_j$, $K_a^i$ is the (mixed triadic projection of the) extrinsic curvature tensor and $\gamma$ is a parameter that enters this formulation of GR. This so-called Barbero-Immirzi parameter $\gamma$ is expected to have a value close to $0.24$ if one considers the black hole entropy calculation \cite{Meissner:2004ju}. It enters in the spectrum of the geometrical operators like area and volume, but does not change the classical equations of motion, {\it i.e.} Einstein's equations. Like all gauge theories, GR is a constrained system, more specifically, a \textit{totally} constrained one, as its Hamiltonian vanishes on physical trajectories. Written in Ashtekar variables, it turns out to be encoded in three constraints generating SU(2) gauge transformations (the Gauss constraint), spatial diffeomorphisms (the Diffeomorphism constraint) and time reparametrization (the Hamiltonian constraint). \\ Quantization starts using a ``technology" borrowed from lattice gauge theories in order to provide a (background-independent) smearing of the canonical algebra generated by $A_{a}^i(x;t)\,$ and $E^a_i(x;t)$, leading to the holonomy-flux algebra. The Ashtekar connection $A_a^i(x)$ is replaced by its holonomy $h_{l}[A]$ along arbitrary paths $l$- and the densitized triad $E^a_i(x)$ is replaced by its flux $E_i(S)$ across a surface $S$. Quantization follows implementing the (unique \cite{Lewandowski:2005jk}) quantum representation of the holonomy-flux algebra and computing the kernel of all the quantum operator-promoted constraints of the theory, according to Dirac's procedure \cite{DIRAC} for constrained systems. Solving the Gauss and Diffeomorphism constraints leads to the definition of a Hilbert space with states $|\Gamma,j,i\rangle$. Those states are labeled by graphs $\Gamma$ given by links associated to the holonomies (dual to the surfaces used for defining fluxes) and nodes. Links are colored by spins $j$, {\it i.e.} by representations of $SU(2)$, and nodes by intertwiners $i$, {\it i.e.} $SU(2)$ invariant tensors. Geometric quantities can be turned in Hermitian operators and it turns out that they have a discrete spectrum \cite{Rovelli:1994ge}. The area operator has a spectrum with a minimal nonvanishing eigenvalue $\Delta= 4\sqrt{3}\pi G\,\gamma\, l_P^2$ proportional to the Barbero-Immirzi parameter $\gamma$ and the square of the Planck length $l_P:=\sqrt{\hbar G/c^3}$. The picture provided by LQG is clear and beautiful: quantum gravity appears as a quantum theory of geometry, in which the spacetime continuum disappears leaving place to a relational net of fuzzy quanta of space.\\ Beside these achievements, problems arise when addressing the Hamiltonian constraint. Only trivial and formal solutions \cite{Alesci:2011ia} are indeed known and a complete characterization of the full spectrum is still missing. A retrospective look at this difficulty is not so discouraging: after all, the general solution to the analogue classical problem, {\it i.e.} Einstein's equations, is still unknown too, but this has not prevented GR to become a powerful tool for gravity. During the past years several paths to overcome the issue of quantum dynamics have been followed, both implementing different reformulations, {\it e.g.} using spinfoam models \cite{Perez:2012wv}, and/or addressing the dynamics of \textit{ symmetric } sectors of the full theory. The pioneering spin-off of LQG that follows this last direction is the "minisuperspace" quantization of spacetimes pursued by LQC.\\ Calculating the Ashtekar variables for a chosen spacetime, LQC follows a polymerlike quantization that \textit{mimics} the one pursued by LQG and provides the quantum dynamics for symmetry reduced models at the classical level, such as FLRW and Bianchi spacetimes \cite{Ashtekar:2011ni}. The resolution of the cosmological singularity comes out naturally, replacing the Big bang scenario by a nonsingular bouncing universe. Looking forward in time, there is a contracting phase which ends when the density and the curvature reach near-Planckian values, then a bounce happens and an expanding phase follows (the late-time behavior is exactly as in GR). The singularity is resolved because even though zero is in the spectrum of the volume operator, it is never dynamically reached. Despite this remarkable result, one should look at traditional LQC as a first attempt in applying LQG ideas to the simplest class of gravitational symmetry-reduced systems. The limits of this approach are mainly due to the fact that the quantization is performed only after a classical symmetry reduction and this does not prevent ambiguities in the corresponding quantum theory (see {\it e.g.} \cite{Gupt:2011jh}). Working only with few degrees of freedom, LQC needs to import from the full theory both a graph structure and a minimum value for physical areas in order to regularize the symmetry-reduced Hamiltonian operator.\\ QRLG is a program that attempts to implement a dynamical reduction of the full theory to a given symmetry-reduced setting, {\it i.e.} first quantizes and then reduces. This is achieved in several steps: one begins by implementing a gauge fixing at the quantum level (defining a gauge-fixed kinematical Hilbert space, called the reduced Hilbert space $\mathcal{H}^R$) and then one uses coherent states peaked on symmetric spaces over which one evaluates the operator version of a new set of constraints that preserve the gauge (built according to the gauge unfixing procedure \cite{Mitra:1989fg, MITRA1990137, Neto:2009rm}).\\ In the cosmological setting of the FLRW geometry (and Bianchi models), this reduced space is selected by (partially) gauge fixing the SU(2) and the Diffeomorphism gauge of the full theory to diagonal metrics and triads. Only a small class of spatial diffeomorphisms are still compatible with this choice (called \textit{reduced diffeomorphisms}), leading to the result that at the quantum level only cuboidal graphs (colored with $U(1)$ representation numbers) are allowed, {\it i.e.} the ones with links parallel to the fiducial triad field. Computing expectation values of the (gauge preserving part of the) LQG Hamiltonian constraint, QRLG effective Hamiltonians for the FLRW and Bianchi I cases can be explicitly obtained \cite{Alesci:2017kzc}. They depend on the choice of coherent states used to define the symmetry-reduced sectors.\\ Importantly, the much discussed $\mu_0$ or $\bar{\mu}$ LQC regularization schemes appear in QRLG as particular choices of coherent states. QRLG allows to reproduce LQC schemes and to generalize them \cite{Alesci:2016xqa,Alesci:2017kzc} with the so-called {\itshape statistical} regularization. This is based on ensembles of coherent states peaked on homogeneous phase space points defining macrostates. Every homogenous coherent state at a fixed graph represents a given cosmological \textit{macrostate} and statistical superposition of graphs can be considered. To the same macrostate (labeled by $(a,\dot{a})\,,$ for FLRW) corresponds several coherent \textit{microstates} labeled by different quantum numbers and graphs. For each given probability distribution counting the occurence of microstates associated to a fixed macrostate, an effective Hamiltonian can be computed taking the expectation value of the Hamiltonian operator over the chosen ensemble, as done in the aforementioned references where Gaussian ensembles were chosen.\\ All the computed QRLG effective Hamiltonians bring corrections to the LQC ones \textit{that are subleading only much after the Big Bounce}. For the FLRW case, at earlier times, the Universe oscillates and eventually reaches a stationary phase of constant finite volume (the meaning of the ``volume of the Universe" will be discussed later on). Looking forward in time, a Planckian universe \textit{emerges} from the infinite past. It is stationary until a transient phase is reached and, after few bounces, the dynamics matches the LQC's one from the (last) Big bounce all the way to the far future. This emergent behavior is a peculiar property of the isotropic sector and exploring its observational consequences constitutes the main goal we address in the rest of the paper. As far as perturbations are concerned, we use here the usual formalism and we apply only QRLG correction to the background. This is a heavy hypothesis. In the next section, the effective quantum background is described. Then, the corresponding basic features are investigated. At the background level, the duration of inflation is calculated for most of the parameter space. Regarding perturbations, the tensor power spectra are computed and scalar ones discussed. Finally, the effects of the inflaton field mass are considered | Quantum reduced loop gravity is an important step in trying to bridge that gap between full quantum gravity and effective quantum cosmology. As the kinematics is defined before the minisuperspace reduction, some important features of LQG, such as the graph structure and SU(2) quantum numbers, are preserved although simplified to make relevant calculations analytically tractable. The key point is to impose the gauge-fixing conditions to the diagonal spatial metric. The minisuperspace reduction is then implemented at the dynamical level, keeping terms preserving the diagonality conditions.\\ The main result of QRLG is the replacement of the usual LQC bounce by an ``emergent + bounce'' scenario. In this article we have studied the inflationary dynamics in this framework. The main result when scanning the full parameter space is that the number of inflationary e-folds is always greater that the experimental lower bound around 60-70. This not fully true in LQC where the number of e-folds can be tuned to an arbitrary small number by choosing appropriate initial conditions. \\ We have also calculated the tensor power spectrum and shown its dependence upon the parameters of the model. The IR part is blue, the intermediate part is oscillatory and and the UV part is nearly scale invariant. Following the study on the number of e-folds, the observational window falls on the UV part and a flat tensor power spectrum is therefore predicted.\\ Several improvements are possible for future studies: \begin{itemize} \item The scalar power spectrum should be better investigated. This requires a deeper understanding of the background behavior in the remote past of the static phase. \item It might be possible to assign a known probability distribution function to a parameter driving the dynamics (like in \cite{bl,Martineau:2017sti}), but this requires a ``harmonic oscillator-like'' behavior in the deep past and this is not established at this stage. \item Cosmological perturbations should also be QRLG-corrected. \item The anisotropic version of QRLG should be investigated as the shear is expected to be possibly important at the bounce. \end{itemize} Refining quantum cosmological models is a major challenge. Although quite a lot of subtleties do appear when going from LQC or QRLG or group field theory (GFT) \cite{Gielen:2017eco,Gerhardt:2018byq}, it is interesting that the main global features seem to be preserved, making the overall picture more and more reliable. | 18 | 8 | 1808.10225 |
1808 | 1808.05210_arXiv.txt | { We consider the polarization characteristics of the electromagnetic (EM) counterpart of the gravitational wave (GW) created by coalescence of the binary sources. Here, we explore the impact of the photon-graviton interaction on the polarization evolution of X-ray emission of Gamma-Ray Bursts (GRBs). We show that significant circular polarization can be generated due to the gravitational wave from the binary merger. The circular polarization besides photon energy depends on parameters of GW source such as the chirp mass of the binary, frequency of the GWs and radial distance from the source. Our predicted signal can be used as an indirect probe for GW events and also the nature of photon-graviton interaction. We argue that this polarization signal might be in sensitivity range of upcoming X-ray polarimetry missions.} \begin{document} | Detection of the gravitational-wave signal GW170817 by LIGO-Virgo collaboration associated with a short-duration gamma-ray burst (SGRB) observed by the Fermi-satellite, GRB 170817A, has marked the advent of multi-messenger cosmology \cite{GBM:2017lvd, Abbott:2017xzu,Lazzati:2017zsj}. The wealth of science that joint detections bring is not available from either messenger alone. Thus, joint detections can break the degeneracies of the binary parameters and allow to localize the source of the GW event. SGRBs are the most promising EM counterparts associated with double neutron star (NS-NS) or neutron-star-black-hole (NS-BH) mergers which are detectable in the sensitivity ranges of both current GW and EM detectors \cite{Metzger:2011bv,Eichler}. In their energy spectrum a high energy prompt emission is followed by X-rays to radio afterglow emissions. These EM counterparts last for seconds to days after the GW event \cite{Metzger:2011bv}. A key question is the origin of the EM counterparts following the merger. Unambiguous association of GRB signal to GW signal is investigated in Ref \cite{Monitor:2017mdv}. Other counterparts like neutrino emissions associated to the GW event can shed more light on the nature of the merger \cite{ANTARES:2017bia}. The aim of this article is to introduce a new indicator of the GW events by the polarization features of its EM counterpart. We show that the circular polarization of EM emission can serve as a peculiar signature of photon-graviton interaction originating from the binary merger. In this work, we focus on the polarization properties of the very early time X-ray photons. Generally, synchrotron radiation as an intrinsic mechanism is applied to explain GRBs polarization, where the level of polarization depends on the magnetic field configuration and the geometry of the emission region \cite{Westfold,Mao:2017dlb,Mao:2018rsr}. The high degree of linear polarization is expected in the presence of an ordered magnetic field and there are several measurements of linear polarization related to GRB prompt and afterglow emissions \cite{Covino:2016cuw,McConnell:2016lwd}. However, the only circular polarization measurement belongs to the optical afterglow of GRB 121024A at the level of 0.6 percent \cite{Wiersema:2014bha}. It has been shown that the origin of the observed circular polarization can not be intrinsic to an optically thin synchrotron process \cite{Nava:2015sba,Matsumiya:2003pw}. There are few mechanisms to generate circular polarization in the usual scattering processes in the astrophysical medium. The circular polarization of GRBs can be generated due to the propagation effects through the conversion of linear polarization of radiation known as Faraday conversion. The generation of the circular polarization for GRBs has recently been investigated in Ref. \cite{Batebi:2016efn}, taking into account different types of interactions through the scattering from cosmic particles or being in a background field. These interactions do not produce huge amounts of circular polarization component. Additionally, it has been shown that nonlinear QED effects in the strong-field regime lead to circular polarization in NS \cite{Shakeri:2017knk}. In the case of CMB photons the circular polarization is estimated in Ref. \cite{Montero-Camacho:2018vgs} and reconsidered by a new approach in \cite{Kamionkowski:2018syl}. The impact of primordial anisotropic background of GWs on the CMB polarization is considered and an unmeasurably low signal is reported in Ref. \cite{Bartolo:2018igk}. We argue that the considerable values of the circular polarization can be generated by GWs from the binary mergers. On the other hand, we show that the predicted signal might be observable from polarization analysis of the EM counterpart. More surprisingly, the circular polarization depends on the essential parameters of GW sources such as the chirp mass of the binary, frequency of the GWs, radial distance from the source and moreover the photon energy. Recently, it is shown that the circularly polarized EM radiation can be generated due to the photon-graviton mixing \cite{Ejlli:2018hke} in which GWs and EM waves mixing in the presence of external EM fields has been considered. This mixing changes the intensity of both gravitons and photons. However, we consider photon-graviton forward scattering where the total intensity of photons does not change during interaction with gravitons This paper is organized as follows. In section II, we present the formalism of photon-graviton scattering where we specialize it to a GW event. In Section III, we briefly present the expressions for GWs from binaries. In section IV, the emission of EM radiation for SGRBs is discussed. We also drive how circular polarization is generated from the binary mergers and provide an order of estimate for the circular polarization. Finally, we conclude in section V. | In this paper, we have investigated the circular polarization induced on EM radiation accompanying gravitational waves from binaries. We use the quantum Boltzmann equation for the evolution of the polarization, taking into account photon-graviton interaction. We proposed a scenario for the interaction of GRB photons with gravitational waves due to the binaries. Using the relevant parameters of recent observations for the GRB-GW event, we solved the set of equation describing the evolution of Stokes parameters. Here, we considered X-ray photons of SGRBs. The photon polarization has a characteristic dependence on binary parameter as the GW source. We conclude that the substantial amount of circular polarization can be generated due to the GW-EM interaction in binaries. Hence, the circular polarization associated to a GW merger might be observed in the prospective X-ray polarimetry experiments. Although our scenario is based on some simple assumptions, it captures novel aspects of the polarization signals due to photon-graviton interaction in the EM counterpart of GWs. Precise measurement of GRB polarization is one of the main goals for future GRB observations which can yield valuable information about the radiation mechanisms and the photon interactions, especially photon-graviton interaction. Several polarimeters are expected to be launched within several years \cite{Bellazzini:2010rw,Costa:2001mc,Bellazzin2,Soffitta2,Soffitta3}, such as the X-ray Imaging Polarimetry Explorer (XIPE), the Imaging X-ray Polarimetry Explorer (IXPE) and the Polarimeter for Relativistic Astrophysical X-ray Sources (PRAXyS). These instruments might be able to detect the polarization signals from photon-graviton interaction accompanying binary mergers and can shed light on the nature of this interaction. | 18 | 8 | 1808.05210 |
1808 | 1808.07812_arXiv.txt | We have obtained polarimetric measurements of asteroid (101955) Bennu, a presumably primitive near-Earth object (NEO) that is the target of NASA's sample return mission OSIRIS-REx. During our observing campaign, Bennu was visible from Earth under a wide range of illumination conditions, with phase-angle in the range 16\degr\ to 57\degr. Together with (3200) Phaethon and (152679) 1998 KU2, observed very recently, Bennu is the only existing example of a primitive NEO observed in polarimetric mode over a wide interval of phase angles. Based on our polarimetric data, we propose that Bennu belongs to the unusual F taxonomic class defined in the 80s. According to previous works, the F-class includes objects with cometary features. This fact can be of great importance for the interpretation of the results of the exploration of this object by OSIRIS-REx. From polarimetry we also derive an estimate of the geometric albedo of Bennu: $p_R=0.059 \pm 0.003$. | Asteroid (101955) Bennu is the asteroid target of the OSIRIS-REx space mission \citep{OSIRIS-REx}. From ground-based observations we know that this object is 550 meters in size and has a rather spheroidal shape \citep[][and references therein]{Laurettaetal15}. By applying to radar and thermal IR observations a sophisticated thermophysical model, \citet{Yu&Ji15} found for Bennu a geometric albedo of $0.047^{+0.008}_{-0.001}$, and a thermal inertia suggesting a surface covered by a fine-grained regolith. Its spectral reflectance properties make Bennu a member of the B taxonomic class, according to the SMASS-based classification by \citet{BusBin02}. Bennu was chosen as the target of OSIRIS-REx because it satisfied some basic requirements: it is representative of the population of primitive, low-albedo asteroids orbiting in the inner Solar System, which are thought to be the parent bodies of the most ancient classes of primitive meteorites, including Carbonaceous Chondrites. Moreover, it has a very suitable orbit for a sample-return mission. The modern B taxonomic class as defined by \citet{BusBin02} (SMASS taxonomy) includes asteroids that in the 80s were classified into two separate classes, named B and F. These classes were distinguished on the basis of subtle differences in the spectral reflectance behaviour at $\lambda \le 0.4\,\mu$m. In particular, the F class, first proposed by \citet{GraTed82}, exhibits a flat spectrophotometric trend over the whole interval of covered wavelengths, including the blue region, whereas other classes of objects exhibiting an overall flat spectral trend show a clear decrease of flux shortward of 0.4\,$\mu$m \citep[see Fig.~9 of][]{Tholen84}. Because the bluest spectral region is rarely observed in modern CCD-based spectroscopic surveys, asteroids originally classified as F belong now to the modern B class defined by \citet{BusBin02}, characterized by a generally flat or slightly blueish reflectance spectrum over an interval of wavelengths between 0.5 and 1\,$\mu$m. For example, asteroid (2) Pallas is the largest member of the B class in both the SMASS and in the Tholen's taxonomy, whereas the largest F-class asteroid, (704) Interamnia, is B-type in the current SMASS taxonomy. Apart from their spectrophotometric properties, asteroids can be distinguished also by measuring the varying state of polarisation of the sunlight scattered by their surfaces in different illumination conditions \citep[see, e.g.][]{Kolobook}. The main source of information are the so-called phase-polarisation curves, i.e, the polarisation value as a function of the phase-angle (which is the angle between the Sun, the target, and the observer). Asteroids with similar spectroscopic characteristics often share similar polarimetric properties \citep{Penetal05,Beletal17}. There are, moreover, cases in which the polarimetric behaviour sharply characterizes some objects that would be ambiguously characterized based on reflectance spectra. The two most important cases are those of the so-called Barbarians \citep{Celetal06}, which are beyond the scope of the present paper, and of the asteroids previously classified as members of the old F taxonomic class \citep{Beletal05}. In both cases, we find unusual values of the so-called inversion angle of polarisation. It is known that at small-phase angles, atmosphere-less objects of our solar system exhibit the phenomenon of so-called ``negative'' polarisation, which means that the scattered sunlight is linearly polarised in the direction parallel to the scattering plane. For the vast majority of asteroids the polarisation changes its sign (i.e., becomes perpendicular to the scattering plane) at phase-angles $\ga 20\degr$ (the "inversion angle" \ainv). However, in the case of the F-class asteroids, the inversion angle occurs at the distinctly lower phase-angle of $\sim 16\degr$ \citep{Beletal17}. Furthermore, the slope of the polarimetric curve around the inversion angle tends to be substantially steeper for F-class asteroids with respect to other taxonomic classes. It is not yet fully understood what physical properties are responsible for such behaviour, but it is believed that it is due to an interplay of composition, refractive index and sizes of surface regolith particles \citep{Beletal05}. Although no longer retained in modern classification systems, the old distinction between F-class and B-class asteroids is therefore meaningful, and is very interesting also in other respects. \citet{Celetal01} noted that the Polana family, located in a region of the asteroid main belt which may be an important source of NEOs, includes several F-class members \citep{Botetal15,deLetal18}. Perhaps more interestingly, the peculiar polarimetric properties of the F-class asteroids, in particular a low value of the polarimetric inversion angle, seem to be shared also by cometari nuclei, in a few cases of polarimetric measurements of cometary nuclei observed in conditions of absence of the coma \citep{Stinson17}. In the past, the object (4015) Wilson-Harrington, originally discovered and classified as an F-class asteroid in 1992, was later found to exhibit cometary activity \citep[see][and references therein]{Fernandezetal97}. 133P/Elst-Pizarro, an object described as either an active asteroid or a cometary object in the main asteroid belt, which exhibits recurrent cometary activity, was also found by \citet{Bagetal10} to exhibit a low value of the inversion angle of polarisation. There is therefore some evidence that at least a subset of the old F-class asteroids may include active, or sporadic, or nearly extinct (as in the case of Wilson-Harrington) comets \citep[see also][]{BelAstIV, Kolobook}. Knowing that it was classified as B-class, we have decided to carry out a polarimetric investigation of (101955) Bennu, and perform a comparison with the polarimetric properties of F-type objects. | 18 | 8 | 1808.07812 |
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1808 | 1808.09514_arXiv.txt | Stellar activity is one of the main obstacles to high-precision exoplanet observations and has motivated extensive studies in detection and characterization problems. Most efforts focused on unocculted starspots in optical transit spectrophotometry, while the impact of starspot crossings is assumed to be negligible in the near-infrared. Here, we present \textit{HST}/WFC3 transit observations of the active star WASP-52, hosting an inflated hot Jupiter, which present a possible starspot occultation signal. By using this data set as a benchmark, we investigated whether the masking of the transit profile distortion or modeling it with both a starspot model and a Gaussian process affects the shape of the transmission spectrum. Different methods produced spectra with the same shape and a robust detection of water vapor, and with $\lesssim 1 \sigma$ different reference radii for the planet. The solutions of all methods are in agreement and reached a similar level of precision. Our WFC3 light curve of WASP-52b hints that starspot crossings might become more problematic with \textit{JWST}'s higher sensitivity and complete coverage of the transit profile. | Transiting extrasolar planets offer the unique opportunity to study stellar activity via the detection of starspots on the surface of their hosts \citep{silva2003}. Since the \textit{Hubble Space Telescope} (\textit{HST}) observations of starspots on HD209458 \citep{brown2001,deeg2001}, the \textit{CoRoT} \citep{auvergne2009} and \textit{Kepler} \citep{borucki2010} space telescopes opened new possibilities in the study both of stellar activity and of star-planet interactions \citep[e.g.][and references therein]{affer2012,mcquillan2014,lanza2014}. These observations presented a variety of cases in which the stellar signal also hampers the interpretation of the exoplanet signal. The transit observations of the extensively studied HD189733 \citep{pont2007}, CoRoT-2 \citep{alonso2008}, CoRoT-7 \citep{leger2009} and Kepler-17 \citep{desert2011} showed how unocculted and occulted activity features deform the shape of a transit by modulating the the host star's brightness. Unocculted starspots (i.e., those lying out of the transit chord) can affect the transit baseline and possibly induce an overestimate of the planet radius \citep[e.g.][]{czesla2009}. Occulted spots can affect the transit shape, which can possibly cause an underestimate or an overestimate of the transit depth, depending on the presence of dark or bright spots, respectively \citep[e.g.][]{silva-valio2010,desert2011,bruno2016}. The measurement of other parameters can also be biased, such as the orbital inclination, stellar density and limb darkening coefficients \citep[e.g.][]{leger2009,csizmadia2013}. Published strategies for the correction of the starspot signal in broadband transit photometry span from modeling the stellar surface in a grid \citep[e.g.][]{huber2010}, to maximum entropy regularization \citep[e.g.][and references therein]{lanza2009}, combined planet-starspot modeling \cite[e.g][]{tregloan-reed2015,bruno2016} and Gaussian processes on unocculted starspots \citep[e.g.][]{haywood2014,aigrain2016}. The study of the effect of starspots on the measure of planetary masses through radial velocity is another active area of investigation \citep[e.g.][]{saar1997,hatzes1999,queloz2001,melo2007,desort2007,boisse2011,boisse2012,robertson2014,dumusque2017,feng2017}. In transmission spectroscopy, the transit depth of a planet with an atmosphere can be observed to vary with wavelength. This is due to the variation of the atmospheric opacity with wavelength, which in turn affects the radius at which the atmosphere becomes optically thick \citep{seager2000,brown2001,hubbard2001}. During primary transit, unocculted spots are known to mimic the Rayleigh scattering feature at visible wavelengths \citep[][]{pont2013,mccullough2014,oshagh2014,rackham2017}. As a result, consecutive observations of the same targets often yield different results \citep[e.g.][and references therein]{mackebrandt2017}. Here too, various techniques have been adopted to correct for stellar activity, including the modeling of starspot brightness with stellar models \citep[e.g.][]{mccullough2012,sing2016}, transit-spot modeling \citep[e.g][]{mancini2014} and Gaussian processes \citep[e.g.][and references therein]{gibson2013gemini,louden2017,sedhaghati2017}. Recent studies attempted to forecast the biases and uncertainties that unocculted starspots will produce on the \textit{James Webb Space Telescope} (\textit{JWST}) spectra \citep{barstow2015,barstow2015err,zellem2017,serrano2017,deming2017}. As they are less prominent at longer wavelengths, occulted starspots are generally considered less problematic in the near-infrared than in the visible. Furthermore, only very cool ($\lesssim 3000$ K) starspots in solar-type stars could contaminate the water absorption feature of a planetary spectrum \citep{pont2013,fraine2014}. It is usually assumed that the portions of a transit profile affected by starspot crossings can be safely removed from the analysis, especially with \textit{HST} data. As this observatory is periodically occulted by the Earth, it only gives a partial phase coverage of transit profiles. Hence, parameters such as limb darkening coefficients and orbital inclination (which in turn affect the measured transit depth) are poorly constrained by observations and are often fixed in the transit profile fitting. \textit{JWST} observations, which will not be limited in phase coverage, will be sensitive to the effect of stellar activity on transit parameters other than the transit depth. As the cases of e.g. CoRoT-2 \citep{silva-valio2010} and Kepler-117 \citep{desert2011} showed, a large fraction of the transit profile can be affected by starspot occulations, and the variation of these features in time could cause erroneous detections of ``weather'' variability on the planets \citep{pont2013}. Additionally, cool, low-mass stars, which are the main focus of upcoming exoplanet searches such as the \textit{Transiting Exoplanet Survey Satellite} \citep[\textit{TESS},][]{ricker2014}, are mainly convective and often have a larger starspot coverage than solar type stars \citep{chugainov1966,chugainov1971,berdyugina2011,mandal2017}. If several occultations of small -- but still detectable -- starspots affect a single transit profile, masking them will not be a satisfactory strategy. Even if longer wavelengths are less affected by occulted starspots, very cold activity features will be cause of additional concern in the interpretation of planetary spectra. \textit{HST} observations of active planet host stars are a great opportunity to explore this problem, as in the case of the K star WASP-52. \cite{hebrard2013_w52} observed long-term modulations in photometry and CaII H\&K lines chromospheric emission peaks, suggesting the presence of starspots on the stellar surface. Moreover, gyrochronology and lithium abundance yielded contrasting estimates of the stellar age -- from less than one to several Gyr. Different age indicators might be indicative of planet-induced magnetic and tidal spinning up of the star, with consequences on its overall activity \citep[e.g.][]{shkonlnik2005,dawson2014_tidal,damiani2015}. Alternatively, or simultaneously, enhanced lithium depletion in the star might have happened because of planet-induced alterations of the stellar surface convective mixing \citep{israelian2009,sousa2010}. The inflated hot Jupiter WASP-52b orbits its star with a 1.7-day period. \cite{hebrard2013_w52} measured a stellar spin-planetary orbit misalignment of $24^{+17}_{-9}$ deg via the Rossiter-McLaughlin effect \citep{rossiter1924,mclaughlin1924}, while \cite{mancini2017}, assuming that their multiple transit observations were affected by the same starspot, calculated a negligible misalignment. The system parameters, summarized in Table \ref{parameters}, make WASP-52b particularly interesting for transmission spectroscopy, as it shows a 2.7\% transit depth in WASP photometry and an estimated scale height of 730 km. This translates in a predicted 440 ppm difference in transit depth corresponding to one atmospheric scale height, at least three times stronger than that of HD189733b \citep{kirk2016}. This motivated ground-based follow-ups by various teams, which led to the likely detection of crossing events of both starspot and bright regions in the visible \citep{kirk2016,mancini2017}. Primary transit spectroscopy of WASP-52b in the 0.4-0.9 $\mu$m spectral window resulted in a flat transmission spectrum (i.e., no Rayleigh scattering detection), likely due to a gray cloud which could balance the expected short wavelength slope \citep{louden2017}. The possible contribution of bright spots in the visible spectrum, which could compensate for the scattering slope, should also not be excluded \citep{rackham2017}. In addition, a narrow NaI absorption feature \citep{kirk2016,louden2017,chen2017}, KI absorption and indications of a thermal inversion in the high atmosphere \citep{chen2017} have been found. We collected \textit{HST}/Wide Field Camera 3 (WFC3) G141 observations of WASP-52 as part of a large program for the analysis of exoplanet atmospheres with \textit{HST} (GO 14260, PI Deming). In this work, we compared the main approaches currently used in the literature to deal with starspot occultations, which likely affect our spectroscopic observations. Our goal was to identify, if any, differences in the transmission spectrum which can be attributed to the choice of the starspot correction method. The data set is presented in Section \ref{observations} and the various models on the band-integrated transit in Section \ref{transitmodeling}. The derivation of the transmission spectrum is discussed in Section \ref{spectrotr}, and the implications of our analysis are presented in the concluding Section \ref{discussion}. \begin{table}[htb] \begin{center} \caption{WASP-52 system parameters, from \cite{hebrard2013_w52}.} \label{parameters} \begin{tabular}{ll} \hline \hline Spectral type & K2V \\ Stellar $V$ magnitude & 12.0 \\ Stellar $J$ magnitude$^{(\ast)}$ & 10.6 \\ Stellar $H$ magnitude$^{(\ast)}$ & 10.1 \\ Stellar $K$ magnitude$^{(\ast)}$ & 10.2 \\ Stellar effective temperature $T_\mathrm{eff, \star}$ [K] & $5000\pm100$ \\ Stellar $\log g$ [cgs] & $4.5 \pm 0.1$ \\ Stellar [Fe/H] [dex] & $0.03 \pm 0.12$\\ Stellar radius [$R_\odot$] & $0.79 \pm 0.02$\\ Stellar density [$\rho_\odot$] & $1.76 \pm 0.08$ \\ Stellar rotation period [days] & $11.8 \pm 3.3$\\ $\log R'_{HK}$ & $-4.4\pm0.2$ \\ Orbital period [days] & $1.7497798\pm0.0000012$ \\ Transit duration [days] & $0.0754\pm0.0005$ \\ Radius ratio $R_\mathrm{p}/R_\star$ & $0.1646\pm0.0012$ \\ Orbital inclination [$^{\circ}$] & $85.35\pm0.20$\\ Scaled semi-major axis $a/R_\star$ & $7.3801\pm0.0148$ \\ Orbital eccentricity & 0 (fixed) \\ Spin-orbit misalignment [$^\circ$] & $24^{+17}_{-9}$\\ Planet mass [$M_J$] & $0.46\pm0.02$ \\ Planet radius [$R_J$] & $1.27\pm0.03$ \\ Planet density [$\rho_J$] & $0.22\pm0.02$ \\ Planetary equilibrium temperature [K] & $1315\pm35$ \\ Planet surface gravity [$\mathrm{m \, s}^{-2}$] & $6.46\pm0.45$ \\ \hline \end{tabular} \end{center} \begin{tablenotes}\footnotesize \item $^{(\ast)}$ From the CMC15: Carlsberg Meridian Catalogue (\texttt{http://svo2.cab.inta-csic.es/vocats/cmc15/}, retrieved through \textit{VizieR} on the Strasbourg astronomical Data Center (\texttt{http://cds.u-strasbg.fr/}). \end{tablenotes} \end{table} | \label{discussion} Starspot crossings are not generally considered an issue in infrared transmission spectroscopy, because of the negligible contribution of their black-body emission compared to the stellar one. In this work, we presented the possible detection of a starspot occultation in near-infrared observations of WASP-52 and discussed different ways of correcting the spectroscopic transits before deriving the transmission spectrum. We found that the transit distortion is only likely to affect the reference radius of the planet, much like an unocculted starspot in the visible. With high-resolution, continuously observing instruments such as \textit{JWST}, masking starspot occultations might become a less convenient strategy than with \textit{HST}. The focus on cool, active stars identified by upcoming surveys such as \textit{TESS} will result in more starspot occultations, whose masking will hide relevant information on the transit parameters. While only starspot models allow the reconstruction of the occultation geometry, the computational cost of comparing multiple scenarios across long baselines could become prohibitive. In this context, the use of non-parametric models such as Gaussian processes (GPs) can be explored as a viable alternative. In search of an optimal strategy for correcting the spectrum from the possible starspot occultation, we compared the implications of masking the transit distortion and of modeling it both with a starspot model and with a GP. We showed that the transit distortion is wavelength-independent at the precision of our data. With a geometric model approach, we obtained a $\simeq 4050^{+370}_{-230} \, \mathrm{K}$ fit on the spot temperature, which makes the possibility of stellar water contamination in the transmission spectrum unlikely. As WASP-52A is an active star, the possibility that other, colder non-occulted starspots could be present on the stellar disk also cannot be excluded. As we found no dependence of the spot contrast among spectroscopic channels, however, the possibility that the transit distortion is not due to a starspot remains valid. Despite this, given the agreement of all reduction methods, the water absorption feature in the \textit{HST}/WFC3 G141 spectrum of WASP-52b is unlikely to be affected by the starspot-like distortion. The \cite{stevenson2016} indicators of the significance of the water feature on the three resulting spectra are all in agreement, supporting a robust water feature detection which is likely muted by aerosols in the atmosphere of the planet. While our analysis showed that different approaches can result in $\lesssim 1\sigma$ variations of the spectrum baseline, the uncertainty in the reference planet radius, and therefore in the spectrum baseline, can likely be taken into account in retrieving the atmospheric state by the use of a scaling factor \citep[e.g.][]{benneke2012, line2013}. We found similar uncertainties on the transit depth from the three analyses. Moreover, the GP model resulted in a transit midtime $\lesssim 2$ minutes earlier than the model in which the spot is masked (but still within the uncertainties of $\sim 3$ minutes). To our knowledge, this is the first time a non-stationary GP kernel is used for the specific purpose of modeling a possible starspot occultation in a transit profile. This promising result needs to be further investigated, and can find applications both in transmission spectroscopy and broadband photometry. In particular, stationary kernels could be the most convenient choice for modeling other forms of stellar noise which occur on shorter time scales than the transit, such as granulation, which happens over tens of minutes and can affect the apparent \kr~ \citep{chiavassa2017}. Higher-precision instruments such as those aboard \textit{JWST}, thanks also to their ability of completely covering the transit profile, will likely provide additional constraints in these kinds of scenario. As spot models over large data sets, GPs become computationally demanding when applied on $\gtrsim1000$ points, because of the need of iterating large matrix inversions. \cite{gibson2013gemini} proposed to use the maximum likelihood type II method in the MCMC exploration, i.e. to fix the hyperparameters to their least-squares best value, in order to reduce the computation time. With our small data set of a few tens of data points per transit, this was not an issue, while with \textit{JWST} observations it might affect the choice of the most convenient approach. WASP-52A is a $\sim 5000$ K star, but starspots in colder stars might contribute more significantly to the water feature in a transmission spectrum than what was found with this study. Predicting how activity features will affect \textit{JWST} observations -- and the computation cost of using GPs in place of starspot modeling -- requires an analysis of multiple transit shapes and of varying sizes and temperatures for the occulted starspots, which is beyond the scope of this paper. We plan to carry out a study of this nature with the use of synthetic data. We expect a stronger relative impact in \textit{JWST} than in \textit{HST} observations, as error bars on the transmission spectrum will be smaller than the few 100 ppm observed for this 10.1 mag$_H$ star. Many future studies will focus on WASP-52b. Combined \textit{HST}/STIS observations obtained from the Panchromatic Comparative Exoplanetology Treasury (PanCET) program (GO 14767, PIs Sing \& L\'{o}pez-Morales) and \textit{Spitzer}/IRAC observations will be presented in a forthcoming paper \citep{alam2018}. We will then use STIS, WFC3 and IRAC data to retrieve the composition and structure of this planet's atmosphere. Additional constraints will be placed by \textit{JWST}, which will observe WASP-52b in emission spectroscopy as part of the GTO program 1224 (PI Birkmann). | 18 | 8 | 1808.09514 |
1808 | 1808.05356_arXiv.txt | The Juno mission is delivering spectacular data of Jupiter's magnetic field, while the gravity measurements finally allow constraining the depth of the winds observed at cloud level. However, to which degree the zonal winds contribute to the planet's dynamo action remains an open question. Here we explore numerical dynamo simulations that include an Jupiter-like electrical conductivity profile and successfully model the planet's large scale field. We concentrate on analyzing the dynamo action in the Steeply Decaying Conductivity Region (\SDCR) where the high conductivity in the metallic Hydrogen region drops to the much lower values caused by ionization effects in the very outer envelope of the planet. Our simulations show that the dynamo action in the \SDCR\ is strongly ruled by diffusive effects and therefore quasi stationary. The locally induced magnetic field is dominated by the horizontal toroidal field, while the locally induced currents flow mainly in the latitudinal direction. The simple dynamics can be exploited to yield estimates of surprisingly high quality for both the induced field and the electric currents in the \SDCR. These could be potentially be exploited to predict the dynamo action of the zonal winds in Jupiter's \SDCR\ but also in other planets. | 18 | 8 | 1808.05356 |
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1808 | 1808.07486_arXiv.txt | The fine-structure constant, $\alpha$, controls the strength of the electromagnetic interaction. There are extensions of the standard model in which $\alpha$ is dynamical on cosmological length and time-scales. The physics of the cosmic microwave background (CMB) depends on the value of $\alpha$. The effects of spatial variation in $\alpha$ on the CMB are similar to those produced by weak lensing: smoothing of the power spectrum, and generation of non-Gaussian features. These would induce a bias to estimates of the weak-lensing potential power spectrum of the CMB. Using this effect, \textit{Planck} measurements of the temperature and polarization power spectrum, as well as estimates of CMB lensing, are used to place limits (95\% C.~L.) on the amplitude of a scale-invariant angular power spectrum of $\alpha$ fluctuations relative to the mean value ($C_L^{\alpha}=A^\alpha_{\rm SI}/[L(L+1)]$) of $A^\alpha_{\rm SI}\leq 1.6 \times 10^{-5}$. The limits depend on the assumed shape of the $\alpha$-fluctuation power spectrum. For example, for a white noise angular power spectrum ($C_L^{\alpha}=A^\alpha_{\rm WN}$), the limit is $A^\alpha_{\rm WN}\leq 2.3 \times 10^{-8}$. It is found that the response of the CMB to $\alpha$ fluctuations depends on a separate-universe approximation, such that theoretical predictions are only reliable for $\alpha$ multipoles with $L\lesssim 100$ . An optimal trispectrum estimator can be constructed and it is found that it is only marginally more sensitive than lensing techniques for \textit{Planck} but significantly more sensitive when considering the next generation of experiments. For a future CMB experiment with cosmic-variance limited polarization sensitivity (e.g., CMB-S4), the optimal estimator could detect $\alpha$ fluctuations with $A^\alpha_{\rm SI}>1.9 \times 10^{-6}$ and $A^\alpha_{\rm WN} > 1.4 \times 10^{-9}$. | Ever since Paul Dirac hypothesized the Law of Large Numbers \cite{1938RSPSA.165..199D}, physicists have explored the possibility that constants of nature are not in fact constant. Dirac proposed time variation of the gravitational constant $G$ to ensure that certain large numbers in cosmology would be the same order of magnitude throughout time \cite{1938RSPSA.165..199D,Brans:1961sx}, and Gamow then suggested that time variation of the electric charge $e$ could explain the same coincidences \cite{Gamow:1967zz,Gamow:1967zza}. The time dependence required to explain these coincidences has been ruled out by stellar evolution and a variety of anthropic arguments \cite{Teller:1948zz}, but others have since explored more subtle variations in these and other fundamental constants, which emerge as predictions of theories with large extra dimensions \cite{PhysRevD.21.2167,Kolb:1985sj,PhysRevD.60.116004}. There are several theories which naturally incorporate a dynamical fine-structure constant, $\alpha$. Bekenstein proposed a model for a varying $\alpha$ which suppresses violations of the Weak Equivalence Principle (WEP) to undetectable levels \cite{Bekenstein:1982eu}. The full theory, known as the Bekenstein-Sandvik-Barrow-Magueijo (BSBM) model, places Bekenstein's scalar field in a cosmological context, allowing it and $\alpha$ to evolve with the expansion of the universe. The BSBM model makes predictions for how $\alpha$ will vary in time and space \cite{Barrow:2002db,Barrow:2002zh}. Variations and extensions of the BSBM model exist that consider other effects such as density inhomogeneities \cite{Mota:2003tm}, as well as more complicated scalar field couplings and potentials \cite{Barrow:2013uza, Graham:2014hva}, including a quintessence field \cite{Copeland:2003cv}, among others. There has also been growing interest in models that `disformally' couple electromagnetism to a scalar field \cite{Bekenstein:1992pj,vandeBruck:2015rma}, as well as string-inspired `runaway dilaton' models with dynamical extra dimensions that are stabilized by matter couplings in a way that yields potentially observable time evolution and spatial fluctuations in $\alpha$ \cite{Damour:1994zq,Damour:2002nv,Damour:2002mi,Martins:2017yxk}, as well as models in which a light scalar dark matter component induces $\alpha$ fluctuations \cite{Sigurdson:2003pd,Stadnik:2015kia}. On the observational side, claims have been made that the absorption spectra of distant quasars support cosmological time variation and a dipole in $\alpha$ \cite{Webb:2010hc, King:2012id, Webb:1998cq, Murphy:2002jx, Murphy:2003hw}. More recent observations and analyses have failed to reproduce such a result consistently \cite{Songaila:2014fza, Martins:2017qxd}, calling into question the method (in particular, the spatial stability of the wavelength calibration) used to obtain the spatial dipole result \cite{Murphy:2017xaz}. Future efforts at the Very Large Telescope (VLT) \cite{Martins:2017yxk} could improve sensitivity to $\alpha$ variations by an additional two orders of magnitude. Other observational techniques have been used to attempt to constrain the magnitude of time variation in $\alpha$. For example, the rare-earth element abundance data from Oklo (a naturally occurring uranium fission reactor from approximately 2 billion years ago in Gabon), which is completely independent of cosmological models, places constraints on the possible temporal variations of $\alpha$ to $-6.7\times10^{-17}\text{yr}^{-1}<\dot{\alpha}/{\alpha}<5.0\times10^{-17}\text{yr}^{-1}$ at the 2$\sigma$ level \cite{Damour:1996zw}. As $\alpha$ affects the recombination history and diffusion damping of sound waves in the baryon-photon plasma, models with varying $\alpha$ can be probed using cosmic microwave background (CMB) anisotropies, now characterized at $\sim 0.1\%$ precision using data from the \textit{Planck} satellite \cite{Ade:2015xua,Aghanim:2018eyx} as well as a variety of ground-based experiments like the South Pole Telescope (SPT) \cite{Story:2012wx,Benson:2014qhw} and Atacama Cosmology Telescope (ACT) \cite{Louis:2016ahn}. These measurements require that the difference between the fine-structure constant today and at recombination obey the limit $\delta{\alpha}/\alpha\leq 7.3 \times 10^{-3}$ at 68\%~C.~L. \cite{Avelino:2001nr,Martins:2003pe,Rocha:2003gc,Ichikawa:2006nm,Menegoni:2009rg,2010PhRvD..82l3504G,2012PhRvD..85j7301M,Ade:2014zfo,deMartino:2016tbu,Hart:2017ndk}. Measurements of the CMB anisotropies by \textit{Planck} provide an additional motivation for considering a spatially varying $\alpha$. Gravitational lensing smooths the CMB power spectrum while also inducing a non-Gaussian contribution to the trispectrum. It has been noted that the level of smoothing in the power spectrum is larger than what is expected given the measured amplitude of the non-Gaussian part of the trispectrum \cite{Ade:2015xua,Aghanim:2018eyx}. Analogous to the effects of weak gravitational lensing, the spatial variation of $\alpha$ smooths the CMB power spectrum and contributes to the non-Gaussian part of the trispectrum. It is thus possible that the measured smoothing/trispectrum discrepancy points towards modulation of the primordial CMB anisotropies beyond weak gravitational lensing at the level of about three standard deviations. In fact this possibility was extensively explored in Ref.~\cite{Aghanim:2018eyx}. There, the \textit{Planck} collaboration considered the effects of compensated isocurvature perturbations (CIPs) to explain this anomaly. A spatially varying $\alpha$ produces effects very similar to CIPs and may provide an alternative explanation. At a similar level of significance, the \textit{Planck} measurements confirm a previously identified deviation from isotropy \cite{Ade:2015hxq}- a `hemispherical asymmetry' in the CMB power spectra. The presence of a large-scale spatially varying $\alpha$, possibly correlated with the primordial anisotropies, may explain such an apparent deviation from isotropy in the CMB. Spatial fluctuations in $\alpha$ modulate the recombination history and rate of diffusion damping of baryon-photon plasma perturbations, and thus induce higher-order (and non-Gaussian) correlations in the CMB. This was pointed out in Ref.~\cite{Sigurdson:2003pd} and applied to data in Ref.~\cite{OBryan:2013nip}, followed by Ref.~\cite{Ade:2014zfo}, in which the spatial dipole in $\alpha$ at recombination was directly limited to $C_{L=2}^\alpha \leq 1.3 \times 10^{-2}$ at 68\%~C.~L. For a scale invariant power spectrum this can be translated into a constraint to the amplitude of $A_{\rm SI}^\alpha = 2 C_{L=1}^{\alpha} < 2.6 \times 10^{-2}$. Here, we use 2015 \textit{Planck} satellite data (which includes small-scale polarization measurements) to test for spatial variation of the fine-structure constant on smaller scales ($\alpha$ multipoles $L\geq 8$). We find that the amplitude of a scale-invariant spectrum must have $A_{\rm SI}^\alpha < 8 \times 10^{-6}$ at 68\% C.~L. The dramatic improvement in the overall order-of-magnitude of the sensitivity results from the use of many more multipoles ($8\leq L\leq 100$) to search for $\alpha$ variations. All attempts at using the CMB to search for the spatial variation of the fine-structure constant rely on a `separate-universe' (SU) approximation (for the response of CMB fluctuations to $\alpha$ variations) \cite{Sigurdson:2003pd,OBryan:2013nip,Ade:2014zfo}. Here we show that this approximation breaks down if the length scale of $\alpha$ fluctuations is smaller than the sound horizon at the surface of last scattering (SLS), analogous to an effect that occurs for compensated isocurvature perturbations \cite{He:2015msa}. This, in turn, implies that a more complete treatment of these types of effects may lead to additional sensitivity. This paper is organized as follows. In Sec.~\ref{sec:alphaCMB}, we explore the effect of varying $\alpha$ on the visibility function, and briefly describe how these changes propagate to the CMB power spectrum and then lay out the details of the relevant calculation using the codes \textsc{HyRec} \cite{HyRec} and \textsc{Camb} \cite{camb}. We then determine how the additional non-Gaussian correlations induced by $\alpha$ fluctuations can be detected using an optimal estimator or existing CMB weak lensing data products. In Sec.~\ref{sec:su_limits}, we use a toy model to show that the SU approximation should break down for $\alpha$-modulation on angular scales smaller than the acoustic horizon at the SLS ($L\gtrsim 100$). In Sec.~\ref{sec:current}, we compare this theory to data to search for spatial variation in $\alpha$ and generate constraints. At the current level of experimental precision, these (lensing-data derived) constraints are essentially optimal. In Sec.~\ref{sec:optimal}, we forecast the sensitivity of future experiments to $\alpha$ fluctuations using an optimal estimator. In Sec.~\ref{sec:discussion}, we explore the possibility that $\alpha$ fluctuations could explain apparent anomalies between theory and the observed amplitude of weak gravitational lensing the CMB. There, we also estimate the implications of our work for specific varying-$\alpha$ models, with an eye towards those that could explain the claimed dipole in $\alpha$ seen in observations of quasar spectra. We conclude in Sec.~\ref{sec:conclude}, summarizing our constraints and discussing how sensitivity to $\alpha$ fluctuations could be improved with novel cosmological observables. We present some of the detailed expressions used in this paper in Appendix \ref{sec:details}. The second derivatives of CMB power spectra, needed to construct $\alpha$-induced corrections to the observed power spectra are described in Appendix \ref{sec:step_optimal}. | \label{sec:conclude} A variety of theoretical ideas motivate the consideration of a spatially-varying fine-structure constant. By modulating the recombination history and Thomson scattering rate of the early universe, such a scenario would alter CMB statistics. The mathematical formalism is similar to that used in studies of compensated isocurvature perturbations (CIPs) and weak gravitational lensing of the CMB, but with a specific response to the physics of $\alpha$ modulation. Using a toy model, we find that this response falls off for scales $L\geq 100$, just as for CIPs. Here, we used measurements of CMB trispectra (as captured by the optimal estimator of the weak-lensing power spectrum) and power spectra to test for the presence of a scale-invariant power spectrum of $\alpha$ fluctuations. This is an interesting possibility as any fluctuation in $\alpha$ sourced by a massless field present during inflation would naturally have a scale-invariant spectrum. Using just the $\alpha$ contribution to the lensing potential power spectrum for a scale invariant power spectrum ($C_L^{\alpha} = A_\alpha^{\rm SI}/[L(L+1)]$), we find the constraint (at 95\%~C.~L.) $A_\alpha^{\rm SI} < 1.6 \times 10^{-5}$, which implies a fractional variation in $\alpha$ on tens of degrees or larger of $(\sigma_\alpha/\alpha_0)_{\theta > 10^\circ} < 2.5 \times 10^{-3}$ [constraints to the variance, a derived parameter, are obtained using Eq.~(\ref{eq:normps}) but with the multipole range $2\leq L\leq 20$]. For a constant (white noise) power spectrum $C_{L}=A_\alpha^{\rm WN}$, we find that $A_\alpha^{\rm WN} < 2.3 \times 10^{-8}$ and $ (\sigma_\alpha/\alpha_0)_{\theta > 10^\circ} < 8.9 \times 10^{-4}$, all at $95\%$~C.~L. This is an improvement over the constraints found using the 2013 \textit{Planck} data \cite{OBryan:2013nip}. Furthermore, we find that at \textit{Planck} noise levels, the sensitivity of our estimator (based on lensing data products) is nearly optimal, as shown by the Fisher analysis for scale-invariant $\alpha$ fluctuations in Sec.~\ref{sec:optimal}; we performed the same analysis for white-noise power spectrum, and again found that our lensing-based constraint is comparable in sensitivity to a full trispectrum analysis for \textit{Planck} noise levels. Future experiments (e.g.~CMB-S4 \cite{Abazajian:2016yjj}) will achieve nearly cosmic-variance limited measurements of CMB polarization, thus pushing the sensitivity to scale-invariant $\alpha$ fluctuations as low as $A_\alpha^{\rm SI}= 1.9 \times 10^{-6}$ (or in the white-noise case, $A_\alpha^{\rm WN}=1.4 \times 10^{-9}$), or variances as low as $(\sigma_\alpha/\alpha_0)_{\theta > 10^\circ} = 8.6 \times 10^{-4}$ (or in the white-noise case, $(\sigma_\alpha/\alpha_0)_{\theta > 10^\circ} = 2.2 \times 10^{-4}$). We considered the possibility that $\alpha$ may alleviate the anomalously large smoothing of the CMB power spectra relative to the amplitude of the lensing potential power spectrum. In the end, scale-invariant $\alpha$ fluctuations cannot resolve this tension, due to trispectrum estimates of the lensing potential power spectrum. This conclusion depends on the shape of the modulating field's power spectrum and precise response of observables to the modulating field. In future work, it will be interesting to explore what type of long-wavelength modulation could explain anomalous smoothing of the CMB power spectra while satisfying trispectrum constraints. Above, we used our phenomenological limits to estimate constraints to actual dynamical theories of varying $\alpha$, appropriating a CMB analysis that treated $\alpha$ as spatially varying but constant in time. We thus remind the reader that the translation of our constraints to limits on specific models of varying $\alpha$ are just order-of-magnitude estimates. Robust tests require a proper evolution of the background $\alpha$ value, a proper relativistic treatment of perturbation evolution, and a computation of the imprint of these dynamics on observables using a Boltzmann code like \textsc{Camb} \cite{camb} or \textsc{Class} \cite{Lesgourgues:2011re}, with appropriate modifications for the model of interest. Additional improvements could also follow from analyzing CMB trispectra directly (rather than a lensing power-spectrum based estimator) and doing a map-level analysis for the time-evolved imprint of the claimed QSO dipole. We will pursue a more complete analysis along these lines in future work, which will also update our analysis to include power spectra and lensing \cite{Aghanim:2018oex} results from the \textit{Planck} 2018 data release \cite{Aghanim:2018eyx}, which indeed contain statistically marginal hints for CIPs, which could also be caused by $\alpha$ fluctuations \cite{Akrami:2018odb}. Indeed, as noted in Ref.~\cite{Hill:2018ypf}, there are still systematic (but unsubtracted) biases contributing to estimators of non-Gaussianity in the CMB. These could also affect observable signatures of $\alpha$ modulation; a full trispectrum analysis including these biases and a variety of interesting theoretical possibilities (CIPs, $\alpha$ fluctuations, etc...) is thus in order. Looking beyond CMB anisotropies, the full network of bound-bound and bound-free transition during the recombination era will produce spectral distortions of the CMB away from a perfect thermal spectrum (See Refs.~\cite{RubinoMartin:2006ug,Chluba:2015gta} and references therein). The rates of the relevant transitions depend very sensitively on $\alpha$, and so a futuristic measurement of spatially-dependent CMB spectral distortions from recombination lines would offer an interesting (and more primordial) test of the possibilities explored here. Furthermore, the rate of diffusion damping /efficiency of generating CMB spectral distortions all depend sensitively on $\alpha$ \cite{Chluba:2012gq,Khatri:2013dha}. Anisotropies of continuum CMB spectral distortions could thus also be an interesting test of spatially variations in $\alpha$ (as well as to time evolution of the background value, as noted in Ref.~\cite{Hart:2017ndk}). In coming decades, observations of absorption in the 21-cm (hyperfine) transition of neutral hydrogen may help us to finally understand the `dark ages', the epoch between CMB decoupling at $z\sim 1090$ and the formation of the first stars near $z\sim 10-20$ (see Ref.~\cite{2012RPPh...75h6901P} and references therein for a more comprehensive discussion). As noted in Refs. \cite{Khatri:2007yv}, the $21$-cm line rest frame frequency scales as $\nu_{21}\propto \alpha^{4}$, the Einstein rate coefficient for the relevant decay scales as $A\propto \alpha^{13}$, and the spin-changing collisional cross sections of hydrogen also depend sensitively on $\alpha$. As a result, $21$-cm cosmology should provide a new probe of spatial fluctuations in $\alpha$, with the added advantage that measurements (by experimental efforts like HERA \cite{DeBoer:2016tnn} and SKA \cite{Maartens:2015mra}) at many redshifts should facilitate stringent tests of the time evolution of perturbations in different models of spatially varying $\alpha$. | 18 | 8 | 1808.07486 |
1808 | 1808.09452_arXiv.txt | The $\Mblack - \sigma$ relation establishes a connection between central black holes (BHs) and their host spheroids. Supported by observations at $\Mblack \gtrsim 10^5 \Msun$, there is limited data on its validity at lower masses. Employing a semi-analytical model to simulate the combined evolution of BHs and their host galaxies, we predict the observational consequences of assuming a bimodality in the accretion efficiency of BHs, with low-mass BHs ($\Mblack \lesssim 10^5 \Msun$) accreting inefficiently. We predict a departure from the $\Mblack - \sigma$ relation at a transitional BH mass $\sim 10^5 \Msun$, with lower-mass BHs unable to reach the mass dictated by the relation and becoming disconnected from the evolution of the host galaxy. This prediction is an alternative to previous works suggesting a flattening of the relation at $\sim 10^5-10^6 \Msun$. Furthermore, we predict a deficit of BHs shining at bolometric luminosities $\sim 10^{42} \, \mathrm{erg \, s^{-1}}$. Joined with a detection bias, this could partly explain the scarce number of intermediate-mass BHs detected. Conversely, we predict an increase in source density at lower bolometric luminosities, $<10^{42} \, \mathrm{erg \, s^{-1}}$. Because our predictions assume a bimodal population of high-redshift BH seeds, future observations of fainter BHs will be fundamental for constraining the nature of these seeds. | \label{sec:intro} It is commonly accepted that the central region of all massive galaxies contains a super-massive black hole (BH, $\Mblack \gtrsim 10^6 \Msun$, see e.g. \citealt{King_Pounds_2015}). There seems to be a tight correlation between the mass of the BH and the properties of the host galaxy spheroid, such as the velocity dispersion of stars. This correlation, named the $\Mblack - \sigma$ relation \citep{Ferrarese_Merritt_2000, Gebhardt_2000, Kormendy_Ho_2013, McConnell_Ma_2013}, is surprising as there is a wide separation between the physical scale of the bulge of a galaxy and the sphere of influence of its central BH. The bulge of the Milky Way galaxy, for example, is $\sim 10^{4}$ times larger than the radius of influence of its BH. The feedback resulting from BH accretion is thought to be the driving force in establishing the $\Mblack - \sigma$ relation, regulating both the star formation in massive host galaxies and the gas inflow onto the central BH \citep{Fabian_2000, Begelman_2005, King_Pounds_2015, Martin-Navarro_2018}. \cite{Vdb_2016}, employing a heterogeneous set of 230 BHs with a minimum mass $\sim 4\times 10^5 \Msun$, found a relation of the form \begin{equation} \log \Mblack = (8.32\pm0.04) + (5.35\pm0.23)\log \sigma_{200} \, , \label{eq:M-sigma} \end{equation} where $\Mblack$ is in solar masses and $\sigma_{200}$ is expressed in units of $200 \, \mathrm{km \, s^{-1}}$. Due to observational constraints, the low-mass regime of the relation is far less explored. Currently, the lightest central BH ($\Mblack \sim 3\times 10^4 \Msun$) is observed in a dwarf galaxy at $z \sim 0.03$ \citep{Chilingarian_2018}. Due to the paucity of the detected intermediate-mass BHs ($10^2 \Msun \lesssim \Mblack \lesssim 10^6 \Msun$, e.g. \citealt{Greene_Ho_2004, Reines_2013, Baldassare_2015,Mezcua_2015,Mezcua_2016_X,Mezcua_2018_b}; see the review by \citealt{Mezcua_2017_review}), it is still hard to infer whether or not low-mass galaxies follow the extrapolation of the $\Mblack - \sigma$ relation \citep{Xiao_2011, Baldassare_2015, Mezcua_2017_review, MN_Mezcua_2018}. A complete description of galaxy evolution requires a better understanding of the low-mass BH regime. Star formation and BH quenching in low-mass galaxies could be driven by different mechanisms, involving young stars and supernovae instead of the central BH \citep{Dubois_2015,Alcazar_2017,Habouzit_2017}. For masses lighter than a transition mass, the central BH might be disentangled from the evolution of the host galaxy. In this Letter we assume a bimodality in the accretion efficiency of BHs \citep{Pacucci_2017}, and predict the shape of the $\Mblack - \sigma$ relation and of the luminosity function for BHs with $\Mblack \lesssim 10^5 \Msun$. Our predictions, when compared to future observations of BHs in dwarf galaxies, will provide important constraints on the nature of BH seeds at high redshift, which constitute the progenitors of the $z \sim 7$ quasar population \citep{Fan_2006, Natarajan_2012, Volonteri_2016,Ricarte_2018}. | \label{sec:disc_concl} We have employed a semi-analytical model to investigate the low-mass regime of the $\Mblack-\sigma$ relation and of the quasar luminosity function. Our model is based on two main assumptions: (i) low-mass and high-mass seed populations form at $z \sim 20$; (ii) the accretion process is bimodal, with BHs with $\Mblack \lesssim 10^5 \Msun$ accreting inefficiently. The $\Mblack-\sigma$ relation is somewhat tricky for low-mass galaxies, as $\sigma$ is defined as the velocity dispersion of stars inside bulges. An alternative to the $\Mblack-\sigma$ relation would be the $\Mblack-M_{\star}$ relation, where $M_{\star}$ is the stellar mass of the galaxy \citep{Reines_Volonteri_2015}. We note, however, that many dwarf galaxies do have bulges (e.g., NGC 4395, POX52, RGG 118, see \citealt{Baldassare_2015}) and that the definition of $\sigma$ can always be interpreted as the velocity dispersion of stars within some effective radius from the center of mass of the system. In this Letter we chose to focus on the $\Mblack-\sigma$ because it seems to provide a tighter relation (e.g., \citealt{Shankar_2016}), indicating a more fundamental connection. As a test, we performed our simulations also in the $(\Mblack, M_{\star})$ parameter space, using the theoretical relation presented in \cite{Reines_Volonteri_2015}. We confirm, also in the $\Mblack-M_{\star}$ space, the presence of the same departure from the theoretical relation, occurring at $\Mblack \sim 10^5 \, \mathrm{\Msun}$. Below we discuss the consequences of our results for BH seed models at high redshift. \subsection{Observational predictions for BH seeding models} Our main prediction is that central BHs and their host galaxies depart from the $\Mblack-\sigma$ relation for masses $\Mblack \lesssim 10^5 \, \mathrm{\Msun}$, becoming under-massive with respect to the extrapolation of the $\Mblack-\sigma$ to lower masses. The $\Mblack-\sigma$ relation reflects, for $\Mblack \gtrsim 10^5 \Msun$, the connection between galaxy evolution and BH growth. The link is driven by the outflows generated by the BH energy and momentum output. Smaller BHs grow inefficiently and are unable to generate strong outflows triggering the growth-regulation process. For this reason, BHs with $\Mblack \lesssim 10^5 \Msun$ fail to reach the mass dictated by their velocity dispersion and become under-massive. Previous observations (e.g., \citealt{Martin-Navarro_2018,MN_Mezcua_2018}) and simulations (e.g., \citealt{Alcazar_2017,Habouzit_2017}) already suggested that feedback is driven by BH activity for $\Mblack \gtrsim 10^5 \Msun$ and by supernova-driven winds for $\Mblack \lesssim 10^5 \Msun$. Some papers (e.g., \citealt{Greene_2006, Mezcua_2017_review, MN_Mezcua_2018}) suggest an alternative scenario for the low-mass regime of the $\Mblack-\sigma$ relation, predicting a flattening at masses $\sim 10^5-10^6 \Msun$. \cite{MN_Mezcua_2018} explained this putative flattening with a weaker coupling between baryonic cooling and BH feedback, disconnecting the BH from the evolution of the host spheroid. Alternatively, the flattening could be explained with the prevalence of a high-mass formation channel for early seeds \citep{Volonteri_2010}. These high-mass seeds would fail to grow and just accumulate around their original mass, $\sim 10^5-10^6 \Msun$. In this Letter, we envisage that a flattening toward $\sim 10^5-10^6 \Msun$ would be due to an \textit{observational bias}. Observing BHs with $\Mblack \lesssim 10^5 \Msun$ is currently challenging, and the predicted paucity of BHs shining at $L_{\rm bol} \sim 10^{42} \, \mathrm{erg \, s^{-1}}$ (Sec. \ref{subsec:LF}) could add to this effect. Instead of a flattening, our model clearly predicts a \textit{downward} departure from the $\Mblack-\sigma$ relation. \textit{A detection for $\Mblack \lesssim 10^5 \Msun$ of a relation of the form $\Mblack \sim \sigma^{\alpha}$ with $\alpha \gtrsim 7$ would be an important indicator of the existence of a bimodal population of BH seeds.} Pushing the detection limit to $\Mblack \lesssim 10^4 \Msun$ \citep{Baldassare_2017,Chilingarian_2018} will enable to determine the relevance of the BH - galaxy connection for lower-mass galaxies, and whether or not a departure from the $\Mblack-\sigma$ relation occurs. A major role in this observational challenge will be played by future observatories, both in the electromagnetic (e.g., Lynx; see \citealt{Ben-Ami_2018}) and in the gravitational (e.g., LISA; see \citealt{LISA_2017}) realms. This effort will not only shed light on the interconnection between BH and its host galaxy, but will ultimately provide important constraints on the seed formation mechanisms active in the high-redshift Universe. The observation in the local Universe of intermediate-mass BHs, as well as other proposed techniques (e.g., deriving the local super-massive BH occupation fraction, \citealt{Miller_2015}) will help us to understand processes occurred early in the history of the Universe. \vspace{0.3cm} F.P. acknowledges support from the NASA Chandra award No. AR8-19021A, and enlightening discussions with Vivienne Baldassare and Elena Gallo. M.M. acknowledges support from the Spanish Juan de la Cierva program (IJCI-2015-23944). I.M.N. acknowledges support from the EU Marie Curie Global Fellowships. This work was supported in part by the Black Hole Initiative at Harvard University, which is funded by a JTF grant. | 18 | 8 | 1808.09452 |
1808 | 1808.05951_arXiv.txt | Magnetic reconnection, the central engine that powers explosive phenomena throughout the Universe, is also perceived as one of the \edit1{principal} mechanisms for accelerating particles to high energies. Although various signatures of magnetic reconnection have been frequently reported, observational evidence that links particle acceleration directly to the reconnection site has been rare, especially for space plasma environments currently inaccessible to \textit{in situ} measurements. Here we utilize broadband radio dynamic imaging spectroscopy available from the Karl G. Jansky Very Large Array to observe decimetric type III radio bursts in a solar jet with high angular ($\sim$20$''$), spectral ($\sim$1\%), and temporal resolution (50 milliseconds). These observations allow us to derive detailed trajectories of semi-relativistic (tens of keV) electron beams in the low solar corona with unprecedentedly high angular precision ($<0''.65$). We found that each group of electron beams, which corresponds to a cluster of type III bursts with 1--2-second duration, diverges from an extremely compact region ($\sim$600 km$^2$) in the low solar corona. The beam-diverging sites are located behind the erupting jet spire and above the closed arcades, coinciding with the presumed location of magnetic reconnection in the jet eruption picture supported by extreme ultraviolet/X-ray data and magnetic modeling. We interpret each beam-diverging site as a reconnection null point where multitudes of magnetic flux tubes join and reconnect. Our data suggest that the null points likely consist of a high level of density inhomogeneities possibly down to 10-km scales. These results, at least in the present case, strongly favor a \edit1{reconnection-driven electron acceleration scenario}. | \label{sec:intro} Explosive events on the Sun, thanks to their proximity, serve as an outstanding laboratory to study catastrophic magnetic energy release and particle acceleration processes in great detail, yielding a window into powerful explosions in more extreme astrophysical plasma contexts such as the atmospheres of magnetically active stars \citep{1991ARA&A..29..275H} and possibly, astrophysical jet/accretion disk systems \citep{2010A&A...518A...5D}. During an explosive solar event, a large fraction of electrons can be accelerated to nonthermal energies \citep{1976SoPh...50..153L,2010ApJ...714.1108K}, resulting in a variety of signatures across the electromagnetic spectrum \citep{2017LRSP...14....2B}. The accelerated electrons not only play a crucial role in the dynamics and energetics of explosive solar activities \citep{2017LRSP...14....2B}, but also have the potential of posing threats to the near-Earth space environment, especially for their most energetic form \citep{2006LRSP....3....2S}. Fast magnetic reconnection---a plasma process in which magnetic field lines with opposite directions approach each other and reconfigure---is believed to be the \edit1{principal} mechanism responsible for the impulsive energy release in flares and jets. The released magnetic energy is subsequently converted into other forms of energy in accelerated particles, heated plasma, and bulk plasma flows. Observational evidence for magnetic reconnection in flares and jets has been frequently reported in literature. Examples include cusp- or X-shaped loops \citep{1996ApJ...456..840T,2013NatPh...9..489S,2015SoPh..290.2211G,2015NatCo...6E7598S}, current-sheet- or null-point-like features \citep{2003ApJ...596L.251S,2010ApJ...723L..28L, 2010ApJ...722..329S, 2016ApJ...819L...3Z, 2016ApJ...821L..29Z,2017ApJ...835..139S,2018ApJ...854..122W}, plasmoid ejections, plasma inflows/outflows, supra-arcade downflows, and shrinking loops \citep{1995ApJ...451L..83S, 1999ApJ...519L..93M,2008ApJ...675..868R,2009ApJ...697.1569M,2010ApJ...722..329S,2012ApJ...754...13S,2012ApJ...747L..40S,2013ApJ...767..168L,2014ApJ...797L..14T,2015ApJ...807....7R}, which are typically features that resemble the reconnection-associated magnetic geometry or plasma dynamics outlined by the flare-heated thermal plasma. Radio and hard X-ray (HXR) observations of nonthermal radiation from accelerated electrons provide a complementary view of the high-energy aspects of magnetic reconnection. Previous microwave and HXR observations have revealed nonthermal sources at or above the top of retracted magnetic arcades, implying the presence of accelerated electrons in the close vicinity of magnetic reconnection site \citep[e.g.,][]{1994Natur.371..495M,2008A&ARv..16..155K,2012ApJ...754....9G,2013ApJ...767..168L,2014ApJ...787..125N}. However, it remains an open question where and how the electrons are energized in the context of magnetic reconnection (see, e.g., \citealt{2011SSRv..159..357Z} for a review). This is due, in part, to the lack of sensitivity and/or spatiotemporal resolution needed to directly trace the energetic electrons to their origin, making it difficult to determine whether the nonthermal electrons are accelerated \textit{in situ} or transported from elsewhere. Possible sites for electron acceleration include the reconnection outflow region \citep[e.g.,][]{1997ApJ...485..859S, 1998ApJ...495L..67T, 2008ApJ...676..704L, 2013ApJ...767..168L, 2015Sci...350.1238C}, the underlying retracted magnetic arcades \citep{2008ApJ...675.1645F}, and the magnetic reconnection site itself, i.e., the magnetic null point or current sheet where field lines join and reconnect \citep[e.g.,][]{1985ApJ...293..584H,1996ApJ...462..997L,2000A&A...360..715K,2006Natur.443..553D,2010ApJ...714..915O,2012NatPh...8..321E}. Likewise, little is known about the reconnection sites and the drivers of electron acceleration themselves. Coherent radio bursts from electron beams propagating along magnetic flux tubes at semi-relativistic speeds ($\sim$0.1--0.5$c$ where $c$ is the speed of light), known as type III radio bursts, serve as an alternative, but unique means for tracing accelerated electrons in a wide range of coronal heights---from the low corona to well into the interplanetary space (see, e.g., \citealt{2014RAA....14..773R} for a review). This is largely owing to the coherent radiation mechanism itself, which allows radio emission from a relatively small population of nonthermal electrons to be readily detected (giving that the conditions for the radiation are satisfied). The bursts are emitted at a frequency close to the fundamental or harmonic electron plasma frequency: $\nu\approx s\nu_{pe}\approx 8980s\sqrt{n_e}$ Hz (where $s=$1 or 2 is the harmonic number), which depends only on the plasma density $n_e$ of the coronal environment that the beams traverse. Since the electron beams propagate very rapidly, they encounter a range of coronal densities within a short time, thus producing radio emission with a rapid change of frequency in time. Radio imaging of these bursts at a wide range of densely sampled frequencies with a sufficiently high temporal cadence can be used to map the detailed trajectory of a propagating electron beams in the corona, providing an excellent means of tracing these beams to their acceleration sites. Previous radio imaging of type III bursts (and their variants such as type J and U bursts) at one or several discrete frequencies, particularly from solar-dedicated Culgoora, Clark Lake, and Nan{\c c}ay radioheliographs, as well as general-purpose radio interferometers such as the Very Large Array, has yielded important results on the location and propagation of electron beams in the corona \citep[e.g.,][]{1980A&A....88..203D, 1987SoPh..108..333G, 1992ApJ...391..380A, 2001A&A...371..333P, 2008A&A...486..589K, 2013ApJ...762...60S, 2016ApJ...833...87C}. However, the full capability of radio imaging spectroscopy with spectrograph-like dense spectral sampling and high cadence has not been realized until very recently with the completion of the LOw Frequency Array (LOFAR; \citealt{2013A&A...556A...2V}), the Murchison Widefield Array (MWA; \citealt{2013PASA...30....7T}), the Mingantu Spectral Radioheliograph (MUSER; \citealt{2016IAUS..320..427Y}), and the upgraded Karl G. Jansky Very Large Array (VLA; \citealt{2011ApJ...739L...1P}). Equipped with the new technique, recent studies that utilize LOFAR and MWA observations of type III bursts at metric wavelengths (i.e., $<$300 MHz; LOFAR and MWA operate at 10--240 MHz and 80--240 MHz, respectively) have drawn significant new insights into the propagation of electron beams in the high corona, as well as their temporal and spatial correspondence with flare energy release in the lower corona \citep{2014A&A...568A..67M,2017NatCo...8.1515K,2017A&A...606A.141R,2017ApJ...851..151M,2018A&A...611A..57M,2018NatSR...8.1676C}. However, in order to trace the electron beams to the immediate vicinity of the primary magnetic energy release and electron acceleration site, presumably located in the low corona where the plasma is denser (typically at the order of 10$^{10}$ cm$^{-3}$; \citealt{2002SSRv..101....1A,2008A&ARv..16..155K}), spectral imaging of type III bursts at shorter, decimetric wavelengths (``dm-$\lambda$'' hereafter) is preferred because $\nu_{pe}$, which increases monotonically with $n_e$, falls into this wavelength range. The first work that utilized radio imaging spectroscopy to study \dml\ type III bursts with the VLA has successfully demonstrated the unique power of this technique in tracing electron beams in the low corona \citep{2013ApJ...763L..21C}. However, at that time the VLA was still in its commissioning phase, and the observation was made in its most compact D configuration (maximum baseline length of 1 km) with only part of the array utilized for imaging (17 out of 27 antennas). Hence the array had not reached its full capacity in terms of angular resolution, spectral coverage, imaging dynamic range, and temporal cadence, all of which are important for obtaining the new results reported here. Here we present VLA observations of \dml\ type III bursts at 1--2 GHz associated with a solar jet, taking advantage of VLA's unique capability of radio spectral imaging at hundreds of spectral channels along with unprecedentedly high angular resolution ($\sim$20$''$) and temporal cadence (50 milliseconds). These observations allow us to derive detailed trajectories of type-III-burst-emitting, semi-relativistic electron beams in the low corona with sub-arcsecond spatial accuracy ($<$0$''$.65, or $<$480 km on the solar disk) and moreover, clearly distinguish multitudes of electron beams generated in an individual energy release event that lasts for only 1--2 seconds. By combining the radio observations with extreme ultraviolet (EUV) imaging, X-ray data, and magnetic modeling, we determine the origin of each group of fast electron beams as a single, extremely compact ($\sim$600 km$^2$) region in the low corona trailing the erupting jet spire, interpreted as the magnetic reconnection null point. We present the VLA radio observations in Section \ref{sec:radio}. Context EUV and X-ray observations of the associated jet event are presented in Section \ref{sec:context}. In Section \ref{sec:model}, we utilize three-dimensional (3D) magnetic modeling to place the radio, EUV, and X-ray observations into a physical picture. We discuss implications of the observations for magnetic reconnection and electron acceleration in Section \ref{sec:discussion} and briefly conclude in Section \ref{sec:conclusion}. \newpage | \label{sec:conclusion} We have used the VLA to study \dml\ type III bursts in a solar jet with high angular ($\sim$20$''$), spectral ($\sim$1\%), and temporal resolution (50 milliseconds). These observations allow us to distinguish at least ten distinctive, semi-relativistic electron beams associated with each short, 1--2-s duration type III burst group, both spatially and temporally. By mapping detailed trajectories of the electron beams with unprecedentedly high angular precision ($<$$0''.65$), it is revealed that each group of electron beams diverges from an extremely compact region ($\sim$600 km$^2$) located in the low corona behind the erupting jet spire and above the closed arcades. The beam-origin sites coincide very well with the presumed location of magnetic reconnection in the jet eruption picture supported by EUV/X-ray observations and magnetic modeling. Based on the observational evidence and magnetic modeling results, we interpret each of these beam-origin sites as a magnetic reconnection null point. The appearance of the bursts very close ($<$1,000 km) to the reconnection sites strongly favor a reconnection-driven, field-aligned electron acceleration scenario. Our observations suggest that the production of the electron beams are likely associated with a bursty reconnection scenario. Each fast electron beam, which contains energetic electrons of at least \edit1{tens of keV}, is accelerated at or very close to the reconnection null point within tens of milliseconds. From the density profiles along the EB flux tubes, we infer that the reconnection null points likely consist of a high level of density inhomogeneities ($\delta n_e/n_e>100\%$), possibly down to 10-km scales. Our data provide new observational constrains for future theoretical/modeling studies to examine the responsible electron acceleration mechanisms rigorously. Finally, it is intriguing to ask whether this is only an isolated case or otherwise constitutes a general picture for the production of \dml-type-III-burst-emitting electron beams in solar jets. It also remains to be seen whether the picture can be applied to events of much larger scale, e.g., solar flares and coronal mass ejections. Answering these questions calls for further investigations on more \dml\ type III burst events observed with high-resolution, broadband radio dynamic imaging spectroscopy. | 18 | 8 | 1808.05951 |
1808 | 1808.00573_arXiv.txt | {The Vela~OB2 association is a group of $\sim$10\,Myr stars exhibiting a complex spatial and kinematic substructure. The all-sky \textit{Gaia}~DR2 catalogue contains proper motions, parallaxes (a proxy for distance), and photometry that allow us to separate the various components of Vela~OB2.} {We characterise the distribution of the Vela~OB2 stars on a large spatial scale, and study its internal kinematics and dynamic history.} {We make use of \textit{Gaia}~DR2 astrometry and published \textit{Gaia}-ESO Survey data. We apply an unsupervised classification algorithm to determine groups of stars with common proper motions and parallaxes.} {We find that the association is made up of a number of small groups, with a total current mass over 2330\,M$_{\odot}$. The three-dimensional distribution of these young stars trace the edge of the gas and dust structure known as the IRAS Vela Shell across $\sim$180\,pc and shows clear signs of expansion.} {We propose a common history for Vela~OB2 and the IRAS Vela Shell. The event that caused the expansion of the shell happened before the Vela~OB2 stars formed, imprinted the expansion in the gas the stars formed from, and most likely triggered star formation.} | The Vela~OB2 region is an association of young stars near the border between the Vela and Puppis constellations, first reported by \citet{Kapteyn14}. The association was known for decades as a sparse group of a dozen early-type stars \citep{Blaauw46,Brandt71,Straka73}. The modern definition of the Vela~OB2 association comes from the study of \citet{deZeeuw99}, who used Hipparcos parallaxes and proper motions to identify a coherent group of 93 members. Their positions on the sky overlaps with the IRAS Vela Shell \citep[][]{Sahu92phdt}, a cavity of relatively low gas and dust density, itself located in the southern region of the large Gum nebula \citep{Gum52}. The Vela~OB2 association is known to host the massive binary system $\gamma^2$~Vel, made up of a Wolf-Rayet (WR) and an O-type star; recent interferometric distance estimates have located it at $336^{+8}_{-7}$\,pc \citep{North07}. \cite{deMarco99} estimate the total mass of the system to be 29.5$\pm$15.9\,M$_{\odot}$, while \citet{Eldridge09} propose initial masses of 35\,M$_{\odot}$ and 31.5\,M$_{\odot}$ for the WR and O components, respectively. \citet{Pozzo00}, making use of X-ray observations, identified a group of pre-main sequence (PMS) stars around $\gamma^2$~Vel, 350 to 400\,pc from us. This association is often referred to as the Gamma Velorum cluster, although \citet{Dias02} list it under the name Pozzo~1. \citet{Jeffries09} estimate that this cluster is 10\,Myr old. The \textit{Gaia}-ESO Survey study of \citet{Jeffries14} (hereafter J14) made use of spectroscopic observations to select the young stars on the basis of their Li abundances, and found the Gamma Velorum cluster to present a bimodal distribution in radial velocity. They suggested one group (population A) might be related to $\gamma^2$~Vel, while the other (population B) is not, and is in a supervirial state. The N-body simulations of \citet{Mapelli15} confirmed that given the small total mass of the Gamma Velorum cluster, the observed radial velocities could only be explained if both components were supervirial and expanding. In a study of the nearby 30\,Myr cluster NGC~2547, \citet{Sacco15} (hereafter S15) identified stars whose radial velocities matched that of population B of J14, 2$^{\circ}$ south of $\gamma^2$~Vel, hinting that this association of young stars might be very extended. \citet{Prisinzano16} estimate a total mass of the Gamma Velorum cluster of about 100\,M$_{\odot}$, which is a very low total mass for a group containing a system as massive as $\gamma^2$~Vel. As pointed out by J14, and according to the scaling relations of \citet{Weidner10}, the total initial mass of a cluster should be at least 800\,M$_{\odot}$ in order to form a 30\,M$_{\odot}$ star. It has been suggested \citep[e.g.][]{Sushch11} that the IRAS Vela Shell (IVS) is a stellar-wind bubble created by the most massive of the Vela~OB2 stars. Observations of cometary globules \citep{Sridharan92,Sahu93,Rajagopal98} and gas \citep{Testori06} have shown that the IVS is currently in expansion at a velocity of $8-13$\,km\,s$^{-1}$. \citet{Testori06} point out that stellar winds from all the known O and B stars in the area are probably not sufficient to explain this expansion, and suggest it could have been initiated by a supernova, possibly the one from which the runaway B-type star HD~64760 (HIP~38518) originated \citep{Hoogerwerf01}. We note that \citet{Choudhury09} do not measure a significant expansion of the cometary globule distribution, but do observe that the tails of the 30 globules all point away from the centre of the IVS. Based on \textit{Gaia}~DR1 data, \citet{Damiani17} have shown the presence of at least two dynamically distinct populations in the area. One of this groups includes the Gamma Velorum cluster, while the other includes NGC~2547. Still using \textit{Gaia}~DR1 data, \citet{Armstrong18} found that the young stars in the region are distributed in several groups and do not all cluster around $\gamma^2$~Vel. Recently, \citet{Franciosini18} have used the astrometric parameters of the \textit{Gaia}~DR2 catalogue \citep{GDR2content} to confirm that populations A and B identified by J14 are located $\sim$38\,pc from each other along our line of sight, and observe a radial velocity gradient with distance which they interpret as a sign of expansion. The \textit{Gaia} DR2 catalogue was also used by \citet{Beccari18}, who find that the stars of the age of Gamma Velorum in a $10^{\circ}\times5^{\circ}$ field are not distributed in only two subgroups, but in at least four different subgroups. In this study we use \textit{Gaia}~DR2 data to characterise the spatial distribution and kinematics of stars of the age of the Vela OB2 association. This paper is organised as follows. Section~\ref{sec:data} presents the data and our source selection. Section~\ref{sec:components} contains a description of the observed spatial distribution. Section~\ref{sec:mass} discusses the mass content in the Vela OB2 complex. Section~\ref{sec:IVS} relates our findings to the context of the IVS. Sections~\ref{sec:discussion} discusses the results. Concluding remarks are presented in Sect.~\ref{sec:conclusion}. | \label{sec:conclusion} In this paper we make use of the \textit{Gaia}~DR2 astrometry and photometry to identify the young stars of the Vela~OB2 association over more than 100\,pc. We identify and list 11 main components of a fragmented distribution. They appear to roughly follow an expanding ring-like structure. We observe a good morphological correlation between their three-dimensional distribution and kinematics and the dust and gas structure known as the IRAS Vela Shell. The expanding stellar distribution indicates that the expansion of the shell is not primarily due to the Vela~OB2 stars, but to an event that impacted the local dynamics before the Vela~OB2 stars formed. This observation is compatible with previous suggestions that the shell originates from a supernova explosion. The progenitor of this supernova might have belonged to one of the several clusters with ages $\sim$20\,Myr older than Vela~OB2 located in the region. The lack of radial velocities for all stars in the association prevents us from painting a full three-dimensional dynamic portrait of the region and its expansion. Robust age determinations and orbits for all the populations in the region are necessary in order to establish a physically plausible sequence of events and prove or disprove the hypothesis that the formation of the Vela~OB2 stars was triggered by the supernova that initiated the expansion of the IRAS Vela Shell. | 18 | 8 | 1808.00573 |
1808 | 1808.06480_arXiv.txt | We present a large ensemble of simulations of an Earth-like world with increasing insolation and rotation rate. Unlike previous work utilizing idealized aquaplanet configurations we focus our simulations on modern Earth-like topography. The orbital period is the same as modern Earth, but with zero obliquity and eccentricity. The atmosphere is 1 bar N$_{2}$-dominated with CO$_{2}$=400 ppmv and CH$_{4}$=1 ppmv. The simulations include two types of oceans; one without ocean heat transport (OHT) between grid cells as has been commonly used in the exoplanet literature, while the other is a fully coupled dynamic bathtub type ocean. The dynamical regime transitions that occur as day length increases induce climate feedbacks producing cooler temperatures, first via the reduction of water vapor with increasing rotation period despite decreasing shortwave cooling by clouds, and then via decreasing water vapor and increasing shortwave cloud cooling, except at the highest insolations. Simulations without OHT are more sensitive to insolation changes for fast rotations while slower rotations are relatively insensitive to ocean choice. OHT runs with faster rotations tend to be similar with gyres transporting heat poleward making them warmer than those without OHT. For slower rotations OHT is directed equator-ward and no high latitude gyres are apparent. Uncertainties in cloud parameterization preclude a precise determination of habitability but do not affect robust aspects of exoplanet climate sensitivity. This is the first paper in a series that will investigate aspects of habitability in the simulations presented herein. The datasets from this study are opensource and publicly available. | \label{sec:intro} In recent years studies of the liquid water habitable zone for terrestrial exoplanets have mostly moved from the realm of 1-D \citep[e.g.][]{kasting1993,Forget1998,Selsis2007,pierrehumbert2011b,Kopparapu2013,Popp2013,Kopparapu2014,Ramirez2014b} to fully 3-D coupled Atmophere and Ocean General Circulation Models \citep[e.g.][]{merlisschneider2010,Edson2011,WolfToon2013,Yang2013,leconte2013a,Shields2014,Yang2014,godolt2015,Kopparapu2016,Popp2016,Popp2017,Noda2017,Checlair2017,Boutle2017,Salameh2018}. In general this has shown the value that 3-D modeling can bring to fully characterizing the climate state of a given world, the importance of cloud and ice albedo feedbacks and how different stellar types effect the habitable zone, among many other effects. On the other hand, because of computational limitations the majority of such 3-D studies have neglected the effect of lateral ocean heat transport (OHT). Recent exceptions include the work of \cite{Yang2013,cullum2014,huyang2014,Ferreira2014,Way2015,Way2016,Fujii2017,Way2017b,DelGenio2018,Kilic2018} who utilized a fully coupled ocean, \cite{Charnay2013,Charnay2017} who use a 2-layer ocean \citep{Codron2012} that mimics some aspects of a fully coupled ocean, and \cite{godolt2015,Edson2012,Kilic2017} who specified fixed lateral ocean heat transports perhaps first applied by \cite{russell1985} for Earth climate studies. One of the more stark representations of the effect that OHT has on such 3-D simulations was presented in the work of \cite{huyang2014}. Initial studies of tidally locked aquaplanet simulations around M-dwarfs demonstrated an ``eye-ball" state where open water would appear in a circular region at the substellar point, but the rest of the planet would be covered in ice \citep[e.g.][]{pierrehumbert2011} even for high CO$_2$ concentrations. However, it is known that sea ice dynamics are intimately tied to OHT and has had an effect in simulations of snowball Earth studies \citep[e.g.][]{Yang2012a,Yang2012b}. \cite{huyang2014} showed the ``eyeball" state to be fictional and that a ``lobster" state is a better reflection of reality, but it does require OHT. To better understand the differences that OHT can have on climate dynamics we have analyzed a suite of three-dimensional (3D) General Circulation Model (GCM) simulations of an Earth-like planet on which two parameters, insolation and length of day, are varied over ranges suitable for surface habitability. The study includes a suite of simulations that both include and neglect OHT. Previous studies exploring insolation and rotation have been shown to have a range of effects on exoplanet climates \citep{Yang2014,Kopparapu2016,Noda2017,Salameh2018}, but at the same time OHT has been neglected in these studies. Our use of \rocke{} \citep{Way2017} with OHT and its different treatment of clouds, convection, radiative transfer, dynamical core, and a host of other parameterized physics should help establish the generality of results where they overlap. However, direct comparison with previous work is also limited not only by the different treatment of OHT, but also because most previous work relied upon an aquaplanet setup, whereas we use an Earth-like land/sea mask. One may even consider a planet with Earth's present-day or past land-ocean distribution as a possibly more useful, demonstrably habitable, template for the rise of life as compared with aquaplanets. There is also an on-going debate in the community where some \citep{Abbot2012} argue that it is not possible for an aquaplanet to support a climate stabilizing carbonate-silicate cycle, and those \citep{Charnay2017} who argue otherwise. Until the debate is settled we believe it is a good idea to continue modeling the climates of both types of worlds. | Our results support the conclusions of previous work \citep[e.g.][]{Yang2014} that rapidly rotating planets like Earth are much more susceptible to a runaway greenhouse than are slowly rotating planets at high insolations. As mentioned above, some of the differences between the work herein and previous results may be related to the different GCMs being used, the types of oceans (dynamic ocean versus thermodynamic ocean), and an Earth-like topography and land/sea mask versus aquaplanet configurations. As mentioned in Section \ref{sec:Experimental_Setup} \rocke{} does not yet use high temperature line lists, nor does it account for the effect of water vapor mass on the dynamics, so beyond the fact that \rocke{} lies within the range of previous GCM studies that concluded that the inner edge of the habitable zone must be significantly closer to the Sun than 1-D models estimate, we cannot estimate a precise inner edge location. On the other hand one can look at diagnostics of water vapor transported into the stratosphere, where it can potentially be photodissociated, leading to hydrogen escape and onset of the moist greenhouse, a more conservative definition of the inner edge of the habitable zone. To that end in Figure \ref{fig:h2oclimate} we show water vapor molar concentration in the highest model layer for the grid cell with the largest value (A \& B) and the mean in the highest layer (C \& D) to investigate whether any of our simulations begin to approach the moist greenhouse limit of \cite{kasting1993}, i.e. f(H$_{2}$O)$=$3$\times$10$^{-3}$. Figure \ref{fig:h2oclimate}A shows that for the highest insolation runs of most rotations with a Q-flux=0 ocean the stratosphere exceeds the 3$\times$10$^{-3}$ limit in a given grid cell whereas the mean Figure \ref{fig:h2oclimate}C does not in general. With the dynamic ocean in Figure \ref{fig:h2oclimate}B most of the high insolation rapidly rotating planets (rotations $<$X032) almost reach the moist greenhouse state, whereas for the slower rotating models where S0X$>$2.9 they exceed the 3$\times$10$^{-3}$ limit for the maximum grid cell value. However, if one takes the mean of the highest layer Figure \ref{fig:h2oclimate}D then one finds they are roughly similar to the Q-flux=0 runs in Figure \ref{fig:h2oclimate}B. \begin{figure}[!htb] \includegraphics[scale=0.35]{Figure12a} \includegraphics[scale=0.35]{Figure12b}\\ \includegraphics[scale=0.35]{Figure12c} \includegraphics[scale=0.35]{Figure12d} \caption{Stratospheric water vapor content for Q-flux=0 ocean runs (A/C, left) and Dynamic Ocean runs (B/D, right). Y-axis is the log$_{10}$ of the specific humidity at 0.1 hPa for H$_{2}$O/Air (kg/kg). A \& B are values for the grid cell with the largest value at the highest layer in each simulation whereas C \& D are the mean at the highest layer.} \label{fig:h2oclimate} \end{figure} We have shown that the representation of ocean dynamics is just as important a consideration for extreme exoplanet climates as is the representation of radiation, particularly so for rapidly rotating planets as shown in the 1 d -- 32 d cases herein. It should be noted that \rocke{} cannot actually reach the runaway greenhouse definition of the inner edge of the habitable zone for terrestrial worlds, unlike in many of the works cited above. The radiative transfer in \rocke{} cannot accurately calculate heating rates for temperatures over 400K. In addition, the dynamics begins to lose accuracy when water vapor becomes more than 10\% of the mass of the atmosphere and begins to significantly affect pressure gradients and the assumed ideal gas behavior of the atmosphere. When water vapor starts to becomes a non-negligible fraction of the atmospheric mass it also becomes important to be able to adjust the atmospheric constants such as the atmospheric mass, and heat capacity at constant pressure and volume, which \rocke{} is not presently capable of doing. Future papers in this series will address different habitability metrics such as that of \cite{Spiegel2008} and others related to water availability that are crucial to life on present day Earth. The data from this paper is open source and at publication time will be made available on the \rocke{} NCCS\footnote{NASA Center for Climate Simulation} data portal website: https://portal.nccs.nasa.gov/GISS\_modelE/ROCKE-3D An additional copy of the files will also be made available at https://archive.org/details/Climates\_of\_Warm\_Earth\_like\_Planets \newpage \appendix | 18 | 8 | 1808.06480 |
1808 | 1808.03093_arXiv.txt | We use full sky simulations, including the effects of foreground contamination and removal, to explore multi-tracer synergies between a SKA-like 21cm intensity mapping survey and a LSST-like photometric galaxy redshift survey. In particular we study ratios of auto and cross-correlations between the two tracers as estimators of the ratio of their biases, a quantity that should benefit considerably from the cosmic variance cancellation of the multi-tracer approach. We show how well we should be able to measure the bias ratio on very large scales (down to $\ell \sim 3$), which is crucial to measure primordial non-Gaussianity and general relativistic effects on large scale structure. We find that, in the absence of foregrounds but with realistic noise levels of such surveys, the multi-tracer estimators are able to improve on the sensitivity of a cosmic-variance contaminated measurement by a factor of $2-4$. When foregrounds are included, estimators using the 21cm auto-correlation become biased. However, we show that cross-correlation estimators are immune to this and do not incur in any significant penalty in terms of sensitivity from discarding the auto-correlation data. However, the loss of long-wavelength radial modes caused by foreground removal in combination with the low redshift resolution of photometric surveys, reduces the sensitivity of the multi-tracer estimator, albeit still better than the cosmic variance contaminated scenario even in the noise free case. Finally we explore different alternative avenues to avoid this problem. | \label{sec:intro} Probing the physics of the primeval Universe is one of the main drivers for observational studies of the cosmos. The Gaussianity of the primordial cosmological perturbations remains an open question which provides further insight into the details of the dynamics of the very early Universe. The current state of the art are the Planck bounds derived from the Cosmic Microwave Background (CMB) \citep{2016A&A...594A..13P}. As an example, the bounds on local-type primordial non-Gaussianity (PNG) yield $\fnl\simeq0.8\pm 5.0$. Furthermore, local PNG introduces a scale dependence in the bias between the Dark Matter (DM) halos and the astrophysical objects used as tracers of the matter distribution \citep{PhysRevD.77.123514,Matarrese:2008nc}. This scale dependence becomes relevant on large cosmological (horizon) scales. At the same time, general-relativistic effects become important on such ultra-large scales (past the matter-radiation equality peak), opening the possibility of testing the theory of gravity in this new regime and find possible hints of deviations to General Relativity (for a comprehensive review on "GR effects" see e.g. \cite{2011PhRvD..84d3516C,2011PhRvD..84f3505B,2014CQGra..31w4002B}). The next generations of Large Scale Structure (LSS) surveys such as the Square Kilometer Array (SKA)\footnote{www.skatelescope.org}, Euclid\footnote{www.euclid-ec.org} and the Large Synoptic Survey Telescope (LSST)\footnote{www.lsst.org}, promise to be able to target such effects by observing ever larger volumes of the Universe. Indeed, the forecasts for the next-generation surveys will improve on the Planck constraint on PNG \citep[see, e.g.][]{Giannantonio:2011ya,Camera:2013kpa,Camera:2014bwa,Alonso:2015uua,Raccanelli:2015vla}. Despite the improvements, forecast errors on local PNG from single tracers of the matter distribution will still be unable to push $\sigma(\fnl)$ below (or close to) 1, crucial to distinguishing between single-field and multi-field inflation \citep[see, e.g.][]{dePutter:2016trg}. The crucial limitation on these surveys comes from cosmic variance, which limits measurements on the largest scales. A decade ago \citet{2009PhRvL.102b1302S} proposed a statistical method, often referred to as the multi-tracer technique, to overcome cosmic variance (see also \citealt{McDonald:2008sh, Hamaus:2011dq, Abramo:2013awa}). The basic idea is that, if we only care about effects on the bias of the dark matter tracers and not on dark matter itself, then, by comparing two tracers, we can at least measure the ratio of their bias without requiring to measure the underlying dark matter distribution they trace. This will then avoid cosmic variance, caused by the stochasticity in the particular realization of the matter distribution we observe. By cancelling cosmic variance, we also shift the target set-up of future surveys to probe these large scale effects, since smaller volumes with low noise (e.g. large integration times or higher number densities) are preferred as opposed to huge volumes that sample the modes of interest many times (as long as such smaller volumes include the target scales). Several authors have extensively used the technique to forecast how combinations of future surveys and different DM tracers will impact on the prospects of measuring $\fnl$ as well as other horizon-scale GR effects \citep{PhysRevD.86.063514,Ferramacho:2014pua, Yamauchi:2014ioa,PhysRevD.92.063525,2015ApJ...812L..22F,Fonseca:2016xvi,Abramo:2017xnp,Fonseca:2018hsu,2018PhRvD..97l3540S}. While some combinations do not break the $\sigma(\fnl)<1$ threshold, others have the potential to provide transformational constraints on $\fnl$ and GR effects. Such technique thus opens a new window to probe the physics of inflation and General Relativity with near-future experiments. Despite the plethora of works studying the potential and applicability of the multi-tracer technique, little has been done to test and assess the performance of the technique within realistic observational settings for future surveys (although the technique has been employed in some analysis of current data \citep{2013MNRAS.436.3089B,2014MNRAS.437.1109R,2016MNRAS.455.4046M}, with an emphasis on redshift-space distortions). Questions on what estimators to use and whether they will be biased by contaminants still remain unanswered. This paper attempts to address some of these technical and practical issues. We will focus on the combination of an HI intensity mapping (IM) survey carried out by a SKA-like facility \citep{2015aska.confE..19S} with a LSST-like photometric galaxy survey \citep{2009arXiv0912.0201L}. This is a natural combination choice since both surveys will observe the largest cosmological volumes in an overlapping region of the sky in both the radio and optical/infra-red regimes. Moreover, such surveys will be affected by different sky systematics. Intensity mapping of the 21cm emission line of neutral Hydrogen is contaminated by signal from galactic synchrotron emission, free-free emission from galactic and extra-galactic origin and point sources. \citet{doi:10.1093/mnras/stu1666} compiled all the potential radio foregrounds and tested methods to subtract such contaminants from the HI temperature fluctuations. On the other hand, optical galaxy surveys will be affected by galactic dust extinction and star contamination, as well as several observational systematics, which can affect the observed clustering on large scales \citep{2011MNRAS.417.1350R}. The hope is that a combination of foreground cleaning methods and cross-correlations between surveys can help to make measurements that are reasonably free from such contaminants. Moreover, the specific scale-dependence of the cosmological effects might be used to disentangle this signature from any contaminant residuals. In this paper we explore the multi-tracer technique in the presence of foregrounds in the HI intensity maps using realistic simulations of the observational process. For this purpose we will construct estimators of the bias ratios and assess their performance at each redshift bin. For simplicity we will neglect the presence of PNG on the tracer biases, making the bias ratios scale independent. Note that PNG should have a negligible impact on the extracted estimator errors. We will focus on IM foregrounds, which are likely to be the main contaminant, and neglect the effects of possible systematics in the optical data for now. Crucially, we wish to determine how sensitive the cancellation of cosmic variance is to IM foreground cleaning and to the observational specifications of each experiment. The paper is organized as follows: in section \ref{sec:theory} we discuss possible multi-tracer estimators that can be used to extract the bias ratio of the two tracers and in particular focus on estimators that can be free from foreground or systematic contamination. In section \ref{sec:method} we describe the simulations done for both experiments (SKA1-MID and LSST) and the foreground cleaning method. In section \ref{sec:res} we discuss the results, addressing the performance and errors on the estimators and possible biases. In particular, we discuss the limitations of the current approach and show possible avenues to improve on this technique. We conclude in section \ref{sec:discussion}. | \label{sec:discussion} \begin{table} \begin{center} \begin{tabular}{l|rrrr} \hline Case & $\auto$ & $\cross$ & $\CV$ & $\opt$\\ \hline No noise, no FG & 1291 & 1292 & 192 & 1306 \\ No FG & 495 & 502 & 154 & 509 \\ No noise & 299 & 298 & 155 & 312 \\ Full analysis & 178 & 183 & 120 & 192 \\ \hline \end{tabular} \caption{Signal-to-noise from combining all redshift bins for all estimators and all modelling scenarios of this work. Here using 9 degrees of freedom for the foreground cleaning and a redshift bin width of $\Delta z = 0.1$. While $\auto$ uses the HI and galaxy auto-correlations, $\cross$ uses the HI-g cross-correlation and g-g auto-correlation and $\opt$ is the inverse variance-weighted sum of both (eqs. \ref{eq:est_e1} - \ref{eq:est_opt}). The estimator $\CV$ on the other hand uses auto-correlations with different DM realizations for the galaxy and HI populations and shows the constraints achievable in the absence of multi-tracer cosmic variance cancellation.} \label{tab:S2N} \end{center} \end{table} 21cm intensity mapping and photometric redshift surveys are two promising techniques to study the three-dimensional distribution of matter in the Universe on large scales. A number of cosmological observables, such as the level of primordial non-Gaussianity, benefit from the combined analysis of multiple proxies of the same density inhomogeneities in what is known as the ``multi-tracer'' technique. In this paper we have explored the feasibility of multi-tracer analyses that exploit the combination of the two aforementioned probes, for the particular case of 21cm observations to be carried out by an SKA-like instrument and an LSST-like galaxy sample. For concreteness, we have focused our analysis on two estimators of the bias ratio for both samples, $\auto$ and $\cross$, described in Section \ref{ssec:theory.estimators}. Since these estimators make use of the 21cm auto-correlation and its cross-correlation with galaxies respectively, they allow us to explore both the bias induced on $\auto$ by the presence of foreground residuals, and the potential loss of information associated with dropping auto-correlation information ($\cross$). For completeness, we also consider an optimal inverse-variance combination of both estimators, $\opt$, that uses all the data available. In the absence of foregrounds, we show that both $\auto$ and $\cross$ are able to achieve similar sensitivities, with little improvement when using $\opt$ due to the tight correlation between both estimators. When compared with the a cosmic-variance contaminated measurement of the same bias ratio, we show that these estimators are able to improve the signal-to-noise by a factor of $\sim4$-$5$, even when compared to the cosmic-variance-contaminated, noise-free case, showcasing the tremendous potential gains of the multi-tracer technique. The impact of the presence of foregrounds in the 21cm data is twofold. On the one hand, residuals after foreground removal produce an offset in the \textsc{HI} auto-correlation which biases both $\auto$ and $\cross$ at high significance. We show however, that $\cross$ is immune to this bias, while preserving the same statistical power as the two other estimators. On the other hand, foreground removal is based on the separation of foregrounds and cosmological signal through their different spectral behaviour, effectively down-weighting the radial long-wavelength modes where foregrounds dominate. Since photometric redshifts effectively erase all structure along the line of sight on all but the largest scales, the overlap between SKA and LSST in the $k_\parallel$-$k_\perp$ plane reduces significantly, partially spoiling the cosmic variance cancellation. We show that, in this case, the sensitivity of all estimators drops by more than a factor of $\sim2$, and that the improvement in signal-to-noise ratio with respect to a cosmic-variance-limited measurement made in the same circumstances is now only a factor $\sim2$. This drops to a smaller $\sim50\%$ improvement when we compare either estimator with the cosmic-variance-limited measurement without foregrounds. These results are summarized in Table \ref{tab:S2N}, which shows the cumulative signal-to-noise (quadrature-summed over all multipoles and redshift bins) for the three estimators as well as the CV limit in different scenarios regarding the presence of noise and foregrounds. We have also explored two possible ways to overcome this problem. First, a less aggressive foreground removal that leaves a larger fraction of foreground residuals in the maps, would also leave a larger number of long-wavelength modes untouched, increasing the scale overlap between LSST and SKA. In practice, however, we have seen that the contribution of the foreground residuals to the estimator uncertainties in fact decrease the total SNR when a smaller number of foreground degrees of freedom are subtracted. Another way to increase the scale overlap between both experiments would be to reduce the size of the redshift bins used in the analysis. Although this is not a real possibility for photometric surveys, since structures can never be resolved on scales smaller than the photo-$z$ uncertainty, this case allows us to explore other possible synergies with either spectroscopic surveys or intensity mapping observations of other emission lines. Our results show that in this case the gain in sensitivity associated with the multi-tracer technique is likely restored, with the added advantage that the foreground bias is also reduced due to the larger fraction of signal-dominated modes. Since the shot noise associated with currently planned wide-area spectroscopic surveys is likely to be too large for the multi-tracer technique to be effective, we argue that the most promising way forward for these types of analysis may be the combination of intensity mapping observations for different emission lines. In a follow up work we plan to study these new avenues in more detail, first by considering constraints on $\fnl$ directly, and including estimators that can deal naturally with the mismatch in the modes that are removing in different surveys does allowing a more perfect cancellation. We will also consider other foreground cleaning methods that might be less aggressive on cleaning this large scales and new tracers with higher redshift resolution. | 18 | 8 | 1808.03093 |
1808 | 1808.06814_arXiv.txt | We present the results of ultraviolet (UV) photometry of the old open cluster M67 obtained using Galaxy Evolution Explorer (GALEX) in far-ultraviolet (FUV) and near-ultraviolet (NUV) bands. UV detections of 18 blue straggler stars (BSSs), 3 white dwarfs (WDs), 4 yellow straggler stars, 2 sub-subgiants, and 25 X-ray sources are presented (along with an online catalog). We demonstrate the capability of UV colour magnitude diagrams (CMDs) along with the UV isochrones to identify potential stars which defy standard stellar evolution in this well studied cluster. We also detect a few main sequence turn-off and subgiant branch stars with excess flux in the FUV and/or NUV. UV continuum excess as well as Mg II {\it h} +{\it k} emission lines from the IUE archival spectra for 2 red giants are detected, suggestive of their chromospheric activity. We suggest that a large number of stars in this cluster are chromospherically active, whereas the bright BSS are unlikely to be active. We also estimate the fundamental parameters L/L$_{\sun}$, R/R$_{\sun}$ and T$_{eff}$ of the BSSs and 15 FUV bright stars by constructing the spectral energy distribution (SED) using multi-wavelength data. We identify three groups among the BSSs, based on their properties. The H-R diagram of BSSs with isochrones suggests that the BSSs in M67 are formed in the last 2.5 Gyr - 400 Myr, more or less continuously. We identify 7 potential MS+WD candidates based on large UV excess from a probable 11, based on SEDs. | \label{sec:Intro} M67 is a benchmark cluster to study stellar evolution, dynamics and cluster properties due to its proximity, richness, solar metallicity and exotic stellar populations. This cluster is located at RA = 8h 51m 23.3s and Dec =11\degr 49\arcmin 02\arcsec\, at a distance of $\approx$ 900 pc and has a reddening of E (B$-$V) = 0.015 to 0.056 mag (\citealp{Janes1984}, \citealp{montgomery93} (henceforth MMJ93), \citealp{Taylor2007}). Estimation of the cluster age varies between 3 to 5 Gyr (MMJ93, \citealp{VandenBerg2004}), with the recent findings indicating it to be 3.5 Gyr (\citealp{chen2014}, \citealp{Bonatto2015}). \citet{Gonzalez2016a} estimated a gyro-age of 3.7 $\pm$ 0.3 Gyr, \citet{Gonzalez2016b} revised the estimate to 5.4 $\pm$ 0.2 Gyr, whereas \citet{Barnes2016} estimated an age of 4.2 $\pm$ 0.2 Gyr, \citet{Stello2016} estimated a seismic-informed distance of 816 $\pm$ 11 pc, all from the K2 mission data. The cluster has evolved phases of both single and binary stellar evolution. 38\% of the cluster members are found to be in binaries (MMJ93). The main sequence turn off (MSTO) mass of the cluster is about $\approx$ 1.25M$\sun$ to 1.3M$\sun$ (\citealp{Sandquist2003_EB_TO}, \citealp{Sandquist2004}, \citealp{Gokay2013}). The cluster members are well identified by membership studies using both proper motion (\citealp{Sanders1977}, \citealp{Girard1989}, \citealp{Zhao1993}, \citealp{Yadav2008}, \citealp{Krone-Martins2010}) and radial velocity (\citealp{Matheiu1986}, \citealp{Mathieu1990_SB22}, \citealp{Milone1992}, \citealp{Milone1994}, \citealp{Yadav2008}, \citealp{Pasquini2011}, \citealp{Geller2015}, \citealp{Brucalassi2017}) measurements with various spatial extent and limiting magnitudes. The cluster is exhaustively studied through photometry in the multiwavelength bands (\citealp{Nissen1987}, \citealp{montgomery93}, \citealp{Fan1996}, \citealp{landsman98}, \citealp{Belloni98}, \citealp{VandenBerg2004_Chandra}, \citealp{Sarajedini2009}, \citealp{seigel14}, \citealp{Mooley2015}). Blue straggler stars (BSSs) are cluster members that are brighter, and bluer than stars on the upper main sequence (\citealp{1953Sandage}). The two main leading scenarios proposed for their formation are stellar collisions leading to mergers in high density environments (\citealp{Hills1976}) and mass transfer (MT) from an evolved donor to a lower-mass star in a binary system in low density environments (\citealp{McCrea1964}, \citealp{Chen2008}). An exceptionally large number of 24 BSSs are detected in M67 as compared to any other old open clusters (\citealp{Deng99}). Sub-subgiants (SSGs) are rather a new class of stars (\citealp{Geller2017}), which occupy a unique location in the colour-magnitude diagram (CMD), red ward of the main-sequence (MS) and fainter than the subgiants where normal single star evolution does not predict stars (\citealp{Geller2017_SSG}). Two SSGs (WOCS\footnote[1]{WOCS (WIYN open cluster study) ID is taken from \citet{Geller2015} and we refer to this ID in the entire text, and for stars that were not observed in their study we refer to \citet{montgomery93} with 'MMJ' ID.} 15028 and WOCS 13008) identified in the cluster are also X-ray sources (\citealp{Belloni98}, \citealp{Mathieu2003}). Yellow straggler stars (YSSs) fall above the subgiant branch in optical CMDs, between the BSSs and the red giants (RG). YSSs may represent a population of evolved BSSs (\citealp{Mathieu1990_SB22}, \citealp{Leiner2016}). Four YSSs (WOCS 2002, WOCS 2008, WOCS 1015 and WOCS 1112) often referred as yellow giants are observed in the cluster CMD (\citealp{Geller2015}). \citet{Landsman1997_S1040} detected one of the YSS (WOCS 2002) with a white dwarf companion, that has undergone a mass transfer, where as \citet{Leiner2016} conclude that a merger or collision is most likely to have occured in WOCS 1015 and thus YSSs are likely to be evolved BSSs. ROSAT, Chandra and XMM - Newton studies of the cluster detected at least 36 member stars with X-ray emission (\citealp{Belloni1993}, \citealp{Belloni98}, \citealp{VandenBerg2004_Chandra}, \citealp{Mooley2015}). Hence, M67 has both single and binary stars, along with some exotic stellar systems. A study of Ultraviolet (UV) characteristics of these stellar population will help in understanding their formation and evolution. Previous studies of this cluster in the UV has been done by \citet{landsman98} and \citet{seigel14}. \citet{landsman98} detected 20 stars in M67 which includes 11 BSSs, 7 WD candidates, a YSS$+$WD binary (WOCS 2002) and a non member using Ultraviolet Imaging Telescope (UIT). They also presented a semi-empirical integrated spectrum of M67 showing a domination of BSSs at shorter wavelengths than 2600 \AA\,. However, UIT images are not deep enough to detect fainter population of stars in the cluster. Recently, \citet{seigel14} studied M67 using the Ultraviolet Optical Telescope (UVOT) on Swift Gamma-Ray Burst Mission. They detected 10 BSSs along with a number of stars near the WD cooling sequence. They showed that UVOT could easily distinguish stellar population such as BSSs, WDs and young \& intermediate age MS stars. M67 is well studied in the optical and X-ray, though a deep study in the UV is lacking. The UV observations can detect the presence of possible hot companions that are not evident from optical photometry alone. The presence of a hot component to BSSs was detected by far-UV observations of NGC 188 by the HST (\citealp{gosnell15}). This provided the necessary observational evidence of MT as one of the formation mechanism of BSSs. \citet{2016Subramaniam} identified a post-HB/AGB companion to a BSS in NGC 188 with the help of far-UV and near-UV photometry from the Ultra Violet Imaging telescope (UVIT). In the case of M67, a deep UV study will help in identifying similar systems among the BSSs. The deep far-UV and near-UV data will help in understanding the UV properties of stars, that do not follow the standard single star evolution as well as those of normal stars. Galaxy Evolution Explorer (GALEX) observed this cluster in several pointings to produce deep images of this cluster. In this study, we use these images to understand the UV stellar population in M67. We present a comprehensive study of this cluster using FUV and NUV data from GALEX. In this study, we present the UV properties of optically detected members of M67 using GALEX photometry. The paper is structured as follows: The UV data and their optical counterparts are described in Section \ref{sec:data}. In section \ref{Analysis} we analyse the UV-Optical CMDs \& UV CMDs and focus on UV bright stars observed in GALEX. In Section \ref{discussion} we present the discussion and summarise with the conclusion in section \ref{Conclusions}. | \label{Conclusions} The main conclusions of this study can be summarised as follows: \begin{enumerate} \item{The first comprehensive UV properties of member stars of the old open cluster M67 are presented here. We have compiled the UV magnitudes of 449 stars (92 in the FUV and 424 in the NUV). We have provided an online catalog with FUV and NUV magnitudes, and classification of the detected member stars.} \item{16 BSSs, 3 WDs, 3 YSSs, one SSG, two RGs, 3 triple system in the FUV and 13 BSSs, 2 WDs, 2 YSSs, 2 SSGs and 1 triple system in the NUV.} \item {We detect a few lower MS stars to have large UV excess, suggesting that they could be MS+WD binaries. We identified 11 such systems, which are new identifications, with 7 showing FUV excess.} \item{ We also detect stars near the MSTO and subgiant branch to have excess flux in the FUV and/or NUV. This excess flux could be due to chromospheric activity. 15 stars are found to have relatively large excess in the FUV, which are found to be as bright as the BSSs in the FUV.} \item {The BSS in M67 span a large range in T$_{eff}$ and L/L$_{\sun}$, which is found to correlate well with the large range of FUV magnitude (14-23 mag). The FUV bright BSSs are found to be the hotter, luminous, and probably younger BSSs.} \item{The isochrones overlaid on the H-R diagram suggest that the group (a) including the two YSSs is very young (400 Myr - 1 Gyr). WOCS 2011 and WOCS 1006 could be the most recently formed BSS, good candidates to probe the BSS formation mechanism. The group (c) stars are likely to be the oldest among the BSS in M67. We suggest that the BSS in M67 are formed in the last 2.5 Gyr - 400 Myr, more or less continuously.} \item{We detect 2 RGs to have UV continuum excess as well as emission in the Mg II {\it h} +{\it k} lines from the IUE archival spectra. Along with the scatter of the RG stars in the NUV$-$V CMD, and the detection of stars with UV excess, we speculate that the RGs as well as a good fraction of stars in M67 could be chromospherically active. The bright BSSs stars are not found to be chromospherically active.} \end{enumerate} | 18 | 8 | 1808.06814 |
1808 | 1808.08724_arXiv.txt | { There is both observational and theoretical evidence that the ejecta of core-collapse supernovae (SNe) are structured. Rather than being smooth and homogeneous, the material is made of over-dense and under-dense regions of distinct composition. Here, we explore the effect of clumping on the SN radiation during the photospheric phase using 1-D non-local thermodynamic equilibrium radiative transfer and an ejecta model arising from a blue-supergiant explosion (yielding a Type II-peculiar SN). Neglecting chemical segregation, we adopt a velocity-dependent volume-filling factor approach that assumes that the clumps are small but does not change the column density along any sightline. We find that clumping boosts the recombination rate in the photospheric layers, leading to a faster recession of the photosphere, an increase in bolometric luminosity, and a reddening of the SN colors through enhanced blanketing. The SN bolometric light curve peaks earlier and transitions faster to the nebular phase. On the rise to maximum, the strongest luminosity contrast between our clumped and smooth models is obtained at the epoch when the photosphere has receded to ejecta layers where the clumping factor is only 0.5 -- this clumping factor may be larger in Nature. Clumping is seen to have a similar influence in a Type II-Plateau SN model. As we neglect both porosity and chemical segregation our models underestimate the true impact of clumping. These results warrant further study of the influence of clumping on the observables of other SN types during the photospheric phase. } | The diversity of core collapse supernova (SN) light curves arises from variations in the properties of the shocked progenitor envelope, and the subsequent balance between heating (radioactive decay and recombination) and cooling (expansion and radiation) processes (e.g. \citealt{FA77}). In the explosion of red-supergiant (RSG) stars which lead to Type II-Plateau SNe, the escaping radiation is dominated for several months by the release of the original shock-deposited energy, which is modestly degraded by expansion cooling. In the explosion of the more compact blue-supergiant (BSG) stars, which lead to Type II-peculiar SNe, the stronger expansion cooling produces a fainter SN at early times. The timescale and rate at which the SN subsequently brightens bears critical information about the mass and extent of the hydrogen envelope, the amount and distribution of \nifs, ejecta symmetries, and other progenitor and explosion properties (e.g. \citealt{sn1987A_rev_90}; \citealt{wongwathanarat_15_3d}). Because of the massive and more extended H-rich envelope this information is harder to decipher in Type II-Plateau SNe, although some information can be gleaned from polarization studies (e.g. \citealt{leonard_04dj_06}). There is both observational and theoretical evidence that the ejecta of core-collapse SNe, and SN\,1987A in particular, is structured on both large and small scales. Current radio observations of CO and SiO molecular line emission from the innermost regions of SN\,1987A reveal a clumpy asymmetric structure \citep{abellan_87A_17}. Nebular phase spectra require significant macroscopic mixing, often combined with a clumpy structure \citep{fransson_chevalier_89, spyromilio_87a_90,li_87A_93,jerkstand_87a_11,jerkstrand_04et_12}. A clumpy structure is also suggested by the observed fine-structure in the H$\alpha$ line profile at early times \citep{hanuschik_87a_88}. This `Bochum' event is further supported by the direction-dependent spectra of SN\,1987A observed via light echoes \citep{sinnott_87a_13}. Integral field spectroscopy applied to a selection of near-infrared lines also suggests a large scale asymmetry of the SN\,1987A ejecta \citep{kjaer_87a_10}. The smooth rising optical brightness and the high-energy radiation observed after about 200\,d in SN\,1987A suggest the mixing of \nifs\ out to $3000-4000$\,\kms\ (e.g. \citealt{sn1987A_rev_90}). Numerical simulations of core-collapse SN explosions suggest a strong breaking of spherical symmetry on small and large scales, both from the intrinsic multi-dimensional nature of the explosion mechanism and the shock wave propagation in a stratified massive star progenitor \citep{muller_87A_91,kifonidis_00,sasi_03,wongwathanarat_15_3d}. Despite the widespread knowledge that core-collapse SN ejecta are clumpy, light curve and spectral calculations during the photospheric phase generally assume a smooth ejecta. It is therefore of interest to investigate the impact of clumping on SN observables during the photospheric phase, particularly since multiple effects may produce similar changes in the light curve and spectra. In the next section, we present our numerical approach. In Section~\ref{sect_cl}, we discuss the treatment of clumping in our radiative transfer calculations, the relevant clumping scales for continuum and line radiation, as well as the limitations of our approach. In Section~\ref{sect_res}, we compare the smooth and clumped models Bsm and Bcl, including the differences in bolometric light curve, color, and spectral evolution. A comparison of the models with observation is made in Section~\ref{sect_comp_obs}. In this section we also argue that the early rise in SN\,1987A may be in part driven by ejecta clumping, rather than \nifs\ mixing alone as generally stated. Clumping can thus modulate the rate of energy release from Type II SN ejecta, impacting the photospheric phase duration and brightness. In Section~\ref{sect_disc}, we summarize our results and discuss how clumping might alter current inferences of ejecta properties across SN types and how this alteration might impact our model of the progenitor stars. | \label{sect_disc} We have presented non-local thermodynamic equilibrium time-dependent radiative transfer simulations for the ejecta resulting from a BSG explosion. The basic ejecta properties are broadly compatible with SN\,1987A. The goal of the paper was to describe the impact of ejecta clumping on SN radiation properties. With our 1-D treatment of clumping, which leaves unchanged the radial column density, the rate of recession of the photosphere is increased because of the greater recombination at the photosphere. The greater material density also leads to enhanced blanketing and redder optical colors. The impact on the spectral morphology is subtle, with a slight reduction of the H$\alpha$ emission and slight increase in metal line strength. Of all observables, the bolometric luminosity (or optical flux) is the most influenced, through an increase of at most $10-15$\,\% at 50\,d, a shorter rise to maximum, and an earlier transition to the nebular phase. This effect of clumping is analogous, for example, to what would occur if the ejecta had a lower mass or a greater helium mass fraction. The spectral peculiarities of SN\,1987A at 30\,d (abnormally weak H$\alpha$, absent H$\beta$, strong Ba\two\ lines) cannot be explained by time dependence, and are not compatible with a stronger \nifs\ mixing. They are, however, compatible with the effect of clumping, which in our simulations is probably too small -- the clumping factor at the photosphere at 30\,d is only 0.65 (over-density by a factor of 1.55 compared to the smooth model counterpart). Clumping, as currently implemented in \cmfgen, leads to a higher recombination rate, causing the faster recession of the photosphere and the faster release of stored internal energy. This is the main effect captured here. However, because our clumping is 1-D, it does not alter the (radial) column density and thus underestimates the impact that clumping would have (e.g. by introducing porosity). Even with clumping, we continue to assume chemical homogeneity while, for example, the \nifs\ rich material should be under-dense relative to the H-rich material. A porous medium in 3-D would thus impact the mean free path of $\gamma$-ray and optical photons differently. Porosity will exacerbate the effect of clumping described here. The linear polarization detected at early times in some Type II-Plateau SNe \citep{leonard_12aw_12} suggests the presence of inhomogeneities in the outer ejecta, thus further out than adopted here. We have performed a similar exploration for the RSG explosion model m15mlt3 of \citet{d13_sn2p}. We computed two such models of Type II-Plateau SNe (Rsm and Rcl) in an analogous fashion to what is described above for model Bsm and Bcl. Model Rsm is smooth (identical to m15mlt3) and model Rcl is clumped (we adopted $a=$\,0.1 and $b=$\,3000\,\kms). We found a very similar behaviour to Bsm versus Bcl simulations, although here the effect at early times is invisible due to the large SN brightness. However, at the end of the plateau (corresponding to the epoch of bolometric maximum in a Type II-peculiar SN), model Rcl is brighter by about 10\,\% and it also falls off the plateau (i.e., it enters the nebular phase) 10\,d earlier. Clumping might thus help resolve a problem with (smooth) \cmfgen\ SN II-Plateau models, because these tend to underestimate the brightness at the end of the plateau \citep{d13_sn2p}. It also suggests that clumping can impact the inferred ejecta mass of Type II-Plateau SNe since the ejecta mass is in part constrained by the plateau (or the photospheric phase) duration. Our smooth BSG explosion model Bsm systematically underestimates the Ba\two\ line strength observed in SN\,1987A, in spite of our time-dependent non-LTE treatment \citep{UC05,D08_time}. Increasing the Ba abundance by a factor of 5 has little impact on the predicted line strengths, primarily because the ionization of Ba remains too high. Clumping is a powerful means to reduce the ejecta ionization and enhance the strength of Ba\two\ lines after 20\,d. With time dependence, the ejecta ionization is maintained higher, which tends to inhibit recombination. In the simulations of \citet{D08_time}, assuming steady state yields an ejecta more recombined, hence with a lower radial optical depth. This process may be one reason why our \cmfgen\ simulations tend to yield a longer photospheric phase than in seemingly identical radiation hydrodynamics simulations with a simplified treatment of the gas \citep{utrobin_etal_15}. This issue requires further study. In this study, the properties for clumping (depth dependence and magnitude) were largely ad-hoc. Enhancing the magnitude and extent of clumping exacerbates its impact. In the future, we will need to perform a systematic study to quantify the impact of clumping for different clumping properties. We will also need to seek constraints from high-resolution 3D explosion simulations, in which both large scale and small scale inhomogeneities are resolved. The effects of clumping discussed here for Type II SNe may be relevant for other SN ejecta and SN types. Although not modeled here and therefore speculative, clumping may help to resolve the discrepancy between the mass inferred for SN Ibc \citep{drout_11_ibc} and those expected from single W-R stars. The luminosity boost caused by clumping in our Bcl and Rcl models may also explain why some standard SNe Ibc have abnormally large inferred \nifs\ masses \citep{drout_11_ibc}. At present, while one can explain easily the production of Type IIb/Ib SNe through the binary channel \citep{yoon_ib_17}, the origin of Type Ic SNe remains debated. Continued evidence supports the notion that SNe Ic must come from higher-mass progenitors, including single W-R stars \citep{maund_snibc_18}. Clumping, which to this day has never been treated in light curve calculations, may afford larger ejecta masses that may help resolve this long standing problem. | 18 | 8 | 1808.08724 |
1808 | 1808.10633_arXiv.txt | {In galaxy clusters, modern radio interferometers observe non-thermal radio sources with unprecedented spatial and spectral resolution. For the first time, the new data allows to infer the structure of the intra-cluster magnetic fields on small scales via Faraday tomography. This leap forward demands new numerical models for the amplification of magnetic fields in cosmic structure formation - the cosmological magnetic dynamo. Here we present a novel numerical approach to astrophyiscal MHD simulations aimed to resolve this small-scale dynamo in future cosmological simulations. As a first step, we implement a fifth order WENO scheme in the new code \wombat. We show that this scheme doubles the effective resolution of the simulation and is thus less expensive than common second order schemes. \wombat uses a novel approach to parallelization and load balancing developed in collaboration with performance engineers at Cray Inc. This will allow us scale simulation to the exaflop regime and achieve kpc resolution in future cosmological simulations of galaxy clusters. Here we demonstrate the excellent scaling properties of the code and argue that resolved simulations of the cosmological small scale dynamo within the whole virial radius are possible in the next years.} \keyword{galaxy clusters; magnetic fields; numerical methods; magneto-hydrodynamics} \begin{document} | Most of the Baryonic matter in our Universe is in the form of magnetized plasma. Hence, astronomers observe the signature of astrophysical magnetic fields from the solar system to the large scale structure. In galaxy clusters, radio telescopes detect the synchrotron radiation ($50 \,\mathrm{MHz} - 30 \,\mathrm{GHz}$) emitted by relativistic electrons ($\gamma > 1000$) gyrating in the magnetic field ($B \sim 1 \,\mu\mathrm{G}$) of the intra-cluster-medium (ICM), a hot and underdense plasma ($T\sim10^8\,\mathrm{K}, n_\mathrm{th} \sim 10^{-3}\,\mathrm{cm}^{-3}$). The next generation of radio interferometers will infer the three dimensional structure of the field through \emph{Faraday tomography} on kpc scales. This represents a first serious probe of the small scale properties of the whole intra-cluster-medium that demands detailed predictions to interpret the new data. As radio brightness is not strongly correlated with thermal density, upcoming studies will probe the whole virial volume of a cluster. \par The ICM itself is a weakly-collisional plasma, whose micro-physical properties are set by turbulence and electromagnetic interactions (plasma-waves), not particle Coulomb scattering \citep{2007mhet.book...85S}. Thus the magnetic field plays a crucial role in making the medium ''collisional'' on large scales, i.e. behave like a magnetised fluid \citep{2007MNRAS.378..245B}. In the currently favoured model of the ICM, the evolution of the magnetic field is governed by a turbulent small-scale dynamo that grows small seed fields at high redshift ($B \sim 10^{-13} \,\mathrm{G}$) into $\mu$G fields via an inverse cascade at the Alfv\'{e}n scale of the medium \citep{sch05,po15}. In merging galaxy clusters the Alfv\'{e}n scale\footnote{The scale where magnetic and turbulent pressure are comparable, i.e. where the Lorentz force becomes important \citep{1995ApJ...438..763G}} reaches a few kpc, thus it is now in range of next-generation radio interferometers for Faraday tomography studies. \par The strength and geometry of the magnetic field is set by the local seeding and turbulence history of the gas parcel under consideration, thus the new data demands numerical simulations to compare with expectations from dynamo theory. However, the nature of the small scale dynamo has made it very difficult to obtain accurate numerical models for the ICM magnetic field \citep{bm16}. The crucial time scale of magnetic field growth is set by the smallest length scale available in the turbulent system, where the eddy turnover time is smallest. In nature, this can be far below pc scale, in simulations this is at best the resolution scale. Current state-of-the-art Eulerian simulations start seeing numerical effects below scales of 10 kpc, Lagrangian simulations reach better resolution in the cluster center, but do not come close at the cluster outskirts due to density adaptivity (see Donnert et al., subm. to SSRv for a review). Thus resolving the Alfv\'{e}n scale at ~3 kpc in the whole cluster volume and faithfully evolving the magnetic field through structure formation is not possible with current community codes. \par In the preferred Eulerian approach, such simulations would require $\sim4096^3$ zones inside the virial radius, run with a highly accurate finite volume or finite difference scheme. This translates into 50--100 TBytes of memory and would generate 1--4 PByte of data. This is well in range of current Petascale and upcoming Exascale supercomputers, but requires near ideal weak scaling of the simulation code to 5--10 thousand compute nodes. Current state-of-the-art simulations typically run on a few thousand nodes, to maximize parallel efficiency \citep{2014ApJ...782...21M}. Hence, it stands to reason that in practice resolutions close the Alfv\'{e}n scale in the ICM will be challenging to achieve with current codes. \par Here we present a performance-aware implementation of the a fifth order constrained transport weighted essentially non-oscillatory (WENO) scheme in the scalable \wombat code\footnote{\url{wombatcode.org}}. This implementation represents a first step towards simulations of the small-scale dynamo in the ICM in a cosmological framework that resolve the Alfv\'{e}n scale. We will show that WENO doubles the effective resolution of the simulation, but is only a factor 10 more computationally expensive than commonly used 2nd order schemes at the same resolution. Hence it is a more efficent algorithm. \wombat itself is an on-going research effort of performance engineers at Cray Inc. to maximize computational efficiency on upcoming exascale systems \citep{2017ApJS..228...23M}. We will show that the new code indeed achieves excellent performance on large supercomputers. | We have presented a new implementation of a fifth order WENO5 scheme for constrained transport magneto-hydrodynamics in the \wombat framework. Our code is aimed at the simulation of cosmic magnetic fields in galaxy clusters, in particular the turbulent small-scale dynamo in the ICM and its Faraday tomography signal. We have motivated the need for new community codes for this particular problem as supercomputers enter the exasflops regime. We have given a concise overview of the WENO5 algorithm and the implementation in \wombat. Finally we shown a few code tests with the new code and argued that the algorithm represents an efficiency optimum as it doubles the effective resolution compared to second order codes common in the field today. We have also shown that given the same resolution, WENO5 resolves instabilities better than second order TVD+CTU and improves on magnetic energy conservation. Finally we have shown cache optimization tests and demonstrated excellent weak scaling of the code up to realistic problem sizes of 4.5 billion zones on a current Cray XC40 supercomputer. Thus we are confident that accurate predictions of the magnetic field distribution in galaxy clusters from the small scale dynamo with resolved Alfv\'{e}n scale are within reach in the next 2 years. | 18 | 8 | 1808.10633 |
1808 | 1808.07435_arXiv.txt | We present an analysis of the narrow Fe~K$\alpha$ line in {\em Chandra}/HETGS observations of the Seyfert AGN, NGC 4151. The sensitivity and resolution afforded by the gratings reveal {\it asymmetry} in this line. Models including weak Doppler boosting, gravitational red-shifts, and scattering are generally preferred over Gaussians at the $5\sigma$ level of confidence, and generally measure radii consistent with $R\simeq 500-1000~GM_{BH}/c^{2}$. Separate fits to ``high/unobscured'' and ``low/obscured'' phases reveal that the line originates at smaller radii in high flux states; model-independent tests indicate that this effect is significant at the 4--5$\sigma$ level. Some models and $\Delta t\simeq 2\times 10^{4}$~s variations in line flux suggest that the narrow Fe~K$\alpha$ line may originate at radii as small as $R\simeq 50-130~GM_{BH}/c^{2}$ in high flux states. These results indicate that the {\em narrow} Fe~K$\alpha$ line in NGC 4151 is primarily excited in the innermost part of the optical broad line region (BLR), or X-ray BLR. Alternatively, a warp could provide the solid angle needed to enhance Fe~K$\alpha$ line emission from intermediate radii, and might resolve an apparent discrepancy in the inclination of the innermost and outer disk in NGC 4151. Both warps and the BLR may originate through radiation pressure, so these explanations may be linked. We discuss our results in detail, and consider the potential for future observations with {\em Chandra}, {\em XARM}, and {\em ATHENA} to measure black hole masses and to study the intermediate disk in AGN using narrow Fe~K$\alpha$ emission lines. | In many respects, NGC 4151 is a normal, if not a standard or archetype Seyfert-1 active galactic nucleus (AGN). The host galaxy is a (weakly) barred Sab at a redshift $z=0.00332$ (Bentz et al.\ 2006), or approximately 19 Mpc via dust parallax (Honig et al.\ 2014). The spectra and variability of the radiation produced from accretion onto the central black hole have been studied extensively. Indeed, NGC 4151 was among the first Seyfert-I AGN wherein strong correlations between continuum bands and high ionization lines were detected (e.g., Gaskell \& Sparke 1986). The 5 light-day delay detected in early data is echoed in recent efforts: Bentz et al.\ (2006) measure a delay of $6.6^{+1.1}_{-0.8}$~days between the 5100\AA~ continuum and H$\beta$ line, giving a ``broad line region'' (BLR) reverberation mass for the black hole of $M_{BH} = 4.6^{+0.6}_{-0.5}\times 10^{7}~M_{\odot}$. An updated estimate, including the latest information on scale factors in reverberations studies, gives $M_{BH} = 3.6^{+0.4}_{-0.4}\times 10^{7}~M_{\odot}$ (Bentz \& Katz 2015). NGC 4151 also appears to be a normal Seyfert-I in terms of its radio properties. It is ``radio-quiet'', meaning that any jet emission is relatively unimportant compared to the energetic output of the accretion disk. A combination of VLBA and large-dish radio campaigns have studied the central region of NGC 4151 at high angular resulotion and high sensitivity. The central source has a flux density of just 3~mJy, and a size less than 0.035~pc (Ulvestad et al.\ 2005); this is only 10 times the size of the optical ``broad line region'' and much smaller than a typical pc-scale torus geometry. On arcsecond scales, the radio emission takes the form of a two-sided radio jet, but the outflow speed is constrained to be $v_{jet} \leq 0.16c$ and $v_{jet} \leq 0.028c$ for distances of 0.16 and 6.8~pc from the nucleus (Ulvestad et a.\ 2005). NGC 4151 is also understood well on larger scales. {\it Hubble} spectroscopy strongly suggests that the optical narrow line region (NLR) takes the form of a biconical outflow, at an inclination of $45^{\circ}\pm5^{\circ}$ relative to our line of sight (Das et al.\ 2005). This inclination is consistent with the fact that both sides of a low-velocity radio jet are observed; higher inclinations and/or higher velocities might boost the counter jet out of the observed band. The NLR is also resolved in soft X-ray images obtained with {\it Chandra}. The diffuse X-ray emission appears to be dominated by photoionization from the nucleus, and the overall morphology and energetics are consistent with a biconical outflow with a kinetic luminsosity that is just 0.3\% of the bolometric radiative luminosity of the central engine (e.g., Wang et al.\ 2011). X-ray emission from the central engine in NGC 4151 paints a different picture than that obtained in other wavelengths, and on larger scales. The soft X-ray spectrum of NGC 4151 is sometimes heavily obscured; complex, multi-zone absorption is required in these phases (e.g., Couto et al.\ 2016, Beuchert et al.\ 2017). Spectra such as this are typically obtained from Seyfert-2 AGN, wherein the ``torus'' blocks most of the direct emission from the central engine. Since the fraction of Compton-thin AGN in the local universe is about 0.5 and the average viewing angle of a disk in three dimensions is $\theta = 60^{\circ}$ (e.g., Georgakakis et al.\ 2017), obscuration is likely tied to higher viewing angles. The detection of highly obscured X-ray spectra in NGC 4151 nominally indicates that its accretion flow is observed at a {\it higher} inclination than indicated by its NLR. It is unclear if simple inferences about viewing angles hold when the obscuration is observed to be highly variable. In NGC 4151, there are phases wherein the continuum flux is higher and the obscuration is greatly reduced. If the torus is clumpy or irregular, and if our line of sight to the central engine were to merely graze this structure, periods of different obscuration might result. The fact that changes in NGC 4151 can occur fairly quickly -- within months and years -- indicates that at least some of the obscuration in NGC 4151 is closer than torus. Rather, it may originate as close as the optical BLR, or even closer. This may not be unique to NGC 4151; even in some bona fide Seyfert-2 AGN, there are indications that the obscuration is much closer than the torus (e.g. Elvis et al.\ 2004). It has been apparent for some time that the optical BLR can be divided into low-ionization and high-ionization regions (e.g., Collin-Souffrin et al.\ 1988, Kolatchny et al.\ 2003). Whereas the high-ionization lines are often shifted with respect to the host frame and likely originate in a wind, the low-ionization lines are typically not shifted and may originate closer to the disk surface. In at least some cases (perhaps those viewed at low inclination angles), double-peaked emission lines consistent with photoionization of the accretion disk are observed, strongly suggesting a close association with the disk itself (e.g., Eracleous \& Halpern 2003). This complexity may be echoed in X-ray studies. Some highly ionized X-ray ``warm absorbers'' appear to be coincident with the optical BLR (e.g., Mehdipour et al.\ 2017). However, X-rays also indicate that cold, dense gas is cospatial in this region. A systematic study of narrow Fe K$\alpha$ lines observed with the {\it Chandra}/HETGS was undertaken by Shu et al.\ (2010); the width of the observed lines varies considerably, but most lines signal contributions from radii consistent with the BLR. Studies that probe the regions closest to the black hole in NGC 4151 -- near to the innermost stable circular orbit (ISCO) -- give a different view of this AGN. Recent efforts to study this regime using time-averaged, flux- and time-selected intervals, and even reverberation lag spectra demand that the innermost disk is viewed at a {\em low} inclination with respect to the line of sight. The most complete analysis, including data from several missions and models that allow for complex, multi-zone absorption at low energy, measures an inclination of just $\theta = 3^{+6}_{-3}$~degrees (Beuchert et al.\ 2017; also see Keck et al.\ 2015, Cackett et al.\ 2014, and Zoghbi et al.\ 2012). The simplest picture that can be constructed from AGN unification schemes (e.g., Antonucci 1993, Urry \& Padovani 1995, Urry 2003) is likely one where the angular momentum vectors and/or symmetry axes of the black hole, accretion disk, BLR, torus, and NLR are all aligned. Potential causes of misalignment include super-Eddington accretion (e.g., Maloney, Begelman, \& Pringle 1996) and binarity (e.g, Nguyen \& Bogdanovic 2016). Therefore, evidence of misalignment in a given AGN is potentially an important clue to recent changes in the accretion flow and/or the recent evolution of the AGN. If a corresponding warp or transition region exposes more cold gas to the central engine than a flat disk would at the same radius, a characteristic Fe~K emission line may be produced. The same warp may help to launch a wind, providing a potential connection to the BLR. Motivated by the need to better understand the nature and origin of the BLR in Seyferts, and by the potentially linked question of a misalignment of the innermost and outer accretion flows in NGC 4151, we have undertaken a dedicated study of the narrow Fe~K$\alpha$ line in this source. In order to achieve the best possible combination of sensitivity and resolution, we have restricted our analysis to obserations made using the {\it Chandra}/HETGS. In section 2, we detail the observations that we have considered, and the methods by which the data are reduced. Section 3 summarizes the different analyses that are attempted using a variety of techniques, models, and data selections, and the results. In Section 4, we discuss these results in a broader context and highlight potential future investigations. | We have analyzed deep {\it Chandra}/HETG spectra of the Seyfert-1 AGN, NGC 4151. We find that the narrow Fe~K$\alpha$ emission line -- sometimes associated with the torus or outer optical BLR in Seyferts -- is asymmetric and likely shaped at least partially by Doppler shifts and weak gravitational red-shifts. Many of the models that we considered suggest that the line originates approximately $R\simeq 500-1000~ GM/c^{2}$; this region is already closer to the black hole than the optical BLR, and may be tied to a kind of X-ray broad line region (or, XBLR). If so, it is the first time that dynamical imprints have clearly revealed this region in X-rays. Some spectral fits suggest that the line could arise at radii as small as $R\simeq 50-100~ GM/c^{2}$; this appears to be weakly confirmed by independent variability signatures. Changes in the shape (and, production radius) of the line between ``high/unobscured'' and ``low/obscured'' phases, and on shorter times within the ``high/unobscured'' state, pose some challenges. In this section, we review the strengths and limitations of our analysis and results, discuss how our work impacts our understanding of NGC 4151 and Seyferts in general, and explore the potential for future observations to build on our work. \subsection{Central results} We made fits to the narrow Fe~K$\alpha$ emission line in NGC 4151 using many different models (see Table 2 and Table 3). Simple fits with Gaussians did not fit the data well. Similarly, fits with models that attempt to account for scattering in dense media and/or ionization effects also failed to deliver acceptable fits. In all cases, some degree of dynamical broadening is required by the data. Fits with the ``diskline'' model (Fabian et al.\ 1989) suggest that the narrow Fe~K$\alpha$ line may originate as close as $R = 50~GM/c^{2}$ from the black hole, or potentially even closer. When the line is fit with a ``mytorus'' function (Murphy \& Yaqoob 2009, Yaqoob \& Murphy 2010) that includes distortions to the line shape from scattering in dense media, the required dynamical broadening is consistent with $R\simeq 1000~GM/c^{2}$ in the summed and ``high/unobscured'' phase data when the emissivity is fixed at $q=3$ as per simple expectations far from a black hole (the radius is largely unconstrained in the ``low/unobscured'' phase). Separate fits with flatter emissivity profiles return smaller radii but do not represent statistically significant improvements. Fits to the summed and ``high/unobscured'' spectra with a dynamically broadened ``pexmon'' reflection model (Nandra et al.\ 2007) also measure radii consistent with $R\simeq 1000~M/c^{2}$. However, fits with the ``relxill'' model (Garcia et al.\ 2013) are statistically superior and require smaller radii consistent with $R\simeq 500~ GM/c^{2}$, and much smaller radii are not strongly excluded. In short, radii as small as $R = 50-100~GM/c^{2}$ are allowed by the data but are only marginally preferred over radii of $R = 500-1000~ GM/c^{2}$. As noted in Section 1, Bentz et al.\ (2007) used optical BLR reverberation to derive the mass of the central black hole in NGC 4151. Variations in the H$\beta$ line are found to lag variations in the 5100\AA~ continuum by $\tau = 6.6^{+1.1}_{-0.8}$ days. The size of the H$\beta$ region can then be estimated in units of gravitational radii via $c\tau / R_{g}$, where $R_{g} = GM_{BH}/c^{2}$. This simplistic estimate gives $R_{H\beta} = 3200^{+600}_{-400}~R_{g}$ for $M_{BH} = 3.6\times 10^{7}~ M_{\odot}$. Our results clearly suggest that the narrow Fe~K$\alpha$ line in NGC 4151 originates at a radius that is at least a factor of a few -- and possibly an order of magnitude -- smaller than the optical BLR (at least in the ``high/unobscured'' state). The narrow Fe~K$\alpha$ line might be regarded as originating in a distinct XBLR; however, it is already clear that the BLR is a complex, stratified goemetry, and the narrow Fe~K$\alpha$ line could also be regarded as simply arising in its innermost extent. In all of the fits that we made to the narrow Fe~K$\alpha$ line in NGC 4151, a low inclination is strongly preferred in a statistical sense. The best-fit ``diskline'' and dynamically-broadened ``mytorus'' models for the ``high/unobscured'' state spectrum both give $\theta = 9(1)$~degrees (see Table 2). The best-fit reflection models for the ``high/unobscured'' spectrum measure $\theta = 3(3)$~degrees and $\theta = 8(2)$~degrees (see Table 3). Error bars are much larger in fits to the ``low/unobscured'' state but values are again small, and broadly consistent with the results obtained in the more sensitive spectra. The inclination of the intermediate disk, then, appears to be more consistent with values obtained via reflection studies of the innermost disk (see, e.g., Keck et al.\ 2015, Beuchert et al.\ 2017; also see Cackett et al.\ 2014), than with the inclination of the optical NLR ($\theta = 45\pm5$~degrees; Das et al.\ 2005). It is possible that a warp in the accretion disk -- potentially tied to the BLR -- could be the origin of this discrepancy. In this case, the region of the BLR that is traced by the narrow Fe~K$\alpha$ line would still be aligned with the innermost disk (perhaps anchored into the black hole spin plane by GRMHD effects), and the warp must occur further out in the BLR or outer disk. The warp would likely have to be more extreme than the one detected in NGC 4258, which only deviates from the midplane by $\Delta\theta = 4$~degrees (Moran et al.\ 1995). Warps can be excited through radiation pressure (e.g., Maloney et al.\ 1996). However, warps and other asymmetries in AGN accretion disks, including orbital eccentricities and spiral arm structures, can be excited by the tidal effects of a binary companion or the orbital passage of a massive stellar cluster (e.g., Chakrabarti \& Wiita 1993, 1994). It is at least remotely possible, then, that the observed inclination discrepancy is excited by another black hole or a massive stellar cluster. There is currently no evidence of a binary black hole system in NGC 4151, but the system has many pecularities. Future monitoring of NGC 4151 in multiple bands, and eventually with high-resolution X-ray spectroscopy, can help to definitively rule out a binary black hole system. It may be as interesting -- and more productive -- to explore if the passage of a massive stellar cluster can be detected or rejected. Time-averaged spectroscopy and reverberation results strongly suggest that the accretion disk extends close to the ISCO in NGC 4151 (e.g., Zoghbi et al.\ 2012, Keck et al.\ 2015, Beuchert et al.\ 2017). The fact of a narrow Fe~K$\alpha$ line with mild relativistic shaping merely points to an intermediate disk structure. Our modeling is insensitive to reflection from the innermost accretion disk, and our results do not imply that the accretion disk is truncated at intermediate radii. \subsection{Long term variability and radius variations} Lines excited by radiation from central engine are expected to follow $R \propto L^{1/2}$. This trend is certainly observed in studies of the optical continuum and high-ionization optical lines linked to the BLR, including H$\beta$ in NGC 4151 (e.g., Bentz et al.\ 2013). Indeed, the tight relationship between AGN luminosity and BLR size suggests that the BLR may originate in the disk itself and generate a failed wind. Some of our fits nominally suggest an {\it inverse} relationship between the X-ray continuum and the radius at which the narrow Fe~K$\alpha$ line is produced. If this line is tied to the innermost extent of the BLR or XBLR, it would suggest that the inner radius is changing, or that the radius at which the line is detectable is changing in an unexpected manner. It is therefore worth critically examining the data, and exploring possible explanations. Evidence of dynamical broadening of the Fe~K$\alpha$ line is strongest in the summed spectrum, and in the ``high/unobscured'' state; the evidence is weaker in the ``low/obscured'' phase. Accordingly, direct spectral fits to the ``low/obscured'' state with various models yield correspondingly larger errors on the line production region (see Tables 2 and 3). However, the ``high/unobscured'' minus ``low/obscured'' {\it difference} spectrum makes clear that the narrow Fe~K$\alpha$ line is more skewed -- and originates at smaller radii -- in the ``high/unobscured'' state (see Section 3.7 and Figure 4). Fits to this difference spectrum nominally indicate that a fairly narrow range of radii may be emphasized in the ``high/unobscured'' state. This could indicate changes in the local disk structure that enhance reflection; warps and clumpy, failed winds may be viable explanations. Structures of this sort might help to explain evidence of a second reprocessing in NGC 4151, based on UV and X-ray monitoring (Edelson et al.\ 2017). The physical processes that could underpin such explanations may reach to the nature and origin of the BLR: High ionization optical lines in the BLR are likely produced at a greater height above the disk than lower-ionization optical lines; this is consistent with a wind that has had the chance to flow some distance (e.g., Collin-Souffrin et al.\ 1998, Kolatchny et al.\ 2003; also see Czery et al.\ 2016). The relatively simple and unobscured path for radiation between the central engine and optical BLR high above the disk means that $R\propto L^{1/2}$ can play out. This expected radius--luminosity relationship implicitly assumes that the geometry of the irradiated gas, and relevant optical depths, do not change in response to flux variations from the central engine. This assumption may not be valid for the narrow Fe~K$\alpha$ line in some Seyferts. At least in NGC 4151, the narrow Fe~K$\alpha$ line now appears to originate at smaller radii than the optical BLR, though it traces cold gas (where dust may be present). It has been suggested that the BLR may be exist at least partially owing to the influence of dust: the higher cross section of dust relative to gas may be the key to lifting material above the disk (see, e.g., Czerny et al.\ 2011, Czerny et al.\ 2016). It is possible, then, that the narrow Fe~K$\alpha$ traces the region where dust and gas are initially lifted upward. The enhanced local solid angle creted through this process might mimic a warp, but it is also the case that dust can be an important factor in creating actual warps within disks (Maloney et al.\ 1996). Enhanced radiation from the central engine might eventually destroy dust within a larger radius, reducing contributions to the Fe~K$\alpha$ line from small radii. However, the enhanced local solid angle might also shield larger radii from the central engine and serve to limit narrower contributions to the Fe~K$\alpha$ emission line. At least one aspect of this explanation can be explored quantitatively. Czerny et al. (2016) predict the dust sublimation radius -- possibly the effective inner edge of the BLR -- as a function of black hole mass and Eddington fraction. Based on UV and X-ray data, Crenshaw et al.\ (2015) report that NGC 4151 has an average bolometric luminosity of $L_{bol} = 7.4\times 10^{43}~ {\rm erg}~ {\rm s}^{-1}$. Assuming a mass of $3.6\times 10^{7}~M_{\odot}$ (Bentz \& Katz 2015), this equates to an Eddington fraction of $L_{bol}/L_{Edd} \simeq 0.016$. The work by Czerny et al.\ (2016) then predicts a dust sublimation radius of $R_{dust} \simeq 1-2\times 10^{16}~ {\rm cm}$, or $R_{dust} \simeq 1900-3800~ GM/c^{2}$. This radius is at least a factor of a larger than our estimates based on fits to the narrow Fe~K$\alpha$ line, and possibly an order of magnitude larger. Given the numerous uncertainties in the input parameters, however, the prediction might be regarded as broadly consistent with our results. Further development of the Czerny et al.\ (2016) model incorporating explicit consideration of Fe~K$\alpha$ line production, and more sensitive data, may be able to formally reconcile the details. \subsection{Mass Estimates via the Narrow Fe K$\alpha$ Line} Within the ``high/unobscured'' state, the continuum flux is highly variable (see Figure 5). Selecting the ``crests'' and ``troughs'' of the light curve (periods greater than 4\% above and below the mean), direct fits to the separate spectra reveal variations in line flux that are significant at the $3\sigma$ level of confidence (see Section 3.8). The ``crests-troughs'' difference spectrum also reveals an Fe~K$\alpha$ line significant at the $3\sigma$ level of confidence (see Figure 6). This signals that the line is responding to the continuum variations on the characteristic time scale of the variability ($\Delta t = 23.0$~ks), independently indicating that inner extent of the line production region may be as small as $R\simeq 130~GM/c^{2}$, or even smaller. Potentially coupled variability in the X-ray continuum and narrow Fe~K$\alpha$ line, combined with the ability measure subtle dynamical shaping of the line, opens the possibility of adapting optical BLR reverberation techniques and measuring black hole masses in X-rays. Whether the narrow Fe~K$\alpha$ line originates in the disk, in a wind, or in a combination of these that marks the innermost extent of the BLR, the local gas motions are likely to be largely Keplerian. In this case, the black hole mass can be estimated by: \[M_{BH} \propto rv^{2}/G\] \noindent where $M_{BH}$ is the mass of the black hole, $r$ is the radius (in physical units) where the line is produced, $v$ is the {\it full} velocity of the gas, and $G$ is Newton's gravitional constant. In the limit of excellent data, fits with a relativistic line model (or, reflection model modified by dynamical broadening) will give tight constraints on the innermost line production radius. These models map the radius in units of gravitational radii, $GM/c^{2}$. The full velocity in Keplerian orbits is then given by $v^{2}/c^{2} = 1/N$, where $N$ counts the number of gravitational radii. Thus, the velocity $v$ can actually be deduced through the radius in gravitational units. The radius $r$ must be in physical units, however, and obtained from the characteristic variability timescale: $r = c\Delta t$. The overall best-fit model for the Fe~K$\alpha$ line in the variable ``high/unobscured'' phase of NGC 4151 is obtained with ``relxill'' (see Table 3), which measures an inner line production radius of $R = 520^{+10}_{-350}~ GM/c^{2}$. Again assuming $\Delta t = 23.0$~ks, a black hole mass of $M_{BH} = 0.9-2.6\times 10^{7}~M_{\odot}$ results. This mass is 1.4--4.0 times lower than that derived by Bentz \& Katz (2015) using optical reverberation techniques, but the difference is comparable o the scatter of the $M-\sigma$ relationship (0.46 dex, Gultekin et al.\ 2009). Higher mass estimates result from smaller estimates of the Fe~K$\alpha$ line emission radius. Some aspects of our analysis point to smaller radii, especially within the ``high/unobscured'' state; additional data and improved modeling may strengthen these hints and could potentially result in higher mass estimates. Estimates of this sort are at the limit of the {\it Chandra} data that have been obtained so far. The sensitivity of these data curtails the quality of the radius constraints that can be obtained, in part because various plausible models are not differentiated at a high level of statistical confidence. More precise radii should be readily obtained from nearby Seyferts using the calorimeter spectrometers aboard {\it XARM} and {\it ATHENA} (see below). However, further observations of NGC 4151 and other Seyferts with {\it Chandra}, and more distant and/or fainter Seyferts with {\it XARM}, may result in data of similar quality. In this case, it may be pragmatic to adapt the technique to rely on simpler line models and measurements of the inclination. The {\it observed} width of the Fe~K$\alpha$ line -- as measured by a Gaussian -- does not reflect the full velocity that is required in the equation. Rather, $v_{obs.} = v_{Kepl.}\times {\rm sin}(\theta)$, where $\theta$ is the inclination of the disk relative to the line of sight. If the narrow Fe K$\alpha$ line at 6.40~keV is crudely fit with a simple Gaussian function that gives the width $\sigma$ of the line in units of eV, then the full velocity would be \[v = (c\sigma/6400)/sin(\theta).\] The shifts that relativistic orbital motion imprint onto line profiles depend on the depth of the local potential, and the inclination at which the disk is viewed. Thus, in cases where the narrow Fe~K$\alpha$ line is asymmetric and can constrain the parameters of a relativistic line model, the inclination $\theta$ can be measured directly. In other cases, it may be more pragmatic to take a value of $\theta$ from fits to reflection from the innermost accretion disk, close to the ISCO. {\it Physical} radii cannot be determined using relativistic line models; the line shifts only depend on the radius in units of $GM/c^{2}$. Again writing the radius in physical units via $r = c\Delta t$, where $\Delta t$ is the characteristic timescale on which the line varies. Then, \[M_{BH} \propto (c\Delta t) (c\sigma/6400)^{2}/ G sin^{2}(\theta).\] \noindent To be clear, the inclination is taken from fits to the data with a relativistic line function (or independent fits to reflection from the innermost disk), and the gas velocity $\sigma$ is measured from separate fits to the data with a simple Gaussian function. Sensible minimal requirements for estimating a black hole mass using this method might include flux variability in the continuum and Fe~K$\alpha$ line, and exposure durations that sample enough eposides of the variability. When implemented in this manner, we expect that the errors on mass will be driven by the errors on the inclination, $\theta$. These errors will also be minimized in high-resolution, calorimeter spectra. In the case of NGC 4151, Gaussian fits to all of the summed, and time-averaged spectra from the ``high/unobscured'' and ``low/obscured'' states are consistent with $\sigma = 23(2)$~eV. However, it is more appropriate to use the variable line width of $\sigma = 55^{+42}_{-22}$~eV, based on the ``crests-troughs'' difference spectrum obtained in the ``high/unobscured'' state. Again, the mean time beteen the ``crests'' and ``troughs'' of the light curve is $\Delta t = 23.0$~ks. We made numerous fits with several different models, but the average of the centroid values derived in models allowing for dynamical broadening in the ``high/unobscured'' state is $\theta = 7.7$~degrees. These numbers yield a black hole mass of $M = 0.7-6.0 \times 10^{7}~M_{\odot}$. This estimate is formally consisent with the optical BLR reverberation mass, but with a larger uncertainty. It must be noted that the estimate is very sensitive to the inclination. The estimates explored here should likely not be regarded as measurements, but rather as early proofs-of-principle. For instance, the characteristic time scale used in these calculations is treated as a delay time, but only a small number of variations have been observed. The characteristic time scale could have a different explanation tied to accretion phenomena at smaller radii; in that case, it may still be possible to derive masses, but the origin of the characteristic time scale will have to be understood in terms of thermal or viscous times. If reverberation from the XBLR using Fe K$\alpha$ lines proves viable, the improved sensitivity of the X-ray calorimeter spectrometers aboard $XARM$ and {\it ATHENA} may enable mass estimates via this means in a large set of AGN (see below). \subsection{Comparisons to prior work} Shu et al.\ (2010) examined narrow Fe~K$\alpha$ emission lines in a set of Seyfert AGN observed with the {\it Chandra}/HETGS. The summed line profile in NGC 4151 is found to have a width of $FHWM = 2250^{+400}_{-360}$~km/s. Our measurement of the width using Gaussian models to the time-averaged summed spectrum produces formally consistent results. Via Gaussian modeling, then, the FWHM suggests a region with a size of $R_{Fe~K\alpha} = 17800^{+7400}_{-5000}~ R_{g}$. This is nominally several times {\it larger} than the H$\beta$ line region inferred from via optical reverberation mapping. Our work expands upon that undertaken by Shu et al.\ (2010) in numerous ways. Among these is that we considered additional observations (ObsIDs 16089, 16090; see Table 1), we binned the data more aggressively and employed improved weighting techniques, we examined a broad array of non-Gaussian functions that allow for asymmetry driven by dynamical effects and scattering, and we examined the variability of the line in numerous ways. Our results suggest that the Gaussians employed by Shu et al.\ (2010) measured projected velocities that are a small fraction of the full velocity because the central engine is viewed at a low inclination. Improved modeling that accounts for inclination effects places the narrow Fe~K$\alpha$ line production region within the optical BLR, or likely at even smaller radii. It is possible to utilize higher order {\it Chandra}/HETG spectra to better understand some sources (see, e.g., Miller et al.\ 2015, 2016). In the Fe~K band, the resolution of third-order HEG spectra is approximately 15~eV, midway between the resolution of the first-order {\it Chandra} HEG and that anticipated with {\it XARM}. Liu (2016) considered the third-order HEG spectrum of NGC 4151, in an effort to better understand the true velocity width of the Fe~K$\alpha$ line. Indeed, the best-fit Gaussian model for the the line in the third-order spectrum was nominally measured to be narrower than the line width derived from the first-order spectrum. However, the errors on the third-order spectrum are 2--3 times larger than in the first-order spectrum, and the $1\sigma$ confidence intervals from the spectra easily overlap. In a formal statistical sense, the measurements are consistent. There is no evidence that the first-order spectra has provided a false view of the narrow Fe~K$\alpha$ emission line in NGC 4151. The low inclinations that have recently been measured from the innermost disk in NGC 4151, and now also from the narrow Fe~K$\alpha$ line, are notionally incongruous with obscuration that is -- at least in some phases -- more like that observed in Seyfert-2 AGN and attributed to an equatorial line of sight. Although NGC 4151 is a standard Seyfert-1 in optical, it is apparently more complex in X-rays. Recent work on NGC 5548 and NGC 3783 has shown that these well-known Seyfert-1s occasionally undergo episodes of strong obscuration (Kaastra et al.\ 2014, 2018). These episodes only came to light through unprecedented monitoring and joint observing campaigns, so it is possible that enhanced obscuration in Seyfert-1s is fairly common but has simply evaded detection. It is interesting to note that Shu et al.\ (2010) found two more Seyferts wherein the narrow Fe~K$\alpha$ line is narrower than the H$\beta$ line: NGC 5548 and NGC 3783. The same projection effects that we infer in NGC 4151 may be at work in these famous sources. The narrow Fe~K$\alpha$ emission lines in NGC 3783 and NGC 5548 are not as bright nor as prominent as the line in NGC 4151, and this may hinder a clear result using {\it Chandra}. X-ray grating spectroscopy of other Seyferts has previously revealed some evidence that the BLR may extend as close to the central black hole as $R \simeq few\times 100~GM/c^{2}$. A deep {\it Chandra}/LETGS spectrum revealed evidence of broadened He-like and H-like C, N, O, and Ne lines in Mrk 279 (Costantini et al.\ 2007), with typical velocities of $1-2\times 10^{4}$~km/s (FWHM). Later observations with the {\it XMM-Newton}/RGS only found marginal evidence for broadened lines (Costantini et al.\ 2010). Additional evidence of X-ray lines from $R\simeq few\times 100~GM/c^{2}$ has recently been detected in Mrk 509 (Detmers et al.\ 2011), and NGC 3783 (Kaastra et al.\ 2018), among others. In each of these cases, the broadening is symmetric. \subsection{Future studies} The X-ray flux of NGC 4151, and the strength of its Fe K$\alpha$ line, set it apart from other Seyferts. A dedicated multi-cycle {\it Chandra}/HETGS monitoring program that systematically samples the relevant time scales can potentially achieve the first X-ray reverberation study of intermediate regions of the accretion disk. Such a study could set the stage for future efforts with {\it XARM} and {\it ATHENA}. Although the potential of calorimeters for reflection spectroscopy of reflection from the innermost accretion disk has been examined, studies of intermediate disk radii and the BLR are less developed (see, e.g., Nandra et al.\ 2013, Reynolds et al.\ 2014). We have therefore constructed a small set of simulations to illustrate the potential of future calorimeter spectra. Current versions of the ``xillver'' and ``relxill'' models (e.g., Garcia et al.\ 2013) are not yet suited to calorimeter data: the energy resolution of these models in the Fe K band is approximately 18--20~eV, which is coarser than the 5~eV and 2.5~eV resolution anticipated from {\em XARM} and {\em ATHENA} (e.g., Barret et al.\ 2018). The ``pexmon'' model (Nandra et al.\ 2007) includes multiple lines at proper relative strengths, but the model does not include complex line structure. In contrast, ``mytorus'' (Murphy \& Yaqoob 2009, Yaqoob \& Murphy 2010) has a resolution of 0.4~eV in the Fe K band, and includes line structure created by scattering in dense gas. Whereas the advantages of ``mytorus'' are small at HETGS resolution, they may be important at calorimeter resolution. For this reason, we have built simulations based on the best-fit broadened ``mytorus'' models with $q=3$ in Table 2. We examined two of the larger innermost line production radii indicated by the data, $R = 500~GM/c^{2}$ and $R=1000~GM/c^{2}$, as large radii have smaller impacts on the line asymmetry and require calorimeter resolution in a greater degree. The line flux was held constant as the radius was varied. We adjusted the internal resolution of the ``rdblur'' function from 20~eV to 0.4~eV in order to generate the simulated spectra. Based on the characteristic $\Delta t\simeq20$~ks variations in NGC 4151, we created sets of 20~ks snapshot spectra using established {\it Hitomi} (as a proxy for {\it XARM}) and {\it ATHENA} responses, and the ``fakeit'' function within XSPEC. Figure 8 shows the results of fits to these simulated spectra. The dynamical content of the line profiles is especially clear. Even in shorter exposures, strong constraints on the line production radius would be obtained using {\it XARM}. The sensitivity achieved in short {\it ATHENA} exposures is tremendous; fine details should be detectable that will allow for precise reverberation mapping of the emission region. More importantly, the sensitivity afforded by {\it ATHENA} should enable narrow Fe~K$\alpha$ emission line spectroscopy in far more distant galaxies, greatly increasing the total number of AGN in which such studies are possible.\\ JMM acknowledges Keith Arnuad, Xavier Barcons, Misty Bentz, Niel Brandt, Bozena Czerny, Javier Garcia, Julian Krolik, Mike Nowak, and Tahir Yaqoob for helpful discussions. We thank the anonymous referee for a careful examination of this paper that led to improvements. JMM is grateful to NASA for support through the {\em Astro-H} Science Working Group. | 18 | 8 | 1808.07435 |
1808 | 1808.10405_arXiv.txt | Early-type retired galaxies (RGs, i.e. galaxies which no longer form stars) can be divided into two classes: those with no emission lines, here dubbed lineless RGs, and those with emission lines, dubbed liny RGs. Both types of galaxies contain hot low-mass evolved stars (HOLMES) which emit ionizing photons. The difference must thus lie in the presence or absence of a reservoir of ionizable gas. From a volume-limited sample of 38\,038 elliptical galaxies, we explore differences in physical properties between liny and lineless using data from the SDSS, WISE and GALEX catalogues. To avoid biases in the comparison, we pair-match liny and lineless in stellar-mass, redshift and half-light Petrosian radius. We detect marginal differences in their optical stellar ages and NUV luminosities, indicating that liny RGs have an excess of intermediate-age (0.1--5 Gyr) stellar populations. Liny RGs show higher dust attenuation and $W3$ luminosities than their lineless counterparts. We also find that the amount of warm gas needed to explain the observed \Ha luminosity in liny RGs is $10^5$--$10^8$\msun, and that their \nii/\oii emission-line ratios are typical of those of the most massive star-forming galaxies. Taken together, these results rules out the following sources for the warm gas in liny RGs: mass-loss from intermediate-mass stars, mergers with metal-poor galaxies and intergalactic streams. They imply instead an inflow of enriched gas previously expelled from the galaxy or a merger with a metal-rich galaxy. The ionization source and the origin of the gas producing the emission lines are thus disconnected. | \label{sec:intro} Until recently the text-book vision of early-type galaxies (ETGs) was that they are composed mostly of old stars and almost devoid of cold gas and dust. However, already five decades ago it was realised that a non negligible fraction of them contained some gas, either neutral \citep[e.g.][]{Balkowski1972AA21303B,Gallagher1975ApJ2027G} or ionized \citep{Mayall1958IAUS523M,Osterbrock1960ApJ132325O}. It was also pointed out \citep[e.g.][]{Tinsley1972ApJ178.319T} that continuous mass-loss from old stars could lead to the formation of younger generations of stars in early-type galaxies. The far ultraviolet excess observed in the central region of M31 \citep{Code1969PASP81.848C}, first tentatively attributed to hot, highly evolved stars \citep{Hills1971AA12.1H}, was later suggested to arise from hot young main-sequence stars \citep{1971AA15.403T}. Various ionization sources for the emission-line gas observed in elliptical galaxies were considered, such as decay of turbulence or ultraviolet radiation from hot stars \citep{Osterbrock1960ApJ132325O}. In 1980, \citet{Heckman1980AA87.152H} performed a systematic spectroscopic survey of the nuclei of nearby galaxies, and found that, while the nuclei of spiral galaxies often had spectra similar to \hii regions, those of elliptical galaxies looked like the scaled-down version of the spectra of active galactic nuclei (AGN), with low luminosity and low excitation (but different from that of \hii regions). He called those objects LINERS, for `low ionization nuclear emission-line regions'. A wealth of hypotheses were proposed to explain the spectra of LINERs, such as nuclear activity \citep[e.g.][]{Ho1996ApJ.462.183H,Barth2001ApJ.546.205B,Sabra2003ApJ.584.164S,Filippenko2003ASPC.290.369F,Chiaberge2005ApJ.625.716C,Ricci2015MNRAS.451.3728R}, shocks \citep{Filippenko1984ApJ.285.458F,Ho1993ApJ.417.63H}, young, massive stars \citep[e.g.][]{Filippenko1992ApJ.397L.79F,Shields1992ApJ.399L.27S,Ho1993ApSS.205.19H,Ho1996ApJ.462.183H,Colina1997ASPC.113.477C,Alonso-Herrero2000ApJ.530.688A,Eracleous2002ApJ.565.108E,Rampazzo2005AA.433.497R}, or evolved low-mass stars \citep[e.g.][]{Stasinska2008,Annibali2010AA.519A.40A,Capetti2011AA.529A.126C,Yan2012,Yan2013IAUS.295.328Y,Singh2014IAUS.304.280S,Hsieh2017ApJ.851L.24H}. There is still no consensus. The LINER problem has become one of the most discussed topics concerning galaxies with emission lines. In the 1990s, much progress had been achieved in the theoretical evolutionary synthesis of stellar populations, and some works described the spectral evolution of coeval stellar populations until very late stages where low mass stars reached the white dwarf stage \citep{Bruzual1983ApJ273105B,Bruzual1993ApJ.405.538B,Fioc1997ASSL210.257F}. \citet{Binette1994} then showed that the observed emission-line spectra in elliptical galaxies (for which data were still very scarce at that epoch) could well be explained by the ionization of hot, low-mass evolved stars (dubbed HOLMES\footnote{We prefer the denomination of HOLMES to that of `post-AGB stars' since in the stellar evolution community the latter term has for the last thirty years been used exclusively to designate the late stage of stellar evolution \textit{previous} to the planetary nebula phase \citep[see][]{vanWinckel2003ARAA41.391V}.} in later studies; e.g. \citealt{Flores-Fajardo2011MNRAS415.2182F} and \citealt{CidFernandes2011}, hereafter CF11). In the 2000s, the Sloan Digital Sky Survey \citep[SDSS; ][]{York2000}, which obtained imaging photometry and optical spectra for nearly one million galaxies, revolutionised the field of galaxy studies. At the same time, techniques were developed to analyse the stellar populations of the galaxies and extract the pure emission-line spectra from the observed one which included information on both the stellar populations and the interstellar gas \citep{CidFernandes2005,Roig2015ApJ808.26R,Morelli2016MNRAS463.4396M}. This allowed for the first time a correct determination of the emission-line spectra of ETGs and a panoramic view of the galaxy spectra in emission-line diagnostic diagrams \citep{Kauffmann2003a}. In the \oiii/\Hb vs \nii/\Ha plot (the so-called BPT diagram after \citealt*{Baldwin1981}) the emission-line galaxies were cleanly separated between a `star-forming' (SF) wing and a wing containing hosts of active galactic nuclei (AGN). The lower part of the AGN wing was inappropriately labelled LINER \citep{Kauffmann2003a,Kewley2006}, creating some confusion: in the SDSS, spectra were obtained through a 3 arcsec fibre, and for objects at redshifts larger than about 0.03, covered much more than the sole nucleus. Later, the denomination LIER \citep{Belfiore2016MNRAS461.3111B} was proposed to underline that the spectra did not necessarily concern galaxy nuclei. In 2008, \citet{Stasinska2008} showed that ionization by the HOLMES inferred from the stellar population studies of the observed SDSS galaxies could well explain the LINER-type emission-line ratios observed for ETGs. In 2011, \citetalias{CidFernandes2011} proposed a diagnostic diagram (\wha vs \nii/\Ha, dubbed the WHAN diagram) to distinguish true LINERs from galaxies ionized by their HOLMES (the so-called retired galaxies introduced by \citealp{Stasinska2008}, meaning `retired from their star-forming activity'). 2D spectroscopy, now available thanks to integral field units such as CALIFA and MaNGA (\citealt{Sanchez2012AA538A.8S} and \citealt{Bundy2015ApJ798.7B}, respectively) then confirmed that, in many cases, the WHAN diagram correctly distinguished retired galaxies from galaxies hosting a LINER in their nucleus \citep{Sarzi2010,Singh2013,Gomes2015arXiv151100744G}. Presently, the widely accepted view of ETGs is that they contain an interstellar medium containing dust \citep{Goudfrooij1995AA.298.784G}, neutral hydrogen with masses of $10^6$--$10^9$\msun\ \citep[e.g. ][]{Krumm1979ApJ.228.64K,Goudfrooij1994MNRAS.271.833G,Oosterloo2010MNRAS.409.500O,Serra2012MNRAS.422.1835S,Lagos2014MNRAS.443.1002L,Woods2014MNRAS439.2351W}, molecules \citep{Combes2007MNRAS.377.1795C,Kaviraj2012MNRAS.423.49K,Davis2015MNRAS.449.3503D}, and have haloes of hot gas \citep{Sarzi2013MNRAS.432.1845S}. They also contain emission-line zones extending out to several kiloparsecs \citep[e.g.][]{Sarzi2006MNRAS.366.1151S,Singh2013,Woods2014MNRAS439.2351W,Gomes2015arXiv151100744G,Belfiore2017MNRAS.466.2570B}. HOLMES are one of the preferred options for the ionization of this gas. This new and broadly consensual vision of the ETGs seems now to have occulted the old picture and perhaps diminished the interest in those ETGs that \textit{do not present emission lines}. Some notable exceptions are the work by \citet{Rudnick2017ApJ.850.181R} who studied a sample of ETGs with and without \oii emission at redshifts between 0.4 and 0.8, and that by \citet{Belfiore2017MNRAS.466.2570B}, who analysed a sample of ETGs with MaNGA, looking for the reason behind the presence of gas and dust in some of these galaxies. As shown by \citetalias{CidFernandes2011} and \citet{Stasinska2015MNRAS}, such objects constitute about half of the whole population of ETGs. They were dubbed \textit{passive galaxies} (PG) in \citetalias{CidFernandes2011}, and \textit{lineless retired} (LLR) in \citet{Herpich2016MNRAS4621826H}. Here we will call them `lineless' RGs, by opposition to retired galaxies with emission lines, which we will call `liny' RGs. As already shown by \citetalias{CidFernandes2011}, lineless and liny RGs have almost identical distribution of many physical parameters, such as (1) stellar mass; (2) optical colors; (3) stellar populations mean age and metallicity; etc. So how is it that such a large proportion of ETGs does not show emission lines at all? In this series of two papers we try to understand what makes a retired galaxy lineless or liny. More precisely, given that the stellar populations of both types of galaxies are very similar and have been shown to be able to produce a low-level ionization of their gaseous content, why is it that some RGs do not show any emission lines? In this paper, we look at the fossil properties of liny and lineless ETGs, meaning properties linked to their star formation history or to the chemical enrichment of their emission-line gas. In a companion paper (Mateus et al., in prep.), we will discuss environmental clues. We will attack our study by considering the information provided by three large surveys: SDSS in the optical, WISE in the mid-infrared and GALEX in the UV. This paper is organised as follows: Section \ref{sec:datasamples} presents the data and sample selection; Section \ref{sec:diff} presents a differential analysis of the stellar properties of the two classes of RGs that are the subject of this work; Section \ref{sec:gas} discusses the origin of the gas in liny RGs; Section \ref{sec:discussion} puts together our findings; and finally Section \ref{sec:conclusions} summarises our results. Throughout this work we adopt a flat cosmological model with $\Lambda$-$\mathrm{CDM}$ with $H_0 = 70\,\mathrm{km\,s^{-1}Mpc^{-1}},\ \Omega_M = 0.3$ and $\Omega_{\Lambda} = 0.7$. | \label{sec:discussion} The broad conclusion from the previous sections is that, after a careful matching in stellar mass, redshift and fibre covering fraction, we find that the HOLMES populations in liny RGs produce exactly the same number of ionizing photons as in the lineless ones (as shown by Fig.~ \ref{fig:qholmes}). We also note that the \Ha luminosity from liny RGs is compatible with the photons produced by HOLMES populations. Following \citetalias{CidFernandes2011}, we define $\xi = L_{\Ha}^\mathrm{obs}/L_{\Ha}^\mathrm{exp} (t > 10^8\,\mathrm{yr})$, where $L_{\Ha}^\mathrm{exp} (t > 10^8\,\mathrm{yr})$ is the \Ha luminosity expected from HOLMES. This parameter $\xi$ should be $\leqslant 1$ for galaxies whose ionizing spectra is powered by HOLMES (stellar populations with $t > 10^8$\,yr), while any other source of the ionization, such as star formation or an active nucleus should produce a value $\xi \gg 1$. Fig.~\ref{fig:xiliny} shows that liny RGs do not need any source of ionization other than HOLMES. Note that, as a matter of fact, the distribution of the values of $\xi$ peaks at log $\xi = -0.4$, implying that a significant fraction of the ionizing photons produced by the HOLMES actually escapes even from liny RGs \citep{Papaderos2013AA.555L.1P,Gomes2015arXiv151100744G}. \begin{figure} \centering \includegraphics[width=.48 \textwidth]{./figure_xiholmes} \caption{ The equivalent width of \Ha versus $\xi$ for liny RGs from our paired sample. The open circles are the median value of bins containing the same number of objects. The shadow region represent the quartiles of the distribution. } \label{fig:xiliny} \end{figure} We have shown, however, that liny RGs differ from the lineless ones by having slightly higher values of the stellar extinction $A_V$. This is not surprising since lineless RGs having no warm gas are also expected to be devoid of dust. Liny RGs have higher luminosities in the WISE $W3$ band and higher luminosities in the GALEX $NUV$ band. Taken together, both facts point to a relatively recent period of star-formation in liny RGs, which does not occur in lineless RGs. This is also detectable in the diagram showing $D_n4000$ (Fig.~\ref{fig:d4000}) as well as in the one showing the mean luminosity-weighted age derived from \starlight (Fig.~\ref{fig:tstar}). The gas out of which the stars formed and whose remnant is detectable through emission lines cannot come from stellar mass-loss in the old stellar populations, because, as seen in the previous section, it is not nitrogen-enriched. So it must have mainly an external origin. An additional argument for its origin could come from a comparison of the kinematics of the emission-line gas and that of the stars \citep[e.g.][]{Sarzi2006MNRAS.366.1151S,Davis2016MNRAS.457.272D}. The necessary information is not available in our SDSS data, but in a sample of about 50 LIER galaxies with extended emission from the MaNGA survey, \citep{Belfiore2017MNRAS.466.2570B} found that the distribution of the star-gas misalignment indicates an external origin of the emitting gas (although they argue that internal processes may have a secondary role). There are a number of studies that argue that a minor merger could be the cause of infrared and ultraviolet emission in many ETGs \citep[e.g.][]{Salim2010ApJ.714L.290S,Kaviraj2011MNRAS411,Sheen2016ApJ.827.32S}. However, as seen in the previous section, the \nii/\oii ratio of liny RGs indicates that the impacting galaxies cannot be low-metallicity SF galaxies. The only remaining possibilities that we can think of is that the emitting gas comes i) from accretion from the haloes of the galaxies, ii) from the intergalactic medium or iii) from residual streams of metal-rich gas coming from a merger in the recent past. In the case of accretion from the haloes, one would a priori expect the emitting gas to be enriched in products from stellar mass-loss and supernova explosions (the so-called wind-recycling studied by \citealt{vandeVoort2016MNRAS.462.778V}). However, the analysis of the chemical composition of galactic haloes using X-rays or far ultra-violet absorption spectra brought surprises and is not yet fully understood \citep{Pipino2011AA.530A.98P,Su2013ApJ.766.61S,Prochaska2017ApJ.837.169P}. Besides there is presently no measurement of the N/O ratio in halo gas (and no theoretical estimate of it either). Anyway, from the point of view of the chemical composition, accretion from galactic haloes cannot presently be discarded to explain the emission lines in liny RGs. In the second scenario the gas in liny RGs would come from streams of cold gas found in the intergalactic medium, usually associated with galaxy groups or filaments \citep[e.g.][]{Sancisi2008AARv.15.189S,vandeVoort2012MNRAS.423.2991V}. This looks less probable, since the intergalactic medium gas is expected to be very metal poor, $\sim 0.1 Z_\odot$ \citet{Danforth2008ApJ.679.194D,Oppenheimer2012MNRAS.420.829O,vandeVoort2012MNRAS.423.2991V}, which is far below what our most metal-poor liny RGs suggest (see Fig.~\ref{fig:n2o2}). Finally, in the third scenario, cold gas comes from a merger episode with a metal-rich galaxy and now, a few billion years after the merger, it is slowly falling back to the galaxy. The first and third scenarios are the most probable for our liny RGs given the observed \nii/\oii ratios. Our study indicates that liny RGs suffered an intermediate-age episode of star formation which is likely connected with the gas that is now being ionized by the HOLMES from the old stellar populations. Liny RGs \textit{are not} ionized by young stellar populations since in the BPT diagram almost all are located well above the pure SF limit drawn by \citet{Stasinska2006}, as seen in Fig.~\ref{fig:bpt} which shows the values of \oiii/\Hb vs \nii/\Ha \citep{Baldwin1981} for our liny RGs. The figure plots only objects with $SN > 3$ for all four BPT emission lines, which drastically reduce the sample by a factor of 5. Only 0.7 percent o the RGs plotted in the figure are found inside the pure star-forming region. (Note that almost all the liny RGs live in the region previously attributed to LINER galaxies by \citealt{Kauffmann2003a}, \citealt{Kewley2006}, etc.). It must be noted, however, that in some early-type galaxies, massive ionizing stars may still be present, as indicated for example by 2D studies of early-type galaxies using CALIFA, which show zones where the \Ha equivalent width is of the order of 6-8 \AA, therefore not attributable to HOLMES \citep{Gomes2015arXiv151100744G}. \begin{figure} \centering \includegraphics[width=.45\textwidth]{./bpt_for_linys} \caption{ BPT diagram for the 12\,349 liny RGs that survive the four-line $SN$ cut. The blue line (S06) represents the pure-SF separation from \citet{Stasinska2006}, the red one (K01) the so called `upper starburst limit' from \citet{Kewley2001} and the green (CF10) is the Seyfert--LINER separation from \citet{CidFernandes2010}. } \label{fig:bpt} \end{figure} Lineless RGs, on the other hand, did not suffer such recent episodes of star formation, and are thus devoid of cold gas. In a companion paper (Mateus et al., in prep.), we will look for environmental clues for their lack of gas. A major point of concern is what happens to the gas ejected by stellar winds, which should be extensively observed in all retired galaxies. The mass ejected back to the ISM is usually of the order of the galaxy stellar mass ($\sim 4\times10^{9} - 3\times10^{12}\,\mathrm{M}_\odot$ for our sample). However, calculations show that gas from stellar mass-loss \citep{Parriott2008ApJ681.1215P} and planetary nebulae \citep{Bregman2009ApJ699.923B} in ETGs is quickly heated to very high temperatures and it is not clear whether the amount of remaining warm gas is sufficient to explain the observed \Ha luminosities. One can then ask why the same does not occur with the infalling gas. The dynamics of infalling gas is very different. Accretion time-scales of infalling cold gas have been discussed by e.g. \citet{Davis2016MNRAS.457.272D} and argued to be long. The simulation of a test case of a massive ETG experiencing a major merger shows that a disk of gas misaligned with the stellar component is produced and persists for about 2 Gyr \citep{vandeVoort2015MNRAS.451.3269V}. Such conditions can allow the gas to live long enough for the emission lines be noticed. | 18 | 8 | 1808.10405 |
1808 | 1808.00812_arXiv.txt | Shock accelerated electrons are found in many astrophysical environments, and the mechanisms by which they are accelerated to high energies are still not completely clear. For relatively high Mach numbers, the shock is supercritical, and its front exhibit broadband fluctuations, or ripples. Shock surface fluctuations have been object of many observational and theoretical studies, and are known to be important for electron acceleration. We employ a combination of hybrid Particle-In-Cell and test-particle methods to study how shock surface fluctuations influence the acceleration of suprathermal electrons in fully three dimensional simulations, and we give a complete comparison for the 2D and 3D cases. A range of different quasi-perpendicular shocks in 2D and 3D is examined, over a range of parameters compatible with the ones observed in the solar wind. Initial electron velocity distributions are taken as kappa functions, consistent with solar wind \emph{in-situ} measurements. Electron acceleration is found to be enhanced in the supercritical regime compared to subcritical. When the fully three-dimensional structure of the shock front is resolved, slightly larger energisation for the electrons is observed, and we suggest that this is due to the possibility for the electrons to interact with more than one surface fluctuation per interaction. In the supecritical regime, efficient electron energisation is found also at shock geometries departing from $\theta_{Bn}$ very close to 90$^\circ$. Two dimensional simulations show indications of unrealistic electron trapping, leading to slightly higher energisation in the subcritical cases. | Electron acceleration at collisionless shocks is a key process in space and astrophysical plasmas, being observed in situ at planetary bow shocks \citep[e.g.][]{Burgess2007_rev,Masters2017}, and interplanetary shocks \citep[e.g.][]{Potter1981,Dresing2016}. It is also inferred from observations of solar radio Type II emission \citep[e.g.][]{Holman1983,Pulupa2008}, synchrotron emission at SNR shocks \citep[e.g.][]{Koyama1995,Ellison2001} and diffuse radio emission from the intragalactic cluster medium \citep[e.g.][]{Ensslin1998,Kang2017}. Shocks in general convert directed flow energy (upstream) to thermal energy (downstream), and at shocks in collisionless plasmas a small fraction of the energy is available for acceleration of particles to high energies. Space observations and simulation studies have shown that the internal structure of the shock is important for the relevant type of acceleration mechanism, and also its detailed operation \citep{burgess_book}. Depending on its Mach number the shock can be sub- or supercritical, where, for the latter, ion reflection and gyration dominates and controls both the average shock structure and the types of microstructure associated with instabilities. Recent three-dimensional hybrid simulations (kinetic ions and fluid electrons) have revealed more detail of the microstructure of quasi-perpendicular supercritical shocks \citep{Burgess2016}. In this paper we will explore the effects of this microstructure on electron acceleration, starting from just above thermal energies. We will also demonstrate the importance of the sub- and supercritical Mach number regimes for the effectiveness of shocks as sources of electron acceleration; this is important when invoking shocks as electron acceleration sites for any particular astrophysical system. Collisionless shock transitions have an internal structure controlled by many parameters,the most important of which is the angle between the upstream magnetic field and the normal to the shock surface, $\theta_{Bn}$. When $\theta_{Bn}$ $\gtrsim$ 45$^\circ$ (i.e., the upstream magnetic field is almost parallel to the shock surface), the shock is quasi-perpendicular; and when $\theta_{Bn}$ $\lesssim$ 45$^\circ$, the shock is quasi-parallel. In this work we concentrate on electron acceleration at quasi-perpendicular shocks, motivated by both observational and theoretical arguments. Shock accelerated electrons were first observed in situ upstream of the Earth's bow shock, in the region known as the electron foreshock \citep{Anderson1969}. Energetic electrons were observed with energies 50 eV to $>$10 keV streaming away from the bow shock, along magnetic field lines connected to the shock surface. The most energetic backstreaming electrons were found to be confined in a small region, corresponding immediately downstream of the tangent point between the interplanetary magnetic field and the bow shock surface (where $\theta_{Bn} = 90^\circ$). Furthermore, the source was found to be ordered in energy, with less energetic electrons found deeper (further downstream) into the electron foreshock \citep{Gosling1989}. The electrons at intermediate energies (up to about 1 keV) originate in a broad region behind the magnetic tangent surface, i.e., on field lines with connection to the shock at $\theta_{Bn} < 90^\circ$. A thorough review of these observations can be found in \citet{fitz1995}. The first analytical model for accelerated electrons at quasi-perpendicular shocks was based on adiabatic reflection \citep{Leroy1984,Wu1984}, which assumes a 1D, planar and steady shock, and magnetic moment conservation in the Hoffman - de Teller frame (HTF) resulting in magnetic mirror reflection for some electrons. The HTF is the shock frame in which the flow is parallel to the magnetic field, and the motional electric field is zero (assuming ideal MHD, although it can be nonzero within the shock transition). In the HTF, the electron energy is constant, neglecting any change due to electric field in the shock structure. Here the energy gain is associated with the frame transformation from the HTF to the observer frame. In the observer frame (typically the Normal Incidence Frame, NIF, where upstream bulk flow and shock normal are parallel), the electrons gain energy in the reflection process via drift parallel to the motional electric field. The energy gain for reflected electrons depends on the velocity frame transformation from the NIF to the HTF, so increases with $\theta_{Bn}$, and for significant energisation, $\theta_{Bn}$ has to be close to 90$^\circ$. On the other hand, the density of reflected electrons decreases as $\theta_{Bn}$ increases since only electrons from the wings of the incident distribution satisfy the conditions for reflection. The presence of a cross-shock potential modifies the reflection process, acting to reduce reflection at low energies. The resulting distribution function of reflected electrons is a truncated loss-cone \citep{Leroy1984}. The role of self consistent shock structure (e.g., overshoot, cross-shock potential) have been investigated by means of test particle simulation of electrons using electromagnetic fields obtained from 1D plasma simulations \citep{Krauss1989,Krauss1989b}. Later, the role of shock curvature was found to be important in terms of electron energisation, due to the relatively large distance transverse to the shock travelled by electrons during reflection \citep{Krauss1991}. Other studies \citep[e.g.,][]{Zlobec1993,Vandas2002,Knock2003} linked the presence of large scale ripples at the shock surface features to electron acceleration in interpreting solar type II radio bursts. The shock structure depends crucially on the Mach number. A shock can be sub- or supercritical, depending on its Mach number relative to the critical Mach number $M_c$, defined as that at which the downstream flow speed is equal to the speed of sound. Super-critical shocks require a dissipation process other than resistivity, and this is provided by ion reflection and gyration into the downstream. Although the definition of $M_c$ arises from two-fluid theory, usually supercritical shocks are treated as those dominated, in terms of structure and thermalization, by ion reflection and gyration. The structure is usually described as "foot-ramp-overshoot" where the foot is formed by reflected ions gyrating around ahead of the main ramp before returning to the shock. On the other hand low Mach number, subcritical shocks do not exhibit strong structuring around the transition layer, appearing similar to laminar fluid shocks. Non-stationarity and microstructure are important features of collisionless shocks. Self-reformation of supercritical, quasi-perpendicular shocks, with a quasi-periodic steepening of the shock ramp, has been found in simulations \citep[e.g.,][] {Biskamp1972,Quest1985,Lembege1992}. The process of self-reformation is important at low $\beta_i$ (i.e., the ratio of upstream ion plasma to magnetic field pressures), and high Mach number \citep{Hada2003}. It can be inhibited through the emission of nonlinear whistler waves in the shock foot \citep{Krasno1991,Hellinger2007}, although the situation can be complicated by the shock geometry used in the simulations \citep{Lembege2009}. In addition, the shock ramp and foot can be unstable to multiple wave modes, leading to microstructure within the shock transition. The landscape of possible microinstabilities that can be generated in the foot of quasi-perpendicular shocks is broad: \citet{Matsukiyo2006} identified six types of instabilities being excited in short times (less than one ion gyroperiod) using 2D, fully kinetic simulations. Early hybrid 2D simulations of perpendicular shocks with the magnetic field in the simulation plane showed that the surface exhibits fluctuations or ripples associated with ion Alfv\'en cyclotron and possibly mirror instabilities \citep{Winske1988}. The ripples propagate across the shock front at the Alfv\'en speed of the shock overshoot \citep{Lowe2003}. Simulations of perpendicular shocks with the magnetic field out of the simulation plane revealed a different type of fluctuation, directly connected with the reflected ion population \citep{Burgess2007}. Recently, a study of structuring in 3D shock simulations has shown that 2D simulations do not fully capture the dynamics of shock structure since there are processes due to the coupling between field parallel and reflected ion fluctuations \citep{Burgess2016}. Another source of nonstationarity which has been identified at quasi-perpendicular shocks is whistler wave turbulence \citep[e.g.,][]{Krasno1991}. \citet{Oka2006}, using Geotail data, related the electron acceleration at the Earth's bow shock with the presence of whistler waves in the shock foot. Recent observational results obtained using the Magnetospheric Multiscale Spacecraft (MMS) have proven directly and for the first time that quasi-perpendicular, collisionless shocks do have a rippled surface \citep{Johlander2016}. It has been shown that the observed ripples are consistent with results from hybrid simulations, and are modulated by the process of shock reformation \citep[][]{gingell2017}. An extensive review about the dynamics of quasi-perpendicular shocks and their observational properties can be found in \citet{Krasno2013}. A study of the role of surface ripples in electron acceleration was carried out by \cite{Burgess2006}, by means of test particle and 2D hybrid shock simulation. At low Mach numbers a good agreement with adiabatic reflection theory was found, whereas at high Mach numbers the rippled character of the shock enhanced the electron acceleration. This picture of enhanced energisation was extended by considering a turbulent upstream plasma flow, and it was found that electron energy gains are enhanced even at more oblique configurations (departing from the condition for $\theta_{Bn}$ to be close to 90$^\circ$) \citep{Guo2010}. This is due to the fact that large scale upstream fluctuations can mirror the electrons back to the shock, creating a multiple-shock encounter scenario which leads to larger electron energisation \citep{Guo2015}. In the studies discussed so far, the shock structure has been assumed to be dominated by ion scale processes, making the hybrid simulation method appropriate. There are also studies of electron acceleration using fully kinetic Particle-In-Cell (PIC) simulations, which also model electron scale physics. Simulations which display nonstationarity (shock reformation) were found to eject upstream electrons in a bursty fashion \citep{Lembege2002}. Other simulations emphasized the importance of whistler waves excited in the foot of the quasi-perpendicular shock for electron acceleration out of the thermal population, with relevance to super nova remnant shocks \citep{Riquelme2011}. Strong electron acceleration was also observed in full PIC simulations of high Mach number shocks by \citet{Amano2009}, where it was found that electrons were efficiently reflected at the shock front by electron-scale electrostatic fluctuations induced by the modified two-stream instability, and then accelerated by the convective electric field in front of the shock, in a picture known as ``electron surfing acceleration''. At lower Mach numbers, electron surfing acceleration was found to be important for both energisation itself and also as a channel of pre-acceleration for further energisation by shock drift acceleration \citep{Amano2007}. However, fully kinetic simulations have some limitations, for example, using a reduced proton to electron mass ratio can produce large differences in the shock structure compared to when the real ratio is used \citep[e.g.,][]{Scholer2003} (see also \citet{Krasno2013} for a discussion). The motivation of this work is to extend earlier studies, in the picture of hybrid and test-particle simulations, comparing 2D and 3D simulations for a range of non-reforming shock parameters, and using realistic upstream kappa electron distributions, for which there is observational evidence in the solar wind \citep[e.g.,][]{Pierrard1999}. In this framework, we want to demonstrate the importance of the critical Mach number for electron acceleration, being an important issue for many astrophysical environments. The paper is organised as follows: in section \ref{sec:method} the details of the hybrid and test-particle method are presented; section \ref{sec:shock_fluc} shows the different types of surface fluctuations found in the sub- and supercritical regimes; in section \ref{sec:2D_3D} the upstream energy spectra obtained in 2D and 3D simulations are compared; in section \ref{sec:3D_spectra} we focus on electron acceleration in 3D simulations, showing the scenarios for different shock parameters; in section \ref{sec:discussion} we discuss the electron acceleration mechanisms in the simulations and in section \ref{sec:conclusions} the results are summarised. | \label{sec:conclusions} We have performed 2D and 3D hybrid simulations of quasi-perpendicular collisionless shocks and used the test particle method to study electron acceleration starting from suprathermal energies. It is the first time that the full, three-dimensional structure of the shock has been considered in the framework of hybrid plasma and test-particle simulations. The strongest signatures of electron acceleration were found for shocks with a shock normal geometry close to perpendicular. The difference between electron acceleration at subcritical (low Mach number) and supercritical (high Mach number) shocks was addressed with both 2D and 3D simulations. There is a clear difference between these two cases. At low Mach number only moderate energisation is found, consistent with single interaction, coherent reflection models based on adiabatic motion \citep{Leroy1984,Wu1984}. In the supercritical regime enhanced energization is found, which can be explained by considering the small scale structures and fluctuations in the shock ramp \citep[e.g.,][]{Burgess2006,Guo2010}, which produce additional scattering. Comparing 2D and 3D simulations, in 2D we find signatures of enhanced acceleration due to particle trapping in fluctuations, which is an artefact of the reduced dimensionality. In the subcritical regime this leads to slightly higher electron energy gains, and the mechanism appears to be important also for the supercritical regime, accentuating the plateau feature observed in upstream energy spectra. When the full three dimensional structure of the shock front is resolved, slightly higher final electron energies are obtained in the supercritical regime. We believe that this is due to the possibility that the electrons can interact with several surface fluctuations throughout the reflection process, thus being retained in the shock transition layer for longer times where they experience the electric field parallel to the shock surface ($E_z$) responsible for their acceleration. This scenario is corroborated by the analysis of Figure~\ref{fig:fig12}, which illustrates that electrons that penetrate deepest into the shock layer before reflection have the largest final energies. Therefore, any process which tends to retain the electrons at the shock front increases their energy gain. Although the current simulations rely on ion scale fluctuations, a similar scenario has been proposed based on full kinetic PIC simulations \citep{Amano2009}. In the supercritical regime, efficient electron acceleration was also found at more oblique shock geometries, down to $\theta_{Bn}$ = 80$^\circ$ (Figure~\ref{fig:fig7}). It is important to consider that the key ingredient for efficient electron acceleration is the local value of $\theta_{Bn}$, rather than the average one. In this respect, the shock rippling causes local changes in the shock geometry at various spatial scales (see Figures~\ref{fig:fig1} and \ref{fig:fig2}), so when an electron approaches the shock transition, it has a certain possibility to interact with a local part of the shock with temporarily perpendicular geometry, and then later a less perpendicular region allowing upstream escape. This phenomenon leads, statistically, to higher energisation when rippling is present at the shock front. A number of restrictions in this study should be noted. The shock simulations do not include any large scale non-stationarity (such as shock reformation), and the shock fluctuations are self-generated without accounting for any upstream turbulence, which can be important \citep{Guo2010,Guo2015}. The relative roles of these two mechanisms remains a topic for future work. As initial electron distributions kappa functions have been used, motivated by solar wind observations \citep[e.g.,][]{Maksimovic2005}, but similar results have been found using different initial distributions (e.g., Maxwellian). However, electron distribution functions and their features need more observational work for a full characterization in the solar wind \citep[e.g.,][]{Graham2017}. A major issue with this study is the use of a reduced plasma model, such as the hybrid model, for the shock structure fields. The justification for using a hybrid simulation combined with test particles is based on starting from electron superthermal energies, assuming that the electron scale structure (which is absent in the hybrid approximation) does not play an important role for the superthermal electrons. This allows longer time periods to be simulated, so the effects of ion scale structure can be shown to be important. However, the results should be confirmed by fully kinetic simulations, although they have their own limitations such as small spatial extents and unrealistic mass ratio \citep[e.g.,][]{Krasno2013}. From our results we see that electron acceleration is efficient when there is a combination of magnetic mirror reflection and scattering within the shock gradient. There is evidence from fully kinetic PIC simulations that a similar process operates for the thermal electrons \cite{Amano2009}, although the fluctuations producing the scattering are different in nature (lower hybrid rather than ion scale ripples). In either case, depending on initial energy, the importance of scattering is key for efficient acceleration. The additional point made by this work is that the presence of ion scale ripples as a source of scattering requires that the Mach number should be supercritical. Finally, as for all simulation work, validation for this picture is required by observational means. It is important to remark that the critical Mach number, at which shocks develop surface fluctuations, is relatively low ($M_c \approx 3.5$). Solar wind observations show that, at 1 AU, the range of observed shock parameters covers both sub- and supercritical regimes, so it is possible, in principle, to test the results of analytical and numerical studies. However, further observational work is required towards a deeper understanding of electron acceleration: in particular in order to investigate the role of upstream solar wind turbulence, which is expected to enhance the electron energisation. Another challenging topic is to look at how sub- and supercritical shock regimes can effect electron injection into other mechanisms leading to higher energies and observed in large scale astrophysical environments, such as giant radio relics in the intracluster medium \citep[e.g.,][]{Brunetti2016,Kang2017}, and this will be the object of future investigations. | 18 | 8 | 1808.00812 |
1808 | 1808.02483_arXiv.txt | We utilize the more than 100 gravitationally-bound dense cores formed in our three-dimensional, turbulent MHD simulations reported in \cite{2015ApJ...810..126C} to analyze structural, kinematic, and magnetic properties of prestellar cores. Our statistical results disagree with the classical theory of star formation, in which cores evolve to be oblate with magnetic field parallel to the minor axes. Instead, we find that cores are generally triaxial, although the core-scale magnetic field is still preferentially most parallel to the core's minor axis and most perpendicular to the major axis. The internal and external magnetic field directions are correlated, but the direction of integrated core angular momentum is misaligned with the core's magnetic field, consistent with recent observations. The ratio of rotational/total kinetic and rotational/gravitational energies are independent of core size and consistent in magnitude with observations. The specific angular momentum also follows the observed relationship $L/M \propto R^{3/2}$, indicating rotation is acquired from ambient turbulence. With typical $E_\mathrm{rot}/E_K \sim 0.1$, rotation is not the dominant motion when cores collapse. | \label{sec:intro} In molecular clouds (hereafter MCs), multi-scale supersonic flows compress material and initiate creation of filamentary structures \citep{2014prpl.conf...27A}. Within filaments, some of the overdense regions will shrink under self-gravity to form prestellar cores and then collapse to create protostellar systems, which later become stars \citep{1987ARA&A..25...23S}. Dense cores are therefore the immediate precursors of at least low-mass stars or close binary systems \citep{2007ARA&A..45..565M}. Their properties provide the initial conditions of star formation, and determine the local environment of protostellar disks and outflows. Cores are observed in dust continuum and molecular lines. Recent results from the Herschel Gould Belt Survey \citep{2010A&A...518L.102A} suggest that dense cores are mostly associated with filaments (\citealt{2010A&A...518L.106K}; or see review in \citealt{2014prpl.conf...27A}). This association is consistent with the theoretical expectation that thermally supercritical filaments (mass-per-unit-length $M/L > 2 {c_s}^2/G$; \citealt{1964ApJ...140.1056O}) would fragment longitudinally into cores \citep[e.g.][]{1992ApJ...388..392I,1997ApJ...480..681I}. However, in a turbulent environment like a MC, dense filaments are not quiescent structures in which perturbations slowly grow. Rather, various simulations with turbulence have shown that filaments and cores develop simultaneously \citep[e.g.][]{2011ApJ...729..120G,2014ApJ...785...69C,2015ApJ...810..126C,2014ApJ...791..124G,2014ApJ...789...37V,2015ApJ...806...31G}, in contrast to the two-step scenario, because multi-scale growth is enabled by the non-linear perturbation generated by turbulence. In combination with turbulence and gas gravity, magnetic effects are considered one of the key agents affecting the dynamics of star formation in MCs, at all physical scales and throughout different evolutionary stages \citep{2007ARA&A..45..565M}. At earlier stages and on larger scales, the magnetic field can limit compression in turbulence-generated interstellar shocks that create dense clumps and filaments \citep{1956MNRAS.116..503M}. Meanwhile, the core-scale magnetic field is expected to be important in affecting the gas dynamics within cores, and is interconnected with the cloud-scale magnetic field. The magnetic field within collapsing cores provides the main channel for the gas to lose angular momentum via ``magnetic braking" during the collapse of prestellar cores and the formation of protostellar disks (\citealt{1956MNRAS.116..503M,1974Ap&SS..27..167G,1976ApJ...207..141M,1991ApJ...373..169M}; see review in \citealt{2014prpl.conf..173L}). In strict ideal MHD, magnetic braking can be simply understood as the inner, faster-rotating material being slowed down by the outer, more slowly-rotating material because they are interconnected by magnetic field lines \citep{1979ApJ...230..204M,1980ApJ...237..877M}. Numerical simulations also showed that the formation of rotationally supported disks is suppressed by catastrophic magnetic braking, unless the dense cores are weakly magnetized to an unrealistic level \citep{2003ApJ...599..363A,2008A&A...477....9H,2008ApJ...681.1356M,2011A&A...528A..72H}. Many solutions have been proposed to solve this problem, including non-ideal MHD effects \citep{2010ApJ...716.1541K,2011ApJ...738..180L,2011PASJ...63..555M,2012A&A...541A..35D,2013ApJ...763....6T}, turbulence-induced diffusion \citep{2012ApJ...747...21S,2012MNRAS.423L..40S,2013MNRAS.432.3320S,2013A&A...554A..17J}, and the magnetic field-rotation misalignment \citep{2009A&A...506L..29H,2010MNRAS.409L..39C,2012A&A...543A.128J,2013ApJ...767L..11K}. The initial magnetic field structure and strength within prestellar cores are therefore important for late evolution during core collapse, since they control the efficiency of this magnetic braking process. Rotation is also important in the evolution leading to the creation of protostellar systems within dense cores. The angular momentum of star-forming cores is a critical parameter in protostellar evolution, but its origin is not well understood \citep[see review in][]{2014prpl.conf..173L}. It is known that some dense cores show a clear gradient in line-of-sight velocity, while others have a relatively random velocity field \citep[e.g.][]{1993ApJ...406..528G,2002ApJ...572..238C}. The observed velocity gradient is commonly used, when present, to estimate a core's angular momentum. Observational and theoretical understanding of core angular momentum is important as this property is essential to subsequent evolution: whether a single star or multiple system is formed \citep{2002ARA&A..40..349T}, and whether a large or small disk is produced \citep[see review in][]{2014prpl.conf..173L}. There have been several observational projects aimed at resolving the velocity structure within dense cores. Linear fitting is generally applied to observed velocity gradients across cores, regardless of the complex nature of the velocity field. It is assumed that rigid body rotation applies and that the angular speed is roughly the gradient of line-of-sight velocity \citep{1993ApJ...406..528G}. Previous observations \citep{1993ApJ...406..528G,2002ApJ...572..238C,2003A&A...405..639P,2007ApJ...669.1058C,2011ApJ...740...45T} have found a power-law relationship between the specific angular momentum, $L/M$, and radius, $R$, for dense cores/clumps with radii $\sim 0.01-1$~pc, $L/M \propto R^\alpha$ with $\alpha \approx 1.5$. The $L/M-R$ correlation over a huge range of spatial scales suggests that gas motion in cores originates at scales much larger than the core size, or the observed rotation-like features may arise from sampling of turbulence at a range of scales \citep{2000ApJ...543..822B}. Simulated cores from our previous work \citep[][hereafter CO14 and CO15]{2014ApJ...785...69C,2015ApJ...810..126C} provide a suitable database to test whether the $L/M-R$ correlation extends to even smaller scales ($R$~$\sim$~0.008--0.05~pc), and whether the assumption of rigid body rotation is valid in simulated cores. These questions are one focus of the present study. In this paper, we present our results on structural, kinematic, and magnetic properties of simulated prestellar cores formed in three-dimensional (3D) MHD simulations; the simulation ingredients include convergent flow, multi-scale turbulence, and gas self-gravity. This set of simulations was first introduced in \hyperlink{CO15}{CO15} to investigate the forming process of prestellar cores and how it correlates with the cloud environment. We have shown in \hyperlink{CO15}{CO15} that these cores have masses, sizes, and mass-to-magnetic flux ratios similar to the observed ones. Here, we extend our previous study to include analysis of the geometry and kinematic features of cores, as well as the relative direction of core-scale magnetic field. The outline of this paper is as follows. We describe our simulation models, numerical methods, and analytic algorithms in Section~\ref{sec::method}. Our results on core geometry and other structural properties are presented in Section~\ref{sec::physical}, while Section~\ref{sec::dyn} focuses on the kinetic features of dense cores. Based on these results, we discuss the origin of core angular momentum in Section~\ref{sec::discussion}. Finally, Section~\ref{sec::summary} summarizes our conclusions. | \label{sec::discussion} \label{sec::turborigin} It has been known that the specific angular momentum of observed dense cores/clumps are correlated with their sizes, approximately following a power law, $L/M \propto R^{\alpha}$, with $\alpha \approx 1.5$. This was first reported in \citet{1993ApJ...406..528G}, and was later confirmed by many follow-up studies \citep[e.g.][]{2002ApJ...572..238C,2003A&A...405..639P,2007ApJ...669.1058C}. Also, these observations suggest that the ratio between rotational energy and gravitational energy, $\beta_E \equiv (L^2/(2I))/(qGM^2/R)$ (where $q=3/5$ for a uniform density sphere; see definition in \citet{1993ApJ...406..528G}), is relatively independent of core/clump size. In Figure~\ref{rotEng} we show the $L/M$ vs.~$R$ relationship (bottom panel) from several observational studies \citep{1993ApJ...406..528G,2002ApJ...572..238C,2003A&A...405..639P,2007ApJ...669.1058C,2011ApJ...740...45T}. We compare to the $L/M$ vs.~$R$ relationship in our simulated cores considering $R \equiv \sqrt[3]{a\cdot b\cdot c}$ (i.e.~the geometric mean of the three axes), which follows the same correlation as the observations. The agreement of the simulations with observations confirms the positive correlation between the specific angular momentum and spatial scale of dense cores/clumps. Also plotted is the rotational-to-gravitational energy ratio $\beta_E$ (middle panel) as a function of core radius $R$ for both our simulations and observations. The independence of core rotational-to-gravitational energy ratio with core size is also confirmed. Quantitatively, the range of $\beta_E$ for our simulated cores agrees with observations. \begin{figure} \begin{center} \includegraphics[width=\columnwidth]{J_betaE_ErotEK_radius.pdf} \caption{The rotational-to-total kinetic energy ratio ({\it top}), rotational-to-gravitational energy ratio $\beta_E$ ({\it middle}) and the specific angular momentum $L/M$ ({\it bottom}) as functions of core/clump radius, from both observations (see text) and the simulated cores discussed in this study. The energy ratio distributions are independent of core size, while the specific angular momentum appears to roughly follow a power law of core size, $L/M \propto R^\alpha$ for $\alpha \sim 1.5$, over more than two orders of magnitude in spatial scales. This may suggest that the prestellar core acquires angular momentum from a much larger scale than the immediate surrounding of the core, or the so-called rotation within dense cores is inherited from turbulent motions at cloud scales.} \label{rotEng} \end{center} \end{figure} The fact that $L/M \sim R \cdot v_\mathrm{rot} \propto R^{3/2}$ suggests that $v_\mathrm{rot} \propto R^{1/2}$. In combination with the well-known result that turbulent velocities increase roughly $\propto R^{1/2}$ in supersonic turbulence (both in observations and simulations; see review in \citealt{2007ARA&A..45..565M}), this suggests that the rotational velocity in cores is inherited from the overall turbulent cascade. In addition, the top panel of Figure~\ref{rotEng} shows the rotational-to-kinetic energy ratio, $E_\mathrm{rot} / E_K$, as a function of core radius $R$ for both simulated and observed cores.\footnote{To estimate the kinetic energy of observed cores, we used the total observed linewidths $\sigma_v$ within cores reported by the cited observation studies and calculated $E_K \approx 3/2 \cdot M_\mathrm{core} {\sigma_v}^2$.} For both simulated and observed cores, the range of $E_\mathrm{rot} / E_K$ is similar and independent of $R$. This suggests that whatever size a core/clump is, it is sampling from the turbulence at that corresponding scale in setting its rotation. Though this rotational energy could be sub-dominant at core scales, it is essential to subsequent disk formation. Once a star-disk system forms in the interior (at much smaller scales than that studied here), the core's velocity structure (and angular momentum) may be altered by outflows and/or other feedback mechanisms \citep[see e.g.][]{2017ApJ...847..104O}. To investigate the accuracy of our estimated core angular momentum, we ran a set of tests to examine the analysis method, which is described in the Appendix. These tests show that the measured $E_\mathrm{rot}/E_K$ ratio within the core could in principle reflect the relative significance of turbulence with respect to rigid-body rotation (see Figure~\ref{ErotEturb}, right panels). More importantly, we showed that for a pure-turbulent core (net angular velocity $\Omega=0$), the ``projection" of turbulence within it will naturally lead to $E_\mathrm{rot}/E_K \sim 0.1$ (Figure~\ref{ErotEturb}, left panels), consistent with the values measured from our simulated cores. We therefore conclude that rotation is not the dominant motion within prestellar cores, and the ratio between the turbulence amplitude $\sigma_v$ and maximum rotational speed ($v_\mathrm{rot,max} \sim \Omega \cdot R_\mathrm{core}$) must be $\gtrsim 1$ within prestellar cores. In this paper, we investigated the $> 100$ dense cores formed naturally in the \hyperlink{CO15}{CO15} MHD simulations to examine the structural, magnetic, and kinetic properties of prestellar cores with masses $M_\mathrm{core}\sim 0.01-5~\mathrm{M_\odot}$ and sizes $R_\mathrm{core}\sim 0.005-0.1$~pc. We found that our simulated cores are generally triaxial, unlike the idealized oblate cores of classical theory. We showed that environmental effect plays an important role in shaping prestellar cores, especially by providing spatial constraints via ram or magnetic pressure. In addition, the formation of prestellar cores is strongly affected by gas turbulence, in the way that cores acquire rotational energy from local turbulence, which leads to the misalignment between magnetic fields and rotational axes within dense cores. Our main conclusions are as follows: \begin{enumerate} \item When present, a stagnant sub-layer \citep[see discussions in][]{2017ApJ...847...140C} in the post-shock region (Figure~\ref{pslayer}) is critical in setting up the environment wherein prestellar cores form. Core formation within this sub-layer (models M5 and B20) is more quiescent and more similar to classical theory, while cores formed without this sub-layer (models M20 and B5) are more disturbed by local gas turbulence. \item Cores preferentially have their major axes in the plane parallel to the shock front ($x$-$y$ plane; see Figure~\ref{acdir}, left), because the ram pressure of inflow limits core growth along $z$. This might help explain the mass-size relation of dense cores reported in both numerical (\hyperlink{CO15}{CO15}) and observational \citep{2013MNRAS.432.1424K} studies, $M\propto R^k$ with $k\sim 2-2.5$, because for cores formed within shock-compressed, locally-flat regions core growth is basically two-dimensional. On the other hand, we find that most of the cores have both their minor axes and mean magnetic fields lying in the $x$-$z$ plane (Figure~\ref{acdir}, middle and right panels) defined by the direction of inflow and the cloud-scale magnetic field. The minor axis is rarely along the $\hat y$ direction because it is difficult for the gas to flow or compress the magnetic field in this direction. \item Though cores are generally triaxial (Figure~\ref{aspRatio}, top) rather than having the oblate shape often adopted in classical theory, the core-scale magnetic field is still generally aligned with core's minor axis and perpendicular to the major axis (Figure~\ref{hist_B}). Only those cores formed under a more perturbed environment (without the stagnant sub-layer; models B5 and M20) can have magnetic field nearly perpendicular to their minor axes. However, these cores also tend to be more prolate ($b\sim c$; see Figure~\ref{aspRatio}, bottom), which means the direction of $c$ is less meaningful in these cases. \item The integrated angular momentum vector within cores does not have a preferred orientation with respect to the core's three axes (Figure~\ref{hist_L}), except being generally perpendicular to the major axis, which is a mathematical result from the definition of angular momentum (for cell $i$ at a distance of $r_i$ from the rotational axis, its angular momentum $L_i \propto r_i$). More importantly, there is no preferred alignment between the magnetic field and angular momentum within cores (Figure~\ref{hist_BL}), as reported in the TADPOL observational survey \citep{2014ApJS..213...13H} and a follow-up numerical study considering different viewing angles of two simulated protostellar envelopes \citep{2017ApJ...834..201L}. Since misalignment between a core's rotational axis and magnetic field may be critical in reducing magnetic braking during core collapse, this may be important to understanding of protostellar disk formation. \item Our analyses indicate that the commonly-adopted assumption of rigid-body rotation may underestimate the rotational motion in most dense cores. We presented a new method of calculating core angular momentum, {\it the ring-fit} (see Sections~\ref{sec::anacode} and \ref{sec::nrbRot}), which gives a factor of 2 higher measurement of rotational energy (see Table~\ref{CoreKE}). Our results also suggest that the measured angular momentum within cores could simply be from the projection of ambient turbulence at core scale (see Figure~\ref{ErotEturb}) as previously suggested by \cite{2000ApJ...543..822B}. \item With our detailed analysis of core-scale kinematics, we have revisited the specific angular momentum$-$size correlation of dense cores/clumps reported in many observations (Figure~\ref{rotEng}, bottom). Our simulated cores fit with the observational results well, and extend to smaller spatial scales. The correlation of $L/M$ with $R$ over two orders of magnitude in spatial scale suggests that ``rotation" within these cores/clumps shares the same origin with the velocity scaling consistent with larger-scale turbulence. We find that the rotational-to-gravitational energy ratio $\beta_E$ (Figure~\ref{rotEng}, middle) and the relative rotational energy $E_\mathrm{rot}/E_K$ ((Figure~\ref{rotEng}, top) have similar ranges and are independent of scale for both simulated and observed cores. Taken together, these results suggest that prestellar cores inherit their original angular momentum from cloud-scale turbulence, which may in part be driven by feedback (outflows, etc.) from other stars that formed earlier. \end{enumerate} We note that our simulations and analyses only focus on cores in early (prestellar) evolutionary stages and therefore do not include effects from stellar feedback. There are also various idealizations in our simulations that could potentially affect our conclusions. The converging-flow setup intrinsically excludes scales $\gtrsim L_\mathrm{box}$, and therefore cannot capture effects of large-scale turbulence (including turbulence driven by feedback in other nearby stars) in development of core rotation. Also, we assumed uniform magnetic fields in the initial conditions, and this lack of magnetic field variation may affect the structure of local turbulence and hence rotation at core scales. Our results could also be biased by the limited parameter range (in terms of magnetic field strength, gas density, inflow velocity, etc.) investigated in this study. Nevertheless, the connection between core-scale angular momentum and the immediately-surrounding cloud-scale turbulence is clear in both our numerical results and previous observations. | 18 | 8 | 1808.02483 |
1808 | 1808.07059_arXiv.txt | Mid-late M stars are opportunistic targets for the study of low-mass exoplanets in transit because of the high planet-to-star radius ratios of their planets. Recent studies of such stars have shown that, like their early-M counterparts, they often host multi-resonant networks of small planets. Here, we reanalyze radial velocity measurements of YZ Ceti, an active M4 dwarf for which the HARPS exoplanet survey recently discovered three exoplanets on short-period (P = 4.66, 3.06, 1.97 days) orbits. Our analysis finds that the orbital periods of the inner two planets cannot be uniquely determined using the published HARPS velocities. In particular, it appears likely that the 3.06-day period of YZ Ceti c is an alias, and that its true period is 0.75 days. If so, the revised minimum mass of this planet is less than 0.6 Earth masses, and its geometric transit probability increases to 10\%. We encourage additional observations to determine the true periods of YZ Ceti b and c, and suggest a search for transits at the 0.75-day period in TESS lightcurves. | Mid-late M stars are increasingly common targets of exoplanet surveys. \kep \citep{borucki10} included relatively few such stars in its target list, but its extended mission K2 has revealed several systems of small planets orbiting very low-mass stars \citep[e.g.][]{mann16,hirano16}. TESS \citep{ricker15} has started science operations, and will add many more systems to the catalog of exoplanets around late-type stars. At the same time, a collection of near-infrared Doppler spectrographs is going into operation, beginning with CARMENES \citep{quirrenbach16} and HPF \citep{mahadevan14}, which will enable ground-based follow-up to determine the masses of planets transiting these cool, faint stars. Already, several of the most high-profile recent exoplanet discoveries have been around mid-late M stars. TRAPPIST-1, a nearby M8 dwarf, was shown to host a multi-resonant network of seven low-mass exoplanets \citep{gillon17}, three of which lie within the liquid-water habitable zone \citep[HZ;][]{kopparapu13}. Radial velocity (RV) surveys have also discovered low-mass exoplanets around nearby mid-late M stars. \citet{anglada16} found evidence for a terrestrial-mass planet in the HZ of Proxima Centauri. More recently, \citet{astudillo-defru17} announced the discovery of three Earth-mass exoplanets orbiting the M4.5 dwarf YZ Ceti based on observations from the HARPS spectrograph. At candidate periods of 1.97, 3.06, and 4.66 days, the YZ Ceti system potentially represents another compact multi-harmonic system like TRAPPIST-1. TESS will observe YZ Ceti in late 2018, and all of the reported planets have relatively high ($P \sim 5$\%) geometric transit probabilities. Ground-based exoplanet surveys are plagued by difficulties associated with temporal sampling. Uneven time sampling caused by shared telescope resources, seasonal target observability, weather, and the day/night cycle limit sensitivity in certain regions of frequency space, and can create ambiguities in others. Aliasing occurs when a continuous signal is observed at a cadence such that the observations cannot distinguish between the true signal frequency and a combination of the signal and observing frequencies. RV surveys are commonly hampered by the ``1-day alias", and periodograms of RV data will often show peaks at the frequency of a planet ($f_p$) and its alias at $f_a = f_p \pm 1$ day$^{-1}$. This effect was demonstrated most powerfully by \citet{dawson10}, who revised the period of 55 Cnc e from 2.8 days \citep{mcarthur04} to its true value of 0.75 days, where it was later found to transit \citep{winn11}. In this Letter, we argue that the periods of two of the three planets orbiting YZ Ceti are not well determined due to aliasing in the HARPS RV time series. For planet b, which has a period of either 1.97 or 2.02 days, the difference is primarily important for the efficiency of identifying potential transits. On the other hand, the period of planet c may be 0.75 days rather than 3.06 days, which significantly alters its derived physical properties and geometric transit probability. Given that the available RVs are unable to clearly distinguish between these candidate periods, it will be especially important to examine all potential transit windows in TESS lightcurves of YZ Ceti. | Our analysis suggests the available HARPS RVs of YZ Ceti are incapable of distinguishing unambiguously between 1-day aliases for the periods of planets b and c. Our periodograms and model comparisons show a slight preference for revising the period of planet c to 0.75 days, but determining an exact period for planet b is more difficult. If the period of planet c is in fact 0.75 days, its minimum mass drops to just above half the Earth's mass, and its transit probability increases to 10\%. | 18 | 8 | 1808.07059 |
1808 | 1808.04746_arXiv.txt | Axions are increasingly favoured as a candidate particle for the dark matter in galaxies, since they satisfy the observational requirements for cold dark matter and are theoretically well motivated. Fluctuations in the axion field give rise to stable localised overdensities known as axion stars, which, for the most massive, compact cases, are potential neutron star mimickers. In principle, there are no fundamental arguments against the multi-messenger observations of GW170817/GRB170817A/AT2017gfo arising from the merger of a neutron star with a neutron star mimicker, rather than from a binary neutron star. To constrain this possibility and better understand the astrophysical signatures of a neutron star--axion star (NSAS) merger, we present in this work a detailed example case of a NSAS merger based on full 3D numerical relativity simulations, and give an overview of the many potential observables - ranging from gravitational waves, to optical and near-infrared electromagnetic signals, radio flares, fast radio bursts, gamma ray bursts, and neutrino emission. We discuss the individual channels and estimate to which distances current and future observatories might be able to detect such a NSAS merger. Such signals could constrain the unknown axion mass and its couplings to standard baryonic matter, thus enhancing our understanding of the dark matter sector of the Universe. | Introduction} The breakthrough discovery of GW170817~\cite{TheLIGOScientific:2017qsa} with the combined detection of the gamma-ray burst GRB170817A~\citep{Monitor:2017mdv} and the transient AT2017gfo~\citep{GBM:2017lvd} was the first coincident observation of gravitational waves (GWs) and electromagnetic (EM) waves from the same astrophysical source, and heralded a new era of multi-messenger astronomy. While there is good evidence that GW170817, GRB170817A, and AT2017gfo were created by the coalescence and merger of two neutron stars (NSs)~\citep{Abbott:2018wiz,Abbott:2018exr}, it cannot yet be ruled out that the observed GW and EM signals came from the merger of a NS with a NS-mimicker. As shown in~\cite{Cardoso:2017cfl,Sennett:2017etc} it is difficult to clearly distinguish NSs from exotic compact objects, e.g.~boson stars (BSs), with second generation GW detectors. BSs are stable solitonic solutions to the coupled Einstein-Klein-Gordon equations, which describe a massive scalar field in the presence of gravity. Axion stars (ASs) are a particular kind of BS - real scalar field oscillotons with additional self interactions given by their non trivial field potential $V(\phi)$. Axions, although still unobserved, are theoretically well motivated: they explain the observed matter-anti-matter asymmetry via CP violation~\citep{Peccei:1977hh}, arise naturally in string theory compactifications (see e.g.~\cite{Arvanitaki:2009fg}), and are promising candidates for dark matter (DM) (see ~\cite{Marsh:2015xka} for a comprehensive review). ASs can form dynamically during the collapse of axion miniclusters in the early universe \citep{Hogan:1988mp,Kolb:1993zz} in a process similar to galactic core formation in ultra-light axion cosmologies \citep{Schive:2014dra,Veltmaat:2018dfz}, by wave condensation \citep{Levkov:2018kau}, or from non-standard primordial perturbations with enhanced small-scale power \citep{Widdicombe:2018oeo}. Whilst these scenarios generally predict the substantial majority of axionic dark matter to remain unbound, or bound in ASs in the low mass range, the high-mass tail of the AS mass fraction at low redshifts is widely unconstrained, motivating an exploration of observable signatures. In this work we build on the results of~\cite{Clough:inprep} in which a large number of different NSAS configurations were simulated. Although restricted to head-on collisions the simulations showed that for NSAS systems close to the threshold of BH formation a large fraction of the bosonic and baryonic material can be ejected from the system and that a significant release of GW energy occurs during the collision and the post-merger phase. Here we present a detailed case study of the observables from a particular NSAS merger based on the full 3D numerical relativity simulations. Using our simulation results, we also consider semi-analytically the potential conversion of axions to photons due to couplings to standard matter. Combined, these multi-messenger signals would lead to a unique signature for NSAS mergers. Note that to facilitate easier comparison with existing literature, we have used different unit systems for different multi-messenger channels, i.e., we employ geometric units for describing the GW signal, $\rm cgs$-units for the kilonova and radio observations, and Planck units for the discussion of observables caused by the conversion of axions to photons. \begin{figure} \includegraphics[width=\columnwidth]{fig01.png} \caption{Energy density of the axionic matter (top part of each panel) and the baryonic density (bottom part of each panel) for the times $t=9.3,10.8,17.6 \ {\rm ms}$. We also include contour densities lines corresponding to $10^{-7},10^{-6},10^{5},10^{-4},10^{-3},10^{-2}$ for the bosonic energy density (white dashed lines) and baryonic energy density (black dashed lines).} \label{fig:dynamics} \end{figure} | \label{sec:summary} \begin{table} \centering \caption{ A wanted poster: Multimessenger channels for a NSAS merger. The columns refer to: the channel, the observable distance with current state-of-the-art techniques and the estimated observable distance with techniques anticipated for the near future.} \begin{tabular}{l|cc} \hline Channel & $D_{\rm today}$ & $D_{\rm future}$ \\ \hline GW$_{\rm head-on}$ & $\sim 0.1\rm {\rm Mpc}$ & $\sim 10\rm {\rm Mpc}$ \\ GW$_{\rm inspiral}$ & $\sim 100\ {\rm Mpc}$ & $\sim 1000\ {\rm Mpc}$ \\ Kilonova$_{\rm u-band}$ & $\sim40\ {\rm Mpc}$ & $\sim1.5\ {\rm Gpc}$ \\ Kilonova$_{\rm K-band}$ & $\sim250\ {\rm Mpc}$ & $\sim2.5\ {\rm Gpc}$ \\ Radio flare & $\sim1\ {\rm Gpc}$ & $\sim10\ {\rm Gpc}$ \\ Neutrino$_{\rm shock}$ & $\sim 0.1\ {\rm Mpc} $ & $\sim 2\ \rm Mpc$ \\ Neutrino$_{\rm axion-heating}$ & $\sim1\ {\rm Mpc}$ & $\sim 20\ \rm Mpc$ \\ EM burst$_{\rm axions-photon}^{\rm unbeamed}$ & $\sim 40\ {\rm Mpc}$ & $\sim 90\ {\rm Gpc}$ \\ EM burst$_{\rm axions-photon}^{\rm beamed}$ & $\sim 230\ {\rm Mpc}$ & $\sim 580\ {\rm Gpc}$ \\ \hline \end{tabular} \label{tab:observables} \end{table} We have quantified the possibility of observing our example NSAS merger with different multi-messenger channels, cf.\ Table~\ref{tab:observables}. Interestingly, we found that a number of observables usually connected with BNS or NSBH mergers are also present for NSAS mergers. This could lead to a misinterpretation of observable data, and so further studies identifying clear differences between BNSs and NSASs are required for a less ambiguous interpretation of future multi-messenger observations. Consider for example GW170817 - the optical/infrared/ultra-violet signature of AT2017gfo is broadly consistent with the kilonova signature from NSAS systems, and the signal sGRB170817 could be explained via formation of a BH and disk from a NSAS merger or from axion-photon conversion. We have also shown that NSAS mergers can release up to $M_{AS} = 10^{56}$ GeV in energy in the optical band for reasonable parameter values. Therefore, for some choices of the NS conductivity and magnetic field strength, a NSAS merger could give rise to unusual transients such as AT2018cow~\cite{Prentice:2018qxn}, in which an unexplained optical luminosity of $\sim 44 \, {\rm ergs} \, {\rm s}^{-1}$ was observed. The confirmed detection of a NSAS merger would be a significant discovery, simultaneously confirming the axion as a dark matter component, and constraining its mass, decay constant, and couplings to standard model particles. It would thus provide a lead in our understanding of the nature of dark matter within the Universe. | 18 | 8 | 1808.04746 |
1808 | 1808.06269_arXiv.txt | The total specific angular momentum $j$ of a galaxy disk is matched with that of its dark matter halo, but the distributions are different, in that there is a lack of both low- and high-$j$ baryons with respect to the CDM predictions. I illustrate how \pdf\/ can inform us of a galaxy's morphology and evolutionary history with a spanning set of examples from present-day galaxies and a galaxy at $z\sim 1.5$. The shape of \pdf\/ is correlated with photometric morphology, with disk-dominated galaxies having more symmetric \pdf\/ and bulge-dominated galaxies having a strongly-skewed \pdf\/. Galaxies with bigger bulges have more strongly-tailed \pdf\/, but disks of all sizes have a similar \pdf\/. In future, \pdf\/ will be useful as a kinematic decomposition tool. | Angular momentum (AM) is a fundamental parameter in the evolution of galaxies. A dark matter (DM) halo spinning up in the early universe is subject to the same tidal torques as the baryons at its centre, so the total AM of both components is linked, and the specific AM, $j = J/M$ of the baryons is well matched to $j$ of the DM, (e.g \cite[Catalan \& Theuns 1996]{Catalan+1996}). $j$ is connected to photometric morphology via the stellar mass -- specific AM -- morphology plane, first shown by \cite[Fall 1983]{Fall83}, such that galaxies with higher $M_*$ have higher $j$, modulo morphology, with the relation for earlier type galaxies offset to lower $j$. This has since also been shown by \cite[Romanowsky \& Fall (2012)]{RF12}, \cite[Obreschkow \& Glazebrook (2014)]{OG14}, \cite[Cortese et al. (2016)]{Cortese+2016}, \cite[Posti et al. (2018)]{Posti+2018}, and \cite[Sweet et al. (2018)]{Sweet+2018}. Although the total $j$ for baryons and DM is linked, further physical processes affect the distribution of $j$ for baryons. \cite[van den Bosch et al. (2001)]{vdb+01} studied the probability density function of $j$ normalised to the mean of the galaxy, \pdf, and found that dwarf galaxies had a deficit of high-$j$ and of low-$j$ material with respect to the prediction for a DM halo. They attributed this to tidal stripping of the outer, rapidly-rotating material and feedback ejecting the inner, dispersion-dominated material respectively. \cite[Sharma \& Steinmetz (2005)]{SS05} then predicted the \pdf\/ for baryonic components (see Fig.\,\ref{ss05}), where bulges, which are dominated by random motions, exhibit a peak at $j=0$, and disks have a \pdf\/ of the form $x$exp$(-kx)$ due to their well-ordered rotation. Also see our updated predictions using the NIHAO simulations (Wang+ in prep)). The \pdf\/ encodes more physical information than photometry alone, so in this work I am investigating the utility of \pdf\/ as a kinematic tracer of morphology and kinematic decomposition tool. \begin{figure} \begin{center} \includegraphics[width=0.4\linewidth]{SS05.png} \caption{Predictions from \cite[Sharma \& Steinmetz 2005]{SS05} for baryonic galaxy components. The \pdf\/ for bulge peaks at $j=0$, while disk components have an exponential profile.} \label{ss05} \end{center} \end{figure} | The \pdf\/ traces kinematic morphology of a galaxy. It encodes more physical information than photometry alone, and is a product of the evolutionary history of the galaxy. In future, as spatial resolution increases, I predict that \pdf\/ will be useful to separate out kinematic components: thin disk from thick disk and bulge, clumps from bulges, and pseudobulges from classical bulges. | 18 | 8 | 1808.06269 |
1808 | 1808.01814_arXiv.txt | {Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio- and asteroseismology reveal a strong extraction of angular momentum from stellar radiation zones % over the whole Hertzsprung-Russell diagram.} {Turbulent transport in differentially rotating stably stratified stellar radiation zones should be carefully modeled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. Only phenomenological prescriptions have been proposed for the transport in the horizontal direction, which however constitutes a cornerstone in current theoretical formalisms for stellar hydrodynamics in evolution codes. We aim at improving its modeling.} {We derive a new theoretical prescription for the anisotropy of the turbulent transport in radiation zones using a spectral formalism for turbulence that takes simultaneously stable stratification, rotation, and a radial shear into account. Then, the horizontal turbulent transport resulting from 3D turbulent motions sustained by the instability of the radial differential rotation is derived. % We implement this framework in the stellar evolution code STAREVOL % and quantify its impact on the rotational and structural evolution of solar metallicity low-mass stars from the pre-main-sequence to the red giant branch. } {The anisotropy of the turbulent transport scales as $N^4\tau^2/\left(2\Omega^2\right)$, $N$ and $\Omega$ being the buoyancy and rotation frequencies respectively and $\tau$ a time characterizing the source of turbulence% . This leads to a {horizontal turbulent transport of similar strength in average that those obtained with previously proposed prescriptions even if it can be locally larger below the convective envelope. Hence the models computed with the new formalism still build up too steep internal rotation gradients compared to helioseismic and asteroseismic constraints. As a consequence, a complementary transport mechanism like internal gravity waves or magnetic fields is still needed to explain the observed strong transport of angular momentum along stellar evolution.}}% {The new prescription % links for the first time the anisotropy of the turbulent transport in radiation zones to their stratification and rotation. This constitutes {an important theoretical} progress and demonstrates how turbulent closure models should be improved to get firm conclusions on the potential importance of other processes that transport angular momentum and chemicals inside stars along their evolution.} | Rotation is one of the key physical mechanisms that deeply modify the dynamics and evolution of stars \citep[e.g.][]{Maeder2009}. The transport of angular momentum and chemicals it induces in their stably stratified radiation zones drives their secular rotational and chemical evolution. Rotation modifies the evolutionary path of stars in the Hertzsprung-Russell diagram (hereafter HRD), % their life-time, their nucleosynthesis, chemical stratification and yields, and their magnetism. In this context, helio- and asteroseismology provide key information through the insight they give on the internal rotation profiles of the Sun and stars. On one hand, helioseismic data show that the radiative core of the Sun is rotating as an almost solid body down to $r=0.2R_{\odot}$ {with a potential central acceleration} \citep{Brownetal89,Thompsonetal2003,Garciaetal2007,Fossatetal2017}. On the other hand, asteroseismic data reveal a strong extraction of angular momentum % over the whole HRD. % First, \cite{Becketal2012}, \cite{Mosseretal2012b}, \cite{Deheuvelsetal2012}, \cite{Deheuvelsetal2014}, \cite{Deheuvelsetal2015}, \cite{Spadaetal2016}, and \cite{Gehanetal2018} found a weak core-to-surface rotation contrast in low-mass subgiant and red giant stars. Next, \cite{Benomaretal2015} observed 26 solar-type stars with a small differential rotation between the base of their convective envelope and the upper part of their radiative core. In addition, weak differential rotation rates are found in the radiative envelope of intermediate-mass and massive stars \citep{Kurtzetal2014,Saioetal2015,Trianaetal2015,Murphyetal2016,Aertsetal2017}. Finally, a strong extraction of angular momentum is required to explain the rotation rates of white dwarfs \citep[e.g.][]{Setal2008,Hermesetal2017} and neutron stars \citep[e.g.][]{Hegeretal2005,HM2010}. In his seminal paper, \cite{Zahn1992} proposed for the first time a consistent and complete formalism to describe the secular transport of angular momentum and chemicals under the combined action of rotation-driven vertical and horizontal turbulence and meridional flows \citep[see also][]{MZ1998,MZ2004}. This theoretical treatment of rotation relies on a key physical assumption: an anisotropic turbulent transport in stellar radiation zones stronger in the horizontal (latitudinal) direction than in the vertical one because of the restoring buoyancy force along the radial entropy (and chemical) stratification. This strong horizontal transport erases horizontal gradients of physical quantities, among which angular velocity, thus enforcing a "shellular" rotation depending only on the radial coordinate. This framework allowed for a successful implementation in 1D stellar evolution codes \citep{Talonetal1997,MeynetMaeder2000,Palaciosetal2003,Decressinetal2009,Ekstrometal12,Marquesetal2013,ChieffiLimongi2013} with numerous applications over a broad range of stellar types and evolutionary stages. However, disagreements between the predictions of this formalism and seismic data on internal stellar rotation at various stages of the evolution \citep{TZ1998,TCetal2010,Eggenetal2012,Marquesetal2013,Ceillieretal2013} led the community to examine the role of other transport mechanisms for angular momentum, such as internal gravity waves \citep[e.g.][]{TKZ2002,TC2005,CT2005,Charbonneletal13,Rogers2015,Pinconetal2017} and magnetic fields \citep[e.g.][]{GM1998,Spruit1999,MZ2005,Eggenbergeretal05,DP07,SBZ2011,AcevedoGaraudWood2013,Barnabeetal2017}. At the same time, the physical description of shear-induced vertical and horizontal turbulence in stably stratified stellar layers was not questioned. The aim of the present paper is to bring a new light on the hydrodynamical processes induced by rotation and on their role in the whole picture, based on the most recent numerical and theoretical developments. % In this context, recent high-resolution numerical simulations in local Cartesian configurations that were performed to estimate the turbulent transport induced by the instability of a vertical shear \citep{Pratetal2013,Pratetal2014,Pratetal2016,Garaud2016,Garaud17} can be used for guidance. Their comparison with former phenomenological prescriptions for related turbulent transport coefficients in the radial direction \citep{Zahn1992,TZ1997} indeed invites stellar astrophysicists to reconsider this status. This is particularly true for turbulence in the horizontal direction. Indeed, while strong stratification is invoked as the source of the strong anisotropic transport \citep{Zahn1992}, none of the currently used prescriptions for horizontal turbulent transport coefficients in stellar evolution codes depends explicitly on the two restoring forces in stellar radiation zones: stratification and rotation. Two mechanisms can be identified to sustain the horizontal turbulent transport: (i) the instability of the shear of the latitudinal differential rotation, but also (ii) the 3D turbulent motions induced by the instability of the radial differential rotation that transport momentum and chemicals both in the vertical and horizontal directions. Symmetrically, \cite{Zahn1992} already identified the two sources for the vertical turbulent transport, i.e., (a) the instability of the shear of the radial differential rotation and (b) the transport induced by the 3D turbulent motions induced by the instability of the latitudinal differential rotation. He introduced the corresponding vertical turbulent transport coefficients, $\nu_{\rm v,v}$ and $\nu_{\rm v,h}$, modelled as eddy-viscosities, and the corresponding eddy-diffusivities, $D_{\rm v,v}$ and $D_{\rm v,h}$. Note that in stellar physics modeling though, the simplifying assumption % $\nu_{\rm v,v}\equiv D_{\rm v,v}$ and $\nu_{\rm v,h}\equiv D_{\rm v,h}$ has been % made until now. Symmetrically, % four coefficients $\nu_{\rm h,h}$, $D_{\rm h,h}$, $\nu_{\rm h,v}$ and $D_{\rm h,v}$ can also be defined for the horizontal transport (Tab. \ref{tab:coefficient} is recapitulating the different turbulent diffusivities (viscosities) and their source). On one hand, the first developments focused on the instability of the latitudinal differential rotation (i.e. on $\nu_{\rm h,h}$ and $D_{\rm h,h}$). \cite{Zahn1992} initially proposed a prescription based only on phenomenological arguments. Next, \cite{Maeder2003} derived a prescription based on the evaluation of the dissipation of the energy contained in a horizontal shear. Finally, \cite{MPZ2004}, derived a prescription based on results observed for turbulent transport in a non-stratified Taylor-Couette experiment \citep{RZ1999}. On the other hand, theoretical works \citep[e.g.][]{BC2001,KB2012} and numerical simulations \citep{WB2006,KB2012} in fundamental and astrophysical fluid dynamics have been devoted to characterize key properties of anisotropic turbulent flows in rotating stably stratified media, such as velocities and length scales in the vertical and horizontal directions. This is a good motivation to also consider the horizontal transport induced by 3D turbulent motions sustained by the instability of the radial differential rotation, which has been ignored until now. In this work, we derive a new prescription for the corresponding turbulent transport coefficients (i.e. $\nu_{\rm h,v}$ and $D_{\rm h,v}$). This allows us to propose for the first time an expression that depends explicitly on stratification, rotation, and their ratio. In Sect.~\ref{sec:fluid}, we generalize the spectral model introduced by \cite{KB2012} to study the anisotropy of turbulent flows in differentially rotating stably stratified layers and we derive scaling laws allowing us to establish our new prescriptions. In Sect.~\ref{sec:appli}, we implement them in the stellar evolution code STAREVOL. We study their impact on the rotational and structural evolution of a 1.0$M_\odot$ star during its pre-main sequence and main-sequence and on the subgiant and giant phases of a 1.25$M_\odot$ star. Finally, we discuss results and perspectives of this work in the conclusion (Sect.~\ref{sec:conclusion}). \begin{table*}[ht!] \begin{center} \caption{The turbulent diffusivities (viscosities) and their source.} \begin{tabular}{ c c } \hline \hline $D_{\rm v,v}$ ($\nu_{\rm v,v}$) & Vertical turbulent transport induced by the vertical shear instability \\ $D_{\rm h,v}$ ($\nu_{\rm h,v}$) & Horizontal turbulent transport induced by the 3D motions of the vertical shear instability \\ $D_{\rm h,h}$ ($\nu_{\rm h,h}$) & Horizontal turbulent transport induced by the horizontal shear instability \\ $D_{\rm v,h}$ ($\nu_{\rm v,h}$) & Vertical turbulent transport induced by the 3D motions of the horizontal shear instability\\ \hline \end{tabular} \label{tab:coefficient} \end{center} \end{table*} | \label{sec:conclusion} In this work, we derive new theoretical prescriptions for the anisotropy of the turbulent transport in differentially rotating stellar radiation zones. Extending the theoretical formalism derived by \cite{KB2012} to the case of rotating stably stratified flows with a vertical shear, we find that the ratio between the horizontal and the vertical turbulent transport scales as $N^4\tau^2/\left(2\Omega^2\right)$, where we recall that $N$ and $\Omega$ are the buoyancy and rotation frequencies, respectively, and $\tau$ is the time characterizing the source of the turbulence. This shows that if anisotropy increases with stratification, the Coriolis acceleration constitutes the restoring force in the horizontal direction, which was % ignored in previously derived prescriptions. We propose here three physically-motivated expressions for $\tau$: $\tau=1/S$, $1/\left(2\Omega+S\right)$, and $1/N_{\Omega}$, where $S$ is the shear and $N_{\Omega}$ the epicyclic frequency. The first choice corresponds to the model for the turbulent transport induced along the radial direction by the vertical shear instability proposed by \cite{Zahn1992} and validated by recent direct numerical simulations \citep[][]{Pratetal2013,Garaud2016}. The second and third choices correspond to the introduction of the influence of rotation on the shear-induced turbulence. Their robustness should be validated in a near future by direct numerical simulations of rotating stably stratified flows with an unstable vertical shear in the range of parameters that corresponds to stellar regimes. These needed simulations, which are out of the scope of this work, will also allow us to improve the \cite{Zahn1992}'s turbulent model by taking into account the action of the Coriolis acceleration, of the chemical stratification and viscosity as in \cite{Pratetal2016}, and of the interactions with the horizontal turbulence \citep{TZ1997}. Then, the turbulent transport coefficient in the horizontal direction, induced by the 3D turbulent motions sustained by the vertical shear-driven instability, scales as $Ri_{\rm c}\displaystyle\left(N/2\Omega\right)^2 K f(S,\Omega)$, where $\rm Ri_{c}$ and $K$ are the critical Richardson number and thermal diffusivity, respectively, and $f$ is a function that depends on the prescription chosen for $\tau$, when assuming the model proposed by \cite{Zahn1992} for the vertical turbulent transport coefficient. We identify that $f=1$ for $\tau=1/S$. % We recall that all the previous prescriptions \citep{Zahn1992,Maeder2003,MPZ2004} have no explicit dependence on the entropy (and chemicals) stratification and do not take the action of the Coriolis acceleration into account, although these are the two restoring forces for turbulent flows in differentially rotating stellar radiation zones. When applied to complete stellar evolution models of rotating low-mass, solar-metallicity stars, accounting for the feedback of the vertical shear in the horizontal direction ($D_{\rm h} = D_{\rm h,h}+D_{\rm h,v}$), the new prescriptions do not modify greatly the results previously obtained using the \citet{MPZ2004} prescription ($D_{\rm h} = D_{\rm h,h}$) for the internal and surface rotation rates. Although the horizontal turbulent transport induced by 3D motions triggered by the vertical shear instability can have a very high amplitude locally (for instance below the convective envelope of low-mass main-sequence stars), it is a self-regulated mechanism. Indeed, if the vertical shear is unstable and leads to important $D_{\rm h}$, an efficient meridional circulation is triggered that weakens the radial differential rotation to values below the threshold needed to sustain the vertical shear instability and the source of the associated strong horizontal turbulent transport thus vanishes. This also leads to a quenching of the vertical turbulent transport. As a consequence, this mechanism is not able to provide the extraction of angular momentum from stellar cores needed to explain their rotation rates in the Sun and in main-sequence, subgiant and red giant low-mass and intermediate-mass stars. A supplementary mechanism such as internal gravity waves or/and magnetic fields and their instabilities should thus be invoked. In this framework, this work demonstrates the great importance of pursuing the efforts to consistently model turbulent transport induced by rotation-driven hydrodynamical instabilities, that have a major impact on the structural and rotational evolution of stars. This strongly motivates future works to improve: (i) the physical description of the radial turbulent transport induced by the vertical shear instability with taking the action of the Coriolis acceleration, the effects of the chemical stratification and of viscosity \citep[][]{Pratetal2016}, and the interactions with the horizontal turbulence \citep{TZ1997} into account; (ii) the prescriptions for the horizontal and vertical turbulent transports induced by instabilities of the horizontal differential rotation. Their strengths have to be carefully evaluated in order to be able to discuss in a consistent framework the effects of other transport mechanisms of angular momentum such as internal gravity waves and magnetic fields. | 18 | 8 | 1808.01814 |
1808 | 1808.05231_arXiv.txt | We study an idealized 1D model for the evolution of hot gas in dark matter halos for redshifts $z=[0,6]$. We introduce a numerical setup incorporating cosmological accretion of gas, along with the growth of the halo, based on the Van den Bosch model for the average growth of halos as a function of cosmic time. We evolve one-dimensional Lagrangian shells with radiative cooling of the gas and heating due to feedback from the gas cooling and moving in toward the center. A simple Bondi accretion model on to a central black hole is used to include feedback heating. The setup captures some of the key characteristics of spherically symmetric accretion onto the halos: formation of virial shocks slightly outside $r_{200}$ and long-term thermal balance in the form of cooling and heating cycles. The gas density outside our initial halos at $z=6$ is constrained by requiring that the baryon fraction within the virial radius for non-radiative evolution be equal to the universal value at almost all times. The total mass in the cold phase (taken to be $\sim 10^4$ K) within $40$ kpc is tracked as a function of the halo mass and redshift. We compare the evolution of the cold gas mass to the observed stellar-mass versus halo mass relations, following which, we can constrain the feedback energy required for different halo masses and redshifts. We also compare and match the hot gas density and temperature profiles for our most massive halo to those of clusters observed upto redshift $2$. Our model is thus an improvement over the semi-analytic models in which isothermal condition and $\rho \propto r^{-2}$ are assumed. | Galaxy formation is known to be an outcome of gravitational processes (clustering) and gas-dynamical effects acting together. The success of N-body simulations lies in their ability to predict the detailed clustering properties of galaxies from initial conditions set by the $\Lambda$CDM cosmological model (\citealt{1985Nature_frenk}, \citealt{1985Apj_davis}, \citealt{2000MNRAS_colberg}). However, radiative cooling and dissipation become important when attempting to predict the detailed physical properties of galaxies, such as their stellar masses and star formation rates. Semi-analytic models with radiative cooling, star formation and quenching by AGN and supernova feedback, provide a simple description of the relevant gas physics, but are unable to track the spatial distribution of the gas in any detail (\citealt{2005Nature_sw}, \citealt{2006MNRAS_croton}). The advent of cosmological hydrodynamic simulations (\citealt{1989ApJ_hernquist}, \citealt{2000gadget2}, \citealt{2001gadget}, \citealt{2002ApJ_murali}, \citealt{2014MNRAS_illustris}) provided better means to treat gas dynamics more self-consistently. However, current simulations are very expensive or do not have the sufficient mass resolution to study the small scale physics in detail in very large cosmological volumes (\citealt{2018MNRAS_pillepich}, \citealt{2017MNRAS_tremmel}). In addition, ``sub-grid'' models are used for studying small-scale, unresolved physical processes like star formation and feedback (\citealt{2002MNRAS_Kay}, \citealt{2005Nature_matteo}, \citealt{2008ApJ_puchwein}, \citealt{2015MNRAS_crain}). Three dimensional hydrodynamic simulations have been able to track the spatial distribution of gas with reasonable accuracy, but it is challenging to study the role of different subgrid recipes in a controlled way. Compared to these, one-dimensional hydrodynamic models are computationally less expensive and often provide valuable insight into the physics of gas and its radial distribution, while retaining simplicity. It is easy to generalize these to more realistic 2D/3D simulations and perform controlled parameter survey to elucidate the physical inputs that are necessary to match different aspects of the observational data. In the standard picture of spherical infall of gas (\citealt{1972ApJ_gunngott}, \citealt{1985ApJS_bertschinger}) into the dark matter halos, the accreting IGM is heated to the halo virial temperature behind an expanding virial shock. The gas is first supported by pressure in quasi-hydrostatic equilibrium. It cools radiatively, gradually contracting and forming a cold disk in which star formation happens (\citealt{1980MNRAS_fall}, \citealt{1998MNRAS_momaowhite}). One-dimensional Lagrangian models of gas in dark matter halos, incorporating this standard picture, have been around for a long time. One of the earliest papers (\citealt{1988MNRAS_thomas}) studies multiphase gas in the intracluster medium with balance of cooling and inflow. However, only gas is evolved in this model and not dark matter. \cite{thoul_weinberg1_94} introduced a spherical collapse of two-fluid system including gas (radiatively cooling) and dark matter. % In our model, we use a numerical scheme similar to \cite{thoul_weinberg1_94} but with different treatment of gravity due to dark matter, radiative cooling and heating that is expected from supernovae/AGNs. This combined model of cosmological growth of halos and realistic energetics of gas has not been carried out before in a simple, Lagrangian set-up. The first treatment of gravity as a gradually deepening potential well, that we use in our model, was presented in \cite{1978ApJ_parrenod}. \cite{1997MNRAS_knight} later added radiative cooling and concluded that in low-mass halos the baryon content is overpredicted in such a model. Thus the idea of a central source of heating became indispensable. Through a simple spherical 1D model which incorporates dark matter and gas, \citealt{2003MNRAS_birnboimdekel} (see also \citealt{1991ApJ...379...52W}) showed that the virial shock in smaller halos ($\lesssim 10^{12}~{\rm M_{\odot}}$), is not stable and in such cases gas is not heated to the virial temperature due to efficient radiative cooling and directly falls to the halo center (this is known as cold-mode accretion).\footnote{Even low mass halos may have hot gas because of feedback and mergers (e.g., see \citealt{sokolowska_2017}). Earlier works on cold mode only considered radiative cooling and ignored heating due to mechanical feedback.} In 3-D cosmological simulations the cold mode appears in the form of a number of cold streams feeding the central galaxy (\citealt{2005MNRAS_keres}, \citealt{2009Nature_dekel}, \citealt{2009MNRAS_Keres}; but also see \citealt{2013MNRAS.429.3353N}); however, cold streams cannot be captured by a 1D model such as ours. The virial shock is very stable at cluster scales and the hot gas is close to hydrostatic equilibrium (\citealt{2018arXiv_oppen}), except in the central parts where the cooling time is usually shorter. The gas that cools out within the central region of the massive halos, is considered to be the only source of fuel for star formation. In order to quantify stellar content in halos, the relation between the stellar mass of the central galaxy and the host halo mass has been parameterized extensively for a wide range of halos. The mass function of dark matter halos, calibrated from large-scale simulations, is combined with the observed number density of galaxies as a function of their stellar mass using a technique called statistical abundance matching (\citealt{2010ApJ_moster}, \citealt{2013ApJ_moster}). We adjust our very simple feedback model parameters to match the average stellar mass and halo mass relation. While bigger halos have higher stellar mass, the ones hosting more massive black holes are observed to have smaller star formation rates on average (\citealt{2018Nature_navarro}). But this only indirectly suggests that energy feedback from black hole may regulate cooling in large gaseous halos. The clearest evidence of black hole feedback comes from observations of synchrotron-emitting radio lobes that are co-spatial with the X-ray cavities found in galaxy clusters. The work done to inflate such huge bubbles, comparable to the energy required to prevent cooling flows (\citealt{fabian94}, \citealt{2011ApJ_cavagnolo}) in clusters, can only come from accretion onto supermassive black holes. Earlier detailed observations of gaseous halos study clusters and groups in X-rays at low redshifts. The radial profiles of density, temperature and entropy have been extensively studied for low-redshift ($z=0.05-0.2$) clusters (\citealt{2005ApJ_vikhlinin}, \citealt{2005A&A_pointecouteau},\citealt{2006ApJ_vikhlinin}, \citealt{2006ApJ_kotov}, \citealt{accept09}). Quenching of the cooling of hot gas, has been seen in the observations of cavities that put important constraints on AGN outburst energy and mean jet power (\citealt{2004ApJ_birzan}, \citealt{2011ApJ_cavagnolo}, \citealt{1993MNRAS_boehringer}, \citealt{2003MNRAS_fabian}, \citealt{2000ApJ_mcnamara}). Recently the redshift evolution of galaxy clusters is traced for SZ selected clusters using the X-ray data (\citealt{2011ApJ_marriage}, \citealt{2014ApJ_mcdonald}, \citealt{2013ApJ_mcdonald}, \citealt{2017ApJ_nurgaliev}, \citealt{2017ApJ_mcdonald}). It hints at the invariant cooling properties and X-ray morphology of clusters till $z \approx 2$. We present comparisons of the radial gas density profiles of such SZ selected halos with that of the cluster in our model. Current observations also study the radial profiles of baryon fraction in clusters and groups by tracking the free electrons using kinetic SZ effect (e.g \citealt{2016PhRvD_schaan}) and may provide constraints on the simulations. % In this paper, we propose a very simple yet useful 1-D model for the evolution of the gas in smoothly growing, isolated dark matter halos with only a few adjustable parameters. The model is tuned to match the observed relation between stellar mass and halo mass. We disregard direct effects of mergers as well as processes affecting satellite galaxies, such as ram pressure stripping and strangulation. While this is a limitation, this allows us to focus on the interplay of smooth build-up of the halo and feedback heating and cooling. From our models, we get the following important perspectives on the state of baryons within the halos: (1) the radial profiles of gas density and temperature in massive clusters, (2) total feedback energy required to regulate cooling and heating in halos of different masses (3) how the baryon fraction evolves when we constrain the global energetics using the relation of stellar mass and halo mass. This model can be useful to modify the semi-analytic models of galaxy formation that do not follow gas-dynamical processes in detail. This model may also provide an useful middle-ground between the idealized simulations of isolated clusters, groups and smaller halos (\citealt{2017MNRAS_fielding}) that do not evolve the halo with redshift and the cosmological hydrodynamic simulations. The latter, besides being expensive, often lack sufficient resolution to study the diffuse gas (ICM/CGM) away from the center in an individual halo. Hence future extension of our model to 2D/3D will be relevant for quantifying the content of multiphase gas in the outskirts of the halos, which will be particularly interesting with respect to the COS-HST survey (\citealt{tumlinson17}). The paper is organized as follows. In section \ref{sec:physset} we describe the set-up for our numerical experiments including the initial conditions, in section \ref{sec:res} we present all our results for four different halos with a wide range of masses excluding and including radiative cooling and feedback and finally in section \ref{sec:disc} we discuss the implications of our results and caveats in detail. | \label{sec:disc} We propose a very simple, generalized 1D model for gas in dark matter halos in which the cosmological growth of the halos and accretion of baryons are taken into account on an average. We incorporate idealized models for radiative cooling and feedback heating to quantify the energy budget characteristic of each halo (satisfying the abundance matching relation between stellar mass and halo mass). We extend the existing 1D models (\citealt{1978ApJ_parrenod}, \citealt{1997MNRAS_knight}) and emphasize the importance of central energy source, by adding realistic amount of feedback heating proportional to the spherical accretion rate. This enables us to compare the temporally varying state variables of the medium as well as the time-integrated quantities with those of existing models and observations and test the validity of the model which grows halos smoothly over cosmological times. The thermodynamics of the gas in clusters and groups is interesting to study, particularly with the advent of future galaxy redshift surveys and the measurement of the kinetic and thermal Sunyaev-Zel'dovich signal (\citealt{2017arXiv_lim}, \citealt{2018ApJ_park}, \citealt{2016PhRvD_schaan}) combined with the existing X-ray observations. In order to test a large number of ICM models and reasonable parametric profiles to compare with new observations, simple semi-analytical models (\citealt{2017ApJ_flender} ) are preferred over large scale hydrodynamic simulations. However, our 1D model, with hydrodynamic evolution of baryons, is computationally less expensive. Moreover, this model can be easily extended to multidimensional simulations of gas in halos without directly evolving dark matter particles. Thus great simplification can be achieved without entirely losing the physics of cosmological accretion of baryons and dark matter. Following are the important conclusions from our 1D model: \begin{itemize} \item We see the cosmological infall of gas, starting from a small initial halo, undergoing virial shock at radius slightly greater than $r_{200}$, which is fixed by the mass accretion history. But the virial radius is roughly half of the turnaround radius of the falling gas shells. Using a simple profile for the gas reservoir outside the halo, we can ascertain that the average baryon fraction within the halo, in absence of cooling and feedback, is close to the universal value. This provides an attractive setup for multi-dimensional simulations in which the outer boundary is much further out than the virial radius. % \item For pure radiative cooling, cold mode accretion may dominate for very small halos ($\lesssim 10^{11}~{\rm M}_{\odot}$). This halo mass is a few times smaller than in \cite{2003MNRAS_birnboimdekel}. So our model incorporates both hot and cold mode accretion in appropriate conditions. In the smallest halo, the gas cools out and loses pressure support fast in the absence of central heating and this often raises the baryon fraction beyond the universal value. On the contrary, the biggest halo retains enough hot gas even in the absence of feedback. This causes it to maintain the universal baryon fraction as the outskirts are hot and pressure-supported while only the gas in the central region cools and falls to the center. The cosmological accretion rate in the cluster-scale halos is high and a large amount of shock-heated gas continuously joins the halo. However, we revert to the 2D/3D generalisation for studying the detailed physics and survival of cold streams joining the halo in cold-mode. % \item We tune our feedback (modelled as Bondi-Hoyle-Lyttleton accretion) parameters to obtain a stellar mass-halo mass relation consistent with abundance matching ( \citealt{2010ApJ_moster}). We use the total cold gas mass within the central $40~{\rm kpc}$ as a proxy for the stellar mass. % These fiducial runs including cooling and feedback provide realistic estimates of the energy budget in each halo. These fiducial runs lead to the following inferences: \begin{itemize} \item The baryon fraction evolution of all the halos show signatures commonly predicted; e.g., smaller halos have majority of baryons missing due to the ejection by feedback and the biggest halos maintain the baryons by intermittent cooling and heating cycles (\citealt{prasad15}). In the former case, the cycles are delayed as it takes a long time for the gas to be recycled, while on cluster scales, the feedback-heated gas remains inside the halo and moves to the center quite fast. \item The time-averaged density profile for our cluster-scale halos match well with {\it Chandra} clusters and recent Sunyaev-Zel'dovich-selected clusters followed-up in X-rays (\citealt{2017ApJ_mcdonald}, % Figure \ref{fig:fig17}). Note that, we are only concerned with the average number density profiles in this work. The feedback efficiencies and the mass accretion history can be tweaked to study different kinds of cluster profiles (cool-core properties). We will revert to this in our future multidimensional version of the model. The interplay of local thermal instability and gravity, which gives the important parameter $t_{\rm cool}/t_{\rm ff}$, can also be modelled only in more than one dimensions (\citealt{choudhury16}). \item A flattening of the equation of state (or broken power-law as discussed in \citealt{2017ApJ_flender} ) is seen in all the halos that include cooling and heating. Inside the virial shock, $\Gamma$ (where $p \propto \rho^{\Gamma}$) is around $1.1$ while in the core it falls down to around $\approx 0.4-0.6$. \item We use a crude estimate of the black hole mass from the idealized Bondi accretion rate (Eddington limited). We see that in groups and clusters the black holes, with a reasonably high seed mass at $z=6$, grow significantly till only around $z=2$. \item The supernova power estimated from Kroupa IMF and our simple estimate of the star formation rate, suggest that AGN feedback is relevant for all the halos and absolutely necessary for clusters.% The average feedback power ($\approx 10^{46}$) in $M_{14}$ is comparable to the highest powers observed for many cooling clusters with X-ray cavities and radio lobes. This implies for all our halos, the feedback powers are overestimated. We conclude that in 1D models, a large fraction of the thermal energy gets used up in uplifting the gas. In multidimensional version of our model, AGN jets will uplift gas in its wake, along a specific direction, and the central gas shells are not entirely ejected like in our 1D model. \end{itemize} \end{itemize} However, the general properties of this simple model are consistent with observations and other existing models. It will be extremely efficient and reasonably accurate to survey the physical parameter space using this model in 3D, incorporating smooth cosmological accretion, radiative cooling and feedback heating self-consistently. This may provide an ideal testbed to study the average evolution of the diffuse gas of the CGM, particularly at large radii and outskirts of the halos, which are now observable by current spectroscopic surveys. | 18 | 8 | 1808.05231 |
1808 | 1808.09968_arXiv.txt | Intensity mapping surveys will provide access to a coarse view of the cosmic large-scale structure in unprecedented large volumes at high redshifts. Given the large fractions of the sky that can be efficiently scanned using emission from cosmic neutral hydrogen (HI), intensity mapping is ideally suited to probe a wide range of density environments and hence to constrain cosmology and fundamental physics. To efficiently extract information from 21cm intensities beyond average, one needs non-Gaussian statistics that capture large deviations from mean HI density. Counts-in-cells statistics are ideally suited for this purpose, as the statistics of matter densities in spheres can be predicted accurately on scales where their variance is below unity. We use a large state-of-the-art magneto-hydrodynamic simulation from the IllustrisTNG project to determine the relation between neutral hydrogen and matter densities in cells. We demonstrate how our theoretical knowledge about the matter PDF for a given cosmology can be used to extract a parametrisation-independent HI bias function from a measured neutral hydrogen PDF. When combining the predicted matter PDFs with a simple bias fit to the simulation, we obtain a prediction for neutral hydrogen PDFs at a few percent accuracy at scale $R=5$ Mpc$/h$ from redshift $z=5$ to $z=1$. Furthermore, we find a density-dependent HI clustering signal that is consistent with theoretical expectations and could allow for joint constraints of HI bias and the amplitude of matter fluctuations or the growth of structure. | Upcoming large-scale, post-reionisation intensity mapping surveys like Tianlai \citep{Chen_2012}, BINGO \citep{Battye13BINGO}, CHIME \citep{CHIME14pathfinder}, FAST \citep{fast}, HIRAX \citep{Newburgh16HIRAX}, MeerKAT \citep{MeerKAT}, SKA \citep{Santos15SKA} and SPHEREx \citep{Dore16SPHEREx} will sample the spatial distribution of cosmic matter through tracers of it, such as neutral hydrogen, at redshifts $0<z<6$. The advantages of those surveys with respect to traditional optical methods to map galaxies is that they can sample very large cosmological volumes in a very efficient manner. Following early ideas of intensity mapping \citep{Madau97,Bharadwaj01,Battye04,Barkana05}, the first detection of the 21cm cosmological signal was achieved by cross-correlating 21cm intensity maps from the Green Back Telescope with the DEEP2 optical galaxy survey \citep{Pen09,Chang10,Masui13}. While we have not yet detected the 21cm cosmological signal in auto-correlation in the post-reionisation era\footnote{see \cite{Bowman} for a detection claim at high-redshift.} \citep{Switzer13}, upcoming surveys will have sensitivity enough to allow us to study cosmology at an unprecedented precision with both auto- and cross-correlations \citep{Bull15,Pourtsidou17,Kovetz17,Paco_15, Paco_14, Carucci_15, Andrej_17, Carucci_17,Paco_Lyb}. Furthermore, we can probe dark energy through baryonic acoustic oscillations \citep{Chang08, Paco_17} or approach weak lensing of intensity mapping \citep{Harrison_16, Bonaldi_16, Foreman_18, Schaan18} by using the background as a source image. It is well known that the nonlinear evolution of matter in the Universe introduces a leakage of information from the two-point correlation function (or the power spectrum) into higher-order terms \citep{Scoccimarro_99}. Thus, in order to extract the maximum information from large-scale structure surveys at low redshifts, we need to consider quantities beyond the two-point correlation or to attempt to reconstruct the linear fields \citep{Schmittfull_15}. In this work, we focus on the former approach and consider one-point statistics as complementary source of cosmological information compared to traditional two-point statistics. For the epoch of reionisation, one-point statistics and higher-order moments have been proposed as sources of information about the physics of reionisation and the nature of ionising sources \citep{Harker09,Ichikawa10,Baek10,Shimabukuro15,Kittiwisit18}. At later times, counts-in-cells statistics can capture essential non-Gaussian information from the 21cm intensity (and hence HI density) field that is lost in common two-point statistics and add information about the density-dependence of clustering. Furthermore, the underlying matter statistics in real space can be analytically predicted \citep{Bernardeau2014,Uhlemann16log} from first principles and at percent accuracy for scales at which the variance of the smoothed matter density is below unity. Those scales are typically above $10$ Mpc$/h$ at redshift $z=0$, such that the typical low-angular resolution inherent to intensity mapping is not a major limiting factor. The formalism, based on large-deviation statistics, allows us to access the rare event tails probing large density fluctuations that contain valuable information about fundamental physics (such as neutrino masses, primordial non-Gaussianity and modified gravity) that are inaccessible to common perturbative methods. To tap the potential of this probe for cosmology, we build upon a previous study of dark matter halos \citep{Uhlemann18bias} and quantify the nonlinear bias function that relates matter and neutral hydrogen counts-in-cells on scales where it is nonlinear and distinct from the bias measured from two-point clustering \citep{Castorina17,Villaescusa-Navarro18}. While we focus on cosmology here, counts-in-cells statistics are also used to constrain important astrophysical ingredients such as luminosity functions \citep{Breysse17}. Those could potentially be improved by predictions from large-deviation statistics, which are more accurate than phenomenological lognormal models that are currently used. We use the magneto-hydrodynamic simulation IllustrisTNG simulation to compare counts-in-cells of neutral hydrogen, halos (as galaxy proxies) and matter. Extending on recent results for the clustering statistics of neutral hydrogen \citep{Villaescusa-Navarro18}, we quantify the counts-in-cells bias between the different tracers in IllustrisTNG and determine the effect of redshift-space distortions. Based on this, we assess the promise of mock catalogs to efficiently access exquisitely sampled counts-in-cells while mitigating inaccuracies from neglecting the 1-halo term and Fingers-of-God that appeared as deal breakers for the power spectrum. This paper is organised as follows: Section~\ref{sec:IllustrisTNG} describes the IllustrisTNG simulation and how we extracted counts-in-cells statistics. In Section~\ref{sec:DM} we briefly recap the theoretical formalism that allows us to obtain the probability distribution function (PDF) and the density-dependent correlation of matter densities in spheres. Section~\ref{sec:tracer} discusses how one can relate these results to the tracer PDF and density-dependent clustering using bias models. We present the results for the bias relation between matter and neutral hydrogen along with the combined predictions for the neutral hydrogen PDF and density-dependence of clustering in Section~\ref{sec:results}. Section~\ref{sec:Conclusion} presents our conclusions and provides an outlook of the potential applications of our findings. \begin{figure} \includegraphics[width=\columnwidth]{IllustrisTNG_CIC.png} \caption{Spatial distribution of neutral hydrogen in a $5$ Mpc$/h$ slice of the TNG100 simulation at redshift $z=3$. We also show a small subset of the spheres with radius $R=5$ Mpc$/h$ used for counts-in-cells statistics.} \label{fig:IllustrisTNG} \end{figure} | \label{sec:Conclusion} \textit{Summary.} Building on recent ideas from large-deviation statistics, an accurate theoretical model for counts-in-cells statistics of neutral hydrogen is described. The idea is to rely on analytical predictions for matter and relate them to tracers using a mean bias relation. When combining the analytical results for matter with a nonlinear variance from halofit, one obtains a fully predictive matter PDF that makes it possible to extract a non-parametric bias function from the neutral hydrogen PDF. Based on measurements in the hydrodynamic simulation IllustrisTNG, we determine the relation between matter and neutral hydrogen densities in spheres of $R=5$ Mpc$/h$ from redshift $z=5$ down to $z=1$. The resulting non-parametric bias relation is well-described by a bias expansion up to second order in log-densities, in line with previous results for halos that host most of the neutral hydrogen. The main results for the neutral hydrogen PDF are displayed in Figures~\ref{fig:HIPDF} and~\ref{fig:HIPDFRS} and demonstrate the few percent-level accuracy of the combined analytical model for matter and a mean bias fit both in real and redshift space. In addition, we detect a density-dependent clustering signal for neutral hydrogen (Figure~\ref{fig:spherebiasHI}) that can, in principle, be used to break the degeneracy between the linear tracer bias and the nonlinear variance and jointly constrain $b_1$ and $\sigma_8$. We emphasize that in this paper we are considering single-dish like observations, where neutral hydrogen fluctuations can be directly measured in configuration space. For interferometry observations, the directly observable quantity is the Fourier transform of the intensity flux. Thus, in that case, an approach bearing closer resemblance to observations will be to consider the PDF of mode amplitudes in Fourier-space. \textit{Fundamental physics.} Future intensity mapping surveys will map gigantic volumes that are ideally suited for counts-in-cells statistics that probe the rare event tails and the growth of structure sensitive to dark energy \citep{Codis2016DE}. The regions of particularly low and high density indeed contain considerable information about fundamental physics such as primordial non-Gaussianity \citep{Uhlemann18pNG} and massive neutrinos \Ref{(Uhlemann \& Villaescusa-Navarro, in preparation)}. 21cm offers a unique technique to observe the 3-dimensional matter density field that allows to go beyond current galaxy surveys, where clustering properties of SDSS galaxy clusters are already used to approach constraints on neutrino mass \citep{Emami17}. We also observed a very close correlation between neutral hydrogen and mass-weighted halo densities, which in turn is expected to translate to luminosity-weighted galaxies. This property could be used for synergies between intensity mapping and redshift galaxy surveys \citep{Bull15,Pourtsidou17}. \textit{Astrophysics.} Another interesting direction could be to employ the accurate analytical, beyond lognormal model for one-point statistics of dark matter \citep{Uhlemann16log} to probe high-redshift astrophysics. Intensity mapping can be done with lines different from the 21cm spin-flip line of neutral hydrogen, which are sensitive to different astrophysical processes \citep{Suginohara99,Fonseca17} and can probe various environments such as hotter hydrogen gas (Ly$\alpha$), ionised regions (C II) or cool dense molecular gas (CO). In this context, \cite{Breysse17} introduced the probability distribution of voxel intensities and demonstrated its application to CO emission finding constraints on the luminosity function of the order of 10 percent. In this study, a lognormal matter distribution has been used in combination with a linear relation between halo mass and CO luminosity. The idea is to use the one-point statistics of intensity fluctuations which depend on both the spatial distribution of matter or halos, and also the luminosity function. The luminosity function contains interesting information about the detailed astrophysical conditions within the line emitters, such as star formation rates and metallicities, that can be constrained through the measured PDF of voxel intensity which complements information from the power spectrum \citep{TveitIhle18}. \textit{Foregrounds.} A serious obstacle for intensity mapping observations is the fact that the amplitude of the galactic and extragalactic foregrounds can be several orders of magnitude higher than the one of the cosmological signal. Foreground cleaning is thus of pivotal importance and usually takes advantage of the rather smooth frequency spectra of foregrounds that disentangle them from the cosmic signal which maps the distribution of structures along the line of sight and hence has a significant amount of structure in frequency space. Foregrounds that are constant across the sky are not expected to constitute a serious problem for counts-in-cells statistics, as they just offset the overall mean density. Foregrounds that are spatially varying on scales comparable to the size of the cells would add an extra foreground density fluctuation in every cell, roughly corresponding to extra scatter of the observed intensity around the true density. We have seen before that one-point PDFs are rather robust against scatter such that one has mainly to model the effect of foregrounds on the mean relation. While it is beyond the scope of the present work, one could quantitatively assess the impact of foregrounds on counts-in-cells statistics through mocks built for 21 cm intensity mapping experiments \citep{Alonso14,Villaescusa-Navarro18}. | 18 | 8 | 1808.09968 |
1808 | 1808.00880_arXiv.txt | The fully analytical solution for isothermal Bondi accretion on a black hole (MBH) at the center of JJ two-component Jaffe (1983) galaxy models is presented. In JJ models the stellar and total mass density distributions are described by the Jaffe profile, with different scale-lengths and masses, and to which a central MBH is added; all the relevant stellar dynamical properties can also be derived analytically. In these new accretion solutions the hydrodynamical and stellar dynamical properties are linked by imposing that the gas temperature is proportional to the virial temperature of the stellar component. The formulae that are provided allow to evaluate all flow properties, and are then useful for estimates of the accretion radius and the mass flow rate when modeling accretion on MBHs at the center of galaxies. | Observational and numerical investigations of accretion on massive black holes (hereafter MBH) at the center of galaxies often lack the resolution to follow gas transport down to the parsec scale. In these cases, the {\it classical} Bondi (1952) solution on to an isolated central point mass is then commonly adopted, for estimates of the accretion radius (i.e., the sonic radius), and the mass accretion rate (see Ciotti \& Pellegrini 2017, hereafter CP17, and references therein). However, two major problems affect the direct application of the classical Bondi solution, namely the facts that 1) the boundary values of density and temperature of the accreting gas are assigned at infinity, and 2) in a galaxy, the gas experiences the gravitational effects of the galaxy itself (stars plus dark matter), and the MBH gravity becomes dominant only in the very central regions. The solution commonly adopted is to use values of the gas density and temperature ``sufficiently near'' the MBH. It is therefore important to quantify the systematic effects, on the estimates obtained from the classical Bondi solution for the accretion radius and the mass accretion rate, due to measurements taken at finite distance from the MBH, and under the effects of the galaxy potential well. A first step analysis of this problem was carried out in Korol et al. (2016, hereafter KCP16) where the Bondi problem was generalized to the case of mass accretion at the center of galaxies, including also the effect of electron scattering on the accreting gas. CP17 showed that the whole accretion solution can be given in an analytical way for the {\it isothermal} accretion in Jaffe (1983) galaxies with a central MBH. Ciotti \& Pellegrini (2018, hereafter CP18, in preparation), extend the study to JJ two-component galaxy models (Ciotti \& Ziaee Lorzad 2018, hereafter CZ18), where the {\it stellar} and {\it total} mass density distributions are both described by the Jaffe profile, with different scale-lengths and masses, and a MBH is added at the center. In particular, JJ models offer the {\it unique} opportunity to have a quite realistic family of galaxy models with a central MBH, allowing both for the fully analytical solution of the Bondi (isothermal) accretion problem, {\it and} the fully analytical solution of the Jeans equations. | 18 | 8 | 1808.00880 |
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1808 | 1808.02557_arXiv.txt | {EUSO-Balloon is a pathfinder mission for the Extreme Universe Space Observatory onboard the Japanese Experiment Module (JEM-EUSO). It was launched on the moonless night of the 25$^{th}$ of August 2014 from Timmins, Canada. The flight ended successfully after maintaining the target altitude of \SI{38}{\kilo\meter} for five hours. One part of the mission was a 2.5 hour underflight using a helicopter equipped with three UV light sources (LED, xenon flasher and laser) to perform an inflight calibration and examine the detectors capability to measure tracks moving at the speed of light. We describe the helicopter laser system and details of the underflight as well as how the laser tracks were recorded and found in the data. These are the first recorded laser tracks measured from a fluorescence detector looking down on the atmosphere. Finally, we present a first reconstruction of the direction of the laser tracks relative to the detector.} | 18 | 8 | 1808.02557 |
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1808 | 1808.02885_arXiv.txt | {X-ray observations of merging clusters provide many examples of bow shocks leading merging subclusters. While the Mach number of a shock can be estimated from the observed density jump using Rankine-Hugoniot condition, it reflects only the velocity of the shock itself and is generally not equal to the velocity of the infalling subcluster dark matter halo or to the velocity of the contact discontinuity separating gaseous atmospheres of the two subclusters. Here we systematically analyze additional information that can be obtained by measuring the standoff distance, i.e. the distance between the leading edge of the shock and the contact discontinuity that drives this shock. The standoff distance is influenced by a number of additional effects, e.g. (1) the gravitational pull of the main cluster (causing acceleration/deceleration of the infalling subcluster), (2) the density and pressure gradients of the atmosphere in the main cluster, (3) the non-spherical shape of the subcluster, and (4) projection effects. The first two effects tend to bias the standoff distance in the same direction, pushing the bow shock closer to (farther away from) the subcluster during the pre- (post-)merger stages. Particularly, in the post-merger stage, the shock could be much farther away from the subcluster than predicted by a model of a body moving at a constant speed in a uniform medium. This implies that a combination of the standoff distance with measurements of the Mach number from density/temperature jumps can provide important information on the merger, e.g. differentiating between the pre- and post-merger stages.} | \label{sec:introduction} In the hierarchical structure formation scenario, the growth of galaxy clusters occurs via mergers of less massive structures (e.g. galaxy groups, clusters). Shock waves are naturally formed in this process since the infalling gas haloes usually move faster than the local speed of sound ($c_s$, see e.g. \citealt{Markevitch2007,Bykov2015} for reviews). High-angular-resolution X-ray images are able to identify sharp density and temperature discontinuities of these shocks in the intracluster medium (ICM). Dozens of shocks (or shock candidates) have been discovered so far in this way (e.g. \citealt{Markevitch2002,Markevitch2005,Botteon2018}). The shock Mach number ($\mathcal{M}_s$, typically $\mathcal{M}_s\lesssim4$) is subsequently determined by applying the Rankine-Hugoniot (RH) conditions to the derived gas density and temperature jumps at the shock front (see Fig.~\ref{fig:mach_proxy}). Under the assumption of a steady motion in a homogeneous medium, the shock Mach number coincides with the Mach number of the infalling gas halo ($\mathcal{M}_g$) relative to the atmosphere of the main cluster, i.e. $\mathcal{M}_s=\mathcal{M}_g$. As we discuss below, this equality of the Mach numbers is not necessarily true in the merging clusters. Instead, the shock, the infalling dark matter (DM) halo, and the gas of the subhalo can have appreciably different velocities. Therefore, more parameters are needed to characterize the merger in a more comprehensive way. The geometry of the shock (e.g. Mach angle, standoff distance), may provide independent ways of measuring the Mach number \citep{Vikhlinin2001,Markevitch2002,Russell2010,Wezgowiec2011,Hallman2018}. In these studies, the infalling gas core (colder and denser than the gas in the main cluster) is usually taken as a solid body that diverts the flow and forms a bow shock in front (see a sketch in Fig.~\ref{fig:scheme_merger}). The theory of bow shocks driven by blunt bodies has been extensively studied theoretically and experimentally, including space physics applications \citep[e.g.][]{Dyke1958,Farris1994,Fairfield2001,Petrinec2002,Verigin2003,Keshet2016}. The standoff distance $\Delta$ is defined as the distance between the stagnation point of the body and the closest point on the shock front (see Fig.~\ref{fig:scheme_merger}). In galaxy clusters, it is usually measured as the distance between the cold and shock fronts (see Fig.~\ref{fig:scheme_merger}). In this work, we use the results of \citet{Verigin2003} as a baseline model for the standoff distance (hereafter, $\Delta_V$) for a moving sphere with a radius $R$ (see equation~\ref{eq:proxy_delta}). The normalized standoff distance $\Delta_{V}/R$ is a monotonically decreasing function of the Mach number $\mathcal{M}_s=\mathcal{M}_g$ (particularly sensitive to $\mathcal{M}_s$ when $\mathcal{M}_s\lesssim3$, see Fig.~\ref{fig:mach_proxy}). For galaxy clusters, measuring $\Delta$ from X-ray data is straightforward. The normalized standoff distance $\Delta/R$ is a pure geometrical quantity and there is no need to resolve the structure of the entire Mach cone (here, $R$ refers to the curvature radius of the cold front). It is, therefore, an attractive geometrical proxy for the shock Mach number. However, it has its own issues when applied to real merging clusters. For instance, significant discrepancies between the Mach numbers measured from the standoff distance and the jump conditions are found in many clusters \citep[][and references therein]{Dasadia2016}, which typically show much larger standoff distances than the theoretical expectations, given the shock Mach number (e.g. derived from the X-ray surface brightness jump). These discrepancies might be caused by a variety of reasons, including but not limited to: \begin{itemize} \item Continuous acceleration or deceleration of the subcluster when moving in the potential well of the main halo, i.e. the motion is not stationary. \item Motion of the subcluster through the gas with substantial density (pressure) gradients along the direction of motion. \item Non-trivial (and time variable) shape of the infalling subcluster and projection effects that lead to ambiguities in determining the standoff distance and the curvature radius of the cold front. \end{itemize} Therefore, whether the standoff distance could be a robust proxy of shock Mach number is an open question. At the same time, the discrepancy between the shock Mach number derived from the Rankine-Hugoniot condition and the Mach number derived from the standoff distance has an important diagnostic power that can be used to better characterize the merger configuration. The aim of this work is to systematically investigate various effects that influence the estimates of the Mach number from the standoff distance in galaxy clusters. To isolate issues related to the evolving shape of the subcluster, we mainly concentrate on a model of a rigid body moving in a static potential well. This paper is organised as follows. In Section~\ref{sec:sph}, we use smoothed-particle hydrodynamics (SPH) simulation to illustrate the evolution of the standoff distance during the merger process. We demonstrate that the rigid body approximation captures many, but admittedly not all, important issues associated with using the standoff distance as a proxy for the Mach number. Our main results are presented in Section~\ref{sec:rigid}, where we explore the impact of the gravitational potential, subcluster shape, and projection effects on the standoff distance, respectively. In Section~\ref{sec:conclusion}, we summarize our findings. \begin{figure} \centering \begin{subfigure}[t]{0.45\textwidth} \centering \includegraphics[width=\linewidth]{scheme_merger} \caption{} \label{fig:scheme_merger} \end{subfigure} \begin{subfigure}[t]{0.45\textwidth} \centering \includegraphics[width=\linewidth]{mach_proxy} \caption{} \label{fig:mach_proxy} \end{subfigure} \caption{\textit{Panel (a):} sketch showing a bow shock driven by the infalling subcluster (in the rest frame of the shock). The cold gas core of the subcluster is enveloped by a sharp contact discontinuity (a.k.a. cold front). The standoff distance $\Delta$ and the curvature radius of the cold front $R$ are marked in the figure. \textit{Panel (b):} various observational proxies for the shock Mach number (see Appendix~\ref{sec:appendix:proxy}). The three curves, increasing with Mach number, correspond to the RH relations between the gas properties (density, temperature, and pressure) on the downstream and upstream sides of the shock. The decreasing curve is the normalized standoff distance $\Delta_V/R$ from \citet{Verigin2003} for a moving sphere (see equation~\ref{eq:proxy_delta}). Unlike the RH relations, the standoff distance is an unambiguous function of $\mathcal{M}_s$, only if the sphere is moving at a constant velocity through a homogeneous medium, i.e. $\mathcal{M}_g=\mathcal{M}_s$. } \end{figure} | \label{sec:conclusion} In this paper, we have explored various effects that influence the position of a bow shock relative to the contact discontinuity (a.k.a. cold front) that drives this shock in a context of a cluster merger, specialized for the case of a minor merger. Unlike the textbook case of a bow shock ahead of a small body moving in a homogeneous gas, the standoff distance is not only a function of the body size and velocity, but it is also sensitive to the cluster environment. Therefore, the standoff distance is not only as a complementary proxy for the merger Mach number (see Section~\ref{sec:introduction} for the discussion of different Mach numbers present in the problem), but it also provides information on the merger configuration, that is difficult to obtain from, e.g. the Mach number of the bow shock. Our findings can be summarized as follows. \begin{itemize} \item The standoff distance $\Delta$ is a simple geometrical proxy for the velocity of a supersonically moving body in a uniform medium, which we refer to as a `standard' case. It is a sensitive function of the body Mach number, as long as it is smaller than $\sim 3$. In the context of merging galaxy clusters, it provides a useful and non-trivial diagnostic of the merger process, but its relation with the velocity of the body is complicated. \item One important difference with the standard case is that the velocity of a subcluster does not necessarily coincide with the velocity of the shock it drives (see Sections~\ref{sec:sph} and \ref{sec:rigid:gravity}). This is caused by two effects, namely, (i) the acceleration (deceleration) of the subcluster by the gravitational pull of the main cluster before (after) the core passage and (ii) motion in (against) the direction of density and pressure gradients before (after) the core passage. These two effects work in the same direction and tend to push the shock closer to (farther away from) the body before (after) the core passage. The magnitude of these effects scales with the size of the gaseous core of the subcluster; for a subcluster that is much smaller than the characteristic scale height of the main cluster atmosphere, the effects are small. This means that, before the core passage, the shock Mach number is fairly close to the subcluster (gas) Mach number; while after core passage, the shock can be moving faster (and be farther away) than the subcluster. Therefore, if the analysis of the density/temperature jumps at the shock yield a Mach number significantly larger than the one inferred from the standoff distance, one can then conclude that the subcluster has already passed through the densest part of the main cluster. These effects provide an explanation for an unexpectedly large standoff distance seen in some observations \citep[e.g.][]{Dasadia2016}. \item The non-trivial shape of the infalling subcluster causes ambiguities in determining the normalized standoff distance (see Section~\ref{sec:rigid:shape}). We propose a method to address this issue by decomposing the geometry of the cluster into a series of spheres. The location of the merger shock could be determined by comparing the bow shocks for each sphere and selecting the leading one (see the scheme in Fig.~\ref{fig:scheme_shape}). \item We analyzed the impact of the projection effects on the Mach number proxies, specializing for a subcluster after core passage (see Section~\ref{sec:rigid:projection}). Projection effects tend to underestimate the shock Mach number derived from the density and temperature jumps unless the merger is exactly in the sky plane. The Mach number derived from the surface brightness analysis appears to be the least affected (see Fig.~\ref{fig:foam_mach_time}). The standoff distance analysis produces the smallest Mach number, partly because of the effects mentioned above. \end{itemize} Finally, we emphasize that this study is not intended as a replacement for full dark matter plus gas simulations, that automatically include all the effects discussed above. Instead, this study could be used to guide the interpretation of the observational data, provide initial guess on the merger configuration, and help setting up full hydrodynamic simulations. | 18 | 8 | 1808.02885 |
1808 | 1808.02761_arXiv.txt | We have discovered a new, near-equal mass, eclipsing M dwarf binary from the Next Generation Transit Survey. This system is only one of 3 field age ($>$ 1 Gyr), late M dwarf eclipsing binaries known, and has a period of 1.74774 days, similar to that of CM~Dra and KOI126. Modelling of the eclipses and radial velocities shows that the component masses are $M_{\rm pri}$=\NstarMassA $M_{\odot}$, $M_{\rm sec}$=\NstarMassB $M_{\odot}$; radii are $R_{\rm pri}$=\NstarRadA $R_{\odot}$, $R_{\rm sec}$=\NstarRadB. The effective temperatures are $T_{\rm pri} = 2995\,^{+85}_{-105}$\,K and $T_{\rm sec} = 2997\,^{+66}_{-101}$\,K, consistent with M5 dwarfs and broadly consistent with main sequence models. This pair represents a valuable addition which can be used to constrain the mass-radius relation at the low mass end of the stellar sequence. | M dwarfs are the most numerous stellar spectral type in the Galaxy \citep{henry97}, and have recently become the focus of many transiting planet searches (e.g., TRAPPIST (\citealt{jehin11}), the Next Generation Transit Survey (NGTS: \citealt{ngts}), MEarth (\citealt{berta12})) since their small radii make it easier to detect Earth sized planets. In fact, it appears M dwarfs are more likely to host planets than higher mass stars, and the majority of these are Earth-like, as there is a known dearth of hot Jupiters around M dwarfs, with only three known to date: NGTS-1b \citep{bayliss17}, Kepler-45b \citep{johnson12} and HATS-6b \citep{hartman15}. It is possible to directly measure the radius of M dwarfs via interferometry (e.g. \citealt{Demory2009,Boyajian2012}), however, there are currently no interferometric measurements for M dwarfs later than M6. For the majority of isolated M dwarfs, the mass and radius can only be determined by using evolutionary models such as the BCAH15 \citep{baraffe15} or PARSEC models \citep{parsec}, combined with luminosity measurements, and a mass-luminosity relation (e.g. \citealt{delfosse00}). Therefore it is of great importance that these models are verified to be accurate. \citet{torres13} highlighted that for detached, eclipsing binaries containing M dwarfs (where the radius can be directly measured) inflated radii and cooler effective temperatures in comparison with the theoretical models, are commonly reported. These two effects can roughly cancel each other out, giving a luminosity that is consistent with the model, hinting that this phenomenon is a located on the surface of the star (for instance, due to activity e.g., \citealt{Stelzer2013}, and metallicity e.g., \citealt{stassun2012,lopez07}). For most exoplanet hosts there is no direct measurement of mass and radius, evolutionary models are used and hence this effect will lower the precision of the radii and mass (hence the density) of any planet present. A study by \citet{brown11} showed that while the $Kepler$ KIC parameters are accurate for sun-like stars, they are less reliable for T$_{\rm eff}<$3750 K, where the M dwarfs are fully convective. \citet{muirhead12} also find that the radii for KIC M dwarfs are generally underestimated in the KIC \citep{borucki11}, as do \citet{gaidos12} in their comparison between the KIC and M2K M dwarf survey \citep{apps10}. \citet{mann17} obtained improved parallaxes for eight KIC systems containing M dwarf primary stars, including $Kepler-42$ (KOI 961: \citealt{murihead12a}), which is fully convective. They concluded that once they accounted for the eccentricity of the orbits for the majority of systems, the M dwarfs had masses and radii consistent with the stellar models, however, $Kepler-42$ was still an outlier. Model based densities gave a radius $\sim$6 per cent smaller than empirical determinations from the luminosity, and consequently an effective temperature too hot by $\sim$2 per cent. The $Kepler$ lightcurve shows that the star's variability is less than one per cent, indicating that in this case, activity is unlikely to be the cause of the discrepancy in the radius determinations. Another study by \citet{kesseli} used a combination of mass-radius relations and vsini measurements for the MEarth M dwarfs. They find that stellar evolutionary models underestimate the radii by 10-15 per cent, but that at higher masses (M $>$ 0.18 M$_{\odot}$) the discrepancy is only about 6 per cent, comparable to the results from interferometry and eclipsing binaries. At the lowest masses (0.08 $<$ M $<$ 0.1 M$_{\odot}$), they find the discrepancy between observations and theory is between 13 and 18 per cent, and unlikely to be due to effects from age and rotation. \citet{Mann15} derived an empirical relationship between T$_{\rm eff}$ and radius using spectra of 187 K7-M7 dwarfs, They also found their best fit models overpredicted effective temperature by 2.2 per cent and underpredict radii by 4.6 per cent. They suggest this difference is more likely to be related to the models (e.g. mixing length, opacities) than stellar parameters such as metallicity, activity or rotation. In the rare cases where direct measurements of masses and radii can be made (i.e. low-mass stars in eclipsing binary systems), the radii determined are also often inconsistent with evolutionary models, by as much as 10 per cent \citep{feiden12, terrien12}. For example, \citet{birkby12} determined the radii of their eclipsing M dwarfs were inflated by as much as 3-12 per cent, and that this inflation was not dependent on the activity of the M dwarf. However, this is not a consistent deviation from models - some objects agree very well, for instance the interferometric values determined by \citet{demory09} for M0-M5.5 stars. The models of \citet{spada13}, T$_{\rm eff}$-radius relationships of \citet{Mann15} and observations of \citet{Boyajian2012} suggest that both binary and single M dwarfs suffer from the aforementioned radius discrepancy, and that this discrepancy is largest in binaries with short periods ($<$ 1.5 days) and in lone, low mass (M$<$0.4 M$_{\odot}$), low metallicity objects. This inflation for objects in short period binaries is also seen by \citet{Boyajian2012} and \citet{kraus11} who suggest it is due to the presence of the companion star, probably because they are tidally locked into very high rotation speeds that may enhance activity and inhibit convection. Another issue is that some areas of parameter space surrounding the M dwarfs are only sparsely sampled. In particular the later spectral types. For instance TRAPPIST-1, an M dwarf hosting 7 rocky planets \citep{gillon17}, has a mass of 0.082 M$_{\odot}$. There are very few model-independent mass-radius measurements in this range, one of which is CSS03170 a low-mass star in an eclipsing binary with a white dwarf \citep{parsons12}. Another system is EBLM J0555-57 \citep{boetticher17}, which is a low mass M dwarf (0.081 M$_{\odot}$, 0.084 R$_{\odot}$, log g=5.5) orbiting a sun-like star. This object which is unusually dense for an M dwarf, has a log g similar to that of many field brown dwarfs e.g. \citep{kirkpatrick99,chabrier00}. This M dwarf has masses and radii consistent with the models, and the NextGen models \citep{baraffe98} used in \citep{boetticher17} suggest that EBLM J0555-57B would have an effective temperature of 2200 K, making it an M9 dwarf or later \citep{rajpurohit13}. There are a few other objects within this low mass regime with main sequence companions : \citet{triaud17} performed a survey for M dwarfs in binaries with FGK stars. 31 per cent of their sample had masses of less than 0.2 M$_{\odot}$. However, most of these are too faint to be directly detected in the spectra, hence these are single lined binaries and as yet, no accurate radii are available for these systems. The \gaia\ parallaxes will allow higher precision radius measurements to be made using the mass-luminosity relations for the late M dwarfs (e.g. \citealt{Mann15}). \citet{yilen} discovered 1SWASPJ011351.29+314909.7, a low mass M dwarf in a binary with a much higher mass main sequence star. This system is only a single lined binary, and no secondary eclipse is detected, yet, the mass and radius are consistent with evolutionary models. The effective temperature is $\sim$600 K hotter than the models predict. This effect is also the case for the M dwarf-main sequence binary KIC 1571511 \citep{ofir}. These two objects produce results that are conflicting with those of \citet{torres13}, who found effective temperatures that were consistently cooler than the models predicted. It is clear that in order to achieve a measure of accuracy in planetary mass and radius measurements, we require accurate masses and radii for the primary stars. As models of fully convective M dwarfs seem to overpredict effective temperatures and underpredict the radii (e.g. \citealt{Morales09,kraus11,kesseli}), it is important to observe as many double-lined eclipsing systems as possible to build an empirical mass-radius relation to complement the theoretical ones such as those of \citet{spada13,kraus11,torres10,torres13}. | We have discovered a new eclipsing, late M dwarf binary from NGTS. This is a near-equal mass binary, comprising two M4-5 dwarfs in a $\sim$1.7 day orbit. We determine the masses of the M dwarfs with uncertainties below 1 per cent and their radii with uncertainties below 3 per cent. In this mass regime, there are very few well characterised M dwarfs, thus highlighting the importance of this system. The masses of these stars are lower than the $\sim$0.2 M$_{\odot}$ of both CM Dra and KOI126, both of which have similar periods. Comparisons to isochrones show that the components of \Nstar\ have masses and radii consistent with an age of 5 Gyr although the secondary star in \Nstar\ does show a larger radius than is predicted by models, potentially due to activity. | 18 | 8 | 1808.02761 |
1808 | 1808.04371_arXiv.txt | We report the first detailed measurement of the shape of the CO luminosity function at high redshift, based on $>$320\,hr of the NSF's Karl G.\ Jansky Very Large Array (VLA) observations over an area of $\sim$60\,arcmin$^2$ taken as part of the CO Luminosity Density at High Redshift (COLDz) survey. COLDz ``blindly'' selects galaxies based on their cold gas content through \aco\ emission at $z$$\sim$2--3 and \bco\ at $z$$\sim$5--7 down to a CO luminosity limit of log($L'_{\rm CO}$/\lprime )$\simeq$9.5. We find that the characteristic luminosity and bright end of the CO luminosity function are substantially higher than predicted by semi-analytical models, but consistent with empirical estimates based on the infrared luminosity function at $z$$\sim$2. We also present the currently most reliable measurement of the cosmic density of cold gas in galaxies at early epochs, i.e., the cold gas history of the universe, as determined over a large cosmic volume of $\sim$375,000\,Mpc$^3$. Our measurements are in agreement with an increase of the cold gas density from $z$$\sim$0 to $z$$\sim$2--3, followed by a possible decline towards $z$$\sim$5--7. These findings are consistent with recent surveys based on higher-$J$ CO line measurements, upon which COLDz improves in terms of statistical uncertainties by probing $\sim$50--100 times larger areas and in the reliability of total gas mass estimates by probing the low-$J$ CO lines accessible to the VLA. Our results thus appear to suggest that the cosmic star-formation rate density follows an increased cold molecular gas content in galaxies towards its peak about 10\,billion years ago, and that its decline towards the earliest epochs is likely related to a lower overall amount of cold molecular gas (as traced by CO) bound in galaxies towards the first billion years after the Big Bang. | \label{sec:intro} Our basic understanding of galaxy evolution and the build-up of stellar mass in galaxies throughout the history of the universe is founded in detailed measurements of the star-formation rate density\footnote{Throughout this work, densities in star formation rate, stellar mass, or gas mass refer to cosmic densities (i.e., the amount of material in galaxies per unit co-moving cosmic volume) unless stated otherwise.} as a function of cosmic time (or redshift), the ``star-formation history of the universe'', and measurements of the stellar mass density in galaxies at different cosmic epochs (see \citealt{md14} for a review). In-depth studies of significant samples of high-redshift galaxies appear to indicate that changes in this growth history at different epochs are largely driven by the cold molecular gas properties of galaxies (e.g., \citealt{daddi10a,tacconi13,tacconi18,genzel15,scoville16}), and the growth rate of dark matter halos (e.g., \citealt{genel10,bouche10,faucher11}). The cold gas constitutes the fuel for star formation (see \citealt{cw13} for a review), such that a higher gas content (e.g., driven by high gas accretion rates) or a higher efficiency of converting gas into stars (e.g., driven by galaxy mergers, or by ubiquitous shocks due to high gas flow rates) can lead to increased star-formation activity, and thus, to a more rapid growth of galaxies (e.g., \citealt{dave12}). To better understand how the gas supply in galaxies moderates the star-formation rate density in galaxies at early epochs, it is desirable to complement targeted studies with an integrated measurement of the cold molecular gas density in galaxies at the same epochs, i.e., the ``cold gas history of the universe''. Surveys of cold gas ideally target rotational lines of CO, the most common tracer of the molecular gas mass in galaxies, to measure the CO luminosity function at different cosmic epochs in a ``molecular deep field'' study. The distribution mean of the CO luminosity function then provides a reliable measurement of the cold molecular gas density at a given redshift (\citealt{cw13}; see, e.g., \citealt{scoville17} for an alternative approach). The first such efforts have recently been carried out in the {\em Hubble} Deep Field North (HDF-N) and the {\em Hubble} Ultra Deep Field (H-UDF) with the IRAM Plateau de Bure Interferometer (PdBI) and the Atacama Large Millimeter/submillimeter Array (ALMA; the ASPECS-Pilot program) at 3\,mm and 1\,mm wavelengths, covering fields $\sim$0.5 and $\sim$1\,arcmin$^2$ in size, respectively (see \citealt{decarli14,walter16}, and references therein). At $z$$\sim$2--3, near the peak of the cosmic star-formation rate density $\sim$10\,billion years ago, these studies cover \cco\ and higher-$J$ lines. At $z$=5--7, i.e., in the first billion years after the Big Bang, these surveys cover \eco\ and higher-$J$ lines. The most faithful tracer of total cold gas mass are low-$J$ CO lines, in particular, \aco\ (see, e.g., \citealt{riechers06c,riechers11e,riechers11c,ivison11,aravena12,aravena14,daddi15,bolatto15,sharon16,saintonge17,harrington18}), for which the $\alpha_{\rm CO}$=$M_{\rm H_2}$/$L'_{\rm CO}$ conversion factor from CO luminosity ($L'_{\rm CO}$, in units of \lprime ) to H$_2$ gas mass ($M_{\rm H_2}$, in units of \msol ) has been calibrated locally (see \citealt{bolatto13} for a review), and for which no assumptions about gas excitation are required to derive the total CO luminosity. To complement the initial ``molecular deep field'' studies through improved statistical uncertainties measured over larger cosmic volumes and reduced calibration uncertainties due to gas excitation, we have carried out the VLA COLDz survey,\footnote{See {\tt coldz.astro.cornell.edu} for additional information.} ``blindly'' selecting galaxies through their cold gas content in the \aco\ line at $z$$\sim$2--3, and in \bco\ at $z$$\sim$5--7, over a $\sim$60\,arcmin$^2$ region. The detailed survey parameters, line search and statistical techniques, a catalog of line candidates, and an overview of accompanying papers are presented in the COLDz survey reference paper (\citealt{pavesi18}; hereafter: Paper I). This work focuses on the CO luminosity function measurements to result from the survey data, and the implied constraints on the evolution of the cosmic cold gas density in galaxies as a function of redshift. Section 2 provides a brief description of the data. Section 3 summarizes the selection of CO line candidates and the statistical methods used to characterize the survey parameters, before describing the CO luminosity function and cold gas density measurements. Section 4 provides a discussion of the results in the context of previous surveys and model predictions. Section 5 provides the main conclusions based on our measurements and analysis. We use a concordance, flat $\Lambda$CDM cosmology throughout, with $H_0$\eq69.6\,\kms\,Mpc$^{-1}$, $\Omega_{\rm M}$\eq0.286, and $\Omega_{\Lambda}$\eq0.714 (\citealt{bennett14}). | We have used the ``blind'' molecular line scans over $\sim$60\,arcmin$^2$ in the COSMOS and GOODS-North survey fields taken as part of the VLA COLDz survey (Paper I) to measure the shape of the CO luminosity function at $z$$\sim$2--3 and to constrain it at $z$$\sim$5--7, utilizing \aco\ and \bco\ emission line galaxy candidates. We also provide constraints on the evolution of the cosmic molecular gas density out to $z$$\sim$7. We compare our findings to previous $\sim$0.5 and 1\,arcmin$^2$ surveys in the HDF-N and the H-UDF (ASPECS-Pilot) in higher-$J$ CO lines (\citealt{decarli14,walter16}), estimates based on galaxy stellar mass functions in COSMOS scaled using dust-based interstellar medium mass estimates (\citealt{scoville17}), and a CO intensity mapping study in GOODS-North (\citealt{keating16}), finding broad agreement within the relative uncertainties. The COLDz data provide the first solid measurement of the shape of the CO luminosity function at $z$$\sim$2--3, reaching below its ``knee'', and the first significant constraints at $z$$\sim$5--7. The characteristic CO luminosity at $z$$\sim$2--3 appears to be one to two orders of magnitude higher than at $z$=0 (\citealt{keres03,saintonge17}), which is consistent with the idea that the dominant star-forming galaxy populations $\sim$10\,billion years ago were significantly more gas-rich compared to present day. We also independently confirm an observed apparent excess of the space density of bright CO-emitting sources at high redshift compared to semi-analytical predictions, but our findings are consistent with empirical predictions based on the infrared luminosity function and observed star-formation rates of distant galaxies. Integrating the CO luminosity functions down to the sensitivity limit of our survey, we obtain robust estimates of the volume density of cold gas in galaxies at high redshift. Our measurement is consistent with a factor of a few increase from $z$$\sim$0 to $z$$\sim$2--3, and a decrease towards $z$$\sim$5--7 by about an order of magnitude (which may be less steep in practice if metallicity has an increasing effect on CO-based measurements towards the highest redshifts). This is consistent with semi-analytical and empirical model predictions and previous constraints from the ASPECS-Pilot survey (\citealt{decarli16a}), and with previous findings of increased gas fractions at $z$$>$1--2 (e.g., \citealt{daddi10a,tacconi13,tacconi18,scoville17}). The overall shape of the cosmic gas density evolution resembles that of the star-formation history of the universe, consistent with an underlying ``star-formation law'' relation out to the highest measured redshifts. This suggests that the star-formation history, to first order, follows the evolution of the molecular gas supply in galaxies, as regulated by the gas accretion efficiency and feedback processes. A more direct comparison of the star-formation rate and cold gas density relations as a function of cosmic time holds critical information about the true gas depletion timescales, and thus, the gas accretion rates required to maintain the ongoing build-up of stellar mass. The data appear broadly consistent with a characteristic gas depletion timescale of several hundred million years, but there may be tentative evidence for a shortening in gas depletion times despite the observed increase in cold molecular gas content in star-forming galaxies towards higher redshift. This finding would be consistent with previous, targeted investigations based on \cco\ and dust-based interstellar medium mass estimates (e.g., \citealt{genzel15,scoville17}), and thus, with an effective increase in star formation efficiency in the dominant star-forming galaxy populations towards higher redshifts. While COLDz is the currently largest survey of its kind, the size of the volume probed and the number of line candidates found implies that larger areas need to be surveyed to greater depth in the future to more clearly address effects of cosmic variance and to reduce the error budget due to Poissonian fluctuations. Such studies will be possible with large investments of observing time at the VLA and ALMA in the coming years, until the next large leap in capabilities will become available with the construction of the Next Generation Very Large Array (ngVLA; e.g., \citealt{bolatto17,selina18}). | 18 | 8 | 1808.04371 |
1808 | 1808.01248_arXiv.txt | The hypothesis of an additional planet in the outer Solar System has gained new support as a result of the confinement noted in the angular orbital elements of distant trans-Neptunian objects. Orbital parameters proposed for the external perturber suggest semimajor axes between $500$ and $1000$ au, perihelion distances between $200$ and $400$ au for masses between $10$ and 20 $M_{\oplus}$. In this paper we study the possibility that lower perihelion distances for the additional planet can lead to angular confinements as observed in the population of objects with semimajor axes greater than 250 au and perihelion distances higher than 40 au. We performed numerical integrations of a set of particles subjected to the influence of the known planets and the putative perturber during the age of the Solar System and compared our outputs with the observed population through a statistical analysis. Our investigations showed that lower perihelion distances from the outer planet usually lead to more substantial confinements than higher ones, while retaining the Classical Kuiper Belt as well as the ratio of the number of detached with perihelion distances higher than $42$ au to scattering objects in the range of semimajor axes from $100$ au to $200$ au. | \label{sec:introduction} The existence of trans-Neptunian objects (TNOs) with high perihelion distance ($q\gtrsim40$ au) and semimajor axis ($a\gtrsim200$ au) can not be explained by the sole influence of the known planets. Thus, several mechanisms have been proposed to explain the existence of these objects, whose best known member is Sedna ($a=482$ au and $q=76$ au) \citep{Brown2004}. Some of these mechanisms are: the interaction of the Sun with other stars when it was still in its birth cluster and stellar flybys were common (\cite{Brasser2012}, \cite{Dukes2012}), the capture of planetesimals from the external disk of another star (\cite{Kenyon2004}, \cite{Morbidelli2004}), a planet that could have existed temporarily in the scattered disk (\cite{Gladman2006}) or an existing yet undiscovered planet (\cite{Gomes2006}). From a few years ago several patterns have been noticed in distant TNOs supporting the hypotheses of an outer planet in the Solar System. After announcing the discovery of an object with perihelion distance similar to that of Sedna, 2012 VP$_{113}$ ($a=256$ au and $q=80$ au), \citet{Trujillo2014} noted that objects with $a>150$ au and $q>30$ au exhibit a confinement in their argument of perihelion ($\omega$). They argued that under the influence of the known planets the argument of perihelion of these objects would circulate in a fairly short and different from each other timescale. On the other hand, they showed that a super-Earth mass planet in a circular and low inclination orbit with semimajor axis between $200$ and $300$ au could lead to long period $\omega$- libration around $0^\circ$ for Sedna-like objects, but not for objects with lower perihelia. This opened the interesting possibility that other configurations of an outer planet might give the suitable tuning. Later, \citet{Batygin2016} noted that TNOs with $a>250$ au and $q>30$ au are confined not only in $\omega$, but also in longitude of the ascending node ($\Omega$). They showed that the presence of a distant, eccentric, and massive planet could reproduce such confinements as well as perihelion detachment of distant TNOs as a consequence of secular and resonant interactions (see also \cite{Batygin2017} and references therein). This planet (hereafter named Planet 9, whose orbital parameters will be denoted with the subscript 9) would roughly share the same orbital plane as those of the confined objects and would be apsidally anti-aligned with them. Planet 9 would also predict the existence of apsidally aligned and high perihelion objects, if a wide distribution of perihelion is initially assumed (see also \cite{Khain2018}), and objects that would be compatible with the Centaurs of high semimajor axis and high inclination. Likewise, It offers an explanation for the origin of highly inclined TNOs ($i>60^\circ$) with $a<100$ au \citep{Batygin2016b} and the high inclination of the recently discovered long-period TNO, 2015 BP$_{519}$ ($q=36$ au) (\cite{Becker2018}, \cite{Batygin2017}). \cite{Brown2016} showed that confined TNOs orbits can be produced by a Planet 9 with the following orbital parameters\footnote{These numbers are taken from the paper's Figs (2) and (3) and their empirical expressions of $e_9$ as a function of $a_9$.}: 200 au $<q_{9}<$ $400$ au, 500 au $<a_{9}<$ $1000$ au, $i_{9}\sim30^\circ$, and mass $10 M_{\oplus}<m_{9}<20 M_{\oplus}$. By comparing the allowed orbital paths and estimated brightness of the planet to previous and ongoing surveys, they indicate that Planet 9 would be near aphelion with an apparent magnitude between $22$ and $25$. Subsequent works focused on restricting the location of Planet 9 on its orbit from the reduction of the residuals in Saturn's orbital motion based on Cassini data (\cite{Fienga2016}, \cite{Holman2016b}), or in Pluto's orbit (\cite{ Holman2016}), or assuming that several of the distant TNOs are in mean motion resonance (MMR) with the planet (\cite{Malhotra2016}, \cite{Millholland2017}). An outer planet also provides a better explanation for the fact of there being an excess of bright large semimajor axis Centaurs with respect to classical ones than a scenario without an additional planet \citep{Gomes2015}. Moreover, \cite{Gomes2017} (see also \cite{Bailey2016} and \cite{Lai2016}) provide an explanation for the current inclination of the planetary system invariant plane with respect to the Sun's equator of $\sim6^\circ$. They arrived at parameters for the distant planet compatible with those found by \cite{Brown2016} although with possible larger eccentricities corresponding to a given semimajor axis. As for the proposed mechanisms for its origin, Planet 9 could have been originally dispersed from the giant planets region. In order to avoid that repeated close encounters with a giant planet could end in the ejection of the scattered planet, the perihelion distance of its orbit would have to be lifted by some mechanism. These might include its gravitational interaction with the Sun's birth cluster (\cite{Brasser2006}, \cite{Brasser2012}), dynamical friction due to a planetesimals disk located beyond $100$ au \citep{Eriksson2018} or an either massive and short-lived or low-mass and long-lived gas disk \citep{Bromley2016}. Other proposed scenarios suggest the capture of a planet from another star system or the capture of a free-floating planet in the solar birth cluster (\citet{Li2016}, \citet{Mustill2016}; see, however, \citet{Parker2017}). \citet{Brown2016} present tables with probabilities for a Planet 9 with a given semimajor axis and eccentricity to induce a favorable orbital confinement of large semimajor axis TNOs. One of their criteria to choose the best Planet 9's orbit is to rule out those that produce too many high perihelion and low semimajor axis TNOs. Here we analyze the evidence of a distant planet, without neglecting the case of planets with low perihelion that were naturally neglected in \citet{Brown2016}, since they would assumedly produce an excess of high perihelion TNOs for relatively small semimajor axes. We particularly analyze these low perihelion Planet 9's influence on the Kuiper Belt and on the relation between scattered and detached objects. In Section \ref{methods} we describe the methods used to test the influence of Planet 9 on large semimajor axis TNOs. We present our results in Section \ref{results}. In Section \ref{lowperihelion} we emphasize the case of low perihelion planets. In Section \ref{conclusions} we present our conclusions. | An external perturber was proposed to explain the confinements in the orbital elements $\Omega$, $\omega$ and $\varpi$ of TNOs with $q>30$ au and $a>250$ au. \cite{Brown2016} claimed that good orbits for Planet 9 should have $q_9 > 200$ au, to explain such confinements, where lower perihelia than that above were assigned a null probability arguing that these parameters produce objects with $q>42$ au in the region 100 au $<a<$ 200 au, where no object with such perihelion distance had been observed previously. On the other hand, \cite{Gomes2017} explain the inclination of the solar equator in relation to the invariable plane of known planets showing that parameters of the Planet 9 similar to those found by \citet{Batygin2016} and \citet{Brown2016} are compatible although with slightly higher eccentricities. In this way, we considered perihelion distances for Planet 9 lower than those indicated by \citet{Brown2016} and we tested their influence on the TNOs with $a\geq250$ au and $q\geq40$ au, since these objects would not be greatly influenced by Neptune. In this region there are currently 9 objects whose $\Omega$ exhibit a large confinement ($210.5^\circ$), while the confinement in $\omega$ is $131.7^\circ$ and we assume two confinements in the observational sample of $\varpi$. Through statistical analysis we tested the influence of a Planet 9 with $a_9=700$ au and $a_9=1500$ au and perihelion distances ranging from 60 to 300 au. Our results show that smaller perihelion distances ($q_9=60$ au or $q_9=100$ au) produce narrower confinements. Such confinements are generally best reproduced in $\varpi$ and interestingly in several models there are two confinements in this angular element, as assumed in the observational data, being shepherded by Planet 9. Models with high $q_9$ are generally associated with random distributions in $\Omega$ and $\omega$. We also verified that a planet with low perihelion roughly yielded the current observed ratio between the number of scattered and detached with $q>42$ au objects in the interval 100 au $<a<$ 200 au by applying an observational bias to the particles of our models. We saw that several of our models are compatible with this ratio. Likewise, we verified whether the existence of a Planet 9 with such low perihelion would destroy the Classical Kuiper Belt. Integrations considering the most extreme cases of perihelion distance of Planet 9 from our models on an initially cold disk show that the signature due to the external perturber would be that of moving the semimajor axes of the objects to larger values and the sparseness of particles immediately past the 4:7 MMR. However, when we considered also the hot objects, a Planet 9 with a perihelion at $60$ au would considerably deplete the region with a particularly important depletion for the resonant objects. This motivated us to perform other runs with low perihelion distances but larger than 60 au. For this we considered a theoretical Classical Kuiper Belt and showed that a Planet 9 with $q_9=90$ au produces signatures similar to those produced without an additional external planet. Thus, we concluded that planets with perihelion distances as small as $90$ au should not be discarded in principle. They produce better confinements while preserving the Classical Kuiper Belt and the ratio between the number of detached to scattering objects in the region 100 au $<a<$ 200 au. A last remark is that although a very low perihelion distance for Planet 9 ($\sim 60 - 70$ au) seems to excessively empty the Kuiper Belt region, this may not be too bad, depending on the initial conditions of the particles just after the stabilization of the planets. If these objects were much more concentrated on smaller semimajor axes, a low perihelion Planet 9 could drift these objects outward so as to populate the Kuiper Belt conveniently. This problem is the subject of a following work by the authors. | 18 | 8 | 1808.01248 |
1808 | 1808.08475_arXiv.txt | The {\it Kepler} mission revealed a population of compact multiple-planet systems with orbital periods shorter than a year, and occasionally even shorter than a day. By analyzing a sample of 102 {\it Kepler} and {\it K2} multi-planet systems, we measure the minimum difference $\Delta I$ between the orbital inclinations, as a function of the orbital distance of the innermost planet. This is accomplished by fitting all the planetary signals simultaneously, constrained by an external estimate of the stellar mean density. We find $\Delta I$ to be larger when the inner orbit is smaller, a trend that does not appear to be a selection effect. We find that planets with $a/R_\star$<5 have a dispersion in $\Delta I$ of $6.7\pm 0.6$~degrees, while planets with $5 < a/R_\star < 12$ have a dispersion of $2.0\pm 0.1$~degrees. The planetary pairs with higher mutual inclinations also tend to have larger period ratios. These trends suggest that the shortest-period planets have experienced both inclination excitation and orbital shrinkage. | \label{sec:intro} One of the revelations of the {\it Kepler} mission was that Sun-like stars often host planets with sizes between those of Earth and Neptune and orbital periods shorter than a year \citep{Borucki+2011}. The formation of these short-period planets and their relationship to wider-orbiting planets are not understood. An interesting clue is that the population of planets with the shortest periods ($\lesssim$10 days) is different, in some respects, from the population with longer periods. One difference is in the planet occurrence rate. The function $d\log N/d\log P$, where $N$ is the mean number of planets per star and $P$ is the orbital period, increases with period from 0.2--10 days before leveling off to a constant value out to at least 100 days \citep{Petigura}. Another difference is that stars hosting sub-Neptune planets with periods shorter than about 10 days tend to have higher metallicities than those hosting planets with longer periods \citep{Mulders+2016,Petigura,Wilson+2018}. A third difference is in the period ratios between adjacent planets. When the inner planet's period is shorter than a few days, the period ratio tends to be larger than when both planets have longer periods \citep{Steffen}. This {\it Letter} describes another clue, which we found in the distribution of mutual inclinations. Several scenarios have been proposed to explain the shortest-period planets. In almost all these scenarios, the planet's orbit is initially wider, because of the theoretical difficulty of building a rocky core in close proximity to the star. Some of the proposed mechanisms to shrink the orbits also involve raising the inclination \citep{Hansen,Petrovich}, while others predict low inclinations \citep[e.g.,][]{Lee}. Previous studies of {\it Kepler} systems concluded that the mutual inclinations are typically $\lesssim$$5^\circ$, based on population statistics \citep{Tremaine,Fabrycky,FangMargot2012}. Here, we focus on systems with the closest-orbiting planets, and attempt to measure the mutual inclination of each system directly by fitting the transit light curves. \clearpage | \label{sec:discussion} We found that when the innermost planet has $a/R_\star \lesssim 5$ (or $P= 1.3$ days for a Sun-like star), the minimum mutual inclination is often 5--10$^\circ$. This is somewhat higher than the typical value of a few degrees that has been previously estimated for the more general population of {\it Kepler} systems. We also found $\Delta I$ to decrease with the orbital separation of the innermost planet. This observation does not appear to be purely a selection effect because for planets with $a/R_\star$ between 5 and 10, we could have detected mutual inclinations larger than 5$^\circ$, and we did not. These results may be related to some previously noted trends. \citet{Steffen2016} found that the {\it Kepler} sample of ``hot Earths'' without additional transiting companions is larger than what one would obtain by drawing planets randomly from the multiple-transiting systems. A related observation by \citet{Weiss2018} is that the fraction of {\it Kepler} systems with multiple transiting planets is lower when the innermost planet has a period shorter than a few days. Our results offer a natural explanation: the shortest-period planets tend to have larger mutual inclinations, and thus, are more likely to be observed to transit even when the wider-orbiting companions do not transit. \citet{Zhu} also found evidence for relatively high mutual inclinations in some {\it Kepler} systems, based on the observed frequencies of multiple transiting planets and TTVs. In their model, the inclination dispersion depends on the total number of planets in the system, ranging from $0.8^\circ$ in five-planet systems to $\sim$10$^\circ$ for two-planet systems. It would be interesting to try and extend the model of \citet{Zhu} to allow the mutual inclination to depend on orbital separation in addition to, or instead of, the total number of planets. \citet{2017MNRAS.468.1493B} proposed that the inner protoplanetary disk may have a flat (rather than flared) geometry in which case the innermost planets tend to form with larger mutual inclinations. We emphasize that $\Delta I$ only represents a lower bound on the mutual inclination. Moreover, if there exist systems with much larger mutual inclinations, they would be unlikely to appear in our sample, because the joint transit probability is low. Despite these limitations, our results indicate that the shortest-period planets have a different orbital architecture, with higher mutual inclinations and larger period ratios. This suggests that whatever processes led to the extremely tight orbits of these planets were also responsible for tilting the orbit to higher inclination. Several theories have been offered for the formation of very short-period sup-Neptune planets, which differ in their predictions for mutual inclinations. \citet{Lee} proposed that the magnetospheric truncation radius determines the innermost orbit where planets can form. In this scenario, planets begin with nearly-circular, well-aligned orbits, and the innermost planet undergoes tidal orbital decay.There is no obvious agent for exciting inclinations, and therefore this scenario does not provide an explanation for the larger mutual inclinations of the shortest-period planets. Likewise, the formation scenarios proposed by \citet{Terquem} and \citet{Schlaufman} do not provide an obvious way to excite inclinations. \citet{Spalding2016} proposed a scenario that does involve inclination excitation. If the host star were initially rotating rapidly, with a non-zero obliquity, the planets' orbits would undergo nodal precession at different rates and become misaligned, with the innermost planet being most strongly affected. The star would only need to be tilted by a few degrees to explain the observed values of $\Delta I$. It is not clear whether this scenario would result in an association between higher mutual inclination and larger period ratios, as we have observed. In the ``secular chaos'' or ``high-$e$ migration'' scenario proposed by \citet{Petrovich}, the innermost planet of a multi-planet system is launched into a high-eccentricity orbit via chaotic secular interactions. If the period is short and the eccentricity becomes high enough ($\approx$0.8), tidal interactions with the host star shrink the orbit. Since eccentricity and inclination are excited together, this theory predicts that the shortest-period planets should have larger mutual inclinations, in qualitative agreement with our results. A potential problem with this picture is that for systems in mean-motion resonance (MMR), the dynamics may be dominated by the resonance instead of secular interactions. The sample of USP systems has a decent fraction of systems that are in or near MMR (5 out of 13 systems with at least 2 exterior planets). Another possibility is forced-eccentricity migration, in which the interaction with outer companions (secular-forcing, or MMR) continually excites the eccentricity of the innermost planet. This allows eccentricity tides to dissipate energy and shrink the orbit \citep[see, e.g.,][]{Hansen}. Since the planet's eccentricity never exceeds a few percent, the inclinations are only excited to a few degrees, perhaps not enough to be compatible with our results. | 18 | 8 | 1808.08475 |
1808 | 1808.06142_arXiv.txt | From a magnetohydrodynamic (MHD) simulation of the eruption of a prominence hosting coronal flux rope, we carry out forward synthesis of the circular polarization signal (Stokes V signal) of the FeXIII emission line at 1074.7 nm produced by the MHD model as measured by the proposed COronal Solar Magnetism Observatory (COSMO) Large Coronagraph (LC) and infer the line-of-sight magnetic field $B_{\rm LOS}$ above the limb. With an aperture of 150 cm, integration time of 12 min, and a resolution of 12 arcsec, the LC can measure a significant $B_{\rm LOS}$ with sufficient signal to noise level, from the simulated flux rope viewed nearly along its axis with a peak axial field strength of about 10 G. The measured $B_{\rm LOS}$ is found to relate well with the axial field strength of the flux rope for the height range of the prominence, and can discern the increase with height of the magnetic field strength in that height range that is a definitive signature of the concave upturning dipped field supporting the prominence. The measurement can also detect an outward moving $B_{\rm LOS}$ due to the slow rise of the flux rope as it develops the kink instability, during the phase when its rise speed is still below about 41 km/s and up to a height of about 1.3 solar radii. These results suggest that the COSMO LC has great potential in providing quantitative information about the magnetic field structure of CME precursors (e.g. the prominence cavities) and their early evolution for the onset of eruption. | Coronal mass ejections (CMEs) often originate from regions in the solar corona where there are prominences or filaments, which are elongated large-scale structures of cool and dense plasma suspended in the much hotter and rarefied solar corona supported by the magnetic fields \citep[e.g.][]{Webb:Hundhausen:1987,Gibson:2018}. Features observed surrounding the prominences such as cavities \citep[e.g.][]{Gibson:2015} and hot shrouds \citep[e.g.][]{Hudson:etal:1999,Habbal:etal:2010} represent the coronal environment of the magnetic field structures hosting the prominence. A quantitative measurement of the magnetic field strength and spatial properties of such magnetic structures in the corona would significantly advance our understanding of the physical conditions and mechanisms for the development of CMEs. Direct measurement of the coronal magnetic field strength has been rare \citep[e.g.][]{Lin:etal:2000} and extremely difficult because of the weakness of the coronal magnetic fields and the extremely faint solar corona emission. The optically thin nature of the plasma is also one of the principal reasons for a difficult magnetic field measurement in the corona. The COronal Solar Magnetism Observatory (COSMO), is a proposed synoptic facility designed to measure magnetic fields and plasma properties in the large-scale solar atmosphere \citep{Tomczyk:etal:2016}. Among the suite of three instruments proposed for COSMO is the Large Coronagraph (LC) with a 1.5m aperture to measure the magnetic field, temperature, density, and dynamics of the corona above the solar limb. The COSMO LC measures the line-of-sight (LOS) strength of coronal magnetic fields directly through the Zeeman effect observed in the circular polarization (Stokes V profile) of coronal forbidden emission lines, including the FeXIII emission line at 1074.7 nm. The theoretical formalism for calculating the Stokes profiles of forbidden emission lines such as the FeXIII 1074.7 nm line under coronal conditions has been developed in \citet{Casini:Judge:1999}. A Fortran-77 program, the Coronal Line Emission (CLE) code, that implements the formalism and synthesize the Stokes profiles given the coronal plasma and magnetic field conditions along the observed line-of-sight is described in \citet{Judge:Casini:2001}. Using this code, \citet{Judge:etal:2006} carried out the first forward calculations of the Stokes signals of several coronal emission lines produced by a global, axisymmetric current-carrying magnetic structure embedded in a background isothermal corona to study the signatures of non-potential coronal magnetic fields. \citet{Gibson:etal:2016} has incorporated the CLE code into the SolarSoft FORWARD package and presented forward synthesis of the Stokes signals based on several coronal MHD models. In this paper, we carry out forward synthesis of the Stokes V signal of the FeXIII 1074.7 nm emission line produced by an MHD simulation of a prominence carrying coronal flux rope \citep{Fan:2017}, as would be observed by the COSMO LC. We study the feasibility of measuring the LOS magnetic field of the prominence flux rope above the limb, viewed nearly along its length, from the Stokes V signal measured by the COSMO LC given the error estimation \citep{Tomczyk:2015}. Although the MHD simulation is still highly simplified in its treatment of the thermodynamics, using an empirical coronal heating that depends on height, it does form a prominence condensation supported by the flux rope due to the radiative instability during the quasi-static phase and later develops a prominence eruption as the flux rope erupts due to development of the kink instability \citep{Fan:2017}. Thus we use this MHD model to carry out the forward calculation to get an initial examination of the capability of COSMO LC for quantitatively inferring the magnetic field strength of the observed longitudinally extended prominence-cavity systems \citep[e.g.][]{Gibson:2015}, during both the stable phase as well as the initiation of eruption. | Using an MHD simulation of a prominence carrying coronal flux rope, we have carried out forward synthesis of the circular polarization measurement by the proposed COSMO LC to examine its capability of inferring the LOS magnetic field of the flux rope above the limb, viewed nearly along the length of the flux rope. We found that using an integration time of about 12 min and an observational resolution of 12 arcsec, the LC can measure with sufficient signal to noise ratio ($>3$) the flux rope field strength of a few G in the region around the prominence, within the height range of the prominence. We find that the inferred $B_{\rm LOS}$ can be fairly well approximated by a mean of the LOS component of ${\bf B}$ along the LOS with a weighting that is proportional to $f_{I_0} (T) N_e$, where $f_{I_0} (T)$ describes the temperature sensitivity of the FeXIII line intensity as shown in Figure \ref{fig:fig_tempscan}, with a narrow peak at $1.6 $MK. Because of this and the temperature configuration of the simulated flux rope, we find that for those LOS that intersect the prominence vicinity, the measured $B_{\rm LOS}$ is localized to the region of prominence-to-hot-cavity transition and is fairly close to the axial field strength at the prominence dip. As a result the measurable $B_{\rm LOS}$ shows fairly accurately its increase with height profile, which is a signature of the concave upturning dipped field lines supporting the prominence. Above the prominence heights, the flux rope develops a hot core which reaches a peak temperature of about $3$ MK in our MHD model. As a result the LOSs at these heights tend to sample the field strength outside of the hot core strong field region (e.g. the P2 LOS shown in right column of Figure \ref{fig:fig_p1p2}), and the inferred $B_{\rm LOS}$ is significantly below the axial field at the corresponding height in the mid cross section of the flux rope, and also does not have enough signal to noise ratio to make it measurable. It is likely that our MHD model is over-estimating the temperature in the hot cavity in the flux rope surrounding the prominence condensation due to the simplified empirical coronal heating used and also due to the heating from the numerical diffusion of the magnetic field. This may have unrealistically reduced the sensitivity of the FeXIII emission line measurement for the flux rope cavity region. We have therefore also examined a case where we have replaced the plasma properties in the simulation domain with a hydrostatic isothermal atmosphere at the peak sensitivity temperature of 1.6 MK for the FeXIII line. In that case we found that the measurement sensitivity is greatly improved such that a significant $B_{\rm LOS}$ can be measured throughout the flux rope cross section in the POS. Although the magnitude of the measured field significantly under estimates the axial field strength of the flux rope because of the broad averaging along the LOS, nevertheless it still detects an increase with height profile in the lower height range, indicating the concave up turning field geometry of the flux rope there. On the other hand X-ray observation of a filament cavity by \citet{Hudson:etal:1999} and eclipse observations by \citet{Habbal:etal:2010} have indicated high temperatures, of about 2 MK or even higher, for the cavity regions surrounding the prominences. Thus it may be difficult to measure magnetic field strength in the hot cavity region of the flux rope far away from the prominence itself with the FeXIII line. However, our forward analysis shows that it is feasible to measure the field strength in the vicinity of the prominence with the signal from the region of prominence-to-cavity transition as discussed above. This provides important information about the properties of the prominence carrying magnetic fields. Furthermore, we find that the synthetic observation can measure the outward moving magnetic field around the rising prominence during the slow rise phase as the flux rope develops the kink instability (F17). It can detect the outward moving field up to a height of about $1.3 R_{\rm sun}$, until a time when the flux rope accelerates to about $41$ km/s, after which it can no longer detect a measurable field because of the rapid change and the weakening of the field strength. Thus our synthetic observation can track the field strength evolution of the prominence supporting field into its early phase of the onset of eruption. Examination of the extreme case with the isothermal atmosphere with 1.6 MK shows a greatly improved sensitivity in measuring the outward moving field during the onset of the eruption. It can detect a measurable outgoing $B_{\rm LOS}$ over a larger area of the rising flux rope cross section (Figure \ref{fig:fig_blos_fdl_th90phm90_iso_it358}), to a greater height of about $1.43 R_{\rm sun}$ and until a time when the flux rope has accelerated to a speed of $485$ km/s. A further improved approach that combines measurements of multiple coronal emission lines, with different temperature sensitivities, might allow a more comprehensive picture of the magnetic field throughout the multi-thermal prominence-cavity system. We leave this for a future study. | 18 | 8 | 1808.06142 |
1808 | 1808.07308_arXiv.txt | A knowledge of the particle escape time from the acceleration regions of many space and astrophysical sources is of critical importance in the analysis of emission signatures produced by these particles and in the determination of the acceleration and transport mechanisms at work. This paper addresses this general problem, in particular in solar flares, where in addition to scattering by turbulence, the magnetic field convergence from the acceleration region towards its boundaries also influences the particle escape. We test an (approximate) analytic relation between escape and scattering times, and the field convergence rate, based on the work of Malyshkin and Kulsrud (2001), valid for both strong and weak diffusion limits and isotropic pitch angle distribution of the injected particles, with a numerical model of particle transport. To this end, a kinetic Fokker-Planck transport model of particles is solved with a stochastic differential equation scheme assuming different initial pitch angle distributions. This approach enables further insights into the phase-space dynamics of the transport process, which would otherwise not be accessible. We find that in general the numerical results agree well with the analytic equation for the isotropic case, however, there are significant differences weak diffusion regime for non-isotopic cases, especially for distributions beamed along the magnetic field lines. The results are important in the interpretation of observations of energetic particles in solar flares, and other similar space and astrophysical acceleration sites and for the determination of acceleration-transport coefficients, commonly used in Fokker-Planck type kinetic equations. | \label{intro} The processes involved in the acceleration and transport of energetic particles in many space and astrophysical settings are still a very active topic of investigation after decades of research. These processes can be investigated by the observations of nonthermal radiations emitted from these sites and from the spectrum of cosmic rays (CRs) escaping them. Examples of these are solar eruptive events involving nonthermal radiation produced by flare accelerated particles and solar energetic particles (SEPs) seen by near Earth instruments. The aim of this paper is to clarify the transport coefficients involved in the acceleration-transport processes with particular emphasis on the time the particles spend in the acceleration site, which we refer to as the {\it escape time}, $\tesc$. We will use solar observations as an example for our discussion. The escape time is an important component of acceleration-transport process for several reasons. Clearly, the time spent in the acceleration site is important in shaping the energy, $E$, spectrum of the particles in the acceleration site, $N(E)$. It is also the main factor determining the spectrum of the flux of the escaping particles, ${\dot Q}(E)=N(E)/\tesc(E)$. In most sources, the main transport characteristics that determines the escape time are the crossing, $\tcross=L/v$, and scattering, $\tsc(E)$, times, for a source of size $L$ and a particle with speed $v$. Scattering can be due to Coulomb interactions in a collisional plasma and/or wave-particle interactions in a turbulent plasma. The later is related to the stochastic acceleration rate by turbulence or the acceleration rate in a shock environment \citep[see, e.g.,][]{Petrosian-2012}. In addition, in situations with weaker diffusion rate (i.e.~when $\tsc(E)>\tcross$ due to low particle and turbulence densities), the background guiding magnetic field, $B$, can affect the escape time due to mirroring in a converging field geometry. Thus, for a comprehensive analysis of particle confinement and escape from the acceleration regions, the field convergence towards the boundaries of the acceleration region needs to be considered in a particle transport model. The escape time (through its relation with $\tsc$) is related to all transport coefficients so that clarifications of its role can shed light on many aspects of the acceleration process. In general, in the acceleration process of background thermal particles (with a Maxwellian distribution), the interplay between Coulomb and turbulent scattering usually leads to plasma heating and acceleration, and can also lead to stable particle distributions consisting of a quasi-thermal components with non-thermal tails, often described by kappa distributions \citep{Bian-etal-2014}, for which evidence exists from solar flare observations \citep{Kasparova-Karlicky-2009,Oka-etal-2013,Oka-etal-2015,Oka-etal-2018}. As shown in \citet{Petrosian-East-2008} and \citet{Petrosian-Kang-2015}, in a {\it closed system}, i.e.\ where the particle escape time is longer than all the other timescales, irrespective of the details of the acceleration process, most of the energy goes into heating the plasma rather than producing a nonthermal tail. But, when the escape time is shorter, then a substantial population of nonthermal particles can escape the acceleration site; with an spectrum not necessarily the same as that of the accelerated one. They are distinguished by the escape time. This distinction is important in many space and astrophysical accelerators, in particular in solar eruptive events, as described below. A consequence of the particle interactions in the solar atmosphere is the production of thermal (due to plasma heating) and non-thermal (due to acceleration) radiation, in particular hard X-ray (HXR) bremsstrahlung, as observed for example with the Reuven Ramaty High Energy Solar Spectroscopic Imager \citep[\emph{RHESSI},][]{Lin-etal-2002}. The HXR observations by \rhessi (and earlier by {\it Yohkoh}) have shown the presence of a distinct source near the flaring loop top region (presumably the acceleration site) produced by the accelerated electrons. This is in addition to the more prominent foot point emission produced by escaping electrons. \citep{Masuda-etal-1994,Liu-etal-2008,Krucker-etal-2010,Liu-etal-2013}, which appear to be a common feature of almost all {\it Yohkoh} \citep{Petrosian-etal-2002} and {\it RHESSI} \citep{Liu-etal-2006, Krucker-Lin-2008} flares. These two emissions are related through the escape time. \citet{Petrosian-Donaghy-1999} showed that this requires some confinement of the electrons near the loop top acceleration site, which makes the escape time longer than the crossing time, and proposed turbulence as the agent of scattering and acceleration \citep[see also][]{Kontar-etal-2014}. Coulomb scattering can also trap particles at the loop top if the densities are high. However, because Coulomb energy loss and scattering rates are comparable, in such a case electrons lose most of their energy at the loop top leading to weaker footpoint emission. As shown by \citet{Leach-Petrosian-1983}, with Coulomb collision alone one obtains a gradual decline of emission along the flaring loop with a rapid increase below the transition region. \citet{Leach-Petrosian-1983} also showed that convergence of magnetic field toward the photosphere can enhance the trapping of the particles (see their Fig.~13). These effects were also discussed in \citet{Fletcher-1995} and \citet{Fletcher-Martens-1998} with similar results. They find that the confinement by the loop magnetic field can lead to a loop top emission that is stronger than or comparable to the footpoint emission for densities of $3\times 10^{10} (4\times 10^{9}$) cm$^{-3}$; see \citet{Fletcher-Martens-1998} Figs.~7 and 9, respectively. As evident from the above discussion, observations of loop top and footpoint emissions can provide information on the escape time. The relation of HXR emission and energetic electron properties can be analyzed with forward fitting methods or by regularized inversion using the imaging spectroscopy abilities of \rhessi \citep{Piana-etal-2007}. As shown by \citet{Petrosian-Chen-2010}, the inversion method allows the determination of the escape time from the comparison of loop top and footpoint non-thermal electron images obtained nonparametrically from \rhessi data directly. Subsequently, \citet{Chen-Petrosian-2013} showed that with this technique in addition to $\tesc$, one can obtain the other relevant coefficients (energy loss, acceleration and crossing times). This analysis has provided a paradigm shift indicating that the mirroring effect can be the main source of confinement of particles in the acceleration site. Further evidence supporting this results comes from the interpretation by \citet{Petrosian-2016} of \citet{Krucker-etal-2007} data comparing the spectra of HXR producing and SEP electrons in impulsive, prompt events. These findings can also be useful in the interpretation of the coronal emission close to the acceleration sites in partially occulted flares \citep[e.g.,][]{Krucker-Lin-2008,Effenberger-etal-2016,Effenberger-etal-2017}, with more direct information on the acceleration process. Magnetic field convergence and the mirroring effect can also be important in the transport of particles from coronal mass ejection (CME) shock environments. It is generally accepted that SEPs observed near the Earth are particles escaping from flare sites or the upstream region of such shocks. Recently, the {\it Fermi} large area telescope has detected $>100$ MeV sustained solar gamma ray emission from many eruptive events \citep{Ajello-etal-2014,Pesce-Rollins-etal-2015,Ackermann-etal-2017} associated with fast CMEs, lasting almost as long as the accompanying SEPs. These post-impulsive emission, with no other accompanying radiative signatures, have raised the possibility that they may be produced by particles escaping the turbulent downstream region of the CME-shock back to the Sun along converging field lines \citep{Jin-etal-2018}. Thus again, analysis of these events requires a knowledge of the escape time from a region where turbulence and field geometry can play an important role. An analytic approximation relating the escape and scattering times of particles in a converging field environment has been provided in \citep{Malyshkin-Kulsrud-2001}. One of our goals is to test the validity of this relation with a numerical particle transport model and explore different initial pitch-angle distributions, in addition to the isotropic one considered by these authors. In the next section we describe the origin of this analytic expression, and in \S 3 we present the transport equations of particles in a turbulent site with simple converging field geometry, the simulation scheme we use to determine pitch angle and spatial distribution of particles subject to only pitch angle scattering, and address the determination of the escape time. The results are presented and discussed in \S 4 followed by the summary and conclusions in \S 5. | \label{summary} In this study, we investigated the particle confinement and escape resulting from the interplay of isotropic turbulent pitch-angle scattering and magnetic field convergence. We compared numerical solutions for the relation between scattering and escape time calculated with an SDE scheme for the particle transport equation with an analytical approximation formula, based on the work of \citet{Malyshkin-Kulsrud-2001}. We found good agreement between the approximation and the simulation results but also notable differences in the weak diffusion regime that depend both on the initial pitch-angle distribution of particles and the field convergence rate represented by the mirror ratio $\eta$ or scale height $h_B$. The investigation of the acceleration and transport of particles in magnetized plasmas depends crucially on the escape time, because in most situations we do not observe the particles at the acceleration site. Instead, we observe the particles which have escaped the acceleration site and reached the near Earth instruments as cosmic rays and SEPs or indirectly through the radiation they produce often away from the acceleration sites. In some sources and under favorable observational situations, it is possible to measure the escape time and its energy dependence \citep[see, e.g.][]{Chen-Petrosian-2013,Petrosian-Chen-2014}. The relation we have established here can be used in such situations to determine the scattering time or the pitch-angle diffusion coefficient and hence provide information on acceleration and transport mechanisms. Expansion of these results to a more realistic situation that includes anisotropic pitch-angle diffusion coefficients and the dependence on energy of the processes discussed here can shed light on additional effects and the other important diffusion coefficient, namely energy or momentum diffusion, that plays an equally significant role in acceleration and transport processes. These aspects will be addressed in our future works. | 18 | 8 | 1808.07308 |
1808 | 1808.07078_arXiv.txt | The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has observed dozens of millisecond pulsars for over a decade. We have accrued a large collection of dispersion measure (DM) measurements sensitive to the total electron content between Earth and the pulsars at each observation. All lines of sight cross through the solar wind which produces correlated DM fluctuations in all pulsars. We develop and apply techniques for extracting the imprint of the solar wind from the full collection of DM measurements in the recently released NANOGrav 11-yr data set. We filter out long time scale DM fluctuations attributable to structure in the interstellar medium and carry out a simultaneous analysis of all pulsars in our sample that can differentiate the correlated signature of the wind from signals unique to individual lines of sight. When treating the solar wind as spherically symmetric and constant in time, we find the electron number density at 1~A.U. to be $7.9\pm0.2$ cm$^{-3}$. Our data shows little evidence of long-term variation in the density of the wind. We argue that our techniques paired with a high cadence, low radio frequency observing campaign of near-ecliptic pulsars would be capable of mapping out large-scale latitudinal structure in the wind. | \label{sec:intro} The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has entered a second decade of precisely timing an array of millisecond pulsars (MSPs) in an effort to detect extremely low-frequency ($\sim$nHz) gravitational waves \citep{abb+18_a,abb+18_b}. As part of this effort, NANOGrav has conducted a careful accounting of the noise processes influencing our measurements, with particular attention paid to the effects of the interstellar medium (ISM) \citep{lmj+16,jml+17,lcc+15,lcc+16_1,lcc+17,wh18}. Pulse times of arrival (TOAs) are primarily influenced by the ISM through variable dispersive delays. At a radio frequency $\nu$, the light propagating from a pulsar to the Earth is delayed by an amount $t_d={\cal D}(t)/(K\nu^2)$, where \begin{equation} {\cal D}(t)=\int_{\hat{\bf n}(t)}n_e(t,{\bf r})dl \end{equation} is the dispersion measure (DM), typically expressed in pc cm$^{-3}$, $K=2.41\times10^{-4}$ MHz$^{-2}$ pc cm$^{-3}$ s$^{-1}$, and $n_e(t,{\bf r})$ is the electron number density at time $t$ and position ${\bf r}$. The integration path extends from the Earth to the pulsar along the direction $\hat{\bf n}(t)$, the unit vector pointing towards the pulsar from Earth at time $t$. The solar wind (SW), streams of electrons flowing outward from the Sun, has a distinct and sizable influence on the DM of many pulsars. Over the course of a year, the line of sight (LOS) to a pulsar will sweep out an elliptical cone through the SW, causing annual fluctuations in DM which peak when the Sun and pulsar are in conjunction and the LOS connecting them most closely approaches the Sun. The fluctuations are larger and more peaked for pulsars closer to the ecliptic as the LOS for these pulsars more closely approaches the Sun. This is all well known. Shortly after they were discovered, pulsars were recognized as useful probes of the SW and corona \citep{cs68,h68}. The Crab Pulsar, with an ecliptic latitude $\beta=-1.24^\circ$, has been observed extensively for such applications \citep{gm69,cr72}. TEMPO and TEMPO2 \citep{nds+15,ehm06}, software packages commonly used for pulsar timing, both include constant, spherically symmetric models for the SW that attempt to account for timing perturbations it causes. \citet{abb+18_b} recently demonstrated that NANOGrav's sensitivity to gravitational waves has progressed to the point that our upper limit on the amplitude of the gravitational wave stochastic background depends on our choice of solar system ephemeris. To combat this undesirable model dependence, they developed tools for bridging various ephemerides, allowing the pulsar timing data itself to inform the ephemeris. A need has arisen for a similar treatment of the SW in which pulsar timing data can be used to inform models of the SW. As evidence for this need, \citet{agh+18} recently published important new constraints on general relativity's strong equivalence principle based on observations of a pulsar in a hierarchical triple system. They explicitly discuss issues they faced when trying to include data collected while the pulsar was close to the Sun and maximally influenced by the SW. Building on techniques used by, e.g., \citet{sns+05} and \citet{lkn+06}, \citet{agh+18} adapted the parameters of the SW to their data, but these techniques proved insufficient and systematic artifacts were left behind in their data. With observations of a lone pulsar, it is not possible to fully disentangle the influence of the ISM from that of the SW and it is difficult to constrain spatial and temporal variations in the SW. These purposes are better served by an analysis of data from a large array of pulsars, and in this work, we develop and use the techniques necessary to do just that. In nautical parlance, to ``sound'' is to measure the depth of a body of water, often in fathoms. One common sounding technique is to measure the time it takes for pulses of sound to travel from a ship, bounce off the sea floor, and return to the ship. This is not altogether dissimilar from the techniques we develop in this work: pulsed radio waves, delayed by propagation through a medium of interest---the solar wind---used to probe the distribution of that medium. In Section~2, we describe the data we use for our analysis. In Section~3, we describe DM fluctuations caused by the SW and the ISM and the models for those fluctuations we apply to our data. In Section 4, we lay out the procedure by which we apply our DM fluctuation model to the data. In Section 5, we summarize and discuss the results of our modeling effort. Finally, in Section 6 we discuss future prospects for investigations such as this and offer some concluding remarks. | \begin{figure} \begin{center} \label{fig:population} \includegraphics[scale=.57]{population.png} \caption{\label{fig:population}All pulsars with $|\beta|\leq 5^\circ$ according to the ATNF pulsar catalog \citep{mht+05}. The lines of sight to these pulsars come within 20 solar radii of the Sun (as indicated by the $y$-axis). The dense vertical strip of pulsars near $\lambda=270^\circ$ are in the direction of the Galactic interior and approach the Sun around December or January of every year. The red dots represent millisecond pulsars (MSP) and the black dots represent canonical pulsars (CP). The horizontal dashed line represents the angular extent of the Sun.} \end{center} \end{figure} The NANOGrav 11-yr data set is among the best collections of pulsar timing data in existence for looking for and studying nanohertz gravitational waves, rivaled only by similar data sets from the European Pulsar Timing Array \citep{kc13,dcl+16} and the Parkes Pulsar Timing Array \citep{h13,rhc+16}. But if one set out to observe pulsars for the purpose of investigating the SW rather than gravitational waves, the set of pulsars observed and the observing strategies employed would be quite different. \citet{tv18} recently presented low-frequency (approximately 100~MHz), high cadence (approximately weekly) observations of three pulsars within 9$^\circ$ of the ecliptic conducted with individual stations of the LOFAR telescope. Since dispersive timing delays scale as the inverse square of the radio frequency, variations in the electron content along the LOS lead to bigger and more precisely measurable timing fluctuations at these low radio frequencies. As Figure \ref{fig:Zl} shows, high cadence observations, particularly through solar conjunction, are necessary for probing latitudinal variations in the SW; higher than weekly cadence would be beneficial within approximately 10 days before and after solar conjunction. Figure \ref{fig:population} shows the entire known population of pulsars within 5$^\circ$ of the ecliptic. These pulsars come within 20~$R_\odot$ or less of the Sun when in solar conjunction, some of them being fully eclipsed by the Sun. For comparison, NASA's Parker Solar Probe will come within approximately 5 $R_\odot$ of the Sun's surface. A high-cadence, low frequency pulsar observing campaign through approximately December and January, when the bulk of the near-ecliptic pulsar population drifts behind the Sun, paired with the analysis techniques we have developed here, could map out the large scale structure of the SW and powerfully complement the \emph{in situ} capabilities of the Parker Solar Probe. New telescopes like the Canadian Hydrogen Intensity Mapping Experiment (CHIME) are well suited for this kind of high-cadence observational campaign. Additionally, pulsars are strongly linearly polarized and are thus very useful for probing the Sun's magnetic field \citep{bsv80,ych+12}. The type of many-pulsar analysis we have developed in this work could be straightforwardly extended to an analysis of rotation measures to make unprecedented inferences about the large scale configuration of the Sun's magnetic field. A high cadence, low frequency observing campaign would also be ideal for this application.\newline \emph{Author contributions}: D.R.M. wrote this manuscript and developed the techniques it describes. J.M.C. made code for simulating screens of turbulent material in the interstellar medium. D.J.N. conducted a preliminary analysis of the annual component of dispersion measure variations. J.M.C., C.M.F.M., D.J.N., M.T.L, M.A.M, and S.C. reviewed and substantially improved this manuscript. Z.A., K.C., P.B.D., M.E.D., T.D., J.A.E., R.D.F., E.C.F., E.F., P.A.G., G.J., M.L.J., M.T.L., L.L., D.R.L., R.S.L., M.A.M., C.N., D.J.N., T.T.P., S.M.R., P.S.R., R.S., I.H.S., K.S., J.K.S., and W.Z. contributed to the development of the 11-yr data set, as detailed in \citet{abb+18_a}. | 18 | 8 | 1808.07078 |
1808 | 1808.05885_arXiv.txt | This paper reviews Vlasov-based numerical methods used to model plasma in space physics and astrophysics. Plasma consists of collectively behaving charged particles that form the major part of baryonic matter in the Universe. Many concepts ranging from our own planetary environment to the Solar system and beyond can be understood in terms of kinetic plasma physics, represented by the Vlasov equation. We introduce the physical basis for the Vlasov system, and then outline the associated numerical methods that are typically used. A particular application of the Vlasov system is Vlasiator, the world's first global hybrid-Vlasov simulation for the Earth's magnetic domain, the magnetosphere. We introduce the design strategies for Vlasiator and outline its numerical concepts ranging from solvers to coupling schemes. We review Vlasiator's parallelisation methods and introduce the used high-performance computing (HPC) techniques. A short review of verification, validation and physical results is included. The purpose of the paper is to present the Vlasov system and introduce an example implementation, and to illustrate that even with massive computational challenges, an accurate description of physics can be rewarding in itself and significantly advance our understanding. Upcoming supercomputing resources are making similar efforts feasible in other fields as well, making our design options relevant for others facing similar challenges. | While physical understanding is inherently based on empirical evidence, numerical simulation tools have become an integral part of the majority of fields within physics. When tested against observations, numerical models can strengthen or invalidate existing theories and quantify the degree to which the theories have to be improved. Simulation results can also complement observations by giving them a larger context. In space physics, spacecraft measurements concern only one point at one time in the vast volume of space, indicating that discerning spatial phenomena from temporal changes is difficult. This is a shortcoming that has also led to the use of spacecraft constellations, like the European Space Agency's Cluster mission \citep{Escoubet2001AnnGeo}. However, simulations are considerably more cost-effective compared to spacecraft, and they can be adopted to address physical systems that cannot be reached by \textit{in situ} experiments, like the distant galaxies. Finally, and most importantly, predictions of physical environments under varying conditions are always based on modelling. Predicting the near-Earth environment in particular has become increasingly important, not only because the near-Earth space hosts expensive assets used to monitor our planet. The space environmental conditions threatening space- or ground-based technology or human life are commonly termed as \textit{space weather}. Space weather predictions include two types of modelling efforts; those targeting real-time modelling (similar to terrestrial weather models), and those which test and improve the current space physical understanding together with top-tier experiments. This paper concerns the latter approach. The physical conditions within the near-Earth space are mostly determined by physics of collisionless plasmas, where the dominant physical interactions are caused by electromagnetic forces over a collection of charged particles. There are three main approaches to model plasmas: 1) the fluid approach (e.g., magnetohydrodynamics, MHD), 2) the fully kinetic approach, and 3) hybrid approaches combining the first two. Present global models including the entire near-Earth space in three dimensions (3D) and resolving the couplings between different regions are largely based on MHD \citep[e.g.][]{Janhunen2012}. However, single-fluid MHD models are basically scale-less in that they assume that plasmas have a single temperature approximated by a Maxwellian distribution. Therefore they provide a limited context to the newest space missions, which produce high-fidelity multi-point observations of spatially overlapping multi-temperature plasmas. The second approach uses a kinetic formulation as represented by the Vlasov theory \citep{Vlasov}. In this approach, plasmas are treated as velocity distribution functions in a six-dimensional phase space consisting of three-dimensional ordinary space (3D) and a three-dimensional velocity space (3V). \label{sec:pic}The majority of kinetic simulations model the Vlasov theory by a particle-in-cell (PIC) method (Lapenta, 2012\nocite{LAPENTA2012}; Cerutti et al., Living Reviews in Computational Astronomy, in preparation), where a large number of particles are propagated within the simulation, and the distribution function is constructed from particle statistics in space and time. The fully kinetic PIC approach means that both electrons and protons are treated as particles within the simulation. Such simulations in 3D are computationally extremely costly, and can only be carried out in local geometries \citep[e.g.][]{Daughton11}. A hybrid approach in the kinetic simulation regime means usually that electrons are treated with a fluid description, but protons and heavier ions are treated kinetically. Again, the vast majority of simulations use a hybrid-PIC approach, which have previously concidered 2D spatial regimes due to computational challenges \citep[e.g.,][]{omidi05, karimabadi14}, but have recently been extended into 3D using a limited resolution \citep[e.g.][]{lu15, lin17}. This paper does not discuss the details of the PIC approach, but instead concentrates on a hybrid-Vlasov method, where the ion velocity distribution is discretised and modelled with a 3D-3V grid. The difference to hybrid-PIC is that in hybrid-Vlasov the distribution functions are evolved in time as an entity, and not constructed from particle statistics. The main advantage is therefore that the distribution function becomes noiseless. This can be important for the problem at hand, because the distribution function is in many respects the core of plasma physics as the majority of the plasma parameters and processes can be derived from it. As will be described, hybrid-Vlasov methods have been used mostly in local geometries, because the 3D-3V requirement implies a large computational cost. A global approach, which in space physics means simulation box sizes exceeding thousands of ion inertial lengths or gyroradii per dimension, have not been possible as naturally the large volume has to consider the velocity space as well. The world's (so far) only global magnetospheric hybrid-Vlasov simulation, the massively parallel Vlasiator, is therefore the prime application in this article. This paper is organised as follows: Section \ref{sec:physicalSystems} introduces the typical plasma systems and relevant processes one encounters in space. Sections \ref{sec:vlasoveq} and \ref{sec:numerical} introduce the Vlasov theory and its numerical representations. Section \ref{sec:Vlasiator} describes Vlasiator in detail and justifies the decisions made in the design of the code to aid those who would like to design their own (hybrid-)Vlasov system. At the time of writing, there are no standard verification cases for a (hybrid-)Vlasov system, but we describe the test cases used for Vlasiator. The physical findings are then illustrated briefly, showing that Vlasiator has made a paradigm change in space physics, emphasising the role of scale coupling in large-scale plasma systems. While this paper concerns mostly the near-Earth environment, we hope it is useful for astrophysical applications as well. Astrophysical large-scale modelling is still mostly based on non-magnetised gas \citep{springel2005,Bryan2014}, while in reality astrophysical objects are in the plasma state. In the future, pending new supercomputer infrastructure, it may be possible to design astrophysical simulations based on MHD first, and later possibly on kinetic theories. If this becomes feasible, we hope that our design strategies, complemented and validated by \textit{in situ} measurements, can be helpful. | There are several main conclusions that can be made from all Vlasiator results so far. The first one is related to the applicability of the hybrid-Vlasov system for ions within the global magnetospheric context. When Vlasiator was first proposed, concerns arose as to whether ions are the dominant species controlling the system dynamics or does one need electrons as well. In particular, a physical representation of the reconnection process may require electrons, while the ion-scale Vlasiator would still model reconnection similarly as global MHD simulations, i.e., through numerical diffusion. However, even an MHD simulation, treating both ions and electrons as a fluid, is capable of modelling global magnetospheric dynamics \citep{palmroth06prec, palmroth06hyst}, indicating that reconnection driving the global dynamics must be within the right ballpark. Since Vlasiator is also able to produce results that are in agreement with \textit{in situ} measurements, kinetic ions seem to be a major contributor in reproducing global dynamics. Whether the electrons play a larger role in global dynamics remains to be determined in the future, if such simulations become possible. Another major conclusion based on Vlasiator is the role of grid resolution in global setups. Again, one of the largest concerns in the beginning of Vlasiator development was that the ion gyroscales could not be reached within a global simulation volume, raising fears that the outcomes would be MHD-like, even though early hybrid-PIC simulations were also carried out at ion inertial length scales \citep[e.g.,][]{omidi05}. In this context, the first runs included an element of surprise, as even rather coarse resolution grids induce kinetic phenomena that are in agreement with \textit{in situ} observations \citep{Pokhotelov2013}. Latest results have clearly indicated that kinetic physics emerges even at coarse spatial resolution \citep{PfauKempf2018}. It should be emphasised that this result would not have been foreseeable without developing the simulation first. Further, it indicates that also electron physics could be trialled without resolving the actual electron scales. One can hence conclude that others attempting to develop a (hybrid-)Vlasov simulation may face less concerns due to the grid resolution, even in setups with major computational challenges, like e.g., portions of the Sun. The most common physical conclusion based on Vlasiator simulations is that ``everything affects everything'', indicating that scale coupling is important in global magnetospheric dynamics. One avenue of development for the global MHD simulations in the recent years has been code coupling, where e.g., problem-specific codes have been coupled into the global context \citep{huang06}, or e.g., hybrid-PIC simulations have been embedded within the MHD domain \citep{Toth2016EPICMHD}. While these approaches are interesting and advance physical understanding, they cannot approach scale coupling as the specific kinetic phenomena are only addressed within their respective simulation volumes. A prime example of the scale coupling is the emergence of transient foreshocks, driven by bow waves generated by dayside reconnection \citep{PfauKempf2016}. Another example is the generation of oblique foreshock waves due to a global variability of backstreaming populations \citep{Palmroth2015}. These results could not have been achieved without a simulation that resolves both small and large scales simultaneously. Vlasov-based methods have not yet been widely adopted in the fields of astrophysics and space physics to model large-scale systems beyond the few examples cited in Table \ref{tab:Applications}, mainly due to the truly astronomical computational cost such simulations can have. The experience with Vlasiator nevertheless demonstrates that Vlasov-based modelling is strongly complementary to other methods and provides unprecedented insight well worth the implementation effort. Based on the pioneering work realised in the Solar-Terrestrial physics community, it is hoped that Vlasov-based methods will gain in popularity and lead to breakthrough results in other fields of space physics and astrophysics as well. Finally, it should be emphasized that a critical success factor in the Vlasiator development has been the close involvement with technological advances in the field of high-performance computing. European research infrastructures for supercomputing have been developed almost hand-in-hand with Vlasiator, providing an opportunity to always target the newest platforms thus feeding directly into the code development. Should similar computationally intensive codes be designed and implemented elsewhere, it is recommended to keep a keen eye on the technological development of the supercomputing platforms. | 18 | 8 | 1808.05885 |
1808 | 1808.07880_arXiv.txt | { The X-ray emission of O-type stars was first discovered in the early days of the {\em Einstein} satellite. Since then many different surveys have confirmed that the ratio of X-ray to bolometric luminosity in O-type stars is roughly constant, but there is a paucity of studies that account for detailed information on spectral and wind properties of O-stars. Recently a significant sample of O stars within our Galaxy was spectroscopically identified and presented in the Galactic O-Star Spectroscopic Survey (GOSS). At the same time, a large high-fidelity catalog of X-ray sources detected by the \xmm\ X-ray telescope was released. Here we present the X-ray catalog of O stars with known spectral types and investigate the dependence of their X-ray properties on spectral type as well as stellar and wind parameters. We find that, among the GOSS sample, 127 O-stars have a unique \xmm\ source counterpart and a Gaia data release 2 (DR2) association. Terminal velocities are known for a subsample of 35 of these stars. We confirm that the X-ray luminosities of dwarf and giant O stars correlate with their bolometric luminosity. For the subsample of O stars with measure terminal velocities we find that the X-ray luminosities of dwarf and giant O stars also correlate with wind parameters. However, we find that these correlations break down for supergiant stars. Moreover, we show that supergiant stars are systematically harder in X-rays compared to giant and dwarf O-type stars. We find that the X-ray luminosity depends on spectral type, but seems to be independent of whether the stars are single or in a binary system. Finally, we show that the distribution of \LxLbol\ in our sample stars is non-Gaussian, with the peak of the distribution at $\LxLbol\approx -6.6$. } | Since the era of the {\em Einstein} X-ray telescope (0.2--4.0\,keV) it is known that O-type stars emit X-rays \citep{harndenetal79-1}. Based on the initial sample of 16 OB stars detected by {\em Einstein}, \cite{long+white80-1} noted that their X-ray luminosity correlates with bolometric luminosity as $\Lx\sim 10^{-6\,...\,-8}\Lbol$. \cite{pallavicinietal81-1} extended the study to 35 stars with spectral types in the range from O4 to A9 and concluded that the ratio of X-ray to bolometric luminosity is roughly constant ($\Lx\approx (1.4\pm0.3)\times10^{-7}\Lbol$), breaking down for spectral types later than A5. Later on, \cite{schmittetal85-1} showed that the $\LxLbol\sim -7$ correlation does not hold for A-type stars breaking down already at spectral type B5. \cite{chlebowski+harnden89-1} presented ``The {\em Einstein} X-ray Observatory Catalog of O-type stars''. The catalog contains 289 stars with 89 detections and 176 upper limits. It was found that X-ray luminosities of O stars are in the range $\Lx\approx 10^{-5.44\,...\,-7.35}\Lbol$. The {\em ROSAT} telescope performed an all-sky X-ray survey \cite[RASS,][]{vogesetal99-1,vogesetal00-1} in the 0.2--2.4\,keV energy band and detected many OB-type stars, confirming the $\Lx\propto\Lbol$ correlation \citep[e.g.,][]{motchetal97-1}. \cite{berghoferetal97-1} demonstrated that this correlation flattens considerably below $\Lbol\approx 10^{38}$\,erg\,s$^{-1}$, that is, for mid- and late-type B stars. Since then, the $\Lx\propto\Lbol$ relation was often revisited and confirmed by many independent studies of OB-stars in clusters and in the field. With the advent of modern X-ray telescopes \xmm\ and \cxo, with their broad spectral response (0.2--12.0\,keV) and high spatial resolution, the interest in X-ray properties of O stars was once more renewed. \citet{osk2005} verified the \LxLbol\ correlation selectively, distinguishing between binary and single stars. A linear regression analysis of a sample of spectroscopic binaries showed a correlation $\Lx\approx 10^{-7}\Lbol$. It was found that while binary stars are more X-ray luminous than single ones, the correlations between X-ray and bolometric luminosities are similar for both groups. Great effort has been made to study massive star populations in individual clusters \citep[e.g.,][]{Moffat2002,Wolk2006}. \citet{sanaetal06-1} observed the open cluster NGC\,6231 using \xmm. Based on a rather small sample of 12 O stars they found a much lower scatter than previous studies (\LxLbol$ = -6.91 \pm 0.15$) and showed that the $\Lx\propto \Lbol$ relation is dominated by soft X-ray emission -- the dispersion becomes larger for radiation above 2.5\,keV. X-ray emission from a large number of O-stars in the Carina Nebula cluster was studied by \cite{nazeetal11-1}. Using \cxo\ observations of 60 O stars in this region, a ratio of $\LxLbol=-7.26\pm 0.21$ was determined. The spectral types were collected from the literature as presented in the contemporaneous \citet{skiff14-1} catalog. Interestingly, using \xmm\ observations of the same region, \cite{Antokhin2008} determined $\LxLbol=-6.58\pm 0.79$. \cite{nazeetal11-1} explained the discrepancy by the different reddening laws and bolometric luminosities assigned to O-stars in these studies. An X-ray catalog of OB-stars was presented by \cite{naze09-1}. They cross-correlated the {\em XMM-Newton Serendipitous Source Catalogue: 2XMMi-DR3} \citep{watsonetal09-1} and the all-sky catalog of Galactic OB stars, which contains $\sim 16000$ known or ``reasonably suspected'' OB stars \citep{Reed2003}. Approximately 300 OB stars were found to have an X-ray counterpart. Confirming previous studies, \citet{naze09-1} showed that X-ray fluxes of O stars are well correlated with their bolometric fluxes. However, the scatter was found to be comparable to that of the RASS studies, that is,\ much larger than in individual clusters. The average ratio between X-ray (in the 0.5--10.0\,keV band) and bolometric fluxes for O-stars was found to be $\LxLbol=-6.45\pm 0.51$. Although the \cite{Reed2003} catalog of OB stars is a valuable resource, it is heterogeneous by nature, harvesting data from the SIMBAD data-base,\footnote{\cite{wenger00-1}} and might contain dubious spectral classifications. While significant effort firmly established an $\Lx\propto\Lbol$ correlation for O stars, its origin is still unknown. A standard explanation of X-ray emission from O stars is the presence of plasma heated by shocks intrinsic to radiatively driven stellar winds \citep{lucy+white80-1, Owocki1988, Feld1997}. The X-ray luminosity is therefore expected to correlate with stellar wind parameters. One of the most detailed and careful analyses to date was performed by \cite{sciortino90-1}, who investigated correlations between X-ray luminosity and stellar and wind parameters based on a large sample of O stars detected by the {\em Einstein} observatory. They found that \Lx\ correlates well with mass, the Eddington factor (that describes relative influence of radiation pressure with respect to gravity), \Lbol, wind momentum (\Mdot\Vinf), and kinetic wind luminosity (\Lkin), but only weakly with mass-loss rate (\Mdot) and with terminal wind velocity (\Vinf). Moreover, \cite{sciortino90-1} found that none of these parameters alone can account for the observed dispersion in \Lx, but that a combination of \Lbol, \Vinf\, and \Mdot\ is needed. Motivated by the well-known correlation of \Lx\ with rotation rate in solar-type stars, \citet{sciortino90-1} searched for similar correlations in hot stars but could not find any evidence. Alternative and still speculative explanations for X-ray emission from O stars invoke stellar magnetism. In this case, hot X-ray-emitting plasma could be associated with stellar spots \citep[e.g.,][]{WC2007}. The presence of such magnetic structures in normal stars is gaining support both theoretically and observationally \citep{Cantiello2011, Ram2014}. The aim of the study presented in this paper is to build a homogeneous catalog of X-ray emitting O stars and to study the dependence of their X-ray emission with stellar and wind properties. The time is now ripe for such a study. The Galactic O-Star Spectroscopic Survey (GOSS) by \cite{sotaetal11-1, sotaetal2014} and \cite{maiz-apellanizetal16-1} is now available. GOSS consists of more than 590 O stars with spectral types homogeneously determined from optical spectroscopy. It is complete down to magnitude $B=8$\,mag. As noted by \cite{sotaetal2014}, the previous studies were subject to discrepancies in spectral type determinations which can lead to errors deriving parameters that depend on spectral types (and propagate to X-ray studies). The X-ray catalog we present in this paper is limited to stars from the GOSS sample for the sake of consistency. The release of the GOSS coincides with an on-going improvement and expansion of {\em The XMM-Newton Serendipitous Source Catalogue}. In this paper we consider GOSS stars with X-ray counterparts in the latest \xmm\ catalog at the time of writing. We do not include the information from other X-ray surveys and telescopes in order to study the homogeneous X-ray sample representative for the O star population within our Galaxy. The catalog we present here incorporates distances based on the parallaxes included in the Gaia second data release (DR2). The paper is structured as follows: in Sect\,\ref{sec:asso} we describe the X-ray, optical, and infrared associations. Determinations of stellar and X-ray parameters are described in Sects.\,\ref{sec:parameters} and \ref{sec:xray}, respectively. Correlations between X-ray and wind parameters are discussed in Sect.\,\ref{sec:windparams}, and conclusions are drawn in Sect.\,\ref{sec:concl}. | 18 | 8 | 1808.07880 |
|
1808 | 1808.02141_arXiv.txt | {$\eta$ Car is one of the most intriguing luminous blue variables in the Galaxy. Observations and models of the X-ray, ultraviolet, optical, and infrared emission suggest a central binary in a highly eccentric orbit with a 5.54 yr period residing in its core. 2D and 3D radiative transfer and hydrodynamic simulations predict a primary with a dense and slow stellar wind that interacts with the faster and lower density wind of the secondary. The wind-wind collision scenario suggests that the secondary's wind penetrates the primary's wind creating a low-density cavity in it, with dense walls where the two winds interact. However, the morphology of the cavity and its physical properties are not yet fully constrained.} {We aim to trace the inner $\sim$5--50 au structure of $\eta$ Car's wind-wind interaction, as seen through Br$\gamma$ and, for the first time, through the He {\sc i} 2s-2p line. } {We have used spectro-interferometric observations with the $K$-band beam-combiner GRAVITY at the VLTI. The analyses of the data include (i) parametrical model-fitting to the interferometric observables, (ii) a \texttt{CMFGEN} model of the source's spectrum, and (iii) interferometric image reconstruction. } {Our geometrical modeling of the continuum data allows us to estimate its FWHM angular size close to 2 mas and an elongation ratio $\epsilon$ = 1.06 $\pm$ 0.05 over a PA = 130$^{\circ}$ $\pm$ 20$^{\circ}$. Our \texttt{CMFGEN} modeling of the spectrum helped us to confirm that the role of the secondary should be taken into account to properly reproduce the observed Br$\gamma$ and He {\sc i} lines. Chromatic images across the Br$\gamma$ line reveal a southeast arc-like feature, possibly associated to the hot post-shocked winds flowing along the cavity wall. The images of the He {\sc i} 2s-2p line served to constrain the 20 mas ($\sim$ 50 au) structure of the line-emitting region. The observed morphology of He {\sc i} suggests that the secondary is responsible for the ionized material that produces the line profile. Both the Br$\gamma$ and the He {\sc i} 2s-2p maps are consistent with previous hydrodynamical models of the colliding wind scenario. Future dedicated simulations together with an extensive interferometric campaign are necessary to refine our constraints on the wind and stellar parameters of the binary, which finally will help us predict the evolutionary path of $\eta$ Car.} {} | Massive stars are among the most important chemical factories of the interstellar medium (ISM). This is mainly because their evolution and fate are highly affected by strong stellar winds ($v_{\rm{w}} \sim$10$^3~\kms$), high mass-loss rates ($\dot{M} \sim$ 10$^{-5}$--10$^{-3}$ $M_{\odot}$ yr$^{-1}$) and deaths as supernovae (SNe) \citep[see, e.g., ][]{Conti_1976, Langer_1994, Meynet_2003, Meynet_2011}. One of the evolutionary stages of high-mass stars that exhibit sporadic but violent mass-loss episodes is the luminous blue variable phase \citep[LBV; ][]{Humphreys_1994}. The importance of LBVs to stellar evolution models relies on the possibility of them to directly explode as SN without being a Wolf-Rayet (WR) star \citep{Smith_2007, Smith_2011, Trundle_2008}. Therefore, detailed studies of LBVs are crucial to understand the mass-loss processes in high-mass stars \citep[see e.g., ][]{Pastorello_2010, Smith_2011}. The source, $\eta$ Car, is one of the most intriguing LBVs in the Galaxy. Located at the core of the Homunculus Nebula in the Trumpler 16 cluster at a distance of 2.3 $\pm$ 0.1 kpc \citep{Walborn_1973, Allen_1993, Smith_2006}, it has been identified as a luminous \citep[$L_{\mathrm{tot}} \ge$ 5x10$^6$ $L_{\odot}$][]{Davidson_1997, Smith_2003} colliding-wind binary \citep{Damineli_1997, Hillier_2001, Damineli_2008a, Damineli_2008b, Corcoran_2010} in a highly eccentric orbit \citep[e $\sim$ 0.9; ][]{Corcoran_2005} with a period of 2022.7 $\pm$ 1.3 d \citep{Damineli_2008b}. The primary, $\eta_A$, is a very massive star with an estimated $M \sim$ 100 $M_{\odot}$, a mass-loss rate $\dot{M} \sim$ 8.5 x 10$^{-4}$ $M_{\odot}$ yr$^{-1}$ and a wind terminal speed $v_{\infty} \sim$ 420$~\kms$ \citep{Hillier_2001, Hillier_2006, Groh_2012a, Groh_2012b}. Evidence suggests that $\eta_A$ is near the Eddington limit \citep{Conti_1984, Humphreys_1994}. Therefore, it loses substantial mass in violent episodes such as the ``Great Eruption'' where $\sim$15 $M_{\odot}$, possibly more than 40 $M_{\odot}$ \citep{Gomez_2010, Morris_2017}, were ejected over a period of $\sim$10 yr. Mass-loss events dominate the evolutionary tracks of the most massive stars \citep{Langer_1998, Smith_2006}. In binary star systems, like $\eta$ Car, the presence of a companion affects wind-driven mass loss, providing alternative evolutionary pathways compared to single stars. Therefore, understanding in detail their mass-loss processes is particularly important. The nature of the secondary, $\eta_B$, is even less constrained since it has not been directly observed \citep[it is, at least, of the order of 100 times fainter than $\eta_A$;][]{Weigelt_2007} because it is embedded in the dense wind of the primary. Models of the X-ray emission (kT $\sim$ 4--5 keV) predict a wind terminal velocity $v_{\infty} \sim$ 3000$~\kms$ , a mass-loss rate $\dot{M} \sim$ 10$^{-5}~M_{\odot}$ yr$^{-1}$ \citep{Pittard_2002, Okazaki_2008, Parkin_2011b}, and a T$_{\mathrm{eff}} \sim$ 36000--41000 K \citep{Teodoro_2008}. Models of the mutual motion of the stars suggest an inclination $i \sim$ 130--145$^{\circ}$, an argument of periastron $\omega \sim$ 240--285$^{\circ}$, and a sky projected PA $\sim$ 302--327$^{\circ}$ for the best-fit orbital solution \citep{Damineli_1997, Okazaki_2008, Parkin_2009, Parkin_2011b, Groh_2010b, Gull_2011, Madura_2012a, Madura_2012b, Teodoro_2016}. This suggests that the orbital plane of the binary is almost perpendicular to the Homunculus axis \citep[ $i \sim$ 49$^{\circ}$ with respect to the sky plane; PA$\sim$132$^{\circ}$;][]{Davidson_2001, Smith_2006}. These orbital parameters also imply that the secondary remains in front of the primary (in the line-of-sight -LOS- of the observer) most of the time during the orbital motion, except close to the periastron, where $\eta_B$ goes behind $\eta_A$ and it is obscured by the dense primary wind. Figure\,\ref{fig:EtaCar_orientation} displays the inclination and PA of the Homunculus Nebula and of the orbit of $\eta_B$ around $\eta_A$, according to the orbital solution reported by \citet{Teodoro_2016}. The left panel displays the nebula projected in the plane of the sky. The PA (east to the north) of the semi-major axis is labeled in the image. The right panel displays the position of the nebula and of the orbit of the binary in a plane parallel to the observer's line-of-sight and the sky plane. The inclination angles (relative to the sky plane) of the nebula ($i_{\mathrm{HN}}$) and of the binary's orbital plane ($i_{\mathrm{Binary}}$) are labeled. The secondary, $\eta_B$, photoionizes part of the primary wind, changing the strength of lines such as H$\alpha$, He {\sc i}, [Fe {\sc ii}], and [Ne {\sc ii}] \citep{Hillier_2001, Nielsen_2007, Mehner_2010, Mehner_2012, Madura_2012b, Davidson_2015}. Additionally, it ionizes the inner 1'' circumstellar ejecta \citep[][]{Weigelt_1986, Hofmann_1988, Weigelt_1995}. 2D radiative transfer models and 3D hydrodynamical simulations of the wind-wind collision scenario suggest that the high-velocity secondary wind penetrates the slower and denser primary wind creating a low-density cavity in it, with thin and dense walls where the two winds interact \citep{Okazaki_2008, Groh_2012a, Madura_2012b, Madura_2013, Clementel_2015a, Clementel_2015b}. This wind-wind collision scenario produces the shock-heated gas responsible for the X-ray variability, and the ionization effects observed in the optical, infrared, and ultraviolet spectra. \begin{figure}[thp] \centering \begin{minipage}[c]{0.4\textwidth} \centering \includegraphics[width = 8 cm]{EtaCar_uv_coverage_feb2016.png} \end{minipage} \begin{minipage}[c]{0.4\textwidth} \centering \includegraphics[width = 8 cm]{EtaCar_uv_coverage_june2017.png} \end{minipage} \caption{ $\eta$ Car's $u-v$ coverages obtained during the GRAVITY runs in February 2016 (\textit{top}) and May-June 2017 (\textit{bottom}). Different quadruplets are indicated with different colors.} \label{fig:uv_plane} \end{figure} These aforementioned models also show that during the periastron passage (phase $\phi \sim$ 0.98--1.02) the acceleration zone of the post-shock wind of $\eta_B$ is affected by $\eta_A$. The hot wind of $\eta_B$ pushes the primary wind outward and it ends up trapped inside the cavity walls. The material in the walls is accelerated to velocities larger than $\eta_A$'s wind terminal velocity, creating a layer of dense trapped primary wind. These layers have been observed as concentric fossil wind arcs in [Fe {\sc ii}] and [Ni {\sc ii}] images at the inner 1'' obtained with the HST/STIS camera \citep{Teodoro_2013, Gull_2016}. To explain the wind-wind phenomenology at 2--10 mas ($\sim$5--25 au) scales, several attempts have been made to characterize the core of $\eta$ Car. Particularly, long-baseline infrared interferometry has been a decisive technique for such studies. \citet{Kervella_2002} and \citet{vanBoekel_2003} resolved an elongated optically thick region using the $K$-band (2.0--2.4 $\mu$m) beam-combiner VINCI \citep{Kervella_2000} at the Very Large Telescope Interferometer \citep[VLTI;][]{Glindemann_2003}. Those authors measured a size of 5--7 mas (11--15 au) for $\eta$ Car's core, with a major to minor axis ratio $\epsilon$ = 1.25 $\pm$ 0.05, and a PA = 134 $\pm$ 7$^{\circ}$. Using a Non-Local Thermal Equilibrium (non-LTE) model, a mass-loss rate of 1.6 $\pm$ 0.3 $\times$ 10$^{-3}~M_{\odot}$ yr$^{-1}$ was estimated. Follow-up observations \citep{Weigelt_2007} with the $K$-band beam combiner VLTI-AMBER \citep{AMBER_Petrov_2007} using medium (R = 1500) and high (R = 12000) spectral resolutions of the He {\sc i} 2s-2p (2.0587 $\mu$m) and Br$\gamma$ (2.1661 $\mu$m) lines, resolved $\eta$ Car's wind structure at angular scales as small as $\sim$ 6 mas ($\sim$ 13 au). These authors measured a (50\% encircled energy) diameter of 3.74--4.23 mas (8.6--9.7 au) for the continuum at 2.04 $\mu$m and 2.17 $\mu$m; a diameter of 9.6 mas (22.6 au) at the peak of the Br$\gamma$ line; and 6.5 mas (15.3 au) at the emission peak of the He {\sc i} 2s-2p line. They also confirmed the presence of an elongated optically thick continuum core with a measured axis ratio $\epsilon$ = 1.18 $\pm$ 0.10 and a projected PA = 120$^{\circ} \pm$ 15$^{\circ}$. The observed non-zero differential phases and closure phases indicate a complex extended structure across the emission lines. To explain the Br$\gamma$-line profile and the signatures observed in the differential and closure phases, \citet{Weigelt_2007} developed a ``rugby-ball'' model for an optically thick, latitude dependent wind, which includes three components: (a) a continuum spherical component; (b) a spherical primary wind; (c) and a surrounding aspherical wind component inclined 41$^{\circ}$ from the observer's LOS. New high-resolution AMBER observations in 2014 allowed \citet{Weigelt_2016} to reconstruct the first aperture-synthesis images across the Br$\gamma$ line. These images revealed an asymmetric and elongated structure, particularly in the blue wing of the line. At velocities between $-$140 and $-$380$~\kms$, the intensity distribution of the reconstructed maps shows a fan-shaped structure with an 8.0 mas (18.8 au) extension to the southeast and 5.8 mas (13.6 au) to the northwest. The symmetry axis of this elongation is at a PA = 126$^{\circ}$, which coincides with that of the Homunculus axis. This fan-shaped morphology is consistent with the wind-wind collision cavity scenario described by \citet{Okazaki_2008}, \citet{Madura_2012b, Madura_2013}, and \citet{Teodoro_2013, Teodoro_2016}, with the observed emission originating mainly from the material flowing along the cavity in a LOS preferential toward the southeast wall. Additionally to the wind-wind collision cavity, several other wind structures were discovered in the images reported by \citet{Weigelt_2016}. At velocities between $-$430 and $-$340$~\kms$, a bar-like feature appears to be located southwest of the continuum. This bar has the same PA as the more extended fossil wind structure reported by \citet{Falcke_1996} and \citet{Gull_2011, Gull_2016}, that may correspond to an equatorial disk and/or toroidal material that obscures the primary star in the LOS. At positive velocities, the emission appears not to be as extended as in the blue-shifted part of the line. This may be because we are looking at the back (red-shifted) part of the primary wind that is less extended because it is not as deformed by the wind collision zone. Finally, the wind lacks any strong emission line features at velocities lower than $-$430$~\kms$ or larger than $+$400$~\kms$. \begin{figure*}[htp] \centering \includegraphics[width=\textwidth]{EtaCar_spectrum.pdf} \caption{2016 (blue straight line) and 2017 (black straight line) $\eta$ Car normalized spectra in the 2.0--2.2 $\mu$m bandpass. The vertical red-dashed lines indicate the spectral features identified in the spectrum. } \label{fig:GRAVITY_spectrum} \end{figure*} This work presents VLTI-GRAVITY chromatic imaging of $\eta$ Car's core across two spectral lines in the infrared $K$-band: He {\sc i} 2s-2p and Br$\gamma$. The paper is outlined as follows: Sect.\,\ref{sec:data_reduction} presents our GRAVITY observations and data reduction. In Sect.\,\ref{sec:results} the analyses of the interferometric observables, and the details of the imaging procedure are described. In Sect.\,\ref{sec:discussion} our results are discussed and, finally, in Sect.\,\ref{sec:conclusions} the conclusions are presented. | } \begin{itemize} \item We present GRAVITY interferometric data of $\eta$ Car's core. Our observations trace the inner 20 mas (50 au) of the source at a resolution of 2.26 mas. The spectro-interferometric capabilities of GRAVITY allowed us to chromatically image Br$\gamma$ and He {\sc i} 2s-2p emission regions with a spectral resolution of R = 4000, while the analysis of the Fringe Tracker data allowed us to measure the size of the continuum emission, and the integrated spectrum to characterize the parameters of the primary star. \item From our geometrical model of the Fringe Tracker squared visibilities, we constrained the size of the continuum emission. We derived a mean FWHM angular scale of 2 mas ($\sim$ 5 au) and an elongation ratio $\epsilon$ = 1.06 $\pm$ 0.5 for the compact continuum emission of $\eta_A$, together with an extended over-resolved emission with an angular size of at least 10 mas. These estimates are in agreement with previous interferometric measurements. Some of the plausible hypotheses to explain the observed elongation of the continuum compact emission are the fast rotation of the primary and/or the effect of the wind-wind collision cavity. A future monitoring of the continuum size and elongation with GRAVITY and other interferometric facilities at different wavelengths, in combination with radiative transfer models, would serve to test these scenarios. \item To characterize the properties of $\eta_A$'s wind, we applied a \texttt{CMFGEN} 1D non-LTE model to the GRAVITY spectrum. Our model reproduces the He {\sc i} 2s-2p and He {\sc i} 3p-4s lines, which could not be formed with the parameters used in previous models in the literature. However, the line-emitting regions of the best-fit model are quite small compared to the structure observed in the reconstructed images. These results imply that single-star models are not enough to reproduce all the observational data. Therefore, the role of $\eta_B$ should be taken into account when modeling the $\eta$ Car spectrum. Furthermore, when comparing our model with the $\eta$ Car spectrum in the visible, we could not reproduce the observed metallic features. We suspect that this is caused because many of the metallic lines are forbidden lines with critical electron densities of 10$^{7-8}$ cm$^{-3}$. With the FEROS aperture, this emission is originating in the fossil wind shells and hence not reproduced in the stellar model. \item Our aperture-synthesis images allowed us to observe the inner wind-wind collision structure of $\eta$ Car. Previous AMBER interferometric images of Br$\gamma$ revealed the wind-wind collision cavity produced by the shock of the fast $\eta_B$'s wind with the slow and dense $\eta_A$'s wind. Our new 2016 GRAVITY Br$\gamma$ images show the structure of such cavity at a different orbital phase with a 2.26 mas resolution. The observed morphologies in the images are (qualitatively) in agreement with the theoretical hydrodynamical models of \citet{Madura_2013}. Particularly interesting is the bright SE arc-like feature, which could be interpreted as the hot post-shock gas flowing along the cavity wall (oriented toward the observer) that border the innermost shell of compressed primary wind, which is formed by the shock of the cavity's trailing arm with the leading arm after the most recent periastron passage. \item Due to the sparseness of the 2017 GRAVITY data the quality of the reconstructed images from this epoch is clearly affected. Therefore, those images could not be used for a direct comparison with the 2016 ones. Nevertheless, our analysis of the interferometric observables, in coincidental baselines, reveals changes in the cavity structure. The ulterior characterization of those changes is subject to future imaging epochs with a less limited $u-v$ coverage than the 2017 data. \item We presented, the first images of the He {\sc i} 2s-2p line. They were qualitatively interpreted using the model of \citet{Clementel_2015b, Clementel_2015a}. We hypothesized that the observed emission is coming mainly from the He$^{+}$ at the cavity walls and from a portion of the pre-shock primary wind ionized by the secondary. From the size of the observed emission and the theoretical models, we suspect that the mass-loss rate of the primary is close to 10$^{-3}\,M_{\odot}$ yr$^{-1}$. The emission observed require an active role of $\eta_B$ to ionize the material near the apex of the wind-wind collision cavity. \item Spectro-interferometric imaging cubes offer us unique information to constrain the wind parameters of $\eta$ Car, not accessible by other techniques. In this study, we have shown the imaging capabilities of GRAVITY to carry out this task. A future monitoring of $\eta$ Car over the orbital period (particularly at the periastron passage), in combination with dedicated hydrodynamical models of the imaged $K$-band lines, will provide a unique opportunity to constrain the stellar and wind parameters of the target, and, ultimately, to predict its evolution and fate. \end{itemize} | 18 | 8 | 1808.02141 |
1808 | 1808.09253_arXiv.txt | To understand the physical processes governing accretion discs we can study active galactic nuclei (AGN), X-ray binary systems (XRBs) and cataclysmic variables (CVs). It has been shown that XRBs and CVs show similar observational properties such as recurrent outbursts and aperiodic variability. The latter has been extensively studied for XRBs, but only recently have direct phenomenological analogies been found between XRBs and CVs, including the discovery of the rms--flux relation and the optical detection of Fourier-dependent time-lags. We present a Fourier analysis of the well-known CV SS Cyg in quiescence based on data collected at the 4.2--m William Herschel Telescope using ULTRACAM. Light curves in SDSS filters $u'$, $g'$ and $r'$ were taken simultaneously with sub-second cadence. The high cadence and sensitivity of the camera allow us to study the broad-band noise component of the source in the time range $\approx 10000-0.5$ s ($\approx 10^{-4}-2$ Hz). Soft/negative lags with an amplitude $\approx 5$ s at a time-scale of $\approx250$ s were observed, indicating that the emission in the redder bands lags the emission in the bluer bands. This effect could be explained by thermal reprocessing of hard photons in the innermost region of the accretion disc, assuming a high viscosity parameter $\alpha>0.3$, and high irradiation of the disc. Alternatively, it could be associated with the recombination time-scale on the upper layer of the accretions disc.\\ | Dwarf novae (DNe) are a subclass of cataclysmic variables (CVs) that consist of a primary white dwarf accreting material from a secondary low-mass main-sequence star. The donor overfills its Roche lobe and transfers material onto the compact object through the Lagrangian point L$_{1}$, where an accretion disc is formed to conserve the angular momentum \citep{Frank2002}. Accretion discs are also a common phenomenon in other systems such as X-ray binaries (XRBs) and Active Galactic Nuclei (AGN). Despite the differences in size, central engine and mass, they all share many observational properties. DNe exhibit quasi-periodic outbursts increasing their magnitude up to $\Delta\,\rm m = 2 - 5$ with a duration of $2-20$ days and a recurrence time varying from days to tens of years \citep{Lasota2001discs,Warner2003,Drakeoutburst2014,Coppejans2016}. Outbursts are also a well-known phenomenon observed in XRBs, lasting from days to months \citep{Lewin1995,RemillardXRBs}. Both XRB and CV outbursts are theoretically explained by a sudden onset of thermal and/or viscous instability in the accretion discs surrounding compact objects \citep{Shakura1973,Lasota2001discs}. In XRBs it is common to observe radio emission associated with an out-flowing jet of plasma \citep[e.g.][]{BelloniJets,Fender2004jets}. It is launched during the transition from quiescence to outburst when the spectral state changes from a hard spectrum, dominated by the emission of the corona to a soft spectrum, dominated by the accretion disc. Similar behaviour has been recently reported in the CV SS Cyg, where radio emission associated with a spectral state transition was detected \citep[e.g][]{Kording2008,Russell2016,Mooley2017}. Consistent behaviour is seen in other radio-observed CVs \citep[e.g][]{Coppejans2015,Coppejans2016}. Moreover, all accreting objects show variability on a wide range of time-scales and in a random aperiodic manner or periodic and quasi-periodic variations, e.g. dwarf nova oscillations and quasi-periodic oscillations \citep[e.g.][]{vanDerKlis1989,WarnerWoudt2003,Scaringi2012b}. In particular, the aperiodic variability observed in all these systems is thought to originate in the accretion disc, created by one or several physical processes. The origin is still unclear, and for that reason it is crucial to perform variability studies that can give us insight into the physics governing the accretion flow, the structure and the evolution of the accretion discs. \\ In the past decades, there have been many studies concentrating on the variability properties of XRBs, in light of the existence of dedicated X-ray missions with very high time-resolution \citep[e.g.][]{XRBsbible}. In the case of CVs, the emission peaks in the optical, thus high-speed optical cameras are required to observe at fast cadences. Well-sampled and long duration observations are also required to study these objects as the characteristic time-scales of CVs are of the order of seconds to days, longer than in XRBs where the time-scales span from milliseconds to hours. This is explained by the fact that the inner disc radius in an XRB lies at a few gravitational radii from the compact object, whilst in CVs it lies at thousands of gravitational radii. \ The accretion connection between XRBs and CVs is further supported by recent discoveries. First, the detection of the linear rms--flux relation in a handful of CVs \citep[see][]{Scaringi2012a,vandeSande2015}, showing that as the source gets brighter it gets more variable. This observational property has been extensively reported in many XRBs and AGN \citep[e.g.][]{Uttley2001,Uttley2005}. Secondly, the discovery by \citet[][]{ScaringiMaccarone2015} that CVs follow the scaling relation that connects the black hole XRBs and the AGN, suggests that the physics of accretion is the same regardless of the nature of the accreting object (see \citet{McHardy2006} and \citet{Koerding2007variaplane} for a detailed description of the variability plane). The scaling relation links the observed break frequency measured in the power spectrum of the light curve with a characteristic time-scale governed by the mass accretion rate and the inner disc radius of the object. This time-scale can be associated to the viscous time-scale because the variability is thought to originate in the disc due to changes in the local viscosity, as explained by the fluctuation propagation accretion model of \citet{Arevalo2006}. According to this model, fluctuations in the local accretion rate occurring further out in the disc (due to changes in viscosity) propagate inwards coupling multiplicatively with the fluctuations in the inner parts of the disc. As a result the variability in the innermost region of the disc is larger than in the outer parts of the disc. Hence, this model can satisfactorily explain the shape of the power spectra, the rms--flux relation and the hard lags observed in XRBs and AGN \citep{Uttley2011Lags}. The latter is explained by the fact that when the fluctuations propagate inwards on the viscous time-scale, they pass from cooler (softer photons) to hotter regions (harder photons) leading to the emission of soft photons before the hard ones. \\ The detection of soft/negative Fourier time lags in two CVs MV Lyrae and LU Cam has been reported \citep[e.g.][]{Scaringi2013}. In this case the bluer (harder) photons arrive earlier than the redder (softer) photons. More recently, similar lag behaviour was found in four other CVs using cross-correlation functions (CCFs) \citep[e.g.][]{Bruch2015lags}. In particular SS Cygni seems to show negative/soft time lags of the order of seconds. Here, we explore the time lags using Fourier techniques extensively applied in XRBs. Soft time lags have been also detected in many XRBs and AGN but they arise at higher temporal frequencies than the hard lags. They are thought to represent the light crossing time from a variable continuum source to the disc. In AGN, when the variable source illuminates the disc it leads to a soft photo-ionized reflection spectrum, whilst in XRBs the absorbed photons are reprocessed and re-emitted almost instantly as thermal radiation. The soft time lag is of the order of $10-100$ seconds in AGN, whereas in XRBs the delay is of the order of milliseconds. Nonetheless, according to \citet{Scaringi2013} the soft lags observed in CVs can not be explained by the light travel time-scale, because the reflecting region would lie outside the binary orbit. The authors suggest a different origin associated with the thermal time-scale, so that the soft lags are produced by thermal reprocessing of high-energy photons in the accretion disc, or reverse shocks originated close to the compact object. Supporting a reprocessing scenario, it has been shown that the X-ray binary GRO J1655--40 shows a lag of $10-20$ s between the X-rays and the UV/optical emission. The authors suggested the time-scale of reprocessing to likely be the recombination time-scale \citep[e.g.][]{Hynes1998,obrien2002}. \\ In this work we explore the variability properties of the CV SS Cygni in quiescence, one of the brightest dwarf novae known. The source has a magnitude of $\rm V=12$ in quiescence, it is situated at a distance of 114 $\pm$ 2 pc and has an orbital period of 6.6 hours \citep{Bitner2007,MillerJ2013}. The white dwarf mass is about 0.81 M$_{\sun}$, the secondary late-type star is $\sim0.55$ M$_{\sun}$, and the estimated inclination angle lies in the interval of $45^\circ\,\leq\,\rm i\, \leq\,56^\circ$ \citep{Bitner2007}. The mass accretion rate measured in the optical is ${\rm \dot M}\sim\,3\times\,10^{15}\,\rm g\,\rm s^{-1}$ \citep{Patterson1984,Warner1987a}. It exhibits an outburst every approximately 50 days \citep{Szkody1974} during which it is possible to detect coherent dwarf nova oscillations of $10-30$ s and quasi-periodic oscillations \citep[][]{Pretorius2006}. \\ \begin{table*} \centering \caption{Observation log of SS Cyg with ULTRACAM.} \begin{tabular}{l c c c c c} \hline\hline Date & Run & Start UTC & End UTC & Exposure/frame (s) & Frames \\ \hline 2013 August 1 & 1 & $21:56:40$ & $05:47:06$ &0.2393 & 117933\\ 2013 August 2 & 2 & $00:38:17$ & $02:17:26$ & 0.3215 & 17530\\ 2013 August 2 & 3 & $02:17:28$ & $03:56:32$ & 0.3215 & 17515\\ 2013 August 2 & 4 & $03:56:33$ & $05:35:53$ & 0.3215 & 17563\\ \hline \end{tabular} \label{table:1} \end{table*} \begin{figure*} \centering \includegraphics[width=15cm]{figures/lcrsscygcomparison} \caption{The two upper panels show the light curves of SS Cygni observed during two consecutive nights with ULTRACAM in three colours simultaneously: $r'$, $g'$ and $u'$ . The first night was of $\sim 8$ h duration and the second night SS Cyg was observed during $\sim 5$ h divided in three consecutive runs. For comparison with SS Cyg, the bottom panel shows the light curve of one of the comparison stars TYC 3196-857-1 in the $r'$ band the first night, illustrating the lack of variability compared with SS Cygni. } \label{Fig:lcr} \end{figure*} The paper is organised as follows: the description of the observations, the data reduction and the analysis of the light curves are described in Section \ref{sec:obs}. The results are described in Section \ref{sec:results}, followed by a discussion in Section \ref{sec:discussion} and a summary in Section \ref{sec:summary}. \\ \section[]{Observations and data analysis} \label{sec:obs} We observed SS Cygni when it was in quiescence with ULTRACAM \citep{Dhillon2007} mounted at the Cassegrain focus of the 4.2--m William Herschel Telescope (WHT) on La Palma. ULTRACAM is a high-speed triple-beam CCD camera designed to image faint astronomical objects at high temporal resolutions. It enables the user to observe a target in three optical filters simultaneously with a cadence of up to 0.0033 s (300 Hz). The instrument consists of three frame-transfer chips e2v 47-20 CCDs of 1024x1024 $\rm pixel^{2}$ area, providing a 5 arcminute field at a scale of 0.3 arcsecond/pixel. Incident light from the focal plane of the telescope is collimated and then split by two dichroic beam-splitters into three beams, defined by the SDSS {\it u'} (3543 \AA), SDSS {\it g'} (4770 \AA) and SDSS {\it r'} (6231 \AA) filters. The dead time between exposures is negligible (25 msec) due to the frame-transfer chips. The read-out speed was set to fast and no binning was applied. The observations took place on 2013 August 1 and 2. In Table \ref{table:1} we show the observing log. The first run is the longest, with a total duration of about 8 h and with the highest cadence of $\sim$ 0.24 s. During the second night the cadence had to be reduced in order to maintain a good signal-to-noise in the poorer conditions and we had to check it in between, as a consequence of this the data is in three different runs all taken with the same cadence. Flat fields were taken with the telescope spiralling of the twilight sky before and after the observations. Six--windowed mode was used for the target, and 5 comparison stars to perform differential photometry.\ The data were reduced using the ULTRACAM pipeline reduction package. Every science frame was de-biased and then flat-fielded. We used variable-sized apertures scaled to the seeing for each filter, and we used the normal aperture extraction and applied {\it moffat} profiles. In individual frames of the {\it u'} filter only two comparison stars were bright enough to extract, while for the $r'$ and $g'$ filters we used five. In Fig. \ref{Fig:lcr} we present the light curves for the two nights separately in the upper two panels. We present the normalised counts per cadence of SS Cyg by using the comparison stars to correct for atmospheric variations. An off-set of $\pm0.2$ counts is added for clarity. In the lower panel we show the light curve in the $r'$ band of the comparison star TYC 3196-857-1 with ICRS coordinates $\alpha=21^{\rm h}42^{\rm m} 27.1695^{\rm s} $ and $\delta=+43^{\circ}33'44.601''$ divided by the other comparison stars. Whilst SS Cygni shows strong aperiodic variability in all three colours, the solar-type comparison star is constant.\\ \subsection{Fourier analysis of the light curves} \label{sec:Fourier} We performed a Fourier analysis of the light curves using timing techniques extensively applied in the X-rays and described in \citet{vanDerKlis1989b} and \citet{Nowak1996}. \citet{Scaringi2013} performed a similar analysis as to the one we describe below when studying the CVs MV Lyr and LU Cam. It is important to mention that the light curves are evenly sampled in each run, thus we used the Fast Fourier Transform (FFT). First, we split the light curve into non-overlapping segments of equal duration and applied the FFT to each individual segment. Here we split each run into segments of $\approx48$ minutes ($\sim12.000$ data points), so that for the first night we used nine segments and for the second night six segments (hereafter $k_{1}$ and $k_{2}$, respectively). It is important to note that we performed the Fourier analysis for the two nights separately because they have different sampling as shown in Table \ref{table:1}. Defining $x_{u,i} (t)$ and $x_{r,i} (t)$ as the light curve segments $i$ in the $u'$ and the $r'$ bands, we computed the FFT to obtain the Fourier amplitudes, $X_{u,i} (f)$ and $X_{r,i} (f)$. The power spectra (PSD) were then calculated as $P_{u,i}(f)=|X_{u,i}|^2$ and $P_{r,i}(f)=|X_{r,i}|^2$, respectively. For each night we obtained the power spectrum of each segment independently and then we averaged them. Later we applied logarithmic binning and derived the PSD errors for each bin. The uncertainty is calculated as the power divided by the square root of the number of measurements used in the specific bin, $ m= k_{1,2}\times N$, where $N$ is the number of data points in each bin and $\rm k_{1,2}$ the number of segments used in the first or the second night. We applied the rms normalisation described in \citet{Belloni1990} to the power spectra, so that the square root of the integrated PSD over a frequency range yields the fractional amplitude of variability (see Fig. \ref{Fig:psd}). \\ \begin{figure} \centering \includegraphics[width=7.5cm]{figures/panel25bins_psd7nov} \caption{Power spectrum of SS Cyg on the 1st August (upper panel) and 2nd of August (lower panel). The blue diamonds denote the $u'$ band, green triangles the $g'$ band and the red circles the $r'$ band. The horizontal dashed lines indicate the noise level for each colour. The power spectra show a time-scale break at $333$ s ($\sim3\times10^{-3}$ Hz) followed by a steep power-law with power law index $> -2.0$. } \label{Fig:psd} \end{figure} Subsequently, we performed a cross spectral analysis for each segment calculated as $C_{i}(f)=X_{r, i}^{*}(f)X_{u,i}(f)$, where $X_{r, i}^{*}$ is the complex conjugate. We averaged all the cross spectra and log-binned the average (for each night separately) obtaining $C(f)$. The phase lag between the two simultaneous light curves, $\phi(f)$, is the argument of the complex-valued cross spectrum $C(f)$. The time lag, $\tau (f)$ is computed by dividing the phase lag $\phi(f)$ by $2\pi \rm f$. Thereafter, we calculated the raw coherence function $\gamma^{2}_{\rm raw}$, which is a measure of the degree of correlation between two simultaneous light curves in different bands: \begin{equation} \gamma_{raw}^{2}=\frac{|C(f)|^{2}}{P_{r}(f)P_{u}(f)}, \label{eq:raw} \end{equation} \noindent where $P_{r}(f)$ and $P_{u}(f)$ are averaged and log-binned. The statistical uncertainty is $\delta\gamma_{raw}^{2}=(2/m)^{1/2}(1-\gamma_{raw}^{2})/|\gamma_{raw}|$. The uncertainty of the phase lag is calculated as: \begin{equation} \delta\phi(f) = \frac{1}{\sqrt{m}}\sqrt{\frac{1-\gamma_{raw}^{2}}{2\gamma_{raw}^{2}}}, \label{Eq:phaseerror} \end{equation} \noindent and the error of the time lag is defined as $\delta\tau = \delta\phi(f)/2\pi f$. However, since the coherence of a real signal will be affected by the noise, every single term in Eq. \ref{eq:raw} needs to be corrected from counting noise. That is, correcting the powers in the denominator of the equation by the measured Poisson noise level and then correcting the cross-spectra. The detailed description to compute the intrinsic coherence $\gamma^{2}$ and its error, $\delta\gamma^{2}$ can be found in Eq. 8 of \citet{Vaughan1997}.\ The description given above was only for the $r'$ and $u'$ combination. We followed the same procedure to derive the time lags and the coherence for the other two colour combinations, $r'$ and $g'$, and $g'$ and $u'$. As mentioned before, the cross spectral analysis was performed for the two nights separately, obtaining the raw and the intrinsic coherence and the time lags. To improve the reliability of the result we combined the two nights and computed the phase/time lags and the coherence. For this, we first created an array containing the unbinned time lag values of the two nights and sorted them in frequency. Later we applied a logarithmic binning with the condition of a minimum number of data points per bin, where $N> 5$. Therefore, each bin contains a certain number of data points that correspond to the first night $N_{1}$ and to the second night $N_{2}$, so that $N_{1}+ N_{2} > 5$. The total number of data points per bin is calculated as $m = k_{1}\times N_{1}+ k_{2}\times N_{2}$. To combine the phase lags of the two nights we proceeded in the same way. In order to combine the raw and the intrinsic coherence of the two nights we log-binned all the terms of equation \ref{eq:raw} and Eq. 8 of \citet{Vaughan1997}, in the same manner as we described for the time lags. \\ \begin{figure} \centering \includegraphics[width=8cm]{figures/night1_lagsshade_20feb} \includegraphics[width=8cm]{figures/night2_lagsshade_20feb} \caption{{\it Upper panel:} Time lags observed on the first night. A tentative soft/negative lag is observed at $4\times10^{-3}$ Hz indicating that emission from the blue bands is emitted earlier than the redder band. {\it Lower panel:} Time lags observed during the second night. In both figures the purple circles denote the $r'$ and $u'$ combination, the green diamonds the $g'$ and $u'$ and the orange triangles the $r'$ and $g'$ combination. The shaded region indicates the frequencies that are dominated by Poisson noise.} \label{Fig:lags1} \end{figure} | \label{sec:discussion} We report on the detection of Fourier soft time lags in the DN SS Cygni at $\approx250$ s, with an amplitude of $\sim5$ s ($\approx 20$ cadences) in the $g'$ and $u'$ and $r'$ and $u'$ colour combinations. The soft lag in the $r'$ and $g'$ combination is consistent with a zero lag. As mentioned, the source shows negative lags on the first observing day (see Fig. \ref{Fig:lags1}), and the error bar for the $r'$ and $g'$ colour combination is so large that the findings are consistent with a negative lag, albeit smaller than in the other colour combinations. Part of the reason why the lags in the $r'$ and $g'$ combination are not in agreement with the other colour combinations might be the fact that in the $r'$ band the majority of the flux comes from the companion star, so that the variability coming from the disc is partially masked making difficult the detection of a lag. According to \citet[e.g.][]{MartinezPais1994companion,Harrison2000companion}, the secondary star of spectral type K2 V supplies up to 60 \% of the flux in the $r'$ band ($6500$ \AA), whilst in the $g'$ and $u'$ band the majority of the flux comes from the accretion disc around the white dwarf (see Fig. 10 in \citealt{Harrison2000companion}). A simple constant additive flux will not change the measured lags, only if there is some variability in the added flux, the time lags will change. The K-dwarfs can reach variability amplitudes in the optical bands up to 1-10 milli-mags, or roughly 1 \% \citep[see e.g.][] {Ciardi2011, Basri2013}. Thus, the companion star may add some extra variability predominantly to the $r'$ band and will furthermore reduce the signal-to-noise ratio for the intrinsic variability (due to the added weakly variable flux) and lead to higher uncertainties. Soft lags have been frequently observed in the X-rays in other compact sources such as XRBs and AGN \citep[e.g.][]{Uttleyreverberation,deMarco2015lags}. In these sources, soft lags have been reported at high frequencies and hard/positive lags at lower frequencies. The hard lags are explained in the context of the propagating fluctuations model, where the harder (bluer) photons arrive later than the softer (redder) photons. The soft lags are thought to represent the light travel time from the corona to the disc, so that the reflected redder photons arrive later than the bluer ones. In the context of an XRB the disc briefly reprocesses the hot photons generated at the corona and re-emits them almost instantly \citep{deMarco2016}. Fig. \ref{Fig:combilags} shows a turnover from soft to hard lags at low frequencies as observed in some AGN and XRBs, but only in the $g'$ and $u'$ colour combination. A tentative positive/hard lag is observed in two consecutive bins, thus it might be significant even if the errors in each bin are larger than those measured for the soft lags. \\ \subsection{Effects on the measured lags} Certain effects could alter the amplitude of the lag observed at low frequencies. Firstly, the red noise leakage is known to distort the PSD estimates and the phase lags \citep[e.g.][]{vanDerKlis1989,Uttley2002LEAK}. The red noise leakage occurs because of the finite length of the time series. As a result, power from lower frequencies can leak into higher frequencies affecting the variability properties. The effect has been carefully studied by \citet{Alston2013} using simulations of light curves. They show how the leakage can distort the power spectrum and the cross spectrum leading to a bias on the phase lag and the time lag. The amplitude of the soft lag can be reduced up to 50 \%. For a phase spectrum that changes rapidly with frequency the bias on the measurement of the lag will be larger. Whereas, in a smooth phase spectrum the bias should be small. \\ Second, it has been shown in black hole XRBs and AGN that dilution can have a dramatic effect on the amplitude of the observed lags. The measured lags are a weighted contribution of different spectral components, the disc, the driving power-law continuum and the reflection \citep[e.g.][]{Kara2013b,Cackettdilution2013,deMarco2016}. This mixing of variable components in the different colour bands would reduce the measured lag. In recent studies on XRBs and AGN, the amplitude of the intrinsic lag was expected to be 2 times larger than the measured lag. Moreover, according to \citet{Kara2013b}, a low coherence can be an indication of the mixing of components. In the case studied here, the raw coherence is high but it is not exactly 1 at lower frequencies as one would expect. This might suggest that there is a contribution from different components in each optical band: the reprocessed photons, the intrinsic photons from the disc plus the hotter photons generated in the boundary layer or corona. This effect is extremely difficult to account for in CVs because the relative strength of the different variable components is unknown. Generally, in XRBs and AGN the X-ray spectrum of the source can be obtained so that the lags produced by the different emitting components can be simulated \citep[see][for a detailed explanation of this method]{Kara2013b}.\\ The fluxes measured in different optical filters might additionally come from different regions in the disc, and from different optical depths and even levels of excitation. For example, SS Cyg in quiescence shows strong emission lines and the $u'$ bandpass measures the Balmer continuum in contrast to the other bands \citep{spectroSSCyg}. Moreover, it has been shown that in some CVs there is a optical lag between the line emission and the continuum \citep[e.g.][]{Welsh1998}. This illustrates how complex the interpretation of the optical time lags in CVs can be. This option is one possibility that may explain the non-existence of soft lags between the $r'$ and $g'$ bands: If the lags are between the continuum and the emission lines, one would expect to see lags between $u'$ and the other optical bands, but not between the $r'$ and $g'$ bands. In the following sections we will discuss speculative physical scenarios to explain the negative/soft lags reported here in SS Cygni and investigate the relevant time-scales that might play a role. We will further discuss how the soft lags presented in this work relate to the recent detections of lags in other CVs. \subsection{Geometrical interpretation} \begin{figure} \centering \includegraphics[width=8.0cm]{figures/newcartoonbinary} \caption{Cartoon showing the reprocessing of high-energy photons generated in the boundary layer in the accretion disc. The bluer photons are reprocessed closer to the inner edge of the disc and re-emitted faster so that the redder photons arrive with a delay of seconds.} \label{Fig:piclags} \end{figure} The time-scale of 4.2 min where the lag appears can be associated with the dynamical time-scale of the disc at a radius of $\sim10\,R_{WD}$. For a system like SS Cyg with a large orbital period of $6.6$ h, the disc is expected to be quite large; in particular the circularisation radius where the material starts to follow Keplerian orbits is expected to be at $30\,R_{WD}$. The reason why the lag appears on that time-scale is still puzzling, but we can speculate that this might be a region where the disc becomes optically thin. \\ To explain the observed amplitude of $4-6$ s, we could potentially associate it with the light travel time and instant reprocessing of photons like in XRBs. However, the reflecting region would lie between $2.5-3\,\rm R_{\odot}$ and this region is outside the accretion disc, since the semi-major axis of the orbit of SS Cyg is $1.95\, R_{\odot}$,$\sim4.5$ light seconds (calculated using the binary parameters derived in \citealt{Bitner2007}). Similar conclusions were drawn by \citet{Scaringi2013}; the soft lags observed in LU Cam could not be explained by the light travel time because the emitting region would lie outside of the disc. In the case of CVs, the accretion disc is much cooler than discs in XRBs, and this can be translated into a much longer reprocessing time for the CVs. We can propose two different toy models to explain the reprocessing of photons.\\ \subsubsection{Thermal time-scale} If the reprocessing occurs on a thermal time-scale, as proposed by \citet{Scaringi2013}, we need sufficient irradiation to alter the local thermal equilibrium on the surface of the disc. The thermal time-scale is: \begin{equation} \rm t_{\rm th} = \frac{t_{\phi}}{\alpha} = \frac{1}{\alpha}\left(\frac{G\,M_{\rm WD}}{R^{3}}\right)^{-1/2}, \end{equation} \noindent where $\alpha$ is the viscosity parameter and $R$ is the disc radius \citep{Shakura1973}. If the conditions are such that the energy balance of a specific area in the disc changes due to irradiation of high energy photons, the time-scale for re-adjustment to thermal equilibrium can be associated with the amplitude of the lag. If we associate the observed 5 s lag with the thermal time-scale and use the estimated mass $\rm M_{\rm WD}=0.81\,\rm M_{\odot}$ derived in \citet{Bitner2007}, this would place the reprocessing region between $0.01-0.02\, R_{\odot}$ for $0.3<\alpha<0.7$. This region is at the inner-most edge of the accretion disc, very close to the WD surface. Hence, for viscosity parameters $\alpha > 0.3$ the soft lags of SS Cyg could potentially be explained by the thermal time-scale, so that the higher energy photons are reprocessed very close to the WD and re-emitted after $\sim 5$ s (for a toy model of this process see Fig. \ref{Fig:piclags}). However, values of $\alpha> 0.3$ are higher than those predicted for a DN in quiescence, such as SS Cygni at the time of the observations. Conversely, in quiescence $\alpha$ is expected to be $\approx0.02$, and it can increase by up to one order of magnitude during outburst \citep{Frank2002}. Lower values of the viscosity parameter would then place the reprocessing region too close to the white dwarf, so that the soft lags could not be associated with a thermal time-scale. Nevertheless, there have been claims of a higher viscosity parameter obtained using the flickering mapping technique on V2051 Oph of $\alpha_{\rm quiesc} = 0.1-0.2$ \citep[e.g.][]{Baptista2004}. Furthermore, for the CV HT Cas a value of $\alpha_{\rm quiesc} = 0.3-0.5$ was reported \citep[e.g.][]{Baptista2011,Scaringi2014}. Furthermore, if the effects of the red noise leakage or the dilution are indeed important, the amplitude of the real lag should be slightly larger. Hence, thermal reprocessing of photons in the disc can be a tentative explanation for the observed soft lags in SS Cyg, but only under conditions of high irradiation and high viscosity.\\ \subsubsection{Recombination time-scale} Another relevant time-scale that can play an important role in the reprocessing of photons is the recombination time-scale. The recombination time-scale is: $t_{rec}\sim(n_{e}\alpha_{rec})^{-1}$ seconds \citep{obrien2002}, where $n_{e}$ is the electron density, typically $n_{e}\sim 10^{13}\,cm^{-3}$ at the mid-plane of the accretion disc in CVs \citep[e.g.][]{Warner2003}, and $\alpha_{rec}$ is the recombination coefficient. According to \citet{Hummer1963} the recombination coefficient can be roughly estimated using this analytical expression: \begin{equation} \alpha_{rec}= 1.627\times10^{-13}t_{e}^{-1/2}(1-1.657log_{10}t_{e}+0.584t_{e}^{1/3}), \end{equation} \noindent where $t_{e}=10^{-4}T_{e}$, and $T_{e}$ is the temperature of the disc. For a temperature of $T_{e}\sim10^{4}$ K $\alpha_{rec}=2.5\times10^{-13}\,cm^{3}s^{-1}$. This yields a recombination time-scale of $0.4$ s, smaller than the amplitude of the lag reported here. However, if the recombination occurs in the upper layers of the disc where the density is lower, the recombination time-scale can be adequate to explain the amplitude of the lag seen. At a vertical distance of 2H, where H is the scale height of the disc, the density is 10 times lower, this will mean a 4 s lag. This time-scale has been considered to explain the time lag observed in XRBs between the optical/UV and the X-ray emission \citep[e.g.][]{Hynes1998}. The high energy photons irradiate the disc and are reprocessed and re-emitted in the optical wavelengths in the outer parts of the disc. \subsection{Comparison with previous detections of soft time lags in CVs} Soft/negative lags in SS Cyg were reported by \citet{Bruch2015lags} with a similar amplitude to those observed here. The authors used cross-correlation functions as they consider it more sensitive to detect lags at low frequencies. For comparison we have computed the cross-correlations and found similar soft lags. In this work we used advanced Fourier analysis because it enables us to measure the time lags produced at different time-scales. Thus, in the frequency domain we could detect hard and soft lags as observed in XRBs and AGN. Similar soft lags were also reported for the CVs V603 Aql, TT Ari and RS Oph by \citet{Bruch2015lags}. In addition, Fourier soft lags have been reported in \citet{Scaringi2013}. Thus, with the detection of the soft time lags in SS Cyg there are now three CVs showing Fourier soft time lags, and including the lags detected using the CCFs there are six CVs. The amplitude of the lags found here are similar to the soft lags of MV Lyr and LU Cam, with time delays of $\sim3$ seconds and $\sim10$ seconds respectively. Moreover, the SS Cygni lags are present at a similar time-scale, $\approx250$ s to the soft lags in LU Cam and MV Lyr. \ Given the similarities observed between the soft lags of these three CVs, we believe that the same physical process is creating the negative lags. In \citet{Scaringi2013} the lags were explained by thermal reprocessing of photons for high values of viscosity $\alpha=0.7$. In addition, they discuss a different origin also associated with the thermal time-scale but from reverse shocks within the accretion disc. The difference seen in amplitude of the lags for these CVs cannot be explained by the different estimated masses of the white dwarfs, but accurate masses are difficult to obtain. The difference cannot be associated to other parameters of the system such as the orbital period. The orbital period of MV Lyr is $3.19$ h \citep{SkillmanperiodMVLyr}, for LU Cam $3.6$ h \citep{SheetsperiodLUCam} and for SS Cyg $6.6$ h. Even though the latter is much larger than the other orbital periods, the amplitude of the lag in SS Cyg is slightly shorter than the one in LU Cam. \\ Further investigation of other CVs is required to confirm the presence of soft lags in other sources. With a larger sample it would be possible to search for a correlation of the lags with the system parameters, helping us to understand the physical processes occurring in the accretion discs around white dwarfs. It is equally important to explore whether the lags change sign to positive/hard lags at lower frequencies as observed in XRBs and AGN. For this purpose it would be necessary to monitor the source for a longer time to reach the lower frequencies. Therefore, in order to detect hard lags in CVs, optical instruments in space with the ability to observe in different optical filters simultaneously are required. With PLATO it would be possible to observe in a red and a blue filters simultaneously\footnote{http://sci.esa.int/plato/59252-plato-definition-study-report-red-book/}. This goal is difficult to achieve using ground-based telescopes, as we cannot observe these sources continuously for many hours. It could be possible to use Las Cumbres Observatory as it will enable us to observe continuously for longer time using the telescopes located in different countries in the world. \\ In this work we have performed observations of SS Cygni with ULTRACAM, enabling us to observe it in three filters simultaneously at very high temporal resolution. We have analysed the light curves in the Fourier domain and derived the power spectra, coherence and phase and time lags. We find significant lags of $\sim 5$ s in the $g'$ and $u'$ and $r'$ and $u'$ colour combinations at a time-scale of $\approx250$ s ($\approx4\times10^{-3}$ Hz). This confirms the existence of soft lags in SS Cyg suggested by \citet{Bruch2015lags}. The amplitude of the lags as well as the time-scale where they were observed are consistent with the lags observed in other CVs such as LU Cam and MV Lyr. We propose that the nature of the soft lags could be explained by the reprocessing of higher energy photons coming from the boundary layer in the accretion disc. We considered two different physical processes that could produce the observed amplitude of the lag, namely a thermal re-adjustment of the disc on a thermal time-scale and the recombination of the ionised gas in the disc. The first possibility requires sufficient irradiation and also a high viscosity parameter $\alpha>0.3$. In this case the reprocessing region would be at a radius of $0.01-0.02\, R_{\odot}$. Such high values of $\alpha$ are not expected for a DN in quiescence. The recombination time-scale on the surface of the disc where the density is lower can also explain the amplitude of the lag reported here. Furthermore, apart from these geometrical scenarios to explain the soft lags, it is important to remark that the difference between the flux in the $u'$ and the $g'$ band is not only bluer versus redder, and then hotter versus colder, it is also probing different optical depths and excitation. The study of Fourier time lags can give insights into the physical processes in accretion discs and help us to constrain important parameters of these accreting systems. | 18 | 8 | 1808.09253 |
1808 | 1808.05761_arXiv.txt | The relative importance of the physical processes shaping the thermodynamics of the hot gas permeating rotating, massive early-type galaxies is expected to be different from that in non-rotating systems. Here, we report the results of the analysis of \textit{XMM-Newton} data for the massive, lenticular galaxy NGC~7049. The galaxy harbours a dusty disc of cool gas and is surrounded by an extended hot X-ray emitting gaseous atmosphere with unusually high central entropy. The hot gas in the plane of rotation of the cool dusty disc has a multi-temperature structure, consistent with ongoing cooling. We conclude that the rotational support of the hot gas is likely capable of altering the multiphase condensation regardless of the $t_{\rm cool}/t_{\rm ff}$ ratio, which is here relatively high, $\sim 40$. However, the measured ratio of cooling time and eddy turnover time around unity ($C$-ratio $\approx 1$) implies significant condensation, and at the same time, the constrained ratio of rotational velocity and the velocity dispersion (turbulent Taylor number) ${\rm Ta_t} > 1$ indicates that the condensing gas should follow non-radial orbits forming a disc instead of filaments. This is in agreement with hydrodynamical simulations of massive rotating galaxies predicting a similarly extended multiphase disc. | The long-lasting presence of hot gas in early-type galaxies, its connection to the cold/cool phase and its role in galaxy evolution are still not fully understood. Observations of the most massive ellipticals suggest that the cold interstellar medium in these systems is produced mainly via cooling from the hot X-ray emitting atmospheres \citep{Werner2014,lakhchaura2018}. Conditions required for the development of thermal instabilities in the hot phase are likely different when rotational support prevents the gas from moving in radial directions and thus alters the cooling flow. The hot X-ray emitting gas in fast-rotating galaxies has a systemically lower surface brightness and mean temperature than the hot gas in the non-rotating systems of the same mass \citep[e.g.][]{Negri2014}. This is most likely the result of the combined effect of the centrifugal barrier in the rotating atmosphere and the decreased depths of the effective gravitational potentials due to the rotational support. Apart from affecting the X-ray luminosities and shapes of the hot atmospheres \citep{Brighenti1996,Brighenti1997, Hanlan2000, Machacek2010}, rotation should also influence the conditions that govern thermal instabilities in the hot gas. \citet{Gaspari2015} showed that the top-down multiphase condensation process -- also known as chaotic cold accretion (CCA) -- changes in rotation-dominated atmospheres. When the ratio of the rotational velocity and the velocity dispersion of the hot gas (also called turbulent Taylor number) ${\rm Ta_t} \equiv v_{\rm rot}/\sigma_{\rm v} > 1$, the condensation will produce an extended multiphase disc instead of thin filaments, while suppressing the accretion rate onto the central supermassive black hole (SMBH) due to the centrifugal barrier \citep{Gaspari2017}. Moreover, the criterion $ C \equiv t_{\rm cool}/t_{\rm eddy} \approx 1 $ is expected to be related to the extent of the condensation region \citep{Gaspari2018}. To study thermally unstable cooling in rotating systems, we observed NGC~7049, a rotating early-type galaxy with an extended hot X-ray emitting atmosphere that also harbours a disc of cold/warm gas, which might have formed as a result of cooling from the hot phase onto non-radial orbits. Here, we present an analysis of \textit{XMM-Newton} data for the massive fast rotating unbarred lenticular (SA$0^0$) galaxy NGC~7049, the brightest member of a small group of five to six galaxies. The total mass $M_{\rm p}$ (\citealt{Heisler1985}, equation 11) of the group is $ \log M_{\rm p}/M_{\odot} = 13.16 $ \citep{Makarov2011}. The target was chosen based on the sample of \citet{Werner2014} as an X-ray bright massive galaxy with extended X-ray emission and significant angular momentum. It is inclined by $ \sim 30^{\circ} $ with respect to the line of sight and is relatively nearby \citep[$29.9~\mathrm{Mpc}$;][]{Tonry2001}. \citet{Werner2014} present measurements of optical $ \mathrm{H}\,\alpha \mathrm{+[N\,\textsc{ii}]} $ emission, a tracer of warm ionised gas, observed with the Southern Astrophysical Research (SOAR) telescope, and far-infrared $\mathrm{[C\,\textsc{ii}]\lambda157~\umu m} $, $\mathrm{[O\,\textsc{i}]\lambda 63~\umu m} $, and $\mathrm{[O\,\textsc{i}b]\lambda 145~\umu m} $ emission of cold ($ \sim100~\mathrm{K} $) atomic gas measured with the \textit{Herschel} Photodetector Array Camera \& Spectrometer (PACS). Both the optical and far-infrared emission components have disc-like morphology and extend out to $ r \sim 3.5~\mathrm{kpc} $. The velocity distribution calculated from the $\mathrm{[C\,\textsc{ii}]} $ line indicates that the cold gas rotates with a velocity of $ v_{\rm rot, [C\,\textsc{ii}]} \approx 200~\mathrm{km\, s^{-1}}$ (see Fig. \ref{fig:cii_v}). The radio emission with $ L_{\mathrm{radio}} = 8.4\times 10^{37}~\mathrm{erg~s^{-1}} $ suggests the presence of radio-mode activity of the central active galactic nucleus (AGN). The galaxy has low star formation rate of $ 0.177~\mathrm{M_{\odot}~yr^{-1}}$ \citep{Carlqvist2013}, effective radius of $ 4.4~\rm kpc $ \citep{Blakeslee2001}, absolute magnitude of the bulge in K-band is $ -24.81~\rm mag $ and its K-band bulge-to-total flux ratio is $0.81$; the latter two are presented in \citet{Laurikainen2010}. At the distance of $29.9~\mathrm{Mpc}$ \citep[][]{Tonry2001}, the angular scale is $6.89$ arcseconds per kpc. Throughout the analysis, we use the Solar abundances of \citet{Lodders2009}. All results in the following sections are presented with $ 1\sigma $ error bars. In the data analysis, we also used Python \citep{Python} and its specialised libraries Scipy \citep{Scipy}, Numpy \citep{Numpy} and Matplotlib \citep{Matplotlib}. \begin{figure} \centering \includegraphics[width=0.7\linewidth]{CII_velocity.pdf} \caption{$\mathrm{[C\,\textsc{ii}]} $ line-of-sight velocity map of NGC~7049 based on \citet{Werner2014}. Values are relative to the systemic velocity of the galaxy. The velocity distribution of the $\mathrm{[C\,\textsc{ii}]} $ emitting gas indicates the presence of a disc, rotating with a velocity of $v_{\rm rot}\sim200$~km~s$^{-1}$.} \label{fig:cii_v} \end{figure} The paper is structured as follows. In Sect. \ref{sec:analysis} we describe analysis of the \textit{XMM-Newton} data, in Sect. \ref{sec:results} we show the main results, focusing on X-ray gas morphology (Sect. \ref{sec:morphology}) and global properties of the gas (\ref{sec:global}), we then proceed to their inspection in radial profiles (\ref{sec:radial}) and further on dissected into sectors corresponding with the plane of rotation and the rotational axis (\ref{sec:sectors}). In Sect. \ref{sec:cooling} we present radial profiles of the main criteria which are expected to predict the thermodynamic and kinematic state of the X-ray emitting halo. In Sect. \ref{sec:discussion} we discuss our findings and present our conclusions in Sect. \ref{sec:conclusions}. | \label{sec:conclusions} Our analysis of the {\it XMM-Newton} observation of the massive fast-rotating lenticular galaxy NGC~7049 has led to the following results. \begin{itemize} \item The X-ray spectral modelling properties are: emission-weighted temperature $ k_{\mathrm{B}}T = 0.43^{+0.02}_{-0.01}~\mathrm{keV}$; emission-weighted metallicity: $ Z = 0.7^{+0.2}_{-0.1}~Z_{\odot}$; ellipticity $ \epsilon_{\rm X} = (0.126\pm0.004) $; and central density $ n(0) = (0.031 \pm 0.001)~ \rm cm^{-3}$. \item The hot gas has an unusually high central entropy and a temperature peak. \item While the hot gas in the rotational plane of the cool dusty disc has a multi-temperature structure, the thermal structure along the rotation axis is single-phase. The observed azimuthal difference in the temperature structure indicates that cooling is more efficient in the equatorial plane, where the rotational support of the hot gas may be able to alter the condensation, regardless of the $ t_{\mathrm{cool}}/t_{\mathrm{ff}} $ criterion, which is here relatively high ($\sim40$). \item We analysed other criteria for multiphase gas formation and evolution, finding $C$-ratio $ \approx 1 $, which implies significant condensation, and $ \rm Ta_t > 1$, which indicates such a condensation occurs onto non-radial orbits forming a disc (instead of filaments). This is in agreement with hydrodynamical simulations of massive rotating galaxies predicting a similarly extended multiphase disc \citep[e.g.][]{Gaspari2017}. \end{itemize} | 18 | 8 | 1808.05761 |
1808 | 1808.01142_arXiv.txt | {The radial drift and diffusion of dust particles in protoplanetary disks affect both the opacity and temperature of such disks as well as the location and timing of planetesimal formation. In this paper, we present results of numerical simulations of particle-gas dynamics in protoplanetary disks that include dust grains with various size distributions. We consider three scenarios in terms of particle size ranges, one where the Stokes number $\tau_{\rm{s}} = 10^{-1} - 10^0$, one where $\tau_{\rm{s}} = 10^{-4} - 10^{-1}$ and finally one where $\tau_{\rm{s}} = 10^{-3} - 10^{0}$. Moreover, we consider both discrete and continuous distributions in particle size. In accordance with previous works we find in our multi-species simulations that different particle sizes interact via the gas and as a result their dynamics changes compared to the single-species case. The larger species trigger the streaming instability and create turbulence that drives the diffusion of the solid materials. We measure the radial equilibrium velocity of the system and find that the radial drift velocity of the large particles is reduced in the multi-species simulations and that the small particle species move on average outwards. We also vary the steepness of the size distribution, such that the exponent of the solid number density distribution, $\rm{d}\it{N}/\rm{d}\it{a} \propto \it{a^{-q}}$, is either $q = 3$ or $q = 4$. We overall find that the steepness of the size distribution and the discrete versus continuous approach have little impact on the results. The level of diffusion and drift rates are mainly dictated by the range of particle sizes. We measure the scale height of the particles and observe that small grains are stirred up well above the sedimented midplane layer where the large particles reside. Our measured diffusion and drift parameters can be used in coagulation models for planet formation as well as to understand relative mixing of the components of primitive meteorites (matrix, chondrules and CAIs) prior to inclusion in their parent bodies.} | Protoplanets -- the building blocks of terrestrial planets as well as of the cores of gas giants, ice giants and super-Earths -- form by collisional growth from micrometer dust particles to bodies with sizes of thousands of kilometers. There are, however, several barriers that hinder the formation of planets. One barrier occurs early in the course of planet formation, since pebbles of millimeter-centimeter sizes do not stick efficiently when they collide. Their interaction typically results in bouncing, erosion and fragmentation \citep{Guttler10}. Even if sticking would be perfect, radial drift limits particle growth. Due to the orbital velocity difference between the solid and gas components, the former feels a headwind and spirals in toward the central star. Meter sized solids have drift times of approximately a hundred years at 1 au \citep{Adachi1976, Weidenschilling1977, Youdin2010}. Particles grow maximally to a size where the growth time-scale equals the radial drift time-scale, resulting typically in centimeter sizes interior of 10 au and millimeter sizes in the outer disk \citep{Birnstiel2012, Lambrechts2014, Birnstiel2016}. One way to overcome the radial drift barrier is to concentrate solids into clumps via the streaming instability \citep{Youdin2005, Youdin2007, Johansen2007}. Taking into account the back-reaction of the solids onto the gas, a small over-density of particles accelerates the surrounding gas to a higher speed. The radial drift of the given particle clump is thus reduced, since it feels less drag from the surrounding gas. At the same time, growth to even larger clump size is possible by the accumulation of inwards drifting particles. Once the local solid concentration reaches the Roche density, planetesimals form through gravitational collapse \citep{Johansen2012}. The formation of filaments by the streaming instability occurs above a threshold metallicity slightly elevated relative to solar metallicity \citep{Johansen2009, Bai2010b, Carrera2015, Yang2017}. The metallicity may be increased either by gas photoevaporation \citep{Carrera2017} or by pile-up of drifting solids in the inner regions of the protoplanetary disk \citep{Drazkowska2016, Ida2016, Schoonenberg2017, Drazkowska2017, Gonzalez2017}. In recent years, the amount of protoplanetary disk observations at different wavelengths has increased dramatically. Observations at millimeter and centimeter wavelengths reveal the presence of pebbles while scattered light observations probe the dust population. Spatially resolved ALMA observations of young disks around Class 0 protostars show evidence of the presence of millimeter-sized pebbles, which hints to grain growth via coagulation already at an early stage of disk formation \citep{Gerin2017}. ALMA observations of the spectral index in the rings of the disk around HL Tau also suggests local grain growth up to centimeter sizes \citep{ALMAPartnership2015, Zhang2015}. One of the closest observed systems with a protoplanetary disk, TW Hya, has been studied extensively by several different instruments as well. \cite{Menu2014} reviewed interferometric observations of the disk, from near-infrared up to centimeter wavelengths, that suggest the presence of both micron-sized dust and millimeter-centimeter-sized pebbles. \cite{VanBoekel2016} presented scattered light observations of the TW Hya disk with the Spectro-Polari-meter High-contrast Exoplanet REsearch (SPHERE) instrument on the Very Large Telescope and \cite{Rapson2015} with the Gemini Planet Imager (GPI) on the Gemini South telescope; both these studies showed that the scattered light signal is dominated by dust. This indicates coexistence of solid particles of a range of sizes in young protoplanetary disks. Even though grain growth is seen in observations, the majority of previous models involving the streaming instability focused on monodisperse particle populations. \cite{Bai2010a} filled this gap and considered a distribution of particle sizes to study the dynamics of materials in the midplane of protoplanetary disks. They assumed a discrete size distribution and saw that the radial drift velocity of all particle species is reduced compared to the one single species would have. Moreover, they showed that small grains tend to move outwards in the disk. \cite{Drazkowska2016} also implemented particle size dependent drift velocities into their numerical model and showed that this enhanches particle concentration. Using a fluid formalism, \cite{Laibe2014} provided analytical calculations considering multiple particle species and found the outward migration of small grains in protoplanetary disk settings as well. \cite{Johansen2007a} performed numerical simulations of planetesimal formation by the gravitational collapse of locally overdense regions, where they considered multiple solid sizes. They concluded that different particle sizes collapse into the same gravitationally bound system, despite the difference in their aerodynamic properties. Our goal with this paper is to understand the interaction between the gas and the observed pebble population in protoplanetary disks. We build on the work of \cite{Bai2010a} and study the dynamics of a wide range of particle sizes with the inclusion of mutual drag forces between the gas and solid species. We perform simulations with various particle size ranges and size distributions. More importantly, we study the evolution of both discrete and continuous systems in terms of particle size distributions and compare the results. In Sect. \ref{SectionNum} we discuss the numerical model and the dynamical equations. In Sect. \ref{SectionVelocity} we measure the equilibrium drift velocities in our models and discuss the effect of including a range of particle sizes on the radial drift velocities. In Sect. \ref{SectionScaleHeight} we address the evolution of the particle scale height throughout about 300 orbits and the influence of the particle size distribution on the degree of turbulence in the system. In Sect. \ref{DiffusionSection}, we analyze the radial and vertical diffusion of each solid species. In Sect. \ref{SectionImplication} we discuss potential implications of our results and finally in Sect. \ref{SectionDiscussion} we summarize our work. | \label{SectionDiscussion} In this paper we built on the work of \cite{Bai2010a} and modeled the dynamics of multiple particle species embedded in gas. To do this, we used the Pencil Code and performed 2D fluid-particle simulations that span the radial and vertical plane. We studied three scenarios in terms of particle size, such that the Stokes number of the solid materials in a given model was $\tau_{\rm{s}} = 10^{-4} - 10^{-1}$, $\tau_{\rm{s}} = 10^{-3} - 10^{0}$ or $\tau_{\rm{s}} = 10^{-1} - 10^0$. The size distribution of the particles was distributed according to $\rm{d}\it{N}/\rm{d}\it{a} \propto \it{a^{-q}}$, where $N$ is the total number density and $a$ is the radius of the particles. We considered $q=3$ (shallow) and $q=4$ (steep) so that our assumed size distributions envelope a variety of distributions predicted by observations and numerical simulations. On one hand, we distributed the particles into discrete size bins, in order to compare with \cite{Bai2010a}. On the other hand, we further studied a more realistic case and modeled systems where the particles were distributed continuously in terms of their size. We showed that the dynamics of particles in protoplanetary disks changes once we consider the realistic case of multiple solid sizes embedded in the gas. Our main results can be summarized as follows: \begin{itemize} \item Due to the friction from the sub-Keplerian gas, the particles experience radial drift. At the same time, the large particles trigger the streaming instability and the generated turbulence drives the radial and vertical diffusion of the solid materials. \item Most interestingly, in Fig. \ref{rvst} and Fig. \ref{rvst_disc} we see that small particles move outwards as also observed in \cite{Bai2010a}. This behavior is not seen in previous streaming instability simulations that contain particles of a single species e.g., \cite{Johansen2007}. As the larger species stir up the gas, the gas is accelerated locally and moves outwards, taking the strongly coupled (small) dust particles with it. At the same time, larger species move inwards but at drift velocities slower than expected from the single species NSH solution (e.g., Fig. \ref{disc:f1}). \item From the comparison of models with different size distribution exponents ($q$), particle distribution methods (discrete or continuous) and particle sizes, we see that the sizes of the participating particles is the most important factor. The strength of turbulence appears to be independent of the steepness of the size distribution (see Fig. \ref{v_3_vs_4:f1} and Fig. \ref{v_3_vs_4:f2}). Whether the particles are distributed in a discrete or continuous fashion does not produce large differences in the measured turbulence levels either (see Fig. \ref{v_d_vs_c:f1} and Fig. \ref{v_d_vs_c:f2}). \item As indicated by the relatively uniform level of the vertical component of the gas root-mean-square velocity away from the midplane (see Fig. \ref{GasVelocityFluct} and Fig. \ref{GasVelocityFluct41}), the turbulence generated by the large particles located close to the midplane is not limited to the midplane. The turbulence extends to larger heights and as a result the smaller particle species that reside at these heights also experience stirring generated near the midplane. As a consequence, compared to single species streaming instability simulations \citep{Carrera2015}, the measured particle scale heights in our models are larger by several factors. \end{itemize} The results listed above have important implications for protoplanetary disks. As shown in Fig. \ref{rvst}, in the more realistic case of continuous particle size distribution, both diffusion and differential radial drift contribute to the spreading of particles over time. Contrary to differential drift, diffusion is driven by the self-generated turbulence and is present in all our systems, independent of the particle size distribution we consider. The thickness of the dust layer in protoplanetary disks is an important factor that affects the efficiency of coagulation into dust aggregates \citep{Zsom2011, Drazkowska2016}. In the future, interaction between particle species should be taken into account in planet formation models. | 18 | 8 | 1808.01142 |
1808 | 1808.06624_arXiv.txt | The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of magnetohydrodynamical (MHD) equations. The CME is studied here in numerical simulations with the \pencilc. We discuss how the CME is implemented in the code and how the time step and the spatial resolution of a simulation need to be adjusted in presence of a chiral asymmetry. The CME plays a key role in the evolution of magnetic fields, since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the $\alpha$ effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral $\alpha_\mu$ effect has also been identified in mean-field theory. It occurs in the presence of turbulence, but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can potentially affect the propagation of MHD waves. Our numerical simulations demonstrate strong modifications of the dispersion relation for MHD waves for large chiral asymmetry. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo. \begin{keywords} Relativistic magnetohydrodynamics (MHD); Chiral magnetic effect; Turbulence; MHD dynamos; Numerical simulations \end{keywords} | \label{sec_intro} Research in turbulence physics was always strongly guided by input from experiments and also astronomical observations. This also applies to magnetohydrodynamic (MHD) turbulence, studied in solar and space physics, astrophysics, as well as in liquid sodium experiments \citep{Gal00,SM01,Monchaux07}. These investigations corroborate the existence of the $\alpha$ effect, which enables a large-scale dynamo caused by helical turbulent motions \citep{M78,KR80,ZRS83}. In recent times, MHD turbulence simulations have played important roles in demonstrating various scaling laws that cannot easily be determined observationally. However, under the extreme conditions of the early universe or in neutron stars, for example, only very limited information about the nature of such turbulence is available. Here, numerical simulations play a particularly crucial role. They allow new physical effects to be modeled and studied under turbulent conditions. The \pencilc\footnote{\url{https://github.com/pencil-code}, DOI:10.5281/zenodo.2315093} is designed for exploring the dynamical evolution of turbulent, compressible, and magnetized plasmas in the MHD limit. It is, in particular, suitable for studying a large variety of cosmic plasmas and astrophysical systems from planets and stars, to the interstellar medium, galaxies, the intergalactic medium, and cosmology. In its basic configuration, the \pencilc\ solves the equations of classical MHD, which describe the evolution of the mass density, $\rho$, the magnetic field strength, $\BB$, the velocity, $\UU$, and the temperature, $T$. Interestingly, this set of dynamical variables has to be extended in the limit of high energies, where a new degree of freedom, the \textit{chiral chemical potential}, arises from the chiral magnetic effect (CME). This anomalous fermionic quantum effect emerges within the standard model of high energy particle physics and describes the generation of an electric current along the magnetic field if there is an asymmetry between the number density of left- and right-handed fermions. The CME modifies the Maxwell equations and leads to a system of chiral MHD equations, which turn into classical MHD when the chiral chemical potential vanishes. In this paper, we describe how the CME affects a relativistic plasma and how it can be explored with a new module in the \pencilc. The CME was first suggested by \citet{Vilenkin:80a} and was later derived independently by \citet{NielsenNinomiya83}. These findings triggered many theoretical studies of the effect in various fields, from cosmology \citep{Joyce:97,Semikoz:04a,TVV12,BFR12,Boyarsky:15a,DvornikovSemikoz2017} and neutron stars \citep{DvornikovSemikoz2015,SiglLeite2016,Yamamoto:2016xtu}, to heavy ion collisions \citep{Kharzeev:2013ffa,Kharzeev:2015znc} and condensed matter \citep{Miransky:2015ava}. Some of the theoretical predictions have already been confirmed experimentally in condensed matter \citep{Wang13,ALICE13}. Three dimensional high-resolution direct numerical simulations (DNS) are an additional tool for gaining deeper understanding of the importance of the CME in high energy plasmas. Therefore, a new module for chiral MHD has been implemented in the \pencilc. The module is based on a system of equations that has been derived by \citet{REtAl17}. An important extension of those equations is, however, the inclusion of the evolution of the ordinary (achiral) chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. Previous investigations have demonstrated that a non-vanishing chiral chemical potential can result in chiral MHD dynamos, which have later been confirmed in DNS \citep{SRBBFRK17}. One important implication of chiral MHD dynamos is the generation of chiral-magnetically driven turbulence with an energy spectrum proportional to $k^{-2}$ within well-defined boundaries in wavenumber $k$ \citep{BSRKBFRK17,SBRK18}. In this paper we discuss the implementation of chiral MHD in the \pencilc\ which is, as far as we know, one of the first codes that includes a full implementation of the CME in the MHD limit; but see also \citet{MKTY18} and \citet{DZB18} for more recent examples of other codes. In section~\ref{sec_chiralMHD}, we provide an introduction to the physical background of the CME and highlight the most important properties of the set of chiral MHD equations in terms of numerical modelling. The implementation of chiral MHD in the \pencilc\ is described in section~\ref{sec_implementation}. In section~\ref{sec_usage} we discuss how chiral MHD can be explored in DNS and what to expect in different exemplary numerical scenarios. We discuss chiral MHD dynamos, effects of turbulence, the modification of MHD waves, and finally chiral magnetic waves caused by a non-zero chemical potential. We draw our conclusions in section~\ref{sec_conclusions}. | \label{sec_conclusions} Numerical simulations are a key tool for studying the properties of high-energy plasmas, such as those of the early Universe or of proto-neutron stars. At energies $\kB T > 10 \MeV$, the number of degrees of freedom increases by the chiral chemical potential, which is non-zero in case of an asymmetry between the number of left- and right-handed fermions. Through the additional electric current in the presence of such an asymmetry, the phenomenology of chiral MHD is even richer than that of classical MHD and numerical simulations are needed to gain a deeper understanding of the plasma and magnetic field evolution. To our knowledge, one of the first high-order parallelised codes, which has been used for chiral MHD, is the \pencilc. A central purpose of this paper was to describe the implementation of the chiral MHD module in the \pencilc, to discuss the relevant parameters and initial conditions in a chiral plasma, and to point out crucial differences to classical MHD. We also have presented typical applications of the chiral MHD module and discussed the obtained numerical results. First, we have compared the initially laminar dynamo phase and the dynamo with externally driven turbulence in chiral MHD. The distinct phases in the two cases were reviewed briefly on the basis of time series and energy spectra. We have discussed the mean-field $\alpha_\mu^2$ dynamo, which can be excited in turbulence via the interaction of magnetic fluctuations due to tangling of the mean magnetic field by the fluctuating velocity and magnetic fluctuations produced by the mean chiral chemical potential. In DNS, this effect has been seen by measuring the dynamo growth rate in a stage when turbulence has been produced by the Lorentz force. Predictions of mean-field theory for the dynamo growth rate based on the $\alpha_\mu$ effect are in agreement with the measurements in DNS. Second, the \pencilc\ was used to check the dispersion relation of chiral MHD waves and results were compared with analytical predictions. We find agreement for the frequencies and the growth or damping rates of the chiral MHD waves: The chiral dynamo instability leads to a growth of the wave amplitude and a decrease of the frequency for chiral velocities larger than the Alfv\'en velocity. Finally, we have explored the role of the ordinary chemical potential $\mu$ regarding chiral dynamos. We have demonstrated that $\mu$ can only affect the evolution of $\mu_5$, if the former has strong gradients. An initial sinusoidal spatial variation added to a constant $\mu_0$ can lead to minor variations of the velocity field in chiral-magnetically driven turbulence. Additionally, the \pencilc\ was used to study chiral magnetic waves (CMWs), which occur in the presence of an imposed magnetic field and a non-vanishing coupling between $\mu$ and $\mu_5$. As expected, CMWs are decoupled from chiral MHD waves, at least in the linear regime of the evolution, and their frequency scales with the square root of the product of the coupling constants, i.e.\ $(C_5 C_\mu)^{1/2}$. | 18 | 8 | 1808.06624 |
1808 | 1808.06138_arXiv.txt | We study the jet physics of the BL Lac object PKS~2233$-$148 making use of synergy of observational data sets in the radio and $\gamma$-ray energy domains. The four-epoch multi-frequency (4--43~GHz) VLBA observations focused on the parsec-scale jet were triggered by a flare in $\gamma$-rays registered by the {\it Fermi}-LAT on April 23, 2010. We also used 15~GHz data from the OVRO 40-m telescope and MOJAVE VLBA monitoring programs. Jet shape of the source is found to be conical on scales probed by the VLBA observations setting a lower limit of about 0.1 on its unknown redshift. Nuclear opacity is dominated by synchrotron self-absorption, with a wavelength-dependent core shift $r_{\text{core\,[mas]}}\approx0.1\lambda_{[\text{cm}]}$ co-aligned with the innermost jet direction. The turnover frequency of the synchrotron spectrum of the VLBI core shifts towards lower frequencies as the flare propagates down the jet, and the speed of this propagation is significantly higher, about 1.2~mas~yr$^{-1}$, comparing to results from traditional kinematics based on tracking bright jet features. We have found indications that the $\gamma$-ray production zone in the source is located at large distances, 10--20~pc, from a central engine, and could be associated with the stationary jet features. These findings favour synchrotron self-Compton, possibly in a combination with external Compton scattering by infrared seed photons from a slow sheath of the jet, as a dominant high-energy emission mechanism of the source. | The location of the $\gamma$-ray production zone in active galactic nuclei (AGN) is still an open and actively debated question. Due to a limited angular resolution of the $\gamma$-ray telescopes it is impossible to directly locate the region responsible for the high-energy emission in AGN. A variaty of approaches has been considered to address this problem, and our current understanding is that the regions of $\gamma$-ray production may be at different locations in different sources as evident from observations. One of the two main competing scenarios is based on the observed rapid $\gamma$-ray variability on time scales of a few hours and suggests that the high-energy emission from blazars is generated on sub-pc scales, near the central black hole \citep[e.g.,][]{Tavecchio10,Yan18}. Similarly, the observed strength and variability of the absorption of the $\gamma$-ray emission in the blazar 3C454.3 suggests the location of the $\gamma$-ray emitting zone within the broad-line region \citep{Bai09,Poutanen10}. The second scenario, in contrary, concludes that the dominant population of $\gamma$-ray photons is produced at larger, parsec scales, at distances up to 10--20~pc \citep{Marscher10,Agudo11,Schinzel12,Fuhrmann16,Karamanavis16}, and is based on a joint analysis of data in the $\gamma$-ray and radio bands. \cite{FM2} and \cite{Pushkarev10} showed that variability in $\gamma$-rays leads that of 15~GHz radio core on timescale of up to a few months. In this paper we are concerned with one particular AGN, the BL Lac object 2233$-$148, which was observed during and after the flare in $\gamma$-rays registered in April 2010 by the {\it Fermi}-LAT. The structure of the paper is as follows: in Section~\ref{s:obs} we describe our and archival observational data and reduction schemes; in Section~\ref{s:results}, we discuss our results; and our main conclusions are summarized in Section~\ref{s:summary}. We use the term ``core'' as the apparent origin of AGN jets that commonly appears as the brightest feature in VLBI images of blazars \citep[e.g.,][]{Lobanov_98}. The spectral index $\alpha$ is defined as $S_\nu\propto\nu^\alpha$, where $S_\nu$ is the observed flux density at frequency $\nu$. All position angles are given in degrees east of north. We adopt a cosmology with $\Omega_m=0.27$, $\Omega_\Lambda=0.73$ and $H_0=71$~km~s$^{-1}$~Mpc$^{-1}$ \citep{Komatsu09}. | \label{s:summary} We performed a radio and $\gamma$-ray joint study of the BL Lacertae object PKS~2233$-$148, using multiwavelength data in the period of 2009--2012. The 4.6--43.2~GHz VLBA observations reveal the core dominated, one-sided and relatively straight jet morphology of the source extending up to 8~mas in a position angle $112\degr$. Analyzing jet widths derived from the structure model fits we have established that the outflow has a conical shape. This sets a lower limit of about 0.1 on the source unknown redshift. We have measured the frequency-dependent shift vectors of the apparent core position using a method based on results from (i) structure model fitting and (ii) image alignment achieved by implementing a two-dimensional cross-correlation technique on the optically thin jet regions. The magnitude of the core shifts ranges from 0.04 to 0.7~mas, with a typical uncertainty of 45~$\mu$as. The directions of the shift vectors are predominantly aligned with the median jet position angle, deviating from it by $\lesssim10\degr$ in 68\% of cases. The derived core shifts show a frequency dependence $\propto\nu^{-1/k_\text{r}}$, with $k_r\approx1$ indicating that nuclear opacity is dominated by synchrotron self-absorption, and physical conditions in the jet on scales probed by the VLBA observations are close to equipartition. We did not find an evidence for significant changes in $k_\text{r}$ between the observing epochs covering a time scale of four months, during which a flare was developing down the jet. It suggests that the transverse size of the disturbance area is significantly smaller than the jet part constrained by the magnitude of the core shift effect within a frequency range 5--43~GHz. The VLBI core position $r_\text{core}$, as a function of wavelength follows an $r_\text{mas}^\text{core}\approx0.1\lambda_\text{cm}$ dependence. The magnetic field at a distance of 1~pc from the jet apex derived from the core shift measurements is about 1~G. We present a method of independent assessment of jet kinematics based on core shift measurements and evolution of synchrotron spectrum of the VLBI core. The turnover frequency of the core spectrum linearly shifts towards lower frequencies with time, as the flare originated in April 2010 in $\gamma$-rays propagates down the jet. The speed of this propagation is about 1.2~mas~yr$^{-1}$ and likely represents the bulk flow speed. It is much higher comparing to results from traditional kinematics based on tracking bright jet features, 0.045~mas~yr$^{-1}$ \citep{MOJAVE_XIII}. We have found indications that the $\gamma$-ray production zone in the source is located at large distances, 10--20~pc, from a central engine, and can be associated with the stationary radio-emitting jet features observed with VLBI. This favours synchrotron self-Compton scattering as a dominant high-energy radiation mechanism in the relativistic jet of the source. Direct observational evidence for a boundary layer around the jet suggests that the sheath might be an additional source of seed photons for external Compton scattering acting in the source. | 18 | 8 | 1808.06138 |
1808 | 1808.06406_arXiv.txt | {Pulsars scintillate. Dynamic spectra show brightness variation of pulsars in the time and frequency domain. Secondary spectra demonstrate the distribution of fluctuation power in the dynamic spectra.} {Dynamic spectra strongly depend on observational frequencies, but were often observed at frequencies lower than 1.5~GHz. Scintillation observations at higher frequencies help to constrain the turbulence feature of the interstellar medium over a wide frequency range and can detect the scintillations of more distant pulsars.} {Ten pulsars were observed at 2250~MHz (S-band) with the Jiamusi 66~m telescope to study their scintillations. Their dynamic spectra were first obtained, from which the decorrelation bandwidths and time scales of diffractive scintillation were then derived by autocorrelation. Secondary spectra were calculated by forming the Fourier power spectra of the dynamic spectra.} {Most of the newly obtained dynamic spectra are at the highest frequency or have the longest time span of any published data for these pulsars. For PSRs B0540+23, B2324+60 and B2351+61, these were the first dynamic spectra ever reported. The frequency-dependence of scintillation parameters indicates that the intervening medium can rarely be ideally turbulent with a Kolmogorov spectrum. The thin screen model worked well at S-band for the scintillation of PSR B1933+16. Parabolic arcs were detected in the secondary spectra of three pulsars, PSRs B0355+54, B0540+23 and B2154+40, all of which were asymmetrically distributed. The inverted arclets of PSR B0355+54 were seen to evolve along the main parabola within a continuous observing session of 12 hours, from which the angular velocity of the pulsar was estimated that was consistent with the measurement by very long baseline interferometry (VLBI).} {} | Pulsars are radio point sources and often move at high speeds of a few tens to more than a thousand km~s$^{-1}$. When radio signals from pulsars propagate through the interstellar medium, they are scattered due to irregularly distributed thermal electrons. The scattering due to the small scale irregularities of the medium can cause not only the delayed arrival of the scattered radiation, shown as larger temporal broadening of pulse profiles at lower frequencies, but also angular broadening for the scattering disk of a pulsar image that can be observed by VLBI. The random electron density fluctuations in the interstellar medium can be quantitatively described by a power spectrum of $P(k)=C_n^2 k^{-\beta}$ in a given spatial scale range of $L$ for $k=2\pi/L$ in a given interstellar region \citep{ars95}; here, $C_n^2$ is a measure of fluctuations. A Kolmogorov spectrum with $\beta \simeq 11/3$ is widely used to describe the turbulent medium. Nevertheless, the electron density fluctuations in the interstellar medium, at least in some regions, do not follow the Kolmogorov spectrum and may have a different spectral index $\beta$ \citep[e.g.][]{sg90,brg99c}. \input tab1.tex A moving pulsar with a transverse velocity of $V_{\rm p}$ shines through the relatively stable interstellar medium with small scale irregularities of 10$^{6-8}$~cm causing diffractive scintillation. This is exhibited by rapid fluctuations in time and radio frequency in a dynamic spectrum. The typical time-scale, $\Delta t_d$, and decorrelation bandwidth, $\Delta\nu_d$, depend on observation frequency $\nu$ and the amount of intervening medium indicated by $\rm DM$ or roughly by pulsar distance $D$, in the form of \citep[see][]{ric77,wmj+05} \begin{equation} \Delta t_d \propto \nu^{6/5} D^{-3/5} V_{\rm s}^{-1}, \\ \Delta \nu_d \propto \nu^{22/5} D^{-11/5}. \label{eq:parafreq} \end{equation} Here $V_{\rm s}$ is the speed of scintillation pattern past the observer, which is caused by the velocities of the source and the Earth as well as the intervening medium, and has often been used to estimate the pulsar velocity $V_{\rm p}$ assuming other velocities are negligible. The scintillation speed $V_{\rm s}$ can be estimated from $\Delta t_d$, $\Delta \nu_d$ and pulsar distance $D$ by \citep{ls82,cor86,gup95}, \begin{equation} V_{\rm s}= A \left(\frac{D}{\rm kpc}\right)^{1/2} \left(\frac{\Delta \nu_d}{\rm MHz}\right)^{1/2} \left(\frac{\nu}{\rm GHz}\right)^{-1} \left(\frac{\Delta t_d}{\rm s}\right)^{-1}, \label{eq:viss} \end{equation} assuming a thin scattering screen. The constant $A$, depending on the screen location and the form of the turbulence spectrum, was found to be $A=3.85\times10^4~\rm km~s^{-1}$ \citep{gup95} for a screen located at a half way between the pulsar and the observer. The scintillation strength, $u$, originally defined as the ratio of the Fresnel scale $s_F$ with respect to the field coherence scale $s_0$ \citep[i.e, $u=s_F/s_0$, see][]{ric90}, can be estimated from the observation frequency $\nu$ and the decorrelation bandwidth $\Delta \nu_d$ by \begin{equation} u\simeq \left(\frac{\nu}{\Delta \nu_d}\right)^{0.5}. \label{eq:u} \end{equation} The fluctuation measure $C_n^2$ can be estimated from $\nu$, $\Delta \nu_d$ and pulsar distance $D$ by \citep{cwb85} \begin{equation} C_n^2 \approx 0.002 \; \nu^{11/3} D^{-11/6} \Delta \nu_d^{-5/6} \label{eq:cn2} \end{equation} for the Kolmogorov case. When the interstellar medium has a different fluctuation power-law spectrum, i.e. different index $\beta$, these above scaling relations could be different \citep{rnb86,ric90,brg99c}. When pulsar signals propagate through large-scale irregular clouds of 10$^{10-12}$~cm with various electron density distributions, refractive scintillation can be observed as pulsar flux density fluctuations on longer time scales in addition to small-amplitude intensity variations \citep{rcb84}. Refraction moves scintillation pattern laterally and causes its systematic drift, which is manifested as fringes on pulsar dynamic spectra. The slope of the fringes is \citep[e.g.][]{sw85,brg99c} \begin{equation} \frac{{\rm d} t}{{\rm d} \nu} \simeq \frac{D \theta_{r}}{V_{\rm s}} \frac{1}{\nu}, \end{equation} where $\theta_r$ is the refractive angle which is approximately proportional to $\nu^{-2}$ for a given gradient of refractive index. Previously, scintillations of more than 80 pulsars have been observed mostly at lower frequencies \citep[e.g.][]{ls82, ra82,sw85, bk85, cwb85,cor86, cw86,grl94,mss+96, brg99a, gg00,wmj+05}. For a given pulsar, the decorrelation bandwidth $\Delta \nu_d$ and scintillation time-scale $\Delta t_d$ are closely related to observation frequenciess \citep[e.g.][]{cwb85}. Such observed frequency dependencies can be used to estimate the power-law index $\beta$ for electron density fluctuations in the interstellar medium, which has often been found to deviate from the Kolmogorov spectrum \citep{grl94, brg99c, wmj+05}. \input tab2.tex When a high-sensitivity dynamic spectrum of a pulsar is obtained, not only strong large patterns in time and bandwidth are observed; but also faint organized structures on smaller scales may appear in the dynamic spectrum image. These are best studied through the secondary spectrum, which is the power spectrum of the dynamic spectrum; i.e. $S_2 (f_t, f_\nu) = |\tilde{S_1} (t, \nu)|^2$, where $S_1$ is the dynamic spectrum and the tilde indicates a Fourier transform. Assuming that the pulsar velocity dominates and that any linear scattering structure is aligned along the effective velocity vector, one can estimate the fractional distance $d$ of the intervening screen from a pulsar at the distance $D$ with a velocity $V_{\rm p}$ based on the curvature of the arc in the secondary spectrum via \citep[see e.g.][]{crsc06} \begin{equation} f_{\nu} = \frac{\lambda^2 D}{2cV_{\rm p}^2} \left(\frac{d}{1-d}\right) f_{t}^2 , \label{eq:secspec} \end{equation} here, $f_{t}=1/t$ is the conjugate time, $f_{\nu}=1/\nu$ is conjugate frequency, $\lambda$ is the observing wavelength, $c$ is the speed of light. The curvature of a primary arc in the $f_{t}$ and $f_{\nu}$ plane is \begin{equation} \Omega = \frac{\lambda^2 D}{2cV_{\rm p}^2} \left(\frac{d}{1-d}\right). \end{equation} Previously, such arcs in the secondary spectra have been detected for only 13 pulsars: PSRs B1133+16 \citep{cw86,smc+01,hsb+03}, B0823+26, B0834+06 \citep{smc+01,hsb+03}, B0919+06 and B1929+10 \citep{smc+01,hsb+03, sti07}, J0737$-$3039 \citep{shr05}, B1737+13 \citep{crsc06,sti07}, B0355+54 \citep{sti07, xlh+18}, J0437$-$4715 \citep{bot+16}, B1642$-$03, B1556$-$44, B2021+51 and B2154+40 \citep{spg+17}. The placements of the intervening screen have so been estimated. In this paper, we present the scintillation observations of ten pulsars using the Jiamusi 66-m telescope at 2250~MHz. Parameters of these pulsars are listed in Table~\ref{tab1}, and previous scintillation observations are given in Table~\ref{tab2}. The dynamic spectra presented in this paper are valuable supplements to the previous observations and, in some cases, are the first dynamic and secondary spectra ever published. In Section 2 we describe our observation system. Observational results are presented and analyzed in Section 3. Discussion and conclusions are given in Sections 4 and 5, respectively. \input tab3.tex | We have carried out long observation sessions to observe the scintillations of ten pulsars at S-band by using the Jiamusi 66-m telescope. The newly observed dynamic spectra were mostly at the highest frequencies for these pulsars, and some of them are the first dynamic spectra ever published. The decorrelation bandwidths and time scales of diffractive scintillation are derived from fitting to the main peak of autocorrelation functions of dynamic spectra. Well-defined parabolic arcs have been detected in the secondary spectra of some sessions of PSRs B0355+54, B0540+23 and B2154+40, which were used to determine the locations of the scattering screens. The evolution of inverted arclets in the secondary spectrum of PSR B0355+54 was observed, the angular velocity estimated from which was consistent with VLBI measurement. Our measurements show that scintillation parameters vary from session to session. The frequency dependencies of both $\Delta t_d$ and $\Delta \nu_d$ imply that the turbulence feature of the interstellar medium deviates from the Kolmogorov turbulence. It is natural that the intervening medium cannot be so ideally turbulent. However, the thin screen model still holds well for PSR B1933+16. The scintillation velocities are only a rough indication of the pulsar velocities. Data for dynamic spectra of all pulsars presented in this paper are available at http://zmtt.bao.ac.cn/psr-jms/. | 18 | 8 | 1808.06406 |
1808 | 1808.01226_arXiv.txt | We explain the (non)helical dynamo process using a field-structure model based on magnetic induction equation in an intuitive way. We show how nonhelical kinetic energy converts into magnetic energy and cascades toward smaller eddies in a mechanically forced plasma system. Also, we show how helical magnetic energy is inversely cascaded ($\alpha$ effect) toward large scale magnetic eddies in a mechanically or magnetically forced system. We, then, compare the simulation results with the model qualitatively for the verification of the model. In addition to these intuitive and numerical approaches, we show how to get $\alpha$ and $\beta$ coefficient semi-analytically from the temporally evolving large scale magnetic energy and magnetic helicity. | Although the various scales of magnetic field ${\mathbf{B}}$ and conducting fluids (plasma) are ubiquitous in space, it is not yet clearly understood how the magnetic fields and plasmas exchange energy through their mutual interactions \citep{1978mfge.book.....M, 1980opp..bookR....K, 2005PhR...417....1B}. The energy transferred from the conducting fluid to the magnetic field generates various scales of magnetic fields and amplifies them (dynamo). Briefly, the dynamo phenomena are classified as a large-scale dynamo (LSD) and a small-scale dynamo (SSD) depending on the direction of energy transfer. In particular, since many physical turbulent phenomena e.g. transport of momentum or material are mostly controlled by large scale motions, the evolution and role of large scale magnetic field ($\overline{B}$) in a turbulent plasma system are fundamental and practical problems that cannot be limited only to academic interests.\\ Large scale dynamo theory shows how the small scale magnetic energy with helicity ($\alpha$ effect, \citep{2012MNRAS.419..913P, 2012MNRAS.423.2120P}), differential rotation ($\Omega$ effect, \cite{1991ApJ...376..214B}), or shear current (\cite{2003PhRvE..68c6301R}) can be (inversely) cascaded toward ${\overline{\mathbf{B}}}$. Out of them, the $\alpha$ effect is indispensable to the self consistent dynamo process, or inverse cascade of magnetic energy $E_M$ in the helical large scale dynamo. Moreover, since the properties of the helicity provide a relatively clear mathematical advantage in the theoretical description of the LSD phenomena, many LSD theories aim to represent electromotive force (EMF, $\xi \equiv \langle \mathbf{u}\times \mathbf{b}\rangle$), which is a source of $\overline{\mathbf{B}}$, with (pseudo) tensors and $\overline{\mathbf{B}}$.\\%\footnote{EMF is composed of velocity field $\mathbf{u}$ and magnetic field $\mathbf{b}$: $\int \langle \mathbf{u}\times \mathbf{b}\rangle \cdot d\mathbf{l}$. However, we will consider $\xi=\langle \mathbf{u}\times \mathbf{b}\rangle$ as EMF for convenience.}\\ Analytically $\alpha$ effect can be derived with a scale-divided function feedback method which is also a basic principle of numerical calculation. The representative theories like first order smoothing approximation (FOSA, or second order correlation approximation, SOCA, \cite{1978mfge.book.....M, 1980opp..bookR....K, 2005PhR...417....1B}), minimal tau approximation (MTA, \cite{2002PhRvL..89z5007B}), or Quasi Normalized approximation (QN, \cite{1975JFM....68..769F}) are actually based on the method in a dynamic or stationary state. However, since the $\alpha$ effect is not a strict mathematical concept, some ambiguities are inevitable for the analytical derivation, which does not depreciate the importance of $\alpha$ effect in the helical dynamo. Numerically, $\alpha$, $\beta$ coefficient in the $\alpha$ effect can be found applying an external magnetic field $\mathbf{B}_{ex}$ to the system (\cite{2005AN....326..245S}). However, since $\mathbf{B}_{ex}$ affects the dynamo process (\cite{1996PhRvE..54.4532C}), well-designed numerical results without $\mathbf{B}_{ex}$ would be used to derive the coefficients (test field method, \cite{2005AN....326..245S}).\\ Conventional dynamo theories show what happen over the statistical number of realizations of magnetohydrodynamic (MHD) system. The analytical theories give a qualitative and more or less quantitative description of the evolution of magnetic fields in the plasma, but they do not tell us how the actual plasma and magnetic field interact physically within the system. To explain the physical processes of evolving $\mathbf{B}$, a cartoon model of stretching of $\mathbf{B}$ field `($\mathbf{B}\cdot \nabla) \mathbf{u}$' has been used in analogy to stretching vorticity ($\mathbf{\omega}\cdot \nabla \mathbf{u}$, $\mathbf{\omega}=\nabla\times \mathbf{u}$) neglecting tilting effect \citep{1983mfa..book.....Z, 2002ApJ...576..806S}. However, $\mathbf{B}$ is essentially not so directly related to $\mathbf{u}$ as $\mathbf{\omega}$ is. Moreover, the concept of `stretching, twist, folding' is not relevant to any physics law or fluidal equation. Furthermore, the model implying the co-stretching of $\mathbf{B}$ and $\mathbf{u}$ needs to explain the nontrivial EMF ($\sim\langle \mathbf{u}\times \mathbf{B}\rangle \neq 0$). This large gap between the dynamo model and the dynamo mechanism makes it more difficult to derive a more accurate dynamo theory. \\ Here, we introduce an improved field structure model \citep{2017MNRAS.472.1628P} based on magnetic induction equation for the physical mechanisms of a helical large scale dynamo (LSD) and nonhelical small scale dynamo (SSD). The dynamo processes shown in the model are in line with the theory and consistent with the simulation results. Also, we show how to get $\alpha$ coefficients in the helical LSD from large scale magnetic energy $\overline{E}_M\,(\langle \overline{B}^2\rangle /2)$ and magnetic helicity $\overline{H}_M\,(\langle \overline{\mathbf{A}}\cdot \overline{\mathbf{B}}\rangle )$ which can be measured in observation and simulation. | Thus far, we have seen how the field structure model explains the amplification process of the magnetic field in the plasma. Magnetic field $\mathbf{b}_{nl}$ parallel to $\mathbf{u}$ is transferred through $\mathbf{b}\cdot\nabla \mathbf{u}$, and magnetic field $\mathbf{b}_{loc}$ parallel to $\mathbf{b}$ is transferred through $-\mathbf{u}\cdot\nabla \mathbf{b}$. The net magnetic field $\mathbf{b}_{net}$ from $\mathbf{b}_{nl}$ and $\mathbf{b}_{loc}$ is used as a seed magnetic field for the next dynamo step. As the field structure shows, growing $\mathbf{b}_{nl}$ parallel to $\mathbf{u}$ suppresses the dynamo process, whereas growing $\mathbf{b}_{loc}$ perpendicular to $\mathbf{u}$ boosts the dynamo action. This result explains the dependence of dynamo on the magnetic Prandtl number ($Pr_M\equiv\nu/\eta$). With less magnetic diffusion (decreasing $\eta$) and more kinetic dissipation (increasing $\nu$, or increasing $Pr_M$), the dynamo effect elevates. In contrast, the decreasing mechanical dissipation decreases the dynamo effect. These relations imply that the saturation of the magnetic field in an ideal system is related to the field structure between $\mathbf{u}$ and $\mathbf{b}$ (angle $\theta$) rather than the dissipation effect. We also explained the mechanism of the helical dynamo ($\alpha$ effect) using vector field analysis. HKFD and HMFD can generate both of the positive and negative magnetic helicity in principle. However, as we discussed, only opposite (same) sign of magnetic helicity is left in a forced HKFD (HMFD) system. Finally, we derived $\alpha$, $\beta$ coefficients from the large-scale magnetic energy and magnetic helicity. The exact coefficients are useful to understanding more accurate internal dynamo processes in a MHD system, which leads to a more general dynamo theory. At present, the field structure model with various physical conditions such as rotation, shear, or $\mathbf{B}_{ex}$ remains to be done. Before doing that, we will test the method with the simulation results and observation data. | 18 | 8 | 1808.01226 |
1808 | 1808.01967_arXiv.txt | \noindent We present new radio observations of the $z$ = 0.029 radio galaxy NGC 6109, a member of the 3CRR sample. We find the radio morphology of the counter-jet to be highly distorted, showing a unique `doughnut' structure $\sim$6 kpc in diameter. The doughnut is overpressured compared with the surrounding atmosphere as measured with \chandra. We investigate the polarisation properties of the source and find evidence for an interaction between the doughnut and the external environment. This may cause the extreme jet bend. Alternatively, while providing no explanation for the rotation-measure and magnetic field structure seen in the doughnut, a ballistic precession model may be feasible if the ballistic flow persists for a distance much less than the full extent of the 100 kpc-scale jet. A light jet being deflected by gas flows and winds just outside the transition between the galaxy and cluster atmospheres appears to be a more plausible interpretation. | Curved radio structures and bent jet trajectories on kpc scales are frequently observed extending away from AGN. In some cases these bends appear helical in nature, with sinusoidal trajectories and oscillating ridge lines (e.g. NGC 315, \citealp{worrall07}; 3C 273, \citealp{romero00}). Theoretical models for such oscillating, bent structures include helical modes in hydrodynamic (\citealp{hardee87}; \citealp{birkinshaw91}) or magnetised \citep{konigl85} jets. The collision of a jet with a dense or magnetised medium is also capable of producing strong deflections, as seen in NGC 7385 \citep{rawes15}. Alternatively, in both Galactic and extragalactic jets, precession may be a viable mechanism for the production of observed helical signatures (e.g. \citealp{linfield81}; \citealp{gower82}). Most mechanisms suggested for causing jet precession involve creating a misalignment between the accretion disk and the black hole, either through a supermassive black hole binary system (e.g. 4C 73.18, \citealp{roos1993}; OJ 287, \citealp{lehto96}; Cygnus A, \citealp{canalizo03}), or an offset in the angular momentum direction between the accretion disk and the host galaxy. The 3CRR radio sample \citep{laing83} contains 35 low redshift (z $<$ 0.1) radio galaxies. How these galaxies interact with the external environment has been studied in depth for the majority of sources with the aim (among others) of investigating how radio sources are modified by the effect of the intergalactic medium (IGM) and how the IGM is modified by the interaction. A few sources, however, lacked adequate archival radio data for good radio/X-ray comparison. Recent Karl G. Jansky Very Large Array (VLA) observations of two head-tailed galaxies within this sample reveal strong distortions in the radio morphology, and magnetic features in the jet bends. The results for NGC 7385 are given in Rawes et al. (in prep). NGC 6109 is discussed here. NGC 6109 is an FRI-type head-tail radio galaxy located in a poor cluster with redshift z = 0.029 \citep{wegner}. It was mapped with the Westerbork Synthesis Radio Telescope (WSRT) and the extended radio structure was reported by \cite{ekers78}. The radio tail extends for a projected distance of 250 kpc to the NW, and it was noted by \cite{ekers78} that there may be a small component SE of the core of NGC 6109. A high resolution map was published in 1985 in a sample of 57 narrow angle tailed sources \citep{odea85}. The map showed a circular component SE of the core, with no obvious counter-jet. \cite{odea85} suggested that this structure might be produced if the beams were ejected parallel and antiparallel to the direction of motion of the galaxy, in a similar way to NGC 7385 \citep{schilizzi75}. They proposed that the counter-jet ejected in the direction of motion would interact with the ICM in a manner more typical of double radio sources and might form an edge-brightened lobe. New VLA observations presented in this paper reveal that the counter-jet exhibits a highly unusual loop. Such a morphology has not been observed for any other low power radio galaxy. We discuss whether jet precession or gas-dynamical jet bending could produce this unique structure. We use our polarisation data to probe the magnetic field structure of this radio component and we investigate the local X-ray environment with \chandra\ observations. Throughout this paper we adopt the cosmological parameters H$_0$= 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_{\Lambda 0}$ = 0.7, $\Omega_{m0}$ = 0.3. The redshift of NGC 6109 corresponds to a luminosity distance of 123 Mpc and a projected linear scale of 0.59 kpc arcsec$^{-1}$. | NGC 6109 was originally classified as a `head-tail' type galaxy by \cite{colla75}, based on radio observations from WSRT at 50 cm. \cite{odea85} re-classified it as a narrow angle tailed (NAT) source. NAT morphology is attributed predominantly to the interaction of radio emission ejecta by a moving galaxy with the intracluster medium (e.g. \citealp{jones79}; \citealp{christiansen81}). The bending of the radio jets in NAT's provides important constraints on the physical conditions within the jets and the immediate environment in the galaxy and intracluster medium. A faint radio counter-jet is visible in Figure~\ref{Fig:6109}, SE of the core. The expression \begin{equation} R = \left(\frac{1+ \beta \cos\theta}{1 - \beta \cos\theta}\right)^{2+\alpha} \end{equation} \noindent gives $R$, the ratio of the brightness between the jet and the counter-jet where $\alpha$ is the spectral index, $\beta$ is the bulk speed relative to the speed of light and $\theta$ is the angle between the line of sight and the jet for relativistic outflows. This expression follows the assumptions described in detail by \cite{laing13} for modelling intrinsically symmetrical, axisymmetric, decelerating relativistic outflows. At 1.8$''$ from the core, we find $\alpha$ = 0.52 $\pm$ 0.02 and $R$ = 17.0 $\pm$ 0.3, constraining $\beta \cos \theta$ to 0.51 $\pm$ 0.02. This implies $\cos \theta >$ 0.5, thus $\theta <$ 60$^{\circ}$. The expression $D$ = (1 + $\beta \cos \theta$) / (1 - $\beta \cos \theta$) gives the corresponding Doppler distance ratio, $D$ and we find $D$ = 3.1 $\pm$ 0.2. The SE component at a projected distance of 4$''$ from the core, if moving with the same bulk speed as the jet, would be associated with a two-sided ejection event that would produce a matching feature 12.4$''$ along the main jet. Looking at Figure~\ref{Fig:6109}, the bright knot along the main jet lies 12$''$ from the core, suggesting that the flaring region could be an outflow feature emitted at the same time as the SE component, in the opposite direction. We calculated the equipartition energy density using the synchrotron code of \cite{hardcastle98}. We assumed equipartition between the electrons and the magnetic field and negligible relativistic beaming. An electron spectrum with $\gamma_{\text{min}}$ = 10 was used, where $\gamma$ is the Lorentz factor of the electrons ($\gamma$ = $E / m_e c^2$). For the doughnut region with radius 5$''$ and an estimated length along the line of sight of 3$''$, the equipartition energy density is U$_{\rm eq}$ = 9.1 $\times$ 10$^{-12}$ J m$^{-3}$. The NW knot on the main jet side was modelled with a length 20$''$ and radius 1$''$, to include the full extent of the flaring region as indicated by Figure~\ref{Fig:6109}. This gives U$_{\rm eq}$ = 9.5 $\times$ 10$^{-12}$ J m$^{-3}$. The similarity of these energy densities supports the idea that the knot is the counterpart of the doughnut, ejected in the opposite direction. Relativistic effects on the energy density are considered to be minimal for $\beta$ = 0.5. The magnetic field strength in the SW component is calculated as $B_{\text{min}}$ = 3.2 nT and the minimum pressure $P_{\text{min}}$ = 3.0 $\times$ 10$^{-12}$ J m$^{-3}$. The external pressure in X-ray emitting gas measured from the galaxy component of Figure~\ref{fig:gasradial} at 10$''$ from the core is found to be $P = 1.4 ^{+0.5}_{-0.5} \times 10^{-12}$ J m$^{-3}$ (90\% uncertainty). The galaxy gas density is calculated as $n = 5.1 ^{+1.0}_{-1.6} \times 10^{-3}$ cm$^{-3}$. 10$''$ is the central projected angle for the location of the doughnut. For $\theta <$ 60$^{\circ}$ the doughnut will lie further out in the atmosphere where the external pressure will be lower. While we estimate that the inner radio jet and doughnut may be a factor $\geq$ 3 over-pressured, pressure equilibrium between ambient gas and the radio emission in the main jet overall is reported by \cite{feretti95}. However they find that further along the tail, about 100 kpc from the core, there is a larger apparent imbalance towards the external pressure dominating. This is consistent with the findings of \cite{killeen88} and \cite{feretti92}. They argue that it is likely that assumptions used for the calculation of equipartition parameters cause the appearance of imbalance and that the entire tail is confined by the intergalactic medium. They suggest that the energy ratio between relativistic protons and electrons may be between 20-60, rather than unity, or that there may be a population of electrons that would radiate below the low frequency limit of the observable spectrum. If this is true in the doughnut and inner jet then these radio components will be highly over-pressured. The unique shape and extreme distortion of the radio emission require an interpretation that can account for the morphology, polarisation structure and rotation measure presented in the previous sections. Helical motion within jets on a parsec and kpc scale has been modelled in both magnetohydrodynamic and force-free jet models (\citealp{devilliers05}; \citealp{mckinney06}; \citealp{mckinney09}) and these models have sufficient resolution to compare structure with features observed in AGN jets (e.g. \citealp{hardee01}, \citealp{hughes02}). \cite{hardee03} note that the polarisation in helically modelled jets is typically well below the maximum value of 70\% for synchrotron radiation. They attribute this to the magnetic field in jets beyond the acceleration region not being well organised. In NGC 6109 we also see polarisation of $\sim$ 20\% in the jets, which follows this pattern. \subsection{Signatures of helical jets} Observational signatures of helical jets have been found in X-ray binaries (e.g. \citealp{hjellming95}), planetary nebulae (e.g. \citealp{lopez93}) and the jets of AGN. The term `helical jet' can be used to describe at least three different morphological jet structures and these are detailed by \cite{steffen97}. Firstly, ballistic helical jets describe jets in which the individual jet fluid elements flow along straight lines but the overall structure is helical due to the periodic change in the ejection direction of the elements. These jets are described as precessing. Secondly, helically bent jets have fluid elements that flow along a common twisted path, delineated by the curved jet axis. Jets can be bent by several mechanisms, such as transverse winds, collisions with gas clouds, density gradients or a dense ambient medium (e.g. \citealp{ludke94}. Finally, jets with an internal helical structure are straight as a whole, but have fluid flowing along helical trajectories within the jet. Helical trajectories can also be caused by Kelvin-Helmholtz instabilities (e.g. \citealp{hardee87}; \citealp{hardee92}; \citealp{conway93} and hydrodynamical (e.g. \citealp{zhao92}; \citealp{hardee94}) simulations have been carried out to investigate how this can disrupt the path of a jet. \citet{koide96} and \citet{nishikawa99} pioneered magnetohydrodynamic studies of how a strong, ordered magnetic field can affect jet propagation. \citet{koide96} found that the bending scale depended on both jet velocity and jet magnetic field angle. Slower jets with an angle between the jet and magnetic field of 45$^{\circ}$ were bent the most. An important property of helical jet structures is that the observed properties are not always symmetric with respect to the axis of the helix. The proper motion and magnetic field vectors on one side of the helix will point in a direction closer to the line of sight than those on the opposite side. This means that quantities such as the flux, optical depth, polarisation and rotation measure can be asymmetric, especially if the speed of the jet is relativistic. There is no evidence in the local environment of NGC 6109 for collisions with gas clouds or for significant density enhancements in the galaxy or cluster X-ray emitting atmospheres that relate to structures in the radio source. The existence of a high RM along the southern edge of the doughnut component, however, suggests the presence of magnetised plasma interacting with or wrapped around the radio object. This magnetised plasma could be the remnants of a radio trail from a galaxy that has passed close to NGC 6109. The brighter radio surface brightness in this region could suggest shock compression, where the radio emission has encountered magnetised gas and been compressed, resulting in jet deflection. Although a viable possibility, this hypothesis doesn't explain the size of the jet bend, $>$ 180$^{\circ}$. In the following sections we discuss both precessing and helically bent jet models. \subsection{Ballistic model} A ballistic model of a helical jet, based on jet precession, can explain the doughnut-like feature if the angle to the line of sight is small. The component can then be interpreted as a helical outflow, viewed almost end on so that the emission appears approximately circular. This scenario however, offers no clear explanation of the high regions of rotation measure detected in the south of the component. \cite{steenbrugge08} use a ballistic model to interpret the radio emission in Cygnus A. They find that the radio knots that delineate the jet and deviate from a straight line can be satisfactorily fitted with the precession model of \cite{hjellming95}. In this model, symmetric jets are launched along an axis which traces a cone throughout a precession period $P$, of opening angle $\phi$ and inclined to our line of sight at angle $\theta$. We used a similar ballistic model to see whether we could replicate the shape of the observed structure of NGC 6109. We adopted a jet speed of $\beta$ = 0.5, based on the jet/counter-jet ratio calculations with $\theta$ taken to be small, to reproduce the doughnut feature. Figure~\ref{Fig:ballistic} gives a simulation which is able to produce a doughnut-like component, however a looped jet is also ejected on the opposite side of the core. Here $\phi$ = 10$^{\circ}$ and $\theta$ = 20$^{\circ}$. The jet half opening angle is 2$^{\circ}$. The model has a jet precession period of $T_j$ = 1.8 $\times$ 10$^4$ years and reproduces the observed structure reasonably well except for a looping structure in the approaching jet (blue) that is not seen in the data. This blue loop must be disrupted in some way to become non-ballistic at a certain distance from the core, whilst the red loop is unaffected. This could be due to the transition from the galaxy to cluster external atmosphere at $\sim$ 10$''$, however this would require an angle to the line of sight $\theta >$ 35$^{\circ}$ in order to keep the red loop within the region where the galaxy atmosphere dominates. \begin{figure} \begin{centering} \includegraphics[width=8cm]{ball} \caption{A ballistic simulation shows the shape of precessing jets for $\beta$ = 0.5, $\theta$ = 20$^{\circ}$ and other parameters described in the text. The intensity contrast is not modelled, and the blue trajectory is directed towards the observer and the red trajectory is directed away. In this representation, NS orientation is arbitrary.} \label{Fig:ballistic} \end{centering} \end{figure} This ballistic model doesn't include effects such as deceleration of the jet as it propagates beyond a few kpc, and should therefore only be used as a guide to whether such loops can be produced ballistically. Precession models by \cite{gower82} highlight how the beam velocity can cause significant geometry changes in twin relativistic jets. In addition, \cite{gower82} show that at lower values of $\beta$ the swirls can be tighter but the two-sided structures are more symmetric, in contradiction to what is observed for NGC 6109. \subsection{Possible causes for precession} Is it not clear why the jet launch direction would be precessing. A few mechanisms that have been suggested are described below. Evidence for central engines of AGN formed by massive binary systems includes double nuclei (NGC 4486B, \citealp{lauer96}), wiggly jets (e.g. \citealp{kaastra92}) and periodic optical light curves (OJ 287, \citealp{villata98}). Radio structure associated with the AGN, built up over many precession periods, will be aligned with the orbital angular momentum. On the sub-kpc scales observed by the VLA however, precession related curvature could be discernable. In this mechanism, the spin axes will undergo geodetic precession about the total angular momentum. For the more massive black hole the precession period P$_{\text{prec}}$ in years is given by \cite{begelman80} as \begin{equation} P_{\text{prec}} = 600 r_{16}^{5/2} \left( \frac{M_8}{m_8} \right) M_8 \end{equation} \noindent where $r_{16}$ is the distance in units of 10$^{16}$ cm and $M_8$ and $m_8$ are the masses of the larger and smaller black holes in units of 10$^8$ $M_{\odot}$. Using the jet precession period of 1.8 $\times$ 10$^4$ years, as adopted for Figure~\ref{Fig:ballistic}, a black hole mass $M_8$ = 1 and binary mass ratio of 10 gives an orbital radius of order 5 pc. This corresponds to a wide binary system, where the precession time scale should be comparable with the inferred lifetime of extended radio components. The orbital time period for the binary system is given by \begin{equation} P_{\text{orb}} = 1.6 r_{16}^{3/2} M_8^{-1/2} \rm{yr} \end{equation} \noindent assuming Keplerian motion. For $r$ = 5 pc this gives $P_{\text{orb}}$ = 600 yrs. Evidence for a binary system could be provided from the detection of double or displaced emission lines or by looking for proper motion of the AGN ($\sim$ 1 $\mu$as yr$^{-1}$) with multi-epoch VLBI. The Lense-Thirring effect can also cause jet precession. This effect is the frame dragging produced by a rotating compact body and causes precession of a particle's motion if its orbital plane is inclined to the equatorial plane of the rotating object \citep{lense18}. The precession angular velocity $\Omega_{\text{LT}}$ is given by (e.g. \citealp{wilkins72}) \begin{equation} \Omega_{LT}(R) = \frac{2 G}{c^2} \frac{J}{R^3} \end{equation} \noindent where $J = aGM^2/c$ is the black hole angular momentum and $a$ is the black hole spin parameter. For a precession period T$_{\text{prec}}$ = 1.8 $\times$ 10$^4$ years, a black hole mass in the range 1 $\leq$ M$_8$ $\leq$ 100 and a spin parameter $a$ = 0.1 - 0.9, the orbital radius $R$ is constrained to 1 $\leq R \leq$ 40 parsec. The combined action of the Lense-Thirring effect and the internal viscosity of the accretion disk forces alignment between the angular momenta of the black hole and the accretion disk \citep{bardeen75}. This effect only concerns the innermost part of the disk due to the short range of the Lense-Thirring effect, while the outer part of the disk remains in its original configuration. \cite{scheuer96} showed that the disk alignment and precession time scales are identical. This mechanism has been invoked in cases of NGC 1097 \citep{caproni04b}, NGC 1068 \citep{caproni06b} and NGC 4258 \citep{caproni07}. The Bardeen Petterson transition radius between the spin-aligned and outer parts of a thin disk, based on the hydrodynamic simulations of \cite{nelson00}, can be expressed as \begin{equation} R_{BP} = A a^{2/3} R_{g} \end{equation} \noindent where the scaling parameter A is a function of the viscosity of the radial accretion flow \citep{shakura73} and the aspect ratio of the disk, with 10 $\leq$ A $\leq$ 300. This suggests R$_{BP} >$ 1 pc for the NGC 6109 system. Based on the \cite{sarazin80} model of disk-driven precession for SS 433, it was suggested by \cite{lu90} that a tilted accretion disk can also produce jet precession. \cite{petterson77} showed that if an accretion disk is optically thick, radiation pressure can produce nonaxisymmetric torques that will change the initial configuration of the disk. The influence of magnetic fields on accretion disks has also been investigated (e.g. \citealp{lipunov80}; \citealp{terquem00}; \citealp{lai03}; \citealp{pfeiffer04}). These binary and single AGN precession models however are unable to account for the observed magnetic field and rotation measure structure in NGC 6109. In the precessing system SS 433, the magnetic field is found to track the helical trajectory of the jet on a parsec scale (\citealp{hjellming81}, \citealp{stirling04}). If this magnetic field structure remains stable out to kpc scales during jet precession, then we would expect to see a circumferential field within the doughnut component. Although such a field is observed to the south of the component, the majority of the field structure in the component is radial. SS 433 also shows evidence for high fractional polarisation at the leading edges of the helices \citep{roberts08} produced as the jet material flows into an ambient medium containing a tangled magnetic field. The resulting compression orders the field in two dimensions \citep{bridle84}. NGC 6109 is not significantly polarised at the edges of the doughnut, highlighting the lack of large scale ordering of the magnetic field in this region. The presence of a non-uniform rotation measure across the component supports the hypothesis that some external magnetic material may be contributing to, or causing the large jet bending. The orientation of the band of high RM (i.e. anti-parallel to the main jet) however, suggests that it is produced by the counter-jet. Since the doughnut is the more distant structure, the counter-jet is superimposed on top of it. \subsection{Jet deflection models} A significant number of radio galaxies have been reported to display jet bending on kpc scales. Parallels between NGC 6109 and NGC 7385 can be drawn, as both have been categorised as low redshift `head-tail' galaxies by the 3CRR survey \citep{laing83} and exhibit $\geq$180$^{\circ}$ jet deflections. A swirl-like feature has also been observed for the FRI-type radio galaxy NGC 7016 (\citealp{cameron88}; \citealp{worrall14}), though this lies substantially further from the host galaxy. In the case of NGC 7385 our Hubble Space Telescope (HST) data revealed a large optical cloud in the path of the counter-jet, and the interaction between the jet and the cloud is believed to cause the strong jet bending (Rawes et al, in prep). Unfortunately NGC 6109 has not been observed with HST, however infrared and optical observations from \textit{Spitzer}, CFHT and KPNO show no similar deflector in the vicinity of the counter-jet component. Therefore although both objects exhibit significant jet bending, different interaction types are required to explain the deflections. Less extreme jet bending has been observed in other FR I-type galaxies (e.g. 3C 66B, \citealp{hardcastle96}; 3C 321, \citealp{evans08b}), and it is possible that the mechanisms which produce these deflections could also apply to NGC 6109. Various proposals for bending jets include buoyancy or ram pressure in a dense ICM \citep{miley72} and orbital motion (\citealp{blandford78b}; \citealp{roos1993}). \cite{eilek84}, studying the wide-angle tail source 3C 465, modelled the C-symmetric source in several bending scenarios. Since the jets within the host galaxy are straight, all models ascribe the effect to the ICM. They conclude that the most likely model is bending due to the large-scale velocity of magnetised plasma in the ICM. NGC 6109 belongs to a small concentration of galaxies at one edge of the cluster Zw 1611+3717 \citep{ulrich78}, which itself lies in a supercluster extending over 60 Mpc. If large scale velocity structures from the ICM were responsible for the jet bends (and not accurately aligned with the jet direction), then the main jet would also be significantly bent once it reached beyond the galaxy's ISM (a few kpc), and this is not observed. A high fractional polarisation and well ordered magnetic field are often observed in bent jets and indicate shearing or compression of the radio source as it propagates through the intercluster medium. \cite{miley75} attribute the curved path of the radio trail in NGC 1265 to the orbit of the galaxy through the cluster and differential motions of the cluster medium. They report fractional polarisation as high as 60\% and well ordered magnetic field vectors along the radio emission. This is not the case for NGC 6109 since the fractional polarisation reaches 30\% at most and is usually around 10\%. The effect of galactic ram pressure and pressure gradients on jet deflection have been investigated (e.g. \citealp{jones79}; \citealp{begelman79}; \citealp{deyoung91}) in terms of the bending equation: \begin{equation} \frac{\rho_j v^2_j}{R_{\text{bend}}} = \frac{\rho_{\text{atm}} v^2_g}{R_p} \end{equation} \noindent where $\rho_j$ and $v_j$ are the density and velocity of the jet, $R_{\text{bend}}$ is the radius of curvature of the jet deflection, $\rho_{\text{atm}}$ is the density of the atmosphere and $v_g$ is the velocity of the parent galaxy. $R_p$ is the scale over which the ram pressure acting on the beam changes, and we set this equal to the width of the jet (i.e. $R_p \sim$ 1 kpc). Adopting $n_{\text{atm}}$ = 5 $\times 10^{-3}$ cm$^{-3}$ (see section 6.1), $v_g$ = 600 km s$^{-1}$ \citep{ulrich78}, $v_j$ = 1.5 $\times$ 10$^8$ m s$^{-1}$ and $R_{\text{bend}}$ = 3 kpc gives a jet density contrast $\rho_j / \rho_{\text{atm}} \approx$ 2 $\times$ 10$^{-5}$. Therefore a hydrodynamical model is consistent with the tight bending if the jet is very light. The rotation measure in the south of the doughnut component is suggestive of some external magnetic medium being responsible for, or contributing to the large scale bending seen in NGC 6109. Although the precession model can replicate the observed structure, it cannot explain complex RM structure only in the doughnut region. Instead we attribute the structure to an interaction between the radio plasma and some unknown magnetic density enhancement in the intergalactic medium. Evidence for the external magnetic gas is seen in the rotation measure and fractional polarisation maps, where the emission has been depolarised by the presence of structured Faraday rotating material. Figure~\ref{Fig:fpol1} shows alignment between the RM and the jet direction and a `cap' at the SE edge. It is possible that the counter-jet has lifted magnetised material and deposited it along its length and at the point where it turns, perhaps in a similar way to the cold gas uplifted in M 87 (\citealp{churazov01}). This could explain the high RM at the SE edge of the doughnut (the `cap'), however the RM along the main jet does not show a similar structure. If the main jet and the counter-jet both lift a similar amount of material the densities on the two sides will differ due to the Doppler factor of the lifted material, as RM$_{\text{jet}}$ = $\frac{1}{\delta}$ RM$_{\text{counter-jet}}$ (excluding RM due to the Galactic foreground). Our results however require a Doppler factor $\delta$ $\geq$ 7 to produce the observed RM structure, assuming RM$_{\text{galactic}}$ $\sim$ 20 rad m$^{-2}$. Such a high Doppler factor would be unexpected. Under an interaction model, as the counter-jet turns at the collision site, compression of the jet leads to the formation of shocks, which can cause the brightening of the radio emission. South of the doughnut the magnetic field is circumferential, and appears to track the bending of the radio jet. The radio jet continues to deflect around a helical path, and high flux is seen to the NW of the structure, as a result of possible superposition of the jet with itself. The jet is then observed as diffuse emission to the NE. Here the magnetic field is radial as the jet spreads out into the external medium. Along the E edge of the diffuse emission, the magnetic field is longitudinal, possibly tracking the edge of the flow. The radial field lines observed through the centre of the doughnut could possibly be the result of compression due to the action of the external magnetic field. The external gas density of $n_e$ = 5 $\times$ 10$^{-3}$ cm$^{-3}$ at 10 arcsec from the core determined from the X-ray analysis can be used to provide an estimate for the magnetic field strength causing the high RM. The line of sight magnetic field B$_{\parallel}$ is calculated using the equation \begin{equation} RM = 812 \int n_e B_{\parallel} dl \end{equation} \noindent where the rotation measure is measured in rad m$^{-2}$, $n_e$ is the electron density, in cm$^{-3}$, $B_{\parallel}$ is the line of sight magnetic field, in mG, and $dl$ is an element of the path length, in parsec. For RM = 200 rad m$^{-2}$, and $n_e$ = 5 $\times$ 10$^{-3}$ cm$^{-3}$ and assuming a path length of approximately 1 kpc, $B_{\parallel}$ = 50 $\mu$G, or 5 nT. This magnetic field strength is of the same order as that observed in the lobes of AGN and the value of $B_{eq}$ calculated in section 6. This lends support to the idea that the magnetic plasma could be remnants from a radio galaxy that passed close to NGC 6109, leaving behind a magnetised trail. This plasma would have to be well mixed with the IGM to produce RM. One difficulty this model faces is why an interaction with magnetised gas would cause the jet to continuously bend, rather than deflect and then continue on a linear path. A 180$^{\circ}$ jet reversal is observed in NGC 7385, but NGC 6109 requires a further push to complete the observed loop. A high residual vorticity in the trail could explain this; this trail would not be observed by the VLA, but could possibly be found by a low-frequency, high resolution map of the field by (e.g.) LOFAR. In addition, higher resolution (e.g. X-band VLA) observations would enable us to investigate substructure in the loop. If a gas-driven deflection is responsible, we would expect to see substructure transverse to the circumference of the doughnut, showing the effect of the environment on the flow (possibly with a large gradient in polarisation fraction from the inside to the outside of the doughnut). Far weaker radial effects would be expected if the flow is ballistic. Given the difficulties with a ballistic model, it seems most likely that the unusual structure of NGC 6109 is due to an interaction. Further radio observations are required to investigate the nature of this interaction. | 18 | 8 | 1808.01967 |
1808 | 1808.04259_arXiv.txt | We study nonlinear cosmological perturbations and their possible non-Gaussian character in an extended non-minimal inflation where gravity is coupled non-minimally to both the scalar field and its derivatives. By expansion of the action up to the third order, we focus on the non-linearity and non-Gaussianity of perturbations in comparison with recent observational data. By adopting an inflation potential of the form $V(\phi)=\frac{1}{n}\lambda\phi^{n}$, we show that for $n=4$, for instance, this extended model is consistent with observation if $0.013<\lambda<0.095$ in appropriate units. By restricting the equilateral amplitude of non-Gaussianity to the observationally viable values, the coupling parameter $\lambda$ is constraint to the values $\lambda<0.1$.\\ {\bf PACS}: 98.80.Bp, 98.80.Cq , 98.80.Es\\ {\bf Key Words}: Cosmological Inflation, Structure Formation, Perturbations, Non-Minimal Inflationary Models, Observational Data | The idea of cosmological inflation is capable to address some problems of the standard big bang theory, such as the horizon, flatness and monopole problems. Also, it can provide a reliable mechanism for generation of density perturbations responsible for structure formation and therefore temperature anisotropies in Cosmic Microwave Background (CMB)spectrum [1-8]. There are a wide variety of cosmological inflation models where viability of their predictions in comparison with observations makes them to be acceptable or unacceptable (see for instance [9] for this purpose). The simplest inflationary model is a single scalar field scenario in which inflation is driven by a scalar field called the inflaton that predicts adiabatic, Gaussian and scale-invariant fluctuations [10]. But, recently observational data have revealed some degrees of scale-dependence in the primordial density perturbations. Also, Planck team have obtained some constraints on the primordial non-Gaussianity [11-13]. Therefore, it seems that extended models of inflation which can explain or address this scale-dependence and non-Gaussianity of perturbations are more desirable. There are a lot of studies in this respect, some of which can be seen in Refs. [14-19] with references therein. Among various inflationary models, the non-minimal models have attracted much attention. Non-minimal coupling of the inflaton field and gravitational sector is inevitable from the renormalizability of the corresponding field theory (see for instance [20]). Cosmological inflation driven by a scalar field non-minimally coupled to gravity are studied, for instance, in Refs. [21-28]. There were some issues on the unitarity violation with non-minimal coupling (see for instance, Refs. [29-31]) which have forced researchers to consider possible coupling of the derivatives of the scalar field with geometry [32]. In fact, it has been shown that a model with nonminimal coupling between the kinetic terms of the inflaton (derivatives of the scalar field) and the Einstein tensor preserves the unitary bound during inflation [33]. Also, the presence of nonminimal derivative coupling is a powerful tool to increase the friction of an inflaton rolling down its own potential [33]. Some authors have considered the model with this coupling term and have studied the early time accelerating expansion of the universe as well as the late time dynamics [34-36]. In this paper we extend the non-minimal inflation models to the case that a canonical inflaton field is coupled non-minimally to the gravitational sector and in the same time the derivatives of the field are also coupled to the background geometry (Einstein's tensor). This model provides a more realistic framework for treating cosmological inflation in essence. We study in details the cosmological perturbations and possible non-Gaussianities in the distribution of these perturbations in this non-minimal inflation. We expand the action of the model up to the third order and compare our results with observational data from Planck2015 to see the viability of this extended model. In this manner we are able to constraint parameter space of the model in comparison with observation. | We studied an extended model of single field inflation where the inflaton and its derivatives are coupled to the background geometry. By focusing on the third order action and nonlinear perturbations we obtained observables of cosmological inflation, such as tensor-to-scalar ratio and the amplitudes of non-Gaussianities in this extended setup. By confronting the model's outcomes with observational data from Planck2015, we were able to constraint parameter space of the model. By adopting a quartic potential with $V(\phi)=\frac{1}{4}\lambda\phi^{4}$, restricting the model to realize observationally viable spectral index (or tensor-to-scalar ratio) imposes the constraint on coupling $\lambda$ as $0.013<\lambda<0.095$. Also restricting the amplitude of equilateral amplitude of non-Gaussianity to the observationally supported value of $-147<f^{equi}_{NL}<143$, results in the constraint $\lambda<0.1$ in appropriate units. \\ {\bf Acknowledgement}\\ The work of K. Nozari has been supported financially by Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) under research project number 1/5750-1. | 18 | 8 | 1808.04259 |
1808 | 1808.03365_arXiv.txt | We present the second major release of data from the SAMI Galaxy Survey. Data Release Two includes data for 1559 galaxies, about 50\% of the full survey. Galaxies included have a redshift range $0.004 < z < 0.113$ and a large stellar mass range $7.5 < \log (M_\star/M_\odot) < 11.6$. The core data for each galaxy consist of two primary spectral cubes covering the blue and red optical wavelength ranges. For each primary cube we also provide three spatially binned spectral cubes and a set of standardised aperture spectra. For each core data product we provide a set of value-added data products. This includes all emission line value-added products from Data Release One, expanded to the larger sample. In addition we include stellar kinematic and stellar population value-added products derived from absorption line measurements. The data are provided online through Australian Astronomical Optics' Data Central. We illustrate the potential of this release by presenting the distribution of $\sim 350,000$ stellar velocity dispersion measurements from individual spaxels as a function of $R/\re$, divided in four galaxy mass bins. In the highest stellar mass bin ($\log (M_\star/M_\odot)>11$), the velocity dispersion strongly increases towards the centre, whereas below $\log (M_\star/M_\odot)<10$ we find no evidence for a clear increase in the central velocity dispersion. This suggests a transition mass around $\log (M_\star/M_\odot)~\sim10$ for galaxies with or without a dispersion--dominated bulge. | Galaxies are composed of multiple distinct components, such as thin and thick disk, bulge, bar(s), spiral arms, ring(s) and many others. As well as having different spatial structure, these components can also differ in terms of their kinematics and their compositions; either narrowly in terms of differing chemistry, or more broadly into stellar, gaseous and dark matter. Determining how these distinct components interact and change over time is critical to a deeper understanding of galaxy evolution \citep[e.g.,][]{mo2010}. Spatially resolving galaxies is essential to understand the different components. While imaging studies, particularly multi-wavelength imaging, can begin to disentangle these components, access to kinematic and chemical separation is largely unavailable. Spatially resolved spectroscopy is ideally suited to this task, as the simultaneous separation of the observed light, both spectrally and spatially, provides the most detailed dissection of the internal structure of galaxies currently available \citep[e.g.,][]{cappellari2016}. The challenge of spatially resolved spectroscopy is that spreading the light out both spatially and spectrally drastically reduces the signal-to-noise ratio (S/N) per resolving element. This limitation has restricted initial work in this area to relatively small samples of objects, or to specific classes of object that are more easily observed. While these kinds of studies have been very successful in addressing the role of specific physical processes that shape galaxies, a broader view is required to develop a holistic understanding of galaxy evolution. Galaxies are very diverse, and the physical processes involved in galaxy evolution are many and varied. To fully understand the primary drivers of galaxy evolution one requires large samples that encompass the complete diversity of the galaxy population. This can be achieved with spatially resolved spectroscopy by either investing large amounts of telescope time with a single-object instrument, e.g. surveys with $N>250$, ATLAS$^{\rm{3D}}$ \citep{cappellari2011a} and CALIFA \citep{sanchez2012}, or through the use of a multiplexed integral field spectrograph, such as SAMI \citep{croom2012}, MaNGA \citep{bundy2015} or KMOS \citep{wisnioski2015,stott2016}. Since the beginning of this decade, large integral field spectroscopy surveys such as these, have been assembling samples of hundreds or thousands of galaxies, allowing us to dissect, in detail, the entire population of local galaxies. \citet[SAMI Data Release 1, hereafter DR1]{green2018} discussed the broad role integral field spectroscopy has played in furthering our understanding of galaxies. In the current release we hope to push forward the exploration of new analyses that utilise the full power of combining emission, absorption and dynamical measurements by providing extensive value added data products. In this paper we present the second public release (DR2) of SAMI Galaxy Survey observations, including both fully processed spectral data cubes and a large array of derived science products that enable an extremely broad approach for studying galaxies. In Section \ref{sec:overview} we briefly review the survey and instrument design and progress on observing and processing the data since DR1. In Section \ref{sec:dr2_sample} we describe the galaxies presented in this sample. In Section \ref{sec:core_data} we describe the core data of this release; spatially resolved spectral cubes and additional spectral data derived from these cubes, and the quality of the data. In Section \ref{sec:emission_line_products} we describe the emission line products included in this release, with a focus on changes since DR1, and in Section \ref{sec:absorption_line_products} we describe the new absorption line products being released for the first time. Finally, in Section \ref{sec:data_access} we describe how this data can be accessed through the Data Central web service and provide an example science use of these data to illustrate the potential power of this data release. Throughout this release we adopt the concordance cosmology: ($\Omega_\Lambda, \Omega_m, h) = (0.7, 0.3, 0.7)\ $\citep{hinshaw2009}. | \end{figure*} \begin{table*} \centering \caption{Summary of data available for galaxy ID 22887. Along with Figure \ref{fig:so_summary}, this table provides an overview of data available for each galaxy in the release. Note that this table presents data for only one aperture, the R$_e$ aperture, of the six apertures for which data is available in the release. (1) SAMI/GAMA galaxy ID, (2) Right ascension, (3) Declination, (4) Flow-corrected redshift, (5) Stellar mass, (6) GAMA $r$-band effective radius, (7) GAMA light-weighted $r$-band ellipticity, (8) Mean stellar age, (9) Mean stellar metallicity, (10) Mean stellar $\alpha$-abundance, (11) Stellar velocity dispersion, (12) Ratio of stellar velocity to velocity dispersion, (13) Stellar spin parameter proxy, (14) Photometric position angle, (15) Stellar kinematic position angle, (16) Gas velocity dispersion, (17) Star formation rate, (18) H$\alpha$ flux, (19) H$\beta$ flux, (20) Ratio of N[II] to H$\alpha$ flux, (21) Ratio of [OIII] to H$\beta$ flux.} \label{tab:so_summary} \begin{tabular}{l c c c c c c c c c c c c} \hline \hline CATID & RA(J2000) & Dec(J2000) & $z$ & $\log \mstar$ & \re & $\epsilon$ & Age & [Z/H] & [$\alpha$/Fe] & $\sigma_{\rm{e,stars}}$ \\ \hline & deg & deg & & M$_\odot$ & arcsec & & Gyrs & & & \kms \\ (1) & (2) & (3) & (4) & (5) & (6) & (7) & (8) & (9) & (10) & (11) \\ \hline 22887 & 179.403 & 1.14077 & 0.0375 & 10.47 & 6.2 & 0.54 & $2.1\pm0.5$ & $-0.08\pm0.14$ & $0.04\pm0.11$ & $124\pm1$ \\ \hline \end{tabular} \begin{tabular}{c c c c c c c c c c} \hline ($V/\sigma$)$_{\rm{e,stars}}$ &$\lambda_\mathrm{R}$ & PA$_\mathrm{phot}$ & PA$_\mathrm{stars}$ & $\sigma_{\rm{e,gas}}$ & SFR & H$_\alpha$ flux & H$_\beta$ flux & log([NII]/H$_\alpha$) & log([OIII]/H$_\beta$)\\ \hline & & deg & deg & \kms & M$_\odot$ yr$^{-1}$ & 10$ ^{-16}$ ergs & 10$ ^{-16}$ ergs & & \\ & & & & & & cm$^{-2}$ s$^{-1}$ & cm$^{-2}$ s$^{-1}$ & & \\ (12) & (13) & (14) & (15) & (16) & (17) & (18) & (19) & (20) & (21) \\ \hline $0.62\pm0.01$ & $0.51 \pm 0.01$ & -36 & 108 & 101 & 0.72 & $116.7\pm0.3$ & $22.9\pm0.3$ & -0.34 & -0.49\\ \hline \hline \end{tabular} \end{table*} \begin{figure*} \centering \includegraphics[width=0.95\textwidth]{jvds_sami_radial_d_velocity_sigma_examples_LQ_DR2.pdf} \caption{Distribution of individual spaxel velocity (top-row) and velocity dispersions (2$^{\rm{nd}}$-row) as a function of radius, divided into four stellar mass bins. The contours show 68\% and 95\% of the data, and are smoothed with a boxcar filter. The dashed line indicates the adopted velocity dispersion limit of 35 \kms\ as described in Section \ref{subsubsec:kinematic_quality_cuts}. We also show a Hyper Suprime-Cam $g'r'i'$ combined colour image, a SAMI $g^sr^si^s$ colour image reconstructed from the spectra, and the stellar and gas velocity $V$ and velocity dispersion $\sigma$ maps. We indicate the range of the kinematic maps between ``[ ]" brackets. For the velocity fields, blue (stellar) and green (gas) indicate negative velocities, whereas red (stellar) and purple (gas) show positive velocities. For the velocity dispersion maps, yellow-to-red and beige-to-green indicate low-to-high values. In the HSC colour image, the white circle indicates the SAMI hexabundle field-of-view. The blue dashed ellipse in the SAMI reconstructed colour image indicates one effective radius. The small circle in the stellar and gas velocity dispersion map shows the size of the PSF-FWHM. For each mass bin, we highlight one galaxy with coloured points and the image and maps; from left to right we show GAMA560883, GAMA84900, GAMA8353 and GAMA16863. We refer to the text for details on each individual galaxy.} \label{fig:radial_d_sigma_examples} \end{figure*} In this release we make available all 20 Lick index measurements and the three SSP equivalent stellar population measurements for all 6 apertures. For the Lick index measurements, we provide a flag for each aperture to indicate where the measurements may be unreliable, predominantly due to low S/N. For the SSP equivalent measurements, we provide age and [Z/H] only where the S/N of the given aperture spectrum is greater than 10 per \AA. We provide [$\alpha$/Fe] only where the S/N of the aperture spectrum is greater than 20 per \AA. \label{sec:summary} In this paper, we present the SAMI Galaxy Survey's second data release that includes data for 1559 galaxies. This release contains galaxies with redshifts between $0.004 < z < 0.113$ and mass range $7.5 < \log(\mstar/\msun) < 11.6$. We release both the primary spectral cubes covering the blue and red optical wavelength ranges, combined with emission and absorption line value-added products. The data are presented online through Australian Astronomical Optics' Data Central. Observations for the SAMI Galaxy Survey finished May 2018. The next and final data release of the SAMI Galaxy Survey is planned for mid 2020, and will include further data and value-added products. | 18 | 8 | 1808.03365 |
1808 | 1808.06776_arXiv.txt | Progress in understanding of giant planet formation has been hampered by a lack of observational constraints to growing protoplanets. Recently, detection of an H$\alpha$-emission excess via direct imaging was reported for the protoplanet LkCa~15b orbiting the pre-main-sequence star LkCa~15. However, the physical mechanism for the H$\alpha$ emission is poorly understood. According to recent high-resolution three-dimensional hydrodynamic simulations of the flow accreting onto protoplanets, the disk gas flows down almost vertically onto and collides with the surface of a circum-planetary disk at a super-sonic velocity and thus passes through a strong shockwave. The shock-heated gas is hot enough to generate H$\alpha$ emission. Here we develop a one-dimensional radiative hydrodynamic model of the flow after the shock by detailed calculations of chemical reactions and electron transitions in hydrogen atoms, and quantify the hydrogen line emission in the Lyman-, Balmer-, and Paschen-series from the accreting gas giant system. We then demonstrate that the H$\alpha$ intensity is strong enough to be detected with current observational technique. Comparing our theoretical H$\alpha$ intensity with the observed one from LkCa~15b, we constrain the protoplanet mass and the disk gas density. Observation of hydrogen line emission from protoplanets is highly encouraged to obtain direct constraints of accreting gas giants, which will be key in understanding the formation of gas giants. | The origins of the solar system and diverse extrasolar systems have yet to be revealed. In particular, the formation of gas giants would be a high-priority issue, because gas giants are so massive that they have had a dynamical influence on whole planetary systems. Planets are formed in circum-stellar gas disks (or protoplanetary disks) \citep[e.g.][]{Hayashi1981}. A widespread idea, which is called the core accretion model, is that once a core grows to a critical mass via solid accretion, runaway gas accretion of the disk gas takes place and results in forming a massive envelope \citep[e.g.][]{Mizuno1980, Pollack+1996, Ikoma+2000}. It is, however, still uncertain how and when they form. Progress in understanding of gas giant formation is hampered by a lack of direct observational constraints to growing protoplanets. The typical formation timescale of gas giants, which is constrained from the observationally inferred lifetime of protoplanetary disks, is at most 10~Myr \citep[e.g.][]{Hernandez+2008}. Although an increasing number of young exoplanets have been recently detected \citep[e.g., CI Tau b][]{Johns-Krull+2016}, most of gas giants detected so far are several billion years old (e.g., see exoplanet.eu), Those aged gas giants hardly have memory of their formation processes \citep[e.g.][]{Marley+2007}. A challenging issue would be to detect accreting gas giants. Recent observations have detected infra-red (IR) excess from the three young stars, LkCa15 \citep{Kraus&Ireland2012}, HD169142 \citep{Biller+2014, Reggiani+2014}, and HD100546 \citep{Quanz+2015}. Those observed excess is interpreted as infra-red (IR) emission from accreting gas giants \citep{Zhu2015}. Hydrodynamic simulations of gas accretion onto protoplanets show that accreting gas giants are surrounded by circum-planetary disks (CPDs hereafter) \citep[e.g.][]{Miki1982,Tanigawa+2002}. Then, the CPD gas falls toward the gas giant, losing its angular momentum through spiral shock waves and turbulent dissipation. Since the angular momentum loss leads to conversion from gravitational energy to thermal energy, the CPD gas is warmer than the original circum-stellar disk gas. According to theoretical modelling, CPDs are warm and geometrically large enough to generate detectable IR emission \citep{Zhu2015}. Among those stars, in additional to IR, an excess of hydrogen Balmer-$\alpha$ line (H$\alpha$) emission was detected in the circum-stellar disk of the young star LkCa15 of age 2 Myr \citep{Sallum+2015}. In the case of protostars, it is well known that accretion shock near protostars brings about hydrogen line emission \citep{Lynden-Bell&Pringle1974}. Likewise, the H$\alpha$ excess detected for LkCa15 is expected to arise from a shock-heated, accreting gas giant. Theoretical models of stellar accretion developed so far, however, cannot be applied directly to planetary accretion. In general, H$\alpha$ line emission occurs from hot hydrogen of tens of thousands kelvin, which is thought to be reached by accretion-shock heating. In the case of stellar accretion, the strong magnetic field is thought to make a gap between the star and the circum-stellar disk. Then, the accreting gas falls from the disk edge to the stellar surface, resulting in strong shocks \citep{Uchida&Shibata1984, Konigl1991}. The amount of energy generated by the accretion flow (i.e., released gravitational energy) depends on the flow structure. The flow structure around planets is markedly different from that around stars, basically because planets are rotating around central stars. Thus, it is necessary to develop a new model in order to explore whether accreting gas giants yield strong, observable H$\alpha$ emission. Recent high-resolution three-dimensional hydrodynamical simulations of accretion flow onto protoplanets revealed that the flow enters the Roche lobe (or the Hill sphere) not through the Lagrange points in the midplane but from high altitudes \citep{Tanigawa+2012}. Then, the vertically accreting flow hits the surface of the CPD. Because the flow velocity is nearly free-fall velocity, which is much higher than the local sound speed, strong shock occurs at the CPD surface. In the extreme case of strong shock, the gas temperature reaches tens of thousands kelvin just behind the shock front, as shown later in this paper. In such high temperature regions, hydrogen line emission occurs. From their 3D radiative hydrodynamical simulations, \citet{Marleau+2017} and \citet{Szulagyi&Mordasini2017} pointed out the presence of hot regions around accreting gas giants that could be the source of the observed H$\alpha$ line emission. However, they never quantified hydrogen line emission from those hot regions, because those regions, which are much thinner than the CPD thickness, hardly affect the CPD structure. Radiative continuum emission from shock-heated gas was investigated so far for some other astronomical objects and events, which include white dwarf accretion \citep{Frank+1983}, protostar accretion \citep{Calvet+Gullbring1998, Lamzin1998}, the interstellar medium \citep{HM79,HM89,MacLow+Shull1986,Shapiro+Kang1987}, and chondrule formation in protoplanetary disks \citep{Iida+2001}. However, there is no detailed research focusing on hydrogen line emission from highly shock-heated gas, which is of interest in this study. In the case of protostellar accretion, \citet{Calvet+Gullbring1998} investigated the shock heating and atomic line emission at the protostellar photosphere. They, however, assumed weak shock (or C-type shock), because of the magnetic effect, in contrast to strong shock which occurs in our problem. \citet{Lamzin1998} also investigated the recombination lines emitted from the ionized atoms, which came not directly from the postshock gas but from the heated photosphere. In the case of the interstellar shock, although \citet{HM79} investigated the hydrogen line emission, their estimation was simply based on optical depth and the escape probability approximation. Namely, they neglected the absorptive excitation and underestimated the excitation degree in optically thin regions. While hydrogen level population certainly has little influence on the total luminosity from and cooling in the postshock regions, considering it is essential for estimation of each line luminosity. Hence, in order to interpret the H$\alpha$ observation, one must consider transitions between energy levels in hydrogen in more detail. The purpose of this study is to quantify the hydrogen line emission at the surface of the CPD around an accreting gas giant. To that end, we investigate the hydrodynamic, thermochemical, and radiative properties of the vertically accreting flow after the passage of the shock front by performing 1D hydrodynamic simulations with detailed calculations of hydrogen level population. The details of the theoretical model and numerical method are presented in section~\ref{TM}. Then, we show results of numerical simulations in section~\ref{R}, where we estimate the intensities of hydrogen line emission in the Lyman-, Balmer-, and Paschen-series. In section~\ref{D}, we demonstrate that we can obtain constraints to the mass of the accreting gas giant and the density of the surrounding disk gas from observed H$\alpha$ emission, by comparing between the theoretically estimated and measured H$\alpha$ luminosity for LkCa15 as an example. We also discuss the validity of our assumptions and future studies. Finally, we summarize and conclude this study in section~\ref{CS}. | \label{CS} According to recent high-resolution 3D hydrodynamic simulations of accreting flow onto gas giants, the incoming gas falls vertically down to the surface of the circumplanetary disk and then passes through strong shockwaves. Because of strong shock heating, the gas becomes hot enough that hydrogen line emission is generated in postshock regions. To estimate the flux of the hydrogen line radiation, we have developed a 1D radiative hydrodynamic model of the flow after passing through the shockwave, performing the detailed calculations of chemical reactions, electron transitions in hydrogen atoms, and radiative transfer. We have found that most of the energy that the flow has before shock is lost through radiative emission of hydrogen Lyman-$\alpha$ line. Since the Lyman-$\alpha$ line is widely broadened by natural broadening and the postshock region is thin for the radiation from the line wing, absorption of the radiation from downstream by upstream gas has little influence on the Lyman-$\alpha$ flux at the shock front. However, the absorption of line radiation has a great effect on the distribution of energy levels of electrons and enhances emission of other lines such as Balmer-$\alpha$ (H$\alpha$), Paschen-$\alpha$ and so on. Integrating the energy flux throughout the surface of the circum-planetary disk, we have estimated the hydrogen line luminosity from an accreting gas giant as a function of protoplanet mass and circum-stellar disk gas density. Then we have demonstrated that the H$\alpha$ luminosity could be strong enough as the source of the observed H$\alpha$ flux reported by \citet{Sallum+2015}, although the accretion process is to be examined in further detail for confirming whether the H$\alpha$ emission is of planetary origin. Other lines in the atmospheric window such as Paschen-$\alpha$ and Paschen-$\beta$ could be observed with current observation instruments. Observation of hydrogen line emission from protoplanets is highly encouraged to obtain direct constraints to accreting gas giants, which will be key in understanding their formation. \appendix Figure~\ref{fig:FC} is the color contour plot of the Balmer-$\alpha$ (H$\alpha$), Balmer-$\beta$, Paschen-$\alpha$, and Paschen-$\beta$ line energy fluxes versus the preshock velocity $v_0$ and the total number density of hydrogen nuclei $n_\mathrm{H,0}$. \begin{figure*}[htbp] \plottwo{f9a.pdf}{f9b.pdf} \plottwo{f9c.pdf}{f9d.pdf} \caption{ Contour plot of the energy flux of (a) Balmer-$\alpha$, (b) Balmer-$\beta$, (c) Paschen-$\alpha$, and (d) Paschen-$\beta$ lines versus the preshock velocity $v_0$ and total number density of hydrogen nuclei. } \label{fig:FC} \end{figure*} | 18 | 8 | 1808.06776 |
1808 | 1808.00220_arXiv.txt | {Spectral monitoring of the yellow hypergiant $\rho$\,Cas with the by 6-m telescope of the Special Astrophysical Observatory with a spectral resolution of R$\ge$60\,000 has led to the detection of new features in the kinematic state of its extended atmosphere following the ejection of matter in 2013. Significant changes in the profile of the H$\alpha$ line were detected: the line had a doubled core for the first time in a 2014 spectrum, an inverse P\,Cygni profile on December~13, 2017, and the profile was again doubled on August~6, 2017 and September~5, 2017, but was strongly shifted toward longer wavelengths, indicating a rapid infall of matter. Splitting of the profiles of strong, low-excitation absorptions into three components was first detected in 2017. There is no correlation between the evolution of the profiles of H$\alpha$ and the splitted absorptions. Pulsation-like variability with an amplitude of about 10\,km/s is characteristic only of symmetric weak and moderate-intensity absorption lines. Shell emissions of iron-group elements can be identified in the long-wavelength part of a spectrum obtained in 2013, whose intensity decreased until they completely disappeared in 2017. In the absence of emission in the cores of the H and K~lines of Ca\,II, emissions of shell metals are visible in the wings of these lines. \newline {\it Keywords: massive stars, evolution, hypergiants, shell ejections, optical spectroscopy.} } \authorrunning{\it Klochkova et al.} \titlerunning{\it The optical spectrum of the hypergiant $\rho$\,Cas in 2013--2017} | The cool, extremely luminous star $\rho$\,Cas (Sp=G2\,Iae) belongs to a small group of rare yellow hypergiants. The topical nature of a detailed study of these objects is due to the fact that such massive stars are the most probable progenitors of Type~II supernovae (SN~II). Moreover, hypergiants are evolutionarily related to extremely luminous variables such as $\eta$\,Car. In the Hertzsprung--Russell (hereafter HR) diagram hypergiants are close to the luminosity limit of the instability strip for A--M stars [1--3]. In addition to their high luminosities, yellow hypergiants differ from ordinary supergiants in the high rate of their mass loss via their stellar winds and the presence of gaseous--dusty circumstellar shells. The instability of hypergiants is manifest through weak brightness variability (with amplitudes $\approx 0.2\div 0.4^m$), usually referred to as pulsations. The nature of the pulsations of massive stars in the stage of contraction of the helium core has been studied by Fadeev [4], who concluded that long-period, radial pulsations in $\rho$\,Cas have a low probability. Along with the above manifestations of instability, yellow hypergiants also undergo sporadic variations, called ``shell episodes'', when the star loses mass especially intensively, becoming enveloped in cool, ejected matter forming a pseudo-photosphere for several hundred days. Note that the term ``flare'' is used in the Russian literature rather than the English ``outburst''; this is not logical, since the brightness of the star drops significantly during the ejection of the shell. It would be more correct to use the terms ``eruption'' or ``ejection''. In the case of $\rho$\,Cas, the last event of this kind occurred in 2000--2001, when the star lost up to $3\times10 ^{-2} \mathcal{M}_{\sun}$~[5] and its brightness decreased by 1$^m$. Despite its significant loss of mass (the mass-loss rate reaches $10^{-4} \mathcal{M}_{\sun}$/yr), unlike other yellow hypergiants, $\rho$\,Cas lacks circumstellar dust (see [6] and references therein). No extended circumstellar structure has been detected, and the star appears point-like even when observed with high spatial resolution by the Hubble Space Telescope~[7]. At the same time, a thin circumstellar gas envelope is present, and is fairly structured, as is shown by CO observations~[8, 9]. In the HR diagram, $\rho$\,Cas is located at the boundary of the Yellow Void~[1], separating hypergiants and luminous blue variables (LBVs) in their quiescent phase. The amplitudes of pulsations of yellow hypergiants apparently increases sharply at the boundary of the Yellow Void, increasing the instability of their atmospheres and leading to shell ejection~[1]. The results of long-term spectral monitoring~[10--13] of V1302\,Aql, which is a close relative of $\rho$\,Cas, are relevant here. This yellow supergiant, associated with the powerful IR source IRC\,+10420, traversed a path in the HR diagram from the region of red supergiants to the cool boundary of the Yellow Void over the last decade~[13]. High-spectral-resolution monitoring of $\rho$\,Cas has been carried out on the 6-meter telescope of the Special Astrophysical Observatory since 2007. Spectroscopy of $\rho$\,Cas made on this telescope in 2007--2011 were analyzed and presented in~[14]. Observations over a wide range of wavelengths with spectral resolution R$\ge$60\,000 have enabled detailed studies of features in the optical spectrum and the detection of previously unknown properties of the kinematic state of the extended stellar atmosphere. The heliocentric radial velocity derived from symmetric absorption lines of metals varies with an amplitude of about $\pm7$\,km/s relative to the center-of-mass velocity of the system (the systemic velocity) Vsys\,=$-47$\,km/s. This time variability is a consequence of low-amplitude pulsations of near-photospheric layers of the atmosphere. At some epochs, a velocity gradient is observed in deep layers of the stellar atmosphere. Klochkova et al.~[14] found a weak stratification of the velocities in the stellar atmosphere for the first time, manifest as a difference of 3--4 km/s in the velocities measured from absorption lines of neutral atoms and ions. These authors also showed that the long-wavelength components of the splitted absorptions of Ba\,II, Sr\,II, Ti\,II, and other strong lines whose lower levels have low excitation potentials are distorted by a stationary emission in the short-wavelength wings of these components. These non-trivial monitoring results serve as a stimulus for continued spectral monitoring of $\rho$\,Cas. In addition, photometric monitoring of the star (AAVSO) indicates that a new ejection of matter occurred in 2013, during which the brightness of the star decreased by 0.5$^m$. This event occurred only 12 years after the previous one in 2000--2001. Thus, the ejections in $\rho$\,Cas are becoming more frequent. According to~[5, 15], this may indicate that the star is approaching a crossing of the Yellow Void. This fact suggests the urgent need of further monitoring of $\rho$\,Cas. Numerous data have been published for this star, including high-resolution spectral data, however current notions about the kinematic state of its extended, unstable atmosphere do not fit any one, generally accepted interpretation. Resolution of this question also requires long-term, high-quality observations. We present here results based on spectral monitoring in 2013--2017. Section~2 briefly describes the methods used in the observations and analysis of the data. Section~3 presents our results and compare them with earlier data. Main conclusions are presented in Section~4. | We have presented the results of an analysis of optical spectra of $\rho$\,Cas obtained shortly before and just after its brightness minimum in 2013. Various lines in the spectra of this star, which has an extremely extended atmosphere, are variable and always show differential shifts, since the regions of their formation extend from pulsating near-photospheric layers to the non-stationary wind. We have found that the velocity derived from symmetric absorption lines Vr(sym) is variable, with an amplitude of more than 10\,km/s higher than the amplitude found in our previous study of $\rho$\,Cas. Continuation of spectral monitoring using homogeneous material has led to the discovery of new phenomena. This is also true of the behavior of the H$\alpha$ line. While the H$\alpha$ had an almost symmetric absorption profile with the position of the core close to the systemic velocity in 2008--2011, this profile changed substantially after the shell episode, starting from October~1, 2014, when the line acquired a doubled core, with the short-wavelength component shifted by up to 50\,km/s relative to the systemic velocity. At different observing dates in 2017, the H$\alpha$ had an inverse P\,Cygni profile (February~13, 2017) and a doubled profile with a large offset toward longer wavelengths (August~6, 2017). These shifts of the H$\alpha$ profile indicate changes in the structure of the upper layers of the extended atmosphere and enhanced instability of these layers. The shift of the profile towards longer wavelengths indicates an infall of the layers where the line is formed. A comparison of the radial velocities derived from symmetric absorption lines and from the H$\alpha$ line shows that these velocities disagree for most epochs, indicating inhomogeneity of the upper layers of the atmosphere and gaseous envelope of the star. This difference is particularly large in spectra obtained on the descending branch of the brightness. The velocities V(sym) and V(H$\alpha$) agree in the spectra obtained on February~2, 2013 and February~13, 2017, when the brightness was increasing. However, V(sym) and V(H$\alpha$) differ considerably in the 2014 spectra, obtained on the rising branch of the brightness variations, when the doubled core of H$\alpha$ appeared for the first time. In a spectrum obtained on August~8, 2014, we found additional stratification of the velocities derived from lines of ions and neutral atoms. In the long-wavelength region of the spectrum, we identified several weak shell emission lines of iron group elements in the spectrum taken in 2013; the intensity of these emissions decreased in 2017, with only a small fraction being visible in the spectrum for September~5, 2017. Shell emission lines of metals were also detected in the wings of the H and K lines of CaII. The profiles of strongest absorptions remained splitted in all spectra of $\rho$\,Cas obtained in 2014 and 2017. However, unlike the previous observing seasons, these absorptions have three rather than two components in the 2017 spectra. This new property of the splitted absorptions supports our interpretation of this structure: the short-wavelength components of these lines is formed in the circumstellar envelope, where weak emissions of metals and one of the broad components of the NaI~D doublet are also formed. The kinematic instability of the upper atmosphere, which is subject to the influence of the stellar wind, is manifest via the variability of the short-wavelength wing of the BaII~6141\,\AA{} line, which extends to $-150$\,km/s in the spectrum taken on February~2, 2013, before the mass ejection event. In general, we observe that the atmosphere of $\rho$\,Cas has experienced the influence of an additional factor during the ejection episode, which substantially changed the kinematic pattern of its upper layers. | 18 | 8 | 1808.00220 |
1808 | 1808.02225_arXiv.txt | Type I X-ray bursts are thermonuclear explosions on the surface of accreting neutron stars. Hydrogen rich X-ray bursts burn protons far from the line of stability and can release energy in the form of neutrinos from $\beta$-decays. We have estimated, for the first time, the neutrino fluxes of Type I bursts for a range of initial conditions based on the predictions of a 1D implicit hydrodynamics code, \KEPLER, which calculates the complete nuclear reaction network. We find that neutrino losses are between $6.7\E{-5}$ and $0.14$ of the total energy per nucleon, \Qnuc, depending upon the hydrogen fraction in the fuel. These values are significantly below the $35\,\%$ value for neutrino losses often adopted in recent literature for the \textsl{rp}-process. The discrepancy arises because it is only at $\beta$-decays that $\approx35\,\%$ of energy is lost due to neutrino emission, whereas there are no neutrino losses in $(p,\gamma)$ and $(\alpha,p)$ reactions. Using the total measured burst energies from \KEPLER for a range of initial conditions, we have determined an approximation formula for the total energy per nucleon released during an X-ray burst, $\Qnuc=(1.31+6.95\,\Xb-1.92\,\Xb^2)\,\MeVn$, where $\Xb$ is the average hydrogen mass fraction of the ignition column, with an RMS error of $0.052\,\MeVn$. We provide a detailed analysis of the nuclear energy output of a burst and find an incomplete extraction of mass excess in the burst fuel, with $14\,\%$ of the mass excess in the fuel not being extracted. | \label{sec:intro} Since the discovery of bright, energetic explosions from compact objects, known as thermonuclear X-ray bursts \citep{Grindlay1976}, observers have used these events as laboratories for nuclear physics experiments that cannot be replicated on Earth. Type I X-ray bursts are highly energetic ($\sim10^{38}\,$erg) thermonuclear flashes observed radiating from the surface of an accreting neutron star \citep[e.g.,][]{lewin1993}. They are the most frequently observed thermonuclear-powered outbursts in nature and can be used to constrain fundamental information about matter of super-nuclear density and the nuclear reactions and processes that can occur in extreme environments. Thermonuclear X-ray bursts occur at high ($>10^7\,$K) temperatures. They are powered by nuclear reactions, with current theory suggesting five main nuclear reaction pathways involved in the burning in the lead up to a burst, as well as during a burst. These are: the (hot) CNO cycle, the $3\alpha$-process, the $\alpha$-process, the $\alpha$\textsl{p}-process, and the \textsl{rp}-process \citep[e.g.,][]{galloway2017,bildsten1998}. The hot CNO cycle burns hydrogen into helium. The process involves two $\beta$-decays, releasing 2 neutrinos which carry away a total of $\sim2\,$MeV, and is usually responsible for the steady hydrogen burning between bursts, and could be responsible for burst ignition at very low accretion rates \citep{fujimoto1981}. The triple-$\alpha$ process is the pathway by which helium burns to carbon and is thought to be the primary cause of burst ignition \citep[e.g.,][]{Joss1978}. The $\alpha$-process forms heavier elements from the products of the previous two processes and occurs at temperatures $\gtrsim10^9\,$K \citep{fujimoto1981}. The $\alpha$\textsl{p}-process is similar to the $\alpha$-process, but the reaction is catalysed by protons. The \textsl{rp}-process (rapid-proton capture process) is a chain of successive proton captures and $\beta$-decays, beginning with the products of the previous nuclear reaction chains, and quite easily producing elements beyond $^{56}$Fe \citep[see][]{wallace1981}. Each $\beta$-decay releases a neutrino. The primary source of neutrinos during a burst is the $\beta$-decays, where typically $\approx35$\,\% of energy is lost as neutrinos \citep{fujimoto1987}, depending on weak strength distribution, and can be quite different for electron captures. In recent X-ray burst literature, this is often misinterpreted to mean neutrino energy release for the entire \textsl{rp}-process is $35\,\%$ \citep[e.g.,][]{zand2017,cumming2000}. To emphasise this point, again, it is only for the $\beta$-decays that $35\,\%$ of the energy is lost as neutrinos and $\beta$-decays do not dominate the total energy release. Modelling of Type I thermonuclear X-ray bursts has played a significant role in our understanding of their observational properties. Understanding of Type I X-ray bursts must combine theory and observations to comprehensively predict observed burst parameters. Early models \citep[e.g.,][]{fujimoto1981,taam1980,vanparadijs1988,cumming2000}, focus on the correlation between burst energies and recurrence times, to varying success, using an analytic or semi-analytic approach to integrate an ignition column using simple assumptions. More recent models \citep[e.g.,][]{woosley2004,Fisker2008,Fisker2004} have a heavier focus on the nuclear physics driving the bursts, predicting fuel compositions and accretion rates by implementing a deeper understanding of the nuclear reactions that produce the observed energy generation rates. The most advanced of these models, \KEPLER \citep{woosley2004}, uses an adaptive nuclear reaction network to model the burning before, and during a burst in more detail. Based on an incorrect expression for neutrino losses during the $\alpha$\textsl{p}- and \textsl{rp}-process, the energy generation of Type I bursts (\Qnuc) in simple models has often been given by the relation $\Qnuc=(1.6+4\,\Xb)\,\MeVn$, where \Xb is the average hydrogen mass fraction of the ignition column \citep[e.g.,][]{cumming2000}. The formula accounts for helium burning to iron group with an energy release of $1.6\,\MeVn$ and hydrogen burning to iron group with an energy release of $4\,\Xb\,\MeVn$. \Qnuc is directly related to the energy of a burst by multiplying by the number of nucleons (mass) burnt in the burst. As such, this expression for \Qnuc can be used to infer the energy of a simulated burst, given some composition and accretion rate (and hence ignition depth) in simple analytic models \citep[such as][]{cumming2003}. Observers also use this approximation to infer the average hydrogen fraction at ignition, and thus composition of the fuel burnt in the burst from observations of energy \citep[e.g.,][]{galloway2006,Chenevez2016,galloway2008,galloway2004b}. In this work we measure the neutrino fluxes of Type I X-ray bursts based on the predictions of the advanced modelling code \KEPLER \citep{woosley2004}, and develop a new nuclear energy generation approximation using these neutrino estimates. We also examine the metallicity dependence on the neutrino losses and the incomplete burning of the burst fuel. In Section~\ref{sec:methods} we outline the methods and describe the \KEPLER code used in this work, in Section \ref{sec:results} we present the results, giving the expected neutrino losses for Type I X-ray bursts and in Section~\ref{sec:discussion} we discuss the results and provide a case study on the effect that overestimating the neutrino losses has had on composition predictions. Our conclusions are given in Section \ref{sec:conclusion}. | \label{sec:conclusion} We have shown that neutrino losses in Type I X-ray bursts range from $6.7\E{-3}$--$14.2\,\%$ of the total burst energy, which is significantly less than the often-adopted value of $35\,\%$ during the \textsl{rp}-process. We find that by assuming there is $\sim35\,\%$ neutrino losses in hydrogen burning during an Type I X-ray burst, the typically adopted estimate for nuclear energy generation in Type I X-ray bursts of $\Qnuc=(1.6+4\,\Xb)\,\MeVn$ significantly overestimates the neutrino losses by up to a factor of $2$. We find that $\Qnuc=(1.31+6.95\,\Xb-1.92\,\Xb^2)\,\MeVn$, or approximately $\Qnuc=(1.35+6.05\,\Xb)\,\MeVn$, more accurately approximates the nuclear energy generation for Case~III burning \citep{fujimoto1981} as predicted by our multi-zone models. In our models the mass excess of the fuel is incompletely extracted, reducing the energy generation for pure helium fuel from $1.6\,\MeVn$ to $1.35\,\MeVn$ as it does not burn to pure $^{56}$Fe as is classically assumed. For the specific case discussed in detail about $0.3\,\MeVn$ ($14\,\%$ of the initial mass excess relative to iron) remains in the ashes. Interestingly, we found evidence for a significant fraction of energy ($\approx40\,\%$) released in a burst coming from burning below the accretion depth, in the ashes of the previous burst. We also found that the amount of energy carried away by neutrinos does noticeably depend on metallicity even for the same hydrogen fraction of the ignition column. This indicates that for lower metallicity there is stronger \textsl{rp}-process burning and so more neutrinos released by a larger number of $\beta$-decays or reaction pathways with higher-energetic neutrino emission, than for cases with the higher metallicity. | 18 | 8 | 1808.02225 |
1808 | 1808.07400_arXiv.txt | { We present the first family of magnetically polarized equilibrium tori around a Kerr black hole. The models were obtained in the test fluid approximation by assuming that the tori is a linear media, making it is possible to characterize the magnetic polarization of the fluid through the magnetic susceptibility $\chi_{m}$. The magnetohydrodynamic (MHD) structure of the models was solved by following the Komissarov approach, but with the aim of including the magnetic polarization of the fluid, the integrability condition for the magnetic counterpart was modified. We build two kinds of magnetized tori depending on whether the magnetic susceptibility is constant in space or not. In the models with constant $\chi_{m}$, we find that the paramagnetic tori ($\chi_{m}>0$) are more dense and less magnetized than the diamagnetic ones ($\chi_{m}<0$) in the region between the inner edge, $r_{in}$, and the center of the disk, $r_{c}$; however, we find the opposite behavior for $r>r_{c}$. Now, in the models with non-constant $\chi_{m}$, the tori become more magnetized than the Komissarov solution in the region where $\partial\chi_{m}/\partial r<0$, and less magnetized when $\partial\chi_{m}/\partial r>0$. Nevertheless, it is worth mentioning that in all solutions presented in this paper the magnetic pressure is greater than the hydrodynamic pressure. These new equilibrium tori can be useful for studying the accretion of a magnetic media onto a rotating black hole. } | The accretion of a fluid onto a rotating black hole is believed to be the most powerful X-ray source in the universe, causing it to be an active research topic in astrophysics \citep{2002apa..book.....F}. Now, due to the strong gravitational field of the central object, it is necessary to consider a general relativistic approach to properly describe the dynamics of the fluid in the vicinity of the black hole. Additionally, one of the basic features in many theoretical models and numerical simulations of accretion disks is the presence of a strong magnetic field. This field has turned out to be very important because it interacts with the differential rotation of the disk and generates turbulence via the magneto-rotational instability \citep{1991ApJ...376..214B}. This turbulence provides the necessary viscous stress to transfer angular momentum, dissipate energy, and therefore generate the accretion process \citep{1998RvMP...70....1B}. Moreover, it is commonly assumed that strong poloidal magnetic fields are necessary to collimate and accelerate relativistic jets \citep{1977MNRAS.179..433B}. However, the origin and strength of those fields in the accretion disks are still a subject of study. Recent research has shown that a magnetically supported disk may be obtained from a thermally unstable hot disk \citep{2009ApJ...693..771F}. Another possibility is that the magnetic field increases gradually while it is dragged from the outer region to the inner region, near the black hole \citep{2012MNRAS.423.3083M}. It is well known that all substances contain spinning electrons that orbit around the nucleus, meaning we can model the microscopic structure of matter as an assembly of small dipoles, characterized macroscopically by the magnetization vector \citep{citeulike:4033945}. This vector enters in the Maxwell equations as a source of magnetic field, and could be important to understand the problems concerning the origin of the magnetic fields in astrophysical scenarios. Magnetization has already been considered for studying the equilibrium structure of neutron stars. For instance, in \cite{1982JPhC...15.6233B} the authors compute the magnetic susceptibility of the star crust and find that magnetization does not considerably change the surface properties, but may be connected to observable effects. Indeed, \cite{2010ApJ...717..843S} consider the possibility that the soft gamma-ray repeaters and the anomalous X-ray pulsars might be observational evidence for a diamagnetic phase transition that results in a domain formation. Furthermore, as mentioned by \cite{2016PASP..128j4201W}, neutron stars are also important for testing the Haas–van Alphen effect in which the magnetic susceptibility oscillates when the applied magnetic field is increased \citep{de1930dependence}. In the theory of galactic systems, \cite{navarro2018general} presented a static and axially symmetric self-gravitating thin disk in which the magnetic field is generated by a magnetization vector that is normal to the disk plane, presents a maximum at the disk center, and goes to zero at infinity. In accretion disk theory the magnetic polarization of the fluid has not yet been considered. Nevertheless, the first advances in this direction were made by \cite{2018arXiv180602266P}, where we presented the theoretical and numerical background to describe the evolution of a magnetically polarized fluid in a gravitational field. Among some results of this work, we can mention that the propagation speed of the fastest waves in the one-dimensional (1D) Riemann problems is greater in diamagnetic materials than in paramagnetic ones, and that the magnetic field and the relativistic character of the flows may increase considerably with the magnetic susceptibility. Analytical models of accretion disks are of great interest in numerical simulations because they are used as initial data to study the nonlinear evolution of the fluid \citep{2008LRR....11....7F, 2013LRR....16....1A}. Among the analytical models, the Polish doughnuts \citep{1978A&A....63..221A} are the most used in numerical simulations due to their simplicity and the low computational expense they require \citep{2013LRR....16....1A}. These equilibrium models consist of a non-self-gravitating barotropic tori orbiting around a Kerr black hole. Later, \cite{2006MNRAS.368..993K} followed the method of Abramowicz to compute a magnetized tori with a purely toroidal magnetic field. These models have recently been used by \cite{2017MNRAS.467.1838F} to show that a strong toroidal magnetic field cannot be maintained during the disk evolution. Moreover, \cite{2018MNRAS.475..108B} used the Komissarov models to simulate the interplay of the Papaloizou-Pringle instability and the magneto rotational instability. Additionally, it is worth mentioning that \cite{2017A&A...607A..68G}, following the Komissarov procedure, found new magnetized equilibrium tori with a nonconstant angular momentum distribution in the disk. The analytic solutions for magnetized tori presented in the literature do not take into account the contribution of the magnetic dipoles in the torus. We therefore generalize in this work the KomisSarov models by including the magnetic polarization of the matter. For this purpose, we consider the energy-momentum tensor for a magnetically polarized fluid that is given in \cite{Maugin:1978tu, 2010PhRvD..81d5015H, 2015MNRAS.447.3785C}, and follow the Komissarov approach \citep{2006MNRAS.368..993K} to solve the hydrodynamic structure of the tori. These new models may be useful as initial data to study the evolution of a magnetic media in the gravitational field of a Kerr black hole. The organization of this paper is the following: in Sect. \ref{sec:equations} we present the Euler equations that describe the equilibrium structure of a magnetically polarized tori endowed with a toroidal magnetic field around a rotating black hole. To write these equations we concentrate on the special case in which the magnetization vector is parallel to the magnetic field, so that we can relate both vectors through the magnetic susceptibility, $\chi_{m}$. In Sect. \ref{sec:grpic} we present the conditions to write the Euler equations as an exact differential; then, as in \cite{2006MNRAS.368..993K}, we assume a barotropic tori in which the angular velocity is a function of the specific angular momentum only. However, the condition related to the magnetic counterpart is modified in order to include the magnetic polarization of the fluid. In Sect. \ref{sec:results} we present two kinds of magnetized tori: when the magnetic susceptibility is constant in space (Sect. \ref{subsec:case1}), and when it changes with coordinates (Sect. \ref{subsec:case2}). Finally, the main results are presented in Sect. \ref{sec:conclusions}. In this paper we use the signature ($-,+,+,+$) and geometrized units, for which $G=c=1$. | \label{sec:conclusions} In this paper we obtain for the first time a stationary and axisymmetric family of solutions for magnetized tori with magnetic polarization around a Kerr black hole. The magnetized tori was built by assuming a barotropic equation of state, a constant angular momentum, and a purely toroidal magnetic field. These features were previously considered by \cite{2006MNRAS.368..993K} to construct tori with dynamically important magnetic fields. In addition, the polarization of the tori was introduced by assuming the usual linear constitutive relation in which the magnetization vector and the applied magnetic field are linearly related by the magnetic susceptibility $\chi_{m}$. We show that our models reduce to the Komissarov solution when we set the magnetic susceptibility to zero, making it possible to determine the differences in the physical variables of a tori without magnetic polarization and a paramagnetic or diamagnetic tori. With the aim of obtaining an analytical solution of the relativistic Euler equations, we assumed that $\chi=\chi(\mathcal{L}(r,\theta))$, and in particular, that $\chi$ takes the form (\ref{chi}). In this way, the polarization state of the tori is completely defined by choosing the constants $\alpha$, $\chi_{0}$, and $\chi_{1}$. In this paper we present two kinds of magnetized tori, one with constant magnetic susceptibility and one where this susceptibility varies. In the models of Sect. \ref{subsec:case1}, where $\chi_{m}$ is constant, we find that a paramagnetic torus ($\chi_{m}<0$) is more compact than a diamagnetic one ($\chi_{m}<0$), because the matter is more concentrated in the region between the inner edge and the center of the disk. However, in $r<r_c$ the diamagnetic tori are more magnetized than those obtained by Komissarov, and therefore, more magnetized than the paramagnetic ones. The opposite behavior for the magnetization parameter is obtained in the region $r>r_c$, where the paramagnetic tori are more magnetized than the case with $\chi_{m}=0$. Finally, in the models of Sect. \ref{subsec:case2}, where the magnetic susceptibility is non-constant in the torus, we note that the rest mass density does not change its qualitative behavior, as compared with the models of constant $\chi_{m}$. Therefore, the way in which the matter is distributed in the tori depends on whether the fluid is diamagnetic or paramagnetic, the paramagnetic tori being more compact than the diamagnetic ones. Nevertheless, we find that the magnetization state of the tori also depends on the spatial changes of the magnetic susceptibility. In particular, when $\partial\chi_{m}/\partial r<0$ (models M1 and M3), the tori become more magnetized in $r<r_{c}$ than the Komissarov solution, and when $\partial\chi_{m}/\partial r>0$ (models M2 and M4), the tori lose considerable amounts of their magnetization in the same region of the disk. All these effects are more appreciable when the changes in the magnetic susceptibility are large, as in the inner region of the tori in our models. The next step in this direction is to add this solution as initial data, in the CAFE code \citep{2015ApJS..218...24L}, in order to carry out numerical simulations and see the dynamics of the accretion disk once it is being accreted onto the black hole. It is worth mentioning that in the last version of CAFE the magnetic polarized matter terms were implemented following the characteristic approach presented in our recent work \citep{2018arXiv180602266P}. | 18 | 8 | 1808.07400 |
1808 | 1808.02539_arXiv.txt | We study a scalar particle of mas $m_1$ decaying into two particles of mass $m_2$ during the radiation and matter dominated epochs of a standard cosmological model. An adiabatic approximation is introduced that is valid for degrees of freedom with typical wavelengths much smaller than the particle horizon ($\propto$~Hubble radius) at a given time. We implement a non-perturbative method that includes the cosmological expansion and obtain a \emph{cosmological Fermi's Golden Rule} that enables one to compute the \emph{decay law} of the parent particle with mass $m_1$, along with the build up of the population of daughter particles with mass $m_2$. The survival probability of the decaying particle is $P(t)=e^{-\widetilde{\Gamma}_k(t)\,t}$ with $\widetilde{\Gamma}_k(t)$ being an \emph{effective momentum and time dependent decay rate}. It features a transition time scale $t_{nr}$ between the relativistic and non-relativistic regimes and for $k \neq 0$ is \emph{always} smaller than the analogous rate in Minkowski spacetime, as a consequence of (local) time dilation and the cosmological redshift. For $t \ll t_{nr}$ the decay law is a ``stretched exponential'' $P(t) = e^{-(t/t^*)^{3/2}}$, whereas for the non-relativistic stage with $t \gg t_{nr}$, we find $P(t) = e^{-\Gamma_0 t}\,(t/t_{nr})^{\Gamma_0\,t_{nr}/2}$, with $\Gamma_0$ the Minkowski space time decay width at rest. The Hubble time scale $\propto 1/H(t)$ introduces an energy uncertainty $\Delta E \sim H(t)$ which relaxes the constraints of kinematic thresholds. This opens new decay channels into \emph{heavier particles} for $2\pi E_k(t) H(t) \gg 4m^2_2-m^2_1$, with $E_k(t)$ the (local) comoving energy of the decaying particle. As the expansion proceeds this channel closes and the usual two particle threshold restricts the decay kinematics. | Particle decay is an ubiquitous process that has profound implications in cosmology, for baryogenesis \cite{decaybaryo,decaybaryo2}, leptogenesis \cite{wimpdmlepto,leptodecay}, CP violating decays \cite{roulet}, big bang nucleosynthesis (BBN) \cite{zw2002,bbnconstdecay,bbnlonglivedecay,fieldsbbn,ishidabbn,serpicobbn,pospelovbbn,poulinbbn,salvatibbn}, and dark matter (DM) where large scale structure and supernova Ia luminosity distances constrain the lifetimes of potential, long-lived candidates \cite{zw2002,zentner,zentnerlyalfa,koush,dmdecayconst,dmconst2}. Most analyses of particle decay in cosmology use decay rates obtained from S-matrix theory in Minkowski spacetime. In this formulation, the decay rate is obtained from the total transition probability from a state prepared in the infinite past (in) to final states in the infinite future (out). Dividing this probability by the total time elapsed enables one to extract a transition probability per unit time. Energy conservation emerging in the infinite time limit yields kinematic constraints (thresholds) for decay processes. The decay rate so defined, and calculated, is an input in analyses of cosmological processes. In an expanding cosmology with a time-dependent gravitational background, there is no global time-like Killing vector; therefore, particle energy is not manifestly conserved, even in spatially flat Friedmann-Robertson-Walker (FRW) cosmologies, which do supply spatial momentum conservation. Early studies of quantum field theory in curved space-time revealed a wealth of unexpected novel phenomena, such as particle production from cosmological expansion \cite{parker,zelstaro,fulling,birford,bunch,birrell,fullbook,mukhabook,parkerbook,parfull} and the possibility of processes that are forbidden in Minkowski space time as a consequence of energy/momentum conservation. Pioneering investigations of interacting quantum fields in expanding cosmologies generalized the S-matrix formulation for in-out states in Minkowski spacetimes for model expansion histories. Self-interacting quantized fields were studied with a focus on renormalization aspects and contributions from pair production to the energy momentum tensor \cite{birford,bunch}. The decay of a massive particle into two massless particles conformally coupled to gravity was studied in Ref.~\cite{spangdecay} within the context of in-out S-matrix for simple cosmological space times. Particle decay in inflationary cosmology (near de Sitter space-time) was studied in Refs.~\cite{boydecay,mosca}, revealing surprising phenomena, such as a quantum of a massive field decaying into two (or more) quanta of the \emph{same} field. The lack of a global, time-like Killing vector, and the concomitant absence of energy conservation, enables such remarkable processes that are forbidden in Minkowski spacetime. More recently, the methods introduced in Ref.~\cite{spangdecay} were adapted to study the decay of a massive particle into two conformally massless particles in radiation and ``stiff'' matter dominated cosmology, focusing on extracting a decay rate for \emph{zero momentum} \cite{vilja}. The results of Ref.~\cite{vilja} approach those of Minkowski spacetime asymptotically in the long-time limit. \vspace{1mm} \textbf{Motivation, goals and summary of results}. The importance and wide range of phenomenological consequences of particle decay in cosmology motivate us to study this process within the realm of the standard post inflationary cosmology, during the radiation and matter dominated eras. Our goal is to obtain and implement a quantum field theory framework that includes consistently the cosmological expansion and that can be applied to the various interactions and fields of the standard model and beyond. \vspace{1mm} \textbf{Brief summary of results:} We combine a physically motivated adiabatic expansion with a non-perturbative method that is the \emph{quantum field theoretical} version of the Wigner-Weisskopf theory of atomic line-widths\cite{ww} ubiquitous in quantum optics \cite{book1}. This method is manifestly unitary, and has been implemented in both Minkowski spacetime and inflationary cosmology \cite{boyww,boycosww}, and provides a systematic framework to obtain the \emph{decay law} of the parent along with the production probability of the daughter particles. One of our main results, to leading order in this adiabatic expansion, is a \emph{cosmological Fermi's Golden Rule} wherein the particle horizon (proportional to the Hubble time) determines an uncertainty in the (local) comoving energy. We find that the parent survival probability may be written in terms of an \emph{effective time-dependent decay rate} which includes the effects of (local) time dilation and cosmological redshift, resulting in a delayed decay. This effective rate depends crucially on a transition time, $t_{nr}$, between the relativistic and non-relativistic regimes of the parent particle, and is always \emph{smaller} than that in Minkowski spacetime, becoming equal only in the limit of a parent particle always at rest in the comoving frame. An unexpected consequence of the cosmological expansion is that the uncertainty implied by the particle horizon opens new decay channels to particles \emph{heavier} than the parent. As the expansion proceeds this channel closes and the usual kinematic thresholds constrain the phase space for the decay process. While in this study we focus on the radiation dominated (RD) era, our results can be simply extended to the subsequent matter dominated (MD) and dark energy dominated eras. In appendix (\ref{app:Mink}) we implement the Wigner-Weisskopf method in Minkowski spacetime to provide a basis of comparison which will enable us to highlight the major differences with the cosmological setting. | Motivated by the phenomenological importance of particle decay in cosmology for physics within and beyond the standard model, in this article we initiate a program to provide a systematic framework to obtain the \emph{decay law} in the standard post inflationary cosmology. Most of the treatments of phenomenological consequences of particle decay in cosmology describe these processes in terms of a decay rate obtained via usual S-matrix theory in Minkowski space time. Instead, recognizing that rapid cosmological expansion may modify this approach with potentially important phenomenological consequences, we study particle decay by combining a physically motivated adiabatic expansion and a \emph{non-perturbative} quantum field theory method which is an extension of the ubiquitous Wigner-Weisskopf theory of atomic line widths in quantum optics\cite{book1}. The adiabatic expansion relies on a wide separation of scales: the typical wavelength of a particle is much smaller than the particle horizon (proportional to the Hubble radius) at any given time. Hence we introduce the \emph{adiabatic} ratio $H(t)/E_k(t)$ where $H(t)$ is the Hubble rate and $E_k(t)$ the (local) energy measured by a comoving observer. The validity of the adiabatic approximation relies on $H(t)/E_k(t) \ll 1$ and is fulfilled under \emph{most} general circumstances of particle physics processes in cosmology. The Wigner-Weisskopf framework allows to obtain the survival probability and \emph{decay law} of a parent particle along with the probability of population build-up for the daughter particles (decay products). We implement this framework within a model quantum field theory to study the generic aspects of particle decay in an expanding cosmology, and compare the results of the cosmological setting with that of Minkowski space time. One of our main results is a \emph{cosmological Fermi's Golden Rule} which features an energy uncertainty determined by the particle horizon ($\propto 1/H(t)$) and yields the\emph{ time dependent decay rate}. In this study we obtain two main results: i) During the (RD) stage, the survival probability of the decaying (single particle) state may be written in terms of an \emph{effective time dependent rate} $\widetilde{\Gamma}_k(t)$ as $P(t) = e^{-\widetilde{\Gamma}_k(t)\,t}$. The effective rate is characterized by a time scale $t_{nr}$ (\ref{gammainter}) at which the particle transitions from the relativistic regime ($t \ll t_{nr}$) when $P(t) = e^{-(t/t^*)^{3/2}}$ to the non-relativistic regime ($t\gg t_{nr}$) when $P(t)= e^{-\Gamma_0\,t}\, \Big(\frac{t}{t_{nr}}\Big)^{\Gamma_0 t_{nr}/2}$ where $\Gamma_0$ is the Minkowski space-time decay width at rest. Generically the decay is \emph{slower} in an expanding cosmology than in Minkowski space time. Only for a particle that has been produced (``born'') at rest in the comoving frame is the decay law asymptotically the same as in Minkowski space-time. Physically the reason for the delayed decay is that for non-vanishing momentum the decay rate features the (local) time dilation factor, and in an expanding cosmology the (local) Lorentz factor depends on time through the cosmological redshift. Therefore lighter particles that are produced with a large Lorentz factor decay with an effective longer lifetime. ii) The second, unexpected result of our study is a \emph{relaxation of thresholds} as a consequence of the energy uncertainty determined by the particle horizon. A distinct consequence of this uncertainty is the opening of new decay channels to decay products that are \emph{heavier} than the parent particle. Under the validity of the adiabatic approximation, this possibility is available when $2\pi E_k(t) H(t) \gg 4m^2_2-m^2_1$ where $m_1,m_2$ are the masses of the parent, daughter particles respectively. As the expansion proceeds this channel closes and the usual kinematic threshold constrains the phase space available for decay. Both these results \emph{may} have important phenomenological consequences in baryogenesis, leptogenesis, and dark matter abundance and constraints which remain to be studied further. \vspace{1mm} \textbf{Further questions:} We have focused our study on a simple quantum field theory model that is not directly related to the standard model of particle physics or beyond. Yet, the results have a compelling and simple physical interpretation that is likely to transcend the particular model. However, the analysis of this study must be applied to other fields in particular fermionic degrees of freedom and vector bosons. Both present new and different technical challenges primarily from their couplings to gravity which will determine not only the scale factor dependence of vertices but also the nature of the mode functions (spinors in particular). As mentioned above, cosmological particle production is not included to leading order in the adiabatic approximation but must be consistently included beyond leading order. The results of this study point to interesting avenues to pursue further: in particular the relaxation of kinematic thresholds from the cosmological uncertainty opens the possibility for unexpected phenomena and possible modifications to processes, such as inverse decays, the dynamics of thermalization and detailed balance. These are all issues that merit a deeper study, and we expect to report on some of them currently in progress. | 18 | 8 | 1808.02539 |
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