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1808 | 1808.05774_arXiv.txt | The Pulsed All-sky Near-infrared Optical Search for ExtraTerrestrial Intelligence (PANOSETI) is an instrument program that aims to search for fast transient signals (nano-second to seconds) of artificial or astrophysical origin. The PANOSETI instrument objective is to sample the entire observable sky during all observable time at optical and near-infrared wavelengths over 300 - 1650 nm \cite{Wright2018}. The PANOSETI instrument is designed with a number of modular telescope units using Fresnel lenses ($\sim$0.5m) arranged on two geodesic domes in order to maximize sky coverage \cite{Maire2018}. We present the prototype design and tests of these modular Fresnel telescope units. This consists of the design of mechanical components such as the lens mounting and module frame. One of the most important goals of the modules is to maintain the characteristics of the Fresnel lens under a variety of operating conditions. We discuss how we account for a range of operating temperatures, humidity, and module orientations in our design in order to minimize undesirable changes to our focal length or angular resolution. | \label{sec:intro} The PANOSETI instrument is designed to sample the entire observable sky during all observable time at optical and near-infrared wavelengths in search of pulsed signals of astrophysical or artificial origin. Signals of artificial origin may come from pulsed laser communication \cite{Horowitz1993, Howard2004} or leakage from energy transmission (e.g., to propel spacecraft with light sails \cite{Guillochon2015}). These types of pulses could be easily detected with a 10m class telescope, being $\sim10^4\times$ brighter than a Sun-like star \cite{Howard2004}. Previous optical SETI searches have either been targeted or wide field surveys making use of only a single aperture \cite{Howard2004, Wright2014}. This leads to low dwell times per source, greatly reducing the chances of detecting intermittent signals. PANOSETI aims to be the first dedicated all-sky optical and near-infrared SETI experiment targeting the entire northern hemisphere with $\gtrsim$2 steradians of instantaneous sky coverage \cite{Maire2018}. Geodesic domes at two sites--Mt.~Laguna and Lick Observatory--will be used for coincidence detection of signals with each dome containing some one-hundred individual telescope modules. Figure \ref{fig:FoV} shows an illustration of the sky coverage from these two observing facilities. \begin{figure}[h] \begin{subfigure}{0.49\textwidth} \centering \includegraphics[scale=0.33]{2domes.png} \caption{} \end{subfigure} \begin{subfigure}{0.49\textwidth} \centering \includegraphics[scale=0.47]{FoV_square.png} \caption{} \end{subfigure} \caption{(a): Two PANOSETI geodesic dome facilities planned to be located at Lick Observatory near San Jose, CA and Mt.~Laguna Observatory near San Diego, CA ($\sim$690km or $\sim$430 miles apart). Each facility will have some one-hundred individual telescope modules in the final phase of the PANOSETI design. Both locations will observe the same field of view to confirm events via coincidence detection. The blue hexagons correspond to modules operating at optical wavelengths, while the red hexagons represent the two modules at each site operating at the near-infrared. (b): Instantaneous field of view from the two dome facilities \cite{Maire2018}. Each square represents the projection of a 32x32 pixel Hamamatsu silicon photo-multiplier (SiPM) detector array in an individual telescope module containing a $\sim$0.5m Fresnel lens aperture.} \label{fig:FoV} \end{figure} Each telescope module will make use of a $\sim$0.5m f/1 Fresnel lens as a lightweight, cost-effective alternative to traditional apertures, ideal for use in a large scale instrument with a total of some two-hundred apertures between the two domes. A Fresnel lens makes use of concentric grooves that maintain the curvature of a traditional lens in a thinner, lighter format \cite{Davis2011} (see Figure \ref{fig:lens_schem} for schematic of Fresnel lens characteristics and terminology). These modules will be self-contained and interchangeable to be placed at any location in the geodesic dome. Each module will be fixed to the dome and rotated to the proper position angle (PA) to maximize sky coverage \cite{Maire2018}. \begin{figure}[h] \begin{subfigure}{0.49\textwidth} \centering \includegraphics[scale=0.15]{535px-Fresnel_lens.png} \caption{} \end{subfigure} \begin{subfigure}{0.49\textwidth} \centering \includegraphics[scale=0.5]{Schematic_of_Fresnel_lens.png} \caption{} \end{subfigure} \caption{(a): Comparison of traditional convex lens and a Fresnel lens of equivalent surface curvature. Significantly less material volume is required for the Fresnel lens. (b): Image credit: Davis \& K\"{u}hnlenz (2011)\cite{Davis2011}. Illustration of Fresnel lens schematic showing the terminology used to describe the lens as well as the potential for losses in the shadow of the draft facet.} \label{fig:lens_schem} \end{figure} The individual modules required for the full PANOSETI instrument will be developed in phases detailed in Section \ref{sec:phases}. The primary mechanical loads impacting these modules are discussed in Section \ref{sec:loads} and the key components of each module design are discussed in Section \ref{sec:module}. We summarize the component design for each module phase in Section \ref{sec:summary}. | \label{sec:summary} The Beta-1 module was designed as a proof of concept for employing a single Fresnel lens in an optical telescope and for initial on-sky measurements at Mt.~Laguna Observatory. An Edmund Optics 46-392 lens was fixed in a hexagonal mount with silicone rubber in oversized slots allowing for thermal expansion while fixing the location of the lens. A protective layer of acrylic was mounted on the outside of this frame to prevent damage to the Fresnel lens. Lightweight, hollow steel rods connect the hexagonal lens mount to an aluminum plate at the back of the module on which the camera or detector can be attached for testing. To prevent scattered light from affecting measurements, a neoprene baffling is wrapped around the module and secured with snaps to be easily removed. This lightweight module can be mounted to both an optical bench for testing or to the wood base for measurements on-sky. The Prototype module improves on and refines the design of the Beta-1 module for use at a fixed location. Aluminum rings with larger diameters than the Orafol SC214 Fresnel lens make up the lens mount. The larger diameter allows for free expansion of the lens and protective acrylic plate with changes in temperature. Set screws fix the positions of the Fresnel lens and protective acrylic while stiffening beams prevent unacceptable deflection due to gravity or wind. A manually adjustable focus stage will be included at the back of the module mounted on a rotating back plate. The module will be housed in a wood box for baffling and attaching to a Dobsonian mount for observations. Four of these modules will be used for the prototype phase with two located at each observatory for testing coincidence detections at one location and between the two future domes. The final module design will make use of the lens mount in the Prototype module with minor adjustments determined as necessary. Aluminum struts will connect the lens mount to an aluminum plate at the back of the module with an opening for light to pass through to the detector. A focus stage modified from the Prototype module to accommodate a larger detector array will be mounted behind this plate and adjusted with two stepper motors. Baffling of the module frame and electronics will be accomplished with two separate components. Some one-hundred of these modules will be incorporated in each geodesic dome--one at Mt.~Laguna and one at Lick Observatory--monitoring for fast transient signals in the entire observable sky at all observable times. | 18 | 8 | 1808.05774 |
1808 | 1808.06966_arXiv.txt | {We analyzed two {\it Chandra} observations of PSR\, J2055+2539 for a total integration time of $\sim$130 ks to measure the proper motion and study the two elongated nebular features of this source. We did not detect the proper motion, setting an upper limit of 240 mas yr$^{-1}$ (3$\sigma$ level), which translates into an upper limit on the transverse velocity of $\sim$700 km s$^{-1}$, for an assumed distance of 600 pc. A deep H$\alpha$ observation did not reveal the bow shock associated with a classical pulsar wind nebula, thus precluding an indirect measurement of the proper motion direction. We determined the main axes of the two nebulae, which are separated by an angle of 160\fdg8$\pm$0\fdg7, using a new approach based on the rolling Hough transformation (RHT). We analyzed the shape of the first 8\arcmin\ (out of the 12\arcmin\ seen by {\it XMM-Newton}) of the brighter, extremely collimated nebula. Based on a combination of our results from a standard analysis and a nebular modeling obtained from the RHT, we find that the brightest nebula is curved on an arcmin scale and has a thickness ranging from $\sim9\arcsec$ to $\sim31\arcsec$ and a possible (single or multiple) helicoidal pattern. We could not constrain the shape of the fainter nebula. We discuss our results in the context of other known similar features and place particular emphasis on the Lighthouse nebula associated with PSR\, J1101$-$6101. We speculate that a peculiar geometry of the powering pulsar may play an important role in the formation of such features. } | Rotation-powered pulsars are known to produce magnetized winds responsible for a significant fraction of the energy loss of the pulsar. Pulsar wind nebulae (PWNe) are prominent sites of such particle acceleration detected as extended sources of nonthermal high-energy and radio emission. The outflow morphology is influenced by the interaction with the ambient medium and by the pulsar motion. If the pulsar velocity exceeds the sound speed in the ambient medium, a bow shock is typically present and the outflow takes a cometary-like shape \citep[for a review on PWNe, see][]{gae06}. This classical PWN model requires an associated highly energetic pulsar ($\dot{E}\ga10^{34}$ erg s$^{-1}$) and is associated with a bright X-ray emission surrounding the pulsar \citep[see, e.g.,][]{gae04,mcg06,kar08b}. The PWN emission covers a wide range of energy bands, from $\gamma$-rays \citep{ack11} to the optical \citep{tem17}, where bow shocks are more prominent in the H$\alpha$ band \citep[see, e.g.,][]{cor93,pel02}, to radio. However, in recent years some examples of nebulae associated with $\gamma$-ray and X-ray pulsars are adding complexity to the general picture or even challenging this model, pointing to different physical mechanisms being responsible for the emission of these objects \citep[][]{mar13,hui07,pav14a,kli16a,kli16b,pos17}. The recent increase in the number of $\gamma$-ray pulsars \citep[][]{2pc}\footnote{\url{https://confluence.slac.stanford.edu/x/5Jl6Bg}} has been crucial to study the emission phenomena related to highly energetic pulsars, such as X-ray and radio nebulae. PSR\, J2055+2539 (J2055 hereafter) was discovered with {\it Fermi-LAT} as 1 of the 100 brightest $\gamma$-ray sources \citep[][]{saz10,0fgl}. J2055 is radio-quiet, among the least energetic and oldest nonrecycled pulsars in the {\it Fermi} LAT sample and has a spin-down energy $\dot{E}$ = 5.0 $\times$ 10$^{33}$ erg s$^{-1}$ and a characteristic age $\tau_c$ = 1.2 Myr. \citet{mar16} analyzed a deep {\it XMM-Newton} observation of this pulsar. We found the X-ray counterpart of the pulsar, emitting nonthermal, pulsed X-rays. Taking into account considerations on the $\gamma$-ray efficiency of the pulsar and its X-ray spectrum, we inferred a pulsar distance ranging from 450 pc to 750 pc. More interestingly, we found two different and elongated nebular features associated with J2055 and protruding from it. The main, brighter feature (hereafter referred to as the main nebula) is 12\arcmin\ long and locally $<$20\arcsec\ thick and is characterized by an asymmetry with respect to its main axis that evolves with the distance from the pulsar. The secondary feature (hereafter referred to as secondary nebula) is fainter, shorter and broader. Both nebulae present an almost flat brightness profile along their main axis with a sudden decrease at the end. We analyze two new {\it Chandra} observations of the J2055 system: the first, deeper observation allows for a spatial characterization of the nebulae, while the second observation two years later allows for the measurement of the pulsar proper motion. Because of the accurate spectral results already reported in \citet{mar16}, based on a much more sensitive {\it XMM-Newton} observation, our current work does not focus on the spectral study of the system.\\ The analysis of the data is described in Section \ref{data}. In Section \ref{results} we report our investigation into the pulsar proper motion (Section \ref{propermotion}), short-scale (Section \ref{smallsc}) and long-scale (Section \ref{largesc}) analyses of the nebulae and the analysis of the nebular shape (Section \ref{shape}). We also observed J2055 with the 10.4 m Gran Telescopio Canarias (GTC) through an H$\alpha$ filter to search for a bow shock. This analysis is presented in Section \ref{ottico}. A general discussion of our results in terms of physical models is reported in Section \ref{discussion}. We developed and used a new technique for the spatial analysis of elongated features, allowing for a better analysis of diffuse emission in the X-ray band than classical methods. This technique, based on the Hough transformation, is explained in Appendix \ref{app-ht}. | Using two recently obtained {\it Chandra} observations of PSR J2055+2539, we set an upper limit on its proper motion of 240 mas yr$^{-1}$, which translates into an upper limit on its transverse velocity of $\sim$700 km s$^{-1}$ at 600 pc. We found no evidence of bow shocks, either in the X-rays or in H$\alpha$, at scales $\gtrsim$0\farcs5. Two almost-linear features protrude from the pulsar. The main, brighter nebula is highly collimated and its shape is reminiscent of a (multi)helicoidal pattern, resembling the long, motion-misaligned feature seen in the Lighthouse Nebula. Because of its brightness, shape, lack of a bow shock, and low pulsar energetics we rule out the main nebula as a classical PWN. Four other known systems present long, very collimated nebulae misaligned with the pulsar proper motion, one of which has a (multi)helicoidal shape. We conclude that the main nebula is produced by the same physical process as these four. We speculate that this process might be related to a peculiar geometry of the magnetosphere of the powering pulsar, which is confirmed in the case of J2055 via its $\gamma$-ray properties.\\ The secondary nebula is consistent with a classical PWN model, based on the pulsar energetics and nebular luminosity, and on the lack of a detected bow shock. However, only future observations including the detection of the pulsar proper motion can confirm our hypothesis. | 18 | 8 | 1808.06966 |
1808 | 1808.01294_arXiv.txt | Mira variables are useful distance indicators, due to their high luminosities and well-defined period-luminosity relation. We select 1863 Miras from SAAO and MACHO observations to examine their use as distance estimators in the Milky Way. We measure a distance to the Galactic centre of $R_0 = 7.9 \pm 0.3$ kpc, which is in good agreement with other literature values. The uncertainty has two components of $\sim$0.2 kpc each: the first is from our analysis and predominantly due to interstellar extinction, the second is due to zero-point uncertainties extrinsic to our investigation, such as the distance to the Large Magellanic Cloud (LMC). In an attempt to improve existing period-luminosity calibrations, we use theoretical models of Miras to determine the dependence of the period-luminosity relation on age, metallicity, and helium abundance, under the assumption that Miras trace the bulk stellar population. We find that at a fixed period of $\log P = 2.4$, changes in the predicted $K_s$ magnitudes can be approximated by $\Delta M_{Ks} \approx -0.109(\Delta \rm{[Fe/H]}) + 0.033( {\Delta}t/\rm{Gyr}) + 0.021 ({\Delta}Y/0.01)$, and these coefficients are nearly independent of period. The expected overestimate in the Galactic centre distance from using an LMC-calibrated relation is $\sim$0.3 kpc. This prediction is not validated by our analysis; a few possible reasons are discussed. We separately show that while the predicted color-color diagrams of solar-neighbourhood Miras work well in the near-infrared, though there are offsets from the model predictions in the optical and mid-infrared. | \label{sec:Introduction} Measurements of Hubble's constant, i.e. the current expansion rate of the universe, are of great interest in modern astrophysics, since its value is a fundamental parameter of $\Lambda$-CDM cosmology. \cite{2012ApJ...758...24F} and \citet{2018ApJ...855..136R} have respectively measured Hubble's constant in the local universe to 3.5\% and 2.3\% uncertainty. These values are now in tension with other measurements, such as those determined from the cosmic microwave background \citep{2017arXiv170706547A,2018arXiv180706209P}. This tension might be due to ground-breaking new physics, so to study the discrepancy it is critical to probe and extend the local distance ladder by independent means. Mira variables provide a plausible extension to the extragalactic distance scale. They are bright in the infrared for both intermediate-age and old stellar populations, fairly numerous, and have a well-defined period-luminosity relation \citep{1989MNRAS.241..375F,1990AJ.....99..784H,2008MNRAS.386..313W}. Thus, one can envisage future catalogues of Mira variables toward great distances produced from \textit{James Webb Space Telescope (JWST)} photometry. Miras are pulsating variable stars that lie in the late evolutionary stages of the asymptotic giant branch (AGB). They are characterized by long pulsation periods of greater than 100 days and high near-infrared and bolometric luminosities. In particular, they have large amplitude variations in infrared and visual wavelengths. Mira variables eject a considerable portion of their mass into surrounding regions, due to their pulsation, and the mass of the resulting circumstellar dust shells is correlated to their periods \citep{1993A&A...273..570A}. Therefore, while all stars experience extinction due the intervening interstellar dust, Miras also experience intrinsic extinction due to circumstellar dust, and this latter phenomenon affects longer period stars the greatest. AGB variables lie on distinct sequences in diagrams of period versus luminosity, with each sequence corresponding to a different normal mode of pulsation. Mira variables lie on a single sequence, which corresponds to the fundamental mode \citep{1996MNRAS.282..958W,2015MNRAS.448.3829W}. While these sequences are not as tight as those of some other types of variables, most notably Cepheids, they are still quite well-defined. For example, \citet{2015AJ....149..117M} measured a root-mean-square of 0.087 for the $K_{s}$-band near-infrared period-luminosity relation of Large Magellanic Cloud (LMC) fundamental-mode Cepheids, \citet{2017AJ....154..149Y} measured a scatter of 0.118 mag to the period-luminosity relation of the oxygen-rich Miras in the LMC with periods shorter than 400 days. The Mira period-luminosity relations can be expressed in the form $M_{Ks} = \delta + \rho [\log P - 2.38]$, where the period $P$ is measured in days. For example, \cite{2008MNRAS.386..313W}, who used a sample of LMC Miras, measured the slope to be $\rho = -3.51 \pm 0.2$, while the zero-point, which was derived using solar-neighbourhood Miras, was determined to be $\delta = -7.15 \pm 0.07$, assuming an extinction-corrected LMC distance modulus of $\mu_{LMC}= 18.39 \pm 0.05$ \citep{2007MNRAS.379..723V}. Thus, the parameters of the Mira period-luminosity relation can be calculated to better than 6\% uncertainty. More recently, \citet{2017AJ....154..149Y} measured $M_{Ks} = \mu_{LMC} + (-7.23 \pm 0.001) + (-3.77 \pm 0.07) [\log P - 2.38]$, which is written in Table 3 of that work as $K_{s} = (-6.93 \pm 0.001) + (-3.77 \pm 0.07) [\log P - 2.30]$. If the total extinction of the Miras' light is known, then the period-luminosity relation makes Mira variables useful distance indicators, since \begin{equation} \mu = m - M - A \label{eqn:distmod} \end{equation} where $\mu$ is the distance modulus, $m$ is the apparent magnitude, $M$ is the absolute magnitude, and $A$ is the amount of extinction. One goal of this paper is to determine the viability of this technique, since a number of difficulties can arise in making such a distance estimation. First, it is important to select a sample of Mira variables that has sufficient photometric completeness. Nearer stars tend to be brighter, while distant stars tend to be fainter; therefore, if the sample contains a disproportionate amount of bright or faint stars, there may be a bias in the distance determinations. Secondly, the local Galactic Mira period-luminosity relation determined by \cite{2008MNRAS.386..313W} has a slope and zero-point based on Miras from the LMC; however, different galaxies vary widely in age and metallicity. The dependence of the period-luminosity relation on properties such as age and chemical composition has not been probed in great depth, so measurements of distances to other galaxies that rely on an LMC-based period-luminosity relation may require a correction based on these differences. Therefore, another goal of this paper is to use theoretical models to determine whether such corrections are needed. We use a complete sample of Miras and improved extinction estimates to measure the distance to the Galactic centre. The Galactic centre provides a useful testbed for using Miras as distance indicators, as its mean distance is measured precisely, and the characteristics of the stellar population in the surrounding Bulge are well-measured. Currently, the best estimate of the distance is $R_0 = 8.122 \pm 0.031$ kpc \citep{2018A&A...615L..15G}, which comes from modelling the astrometric and radial velocity time-series data of the orbit of the star S2 around the supermassive black hole in the Galactic centre. This result is consistent with the prior literature value of $R_0 = 8.2 \pm 0.1$ kpc \citep{2016ARA&A..54..529B}, which was determined by examining distance measurements made using a variety of techniques; however, there is tension between these values and a recent measurement of 8.9 kpc made using Miras \citep{2016MNRAS.455.2216C}. In this paper, we calculate our own distance estimate, as well as examine issues contributing to the uncertainty in this measurement. In Section \ref{sec:Data}, we select a photometrically complete sample of Bulge Miras and state the assumptions we make about the Bulge in fitting the distance to the Galactic centre. In Section \ref{sec:Extinction}, we compare the results of measuring distance using different extinction estimates. In Section \ref{sec:Models}, we examine the dependence of the Mira period-luminosity relation on age, helium abundance, and metallicity using theoretical models of Mira variables. We conclude our results in Section \ref{sec:Conclusion}. | \label{sec:Conclusion} In this study, we examine the validity of making distance measurements using Mira variables by using them to measure the distance to the Galactic centre, as well as probing the dependence of the Mira period-luminosity relation on a galaxy's age and composition. In selecting an ideal sample of Bulge Miras for fitting the distance to the Galactic centre, we find that the OGLE catalogue \citep{2013AcA....63...21S} has low completeness for brighter stars (i.e., stars on the near side of the Bulge) due to saturation, making it unsuitable to use for our distance study. In comparing several methods of estimating extinction, we find that color-based techniques for calculating extinction towards Miras work better than Galactic dust maps. That may be because former method is less sensitive to the effects of circumstellar extinction. After applying such a method, choosing stars with periods $\log P < 2.6$, and making a geometric correction, we determine that our best estimate for the distance to the Galactic centre is $R_0 = 7.9 \pm 0.3$ kpc, which is in good agreement with measurements of $R_0$ based on other methods in the literature \citep{2016ARA&A..54..529B,2018A&A...615L..15G}. We use theoretical tracks and bolometric corrections to model Mira period-luminosity and period-color relations and study their dependence on age and chemical composition. In comparing the colors predicted by these models to the colors of solar-neighborhood Miras, we find discrepancies in the optical and near-infrared photometric bands, which is either due to saturation or deficiencies in the models. This suggests that the relations we derive should only be used as approximations. However, assuming that these models are valid for Galactic Miras, we find that there is a non-negligible dependence of the relations on metallicity and helium, with a smaller effect from stellar age. Since the Milky Way Bulge is about twice as old and twice as metal-rich as the LMC, using relations based on the LMC should cause an overestimate of $R_0$ on the order of $\sim 0.3$ kpc. This has not been validated by our analysis, and we look forward to more precise tests from future investigations. Thus, as we strive to use Mira variables to make increasingly precise distance estimates, both within and outside of the Galaxy, accurately determining the variation of the period-luminosity relations from galaxy to galaxy will become more important. | 18 | 8 | 1808.01294 |
1808 | 1808.03402_arXiv.txt | {Binary population synthesis predicts the existence of subdwarf B stars (sdBs) with neutron star (NS) or black hole (BH) companions. Several works have been dedicated to finding such systems, but none has been confirmed yet. Theoretically, the formation of sdBs with white dwarf (WD) and main sequence (MS) companions has been well investigated, while those with NS or BH companions remain to be explored further. } {We systematically investigate the formation of sdB+NS binaries from binary evolution and aim to obtain some clues for a search for such systems. } {We started from a series of MS+NS systems and determined the parameter spaces for producing sdB+NS binaries from the stable Roche-lobe overflow (RLOF) channel and from the common envelope (CE) ejection channel. The parameters for sdB+NS binaries were obtained from detailed binary evolution calculation with the code called \emph{\textup{modules for experiments in stellar astrophysics}} (MESA), and the CE parameters were given by the standard energy budget for CE evolution. The MS star had an initial mass ranging from 0.8 to $5 \,M_\odot$. Various NS accretion efficiencies and NS masses were examined to investigate the effects they have. We show the characteristics of the produced sdB+NS systems, such as the mass of components, orbital period, the semi-amplitude of the radial velocity ($K$), and the spin of the NS component.} {sdB+NS binaries can be produced either from stable RLOF or from CE ejection. In the stable RLOF channel, sdBs can be formed when the donor starts mass transfer close to the tip of the giant branch if the donor has an initial mass $\leq 2.0M_{\odot}$. For more massive donors, sdBs can be formed when the donor starts mass transfer during the Hertzsprung gap or near the end of the MS. The orbital period of sdB+NS binaries produced in this way ranges from several days to more than 1000 days and moves toward the short-period ($\sim$ hr) side with increasing initial MS mass. The highest $K$ is about $150 {\rm km\ s^{-1}}$ for an MS star of initially $5M_\odot$ . However, the sdB+NS systems that result from CE ejection have very short orbital periods and then high values of $K$ (up to $800 \rm km\ s^{-1}$). Such systems are born in very young populations (younger than 0.3 Gyr) and are potential gravitational wave sources that might be resolved by the Laser Interferometer Space Antenna (LISA) in the future. Gravitational wave radiation may again bring them into contact on a timescale of only $\sim$ Myr. As a consequence, they are rare and hard to discover. The pulsar signal is likely a feature of sdB+NS systems caused by stable RLOF, and some NS components in sdB binaries may be millisecond pulsars. Various NS accretion efficiencies and NS masses change some properties of sdB+NS binaries, but not our general results.} {} | Hot subdwarf-B stars (sdBs) are located at the extreme horizontal branch (EHB) in a Hertzsprung-Russell diagram (HRD). These objects have relatively high temperatures ($\mathit{T}_{\mathrm{eff}}\approx 20000- 40000\mathrm{K}$) and high surface gravities ($\log \mathit{g}$ between $\sim$ 5.0 and 6.5). The structure of an sdB typically consists of a helium-burning core and a thin hydrogen-rich envelope ($\lesssim 0.02 \,M_\odot$) \citep{Heber1986}. Theoretical studies show a wide mass range for sdB stars from 0.3 to 0.8$M_\odot$ in \citet{Han2002,Han2003} and from 0.35 to 1.7$M_\odot$ in the recent study of \citet{2018arXiv180203018G}. SdBs are in a special stage in stellar evolution, which occurs after a star has lost almost the whole hydrogen envelope before it ignites helium degenerately or non-degenerately in the core. It has been discovered that two types of pulsations exist in some sdBs: pressure-mode (p-mode) pulsations \citep{Charpinet}, and gravity-mode (g-mode) pulsations \citep{Fontaine}, but both may also be present in an sdB. An sdB stays on the EHB for roughly $10^8$ years and directly evolves along with the white dwarf (WD) cooling track after its core helium has been exhausted. \citet{Heber2016} provided a comprehensive review of sdBs as a whole. It is widely accepted that the sdBs are formed from binary evolution, that is, common envelope (CE) ejection, stable Roche-lobe overflow (RLOF), and the merger of double helium WD (He-WD) {\citep{2018MNRAS.476.5303S}.} sdB binaries with short orbital periods account for a comparatively large portion of sdBs, and their companions are generally main-sequence (MS) stars or WDs \citep{Maxted,Napiwotzki2004}. The sdBs with massive WD companions, such as KPD 1930+2752 and CD-30 11223, have been considered good candidates of Type Ia supernovae (SN Ia) progenitors \citep{Maxted2000,Geier2007,2013ASPC..469..373G,Wang2009,Vennes2012}. Numerous investigations have been reported that focused on the formation of sdB+WD and sdB+MS systems \citep{Han2002,Han2003,Chen2013}. The formations of sdB+neutron star (NS) and sdB+black hole (BH) systems, however, have so far not been studied systematically and remain to be explored. In recent years, considerable attentions have been paid to the systems of sdBs coupled with a massive companion on observations, e.g. the project Massive Unseen Companions to Hot Faint Under-luminous Stars from SDSS (MUCHFUSS). This project seeks to find sdBs with massive compact companions such as massive WDs (> $1.0 \,M_\odot$), NSs or stellar mass BHs \citep{Geier2011}. In this project, objects which have high radial velocity (RV) variations from Sloan Digital Sky Survey (SDSS) have been selected as good candidates and re-observered to obtain the medium resolution spectra. Until now, there are 129 sdB samples discovered by MUCHFUSS \citep{Geier2015,Geier2017a}. The majority of the sdB samples have RV semi-amplitude $\mathit{(K)}$ values in a range of 50 - 160 $\mathrm{ km\ s^{-1}}$, and the highest $\mathit{K}$ value is $\mathrm{359 km\ s^{-1}}$. Most objects exceeding $\mathit{d} \sim$ 3 kpc may be located in the Galactic halo due to the fact that the coverage of SDSS roughly belongs to high Galactic latitudes. No sdBs with NS or BH companions have been confirmed yet and the fraction of close sdB+NS/BH binaries has been constrained to be less than 1.5\% \citep{Geier2017a} based on the results from the MUCHFUSS project. A possible candidate for sdB+NS binaries is the millisecond pulsar, PSR J1816+4510, which has been identified by \citet{Kaplan2013}. Its companion has atmospheric parameters similar to those of an sdB, that is, $\mathit{T}_{\mathrm{eff}}\approx 16000\mathrm{K}$, $\log \mathit{g}\approx 4.9$. However, \citet{2014A&A...571L...3I} suggested that the companion might be an extremely low-mass proto-He WD. The object HD 49798 is a subdwarf O star (sdO) \citep{Jaschek1963} with a massive compact companion ($1.28\pm 0.05M_\odot$). It is the first sdO star to have been detected with X-ray emission, and the companion spins at 13.2s in a 1.55day orbit \citep{Thackeray1970,Israel1996}. Some hypotheses have been made on the type of the compact companion. Most recently, the companion has been suggested to be an NS based on the spin-up rate derived from the observations of X-ray pulsations. The possibility of a massive WD companion cannot be excluded, however \citep{Mereghetti2016}. Owing to the lack of direct evidence for sdB+NS/BH binaries from observations, it is doubtful whether such systems might indeed be produced, since binaries are likely to be disrupted by supernova explosions when the NS/BH forms. However, the existence of numerous X-ray binaries, the majority of which have NS/BH companions, removes this concern. Meanwhile, \citet{2011MNRAS.416.2130T} modeled the formation of the massive millisecond pulsar binary PSR J1614-2230, and clearly showed the progenitor phase for a NS+sdB binary. NSs can be produced by core-collapse supernovae (CC), electron-capture supernovae (ECSNe), and accretion-induced collapse (AIC) from an oxygen-neon-magnesium (ONeMg) WD \citep{Miyaji1980,Nomoto1984,Nomoto1987,1987Natur.329..310M}. NS with the lowest ( $ 1.15M_{\odot }\sim 1.22M_{\odot }$) and highest ($\ge \sim 1.4M_{\odot }$) mass are both expected to be produced by the CC scenario, while NSs with masses of about 1.25$M_{\odot }$ are more likely from the ECSNe and the AIC scenario \citep{1996ApJ...457..834T,2011BASI...39....1V}. The natal kicks of NSs imparted by ECSNe and by AIC are believed to be much smaller than the kick imparted in the CC scenario \citep{Pfahl2002}. \citet{Zhu2015} studied the formation of millisecond pulsars (MSPs) through a population synthesis approach and showed that approximately 58\% of radio MSPs are produced in the CC, 35\% in the ECSNe, and 7\% in the AIC scenario. Taking into account the asymmetric kicks contributed by the formation of NS/BH in the population synthesis model, \citet{Nelemans2013} predicted that about 1\% of the sdB binaries have NS companions and about 0.1\% have BH companions. However, the details of the formation process of sdB+NS binaries have not been considered adequately in that study. The primary objective of this research is to systematically study the formation of sdB+NS systems. By associating simulation results with the observations, we could obtain some valuable hints for observations and also boost the insights into the evolutionary process of sdBs. The remainder of this paper is structured as follows. Sect. 2 introduces the models, simulating methods, and assumptions we made for mass transfer process and NS accretion. The results are presented in Sect. 3 for the stable RLOF and in Sect. 4 for the CE ejection channel. Our main conclusions are summarized in Sect. 5, followed with a discussion of future research. | We investigated the formation of sdB+NS systems from a series of MS+NS binaries. The parameter space for producing sdB+NS binaries was obtained for this study for the stable RLOF channel and the CE ejection channel. If the MS mass is initially lower than $2M_\odot$ , the mass transfer process from the donors to NSs is dynamically stable and the sdBs can only be formed when the donor starts mass transfer close to the tip of FGB. For more massive MS stars, however, the sdBs can be produced when the donor starts mass transfer during the HG or even earlier (near the end of the MS). If the donor is more massive than $3.2M_\odot$ and starts mass transfer on the GB, the mass transfer is assumed to be dynamically unstable, then a sdB+NS binary is formed if the CE can be ejected based on the standard energy budget, and the He core is ignited after the CE ejection. The sdB+NS binaries from the stable RLOF generally have long orbital periods, as expected, ranging from several days to more than 1000 days, and the range of the orbital period moves toward the short-period side with increasing initial MS mass. The largest RV semi-amplitude is derived at about $150 {\rm km\ s^{-1}}$ for an MS star with initially $5M_\odot$ . We studied Population I stars here. With decreasing metallicity, the orbital periods from the stable RLOF are expected to be significantly shorter than the period shown in this paper, according to the study of \citet{Chen2013}. As a consequence, the value of $K$ increases and the resulting sdB+NS binaries at low metallicity could be discovered more easily. The sdB+NS systems that resulted from the CE ejection have very short orbital periods and then a large RV semi-amplitude (the value of $K$ may be up to $800 \rm km\ s^{-1}$). Such systems are born in very young populations, that is, younger than $\sim$ 0.3 Gyr, and are potential strong GW sources with frequencies between $10^{-4}-1$, and could be resolved by LISA in future. Their lifetimes are very short ($\sim$ Myr) because of the GW radiation, which means that such systems must be rare and also hard to detected. In the sdB+NS systems from the stable RLOF, almost all the NSs have been spun up to be millisecond pulsars in our study. The observations of binary pulsars with WD companions indicates that the models from relatively massive MS stars ($M_{\rm d}^{\rm i} \ge 2.5M_\odot$) are generally consistent with the observations, but a discrepancy appears if the donors have lower initial masses. The sdB+NS binaries from the latter have long orbital periods ($P>>100$ d) and very short spin periods, more than one order of magnitude shorter than that of observed binary pulsars with long orbital periods. This indicates that the real accretion efficiency could be far lower than we assumed when the mass transfer rate is dramatically higher than the Eddington rate, for instance, when mass transfer occurs when the donor is on the GB. Nevertheless, the pulsar signal is likely a feature of sdB+NS systems that result from the stable RLOF channel. The NS accretion efficiency has significant effect on the final NS mass if the donor starts mass transfer on the MS, but little effect on the sdB mass and the parameter space for producing sdB+NS systems. In comparison to the case of $1.4M_\odot$ NS, a $1.25M_\odot$ NS leads to a significantly shorter final orbital period becausee the mass transfer rates induced by the higher initial mass ratio are relatively higher. Therefore more mass and then more angular momentum have been lost from the system, leading to a more dramatic shrinking of the orbit. The X-ray irradiation from the NS to the donor during accretion may affect the detailed evolutionary process. This would be important and needs further studies. The numbers and statistical properties of binary parameters for sdB+NS binaries will be given from binary population synthesis in the next paper. | 18 | 8 | 1808.03402 |
1808 | 1808.05224_arXiv.txt | {We present a new approach to component separation in multifrequency CMB experiments by formulating the problem as that of partitioning the sky into pixel clusters such that within each pixel cluster the foregrounds have similar spectrum, using only the information available in the data. Only spectral information is used for partitioning, allowing spatially far away pixels to belong to the same cluster if their foreground properties are close. We then apply a modified internal linear combination method to each pixel cluster. Since the foregrounds have similar spectrum within each cluster, the number of components required to describe the foregrounds is smaller compared to all data taken together and simple pixel based ILC algorithm works extremely well. We test our algorithm in the full focal plane simulations provided by the Planck collaboration. We apply our algorithm to the Planck full mission data and compare our CMB maps with the CMB maps released by the Planck collaboration. We show that our CMB maps are clean and unbiased on a larger fraction of the sky, especially at the low Galactic latitudes, compared to publicly available maps released by the Planck collaboration. This is important for constraining beyond the simplest $\Lambda$CDM cosmological models and study of anomalies. Our cleaned CMB maps are made publicly available for use by the cosmology community. } | The Cosmic Microwave Background (CMB) experiments observe the sky in broad frequency bands. The data thus obtained contains not only the CMB but emission from gas and dust in our own Galaxy as well as the integrated emission from all the galaxies since the formation of the first stars. There is a broad window where the CMB dominates over all other astrophysical emissions in a large part of the sky and the CMB experiments from the ground as well as space have taken advantage of this. With the Planck experiment \cite{planck} and the ground based experiments such as South Pole Telescope (SPT) \cite{spt}, Atacama Cosmology Telescope (ACT) \cite{act} and BICEP2 \cite{bicep2}, the experimental sensitivity has reached a point where we are limited not by the detector noise but by the residual foreground contamination in the data. Multifrequency experiments such as Wilkinson Microwave Anisotropy Probe (WMAP) \cite{wmap} and Planck allow us to use the fact that the CMB and the foregrounds have different frequency spectrum to separate the CMB from the other Galactic and extragalactic components present in the data. However, in any experiment, we have a limited number of channels available while the foreground properties, the amplitude as well as the shape of the spectrum of different physical components, such as thermal and spinning dust emission, line emission from CO and other molecules and atoms, synchrotron emission etc., vary over the sky from pixel to pixel. If we have a physical parametric model for all the cosmological components and the foregrounds, and a sufficient number of frequency channels, we can fit for the parameters of the model in each pixel. This is the approach followed in the Commander \cite{eriksen2006} and Linearized Iterative Least-squares (LIL) \cite{lil} algorithms. However, the measured intensity in every frequency band in any given pixel is a superposition of many different sources along the line of sight. For example, thermal dust emission from many molecular clouds along the line of sight, which may have different physical properties such as temperature, and different angular sizes on the sky, may contribute to the intensity observed in a single pixel. This makes the description of the foreground emissions by simple parametric models, at the required accuracy, difficult. These difficulties have been the motivation towards the development of the so called non-parametric or \emph{blind} component separation methods which need only the spectrum of the cosmological signal of interest to be known. These methods, in particular, do not need any knowledge about the foregrounds except that their spectrum is different from the signal of interest and some additional statistical requirements about the independence of components or that the angular variations of the foregrounds are uncorrelated with the signal of interest. These methods such as Spectral Estimation Via Expectation Maximization (SEVEM) \cite{sevem}, Spectral Matching Independent Component Analysis (SMICA) \cite{smica2003,smica}, Fast Independent Component Analysis (FASTICA) \cite{fastica2002}, Needlet Internal Linear Combination (NILC) \cite{nilc}, scale discretized ILC (SILC) \cite{rpl2016} or iterative ILC approach \cite{say2017} compute the desired cosmological signal (e.g. CMB) map as a linear combination of the available different frequency channel sky maps. Different choices of how we combine the available frequency channel maps and what quantity we optimize to get the weights at different frequencies gives us different algorithms. These blind algorithms however work best when the foregrounds can be described by the superposition of a small number of spectral shapes, smaller than the number of frequency channels available. As we noticed earlier, the foreground properties, specifically the spectral shape of the foregrounds, varies over the sky. This means that we cannot apply a blind algorithm to the full sky but must divide the data into clusters such that within each cluster the data can be described by a superposition of a small number of foreground components. Different criteria for clustering of the data will lead to different solutions for the cosmological signal. The above mentioned algorithms differ also in how they cluster or partition the data, with SEVEM clustering the data in pixel space into a small number of regions based on the \emph{amplitude} of the foregrounds, SMICA clusters the data in harmonic space with the weights a function of the multipole $\ell$ and NILC clusters the data using spherical needlets achieving localization or clustering in broad multipole bands as well as in real space. In all of these cases, the clustering or partitioning of the data is done without using the information about the foreground spectrum available in the data but is instead motivated more by heuristic arguments and prior assumptions about the foregrounds. Also, all current algorithms use a single partitioning of data with some smoothing prescription across the partitions. It is not clear a priori why a particular partitioning scheme should be chosen over another and whether there exists a single optimal partitioning of the data given our limited knowledge of foregrounds and limited number of frequency channels available. The main new feature of our approach that distinguishes it from the existing algorithms is how we cluster the data. We will work in pixel space and use Internal Linear Combination (ILC) \cite{te1996,tegmark1998,wmapilc, Eriksen2004} as our component separation method within each cluster. However the basic ideas about the partitioning of data can be applied in any other basis, including the spherical harmonic basis, and any other basic component separation algorithm. The following two main ideas underlie our new approach to component separation: \begin{enumerate} \item There is no single optimal partitioning of the data, given our limited knowledge of the foregrounds. We must therefore explore all possible partitionings probabilistically, subject to the constraint in the second point. We will see that this approach automatically blurs the boundaries between the partition and thus does not require any extra smoothing across the partition boundaries. By allowing the partitions or clustering of the data to vary we essentially want to take into account the uncertainties in our knowledge of the foregrounds. \item The data should be clustered so that the data within each cluster has similar foreground properties, in particular the spectrum, since we will be using the spectral information to distinguish the signal of interest from other components. \end{enumerate} We note that such a problem on \emph{clustering} of data is well suited for machine learning and in that context it also goes by the name of \emph{unsupervised learning}. We will however not go by the machine learning route but follow a very simple prescription for the clustering of data with the spectral properties of the foregrounds quantified by a single parameter i.e. we will cluster data along a single dimension. We will see that our simple approach already works very well for Planck data and motivates more sophisticated machine learning based clustering in more than one dimensions as well as Bayesian extensions \cite{vw2016} which we leave for future work. In particular, the small number of high resolution frequency channels available in Planck do not allow a more sophisticated clustering approach than a single parameter one we describe below. A single parameter is however not sufficient to quantify the differences in shapes of multicomponent foregrounds. Future experiments such as LiteBIRD \cite{litebird}, Primordial Inflation Explorer (PIXIE) \cite{pixie}, Cosmic Origins Explorer (CORE) \cite{core} and Probe of Inflation and Cosmic Origins (PICO) \cite{pico} would have more than twice the number of channels available in Planck and would allow implementation of more accurate multi-parameter clustering as well as use of machine learning to partition the data. In this paper we will be only interested in the CMB to demonstrate our algorithm but it can equally well be used for any other component for which the spectrum is known, such as the Sunyaev-Zeldovich (SZ) effect \cite{zs1969}. We will explore the SZ effect and other applications in separate publications. We make the full sky cleaned CMB maps constructed from the Planck public release 2 (PR2) data release \cite{planckpr2} by our algorithm publicly available. | We have presented a new approach to foreground cleaning and component separation in the multifrequency CMB experiments. Our approach is to cluster together the data into groups or partitions, such that in each partition the foreground properties of the data are similar. This makes the problem of component separation more tractable since in each partition the data can be \emph{accurately} described by a small number of components, ideally smaller than the number of frequency channels available. Our approach differs from the existing algorithms, which also try to cluster the data in pixel and/or harmonic space. Instead of a pre-determined clustering of data, we estimate the foreground properties from the data first summarizing it into a measure $m$ and then use this measure $m$ to partition the data \emph{probabilistically}. This step of first estimating the foreground properties, other than the amplitude, is the new ingredient. We have implemented our approach into a algorithm called FC-ILC. At present FC-ILC uses a single measure, constructed from two foreground dominated Planck HFI (high frequency instrument) channels and one clean channel, and performs the component separation in pixel space. However, FC-ILC approach can be extended to use more than one measure and use harmonic space. The second important new ingredient of our algorithm is to cluster the data randomly many times and use the average solution over these many random realizations of partitions. This probabilistic approach to the clustering of data allows solution in a particular pixel to be influenced by all pixels close to it in terms of the measure $m$. There are no sharp boundaries in our solutions (CMB maps) that would need to be artificially smoothed. The third ingredient is that we construct many different solutions, each with different number of channels, and each solution at the best resolution allowed by the channels being used. These different resolution solutions are than combined in such a way so as to use the information from the best solutions available at a given scale $\ell$. We have tested our algorithm on FFP6 simulations and shown that it works as well as can be expected, especially compared with the results of other algorithms on the same simulations. We have also applied our algorithm to the Planck PR2 temperature maps and produced new cleaned CMB maps (half-ring maps and full mission map) which are made publicly available for use by the cosmology community\footnote{\url{http://theory.tifr.res.in/~khatri/CMB}}. We compare the properties of our maps with the Planck power spectrum results from the PR2 release as well as the foreground cleaned maps made available by the Planck collaboration. We find that while using the UT78 mask, giving approximately $78\%$ of sky fraction for calculating the power spectrum, our results are consistent with SMICA, NILC and Commander maps, having similar residual contamination as SMICA, which is slightly better than Commander at high $\ell$. However when using a larger sky fraction, using our masks constructed by thresholding our measure $m$ and the 545 GHz channel map, both Commander and SMICA show a \emph{negative} contamination. In particular there seems to be a constant offset between the SMICA and FC-ILC power spectra, indicating that SMICA map has been \emph{over-cleaned}. It is overall difficult to say which of the maps is best or most free of contamination. We hope that our independently produced maps with a different algorithm, with similar in amplitude if not smaller but qualitatively different residuals as the maps released by the Planck collaboration, would be useful in testing for the effect of residual foregrounds on cosmological parameters, in particular when studying the marginally significant anomalies. We have chosen a particular clustering method based on a very simple one-dimensional measure of foreground shape. The shape of the foregrounds is of course much more complicated to be captured adequately by a single measure. We cannot therefore claim that our clustering is optimal. We have however shown that our simple foreground clustering approach is reasonable in the sense that it works as well as any of the other component separation algorithms used by the Planck collaboration. There is however definite room and clear direction for further improvement and optimization, especially using machine learning to cluster data using more than one measure, which we defer to a future publication. | 18 | 8 | 1808.05224 |
1808 | 1808.05538_arXiv.txt | Whether aimed for the study of the planetary systems, the distribution of the stars in the galaxies or the formation of the large-scale structures in the Universe, the sizes of numerical simulations are becoming increasingly important in terms of their virtual volumes and computer memories. The visualization of the data becomes more complicated with the requirement of the exposition of the large number of data points. In order to lighten such burden, Virtual Observatories (VO) have been developed and are now essential tools in astronomy to share existing data, for visualization and for data analysis. Using a software, currently being developed at the Centre de Donn\'ees de Strasbourg (CDS) jointly with the Astronomical Observatory of Strasbourg, we show how three-dimensional radiative transfer simulations of active galactic nuclei (AGN) can be visualized in order to extract new information. The ability to zoom over ten orders of magnitude and to journey inside/between the multiple scattering regions allows to identify where emission, scattering, and absorption truly take place. Among all the new possibilities offered by the software, it is possible to test the single-scattering hypothesis or evaluate the impact of fragmentation onto the propagation of light echoes within the broad line region (BLR) or the circumnuclear region (torus). | In the center of each massive galaxy lies a supermassive black hole \cite[see, e.g.,][]{Silk1998}, but most of those monsters are quiescent. Due to the lack of neighboring stars, gas and dust material they are not actively fed, which results in very low light emission. However, when accretion onsets and matter spirals downward the potential well, the tremendous near-infrared, optical and ultraviolet bolometric luminosity emitted by the system often outshines starlight emission from the host galaxy \citep{Pringle1972, Shakura1973}. The supermassive black hole becomes active and the object is called an active galactic nuclei (AGN). What is truly fascinating is that this object that has the size of a solar system can in effect have a profound impact on the galaxy it resides in \citep{George2018}. This involves more than ten orders of magnitudes, ranging from the Scharzschild radius (a few 10$^{-6}$ pc for a 10$^8$ solar masses black hole) to the extent of the polar outflows (the narrow line region, NLR) that can reach several kilo-parsecs. If we want to simulate the radiative transfer of photons from the accretion disk to a distant observer, it implies to simulate a variety of environments, from the highly ionized broad line region (BLR) clouds to the dusty circumnuclear torus, involving continuous or fragmented/filamentary structures. This demands heavy numerical calculations that are both time consuming and computationally expensive. Still, several softwares are now able to handle such large scale simulations \cite[see, e.g.,][]{Goosmann2007,Baes2011,Grosset2018}. What is less mastered, however, is the display of the results. We usually rely on two-dimensional projections that can suffer from projection effects such as aberrations and deformations. Three-dimensional visualizations are usually hampered by the large volume of data that must be loaded and stored in the computer. In this conference proceedings we present a new software that is currently being developed in Strasbourg as part of the global Virtual Observatory (VO). This tool is meant for displaying large simulations in both degraded and full resolution. The software allows the user to freely journey inside the simulation, isolate a given volume and create videos from several snapshots. | In this contribution we have shown a proof of concept regarding the visualization of huge radiative transfer simulations using VO tools. We focused on the three-dimensional representation of scattering events in AGN using the client side of the {\sc jasmine} software. The numerical tool allows the observer to circulate within the simulation itself, examine where emission, scattering or absorption take place, and test various scenarios. For example, it is possible to simulate the disruption of a star by the central supermassive black hole (a tidal disruption event) and follow the resulting light echo as it propagates within the AGN. Several theories, such as the bird's nest appearance of the BLR, can be tested this way. The importance of multiple scattering is also naturally highlighted here. We intend to develop the combined use of {\sc jasmine} and {\sc stokes} in various situations, such as AGN variability to be probed in polarized light \citep{Rojas2018}, demonstrating the growing importance of VO tools in the future of astronomical visualization of large simulations. | 18 | 8 | 1808.05538 |
1808 | 1808.02890_arXiv.txt | We present the discovery of PS18kh, a tidal disruption event (TDE) discovered at the center of \host{} ($d\simeq322$~Mpc) by the Pan-STARRS Survey for Transients. Our dataset includes pre-discovery survey data from Pan-STARRS, the All-Sky Automated Survey for Supernovae (ASAS-SN), and the Asteroid Terrestrial-impact Last Alert System (ATLAS) as well as high-cadence, multi-wavelength follow-up data from ground-based telescopes and {\swift}, spanning from 56 days before peak light until 75 days after. The optical/UV emission from PS18kh is well-fit as a blackbody with temperatures ranging from $T\simeq12000$~K to $T\simeq25000$~K and it peaked at a luminosity of $L\simeq8.8\times10^{43}$~ergs~s$^{-1}$. PS18kh radiated $E=(3.45\pm0.22)\times10^{50}$~ergs over the period of observation, with $(1.42\pm0.20)\times10^{50}$~ergs being released during the rise to peak. Spectra of PS18kh show a changing, boxy/double-peaked \halpha{} emission feature, which becomes more prominent over time. We use models of non-axisymmetric accretion disks to describe the profile of the H$\alpha$ line and its evolution. We find that at early times the high accretion rate leads the disk to emit a wind which modifies the shape of the line profile and makes it bell-shaped. At late times, the wind becomes optically thin, allowing the non-axisymmetric perturbations to show up in the line profile. The line-emitting portion of the disk extends from $r_{\rm in}\sim60r_{\rm g}$ to an outer radius of $r_{\rm out}\sim1400r_{\rm g}$ and the perturbations can be represented either as an eccentricity in the outer rings of the disk or as a spiral arm in the inner disk. | \label{sec:intro} Tidal disruption events (TDEs) occur when a star crosses the tidal radius of a supermassive black hole (SMBH) and the tidal shear forces of the SMBH are able to overcome the self-gravity of the star. For main-sequence stars, approximately half of the stellar material is ejected from the system, while the other half remains bound to the SMBH. The bound material falls back to pericenter at a rate proportional to $t^{-5/3}$ and a fraction of it is accreted onto the black hole, resulting in a short-lived, luminous flare \citep[e.g.,][]{lacy82,rees88,evans89,phinney89}. Initially, it was commonly assumed that the flare emission would peak at soft X-ray energies and that the luminosity would be proportional to the $t^{-5/3}$ rate of return of the stellar material to pericenter. However, in recent years a number of well-studied TDEs have been discovered that exhibit a wide range of observational properties \citep[e.g.,][]{velzen11,cenko12a,gezari12b,arcavi14, chornock14,holoien14b,gezari15,vinko15,holoien16a,holoien16b,brown16a,auchettl17,blagorodnova17,brown17a,brown17b,gezari17,holoien18a}. It is now known that the emission depends on many factors, including the physical properties of the disrupted star \citep[e.g.,][]{macleod12,kochanek16}, the evolution of the accretion stream after disruption \citep[e.g.,][] {kochanek94,strubbe09,guillochon13,hayasaki13,hayasaki16,piran15,shiokawa15}, and radiative transfer effects \citep[e.g.,][]{gaskell14,strubbe15,roth16,roth18}. However, there have been few TDEs monitored in sufficient detail to directly infer these properties. In particular, most TDE candidates have been discovered after peak light, making it difficult to study the formation of the accretion disk and the evolution of the stellar debris. Here we present the discovery of PS18kh, a TDE candidate discovered by the Pan-STARRS Survey for Transients\footnote{\url{https://star.pst.qub.ac.uk/ps1threepi/psdb/}} \citep[PSST;][]{chambers16} on 2018 March 02 in the spectroscopically unobserved galaxy SDSS J075654.53+341543.6. The discovery was announced publicly on 2018 March 04 on the Transient Name Server (TNS) and given the designation AT 2018zr\footnote{\url{https://wis-tns.weizmann.ac.il/object/2018zr}}. The discovery image indicated that the position of the transient was consistent with the nucleus of the host, with the Pan-STARRS coordinates lying within 0\farcs{1} of the measured center of the host in SDSS. The transient was first spectroscopically observed by the Spectral Classification of Astronomical Transients \citep[SCAT;][]{SCATref} survey, which uses the SuperNova Integral Field Spectrograph \citep[SNIFS;][]{lantz04} on the University of Hawaii 88-inch telescope. The initial spectrum obtained on 2018 March 07 showed a blue continuum with no obvious emission or absorption features, and a second spectrum obtained on 2018 March 18 was very similar, with a strong blue continuum, but with the possible addition of broad Balmer emission lines \citep{ps18kh_spec_atel}. Based on these spectra, we obtained two additional low-resolution optical spectra on 2018 March 20 with the Wide Field Reimaging CCD Camera (WFCCD) mounted on the Las Campanas Observatory du Pont 2.5-m telescope ($3700-9600$~\AA, $\rm R\sim 7$~\AA) and the Fast Spectrograph \citep[FAST;][]{fabricant98} mounted on the Fred L. Whipple Observatory Tillinghast 1.5-m telescope ($3700-9000$~\AA, $\rm R\sim 3$~\AA). Both of these spectra also suggested the presence of broad Balmer emission lines with a strong blue continuum, both features of TDEs \citep[e.g.,][]{arcavi14}, and \citet{ps18kh_spec_atel} publicly announced that PS18kh was a TDE candidate on 2018 March 24. Based on \ion{Ca}{2} H\&K absorption lines visible in the spectra, PS18kh has a redshift of $z=0.071$, corresponding to a luminosity distance of 322 Mpc ($H_0=69.6$~km~s$^{-1}$~Mpc$^{-1}$, $\Omega_M=0.29$, $\Omega_{\Lambda}=0.71$; see Section~\ref{sec:params}). Based on the preliminary classification, we requested and were awarded target-of-opportunity (TOO) observations from the \textit{Neil Gehrels Swift Gamma-ray Burst Mission} \citep[\swift;][]{gehrels04} UltraViolet and Optical Telescope \citep[UVOT;][]{roming05} and X-ray Telescope \citep[XRT;][]{burrows05}. These observations confirmed that the transient was bright in the UV and appeared to have weak soft X-ray emission, so we began an extended multi-wavelength monitoring campaign to characterize PS18kh. With a peak $g$-band magnitude of $m_g\simeq17.3$, PS18kh was also well-observed by a number of ground-based optical surveys, and we include in our analysis multiwavelength pre- and post-discovery light curves from Pan-STARRS, the All-Sky Automated Survey for Supernovae \citep[ASAS-SN;][]{shappee14}, and the Asteroid Terrestrial-impact Last Alert System \citep[ATLAS;][]{tonry18} spanning from 56 days before the peak of the light curve until it became Sun-constrained 75 days after peak, making this one of the best-sampled early light curves for a TDE candidate to-date. In Section~\ref{sec:obs} we describe the available pre-outburst data for the host galaxy and fit the physical properties of the host. We also describe the new observations of the transient that were obtained by the Pan-STARRS, ASAS-SN, and ATLAS surveys and our follow-up campaign. In Section~\ref{sec:params} we perform detailed measurements of the position of PS18kh within its host, its redshift, and the time of peak light. In Section~\ref{sec:phot_anal} we analyze the photometric data and model the luminosity and temperature evolution of PS18kh. In Section~\ref{sec:spec_anal} we analyze the spectroscopic evolution of PS18kh and model the boxy, double-peaked emission line profiles in an attempt to determine the physical properties of the TDE-SMBH system. Finally, in Section~\ref{sec:disc} we compare the properties of PS18kh to those of supernovae and other TDEs and summarize our findings. | \label{sec:disc} The temperature, luminosity, radius and spectroscopic evolution of PS18kh are all consistent with other TDEs. However, many of these features are also common to type II superluminous supernovae (SLSNe II), and some of the observational characteristics of PS18kh (e.g., the UV re-brightening and the double-peaked line profiles) are not common to most (or any) other TDEs. In this Section we compare its luminosity, temperature, radius, and spectroscopic evolution to those of TDEs and SLSNe in literature to further investigate the nature of PS18kh. Our sample of comparison objects includes the TDEs ASASSN-14ae \citep{holoien14b}, ASASSN-14li \citep{holoien16a}, ASASSN-15oi \citep{holoien16b}, and iPTF16fnl \citep{brown17b}, and the supernovae SN 2008es \citep{miller09,gezari09b}, SN 2013hx \citep{inserra18}, and PS15br \citep{inserra18}. The SN sample was chosen because these are the only three SLSNe that show both a broad \halpha{} feature and no signs of strong interaction between fast moving ejecta and circumstellar shells in their early spectra \citep{inserra18}, making them spectroscopically similar to PS18kh. Also included in our comparison sample is ASASSN-15lh, an extremely luminous transient whose nature has been debated, but which is likely either the most luminous SLSN ever discovered \citep{dong16,godoy-rivera17} or an extreme TDE around a maximally spinning black hole \citep{leloudas16}. ASASSN-15lh also exhibited a UV re-brightening, similar to PS18kh \citep{godoy-rivera17}, making it an interesting comparison object. The left panel of Figure~\ref{fig:lum_comp} shows the rest-frame luminosity evolution of PS18kh and the transients in our comparison sample, with TDEs and SNe differentiated by color. The TDE sample has peak luminosities in the range $10^{9.8}$\lsun$\lesssim L \lesssim 10^{10.8}${\lsun} while the SN sample ranges from $10^{10}\lsun\lesssim L \lesssim 10^{10.8}\lsun$, meaning the luminosity of PS18kh is consistent with both types of object. ASASSN-15lh is clearly an outlier in peak luminosity from all the other objects in the sample, including PS18kh. While none of the TDEs in the sample were discovered prior to peak, preventing a comparison of the rising phase of the light curve, the rise time of PS18kh seems to be roughly consistent with that of the SNe in the sample. \begin{figure} \centering \includegraphics[width=0.425\textwidth]{temp_comp_all.pdf} \caption{Temperature evolution of PS18kh taken from blackbody fits to epochs with {\swift} observations compared with the temperature evolution of the objects in our comparison sample. Symbols and colors match those of Figure~\ref{fig:lum_comp} and all times are plotted in days relative to peak or discovery, as outlined in the caption of Figure~\ref{fig:lum_comp}.} \label{fig:temp_comp} \end{figure} To examine the similarity of the re-brightening seen in the light curves of PS18kh and ASASSN-15lh, we scaled the peak luminosity of PS18kh by a factor of 24.5 to match the peak of ASASSN-15lh, and shifted the light curve of PS18kh by 15 rest-frame days so that the peak of the PS18kh light curve aligns with the highest measured luminosity of ASASSN-15lh. The resulting comparison is shown in the right panel of Figure~\ref{fig:lum_comp}. PS18kh rises a bit more steeply than ASASSN-15lh does, but after peak the rate of decline is very similar between the two objects. PS18kh begins to re-brighten sooner, with the rise beginning at $t\simeq59$~rest-frame days, while ASASSN-15lh begins to re-brighten at $t\simeq73$ rest-frame days, but the shape of the two light curves is very similar. Assuming PS18kh is a TDE, this perhaps lends credence to the interpretation that ASASSN-15lh was the result of a TDE. However, the two objects differ in other respects, such as their temperature and radius evolution and their spectroscopic features (see Figures~\ref{fig:temp_comp}, \ref{fig:rad_comp}, and \ref{fig:spec_comp}), which indicates that the physical mechanisms responsible for the re-brightening likely differ between the two transients. Figure~\ref{fig:temp_comp} shows the evolution of the temperature measured from the blackbody fits to the {\swift} observations of PS18kh compared to the temperature evolution of the other objects in our comparison sample. All three hydrogen-rich SLSNe show a very similar temperature evolution, with the temperature declining steadily from a peak of $T\sim10000$~K, while the TDEs all show either rising or constant temperature evolution, with temperatures in the range of $10000~\textrm{K}\lesssim T \lesssim 50000$~K. ASASSN-15lh clearly stands out from the other objects, showing both a decline similar in shape to that of the hydrogen-rich SLSNe, and a later rise similar to that of the TDEs. The temperature evolution of PS18kh very strongly resembles that of ASASSN-14ae in both shape and magnitude, including a rising temperature after $t\sim40$~days. This evolution strongly differentiates it from the SLSN sample and from ASASSN-15lh. Figure~\ref{fig:rad_comp} shows the evolution of the radius measured from the blackbody fits to the {\swift} observations of PS18kh compared to the radius evolution of the other objects in our comparison sample. All three hydrogen-rich SLSNe and ASASSN-15lh stand out very clearly from the TDEs and PS18kh. While the SNe show larger and relatively constant photospheric radii, all the TDEs show a declining radius. PS18kh again very closely resembles ASASSN-14ae in the shape and magnitude of its radius evolution, and is clearly differentiated from the SLSN sample and ASASSN-15lh. Finally, in Figure~\ref{fig:spec_comp} we compare spectra of PS18kh to those of ASASSN-14ae, SN 2013hx, and ASASSN-15oi at two similar rest-frame phases (near peak/discovery and roughly 40 days after peak/discovery). In the early epoch, the spectra of PS18kh resembles both that of ASASSN-14ae and that of SN 2013hx, with a broad \halpha{} emission feature and strong, blue, relatively featureless continuum. However, the later epoch clearly differentiates PS18kh from the SLSN, as both ASASSN-14ae and PS18kh continue to exhibit fairly strong continuum emission and broad hydrogen emission features, while the continuum shape of the spectra of SN 2013hx has started to change, reflecting its cooling temperature, and a number of absorption features have appeared. The spectra of ASASSN-15lh show almost no evolution at all between the two epochs, as it exhibits very blue spectra with broad absorption features at bluer wavelengths and no emission features, and it is clearly differentiated from the other three objects. \begin{figure} \centering \subfloat{{\includegraphics[width=0.47\textwidth]{rad_comp_all.pdf}}} \caption{Radius evolution of PS18kh taken from blackbody fits to epochs with {\swift} observations compared with the radius evolution of the objects in our comparison sample. Symbols and colors match those of Figure~\ref{fig:lum_comp} and all times are plotted in days relative to peak or discovery, as outlined in the caption of Figure~\ref{fig:lum_comp}. The left scale shows the radius in units of cm, while the right scale gives the corresponding radius in units of the gravitational radius for a $10^7$~\msun~black hole.} \label{fig:rad_comp} \end{figure} \begin{figure*} \begin{minipage}{\textwidth} \centering \subfloat{{\includegraphics[width=0.48\textwidth]{spec_comp1.pdf}}} \subfloat{{\includegraphics[width=0.48\textwidth]{spec_comp2.pdf}}} \caption{\emph{Left Panel}: Spectra of PS18kh (black), ASASSN-14ae \citep[red;][]{holoien16a}, ASASSN-15lh \citep[blue;][]{dong16}, and SN 2013hx \citep[green;][]{inserra18} taken at similar phase shortly after rest-frame peak. (Phase for ASASSN-14ae is in days relative to discovery, as it was discovered after peak light.) Spectra have been offset for clarity and the phase is indicated to the right of each spectrum. {Right Panel}: Spectra of the same four objects taken 37$-$39 days after rest-frame peak/discovery.} \label{fig:spec_comp} \end{minipage} \end{figure*} These comparisons show that luminosity evolution does not differentiate between SLSNe and TDEs at early times---while SLSNe tend to be more luminous, objects from both the TDE and SLSN samples show similar peak luminosities and decline rates. Conversely, TDEs and SLSNe quickly differentiate themselves in their temperature, radius, and spectroscopic evolution. SLSNe have smoothly declining temperatures, growing or relatively constant photospheric radii, and absorption features emerge in the spectra over time. TDEs exhibit constant or rising temperatures, shrinking photospheres, and consistently blue spectra with broad hydrogen and helium emission features. ASASSN-15lh is an outlier from both comparison groups in some respects, although its radius evolution very closely matches the SLSN sample and no TDE has shown similar spectra, while numerous SLSNe have similar spectroscopic evolution. While the shape of its luminosity evolution curve is somewhat similar to that of PS18kh, it is more luminous than any other object in the sample, it has a unique temperature evolution, and its spectra show little-to-no evolution between peak light and $\sim40$ days after peak light, with no evidence of the broad hydrogen emission features seen in the other objects' spectra. It is clear from these comparisons that despite the uniqueness of its light curve shape and the double-peaked line profiles, PS18kh bears a strong resemblance to other known TDEs, and this is the most likely origin for the emission we see during the outburst. Our early survey observations allow us to see the rise to peak light in multiple bands and to estimate its luminosity prior to peak, where we see that a significant fraction of the total early radiated energy is emitted during the rise to peak. UV observations obtained prior to peak will allow us to fit the blackbody SED and better quantify the fraction of energy emitted early for future TDE discoveries. Having concluded that PS18kh is likely a TDE, we present a final comparison between it and other TDEs with similar spectroscopic coverage in Figure~\ref{fig:fwhm_comp}. In the Figure we show the FWHM of the most prominent spectroscopic emission line in PS18kh and a sample of TDEs from ASAS-SN and iPTF near peak brightness or near discovery and 20$-$30 days later compared to the luminosity of the TDE at similar times and the mass of the black hole. Data for comparison objects are taken from \citet{hung17}. Comparing the emission line FWHM to luminosity (left panel of Figure~\ref{fig:fwhm_comp}, we see that in all cases the FWHM of the line decreases as the luminosity decreases, with no particular correlation between decline rate or absolute luminosity and FWHM. The comparison between line FWHM and black hole mass (right panel of the Figure) also indicates that there seems to be little correlation between these two properties, with the TDEs in the sample exhibiting a range of FWHM values and decline rates despite spanning roughly 1.5 orders of magnitude in black hole mass. \begin{figure*} \begin{minipage}{\textwidth} \centering \subfloat{{\includegraphics[width=0.48\textwidth]{fwhm_lum.pdf}}} \subfloat{{\includegraphics[width=0.48\textwidth]{fwhm_mass.pdf}}} \caption{\emph{Left Panel}: FWHM of the H$_\alpha$ line (circles) or \ion{He}{2} line (triangles) compared to luminosity for PS18kh and several TDEs from \citet{hung17} for epochs close to peak/discovery (filled points) and epochs 20-30 rest-frame days later (open points). Phase relative to peak/discovery is shown for each point, with an asterisk noting phase relative to discovery (as opposed to phase relative to peak). For PS18kh we show both the epoch at peak and the epoch 6 days later, as the FWHM initially increases before beginning to decline, as seen in the other TDES. {Right Panel}: Comparison of the FWHM of the same lines and epochs to the black hole mass for the same TDEs.} \label{fig:fwhm_comp} \end{minipage} \end{figure*} The early spectroscopic coverage of PS18kh also lets us look at the FWHM of the line at peak, compared to the evolution a few days later, and for the initial few days after peak the FWHM of the H$\alpha$ line increases. The only other TDE in the sample with similarly early coverage, iPTF16fnl, does not show the same behavior, so while it is clear that after an initial period the lines become narrower as the luminosity decreases, it is not clear whether the initial broadening seen in PS18kh is common or not. This highlights the need for more TDEs with spectra before, during, and shortly after peak brightness, as these times are largely unobserved for most TDEs in literature, and thus we cannot draw strong conclusions about possible correlations between the spectroscopic features and the TDE flare or black hole at these times. PS18kh is the third TDE, after PTF09ge and ASASSN-14li \citep{arcavi14,liu17b,cao18}, to exhibit emission lines that can be fit by an elliptical disk model, and the first to have spectroscopic coverage prior to and throughout the peak of the light curve. Our modeling allows us to see the likely origin of the broad emission features that are ubiquitous in optically discovered TDEs, and to develop a physical picture for how these lines form in the early stages after the star is disrupted. Similarly detailed datasets will allow us to perform similar analysis on future TDEs, and will be able to tell us whether the model parameters seen in PS18kh are common to all TDEs, or whether there is a range of physical properties that can produce the observations we see. Real-time, high-cadence sky surveys like Pan-STARRS, ASAS-SN, and ATLAS will be able to provide early detection and long-term monitoring of future TDEs, providing us with a population of objects to study to further develop our physical understanding of these highly energetic events. | 18 | 8 | 1808.02890 |
1808 | 1808.05154_arXiv.txt | A differential algebra based importance sampling method for uncertainty propagation and impact probability computation on the first resonant returns of Near Earth Objects is presented in this paper. Starting from the results of an orbit determination process, we use a differential algebra based automatic domain pruning to estimate resonances and automatically propagate in time the regions of the initial uncertainty set that include the resonant return of interest. The result is a list of polynomial state vectors, each mapping specific regions of the uncertainty set from the observation epoch to the resonant return. Then, we employ a Monte Carlo importance sampling technique on the generated subsets for impact probability computation. We assess the performance of the proposed approach on the case of asteroid (99942) Apophis. A sensitivity analysis on the main parameters of the technique is carried out, providing guidelines for their selection. We finally compare the results of the proposed method to standard and advanced orbital sampling techniques. | Over the last thirty years, significant efforts have been devoted to develop new tools for detection and prediction of planetary encounters and potential impacts by Near Earth Objects (NEO). The task introduces relevant challenges due to the imperative of early detection and accurate estimation and propagation of their state and associated uncertainty set \citep{Chesley2005}. The problem is made more complicated by the fact that the dynamics describing the motion of these objects is highly nonlinear, especially during close encounters with major bodies. Nonlinearities of the orbital dynamics tend to significantly stretch the initial uncertainty sets during the time propagation. Nonlinearities are not confined to object dynamics only: even simple conversions between coordinate systems introduce nonlinearities, thus affecting the accuracy of classical propagation techniques \citep{Wittig2015}. Present day approaches for robust detection and prediction of planetary encounters and potential impacts by NEO mainly refer to linearised models or full nonlinear orbital sampling \citep{Farnocchia2015}. The impact probability computation by means of linear methods in the impact plane was introduced by \citet{Chodas1993}, whereas the introduction of the Monte Carlo technique to this problem was developed by \citet{Yeomans1994} and \citet{Chodas1999a}, who suggested to apply the method to sample the linear six dimensional confidence region at the observation epoch and then numerically integrate over the time interval of investigation using fully nonlinear equations \citep{Milani2002}. \citet{Milani1999}, \citet{Milani1999a} and \citet{Milani2000,Milani2000a} applied the multiple solutions approach to sample the central Line of Variations (LOV) of the nonlinear confidence region at the initial epoch and then numerically integrate over the time span of interest in a similar way. Within the framework of the impact probability computation of resonant returns, a well-known approach relies on the concept of keyholes, small regions of the impact plane of a specific close encounter such that, if an asteroid passes through one of them, it will hit the Earth on subsequent return \citep{Gronchi2001,Milani2002,Valsecchi2003}. The preferred approach to detecting potential impacts depends on the uncertainty in the estimated orbit, the investigated time window and the dynamics between the observation epoch and the epoch of the expected impact \citep{Farnocchia2015}. Linear methods are preferred when linear approximations are reliable for both the orbit determination and uncertainty propagation. When these assumptions are not valid, one must resort to more computationally intensive techniques: among these, Monte Carlo methods are the most accurate but also the most computationally intensive, whereas the LOV method guarantees compute times 3-4 orders of magnitude lower than those required in MC simulations, though the LOV analysis may grow quite complex after it has been stretched and folded by multiple close planetary encounters, leaving open the possibility of missing some pathological cases \citep{Farnocchia2015}. Alternative approaches rely on the use of Differential Algebra (DA). Differential algebra supplies the tools to compute the derivatives of functions within a computer environment, i.e. it provides the Taylor expansion of the flow of Ordinary Differential Equations (ODEs) by carrying out all the operations of any explicit integration scheme in the DA framework \citep{Berz1999,Wittig2015}. DA has already proven its efficiency in the nonlinear propagation of uncertainties \citep{Armellin2010, Morselli2012,Valli2013}. Nonetheless, the accuracy of the method drastically decreases in highly nonlinear dynamics. The propagation of asteroids motion after a close encounter with a major body is a typical case. A DA based automatic domain splitting algorithm was presented by the authors in the past to overcome the limitations of simple DA propagation \citep{Wittig2014,Wittig2014a,Wittig2015}. The method can accurately propagate large sets of uncertainties in highly nonlinear dynamics and long term time spans. The propagation algorithm automatically splits the initial uncertainty domain into subsets when the polynomial expansions representing the current state do not meet predefined accuracy requirements. The performance of the algorithm was assessed on the case of asteroid (99942) Apophis, providing a description of the evolution of the uncertainty set to the epoch of predicted close encounters with Earth in 2036 and 2037 \citep{Wittig2015}. Though representing a significant improvement with respect to simple DA propagation, the approach required a not negligible computational effort in propagating the whole set of generated subdomains. Moreover, no information about the impact probability for asteroid Apophis was provided, as the propagation of the uncertainty set was stopped before the close encounters. We present in this paper an evolution of the automatic domain splitting algorithm. The method, referred to as automatic domain pruning, automatically identifies possible resonances after a close encounter with a major body. Then, assuming no intervening close approaches with other celestial bodies in between, it optimizes the propagation to the first resonant returns, by limiting the propagation of the uncertainty set to the regions that generate a close encounter with that celestial body at the investigated epoch. The result is a list of polynomial state vectors, each mapping only specific subsets of the initial domain to the resonant return epoch. Taking advantage of the availability of the polynomial maps, a DA based Monte Carlo importance sampling technique is then used to generate samples in the propagated subsets and provide an estimate for the impact probability at the epoch of the selected resonant return. The proposed approach does not apply any simplification step on the uncertainty domain associated with the orbit determination process. Thus, the method is proposed as an alternative approach with respect to equivalent techniques, such as a full Monte Carlo simulation or other six dimensional-based orbital sampling techniques, which will represent the main term of comparison for our analysis. The paper is organized as follows. First, we present a description of the automatic domain pruning and importance sampling techniques, showing the application to the case of the first resonant return. Then, we apply the method to the critical case of asteroid (99942) Apophis, providing an estimate of the impact probability for the resonant return in 2036. Finally, we carry out a sensitivity analysis on the main parameters of the method, presenting a comparison with standard and advanced orbital sampling techniques. | This paper introduced the combination of automatic domain pruning and importance sampling for uncertainty propagation and impact probability computation for Earth resonant returns of Near Earth Objects. The automatic domain pruning represents an evolution of the DA based automatic domain splitting technique, it allows us to estimate possible resonances after a planetary close encounter and limit the propagation of an uncertainty set to those subsets that may be involved in the resonant return of interest. During the propagation, the uncertainty domain is divided into subsets (Potentially Hazardous Subdomains) whose propagation stops just before the epoch of the resonant return. The identification of PHS's represents the starting point for the sampling phase. An importance sampling probability density function is defined over these subdomains and samples are drawn directly from this auxiliary pdf. We tested the ADP--IS method on the case of asteroid (99942) Apophis, providing an estimate for the impact probability in 2036. We carried out a sensitivity analysis on the main parameters of the method, providing general guidelines for their selection. The comparison with a standard Monte Carlo approach showed how the ADP--IS method can reduce the computation effort by more than two orders of magnitude, still granting the same accuracy level for the impact probability estimate. In addition, the current algorithm can be implemented to make use of parallelization techniques in both the ADP and the IS phase, thus significantly reduce the required computational time. All these considerations suggest that the method may be used as a valuable alternative to standard MC in all those cases in which the LOV method does not guarantee the required level of accuracy. Future developments include a more rigorous formulation of the reference orbital period for subsets pruning allowing us to extend the pruning algorithm to the more critical case of intervening close encounters with other celestial bodies between the two encounters, and the testing to a wider set of cases. | 18 | 8 | 1808.05154 |
1808 | 1808.02556_arXiv.txt | We study line driven winds for models with different radial intensity profiles: standard Shakura-Sunyaev radiating thin discs, uniform intensity discs and truncated discs where driving radiation is cutoff at some radius. We find that global outflow properties depend primarily on the total system luminosity but truncated discs can launch outflows with $\sim 2$ times higher mass flux and $\sim 50\%$ faster outflow velocity than non-truncated discs with the same total radiation flux. Streamlines interior to the truncation radius are largely unaffected and carry the same momentum flux as non-truncated models whereas those far outside the truncation radius effectively carry no outflow because the local radiation force is too weak to lift matter vertically away from the disc. Near the truncation radius the flow becomes more radial, due to the loss of pressure/radiation support from gas/radiation at larger radii. These models suggest that line driven outflows are sensitive to the geometry of the radiation field driving them, motivating the need for self-consistent disc/wind models. | Outflows are ubiquitous for many compact object systems with accretion discs, including cataclysmic variables (CVs), X-ray binaries (XRBs) and actve galactic nuclei (AGN). A possible mechanism for launching these outflows is radiation pressure due to spectral lines, so called line driving (Lucy and Solomon 1970, Castor, Abbott and Klein 1975). Simulating line driven winds is challenging because it requires both correctly modeling the microphysics governing the ionization state of the gas (Owocki, Cranmer \& Gayley 1996), and the macrophysics governing the hydrodynamics. Both are affected by the radiation field, the former most sensitive to the ionizing flux, and the latter to the flux in UV where there are very many spectral lines. Correctly treating the radiation field is thus critical in modeling line driven winds. For systems with accretion discs an important source of UV radiation is the disc itself. The earliest stationary, thin disc, models assumed that accretion energy, dissipated by an effective viscosity, is radiated as blackbody radiation (Shakura \& Sunyaev 1973). This standard accretion disc model allows one to calculate the temperature and spectral energy distribution (SED) for the entire disc. The disc structure and therefore the radiation field as well, are modified when one accounts for outflows acting as a sink of mass and angular momentum in the disc. This has been shown in both the context of CVs (Knigge 1999) and AGN (Laor \& Davis 2014) where radiation is thought to drive outflows. Further, in the context of AGN, microlensing observations suggest that optical emission regions of the lensed quasars are typically larger than expected from basic thin-disk models by factors of $\sim 3-30$ (e.g. Pooley et al. 2007). Both theory and observations suggest that the standard disc model is an incomplete description of the radiation field near accretion discs. Line driven disc wind simulations have shown that to first approximation global outflow properties (mass flux, outflow velocity and wind opening angle) depend only on the total system luminosity (Proga, Stone \& Drew 1998, hereafter PSD98). However the structure of the flow is sensitive to the geometry of the radiation field. Systems where radiation is sourced primarily from the disc have been found to have small scale structure in both 2D axisymmetric (Proga, Stone \& Drew 1999) and 3D (Dyda \& Proga 2018a, b, hereafter DP18a and DP18b) simulations. This suggests that to correctly model line driven winds we must move beyond the radiating thin disc, and compute the radiation field self consistently. Previous disc wind simulations used a frequency integrated disc intensity. Most spectral lines are in the UV so these models implicitly assume sufficient UV flux to drive the wind. If discs locally emit like blackbodies, there will be a range of radii for which the local disc spectrum peaks in the UV. Interior to some radii, where $T \gtrsim 30 \ 000 \ \rm{K}$ and exterior to some radii where $T \lesssim 7 \ 000 \ \rm{K}$ the spectra will peak outside the $10 \ \rm{nm} \lesssim \lambda_{\rm{UV}} \lesssim 400 \ \rm{nm}$ UV wavelengths, significantly limiting the flux of photons available to drive a wind with radiation pressure due to lines. Proga et al. (2004) investigated this issue in the case of AGN where they showed that even if the UV to X-ray flux ratio was lowered to 1:9, line driven winds could still be launched as when this ratio is 1:1 as in Proga et al. (2000). The full problem of multi-frequency radiation transfer is currently computationally intractable. Therefore as a first step we investigate the effects of changing the radial intensity profile as a proxy for a diminished UV photon flux. Our goal is to correlate the geometry of the radiation field and the geometry of the outflow, to investigte the disc/wind connection in line driven disc winds. In our previous studies of line driven disc winds we assumed the disc radiation field was sourced by a standard accretion disc, locally emitting like a blackbody. We consider two modificaions to this scenario. In one set of models, the intensity profile is as in the standard accretion disc, up until some outer truncation radius, $r_{\rm{c}}$, where the disc is assumed too cold to supply sufficient UV photons and the radiation field is exponentially suppressed. In the other set of models, we assume a constant radial intensity profile interior to the cutoff and keep the total disc luminosity fixed as we vary the truncation radius. We investigate how global outflow properties as well as the geometry of the flow are altered by varying the truncation radius, while controlling for the fact that to first approximation the solution is determined by the total system luminosity. The structure of this paper is as follows. In Section \ref{sec:numerical} we briefly describe our numerical methods and code. In Section \ref{sec:truncation} we describe the effects of varying the truncation radius on outflow properties. In Section \ref{sec:luminosity}, using uniform intensity disc models, we show that changes due to introducing a truncation radius cannot be explained solely due to a change in total disc luminosity. In Section \ref{sec:discussion} we discuss some observational implications for our models, describe some limitations of our approach and sketch some possible future directions for this work. | \end{table*} To study the effects of the radiation field on the flow geometry, we perform a series of disc wind simulations. The fiducial models (A, B, P \& R) correspond to standard radiating discs (see eq. \ref{eq:intensity_SS}) with Eddington fraction $3.76 \ \times 10^{-4} \leq \Gamma_d \leq 1.18 \ \times 10^{-2}$, where the disc is cutoff at $r = 30 \ r_*$ for computational reasons. For the three highest Eddington fraction models ($\Gamma_d = 1.18 \times 10^{-3}$, $3.76 \times 10^{-3}$ and $1.18 \times 10^{-2}$), we simulate discs where the cutoff radius $1.5 \ r_* \leq r_c \leq 4 \ r_*$ (see eq. \ref{eq:intensity}), which we denote by the letter corresponding to the model fiducial luminosity followed by the cutoff radius, i.e B1.5, ..., B4. Finally we perform simulations with a uniform intensity profile (see eq. \ref{eq:intensity_uniform}), where the cutoff again varies from $1.5 \ r_* \leq r_c \leq 4 \ r_*$ which we denote by U1.5, ..., U4. In Table \ref{tab:summary} we list all our model parameters, including the Eddington fraction $\Gamma_d$, truncation radius $r_{\rm{c}}$ and total disc luminosity multiplied by the maximum force multiplier (maximum effective number of lines) $L M_{\rm{max}}$. For each model we summarize the global outflow properties (mass flux $\dot{M}$, maximum outflow velocity $v_{\rm{max}}$ and opening angle $\omega$) and for the flow between streamlines with footpoints fixed at $r = 1.5 \ r_*$ and $r = 3.0 \ r_*$ we show the mean density $\bar{\rho}$, density weighted mean velocity $\bar{v}_r$ and angle between the streamlines $\Delta \omega$ at the outer boundary. \subsection{Truncation Effects} \label{sec:truncation} \begin{figure*} \centering \includegraphics[width=\textwidth]{density_summaryB.pdf} \caption{Time averaged density profile $\bar{\rho}$ (gray contours) and poloidal velocity field $\bar{\mathbf{v}}_p$ (black vectors) for $900 \ \rm{s} \leq t \leq 1000 \ \rm{s}$ for the different radiation models. The colored lines indicate streamlines with footpoint at $r = 1.5 \ r_*$ (red), $3.0 \ r_*$ (orange), $4.5 \ r_*$ (green) and $6.0 \ r_*$ (blue). We only plot streamlines that exit the computational domain. Streamlines interior to the truncation radius are largely unaffected whereas those exterior no longer carry mass out the simulation domain. Streamlines near the truncation radius become more radial, launching a less dense but faster flow.} \label{fig:time_averaged_winds_B} \end{figure*} \begin{figure*} \centering \includegraphics[width=\textwidth]{v_stream.pdf} \caption{Velocity parallel $v_{\parallel}$ (left panels) and perpendicular $v_{\perp}$ (right panels) to time-averaged streamlines shown in Fig. \ref{fig:time_averaged_winds_B} (colored lines) and the corresponding velocity dispersion (shaded region). Outflow velocity decreases very slightly with decreasing truncation radius until the footpoint is interior to the truncation radius and velocity is strongly suppressed. Note the different scales for $v_{\parallel}$ and $v_{\perp}$.} \label{fig:v_stream} \end{figure*} \begin{figure} \centering \includegraphics[width=0.45\textwidth]{mdot_avg.pdf} \includegraphics[width=0.45\textwidth]{vr_avg.pdf} \caption{Time-averaged solutions over $900 \ \rm{s} \leq t \leq 1000 \ \rm{s}$ for models B (black), B4 (red), B3 (green), B2 (blue) and B1.5 (purple) at the outer boundary $r = r_o$. \textit{Top -} Momentum flux $\rho v_r$ (solid lines) and $\theta-$integrated mass flux $\dot{m}$ (dashed lines) as a function of $\theta$. \textit{Bottom -} Velocity $v_r$ (solid lines) and density $\rho$ (dashed lines) as a function of $\theta$.} \label{fig:outflow_avg} \end{figure} \begin{figure} \centering \includegraphics[width=0.45\textwidth]{mdot_summary.pdf} \caption{Mass flux $\dot{M}$ at the outer boundary as a function of time (solid lines) and the time average over $200 \ \rm{s} \leq t \leq 1000 \ \rm{s}$ (dashed line). Time variability is $\sim 20\%$, irrespective of the model.} \label{fig:mdot_summary} \end{figure} We study the effects of radiation field geometry on the flow by varying the radius at which disc intensity is truncated, $r_c$. We choose Model B from DP18b as our fiducial model, and vary the cutoff radius $r_{\rm{c}} = 1.5 r_*, 2 r_*$, $3 r_*$ and $4 r_* $. In Fig. \ref{fig:time_averaged_winds_B}, we plot the time averaged density profile $\bar{\rho}$ (gray contours) and poloidal velocity field $\bar{\mathbf{v}}_p$ (black vectors) for $900 \ \rm{s} \leq t \leq 1000 \ \rm{s}$ for fiducial Model B and the related truncated disc models. The colored lines indicate streamlines with footpoint at $r = 1.5r_*$ (red), $3.0 r_*$ (orange), $4.5 r_*$ (green) and $6.0r_*$ (blue). The basic structure of the winds are very similar, with a low density polar funnel at small $\theta$, a fast-stream carrying most of the mass flux and hydrostatic disc. The wind opening angle is only weakly dependent on total disc luminosity, decreasing from $\omega = 55^{\circ}$ for model B to $\omega = 42^{\circ}$ for model B1.5. This is in line with our expectations whereby the truncated disc models opening angles are bounded from above by non-truncated models (B) and have similar opening angles to non-truncated models with similar total luminosity (model A). These disc wind solutions are non-stationary, so to investigate the effects of disc truncation on time-dependence, we consider the velocity dispersion. In Fig. \ref{fig:v_stream}, we plot the velocity parallel $v_{\parallel}$ and perpendicular $v_{\perp}$ to the time-averaged streamlines shown in Fig. \ref{fig:time_averaged_winds_B}, (colored lines) and the corresponding velocity dispersion (shaded region). We only plot the streamlines that exit the simulation domain, indicating that the flow is relatively stable. Truncating the disc has little effect on streamlines \emph{interior} to $r_c$. For example, all models have the streamline starting at $r = 1.5 r_*$ (red line) exiting the simulation domain. The outflow velocity is relatively constant with $v_{\parallel} \approx 3500 \rm{km/s}$ (model B) to $v_{\parallel} \approx 3000 \rm{km/s}$ (model B2). There is little change in the structure of the fast-stream, because its structure is primarily determined by streamlines in the innermost part of the disc. This explains why the mass flux, which is primarily determined by the fast-stream, is relatively unchanged in the truncated disc models. Streamlines \emph{exterior} to the cutoff radius become unstable and no longer carry mass out from the simulation domain so the line driving does not launch an outflow and only puffs up the disc. Near the disc, geometric foreshortening is important and the radiation force is approximately set by the local disc field. Therefore for $r > r_c$, the radiation force is too weak to vertically lift the gas above the disc where it experiences a force from the interior part of the disc. The exterior streamlines (not shown) typically travel radially inward, indicating that the radiation force is unable to balance gravity. Streamlines originating at radii smaller but close to $r_c$ are the most affected by the truncated disc. Gas is lifted upwards, and because gas exterior to it is not being launched, it feels a pressure gradient (relative to the non-truncated disc) that makes the streamline more radial. The flow is thus able to diverge more as the gas expands out into the region below the fast-stream. There is also a reduced radiation force from exterior parts of the disc which would also tend to make the flow more vertical. We see this most clearly from the streamline with footpoint at $r = 3 r_*$ (orange), which is exiting the domain at $\theta = 52^{\circ}$ for model B and $\theta = 64^{\circ}$ for model B3. By comparison, the $r = 1.5 r_*$ (red) streamline has only shifted from $\theta = 38^{\circ}$ to $\theta = 40^{\circ}$. Globally, the wind has changed very little between these two models, with the wind opening angle changing by only $\delta \omega \approx 5^{\circ}$. The change in separation between the two streamlines has changed from $\Delta \theta \approx 14^{\circ}$ to $26^{\circ}$, significantly more than the global wind opening angle. In Fig. \ref{fig:outflow_avg}, (top panel) we plot the mass flux $\rho v_r$ (solid lines) and $\theta-$integrated mass flux \begin{equation} \dot{m} = 2 \pi \int_0^{\theta} \rho(r_o,\theta') v_r(r_o,\theta') \ \sin \theta' d \theta', \end{equation} (dashed lines) as a function of $\theta$ at the outer boundary $r_o$, time-averaged over $900 \ \rm{s} \leq t \leq 1000 \ \rm{s}$ for models B (black), B4 (red), B3 (green), B2 (blue) and B1.5 (purple). The structure of the outflows is largely the same, with larger truncation radii runs transporting away more mass and having slightly wider opening angles. In the bottom panel, we plot the velocity $v_r$ (solid lines) and density $\rho$ (dashed lines) as a function of $\theta$ for the same models. Decreasing the truncation radii results in a decrease in the maximum outflow velocity. The angle of the velocity peak also increases as the truncation radii decreases, consistent with the angle of the momentum density peak which also increases. This corresponds to our expectation of the flow becoming more radial as the truncation radius is decreased and the driving force becomes more radial. We note that the velocity profile of model B and B4 are very similar, despite the total disc luminosity differing by $\sim 50 \%$. The fast-stream is formed from gas launched in the innermost parts of the disc $r \leq 4 \ r_*$. The local radiation field near the inner disc is the same for these models since B4 has $r_c = 4 \ r_*$. This results in similar fast-stream structures and nearly identical velocity profiles. The difference in the outflows appears for $\theta > 65^{\circ}$, where model B has a denser, slower wind than B4. Truncating the disc results in a less dense but faster wind and a decrease in mass flux of $\sim 45 \%$. The difference in outflows at larger inclination angles can be understood by considering the mass loading in the outermost parts of the flow. Beyond the truncation radius $r > r_c$ the vertical radiation force is weak, resulting in a decreased density. Once high enough above the disc, the gas is accelerated by the radiation field interior to the truncation radius (which are the same in both models). To first order the mass flux is determined by the total luminosity, which are approximately identical since it is dominated by the innermost parts of the disc. The truncated model B4 will therefore have a faster outflow velocity, owing to its decreased density due to suppressed mass loading. In Fig. \ref{fig:mdot_summary}, we plot mass flux $\dot{M}$ at the outer boundary as a function of time (solid lines) and the time average over $200 \ \rm{s} \leq t \leq 1000 \ \rm{s}$ (dashed line) for models B (black), B4 (red), B3 (green), B2 (blue) and B1.5 (purple). The mass flux is non-stationary with deviations ranging between 16\% (model B) to 29\% (model B4). We so no clear trend between time variability of solutions and truncation radius, which tended to be $\sim 20\%$, irrespective of the model. \subsection{Luminosity Scaling} \label{sec:luminosity} \begin{figure} \centering \includegraphics[width=0.45\textwidth]{mdot_global.pdf} \includegraphics[width=0.45\textwidth]{vmax_global.pdf} \caption{Global wind properties as a function of total system luminosity. Red symbols indicate Shakura-Sunyaev models, blue symbols the corresponding truncated disc models and green symbols the uniform disc models. The different symbol shapes indicate the Eddington parameter of the model, Model A (crosses), Model B (circle), Model P (diamond) and Model R (triangle). \textit{Top -} Mass flux $\dot{M}$ at the outer boundary as a function of total luminosity. The Shakura-Sunyaev models display an increasing trend in the mass outflow, with a sharp cutoff when $ L_d \ M_{\rm{max}} \gtrsim 1$. At higher Eddington fractions truncated models approach the CAK solution (green line). \textit{Bottom -} Maximum velocity $v_{\rm{max}}$ at the outer boundary as a function of total disc luminosity. Maximum velocity tends to decrease as the truncation radius decreases but the dependence is weaker than with non-truncated models because the fast-stream originates from streamlines close to the inner disc edge.} \label{fig:gloabl_vs_L} \end{figure} \begin{figure} \centering \includegraphics[width=0.45\textwidth]{density_stream.pdf} \includegraphics[width=0.45\textwidth]{velocity_stream.pdf} \caption{Fast-stream properties as a function of total system luminosity. Symbols have the same meaning as in Fig. \ref{fig:gloabl_vs_L} \textit{Top -} Average density $\bar{\rho}$ at the outer boundary in the fast-stream as a function of total luminosity. Truncated and non-truncated models show the same type of scaling with luminosity. \textit{Bottom -} Average outflow velocity $v_{r}$ in the fast-stream as a function of total disc luminosity. Non-truncated models are relatively luminosity indepenent, whereas truncated disc models show a slight increase in outflow velocity due to the fast-stream being slightly less dense.} \label{fig:stream_vs_L} \end{figure} \begin{figure*} \centering \includegraphics[width=\textwidth]{density_summaryU.pdf} \caption{Time averaged density profile $\bar{\rho}$ (gray contours) and poloidal velocity field $\bar{\mathbf{v}}_p$ (black vectors) for $900 \ \rm{s} \leq t \leq 1000 \ \rm{s}$ for uniform intensity disc. This is the same as Fig. \ref{fig:time_averaged_winds_B} but for model U.} \label{fig:time_averaged_winds_U} \end{figure*} To first approximation, line driven wind properties are determined by the total system luminosity. Hence to better isolate geometric effects due to to the radiation field we compare outflow properties as a function of the total system luminosity. In Fig. \ref{fig:gloabl_vs_L}, we plot global properties of the wind solutions, the time averaged mass flux $\dot{M}$ (top panel) and maximum outflow velocity $v_{\rm{max}}$ (bottom panel) as a function of total disc luminosity multiplied by the maximum force multiplier $L \ M_{\rm{max}}$, in units of the Eddington luminosity. Red symbols indicate Shakura-Sunyaev models, blue symbols the corresponding truncated disc models and green symbols the uniform intensity models. The different symbol shapes indicate the Eddington parameter of the model, Model A (crosses), Model B (circle), Model P (diamond) and Model R (triangle). When $L \ M_{\rm{max}} > 1$ the radiation force can overcome gravity to drive an outflow. Intuitively, this quantity can therefore be thought of as the imbalance between the radiation force and gravity. We see that mass flux increases as a function of system luminosity for the non-truncated Shakura-Sunyaev models (dashed red line), with a particularly sharp increase near $L \ M_{\rm{max}} \gtrsim 1$. This is consistent with results from PSD98 (see their Fig. 8). For fixed Eddington parameter, we see that the mass flux decreases as the truncation radius decreases (blue dashed lines). The decrease in mass flux is less than predicted from the overall drop in luminosity however, with the non-truncated models (red dashed line) being a factor of $\sim 2$ below the truncated models with the same luminosity (dashed blue line). This is consistent with our understanding of the flow geometry that streamlines interior to the cutoff are largely unaffected by truncation and since these carry the bulk of the mass flux, the global outflow properties are therefore less affected by the truncation radius than one would predict from relying only on total disc luminosiy. We see that at higher luminosity and small truncation radius the mass flux approaches the scaling expected from CAK (solid green line). As the truncation radius is decreased, the radiation field becomes more spherically symmetric and we therefore expect better agreement with CAK. Our line driving treatment includes a maximum force multiplier which puts an upper limit on the radiation force as the gas becomes optically thin. The CAK solution therefore \emph{overestimates} mass fluxes at lower luminosities when the force multiplier is saturated. The maximum outflow velocity of non-truncated models likewise shows a decrease as the total system luminosity decreases (red dashed line). As with the mass flux, decreasing the truncation radius leads to a decrease in maximum outflow velocity. However, we see this dependence is weaker, particularly when $r_c = 4 r_*$ and the outflow velocity is barely affected. The maximum velocity occurs in the fast-stream, so as with mass flux this part of the wind is not strongly affected by introducing a cutoff. When the truncation radius is small, $r_c = 1.5 r_*$, the velocity is $\sim 50\%$ greater than for non-truncated models with the same luminosity. In Fig. \ref{fig:stream_vs_L}, we plot properties of the outflow bounded by streamlines with footpoints at $r = 1.5 \ r_*$ and $r = 3.0 \ r_*$. We show the average wind density $\bar{\rho}$ (top panel) and the density weighted outflow velocity $\bar{v}_r$ (lower panel) as a function of total disc luminosity $L \ M_{\rm{max}}$. Meanings of symbols are as in Fig. \ref{fig:gloabl_vs_L}. Density of non-truncated (red dashed line) and truncated (blue dashed lines) models scale approximately the same way for $L \ M_{\rm{max}} \gg 1$ with $\bar{\rho} \sim L^{4/3}$. Near $L \ M_{\rm{max}} \gtrsim 1$ the density drops sharply as we expect from the behaviour of the total mass flux. The velocity of non-truncated models are relatively luminosity indepenent (red dashed line), whereas truncated disc models show an increase in outflow velocity (dashed blue lines). Our analysis showed that mass flux scales approximately with the total luminosity. Therefore, since the density in the fast-stream is lower with decreased luminosity, the velocity must therefore increase. As with the maximum outflow velocity, this increase is approximately $50 \%$ above the non-truncated models. We conclude that truncating the disc allows us to launch \emph{faster} outflows for a given disc luminosity. Our analysis of winds driven by a truncated Shakura-Sunyaev radiation fields suggests that differences in outflow cannot be explained solely by differences in total disc luminosity. To further isolate geometric effects from those of system luminosity we study models with fixed luminosity and variable truncation radius. These models are denoted by the prefix U in Table \ref{tab:summary}. The Eddington fraction is chosen so that the total disc luminosity corresonds to the Shakura-Sunyaev luminosity $L_{SS}$ of a disc with Eddington fraction $1.18 \times 10^{-3}$ of the fiducial model (B) and $L M_{\rm{max}} = 15.6 \ L_{\rm{Edd.}}$. In Fig. \ref{fig:time_averaged_winds_U}, we plot the time averaged density profile $\bar{\rho}$ (gray contours) and poloidal velocity field $\bar{\mathbf{v}}_p$ (black vectors) for $900 \ \rm{s} \leq t \leq 1000 \ \rm{s}$ for uniform luminosity disc models (The analogue to Fig. \ref{fig:time_averaged_winds_B} for model U). Uniform disc winds have a more vertical flow, since the radiation force at the base of the wind does not decrease as distance from the center increases. We can particularly see this with the innermost streamlines of U4, where they do not significantly diverge. For even the most truncated case, all streamlines exit the simulation domain, indicating that the flow is less variable at large radii than for truncated Shakura-Sunyaev models. The total mass flux still varies by $\sim 20\%$ however, suggesting that non-stationarity is a feature of disc winds, irrespective of the radial dependence of the radiation intensity. Unlike with the Shakura-Sunyaev disc, truncating the uniform disc has little effect on the global outflow properties. There is a slight decrease in the total mass flux ($\sim 25 \%$) and a slight increase in the maximum outflow velocity ($\sim 25\%$), but these are not evident from the momentum flux profiles. The shape of the outflow does not change noticably, in terms of the location of the fast-stream (shifted by only $3^{\circ}$) and by the peak in the velocity profile (unchanged). In the fast-stream we find that density decreases by a factor of $\sim 2$ as truncation radius decreases from $4 r_*$ to $1.5 r_*$. The velocity increases by a factor of $\sim 2$, as we would expect for the outflows to have constant mass flux. Our conclusion is the same as from the Shakura-Sunyaev cases, namely that truncating the disc allows us to have \emph{faster} outflows, for fixed disc luminosity. Truncated disc models have higher mass fluxes than non-truncated models with the same total luminosity. We showed that though global outflow properties approximately scale with total system luminosity, radiation field geometry does play an effect. Truncating the disc can yield outflows with $\sim 2$ times greater mass flux and $\sim 50\%$ greater outflow velocity than a non-truncated disc with the same total disc luminosity. Geometry plays a crucial role in determining the ionization state of the wind. Altering the geometry of the UV radiation field changes the geometry of the flow, which alters the ionization state for a particular model of ionizing flux. Alternatively, with a fixed flow geometry, the ionization state changes in changing from a point to an extended ionization source. This points to the inevitable conclusion that correctly infering the radiation field geometry is critical in determining the strength and shape of the wind. The problem is further coupled by the fact that more accurate models of the radiation force due to lines is affected by the ionization state of the gas, which we neglect in the present work. These issues will have to be confronted if we are to properly study the question of self-shielding in AGN for example (see Matthews et al. 2016). We showed that truncating the disc radiation alters the flow near the disc where radiation is suppressed. In the present work we have neglected both thermal and magnetic driving. Though these effects may be too weak to fully overcome gravity, our analysis suggests that this requirement may be too strong a condition as gas must only be lifted high enough above the disc so it may be radiated by the inner disc. It may be possible to radiatively drive outflows where $L M_{\rm{max}} \ll 1$ locally, provided that thermal/magnetic forces are strong enough to lift the gas high enough to overcome geometric foreshortening. Our work has shown that outflows are sensitive to the local radiation field, particularly near the disc where geometric foreshortening is important. An important next step is to compute the local UV intensity at every point in the wind, and use this as the source of line driving. This is different from our current setup, where frequency is integrated locally and this frequency integrated intensity is used to compute the intensity in the wind. If we maintain the assumption that the wind is optically thin to the continuum, intensity is time independent so this computation can be precalculated and simulations performed with no loss in computational efficiency. Our model assumes the radiation field is sourced by a standard accretion disc. However, mass loss in the disc due to outflowing gas explicitly violates the assumption of mass and angular momentum conservation on which this model is based. It is important therefore to model the disc accretion so that the local radiation field can be computed self-consistently. The first step is to introduce an $\alpha-$viscosity as in Shakura \& Sunyaev (1973) and compute the local Eddington fraction as a function of the local accretion rate. This will not significantly increase computational time for the radiation force since we are already integrating over the full disc at every time step to compute the radiation force. The $\alpha$ prescription will add viscous terms to the momentum and energy equations, but this is less computationally expensive than the radiation force since it depends only on local velocity gradients and does not require integrating over the disc. Beyond these models, such as fully resolving the magnetrorotational instability and computing disc accretion without relying on $\alpha-$viscosity, our current approach will no longer be consistent as the disc can no longer be considered optically thin and the key model assumption that the radiation field is emitted from the midplane breaks down. Such an approach is important because a time-varying accretion rate will lead to a time-varying radiation flux. Time-varying radiation fields have been shown to produce density and velocity perturbations at the base of line driven winds (Dyda \& Proga 2018c) and such an approach is necessary to understand disappearing BALs in AGN for example. This approach will require the use full radiation transfer, which we will leave to future work. This work has focused on computing the correct UV flux, responsible for mediating momentum transfer between the radiation field and the gas. Equally important for line driving is correctly computing the internal state the gas. The ionization parameter in the wind depends on the radiation field of the X-rays. Determining the ionization state of the gas is required to self-consistently calculate the force due to line driving, as the force multiplier depends on $\xi$ (Dannen et al. 2018 in prep). Further we should go beyond the isothermal approximation and compute heating/cooling from the relevant SED (Dyda et al 2017), because temperature too can affect the number of available lines and thermal driving may alter the global outflow properties. | 18 | 8 | 1808.02556 |
1808 | 1808.09969_arXiv.txt | The fast radio burst FRB 121102 has repeated multiple times, enabling the identification of its host galaxy and of a spatially-coincident, compact, steady (`persistent') radio synchrotron source. It was proposed that FRB 121102 is powered by a young flaring magnetar, embedded within a decades-old supernova remnant. Using a time-dependent one-zone model, we show that a single expanding magnetized electron-ion nebula (created by the same outbursts likely responsible for the FRBs) can explain all the basic properties of the persistent source (size, flux, self-absorption constraints) and the large but decreasing rotation measure (RM) of the bursts. The persistent emission is powered by relativistic thermal electrons heated at the termination shock of the magnetar wind, while the RM originates from non-relativistic electrons injected earlier in the nebula's evolution and cooled through expansion and radiative losses. The model contains few free parameters, which are tightly constrained by observations: the total energy injected into the nebula over its history, $\sim 10^{50}-10^{51}$ erg, agrees with the magnetic energy of a millisecond magnetar; the baryon loading of the magnetar outflow (driven by intermittent flares) is close to the neutron star escape speed; the predicted source age $\sim 10-40$ years is consistent with other constraints on the nebula size. For an energy input rate $\dot{E} \propto t^{-\alpha}$ following the onset of magnetar activity, we predict secular decay of the RM and persistent source flux, which approximately follow ${\rm RM} \propto t^{-(6+\alpha)/2}$ and $F_{\nu} \propto t^{-(\alpha^2+7\alpha-2)/4}$, respectively. | Fast radio burts (FRB) are short pulses of coherent radio emission lasting less than a few milliseconds \citep{Lorimer+07,Keane+12, Thornton+13, Spitler+14, Ravi+15, Petroff+16, Champion+16,Lawrence+17} with large dispersion measures (DM $\approx 300-2000 \,{\rm pc\, cm^{-3}}$), well above the contribution from the Milky Way and thus implicating an extragalactic origin. The cosmological distance of at least one FRB was confirmed by the discovery of a repeating FRB~121102 \citep{Spitler+14,Spitler+16} and its subsequent localization \citep{Chatterjee+17} to a dwarf star-forming galaxy at a redshift of $z=0.1927$ \citep{tbc+.2017}. Radio interferometric localization of FRB~1211012 revealed a compact (size $<$ 0.7 pc) luminous ($\nu L_{\nu} \sim 10^{39}$~erg\,s$^{-1}$) steady radio synchrotron source coincident to within $\lesssim 40 \, {\rm pc}$ of the FRB location \citep{mph+.2017}. Another important clue to FRB~121102 comes from its enormous rotation measure, RM $\sim 10^{5}$ rad m$^{-2}$ (\citealt{Michilli+18}; see also \citealt{Masui+15}), which greatly exceeds those of other known astrophysical sources, with the exception of Sgr A* and the flaring magnetar SGR J1745-2900 located in the Galactic Center \citep{Eatough+13}. Though dozens of models have been proposed for FRBs, most are ruled out by a repeating, cosmological source like FRB~121102. Among the few surviving possibilities are bursts created from a young flaring magnetar \citep{Popov&Postnov13,Lyubarsky14,Kulkarni+14,Katz16,Lu&Kumar16,Metzger+17,Nicholl+17c,Kumar+17,Beloborodov17,Lu&Kumar17}. Supporting this connection are the atypical properties of the host galaxy of FRB~121102, particularly its small size and high specific star formation rate \citep{Bassa+17}, which are similar to those which preferentially host long gamma-ray bursts and superluminous supernovae \citep{Metzger+17}, transient events independently attributed to magnetar birth (e.g.~\citealt{Duncan&Thompson92,Thompson+04,Kasen&Bildsten10}). In such a model, the spatially-coincident persistent radio source could be understood as emission from a compact magnetized nebula surrounding the young (decades to centuries old) neutron star, embedded behind the expanding supernova ejecta shell \citep{Murase+16,Metzger+17,Kashiyama&Murase17,Omand+18}. The nebula is powered by nearly continual energy release from the magnetar, likely during the same sporadic flaring events responsible for the repeated radio bursts \citep{Beloborodov17}. While no single piece of evidence supporting the magnetar model for FRB~121102 is alone convincing, in aggregate the weight of evidence becomes more compelling. In $\S\ref{sec:magnetar}$, we briefly summarize the physical model and current observational constraints. In $\S\ref{sec:model}$ we present a one-zone model for an expanding magnetized electron-ion wind nebula surrounding the young flaring neutron star. For physically-motivated parameters, we show that the properties of FRB~121102 and its persistent source are quantitatively consistent with the magnetar model. Based on this surprisingly tightly constrained `concordance picture', we make predictions for the future evolution of the source properties. | The radio flux and RM contribution of an expanding magnetized electron-ion nebula, inflated behind the supernova ejecta by a flaring young magnetar, are consistent with the observed properties of the repeating burster FRB 121102 for source ages $t_{\rm age} \sim 10-40$ yr consistent with a variety of other observational constraints (Fig.~\ref{fig:timescales}). Our model predicts the presence of a self-absorption turnover in the spectral energy distribution that should be observable with low frequency observations. Our detailed calculations broadly follow the scenario outlined by \citet{Beloborodov17}. However, we find that non-thermal particle acceleration or sustained heating of the nebular electrons (e.g. \citealt{Yang+16}) is not required. Thermal heating of electrons at the termination shock, for wind baryon-loading $\chi \sim \chi_{\rm min}$ inferred from giant Galactic flares \citep{Granot+06} and the natural scale set by the gravitational potential of a neutron star, is sufficient to explain all the available observations. We predict approximate power-law decays of the RM $\propto t^{-(6+\alpha)/2}$ and persistent source flux $F_{\nu} \propto t^{-(\alpha^2+7\alpha-2)/4}$ (eqs.~\ref{eq:R17_constraint_RM},\ref{eq:Lnu}), where $\alpha \gtrsim 1$ sets the magnetar energy injection rate, $\dot{E} \propto t^{-\alpha}$ (eq.~\ref{eq:Edot}). For the RM, this is an asymptotic scaling and the slope of RM versus $t$ is generally somewhat shallower, while the analytic result for $F_{\nu}$ is significantly modified at times of interest $\sim t_{\rm obs}$ due to self-absorption (decreasing the effective slope dramatically) and by an exponential cutoff at very late times (increasing it). Importantly, in both cases our models describe the secular trend averaged over long baselines, as the turbulent environment of the nebula (and of the ISM of the host galaxy or Milky Way) could produce shorter timescale fluctuations. Our predicted long-baseline secular evolution is distinct from the stochastic or periodic RM evolution implied by models attributing the RM to the environment near a galactic nucleus \citep[e.g.][]{Thompson17,Zhang18}, and thus provides a possible way to distinguish such models. Although FRB\,121102 can be understood in the magnetar picture, the model does place stringent requirements on the source properties. The total energy of the magnetar likely must obey $E_{B_\star} \gtrsim 10^{50}$ erg, requiring a large interior magnetic field strength, $B_\star \gtrsim 2 \times 10^{16} \, {\rm G}$ (eq.~\ref{eq:EB}). While seemingly extreme, such a magnetic energy still represents less than a few percent of the rotational energy present in a millisecond magnetar, the latter being a requirement for powering a GRB or superluminous supernova. Such a strong field may also be required for magnetic flux to emerge from the magnetar on the requisite short timescale of decades (eq.~\ref{eq:tmag}). To reproduce the RM of FRB~121102, the radial component of the nebular magnetic field must possess a coherence length comparable to the nebula size ($\lambda \sim R_{\rm n}$ in eq.~\ref{eq:RM}). Such an ordered field may also be supported {\it empirically} by the $\sim$constant direction of the polarization vector of the bursts from FRB~121102 over several months \citep{Michilli+18}. If FRBs originate from the forward shock generated as flare ejecta collide with the magnetar wind \citep{Beloborodov17}, then this indicates that the upstream magnetic field of the wind itself is fixed in its direction over many flare timescales. One way such a large coherence length might be established is through self-organization of an initially random magnetic field due to an inverse energy cascade in relativistic magnetohydrodynamic turbulence \citep{Zrake14}. In this scenario, the RM may randomly reverse sign over an eddy turnover timescale $\sim R_{\rm n}/v_{\rm A} \sim 4 \, {\rm months} \, R_{17} \sigma_{-1}^{-1/2}$, where $v_{\rm A} = \sigma c$ is the Alfven speed. The secular decline implied by our model (eq.~\ref{eq:RM}) should then be interpreted as a long baseline envelope of $\vert {\rm RM} \vert$. Another possibility is that rotation of the magnetar plays a role in setting the magnetic field orientation. Indeed, a toroidal field perpendicular to the rotation axis is a general feature of pulsar winds. On the other hand, the build-up of too large an ordered field in the nebula could lead to non-axisymmetric kink instabilities \citep{Begelman98} and associated magnetic dissipation that regulates to an ordered component with $\sigma \lesssim 0.1$ (e.g.~\citealt{Porth+13}). Such instabilities could also play a role in generating the necessary radial component of the field needed for the RM. Our representative models have been chosen by hand, with no attempt to rigorously fit the data. Given the number of constraints imposed on the model and its relative simplicity, it is thus non-trivial that we have been able to find reasonable parameters which produce both RM and $L_\nu$ at a given epoch to within an order of magnitude, while also satisfying all other observational constraints (Fig.~\ref{fig:timescales}). As one example, we found that $\dot{E} = {\rm constant}$ ($\alpha = 0$) models cannot reproduce the observations, because the number of electrons injected at early times is too low for values of $\dot{E}$ which continue to power a sufficient radio luminosity at the source's age, resulting in the RM being underproduced. Our finding that FRB~121102 requires an energy injection rate $\dot{E} \propto t^{-\alpha}$ with $\alpha \gtrsim 1$, has potential implications for its FRB activity. This implies that either the rate of FRB activity will slow down, or that flares will on average become less energetic, over a timescale of decades. Assuming energy release tracks FRB activity, we can make a prediction for the range of RM for a population of FRB sources. Under the assumption that all (even currently non-repeating) FRBs are similar flaring magnetars, and that FRBs follow the release of magnetic energy, we can estimate the probability of detecting an FRB at a given RM. Using our analytic prediction for the dependence of RM on time (eq.~\ref{eq:R17_constraint_RM}) along with $E(t)$ from eq.~\ref{eq:Edot}, we find that $(dE/d{\rm RM}) {\rm RM} \propto {\rm RM}^{2(\alpha-1)/(6+\alpha)}$. For the range of $\alpha$ adopted in our representative models, this implies a relatively ``flat'' distribution, e.g. $(dE/d{\rm RM}) {\rm RM} \propto {\rm RM}^{0.08}$ for our fiducial $\alpha=1.3$. Although the RM is highest early in the nebula history when $\dot{E}$ is large, sufficient energy is released at later times that many sources should be detected once the RM has dropped to much lower values. Consistent with such a distribution, a few FRBs other than FRB 121102 have measured RM values, ranging from small values $\lesssim 30 \, {\rm rad \, m}^{-2}$ consistent with the Galactic contribution (\citealt{Ravi+16,Petroff+17}) to higher values still less than in FRB~121102 (\citealt{Masui+15}). Many FRBs with zero measured linear polarization could in fact have similarly high RM to FRB 121102, due to artificial depolarization caused if the observations are taken with insufficient frequency resolution \citep{Michilli+18}. \bigskip We thank Jonathan Zrake for helpful discussions. This research benefited from interactions at the ZTF Theory Network Meeting, funded by the Gordon and Betty Moore Foundation through Grant GBMF5076. B.D.M. and B.M. acknowledge support from NASA through the Astrophysics Research Program (grant number NNX16AB30G). Support for this work was provided by NASA through the NASA Hubble Fellowship grant \#HST-HF2-51412.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. | 18 | 8 | 1808.09969 |
1808 | 1808.07145_arXiv.txt | { In the era of precision cosmology, even percentage level effects are significant on cosmological observables. The recent tension between the local and global values of $H_0$ is much more significant than this, and any possible solution might rely on us going beyond the standard \lcdm cosmological model. For much smaller, yet potentially significant effects, spatial curvature from averaging and cosmological backreaction on observational predictions could play a role. This is especially true with the higher precision of new observational data and improved statistical techniques. In this paper, we discuss the observational viability of a class of physically motivated cosmologies which can be parametrized by a phenomenological two-scale backreaction model with decoupled spatial curvature parameters and two Hubble scales. Using the latest JLA Supernovae data together with some of the latest BAO data, we perform a Bayesian model selection analysis and find that the phenomenological models are not favoured over the standard \lcdm cosmological model. Although there is still a preference for non-zero and unequal dynamic and geometric spatial curvatures, there is little evidence for differing Hubble scales within these phenomenological template models. } | \label{sec:introduction} In the standard \lcdm cosmological model, the Universe is described by a Friedmann--Lemaître--Robertson--Walker (FLRW) geometry satisfying Einstein's field equations (EFE) of general relativity (GR), with a cosmological constant, $\Lambda$. The FLRW model can perhaps be interpreted as a phenomenological template to compare cosmology with observations \cite{review}, since there are issues regarding its physical motivation and underpinning \cite{NotGW}. It is possible that it would be useful to replace the phenomenological FLRW cosmological equations with another extended set of phenomenological equations. For example, in an inhomogeneous universe, while gravity is governed by EFE on small scales, this is not necessarily the case for large-scale averages. Consequently, an important problem in cosmology is to determine the precise size and form of deviations from EFE when considering averaged geometric effects on large scales, and what effects such ``backreactions'' will have on observations \cite{review}. Most authors accept that the effects of backreactions will be important for precision cosmology \cite{NotGW, Sanghai:2017yyn}. In addition, due to the abundance of new observational data \cite{Betoule2014, Wang2017, Carvalho2016, Alcaniz2017} and improved statistical techniques, it is perhaps timely to further study the constraints on cosmological models. In the analysis of standard cosmological models some parameters are purely phenomenological. Therefore, we study a parametrized phenomenological model (which has phenomenological constants), within which we can analyze data, in order to study the potential observational effects of more general cosmological models. If there is any observational evidence that the phenomenological parameters do not to take on their standard conventional values in these more general models, then it will motivate further study of these models. Cosmological observations probe the Universe on different scales; high redshift type Ia supernova (SNe Ia) cover a range of scales out to several Gpc, while the Cosmic Microwave Background (CMB) involves making observations on the scale of the cosmological horizon ($\sim14$\,Gpc). The motivation to study an phenomenological extension to the standard model is two-fold: i) There is a $3.3\sigma$ tension between the local Hubble constant from type 1a supernova and the large-scale Hubble constant obtained from the CMB \cite{R16, planck2015, R18, planck2018}. ii) In previous works \cite{SantosColey, CCCS}, using older Baryonic Acoustic Oscillation (BAO) data \cite{Beutler2011, Ross2015, Anderson2014, Padmanabhan2012, Blake2012}, it has been shown that a simple two-curvature extension to the standard model might be slightly preferred over the \lcdm model. The most recent determination of the local value of the Hubble constant based on direct measurements made with the Hubble Space Telescope \cite{R18}, of $H_0=73.52\pm1.62$ km/s/Mpc, is now more than $3$ standard deviations higher than the value derived from the most recent CMB anisotropy data provided by the Planck satellite in a \lcdm model of $H_0=67.27\pm0.60$ km/s/Mpc \cite{planck2018}. This motivates the simple phenomenological model with different Hubble parameters at different scales which we study here. In addition, \cite{SantosColey} studied the observational viability of a simple phenomenological two-scale model with a simple parametrized backreaction contribution to the EFE with non-equal spatial curvature parameters $\kg$ and $\kd$ \cite{CCCS}, motivated by an exact and fully covariant macroscopic averaging procedure~\cite{Coley:2005ei}. Current constraints on spatial curvature within the standard \lcdm model show that it is dynamically negligible: $\Omega_k \sim 5\times 10^{-3} $ (95\%CL) \cite{planck2015}. However, using recent SNe Ia data and measurements of the BAO scale, it was found that the combination of these data sets suggest unequal values of the two spatial curvature parameters, with the constraints on the spatial curvature parameter being significantly weaker than those in the standard model. Such a relatively large positive detection of spatial curvature, together with evidence of scale dependence of the spatial curvature, is a sure sign of non-trivial averaging effects \cite{Coley:2005ei}. In addition, such a value cannot be naturally explained by inflationary models that allow a large number of e-foldings which predict that the effective curvature within our Hubble radius should be of the order of the amplitude of the curvature fluctuations generated during inflation, i.e. $\Omega_k \sim 10^{-5}$ \cite{DiDio}. Note, however, that an open Universe is strongly suggested by the string multiverse \cite{Leonard}. In section \ref{back}, we begin by briefly recapping the tension in the Hubble constant and the proposals that have been put forward to alleviate this tension. We then briefly discuss the work done to motivate the study of spatial curvature in cosmology. Also, we recap the standard Bayesian statistical methods used to estimate the standard cosmological parameters. In section \ref{exten}, we introduce a parametrized phenomenological model that is similar to the \lcdm model but, in general, contains two-Hubble constants and two-spatial curvatures, both of which depend on scale. We give examples of three physically motivated models that fit within this framework -- the two curvature model, the two-scale fractal bubble model and the the bi-domain scalar averaging model. In section \ref{method}, we elaborate on the method that we use to perform our statistical analysis, including our choice of priors. Finally, in section \ref{results}, we present the results we've obtained, before we discuss the implications of these results. | We do not necessarily present these results as evidence for or against the simple phenomenological model discussed here, but rather more as motivation for studying more physical models that take into consideration the possible effects of backreaction which can affect cosmological observations at the level of a few percent. In the era of precision cosmology percentage level effects should be considered significant and we might need more sophisticated models beyond the standard model to understand them. In this paper, we review the $H_0$ problem in cosmology. We also review the role of spatial curvature in precision cosmology and how it might might be tied in with the $H_0$ problem and our understanding beyond the standard model. In addition, we present certain physically motivated models that fit under an extended phenomenological template that can be compared to the standard \lcdm model. Finally, we perform a Bayesian analysis to estimate parameters in this extended phenomenological model, and also compute the Bayesian Evidence to do a model comparison between the 2CC-Ext model and standard model. The main results from late time JLA+BAO data tell us that the standard model is weakly preferred, suggesting that studying models that fit within the 2CC-Ext umbrella might be futile. However, this can be confirmed with greater certainty, once we can include the updated Planck CMB data \cite{planck2018}. If there is any indication from CMB data that these models might be interesting to study, these 2CC-Ext models might also be able to resolve the $H_0$ tension. | 18 | 8 | 1808.07145 |
1808 | 1808.09472_arXiv.txt | Combining hydrodynamic planet-disk interaction simulations with dust evolution models, we show that protoplanetary disks having a giant planet can reveal diverse morphology in (sub-)millimeter continuum, including a full disk without significant radial structure, a transition disk with an inner cavity, a disk with a single gap and a central continuum peak, and a disk with multiple rings and gaps. Such a diversity originates from (1) the level of viscous transport in the disk which determines the number of gaps a planet can open; (2) the size and spatial distributions of grains determined by the coagulation, fragmentation, and radial drift, which in turn affects the emmisivity of the disk at (sub-)millimeter wavelengths; and (3) the angular resolution used to observe the disk. In particular, our results show that disks having the same underlying gas distribution can have very different grain size/spatial distributions and thus appearance in continuum, depending on the interplay among coagulation, fragmentation, and radial drift. This suggests that proper treatments for the grain growth have to be included in models of protoplanetary disks concerning continuum properties and that complementary molecular line observations are highly desired in addition to continuum observations to reveal the true nature of disks. The fact that a single planet can produce diverse disk morphology emphasizes the need to search for more direct, localized signatures of planets in order to confirm (or dispute) the planetary origin of observed ringed substructures. | \begin{figure*} \centering \includegraphics[width=0.95\textwidth]{fig1.pdf} \caption{The semi-major axis and mass of hypothesized planets assumed to reproduce the observed gaps in protoplanetary disks ($\odot$ symbols), compiled from literature: HL~Tau \citep{jin16}, HD~163296 \citep{teague18}, Elias~2-24 \citep{dipierro18}, AS~209 \citep{fedele18}, TW~Hya, HD~169142, HD~97048, LkCa~15, RX~J1615 \citep{dongfung17}, GY~91 \citep{sheehan18}, and V4046~Sgr (Ru\'iz-Rodr\'iguez et al. in prep.). The predictions are made using either planet-disk interaction simulations (HL~Tau, HD~163296, Elias~2-24, AS~209, V4046~Sgr) or empirical relations between planet's mass and gap width (TW~Hya, HD~169142, HD~97048, LkCa~15, RX~J1615, GY~91). For the estimations collected from \citet{dongfung17}, we adopted the masses obtained with a disk viscosity of $\alpha=10^{-3}$. Using a factor of 10 larger/smaller disk viscosity would result in about a factor of 3 larger/smaller planet masses \citep{dongfung17}. Also shown with spiral symbols are the semi-major axis and mass of hypothesized planets needed to reproduce observed spiral arms, based on planet-disk interaction simulations: MWC~758 \citep{dong15}, Elias~2-27 \citep{meru17}, SAO~206462 \citep{bae16c}, and HD~100546 \citep{follette17}. The gray circles present confirmed exoplanets as of 2018 May (\url{https://exoplanetarchive.ipac.caltech.edu/}). The black squares present the eight solar system planets. The over-plotted lines with color show illustrative estimates of the regions for which various exoplanet detection techniques have discovered exoplanets, similar to the shaded regions in Figure 6 of \citet{gaudi12}.} \label{fig:substructure} \end{figure*} Followed by the revolutionary discovery of sets of rings and gaps in the millimeter continuum emission of the HL Tau disk \citep{alma15}, concentric rings and gaps have been imaged in more than a dozen of protoplanetary disks by now thanks to the Atacama Large Millimetre Array and optical/infrared telescopes equipped with adaptive optics. Such ringed substructures are found in disks around stars with a broad range of masses from sub-solar masses (e.g., TW~Hya; \citealt{andrews16,tsukagoshi16}) to $\sim 2$ solar masses (e.g., HD~163296; \citealt{isella16}), but also with various ages spanning from less than 1 million years old (e.g., GY~91; \citealt{sheehan18}) to nearly 10 million years old (e.g., TW~Hya; \citealt{andrews16,tsukagoshi16}). Furthermore, ringed substructures have been observed using different techniques: (sub-)millimeter/centimeter continuum \citep[e.g.,][]{alma15}, molecular line emission \citep{teague18}, and optical/infrared scattered light \citep[e.g.,][]{avenhaus18}. These observations thus seem to suggest that ringed substructures are pervasive on scales of $0''.1$ ($\simeq 10 - 20$~au in linear scale) in protoplanetary disks \citep{zhang16,avenhaus18}. The origin of observed rings and gaps is unfortunately still far from clear. The interaction between planet and disk \citep{lin80} is certainly an intriguing possibility but other processes including various types of fluid instabilities \citep{takahashi14,flock17,dullemond18}, dust property changes across condensation fronts \citep{zhang15,okuzumi16}, and radial variation of magnetic activities \citep{johansen09} can also produce similar ringed substructures, and we do not have a conclusive way yet to differentiate these mechanisms based on observed features. The situation became more complicated as it is shown that one planet can open multiple gaps (\citealt{bae17}; see also \citealt{dong17}). Planets excite multiple spiral arms \citep{baezhu18} and each spiral arm can open a gap at the radial location it shocks the disk gas \citep{bae17}. In such a case, even with arbitrarily powerful observing facilities we would not detect a planet in the planet-induced gaps other than the primary one, paradoxically. Assuming that an observed gap is created by a planet orbiting within them, one can estimate the planet's mass using hydrodynamic simulations or empirical relations between planet mass and gap depth/width \citep[e.g.,][]{kanagawa15}. Figure \ref{fig:substructure} presents such attempts complied from literature, in which we plot the mass and semi-major axis of hypothesized planets required to reproduce the observed gaps. The planet masses obtained by both approaches (i.e., simulations, empirical relations) depend on the physical properties of the underlying disk, including the disk aspect ratio and the level of viscous transport, but it is interesting to note that the estimated masses are broadly consistent for the 11 disks presented in the figure (18 gaps in total). The estimated masses range from about a few percent of a Jupiter-mass to one Jupiter-mass, coincident with the masses of solar system's gas/ice giants. If (and only if) confirmed, these gap-opening protoplanets will provide us critical insights into studies of planet formation. Also, depending on their future migration and accretion we may be witnessing planets that will eventually be mini-Neptune-mass planets or hot/warm Jupiters, for which we now have a decent number of confirmed population in mature planetary systems. As an aside, it is also worth mentioning that the planet masses assumed to reproduce observed gaps are approximately an order of magnitude smaller than the ones needed to reproduce observed spiral arms, presumably because the spiral arms driven by (sub-)Jovian-mass planets are too tightly wound and/or do not produce sufficient perturbations \citep{dongfung17b,baezhu18b}. In this paper, as a step forward to better understand the origin of observed ringed substructures, we examine the morphology of protoplanetary disks in millimeter continuum produced by a Jupiter-mass planet. Since we are concerned with millimeter continuum, we consider grain evolution -- both spatial and size -- in response to the gas structure that a Jupiter-mass planet creates. As we will show, depending on the physical properties of the disk and the angular resolution used for observations, a single giant planet can produce a diverse disk morphology in millimeter continuum emission: (1) a full disk without significant radial structure; (2) a transition disk with an inner cavity; (3) a disk with a single gap with a central continuum peak; and (4) a disk with multiple rings and gaps. From the perspective of differentiating possible gap-opening mechanisms, the diverse morphology a planet can produce emphasizes the need to search for more direct evidence of planets to confirm (or dispute) the planetary origin of observed ringed substructures. This paper is organized as follows. We introduce our hydrodynamic and dust evolutionary models in Section \ref{sec:methods}. We present simulation results in Section \ref{sec:results} and synthesized images of disks' continuum emission in Section \ref{sec:morphology}. We summarize and present an outlook for future studies in Section \ref{sec:summary}. | \label{sec:summary} Using hydrodynamic simulations, dust evolution models, and synthetic observations, we showed that a Jupiter-mass planet can produce a diverse protoplanetary disk morphology, including a full disk, a transition disk with an inner cavity, a disk with a single gap and a central continuum peak, and a multi-gapped disk. Such a diversity originates from the level of viscous transport in the disk which determines the number of gaps a planet can open, the grain size distribution set by the radial drift and fragmentation, and the angular resolution used to observe the disk. Because disks having the same underlying gas distribution can have different millimeter continuum appearance (Model 1 vs. 2), complementary molecular line observations that can constrain the disk gas distribution are strongly suggested. In addition, observations with high spatial resolution and sensitivity are necessary to better understand the true nature of protoplanetary disks. Finally, searches for localized signatures of planets, including accretion on to planets \citep[e.g.,][]{sallum15}, chemical/kinematic signatures in circumstellar disks at the vicinity of planets \citep{cleeves15,pinte18}, and kinematic/thermal signatures associated with circumplanetary disks \citep{perez15,zhu16,zhu17}, are highly desired to confirm (or disprove) the presence of planets in the disks with substructures and to differentiate possible causes of rings, gaps, and inner cavities. As illustrated in Figure \ref{fig:substructure}, the hypothesized gap-opening planets locate in an interesting region of the planet mass -- semi-major axis plane, for which we do not have counterpart exoplanets discovered with the current exoplanet detection techniques. Future observations with 25+ meter class telescopes (e.g., E-ELT, GMT, TMT) will offer unprecedented capabilities to directly detect young, self-luminous planets still embedded in protoplanetary disks, allowing us to have critical insights into the formation and evolution of planets. | 18 | 8 | 1808.09472 |
1808 | 1808.09191_arXiv.txt | {Old-aged stellar distance indicators are present in all Galactic structures (halo, bulge, disk) and in galaxies of all Hubble types and, thus, are immensely powerful tools for understanding our Universe. Here we present a comprehensive review for three primary standard candles from Population II: (i)~RR Lyrae type variables (RRL), (ii)~type II Cepheid variables (T2C), and (iii)~the tip of the red giant branch (TRGB). The discovery and use of these distance indicators is placed in historical context before describing their theoretical foundations and demonstrating their observational applications across multiple wavelengths. The methods used to establish the absolute scale for each standard candle is described with a discussion of the observational systematics. We conclude by looking forward to the suite of new observational facilities anticipated over the next decade; these have both a broader wavelength coverage and larger apertures than current facilities. We anticipate future advancements in our theoretical understanding and observational application of these stellar populations as they apply to the Galactic and extragalactic distance scale.} \clearpage \tableofcontents \clearpage | \label{sec:intro} Standard candles drawn from old stellar populations have a significant advantage for distance scale as, with the exception of young Galactic star clusters, old stellar populations are found in every galactic structural component (disk, halo, bulge), galaxies of all Hubble types, and galaxies of all luminosities (from ultra-faint to ultra-luminous). Most importantly, from these distance indicators it is possible to map both Galactic and extra-galactic objects using tracers pulled from the same underlying stellar population, if not the same class of star. Moreover, due to the presence of old stars in most structural components of galaxies, it is possible to study nearby galaxies in three dimensions (e.g., measuring depths, orientations, etc.) and then to evaluate if there systematics in mean distances due to these complex structures \citep[see e.g.,][]{kunder_2018}. In turn, this helps us to better understand how projection effects and line-of-sight depth could bias mean distances. Thus, by virtue of being ``old'' standard candles have immense potential. The goal of this chapter is to provide a comprehensive review for the primary standard candles drawn from Population II stars. The term Population II (Pop~II) is an old one that originated from \citet{baade_1944} in which the nebulous central regions of the Andromeda, M\,32, and NGC\,205 were first resolved into individual stars. \citet{baade_1944} realized that these stars more closely resembled those in Galactic globular clusters (GGCs) than the ``slow moving'' stars in the solar neighborhood (e.g., disk stars). Later work would frame the differences as a function of age and metallicity, as \citet{baade_review} concisely summarized at the Vatican conference. Interestingly, the nature of the variable stars and their proper classification into Pop~I or Pop~II was intimately entwined \citep{baade58b}. We focus our attention in this chapter to relatively luminous tracers that can be used for a broad range of distances and can be considered ``primary'', in that there exist some absolute calibrations using parallaxes for these standard candles from before the onset of progressive \emph{Gaia} data releases (DR1 and DR2 at the time of writing). These considerations result in three distance indicators: (i)~the RR Lyrae (RRL), (ii)~the Type II Cepheids (T2C), and (iii)~the tip of the red giant branch (TRGB) stars. The basic properties of these standard candles are given in Table~\ref{tab:overview}. Both the RRL and the T2C are pulsational variables that occur when specific Pop~II sequences cross the classical instability strip and these stars adhere to specific period--luminosity (PL) relationships from which distances can be determined to individual stars. In contrast, the stars that comprise TRGB are non-variable in nature\footnote{These stars likely have some intrinsic variability -- as most stars do, but it is on a much smaller scale than the pulsational variables that have amplitudes $\sim$0.3 to \textgreater1~mag.} and as a result, the distance measurement is performed using a population of stars, which makes it statistical in nature. \begin{figure} % \centering \includegraphics[width=0.48\columnwidth]{f01a.pdf} \includegraphics[width=0.48\columnwidth]{f01b.pdf} \caption{ \label{fig:cmd} Optical color magnitude diagrams for the (a) LMC and (b) SMC from the Magellanic Clouds Photometric Survey \citep[black; MCPS][]{zaritsky_2002,zaritsky_2004} with variable star identifications from OGLE-III as follows RRLs (green pluses), T2Cs (red five-pointed stars), and the Classical Cepheids (blue open circles) over plotted \citep[][respectively]{soszynski_2016,Soszynski_2008,soszynski_2015}. The approximate location of the TRGB is indicated with a thick orange arrow. The axes for both panels are identical for ease of comparison. {\bf We note that no corrections for extinction (Galactic or internal to the LMC) have been applied and, thus, the color widths of the populations may be broader, to the red, than their intrinsic range.} } \end{figure} % Figures~\ref{fig:cmd}a and \ref{fig:cmd}b show the relative positions of the Classical Cepheids (blue), RRLs (green), T2Cs (red), and TRGB (orange arrow) for the Large and Small Magellanic Clouds (LMC, SMC) using variable star identifications from OGLE-III\footnote{The full variable star catalog can be queried here: \url{http://ogledb.astrouw.edu.pl/~ogle/OCVS/}} \citep[][]{Soszynski_2008,soszynski_2015,soszynski_2016} overplotted on a color magnitude density diagram from Magellanic Clouds Photometric Survey\footnote{Data is available here: \url{http://djuma.as.arizona.edu/~dennis/mcsurvey/}} \citep[greyscale][]{zaritsky_2002,zaritsky_2004}. Figures~\ref{fig:cmd}a and \ref{fig:cmd}b keenly demonstrate how the T2Cs could have been confused with the Classical Cepheids, as the two populations overlap in magnitude. The three sub-classifications for the T2Cs are also visible by the distinct clumps in the LMC (Figure~\ref{fig:cmd}a) with these distinctions being less clear in the lower-metallicity SMC (Figure~\ref{fig:cmd}b). The difference in the population size for the three variable star classes is also apparent, with the T2Cs being less abundant than either the Classical Cepheids or the RRLs. Figures~\ref{fig:cmd}a and \ref{fig:cmd}b reinforce the mean magnitude differences given in Table \ref{tab:overview}, with the TRGB being more luminous than the bulk of the T2Cs and the T2Cs being brighter than the RRLs. As a class, the RRL have a long history in the optical, having been discovered in the 19th century in cluster diagrams, but recognition of their great potential in the infrared has come only recently \citep[most notably,][]{Longmore_1986}. The short period of RRLs make identifying them relatively simple with observations spanning only a few nights and with numerous Globular Clusters being sufficiently nearby for them to have been readily discovered by early photometric monitoring campaigns \citep[a detailed history is given in][]{smith_1995}. In contrast, the T2Cs were only separated from the classical Cepheids in 1956 by \citeauthor{Baade_1956} and, despite being a solution to a difficulty in reconciling $H_0$ from the distance ladder and cosmological theory, have received little attention until the long-term monitoring from the OGLE project unveiled them {\it en masse} in the LMC \citep[Figure~\ref{fig:cmd}a,][]{Soszynski_2008}. The recognition of the TRGB as a luminosity indicator came later still when the work of \citet{da90} provided high quality homogeneous photometry for a number of Galactic globular clusters (GGCs) transformed into absolute units by their RRL distances. The TRGB was first used to determine distances for galaxies by \citet{lee93}, who developed the analysis techniques necessary to detect the tip from color-magnitude diagrams. Each of these distance indicators, thus, has a different volume of literature accompanying them and, as a result, have different depths of both theoretical understanding and observational applications. Often these vary not only by distance indicator, but also by wavelength regimes and objects (field stars, star clusters, galaxies) in which the techniques have been employed. Thus, the depth and breath of information provided in this review varies for each distance indicator. \begin{table} % \centering \caption{Basic Properties of Population II Distance Indicators.\label{tab:overview}} \begin{tabular}{cl cc c } \hline \hline Star & Sub-Type & $M_V$ [mag] & $M_K$ [mag] & $P$ [days] \\ \hline \hline \multicolumn{5}{l}{{\sc RR Lyrae} (RRL)} \\ & Fundamental Mode (RRab) & $\sim$~+0.6 & $\sim$~-0.6 & 0.3~\textless~$P$ \textless~1.0 \\ & First Overtone Mode (RRc) & $\sim$~+0.6 & $\sim$~-0.4 & 0.2~\textless~$P$ \textless~0.5 \\ \hline \multicolumn{5}{l}{{\sc Type II Cepheids} (T2C)} \\ & BL Herulis (BL~Her) & $\sim$~-0.5 & $\sim$~-1.0 & 1~\textless $P$ \textless~4 \\ & W Virginis (W~Vir) & $\sim$~-1.0 & $\sim$~-4.0 & 4~\textless $P$ \textless~20 \\ & RV Tauri (RV~Tau) & $\sim$~-2.5 & $\sim$~-5.0 & 20~\textless $P$ \textless~80 \\ \hline \multicolumn{5}{l}{{\sc Tip of the Red Giant Branch Stars} (TRGB)} \\ & Metal-Poor & $\sim$~-4.0 & $\sim$~-5.5 & \\ & Metal-Rich & $\sim$~-3.9 & $\sim$~-6.5 & \\ \hline \hline \end{tabular} \end{table} % Generally, a single book chapter cannot fully describe any one of these standard candles. Thus, we refer the reader to more detailed discussions that are in the literature. Of particular note are the following books: \citet{smith_1995} on RRLs and \citet{catelan_2015} on pulsational variables of all kinds, including both RRLs and T2Cs. Additionally, \citet{prestonfest} is a set of online conference articles that present reviews of many aspects of RRL beyond those that will be discussed here, as well as other discussions relating to metal-poor, old stellar populations. \citet{cassisi_book} is an excellent resource on stellar evolution and stellar populations that provides insight into all three of our distance indicators, but most especially the TRGB. Lastly, \citet{beaton2016} provides comparison of RRL and TRGB methods with Cepheids in terms of the extragalactic distance scale that may help the reader understand the recent resurgence of interest Pop~II standard candles. Our goal in this chapter is to place these Population II standard candles into the context of the distance scale by providing a sense of the current theoretical understanding and observational application of these tools. Where possible, we take a multi-wavelength approach discussing optical, near-infrared, and mid-infrared characteristics and applications. In the sections that follow we discuss each of the distance indicators in turn, with parallel discussions of theory and practice for the RRL in Section~\ref{sec:rrl}, a description and homogeneous PL relations for T2C in Section~\ref{sec:2cephs}, and both a physical description and application of the TRGB is given in Section~\ref{sec:trgb}. The absolute scale for each distance indicator and inter-comparisons are described in Section \ref{sec:sys}. We conclude in Section~\ref{sec:future} with an outlook for the future, in particular improvements to our physical understanding from \emph{Gaia} and the observational application with future large-aperture facilities. | 18 | 8 | 1808.09191 |
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1808 | 1808.05971_arXiv.txt | The gravitational stability of a two dimensional self gravitating and differentially rotating gaseous disk in the context of post-Newtonian (hereafter PN) theory is studied. Using the perturbative method and applying the second iterated equations of PN approximation, the dispersion relation for propagating of the small perturbations is found. Using the dispersion relation, we find the PN version of the Toomre's local stability criterion. In other words, we find relativistic corrections to Toomre's criterion in the first PN approximation. Two parameters $\eta$ and $\mu$ are introduced related to gravity and pressure respectively. We have shown that how these parameters determine the stability status of the PN and the Newtonian systems. Moreover, we have shown that in general, the fluid disk is more stable in the context of the PN theory relative to the Newtonian one. Finally we apply the results to the relativistic disks around hyper massive neutron stars, and found that although Newtonian description predicts local fragmentations, the PN theory remains in agreement with the relevant simulations and rules out the existence of local fragmentations. | It has been an interesting challenge to achieve a criterion for gravitational instability of fluid and stellar disks since almost 60 years ago. The first fundamental studies can be found in the works of \cite{safronov1960gravitational} and \cite{toomre1964gravitational}. In the past, gravitational instability was studied for understanding the dynamics of disks and particularly the structure of spiral arms. In other words, it is believed tat star formation occurs in spiral arms and the main characteristics of a galactic disk and interstellar gas are affected by them (\citealp{kormendy2004secular,sellwood2014secular}). Consequently, nowadays it is more interesting to achieve a relation between gravitational instability and star formation rate (\citealp{mckee2007theory,leroy2008star}). Lin and Shu in 1960 claimed that the spiral structure is a density wave. In this case, the linear analysis could be applied to study the gravitational stability of the disk. On the other hand because of the long range nature of gravitational force, it is very difficult to find a criterion for gravitational stability. In fact, only for a special case this task can be done analytically, see \cite{kalnajs1972equilibria}. In fact, the long range nature of the gravitational force leads to some difficulties to compute the potential of a spiral arm. Consequently, the global stability analysis of a galactic disk can not be done straightforwardly (\citealp{kalnajs1977dynamics,jalali2007unstable}). However, for tightly wound density waves, one can ignore the long-range effects and find an analytical solution. This is a local approach, known as WKB approximation, in which the relevant analysis does not depend on the given model for the background disk. Using this approximation one can find a criterion for gravitational stability of the simplest model, namely a one component rotating razor thin disk (\citealp{binney2008galactic}). Furthermore the first more complex case is a zero thickness galactic disk consisting of two components, i.e. stars and gas. This case has been widely studied, for example see \citealp{jog1984two,bertin1988global,wang1994gravitational,jog1996local,rafikov2001local} and \cite{shadmehri2012gravitational} for a two-component study where the gaseous component is turbulent. Furthermore there is a variety of analytical and numerical studies in the context of disks with finite thickness, for example see \cite{vandervoort1970equilibria}; \cite{romeo1990thesis,romeo1992stability,romeo1994faithful}. The effect of magnetic field on the gravitational stability of thin disks can be found in \cite{elmegreen1987supercloud}, \cite{elmegreen1994supercloud}; \cite{gammie1996linear}; \cite{fan1997swing} and \cite{kim2001amplification}. Also the effect of viscosity on the local stability has considered in \cite{gammie1996linear}. In this paper we are interested to relativistic corrections to the Toomre's criterion. More specifically, in relativistic situations the standard gravitational stability criterion needs to be changed. In fact, astrophysical instabilities in relativistic systems may substantially influence the dynamics of the system. For example during the merger of binary neutron stars the Kelvin-Helmholtz instability appears in the system (\citealp{anderson2008magnetized,obergaulinger2009semi,goodman1994parasitic}) . Furthermore, the dynamical bar-mode instability in differentially rotating neutron stars has been studied in the literature. In fact, the bar-mode instability in supernova collapse or binary neutron star mergers, could lead to strong and observable gravitational waves \citep{shibata2000bar}. As another example see \cite{siegel2013magnetorotational}, where the magnetorotational instability (MRI) in the evolution of HMNS has been investigated. The relativistic corrections to the Jeans instability has been investigated in \cite{nazari2017post}. It is shown that, considering the first relativistic corrections to the equations of hydrodynamics, the Jeans mass changes. More specifically, the new Jeans mass is smaller than the standard case. Also, it is interesting that in the PN limit, the pressure and the internal energy, can support the instability in the system (\citealp{nazari2017post}). Since rotation plays important role in relativistic disks, here we generalize \cite{nazari2017post} results to a rotating razor thin disk. The result would be important in the differentially rotating and relativistic disks around HMNSs. Recently, \cite{ellis2017search} have shown that existence of matter fragmentations in the above mentioned disks, can effectively influence the power spectrum of the gravitational waves produced during the merger of two neutron stars. From this perspective, finding an analytical criterion for the growth of local fragmentations in relativistic disks seems interesting. However, the main difficulty is that general relativity's (GR) field equations can not be handled analytically for arbitrary matter configurations. So it is helpful to use numerical approaches as well as approximative methods. The PN approximation is one of the powerful methods for this aim. Within this framework, the relativistic corrections are added to the Newtonian description in an iterative manner. Consequently, this approach is appropriate for systems where the velocities are small compared to the velocity of light. On the other hand gravitational fields are strong enough which one can not use Newtonian gravity, and week enough to ignore full general relativistic effects. For an excellent introduction to PN theory we refer the reader to \cite{poisson2014gravity}. This method proposed by Chandrasekhar (\citealp{chandrasekhar1965post,chandrasekhar1967post,chandrasekhar1969conservation}; \citealp{chandrasekhar1969Second}; \citealp{chandrasekhar1970212}) and extended by Clifford Will with a subsequent series of papers with emphasis on the experimental foundations of GR (\citealp{thorne1971theoreticali,will1971theoreticalii,will1971theoreticaliii}). Furthermore Blanchet developed the PN formalism in the direction suitable to investigate the gravitational emission from inspiralling compact binaries (\citealp{blanchet1989post,blanchet1989higher,blanchet1995gravitational}). One can find some important applications of the PN theory in the literature. For example it can be used to study the equation of motion of binary pulsars (\citealp{blandford1976arrival,epstein1977binary,hulse1975deep,damour1991orbital}), general relativistic tests of GR in solar system (\citealp{thorne1987300, will1994proceedings}), the normal modes of relativistic systems \cite{rezania2000normal}, gravitational radiation reaction (\citealp{chandrasekhar1970212,burke1971gravitational,blanchet2006}), Jeans analysis (\citealp{nazari2017post}), and also accretion disks around black holes (\citealp{demianski1997dynamics}). Furthermore, it has been significantly useful for modeling the gravitational waves. Most recently, \cite{abbott2017gw170817} presents the first detection of gravitational waves from the inspiral of a binary neutron star system. On the other hand, for analyzing the observations of the gravitational-wave detectors, the high accuracy templates predicted by general relativity theory is required. For relativistic systems, such as inspiral of a binary neutron star, the high-order PN framework can accurately model the gravitational wave emmision (\citealp{blanchet2014gravitational}). This framework has been also used in \cite{abbott2017gw170817} to interpret the observed signal. For a comprehensive review of the PN theory and its applications we refere the reader to \cite{will2014confrontation}. In this paper we use the PN approximation up to the 1\tiny PN\normalsize order to find a new version of the Toomre's criterion containing the first relativistic corrections to the standard form. This criterion can be written in terms of the standard Toomre's parameter. In this case the differences between the Newtonian and the PN theories will be more clear. The map of this paper is as following. In Sec. \ref{pnhydro} we introduce the hydrodynamic equation of the gaseous disk in the context of PN theory. In Sec. \ref{dispersion_relation_section}, we linearize the PN equations of hydrodynamics using perturbative method, and then find the PN potentials of a tightly wound spiral pattern. Finally we obtain the dispersion relation for WKB density waves. The PN version of the Toomre's criterion is found in Sec. \ref{Toomre}. In this section, introducing two dimensionless stability parameters $\eta$ and $\mu$, we study the stability of a two dimensional self gravitating and differentially rotating gaseous disk, as a toy model, in the context of PN theory. Sec. \ref{hmns} is devoted to application of our results to disks around HMNS. Finally, we summarize the results and conclusions in Sec. \ref{conclusion}. | We studied the local gravitational stability of a relativistic two dimensional self-gravitating and differentially rotating fluid disk in context of the PN theory. In this approximation one can track the footprint of the relativistic effects on the dynamics of the system. In fact we introduced a relativistic version of the Toomre's criterion including relativistic effects up to 1\tiny PN\normalsize approximation. For this purpose we studied the dynamics of a gaseous disk in Sec. \ref{dispersion_relation_section}, and found the hydrodynamics equation in the PN approximation. Then we linearized these equations and applied the tight winding approximation (WKB) to investigate the local stability of the system. It provided a considerable simplicity in the calculations. Then after finding the PN potentials of the WKB density wave, we solved the linearized PN equations in order to find the dispersion relation of the propagating small perturbations on the surface of the disk. \begin{table}[t] \caption{Toomre's criterion for allowed models} \renewcommand{\arraystretch}{1.2} \begin{center} \begin{tabular}{lcccccc} \hline Model & $y$ & $Q$ & PN R.H.S. & NTC & PNTC & $\Delta$ $\left[\% \right]$ \\ \hline\hline \multirow{2}{*}{GNH3-M125} & $4.9$ & $1.03$ & $0.22$ & \checkmark & \checkmark & $77.70$ \\ \vspace{1.6mm} & $5$ & $1.11$ & $0.17$ & \checkmark & \checkmark & $83.24$ \\ \multirow{3}{*}{H4-M125} & $4.3$ & $0.56$ & $0.57$ & -- & -- & $42.69$ \\ & $4.6$ & $0.68$ & $0.50$ & -- & \checkmark & $49.55$ \\ \vspace{1.5mm} & $4.9$ & $0.84$ & $0.44$ & -- & \checkmark & $56.52$ \\ \multirow{3}{*}{ALF2-M125} & $4.4$ & $0.59$ & $0.54$ & -- & \checkmark & $45.76$ \\ & $4.7$ & $0.72$ & $0.48$ & -- & \checkmark & $52.42$ \\ & $4.9$ & $0.83$ & $0.42$ & -- & \checkmark & $57.61$ \\ \hline \end{tabular} \end{center} \tablecomments{\textcolor{red}{NEW. } Investigating the Toomre's criterion in Newtonian and PN viewpoints. The first column is the model name. The second column shows different radii $y$. The third (forth) column shows the value of Toomre's parameter (R.H.S. of PN Toomre's criterion). The check-marks in the fifth and the sixth columns show the establishing Newtonian and PN Toomre's criterion respectively. The last column is the fractional difference between Newtonian and PN viewpoints. Note that, for each model, radii less than the smallest specified radius do not satisfy the conditions \eqref{cond_eta} to \eqref{cond_em3}. \label{table2}} \end{table} Using the PN dispersion relation and introducing some effective quantities as $G_{\text{p}}$\,, $c_{\text{sp}}$\,, and $\kappa_{\text{p}}$, we found the local stability criterion for the fluid disk in the context of the PN theory in Sec. \ref{Toomre}. In order to compare this criterion with the Newtonian case, we rewrite the PN Toomre's parameter in terms of the Newtonian quantities. The PN Toomre's criterion can be expressed as $Q>1+C(y,\eta,\mu)$, where $C(y,\eta,\mu)$ is the PN correction term. To complete our result and investigate the effect of each PN correction on the local stability, we choose an exponential disk toy model. Also, we have introduced two dimensionless parameters, i.e., $\eta$ and $\mu$, which are made up of a combination of $c$, $G$, $R_{\text{d}}$, $\Sigma_0$, and $K$, to study the behavior of the system more clearly. In fact these parameters represent the strength of gravity and pressure in the system. Also, some restrictions on these parameters have been imposed to satisfy slow-motion conditions in the 1\tiny PN \normalsize approximation. \textbf{At first, after finding a range of $\eta$ and $\mu$ which satisfies the PN conditions at all radii, we have studied the general effects of these parameters on the stability of system. It is clear from the Figure \ref{Dens_plots} that, the role of $\eta$ ($\mu$) is destabilizing (stabilizing) in both Newtonian and PN limits. However each one of the parameters can violate from this rule in some specific situation. For example at small radii, increasing $\mu$ can unexpectedly, destabilize both Newtonian and the PN system. Furthermore, at large radii, in addition to a usual effect of $\eta$, this parameter can also stabilize the PN system too. Although this effect cannot be seen in Newtonian limit. Furthermore, we have shown that, the system is more stable in the PN limit comparing with the Newtonian case. However, the difference between two theories tends to zero for small values of both parameters. Moreover, one can see that, the large radii, are more stable. } Also we have studied the growth rate of the perturbation in both regimes. For this aim, the dimensionless growth rate (see Eq. \eqref{PN growing rate}) is plotted versus the dimensionless wavenumber $q$. Figure \ref{growingRate} shows that, the growth rate decreases (increases) and the instability interval gets shorter (larger), by increasing $\mu$ ($\eta$), in a fixed radius. So, one can see that, in both Newtonian and PN limits, $\mu$ ($\eta$) has stabilizing (destabilizing) effects. It is worth mentioning that, regarding the fact that the fraction of the PN correction terms and the main Newtonian term in Eq. \eqref{PN growing rate} must be less than unity, we can impose some restrictions on $q$. Furthermore, one can see from Fig. \ref{growingRate} that, at a same radius and with the same $\eta$ and $\mu$ parameters, the instability interval is wider in Newtonian limit, and also includes the smaller wavelengths. In addition, the growth rates are larger in the Newtonian viewpoint. Therefor, one can see that, the system is more stable in the PN limit. Finally, we have studied the boundary of the stability using equations \eqref{Q_s} and \eqref{Q(X)}. \textbf{This boundary is investigated for different radii and various values of the parameters. Figure \ref{Boundary} in agreement with Figure \ref{Dens_plots} shows that, the system is more stable in context of the PN theory. Moreover, we have shown that, some large wavelengths can be removed, considering the limitations that PN constraints imposed on the parameters and quantities.} As an application, we have applied our calculations to the relativistic disk around an HMNS. We used a rough estimation, and study the possibility of occurrence of the local gravitational instability in this system. In fact, we showed that, the standard Newtonian Toomre's criterion allows the system to be locally fragmented. Of course, the Newtonian description is not a reliable way to investigate such a relativistic system. On the other hand, we showed that, in agreement with the relativistic simulations, the local fragmentation could not be happened in the HMNS, when we use PN version of the Toomre's criterion. \appendix Appendices can be broken into separate sections just like in the main text. The only difference is that each appendix section is indexed by a letter (A, B, C, etc.) instead of a number. Likewise numbered equations have the section letter appended. Here is an equation as an example. \begin{equation} I = \frac{1}{1 + d_{1}^{P (1 + d_{2} )}} \end{equation} Appendix tables and figures should not be numbered like equations. Instead they should continue the sequence from the main article body. Finally some information about the AAS Journal's publication charges. In April 2011 the traditional way of calculating author charges based on the number of printed pages was changed. The reason for the change was due to a recognition of the growing number of article items that could not be represented in print. Now author charges are determined by a number of digital ``quanta''. A single quantum is 350 words, one figure, one table, and one enhanced digital item. For the latter this includes machine readable tables, figure sets, animations, and interactive figures. The current cost is \$27 per word quantum and \$30 for all other quantum type. The process of rotating tables into landscape mode is slightly different in \aastex v6.2. Instead of the {\tt\string\rotate} command, a new environment has been created to handle this task. To place a single page table in a landscape mode start the table portion with {\tt\string\begin\{rotatetable\}} and end with {\tt\string\end\{rotatetable\}}. Tables that exceed a print page take a slightly different environment since both rotation and long table printing are required. In these cases start with {\tt\string\begin\{longrotatetable\}} and end with {\tt\string\end\{longrotatetable\}}. Table \ref{chartable} is an example of a multi-page, rotated table. \begin{longrotatetable} \begin{deluxetable*}{lllrrrrrrll} \tablecaption{Observable Characteristics of Galactic/Magellanic Cloud novae with X-ray observations\label{chartable}} \tablewidth{700pt} \tabletypesize{\scriptsize} \tablehead{ \colhead{Name} & \colhead{V$_{max}$} & \colhead{Date} & \colhead{t$_2$} & \colhead{FWHM} & \colhead{E(B-V)} & \colhead{N$_H$} & \colhead{Period} & \colhead{D} & \colhead{Dust?} & \colhead{RN?} \\ \colhead{} & \colhead{(mag)} & \colhead{(JD)} & \colhead{(d)} & \colhead{(km s$^{-1}$)} & \colhead{(mag)} & \colhead{(cm$^{-2}$)} & \colhead{(d)} & \colhead{(kpc)} & \colhead{} & \colhead{} } \startdata CI Aql & 8.83 (1) & 2451665.5 (1) & 32 (2) & 2300 (3) & 0.8$\pm0.2$ (4) & 1.2e+22 & 0.62 (4) & 6.25$\pm5$ (4) & N & Y \\ {\bf CSS081007} & \nodata & 2454596.5 & \nodata & \nodata & 0.146 & 1.1e+21 & 1.77 (5) & 4.45$\pm1.95$ (6) & \nodata & \nodata \\ GQ Mus & 7.2 (7) & 2445352.5 (7) & 18 (7) & 1000 (8) & 0.45 (9) & 3.8e+21 & 0.059375 (10) & 4.8$\pm1$ (9) & N (7) & \nodata \\ IM Nor & 7.84 (11) & 2452289 (2) & 50 (2) & 1150 (12) & 0.8$\pm0.2$ (4) & 8e+21 & 0.102 (13) & 4.25$\pm3.4$ (4) & N & Y \\ {\bf KT Eri} & 5.42 (14) & 2455150.17 (14) & 6.6 (14) & 3000 (15) & 0.08 (15) & 5.5e+20 & \nodata & 6.5 (15) & N & M \\ {\bf LMC 1995} & 10.7 (16) & 2449778.5 (16) & 15$\pm2$ (17) & \nodata & 0.15 (203) & 7.8e+20 & \nodata & 50 & \nodata & \nodata \\ LMC 2000 & 11.45 (18) & 2451737.5 (18) & 9$\pm2$ (19) & 1700 (20) & 0.15 (203) & 7.8e+20 & \nodata & 50 & \nodata & \nodata \\ {\bf LMC 2005} & 11.5 (21) & 2453700.5 (21) & 63 (22) & 900 (23) & 0.15 (203) & 1e+21 & \nodata & 50 & M (24) & \nodata \\ {\bf LMC 2009a} & 10.6 (25) & 2454867.5 (25) & 4$\pm1$ & 3900 (25) & 0.15 (203) & 5.7e+20 & 1.19 (26) & 50 & N & Y \\ {\bf SMC 2005} & 10.4 (27) & 2453588.5 (27) & \nodata & 3200 (28) & \nodata & 5e+20 & \nodata & 61 & \nodata & \nodata \\ {\bf QY Mus} & 8.1 (29) & 2454739.90 (29) & 60: & \nodata & 0.71 (30) & 4.2e+21 & \nodata & \nodata & M & \nodata \\ {\bf RS Oph} & 4.5 (31) & 2453779.44 (14) & 7.9 (14) & 3930 (31) & 0.73 (32) & 2.25e+21 & 456 (33) & 1.6$\pm0.3$ (33) & N (34) & Y \\ {\bf U Sco} & 8.05 (35) & 2455224.94 (35) & 1.2 (36) & 7600 (37) & 0.2$\pm0.1$ (4) & 1.2e+21 & 1.23056 (36) & 12$\pm2$ (4) & N & Y \\ {\bf V1047 Cen} & 8.5 (38) & 2453614.5 (39) & 6 (40) & 840 (38) & \nodata & 1.4e+22 & \nodata & \nodata & \nodata & \nodata \\ {\bf V1065 Cen} & 8.2 (41) & 2454123.5 (41) & 11 (42) & 2700 (43) & 0.5$\pm0.1$ (42) & 3.75e+21 & \nodata & 9.05$\pm2.8$ (42) & Y (42) & \nodata \\ V1187 Sco & 7.4 (44) & 2453220.5 (44) & 7: (45) & 3000 (44) & 1.56 (44) & 8.0e+21 & \nodata & 4.9$\pm0.5$ (44) & N & \nodata \\ {\bf V1188 Sco} & 8.7 (46) & 2453577.5 (46) & 7 (40) & 1730 (47) & \nodata & 5.0e+21 & \nodata & 7.5 (39) & \nodata & \nodata \\ {\bf V1213 Cen} & 8.53 (48) & 2454959.5 (48) & 11$\pm2$ (49) & 2300 (50) & 2.07 (30) & 1.0e+22 & \nodata & \nodata & \nodata & \nodata \\ {\bf V1280 Sco} & 3.79 (51) & 2454147.65 (14) & 21 (52) & 640 (53) & 0.36 (54) & 1.6e+21 & \nodata & 1.6$\pm0.4$ (54) & Y (54) & \nodata \\ {\bf V1281 Sco} & 8.8 (55) & 2454152.21 (55) & 15:& 1800 (56) & 0.7 (57) & 3.2e+21 & \nodata & \nodata & N & \nodata \\ {\bf V1309 Sco} & 7.1 (58) & 2454714.5 (58) & 23$\pm2$ (59) & 670 (60) & 1.2 (30) & 4.0e+21 & \nodata & \nodata & \nodata & \nodata \\ {\bf V1494 Aql} & 3.8 (61) & 2451515.5 (61) & 6.6$\pm0.5$ (61) & 1200 (62) & 0.6 (63) & 3.6e+21 & 0.13467 (64) & 1.6$\pm0.1$ (63) & N & \nodata \\ {\bf V1663 Aql} & 10.5 (65) & 2453531.5 (65) & 17 (66) & 1900 (67) & 2: (68) & 1.6e+22 & \nodata & 8.9$\pm3.6$ (69) & N & \nodata \\ V1974 Cyg & 4.3 (70) & 2448654.5 (70) & 17 (71) & 2000 (19) & 0.36$\pm0.04$ (71) & 2.7e+21 & 0.081263 (70) & 1.8$\pm0.1$ (72) & N & \nodata \\ {\bf V2361 Cyg} & 9.3 (73) & 2453412.5 (73) & 6 (40) & 3200 (74) & 1.2: (75) & 7.0e+21 & \nodata & \nodata & Y (40) & \nodata \\ {\bf V2362 Cyg} & 7.8 (76) & 2453831.5 (76) & 9 (77) & 1850 (78) & 0.575$\pm0.015$ (79) & 4.4e+21 & 0.06577 (80) & 7.75$\pm3$ (77) & Y (81) & \nodata \\ {\bf V2467 Cyg} & 6.7 (82) & 2454176.27 (82) & 7 (83) & 950 (82) & 1.5 (84) & 1.4e+22 & 0.159 (85) & 3.1$\pm0.5$ (86) & M (87) & \nodata \\ {\bf V2468 Cyg} & 7.4 (88) & 2454534.2 (88) & 10: & 1000 (88) & 0.77 (89) & 1.0e+22 & 0.242 (90) & \nodata & N & \nodata \\ {\bf V2491 Cyg} & 7.54 (91) & 2454567.86 (91) & 4.6 (92) & 4860 (93) & 0.43 (94) & 4.7e+21 & 0.09580: (95) & 10.5 (96) & N & M \\ V2487 Oph & 9.5 (97) & 2450979.5 (97) & 6.3 (98) & 10000 (98) & 0.38$\pm0.08$ (98) & 2.0e+21 & \nodata & 27.5$\pm3$ (99) & N (100) & Y (101) \\ {\bf V2540 Oph} & 8.5 (102) & 2452295.5 (102) & \nodata & \nodata & \nodata & 2.3e+21 & 0.284781 (103) & 5.2$\pm0.8$ (103) & N & \nodata \\ V2575 Oph & 11.1 (104) & 2453778.8 (104) & 20: & 560 (104) & 1.4 (105) & 3.3e+21 & \nodata & \nodata & N (105) & \nodata \\ {\bf V2576 Oph} & 9.2 (106) & 2453832.5 (106) & 8: & 1470 (106) & 0.25 (107) & 2.6e+21 & \nodata & \nodata & N & \nodata \\ {\bf V2615 Oph} & 8.52 (108) & 2454187.5 (108) & 26.5 (108) & 800 (109) & 0.9 (108) & 3.1e+21 & \nodata & 3.7$\pm0.2$ (108) & Y (110) & \nodata \\ {\bf V2670 Oph} & 9.9 (111) & 2454613.11 (111) & 15: & 600 (112) & 1.3: (113) & 2.9e+21 & \nodata & \nodata & N (114) & \nodata \\ {\bf V2671 Oph} & 11.1 (115) & 2454617.5 (115) & 8: & 1210 (116) & 2.0 (117) & 3.3e+21 & \nodata & \nodata & M (117) & \nodata \\ {\bf V2672 Oph} & 10.0 (118) & 2455060.02 (118) & 2.3 (119) & 8000 (118) & 1.6$\pm0.1$ (119) & 4.0e+21 & \nodata & 19$\pm2$ (119) & \nodata & M \\ V351 Pup & 6.5 (120) & 2448617.5 (120) & 16 (121) & \nodata & 0.72$\pm0.1$ (122) & 6.2e+21 & 0.1182 (123) & 2.7$\pm0.7$ (122) & N & \nodata \\ {\bf V382 Nor} & 8.9 (124) & 2453447.5 (124) & 12 (40) & 1850 (23) & \nodata & 1.7e+22 & \nodata & \nodata & \nodata & \nodata \\ V382 Vel & 2.85 (125) & 2451320.5 (125) & 4.5 (126) & 2400 (126) & 0.05: (126) & 3.4e+21 & 0.146126 (127) & 1.68$\pm0.3$ (126) & N & \nodata \\ {\bf V407 Cyg} & 6.8 (128) & 2455266.314 (128) & 5.9 (129) & 2760 (129) & 0.5$\pm0.05$ (130) & 8.8e+21 & 15595 (131) & 2.7 (131) & \nodata & Y \\ {\bf V458 Vul} & 8.24 (132) & 2454322.39 (132) & 7 (133) & 1750 (134) & 0.6 (135) & 3.6e+21 & 0.06812255 (136) & 8.5$\pm1.8$ (133) & N (135) & \nodata \\ {\bf V459 Vul} & 7.57 (137) & 2454461.5 (137) & 18 (138) & 910 (139) & 1.0 (140) & 5.5e+21 & \nodata & 3.65$\pm1.35$ (138) & Y (140) & \nodata \\ V4633 Sgr & 7.8 (141) & 2450895.5 (141) & 19$\pm3$ (142) & 1700 (143) & 0.21 (142) & 1.4e+21 & 0.125576 (144) & 8.9$\pm2.5$ (142) & N & \nodata \\ {\bf V4643 Sgr} & 8.07 (145) & 2451965.867 (145) & 4.8 (146) & 4700 (147) & 1.67 (148) & 1.4e+22 & \nodata & 3 (148) & N & \nodata \\ {\bf V4743 Sgr} & 5.0 (149) & 2452537.5 (149) & 9 (150) & 2400 (149) & 0.25 (151) & 1.2e+21 & 0.281 (152) & 3.9$\pm0.3$ (151) & N & \nodata \\ {\bf V4745 Sgr} & 7.41 (153) & 2452747.5 (153) & 8.6 (154) & 1600 (155) & 0.1 (154) & 9.0e+20 & 0.20782 (156) & 14$\pm5$ (154) & \nodata & \nodata \\ {\bf V476 Sct} & 10.3 (157) & 2453643.5 (157) & 15 (158) & \nodata & 1.9 (158) & 1.2e+22 & \nodata & 4$\pm1$ (158) & M (159) & \nodata \\ {\bf V477 Sct} & 9.8 (160) & 2453655.5 (160) & 3 (160) & 2900 (161) & 1.2: (162) & 4e+21 & \nodata & \nodata & M (163) & \nodata \\ {\bf V5114 Sgr} & 8.38 (164) & 2453081.5 (164) & 11 (165) & 2000 (23) & \nodata & 1.5e+21 & \nodata & 7.7$\pm0.7$ (165) & N (166) & \nodata \\ {\bf V5115 Sgr} & 7.7 (167) & 2453459.5 (167) & 7 (40) & 1300 (168) & 0.53 (169) & 2.3e+21 & \nodata & \nodata & N (169) & \nodata \\ {\bf V5116 Sgr} & 8.15 (170) & 2453556.91 (170) & 6.5 (171) & 970 (172) & 0.25 (173) & 1.5e+21 & 0.1238 (171) & 11$\pm3$ (173) & N (174) & \nodata \\ {\bf V5558 Sgr} & 6.53 (175) & 2454291.5 (175) & 125 (176) & 1000 (177) & 0.80 (178) & 1.6e+22 & \nodata & 1.3$\pm0.3$ (176) & N (179) & \nodata \\ {\bf V5579 Sgr} & 5.56 (180) & 2454579.62 (180) & 7: & 1500 (23) & 1.2 (181) & 3.3e+21 & \nodata & \nodata & Y (181) & \nodata \\ {\bf V5583 Sgr} & 7.43 (182) & 2455051.07 (182) & 5: & 2300 (182) & 0.39 (30) & 2.0e+21 & \nodata & 10.5 & \nodata & \nodata \\ {\bf V574 Pup} & 6.93 (183) & 2453332.22 (183) & 13 (184) & 2800 (184) & 0.5$\pm0.1$ & 6.2e+21 & \nodata & 6.5$\pm1$ & M (185) & \nodata \\ {\bf V597 Pup} & 7.0 (186) & 2454418.75 (186) & 3: & 1800 (187) & 0.3 (188) & 5.0e+21 & 0.11119 (189) & \nodata & N (188) & \nodata \\ {\bf V598 Pup} & 3.46 (14) & 2454257.79 (14) & 9$\pm1$ (190) & \nodata & 0.16 (190) & 1.4e+21 & \nodata & 2.95$\pm0.8$ (190) & \nodata & \nodata \\ {\bf V679 Car} & 7.55 (191) & 2454797.77 (191) & 20: & \nodata & \nodata & 1.3e+22 & \nodata & \nodata & \nodata & \nodata \\ {\bf V723 Cas} & 7.1 (192) & 2450069.0 (192) & 263 (2) & 600 (193) & 0.5 (194) & 2.35e+21 & 0.69 (195) & 3.86$\pm0.23$ (196) & N & \nodata \\ V838 Her & 5 (197) & 2448340.5 (197) & 2 (198) & \nodata & 0.5$\pm0.1$ (198) & 2.6e+21 & 0.2975 (199) & 3$\pm1$ (198) & Y (200) & \nodata \\ {\bf XMMSL1 J06} & 12 (201) & 2453643.5 (202) & 8$\pm2$ (202) & \nodata & 0.15 (203) & 8.7e+20 & \nodata & 50 & \nodata & \nodata \\ \enddata \end{deluxetable*} \end{longrotatetable} A handy "cheat sheat" that provides the necessary LaTeX to produce 17 different types of tables is available at \url{http://journals.aas.org/authors/aastex/aasguide.html#table_cheat_sheet}. | 18 | 8 | 1808.05971 |
1808 | 1808.05695_arXiv.txt | \vspace*{.0in} Galactic rotation curves exhibit diverse behavior in the inner regions, while obeying an organizing principle, i.e., they can be approximately described by a radial acceleration relation or the Modified Newtonian Dynamics phenomenology. We analyze the rotation curve data from the SPARC sample, and explicitly demonstrate that both the diversity and uniformity are naturally reproduced in a hierarchical structure formation model with the addition of dark matter self-interactions. The required concentrations of the dark matter halos are fully consistent with the concentration-mass relation predicted by the Planck cosmological model. The inferred stellar mass-to-light ($3.6~\micron$) ratios scatter around $0.5M_\odot/L_\odot$, as expected from population synthesis models, leading to a tight radial acceleration relation and baryonic Tully-Fisher relation. The inferred stellar-halo mass relation is consistent with the expectations from abundance matching. These results indicate that the inner dark matter halos of galaxies are thermalized due to the self-interactions of dark matter particles. | Galactic rotation curves of spiral galaxies show a variety of behavior in the inner parts even across systems with similar halo and stellar masses, which lacks a self-consistent explanation in the standard cold dark matter (CDM) model~\cite{Flores:1994gz,Moore:1994yx,Burkert:1995yz,Persic:1995ru,deBlok:2001fe,Gentile:2004tb,KuziodeNaray:2007qi,deBlok:2008wp,Oh:2010ea,Oh:2015xoa,deNaray:2009xj,Oman:2015xda,Bullock:2017xww}. Along with this diversity, a long-standing observation is that many rotation curves can be understood in terms of Modified Newtonian Dynamics (MOND) phenomenology~\cite{Milgrom:1983ca,Milgrom:1983pn} (see~\cite{Famaey:2011kh} for a review), i.e., there exists a characteristic gravitational acceleration scale, $g_\dagger\approx 10^{-10}~{\rm m/s^2}\sim cH_0/7$ with $H_0$ being the present Hubble expansion rate, below which the observed acceleration can be approximated as $\sqrt{g_\dagger g_{\rm bar}}$ with ${g_{\rm bar}}$ being the baryonic acceleration (a.k.a. Milgrom's law). More recently, McGaugh et al.~\cite{McGaugh:2016leg} analyzed the Spitzer Photometry and Accurate Rotation Curves (SPARC) dataset~\cite{Lelli:2016zqa} and showed there is a tight relation between the total gravitational acceleration at any radius and the acceleration contributed by the baryons, assuming a constant stellar mass-to-light ratio $\MLdisk=0.5M_\odot/L_\odot$ and $\MLbulge=0.7M_\odot/L_\odot$ in the $3.6~\micron$ band. The scatter in this radial acceleration relation (RAR) is around $0.1$ dex, and the tightness of this relation has been interpreted as a signature of MOND~\cite{Li:2018tdo}. It has long been argued that the acceleration scale (including the $cH_0$ dependence) can emerge from hierarchical structure formation predicted in CDM~\cite{vandenBosch:1999dz,Kaplinghat:2001me}. Recent hydrodynamical simulations of galaxy formation with CDM have clearly shown that a RAR emerges~\cite{Keller:2016gmw,Ludlow:2016qzh,Navarro:2016bfs}. However, these simulated galaxies do not represent the full range of the diversity in the SPARC dataset and they cannot yet explain the rotation curves of low and high surface brightness galaxies simultaneously. In this paper, we show that self-interacting dark matter (SIDM) provides a unified way to understand the diverse rotation curves of spiral galaxies, while reproducing the RAR with a small scatter. We analyze the SPARC dataset based on the SIDM halo model proposed in~\cite{Kaplinghat:2013xca,Kaplinghat:2015aga} and demonstrate three key observations leading to this result. \begin{itemize} \item For cross section per unit mass $\sigm \gtrsim 1~{\rm cm^2/g}$, dark matter self-interactions only thermalize the inner regions at distances less than about $10\%$ of the virial radius of galactic halos, while the outer regions remains unchanged. Thus, SIDM inherits essential features of the $\Lambda$CDM hierarchical structure formation model such as the halo concentration-mass relation, which sets the characteristic acceleration scale of halos. \item In the inner halo, thermalization ties dark matter and baryon distributions together~\cite{Kaplinghat:2013xca,Vogelsberger:2014pda,Elbert:2016dbb}, and the SIDM halo can naturally accommodate the diverse range of `cored' and `cusped' central density profiles, depending on how the baryons are distributed. Combined with the scatter in the concentration-mass relation, this provides the diversity required to explain the rotation curves~\cite{Kaplinghat:2015aga,Kamada:2016euw,Creasey:2016jaq}. We will demonstrate the SIDM fits are systematically superior to the MOND ones. \item For the same $\sigm$ that addresses the diversity problem, the baryon content of the galaxies and the mass model of their host halos also lead to the RAR with a scatter as small as the one in~\cite{McGaugh:2016leg}. In our SIDM fits, the inferred stellar $\MLdisk$ values for individual galaxies have a distribution peaked toward $0.5M_\odot/L_\odot$, as expected from stellar population synthesis models~\cite{Schombert:2013hga}. \end{itemize} The rest of the paper is organized as follows. In Sec.~\ref{sec:diversity}, we present the SIDM fits to 135 galaxies from the SPARC sample, which exemplify the full range of the diversity. In Sec.~\ref{sec:accel}, we show the radial acceleration relation and the distribution of the stellar mass-to-light ratios from our SIDM fits, compared to the MOND fits. In Sec.~\ref{sec:cosmo}, we discuss the host halo properties and the origin of the acceleration scale. In Sec.~\ref{sec:baryons}, we show the predicted stellar -- halo mass relation and the baryonic Tully-Fisher relation (BTFR). We comment on future directions and conclude in Sec.~\ref{sec:con}. In the appendix, {\bf Methods}, we provide detailed information about the model and the fitting procedure. In {\bf Supplementary Materials}, we present SIDM and MOND fits to $135$ individual galaxies from the SPARC sample and additional results that support the main text, including model fits to simulated halos. | \label{sec:con} In this work, we have investigated SIDM as a solution to two puzzles that are present in galactic rotation curves: (1) the diversity of inner rotation curves in galaxies that have similar baryon content and similar flat circular velocities, and (2) the small scatter in the radial acceleration relation between the total gravitational acceleration and the one inferred from the baryonic mass content, i.e., uniformity. We have fitted our SIDM halo model to the rotation curves of $135$ SPARC galaxies, and found that it reproduces the observed diversity in the inner regions. The distribution of resulting $3.6~\micron$ stellar disk mass-to-light ratios for the sample peaks at $\MLdisk\approx0.5~\MLunits$, in good agreement with the stellar population models. Our fits lead to a radial acceleration relation described by the characteristic acceleration scale $\sim 10^{-10} {\rm m/s}$, with tight scatter of $0.10$ dex. The host halos are fully consistent with the Planck cosmology. The inferred stellar mass-halo mass relation agrees with the result from the abundance matching method, and the fits also predict a tight BTFR. These results provide compelling arguments in favor of the idea that the inner halos of galaxies are kinematically thermalized due to dark matter self-interactions. The SIDM model automatically inherits all of the successes of the CDM model on large scales, as the predictions are indistinguishable at distances larger than about $10\%$ of the virial radius of galactic halos. The required cross section is similar to the proton-neutron elastic scattering cross section and this may be a strong hint that the dark matter sector replicates some elements of the standard model. The large cross section keeps the inner halo isothermal and this makes the predictions for the central halo profile at later times insensitive to the star formation history, as confirmed in recent hydrodynamical N-body simulations~\cite{Robertson:2017mgj,2017MNRAS.472.2945R}. This implies that a large variety of feedback models, e.g,~\cite{Governato:2012fa,Hopkins:2013vha,Onorbe:2015ija,Wang:2015jpa,Read:2017lvq,2018MNRAS.473.4392S}, can be compatible with the SIDM model we have discussed here. The predictions are quantitatively the same for $\sigm\gtrsim 1~{\rm cm^2/g}$. This makes our results robust, but it makes hard to precisely determine the cross section from kinematic datasets on galaxy scales~\cite{Kamada:2016euw}. There are a number of promising directions that can further test SIDM and explore galaxy formation and evolution in this framework. Here, we highlight a few of them. SIDM simulations predict a correlation between the half-light radius of the stars and the dark matter core size in dwarf and low surface brightness galaxies~\cite{Vogelsberger:2014pda}, which should be further explored and may provide an observational test of SIDM. Similarly, the ultra-diffuse galaxies in the clusters could be a test laboratory~\cite{2018arXiv180506896C}. A related issue is the origin of the large spread in the surface brightness of galaxies, which remains poorly understood. Interestingly, hydrodynamical simulations of galaxy clusters show that the stellar density profiles in SIDM are more diverse than in their CDM counterparts~\cite{Robertson:2017mgj}. Is this a more general feature in SIDM due to the dynamical interplay between core formation and feedback? How does this interplay impact the emergence of the BTFR? Finally, at the lowest mass end, the dwarf spheroidal galaxies, including the so-called ultra-faint dwarfs, in the Local Group could provide a key test of SIDM (see~\cite{Valli:2017ktb,Read:2018pft}). Dedicated SIDM simulations with the baryons will be required to explore these exciting topics. The predictive power of the SIDM model, the clear connection to cosmology, and its rich implications for other astrophysical observations and particle physics phenomenology~\cite{Feng:2009mn,Feng:2009hw,Buckley:2009in,Loeb:2010gj,Frandsen:2010yj,Frandsen:2011kt,Aarssen:2012fx,Cline:2013zca,Kahlhoefer:2013dca,Tulin:2013teo,Schutz:2014nka,Boddy:2014yra,Hochberg:2014dra,Hochberg:2014kqa,Cyr-Racine:2015ihg,Blennow:2016gde,Boddy:2016bbu,Tulin:2017ara,Kamada:2018hte,Braaten:2018xuw}, all taken together make a clear case that it should be treated on the same footing as the CDM model. The economical explanation, with the addition of just one parameter, for the diverse rotation curves across the entire range of observed galaxies argues in favor of the idea that the dark matter particles have a large affinity for the self-interactions. | 18 | 8 | 1808.05695 |
1808 | 1808.00415_arXiv.txt | Long-period comets observed in our solar system are believed to originate from the Oort cloud, which is estimated to extend from roughly a few thousand to $10^5$ AU from the Sun. Despite many theoretical arguments for its existence, no direct observations of the cloud have been reported. Here, we explore the possibility of measuring Oort clouds around other stars through their emission at submillimeter wavelengths. Observations with the 545 and 857 GHz bands of the {\it Planck} satellite are well matched to the expected temperatures of Oort cloud bodies (on the order of 10~K). By correlating the {\it Planck} maps with catalogs of stars observed by the {\it Gaia} mission, we are able to constrain interesting regions of the exo-Oort cloud parameter space, placing limits on the total mass and the minimum size of grains in the cloud. We compare our measurements with known debris disk systems -- in the case of Vega and Fomalhaut we find a significant excess that is in agreement with measurements from {\it Herschel}. We use the measurements around Fomalhaut to constrain a possible exo-Oort cloud of that system. We explore an observed excess around the brightest and nearest stars in our sample as arising from possible exo-Oort clouds or other extended sources of thermal emission. We argue that future CMB surveys and targeted observations with far-infrared and millimeter wavelength telescopes have the potential to detect exo-Oort clouds or other extended sources of thermal emission beyond $\sim 1000$ AU from the parent stars. \vspace{1cm} | The observation of comets passing through the inner solar system led \cite{Oort:1950} to hypothesize the existence of a spherical cloud of distant icy bodies, now known as the Oort cloud (OC). Since then, a number of additional theoretical arguments in support of Oort's hypothesis, as well as a more detailed understanding of the cloud's expected properties, have emerged \citep[for a review, see e.g.][]{Dones:2004, Dones:2015}. However, to date, no direct observation of the Sun's OC has been made. The Oort cloud, sometimes also called the \"Opik-Oort cloud, is believed to originate from a population of small, icy bodies within 50 AU of the sun that were present in the young solar system. Orbital perturbations caused by the giant planets would, in a short time, increase the orbital energies of many of these bodies onto highly elliptical orbits with very large semi-major axes. Bodies in regions of relative dynamic stability could remain, mainly in the ecliptic plane, resulting in the Kuiper Belt and ecliptic comet populations that we see today. For bodies with eccentric orbits and semi-major axes of tens of thousands of AU, interactions with nearby stars, the galactic potential, and nearby molecular clouds can stabilize these orbits by increasing the perihelion distances of the orbits so that perturbations by planets in our own solar system are no longer dynamically important. Assuming these gravitational interactions are isotropic, the expected result is a population of comets having semi-major axes between a few thousand and tens of thousands of AU and inclinations that are randomly distributed relative to the ecliptic plane. Since other stars likely experienced similar histories, it is reasonable to expect that they may also host their own Oort clouds, which we refer to as exo-Oort clouds (EXOCs). In fact, there have been several reported detections of exo-comets in the literature through transits (e.g.~\citealt{Rappaport:2018}) as well as the spectral signatures of evaporating small, icy bodies (e.g.~\citealt{Welsh:2016}). Other authors have investigated the fate of EXOCs as stars evolve and proposed potentially detectable signatures associated stellar remnants (e.g. \citealt{Stone:2015}). Directly detecting the OC orbiting the sun, or the EXOC of another star, is extremely challenging. The vast distances of these bodies from their parent stars mean that they are faint in reflected light. While there may be a very large number of OC bodies, their total surface area results in an effective OC optical depth that is extremely small, $\tau<10^{-6}$, even if the OC is very massive (above 100$M_\earth$) and contains a large number of small (micron-sized) particles. Stellar occultations provide a promising avenue for directly detecting bodies in our OC (see \citealt{Lehner:2016, Ofek:2010}), but the events are very short (less than 1~second in duration) and rare, meaning that a large number of stars have to be observed at very high cadence. In principle, the thermal emission from the OC imprints a distortion of the black body spectrum of the CMB, but even for optimistic assumptions about the mass of our OC, this signal is too small to be observed with existing CMB experiments (\citealt{Babich:2007, Babich:2009,Ichikawa:2011}). \citet{Cowan:2016} explored the possibility of detecting thermal emission from the hypothetical `Planet Nine,' believed to reside in the Oort cloud, using existing and future CMB experiments, and found that detection prospects were promising. Detecting thermal emission from OCs around nearby, bright stars is another possibility. Particularly at long wavelengths close to the peak of the EXOC blackbody, the large aggregate surface area of emitters in the EXOC means that thermal emission from the central star itself is expected to be orders of magnitude smaller than that from the EXOC, even though the star is much hotter than the typical EXOC body. \citet{Stern:1991} used IRAS data to search for excess mid-IR emission in the vicinities of a small number of nearby, bright stars in an attempt to place limits on the total masses of their EXOCs. We will pursue longer wavelengths that are more suitable for EXOC detection using a much larger sample of stars. Given that the OCs of nearby stars may be tens of thousands of AU in diameter, they may subtend tens of arcminutes on the sky as seen from Earth. This makes it possible to use high spatial resolution, wide-area CMB surveys like \textit{Planck} (\citealt{Planck:2018}) to place limits on the average excess thermal emission at millimeter and submillimeter wavelengths using large samples of nearby stars having precise distances now measured by \textit{Gaia} (\citealt{Gaia:2018}). Such emission can be distinguished from more localized debris disk or point source emission using the large difference in scales between such emission and that of an EXOC. Typical debris disks extend to only a few hundred AU at most, orders of magnitude smaller than the expected sizes of EXOCs. In this work, we analyze \textit{Planck} 545 and 857 GHz maps to place limits on the total non-stellar thermal emission within the EXOC regions of a sample of main sequence stars within 300~pc of the Sun identified using {\it Gaia} data. We use stacked measurements across these stars to place limits on the properties of EXOCs. Since it is not known how generic EXOCs are, we also explore for the brightest stars the possibility that only some fraction of them have EXOCs. We argue that current and future CMB surveys may offer the possibility of improved limits on EXOC properties, and explore the possibilities for future detections using targeted observations. The paper is organized as follows: in \S\ref{sec:model} we describe the expected properties Oort clouds, and our model for their thermal emission; in \S\ref{sec:data} we describe the datasets used in this analysis; in \S\ref{sec:measurements} we describe our procedure for measuring the thermal emission signal around the {\it Gaia} stars. Our results are presented in two parts: in \S\ref{sec:stacked_results} we show the results averaged over many of the stars in the sample, while in \S\ref{sec:hot_results}, we investigate possible signals around the closest and hottest stars. We conclude and discuss prospects for future measurements in \S\ref{sec:discussion}. | \label{sec:discussion} \subsection{Summary and caveats} The analysis presented here demonstrates that detection of extra solar Oort clouds (EXOCs) with data from CMB surveys is promising. By correlating the 545 and 857 GHz {\it Planck} maps with {\it Gaia}-detected stars, we place limits on the properties of EXOCs, in particular on the mass contained in them and the minimum grain size (Figs.~\ref{fig:exclusion} and \ref{fig:exclusion_fomalhaut}). We compare our measurements with known debris disk systems -- in the case of the stars Vega and Fomalhaut we find a significant excess that is in agreement with measurements from {\it Herschel}. With conservative estimates of the uncertainty due to background fluctuations around these stars, we do not see a significant excess at large distances beyond the debris disk signal convolved with the {\it Planck} beam. We use the measurements around Fomalhaut to constrain a possible EXOC of that system. We have also identified a potentially interesting excess emission signal around nearby hot stars, shown in Fig.~\ref{fig:bright_stars} and \ref{fig:indiv_stars}. We found statistically significant signal in the {\it Planck} 857 GHz and 545 GHz channels at distances of $10^4$ to $10^5$ AU in a sample of 43 nearby hot stars, mostly A stars. This emission can be fit reasonably well with EXOC models, although doing so requires somewhat extreme parameter choices relative to the constraints on the properties of our own Oort cloud. Such extreme EXOC models would also be ruled out by the constraints shown in Fig.~\ref{fig:exclusion}, although those limits could be avoided if only a small fraction of stars host EXOCs. EXOC emission is not the only explanation for the apparent excess emission around our hot star sample. We have described our procedure for masking and subtracting potential contributions from galactic dust, which is our primary source of systematic uncertainty. If the signal is indeed real, it could result from at least two other sources: a ``halo'' of particles ejected from the debris disks by radiation pressure or stellar winds, or nebular emission seen in young stars. The ages of the hot stars in our sample are typically larger than 100 Myr, so the latter explanation appears unlikely. Distinguishing a genuine exo-Oort cloud from a particle ``halo'' appears challenging, as the emission in both cases is dominated by small grains. We have not pursued these possibilities in any detail but future studies with higher resolution and sensitivity data would be valuable. The connection of thermal emission well beyond the scale of debris disks to the planetary system of host stars is a topic of great interest. The generation of extended scattered disks and Oort clouds like our own require the dynamical presence of Neptune-Jupiter sized planets for Sun-like stars. The scale of the Oort cloud is also influenced by the early environment of the star, such as the possible presence of a star cluster. Hence empirical knowledge of the statistics of EXOCs and their correlation with the planets and debris disks of host stars can yield insights on the early stages of the formation of stars and planetary systems. \subsection{Strategies for future measurements} We now turn our attention to prospect for future analyses. In the current analysis, we have focused on two measurement strategies: stacked measurements on many stars, and measurements around individual bright stars. The data requirements and aims of future analyses will depend on which measurement strategy is adopted. The advantage of a stacked analysis is that one can effectively beat down noise sources by averaging. However, it is not clear whether all stars host Oort clouds, so this averaging may also reduce the measured signal. Observations of individual stars do not suffer from this drawback, but must reach significantly higher sensitivities per star to reach the threshold for detection. Both approaches seem worth pursuing in future analyses. For a stacking analysis, wide field survey data is ideal since it will enable averaging over many stars. For measurements around individual stars, targeted observations would likely offer higher signal to noise. In both cases, one must determine a distance threshold to use for identifying stellar candidates. For distances $d \lesssim 300\,{\rm pc}$, the number of stars available for the analysis goes as the distance cubed. At distances of $d \gtrsim 300\,{\rm pc}$, however, one reaches the limits of the disk of the Milky Way, and the number of stars will increase more slowly with distance. Additionally, separating EXOC emission from possible debris disk emission could be very difficult for distant stars. If the EXOC is resolved (which may be realistic up to around 1~kpc), its surface brightness will be independent of distance. Even so, the number of beams one can average, which is desirable, is greater for nearby EXOCs. Given expected temperature estimates in the range of 10 to 50 K for parts of EXOCs, wavelengths from about 60 to 300 $\mu$m or frequencies from about 600 to 5000 GHz would be well matched to detection of EXOC emission. For sun-like stars, the lower wavelength and upper frequencies ends of these ranges would be optimal. While pushing to lower frequencies may not be optimal in terms of the amplitude of the signal, the background from galactic cirrus will also be reduced. As seen in several of the figures above, the error bars for the 545 GHz measurements are typically smaller than those of the 857 GHz measurements for precisely this reason. While the expected temperature ranges of EXOCs are well constrained, the signal amplitude is largely uncertain. For reasonable choices of model parameters, the intensity of the EXOC thermal emission ranges from about $10^{-2}\,{\rm MJy}/{\rm sr}$ in the inner parts of the clouds to $10^{-6}\,{\rm MJy}/{\rm sr}$ in the outer parts (see e.g. Fig.~\ref{fig:model_curves}). Sensitivities better than $10^{-5}\,{\rm MJy}/{\rm sr}$ would be ideal for detecting extended EXOC emission, but there are regions of parameter space where detection could be achieved with considerably less sensitive measurements. In addition to high sensitivity, perhaps the most desirable feature for future observations would be high angular resolution. For reasonable model parameters, the EXOC signal drops rapidly with distance from the star. Consequently, for a large beam, it is difficult to distinguish EXOC emission from point-like emission, which could for example be sourced by a debris disk. Furthermore, the background fluctuations from galactic dust have less power on very small scales, so a small-scale EXOC signal could be more easily separated from backgrounds. Pushing the beam to below $R = 10^3\,{\rm AU}$, either by using nearby stars or a higher angular resolution instrument, would be ideal. \subsection{Prospects for EXOC measurements using CMB and far-infrared datasets} In this analysis, we have used 545 and 857 GHz data from \emph{Planck} to attempt to measure EXOC emission. This dataset is well matched in terms of frequency and has the advantage of large sky coverage. However, the measurements with \emph{Planck} suffer from the effects of a large beam relative to the scales of an EXOC. There are several current and future datasets that may be well matched to detecting Oort cloud emission, which we summarize below. Given their large sky coverage and high sensitivity to microwave frequencies, CMB survey data is well matched to stacked searches for Oort cloud emission. Among ongoing CMB experiments, the South Pole Telescope (SPT; \citealt{Carlstrom:2011}) and the Atacama Cosmology Telescope (ACT; \citealt{Swetz2011}) offer higher resolution and deeper maps over thousands of square degrees of the sky. Future CMB observations from Advanced ACTPol \citep{Henderson:2016}, SPT-3G \citep{Benson:2014}, the Simons Observatory \citep{SOforecast} and CMB-S4 \citep{Abazajian:2016} will provide significantly deeper and higher resolution maps of the microwave sky than the {\it Planck} maps considered here, and over wide regions of the sky. With current {\it Planck} data we have reached sensitivities of roughly $10^{-3}\,{\rm MJy}/{\rm sr}$ in stacked measurements. Future data from stage-III and stage-IV CMB experiments is expected to be roughly 10 and 100 times more sensitive than current \emph{Planck} data, respectively \citep{Abazajian:2016}. However, a significant limitation of the current analysis is our ability to model galactic backgrounds. With higher resolution data, background modeling could be significantly improved, and presumably more stars could be included in the analysis. Assuming a factor of 10 increase in the number of stars and factors of 10 or 100 improvements in the sensitivity, it should be possible to reach sensitivities of roughly $3\times 10^{-6}$ to $10^{-5}\,{\rm MJy}/{\rm sr}$ in stacked measurements. At these sensitivities, reasonable Oort cloud models could be detected out to their edges, at $R \sim 5\times 10^{4}$ AU. Additionally, this level of sensitivity should be sufficient to detect emission from individual EXOCs around nearby stars for reasonable models. Wide-field CMB or infrared surveys are well matched for stacked searches for EXOC emission. Targeted observations at similar frequencies, on the other hand, could be used to detect emission from individual EXOCs. There are several current instruments that could potentially be used to this end, including the Large Millimeter Telescope, MUSTANG-2 \citep{Mustang2}, ALMA \citep{ALMA}, and BLASTPol \citep{Blastpol}. While the peak emission of a 10K Oort cloud is well matched to the 545 and 857 GHz maps considered here, the inner, hotter parts of EXOCs could have peak emission closer to the infrared bands. As noted previously, searches for EXOCs have already been attempted using IRAS \citep{Stern:1991}. Other infrared instruments with capabilities similar to those of {\it Herschel} could be potentially well matched to EXOC detection. Debris disks around stars have already been detected by {\it Herschel}; searching for Oort cloud emission would simply involve extending these searches to larger distances from the parent stars. Further out in time, the WFIRST survey may provide additional constraints on EXOCs in the infrared, including possible detection of bodies in the Inner Oort cloud \citep{Holler:2017}. Finally, we expect our understanding of the properties of our own Oort cloud to improve significantly with future observations from the Large Synoptic Sky Survey (LSST) \citep{LSSTsciencebook,Trilling:2018}. By observing significant numbers of long period comets and Halley-type comets, LSST should constrain dynamical models of the Oort cloud, resulting in improved constraints on e.g. its density profile. Such constraints will inform searches for EXOCs as well. \bigskip \vspace{1cm} {\it Acknowledgements} We are grateful to Gary Bernstein, Mark Devlin, Doug Finkbeiner, Mike Jarvis, Renu Malhotra, Tom Crawford, Gil Holder and Adam Lidz for many helpful discussions and feedback on an early draft. We thank James Aguirre, Ana Bovana, Chihway Chang, Neal Dalal, Meredith Hughes, Jeff Klein, Anthony Lewis, Niall MacCrann, Gemma Moran, Eduardo Rozo, Masao Sako, Carles S\'anchez, Masahiro Takada, Martin White for stimulating discussions. | 18 | 8 | 1808.00415 |
1808 | 1808.09228_arXiv.txt | Molecular species, most frequently H$_2$, are present in a small, but growing, number of gamma-ray burst (GRB) afterglow spectra at redshifts $z\sim2-3$, detected through their rest-frame UV absorption lines. In rare cases, lines of vibrationally excited states of H$_2$ can be detected in the same spectra. The connection between afterglow line-of-sight absorption properties of molecular (and atomic) gas, and the observed behaviour in emission of similar sources at low redshift, is an important test of the suitability of GRB afterglows as general probes of conditions in star formation regions at high redshift. Recently, emission lines of carbon monoxide have been detected in a small sample of GRB host galaxies, at sub-mm wavelengths, but no searches for H$_2$ in emission have been reported yet. In this paper we perform an exploratory search for rest-frame $K$ band rotation-vibrational transitions of H$_2$ in emission, observable only in the lowest redshift GRB hosts ($z\lesssim0.22$). Searching the data of four host galaxies, we detect a single significant rotation-vibrational H$_2$ line candidate, in the host of GRB\,031203. Re-analysis of {\em Spitzer} mid-infrared spectra of the same GRB host gives a single low significance rotational line candidate. The (limits on) line flux ratios are consistent with those of blue compact dwarf galaxies in the literature. New instrumentation, in particular on the {\em JWST} and the {\em ELT}, can facilitate a major increase in our understanding of the H$_2$ properties of nearby GRB hosts, and the relation to H$_2$ absorption in GRBs at higher redshift. | } Gamma-ray burst (GRB) afterglow spectroscopy has shown great promise as a probe of gas and dust properties within, and near, star forming regions in distant galaxies (see e.g. \citealt{Schady} for a review). The bright afterglows serve as backlights with a simple (sometimes reddened) synchrotron spectrum, against which atomic and molecular absorption lines are easily distinguished. In addition, the ultraviolet radiation of the rapidly fading afterglow excites meta-stable and fine structure atomic states. The variability of absorption lines from these transitions allows precise distance determination of the absorbing gas with respect to the GRB in cases with high signal-to-noise spectra (e.g., \citealt{Vreeswijk}). Long gamma-ray bursts (broadly speaking those with a duration longer than $\sim2$ s) are associated with the deaths of massive stars, and their rate is therefore thought to trace cosmic star formation, likely moderated by a metallicity threshold for formation (e.g. \citealt{PerleyShoals2} and references therein). This means that GRBs and their bright afterglows may form a valuable tool to locate, and study, actively star forming galaxies across cosmic time, unbiased by galaxy luminosity (except perhaps through a luminosity-metallicity dependence). A key advantage offered by GRBs over quasars as backlights, is that the host galaxies can be studied in emission once the afterglows have faded, through spectral energy distributions (to obtain stellar population parameters, e.g.~\citealt{PerleyShoals2}) and emission lines (to obtain element abundances and star formation rates, e.g.~\citealt{KruehlerXSHemission}). These studies in emission complement the line of sight studies of afterglows, connecting the afterglow sight lines through their hosts with host galaxy integrated emission properties. Sample sizes of hosts and afterglow spectra are growing, and statistical studies of metal abundances, stellar populations and dust properties are now possible, placing GRB host galaxies in the context of wider galaxy surveys (e.g. \citealt{Vergani}). An important component of the picture, though, the molecular content, is still poorly understood. Of particular interest is the \hmol\ molecule, which plays a key role in the processes of star formation. An additional advantage of host studies is that it is not limited to the subset of GRBs for which the optical afterglow is detected (provided the host can be reliably identified, see e.g. \citealt{Perley020819B}). There is evidence that most of the GRB sightlines that pass by significant column densities of molecules also will contain large dust column densities and hence that such sightlines are underrepresented in the subset of GRBs with well-detected optical afterglows (\citealt{Prochaska080607h2}; \citealt{Kruehlerh2grb120815}). The peculiar case of GRB140506, for which CH+ molecules were detected in absorption along with very steep UV extinction further supports this point (\citealt{GRB140506}; \citealt{Heintz17}). The homonuclear \hmol\ molecule does not have a dipole moment, so electric dipole transitions between levels with different vibrational quantum number ($\nu$) or rotational quantum number ($J$) in the ground state are forbidden. Quadrupole transitions, however, are allowed, and the pure rotational lines (with $\nu = 0-0$) are located at (mid-)infrared wavelengths, which makes them challenging to study, particularly for faint sources like GRB hosts. Of more interest to us are the rotation-vibration (hereafter ro-vibration) transitions in the ground state. In the following we adopt the standard notation, where the difference in $J$ is given by a letter (O, Q, S for $\Delta J = +2,0,-2$, respectively), followed by the final state $J$, and preceded by the vibrational transition (so 1--0 S(1) is $\nu=1-0, J=3-1$). The main ro-vibrational lines are located at near-infrared wavelengths. For example, the 1--0 S(0), 1--0 S(1) and 1--0 S(3) transitions are located at 2.22, 2.12 and 1.96 $\mu$m, respectively, in the restframe. At low redshifts, these transitions can therefore be detected by ground-based observatories. The first allowed transitions out of the \hmol\ ground state to an excited state are the Lyman and Werner bands, which require ultraviolet (UV) photons. These transitions have indeed been observed in a handful of GRB afterglow spectra (\citealt{Prochaska080607h2}; \citealt{Kruehlerh2grb120815}; \citealt{DElia120327molecules}; \citealt{Friis}, and possibly in \citealt{GRB060206}), where the redshifts of the GRBs shift these transitions from the UV to the optical domain. Identification and analysis is difficult: these transitions are located among the atomic hydrogen lines of the dense Lyman forest, and as such a fairly high signal-to-noise and spectral resolution is required to separate them. In very rare cases, highly diagnostic absorption lines of vibrationally excited \hmol\ are found (\citealt{Scheffer2009}; \citealt{Kruehlerh2grb120815}), that are located redwards of the Ly$\alpha$ line. The detection of Lyman-Werner lines, combined with fits to the atomic hydrogen Ly$\alpha$ line (in GRB sight lines often found as a strong, highly damped line, a damped Lyman absorber [DLA], \citealt{Jakobsson06}) has allowed estimates of the molecular gas fraction (integrated over the line of sight), and helps to place the relatively small GRB \hmol\ absorption sample in the context of the much larger sample of quasar DLAs (e.g., \citealt{Noterdaeme08}; \citealt{Noterdaeme}). The sightline selection function of long GRBs is arguably quite different from those of QSO DLAs (e.g. \citealt{ProchaskaDLAs}; \citealt{Fynbo08}; \citealt{Fynbolowressample}), which makes the long GRB afterglow H$_2$ sample especially valuable as a probe of high-redshift star forming regions. Of particular interest is that long GRBs trace cosmic star formation (e.g. \citealt{Greiner}), and therefore the \hmol\ absorption seen in afterglows may probe the conditions in star forming regions within (dwarf) star-forming galaxies at the peak of cosmic star formation ($z\sim2-4$). However, whilst afterglow sightlines likely probe regions near long GRBs in high mass star forming regions, which should be rich in \hmol\ (e.g. \citealt{Tumlinsonnondetections}), the low detection rate, the excitation state of the detected \hmol, and occasionally the association of the \hmol\ absorber with excited atomic metal fine structure lines, have shown that in several cases the \hmol\ absorbers are likely located far from the star forming region in which the GRB progenitor resided (e.g. \citealt{DElia120327molecules}). The low detection rate of \hmol\ in afterglow spectra is puzzling. Several explanations have been put forward, that likely all play a role: dissociation of the \hmol\ molecules by a high UV radiation field from the intense star formation in the host galaxy (e.g. Hatsukade et al. 2014); observational biases against sightlines with high dust columns and against high-metallicity environments (e.g. Ledoux et al. 2009; Covino et al.~2013); and formation of stars from atomic gas before \hmol\ has a chance to form (e.g. Michalowski et al. 2016). An alternative approach to detecting molecular species in GRB host galaxies is through emission line spectra. This has the added advantage of avoiding problems in interpreting line of sight measurements (e.g. the effects of ionisation and excitation by the GRB emission) and can help to place the line of sight absorption in an integrated, or in low-z cases spatially resolved (e.g. \citealt{Hatsukade}), galaxy context (\citealt{Michalowski100316D}). To date, a handful of host galaxies have been detected in molecular line emission, in all cases this is through emission lines of carbon monoxide (CO) (\citealt{Hatsukade}; \citealt{080517CO}; \citealt{Michalowski2016}; \citealt{Arabsalmani}; \citealt{Michalowski2018}). The use of CO as a tracer molecule for \hmol\ is a well established technique, though evidence that the CO to \hmol\ conversion factor in GRB host sightlines is comparable to Galactic translucent clouds, is limited to a single case (\citealt{Prochaska080607h2}): the only afterglow spectrum so far with a detection of CO absorption lines. The metallicity dependence of the CO to \hmol\ conversion factor, and other environmental effects (e.g. \citealt{Bolatto}), make the CO to \hmol\ conversion factor (and therefore a clear picture of whether GRB hosts are deficient in molecules or not) for GRB sightlines uncertain (e.g. \citealt{Arabsalmani}; \citealt{Michalowski2018}). In addition, most of the host galaxies with detected CO emission lines have a detection of only a single transition. These reasons, together with the low detection rate of CO absorption in optical afterglow spectra, makes a direct comparison between host galaxy CO emission and afterglow CO absorption difficult. No detections of \hmol\ emission, through either pure rotational or ro-vibrational transitions, have been reported to date. In this paper we perform a first exploratory search for ro-vibrational \hmol\ lines in a sample of four, low redshift, long GRB host galaxies, to inform more sensitive searches with future observatories. \begin{table*} \centering \caption{ Observations used in this paper. $^*$: Note that the spectroscopic observations discussed in this paper concern the brightest star forming region in this host galaxy, known as source A (\citealt{100316DStarling}). The magnitudes given in this table are all integrated magnitudes for the whole host galaxy. References for spectroscopy data: [1] Watson et al. (2011), [2] Wiersema (2011), [3] This work, [4] Starling et al. (2011). References for the host infrared magnitudes: [5] Prochaska et al. (2004), [6] Hjorth et al. (2012), [7] This work, [8] Micha{\l}owski et al. (2015). References for abundance: [9] Guseva et al. (2011), [10] Wiersema et al. (2007); [11] Stanway et al. (2015a), [12] Starling et al. (2011). \label{table:obslog}} \begin{tabular}{llllll} \hline GRB host & Instrument & Obs date & Redshift & Host IR (Vega) magnitude & $12+\log({\rm O/H})$ \\ \hline 031203 & VLT X-Shooter & 17 March 2009 [1] & 0.105 & $K' = 16.54 \pm 0.02$ [5] & 8.20 [9] \\ 060218 & VLT ISAAC & 17 July + 10 Sep. 2008 [2] & 0.033 & $K_s = 17.94 \pm 0.09$ [6] & 7.54 [10] \\ 080517 & WHT LIRIS & 3/4 March 2015 [3] & 0.089 & $K_s = 15.51 \pm 0.06$ [7] & $\sim$8.7 [11] \\ 100316D$^*$ & VLT X-Shooter & 17 March 2010 [4] & 0.059 & $K_s = 15.93 \pm 0.09$ [8] & 8.23 [12] \\ \hline \end{tabular} \normalsize \end{table*} | \label{sec:conclusions} Motivated by the recent detections of CO molecule emission in GRB host galaxies, we searched rest-frame infrared spectra of a sample of four low redshift GRB host galaxies for signatures of H$_2$ ro-vibrational emission lines. A single ro-vibrational \hmol\ emission line candidate is detected at the position of the 1--0 S(3) transition in the host of GRB\,031203. The other GRB host spectra in our sample show no significant \hmol\ line candidates, which is likely caused by signal-to-noise and resolution limitations, as well as the positions of the lines near telluric absorption features. We re-analysed low resolution {\em Spitzer} mid-infrared spectra of the host of GRB\,031203 to search for \hmol\ rotational lines. A single weak line candidate, at the position of the 0--0 S(7) transition, is seen, but the reality of this line is debatable, because of the low resolution of the {\em Spitzer} spectra. Observations with future facilities with better resolution and higher sensitivity, particularly from space, will provide the means to detect the multiple lines required for proper comparison with low-redshift galaxy samples and high redshift molecule detections in afterglow spectra. | 18 | 8 | 1808.09228 |
1808 | 1808.05230_arXiv.txt | {Core collapse is a prominent evolutionary stage of self-gravitating systems. In an idealised collisionless approximation, the region around the cluster core evolves in a self-similar way prior to the core collapse. Thus, its radial density profile outside the core can be described by a power law, $\rho \propto r^{-\alpha}$.} {We aim to find the characteristics of core collapse in $N$-body models. In such systems, a complete collapse is prevented by transferring the binding energy of the cluster to binary stars. The contraction is, therefore, more difficult to identify.} {We developed a method that identifies the core collapse in $N$-body models of star clusters based on the assumption of their homologous evolution.} {We analysed different models (equal- and multi-mass), most of which exhibit patterns of homologous evolution, yet with significantly different values of $\alpha$ : the equal-mass models have $\alpha \approx 2.3$, which agrees with theoretical expectations, the multi-mass models have $\alpha \approx 1.5$ (yet with larger uncertainty). Furthermore, most models usually show sequences of separated homologous collapses with similar properties. Finally, we investigated a correlation between the time of core collapse and the time of formation of the first hard binary star. The binding energy of such a binary usually depends on the depth of the collapse in which it forms, for example\ from $100\,kT$ to $10^4\,kT$ in the smallest equal-mass to the largest multi-mass model, respectively. However, not all major hardenings of binaries happened during the core collapse. In the multi-mass models, we see large transfers of binding energy of $\sim 10^4\,kT$ to binaries that occur on the crossing timescale and outside of the periods of the homologous collapses.} {} | \label{sec:intro} Two-body relaxation states that any star moving through a field of stars is decelerated by the force of dynamical friction \citep{chandrasekhar}, which is proportional to the mass of the moving star and inversely proportional to its velocity squared. This force is also responsible for mass segregation in multi-mass systems. Since the heat capacity of a self-gravitating system in virial equilibrium is negative \citep[e.g.][]{lb_w,binney_tremaine}, the central region of a star cluster should contract over time. Consequently, the central parts relax more quickly than the halo and the velocity distribution in the centre is almost Maxwellian \citep{larson}. Within the thermodynamic framework, the core is supposed to collapse, reaching infinite density and kinetic temperature in a finite time (also known as the gravothermal catastrophe). Unlike continuum models, in $N$-body models (and real star clusters) this sequence is prevented by the presence of existing or newly formed binary stars in the core, whose ability to efficiently expel other stars via three-body interactions cools the core \citep[e.g.][]{aarseth1972,hut,fujii_pz,oleary}. The cluster core gradually shrinks towards the collapse and then expands rapidly (so called core bounce). Thus, the event of core collapse may be indirectly observed but its exact time is no longer well defined. \cite{lb_e} showed that the evolution of a spherically symmetric collisionless system prior to core collapse should be self-similar (homologous), that is\ its density evolves with respect to the radius and time according to the \hbox{scaling relation} \begin{equation} \label{eq:density} \rho(r, t) = \rhoc(t) \, \rhostar(\rstar) \,. \end{equation} Here, $\rhoc$ is the core density, $\rhostar$ is a dimensionless structure function, and the radius is described using an enclosed mass $m$ and a scaling factor $\rstar$, \begin{equation} \label{eq:radius} r(m, t) = \rc(t) \, \rstar\!\left(\frac{m}{\mc}\right) \,, \end{equation} where $\rc$ stands for the core radius and $\mc \propto \rhoc \rc^3$ is the core mass. The homologous solution implies that the internal structural scaling has an exponent $\alpha$ that remains temporally invariant. As it must also satisfy smoothness conditions for $\rhostar(\rstar)$ and normalisation, generally $\alpha = \mathrm{const.}$ (\citealt{lb_e}, also e.g.\ \citealt{penston}). The core radius then depends on the core density as $\rhoc \propto \rc^{-\alpha}$ and the temporal evolution of the core radius before the time of core collapse, $\tcc$, is \begin{equation} \label{eq:self_similar} \rc(t) \propto (\tcc - t)^{\frac{2}{6 - \alpha}} \,. \end{equation} According to \cite{lb_e}, the radial density profile may be approximated by a double-broken power-law function with the logarithmic density gradient defined as \begin{equation} \label{eq:alpha} a \equiv -\frac{\der \log{\rho}}{\der \log{r}} \, ,\end{equation} which is equal to zero in the cluster core and reaches $\alpha$ asymptotically. In an intermediate region above $\rc$, the logarithmic density gradient has to be larger than $\alpha$ to compensate for the missing mass in the core (see the slopes $a_\I$, $a_\II$ , and $\alpha$ in Fig.~\ref{fig:schema}). \citet{lb_e} found $\alpha \approx 2.208$. Further works based on either isotropic \citep{cohn} or anisotropic models \citep{takahashi} in a Fokker--Planck approximation led to a slightly different value, $\alpha \approx 2.23$. In $N$-body star clusters, the self-similar solution is not infinite. In this case, distant parts of the halo tend to a Maxwellian distribution of velocities on the relaxation timescale. This changes the logarithmic density gradient in the halo to $a = 3.5$ \citep{spitzer_hart}. Hence, we expect the cluster's radial density profile to be approximated by a triple-broken power law as indicated by a solid line in Fig.~\ref{fig:schema}. \begin{figure} \includegraphics[width=\linewidth]{schema-eps-converted-to} \caption{Schematic plot of the radial density profile in an $N$-body cluster during the core collapse with four different values of the logarithmic density gradient, $a_{\I-\IV}$\,. The dotted line has a slope equal to $\alpha$ and shows the asymptotic solution of \citet{lb_e}. The break radius $r_\I$ is identified with the core radius, $r_\III$ roughly corresponds to the half-mass radius, and $r_k$ is the cluster radius. The notation is the same as in Eq. \eqref{eq:broken} that we used for the fitting of our numerical models.} \label{fig:schema} \end{figure} Radial density profiles of numerical $N$-body models \citep[e.g.][]{giersz_heggie,makino,core_collapse} show a good agreement with the expectations above. In this paper we go beyond those works in several aspects: (i) computational resources available nowadays enable us to integrate and analyse hundreds of realisations of models consisting of tens of thousands of particles; (ii) besides equal-mass models, we evaluate models with a Salpeter mass function and; (iii) we not only analyse the density profile of the cluster at the time of core collapse but also test the hypothesis of a homologous evolution in time which, among other things, allows us to formulate a new method for determining the time of core collapse. | We investigated the properties of core collapse in numerical $N$-body models of self-gravitating star clusters. For that purpose, we developed a novel method for the identification of the time of core collapse. The method is based on an assumption proposed for analytic models by \citet{lb_e} that the evolution of the cluster is self-similar. In the case of equal-mass models (\emod\ and \emodi), we found a very good agreement with theoretical expectations. Minima of the Lagrangian radii for small mass fractions are aligned according to a power-law relation $\rlmin \propto \big( \tcc - \tmin \big)^{\frac{2}{6 - \alpha}}$ with the power-law index close to $\alpha \approx 2.3$. At the time of core collapse, the cluster's radial density profile in the intermediate region between the core and the half-mass radius is well approximated by a power law $\rho \propto r^{-a_\III}$, with $a_\III \approx 2.3$. The fact that $a_\III \approx \alpha$ indicates that the cluster's evolution matches the self-similar solution of \citet{lb_e}. The density profile in the halo is best fitted by a power law with index $a_\IV \approx 3.4,$ which is close to the prediction formulated by \citet{spitzer_hart} for the evolution of halos of $N$-body models. Further, we analysed $N$-body models of star clusters with a \citet{salpeter} mass function (\mmod\ and \mmodi). Using our method, we identified the times of core collapse and determined the radial density profile of the clusters at that moment. We found that the cluster's evolution and density profile are qualitatively similar to the previous case, although the power-law index $\alpha$ has a significantly different value. Specifically, the best-fit value of $\alpha$ for temporal evolution of the inner Lagrangian radii is $1.5$, which is nearly identical to the power-law index of the radial density profile beyond the cluster core, $a_\III \approx 1.6$. Thus, we conclude that these models show traces of self-similar evolution. We also studied the evolution of a multi-mass model (\mmodii) with the same slope of the mass function as \mmod\ and \mmodi\ but a higher ratio between the total mass and the most massive star. In terms of self-similar evolution, we expected this model to be a ``bridge'' between the equal- and multi-mass models that we have already discussed. However, there were big differences in the radial profiles across the realisations, caused by random oscillations of the core region. In most realisations, we were unable to successfully fit the minima of the Lagrangian radii and clearly determine the time of core collapse and its homologous properties. Our results show that analytic predictions on the self-similar evolution are valid in the limit of equal-mass $N$-body systems but cannot be straightforwardly generalised for multi-mass (i.e.\ more realistic) star clusters. A further study from both the analytic and numerical point of view is needed to conclude whether multi-mass systems with a general mass function do undergo self-similar core collapse evolution, perhaps with the homologous index dependent on the mass function properties. Any future studies of this topic would certainly benefit from analysing even more populous clusters. In the case of \mmod\ and \mmodi\ as well as in \emodi, we found subsequent phases of coherent evolution of the inner Lagrangian radii even after the core collapse. Evolution toward all those minima have similar characteristics and homologous properties (i.e.\ depth of the core contraction, power-law indices $\alpha$ , and the radial density profiles). Therefore, we conclude that they are observationally indistinguishable from each other. The only prominent difference between the first and subsequent homologous collapses is that the time of the first one is well correlated among different realisations, which corresponds to the argument made by \citet{fujii_pz}. Our values of $\tcc$ are $52.9 \pm 8.1$ (\mmod) and $116 \pm 38$ (\mmodi), while for the second and third collapses, for example\ in \mmod, we have found $101 \pm 21$ and $120 \pm 17$, respectively (see also Table~\ref{tab:Tcc_alpha}). A large deviation of the times of subsequent collapses implies that they are smeared out in the plots of the Lagrangian radii averaged over all realisations of the particular models (see Figs.~\ref{fig:lagr_m20k}~\&~\ref{fig:lagr_m100k}). In the case of \mmod, we identified two such homologous collapses (including the first one) in 80\,\% and three in 45\,\% of the realisations within the integration time. All realisations of \mmodi\ passed at least three homologous collapses. Finally, we studied the correlation of the time of core collapse, $\tcc$, determined by our method with the formation of dynamical binaries in the cluster. In the case of \emod, we found the best correlation of $\tcc$ with the time when the first binary acquired binding energy higher than $100\,kT$ (correlation coefficient of $0.909$), yet only a slightly smaller value ($\approx 0.88$) was obtained for the correlation with the first occurrence of a binary with $\Ebin > 10\,kT$. This indicates that (i) the flow of energy toward the binaries is indeed very fast during the core collapse and (ii) the formation of the first hard binary with relatively poorly constrained binding energy may be used to identify the core collapse. In the multi-mass model we have the best correlations for binding energies between $750\,kT$ and $1250\,kT$, where the correlation coefficient is in the range from $0.53$ to $0.58$. Analytic estimates for the binding energy of binaries formed during the core collapse derived by \citet{fujii_pz} give values of $10\,kT$ and $750\,kT$ for the \emod\ and \mmod\ models, respectively. Detailed inspection of our models revealed that a large transfer of binding energy from the cluster to binaries occurs not only during the core collapse but also during the subsequent homologous collapses. On the other hand, tracking the binding energy of binaries in our models (\mmod\ in particular) revealed that episodes of large energy transfer are much more numerous than the homologous collapses. In other words, there are common events of formation of (or hardening of existing) binaries that cannot be identified with any homologous collapse. In some cases, these interactions led to a change of binding energy of the order of $10^4\,kT$ on a timescale shorter than one crossing time,\ exceeding by an order of magnitude the energy transfer rate related to the homologous collapses. The formation of the first hard binary star (in a system without primordial binaries) is well correlated with the phase of core collapse in a star cluster. As there are no other hard binaries present in the system, it is a good indicator of this event. After the system has already collapsed once and has produced at least one hard binary star, neither the formation of a new hard binary nor a large transfer of binding energy into existing ones can be considered as an indicator of the subsequent homologous contractions. From that perspective, it would be intriguing to examine homologous properties and binary evolution during the core collapse in systems containing a primordial binary population. | 18 | 8 | 1808.05230 |
1808 | 1808.04831_arXiv.txt | The joint detection of gravitational waves (GWs) and $\gamma$-rays from a binary neutron-star (NS) merger provided a unique view of off-axis GRBs and an independent measurement of the NS merger rate. Comparing the observations of GRB170817 with those of the regular population of short GRBs (sGRBs), we show that an order unity fraction of NS mergers result in sGRB jets that breakout of the surrounding ejecta. We argue that the luminosity function of sGRBs, peaking at $\approx 2\times 10^{52}\, \mbox{erg s}^{-1}$, is likely an intrinsic property of the sGRB central engine and that sGRB jets are typically narrow with opening angles $\theta_0 \approx 0.1$. We perform Monte Carlo simulations to examine models for the structure and efficiency of the prompt emission in off-axis sGRBs. We find that only a small fraction ($\sim 0.01-0.1$) of NS mergers detectable by LIGO/VIRGO in GWs is expected to be also detected in prompt $\gamma$-rays and that GW170817-like events are very rare. For a NS merger rate of $\sim 1500$ Gpc$^{-3}$ yr$^{-1}$, as inferred from GW170817, we expect within the next decade up to $\sim 12$ joint detections with off-axis GRBs for structured jet models and just $\sim 1$ for quasi-spherical cocoon models where $\gamma$-rays are the result of shock breakout. Given several joint detections and the rates of their discoveries, the different structure models can be distinguished. In addition the existence of a cocoon with a reservoir of thermal energy may be observed directly in the UV, given a sufficiently rapid localisation of the GW source. | The connection between neutron star-neutron star (NS-NS) or neutron star-black hole (NS-BH) mergers with short-duration Gamma Ray Bursts (sGRBs) and the nucleosynthesis of $r$-process elements dates back to a few seminal works from the nineteen seventies and eighties \citep{Lattimer1974,Lattimer1976,Blinnikov1984,Paczynski1986,Goodman1986,Eichler1989}. In recent years, the rate of $r$-process formation has been constrained using various observational lines of argument \citep{Hotokezaka2015,ji2016Nature,Beniamini2016a,Macias2016,HBP2018,BDS2018}. It was shown to be broadly consistent with the rate of sGRBs \citep{Guetta2006,Guetta2009,Coward2012,wanderman_piran2015,Ghirlanda2016} and with the rate of NS mergers as inferred from observations of Galactic double neutron stars \citep{Kochanek1993,Kim2015}. However, a clear determination of NS-NS mergers being the progenitors of sGRBs and the main source of $r$-process elements remained somewhat uncertain until the recent discovery of the kilonova AT2017gfo \citep{Tanvir2017} and GRB170817 \citep{Goldstein2017}, accompanying the NS-NS merger event GW170817 \citep{GW170817}. This recent discovery also leads to a new and independent estimate of the rate of NS-NS mergers. Furthermore, the observations of a very weak GRB accompanying the event, and detailed modelling of the peculiar and long-lived afterglow that followed the event, provides us with information regarding the opening angle, viewing angle, and core luminosity of GRB170817. The GW170817/GRB170817 event provides an unprecedented opportunity to explore sGRB jets in a broader context: How frequently do sGRB jets manage to break through the ejecta material surrounding the NS-NS mergers? What are the typical opening angles of sGRB jets? What determines the shape of the sGRB luminosity function? These topics have been partially explored in the past, either from an observational point of view, using the data from electromagnetically-detected sGRBs (i.e., not accompanied by a GW event) \citep{wanderman_piran2015,Ghirlanda2016,Moharana2017}, or from hydrodynamical studies of the GRB jet propagation through the NS-NS merger ejecta \citep{Aloy2005,Hotokezaka2013,Nagakura2014,Murguia-Berthier2014,Lazzati2017,Bromberg2018,Duffell2018}. Here, we show that by combining this knowledge with the unique constraint from GW170817 we can probe these questions in greater detail, thus significantly improving our understanding of these issues. The discovery of GRB170817 raised perhaps as many new questions as answers. In particular, the extremely dim prompt GRB accompanying the event has led to different interpretations, according to which the observed $\gamma$-ray emission is either arising from the `wings' of the jet (material beyond the core that is less energetic) due to the same physical process that produces the prompt emission along the jet's axis \citep{Kathirgamaraju2018,Lamb2017,GGG2017}, or is due to shock breakout from the thermal energy stored in the cocoon that was produced by the jet-ejecta interaction \citep{Lazzati2017,Gottlieb2017,Kasliwal2017}. Although GRB170817 alone is not enough to distinguish between the proposed models, we show that our understanding can be significantly improved once a sample of joint GRB and GW detections has been established and their luminosity and viewing angle distributions have been studied. The paper is organized as follows. In \S \ref{sec:failfrac} we revisit the rate and luminosity function of sGRBs and show that the latest results from GW170817 strongly constrain: the fraction of NS-NS mergers accompanied by sGRBs, the opening angles of sGRBs, and the interpretation of their luminosity function. In \S \ref{sec:GRBwjointdet} we consider different models for the off-axis prompt GRB emission. By performing Monte Carlo simulations, we compare the observed properties arising from different emission models, in cases with a joint GW and prompt GRB detection. In \S \ref{sec:cocooncooling} we focus on the cocoon model and discuss an additional observable signal that can directly constrain the thermal energy stored in the cocoon. Finally, we discuss some implications of this work and conclude in \S \ref{sec:discussion}. | \label{sec:discussion} The first discovery of GW from a NS merger allowed us to significantly improve our understanding of sGRB jets. Assuming all sGRBs arise from NS-NS (or NS-BH) mergers, the intrinsic rate of sGRBs should be at most comparable to the merger rate inferred by advanced LIGO/Virgo. This implies that if sGRB jets have a universal, luminosity independent structure, their typical opening angles should be $\theta_0\gtrsim 0.07$ (see \S \ref{sec:angles}). At the same time, the observed population of sGRBs with {\it Swift} in the last 14 years places a lower limit of $\sim 250$~Mpc on the distance from which we have observed an on-axis sGRB. This leads to an upper limit on the rate of local on-axis sGRBs and therefore on their typical opening angles $\theta_0\lesssim 0.1$. These limits on the opening angle are consistent with values inferred for GRB170817 from afterglow modelling and from the measurements of superluminal motion. Furthermore, they imply that the NS merger rate is comparable to that of sGRBs and reveals that a fraction of order unity of NS mergers must lead to sGRBs. In other words, sGRB jets typically manage to breakout of the NS-merger ejecta, in contrast to collapsar GRB jets. The large fraction of successful sGRB jets and the typical opening angles of $ \theta_0 \sim 0.1$ are consistent with a critical breakout luminosity (estimated from hydrodynamical simulations of the interaction between the sGRB jet and the NS merger ejecta) being close to the ``canonically" assumed minimal luminosity of the sGRB luminosity function, namely $L_{\rm min}\approx 5\times 10^{49}\, \mbox{erg s}^{-1}$. This consideration demonstrates that the role of failed jets in shaping the observed luminosity function of sGRBs cannot be significant (see \S \ref{sec:failedjets}). At the same time, we have also shown here that the angular structure of sGRBs is challenged to reproduce the observed luminosity function, given that the required structure is very shallow in contention with observational indications from GRB170817 (see \S \ref{sec:angular}). If this is the case, the implication is that the broken power-law luminosity function of sGRBs has an intrinsic origin and that the inferred break of the luminosity function, at an isotropic $\gamma$-ray luminosity of $L_*\approx 2\times 10^{52}\, \mbox{erg s}^{-1}$ (corresponding to a beaming corrected jet mechanical power of $\sim 10^{51}\mbox{erg s}^{-1}$) reveals an intrinsic characteristic luminosity of sGRB jets. One possible interpretation that holds for magnetic jets, powered by the Blandford Znajek mechanism \citep{BZ1977}, is that the value of $L_*$ reflects a characteristic accretion rate, below which the accretion disk is advection dominated (ADAF), and above which it becomes dominated by neutrino cooling (NDAF) \citep{Giannios2007}. Indeed, \cite{Kawanaka2013} have shown that a sharp change in the jet power may occur due to this transition at accretion rates $\dot{M}\approx 0.003-0.01M_{\odot}\,\mbox{s}^{-1}$, consistent with the beaming corrected jet luminosity mentioned above, assuming $L\approx 0.1\dot{M} c^2$. While the joint discovery of GW170817 and GRB170817 has helped to constrain the fraction of successful GRB jets, their opening angles, and their luminosity function as discussed above, the angular structure of GRB jets and the nature of their $\gamma$-ray emission are still uncertain. In this paper, we considered different off-axis emission models, motivated by the analysis above and by observations of GRB170817. We showed that $90\%-99\%$ of future GW events accompanied by a successful GRB jet and detected up to a distance of $220$~Mpc, should not be accompanied by any detectable prompt GRB signal. In the comparatively rare cases of a joint GRB and GW detections, we find that for each GRB observed on-axis $\sim 1-10$ GRBs should be observed at angles beyond the jet core. The distribution of prompt luminosities and observation angles from joint GRB and GW detections can help to distinguish between off-axis prompt emission models (see figure~\ref{fig:jointdist}). For example, let us assume a NS merger rate of $R_{\rm merg}=1540 \, \mbox{Gpc}^{-3} \mbox{yr}^{-1}$, a ratio of failed to successful GRB jets $r_{\rm fail}=1$, and $\theta_0=0.1$. Then, angular structure models with $L(\theta>\theta_0)\propto \theta^{-\delta}$ and $\delta=4.5$ lead to $\sim 19.2$ GW detectable mergers per year (up to 220~Mpc), out of which $\sim18$ without {\it Fermi}/GBM $\gamma$-ray detection, 0.1 with an on-axis GRB detection, and 1.1 with an off-axis GRB detection. Alternatively, for cocoon models with a breakout efficiency of $\eta_{\rm br}=10^{-3}$ (and $\theta_0=0.1$), we have $\sim 19$ events per year with no accompanying GRB, and 0.1 with on-axis or off-axis GRBs. Table~\ref{tbl:number} summarizes the expected number of events within a period of ten years for the emission models discussed in \S \ref{sec:MC}. Inspection of the table shows that the detection rates of off-axis GRBs accompanying GW-detected mergers are the key for differentiating between the models. For example, the lack of any other prompt GRB detections from NS mergers within the next 10 years (for the assumed parameters), would be in strong tension with the predictions of the structured jet model. The thermal energy in the cocoon may also be observed via its cooling emission that is expected to lead to a UV thermal signal at $\sim 10^3$~s after the trigger (see equations (\ref{eq:tthin}) and (\ref{eq:Lcool})). Provided that the NS merger can be located rapidly enough, the cooling emission of the cocoon may be detectable up to a distance of $\sim 900$~Mpc. It turns out that events similar to GRB170817 are rare. This is a combination of the small distance and observation angle of GRB170817 and the high inferred luminosity at the core of that event compared to typical sGRBs. In conclusion, the discovery of the first GRB associated with a NS merger, GRB170817, has already significantly improved our knowledge of short GRB jets. Nonetheless, the nature of the prompt signal that is seen by observers far from the jet cores remains unclear. The association of a $\gamma$-ray signal with a GW event could allow us to detect orders of magnitude fainter signals associated with GRBs, which would otherwise be undetected for cosmological events \citep[see also][]{Beniamini2018}. This, coupled with the relatively large detection rate of NS mergers as inferred from GW170817, implies that the existing models could be differentiated observationally within the next several years, opening up the window towards a more detailed understanding and future studies of short GRB jets. | 18 | 8 | 1808.04831 |
1808 | 1808.04370_arXiv.txt | We use the \gaia DR2 RR Lyrae sample to gain an uninterrupted view of the Galactic stellar halo. We dissect the available volume in slices parallel to the Milky Way's disc to show that within $\sim30$ kpc from the Galactic centre the halo is triaxial, with the longest axis misaligned by $\sim70^{\circ}$ with respect to the Galactic $x$-axis. This anatomical procedure exposes two large diffuse over-densities aligned with the semi-major axis of the halo: the Hercules-Aquila Cloud and the Virgo Over-density. We reveal the kinematics of the entire inner halo by mapping out the amplitudes and directions of the RR Lyrae proper motions. These are then compared to simple models with different anisotropies to demonstrate that the inner halo is dominated by stars on highly eccentric orbits. We interpret the shape of the density and the kinematics of the \gaia DR2 RR Lyrae as evidence in favour of a scenario in which the bulk of the halo was deposited in a single massive merger event. | In $\Lambda$CDM Cosmology, Dark Matter halos are rarely spherical, their shapes controlled by the environment and the accretion history \citep[][]{Frenk1988,Dubinski1991,Warren1992,Colberg1999,Allgood2006,Bett2007,Hahn2007}. At the early stages of the halo assembly, the shape is typically prolate and aligned with the narrow filaments, via which the mass is supplied, but with passing of time, halos can become triaxial or even oblate, as the feeding filaments swell and the direction of accretion changes \citep[e.g.][]{Cole1996,Tormen1997,Altay2006,Vera-Ciro2011,Libeskind2013}. This metamorphosis does not necessarily imply that the memory of the early halo configuration is completely erased. Instead, at redshift zero, the history of the Dark Matter halo evolution may be deciphered by studying how its shape changes with Galactocentric radius \citep[e.g.][]{Hayashi2007,Vera-Ciro2011}. Note however, that inclusion of baryons \citep[see e.g.][]{Kaza2004,Gnedin2004,Debattista2008,Abadi2010} or adaptation of a different Dark Matter model \citep[e.g.][]{Avila2001,Dave2001,Mayer2002,Peter2013} can affect the details of some of the above calculations. While the behavior of Dark Matter halos shows several coherent trends, stellar halos appear to display a wider diversity, linked to the strong suppression of star formation in low-mass Dark Matter clumps \citep[see e.g.][]{Bullock2005, Cooper2010}. One of the important corollaries of the above stochasticity is the expectation that the bulk of the (accreted) stellar halo of a Milky Way-like galaxy is contributed by a small number of massive dwarf galaxies \citep[see e.g.][]{DeLucia2008,Deason2013}. The picture therefore emerges in which the most massive halo progenitors not only can define the shape of the stellar halo \citep[see][]{Deason2013} but also set its overall metallicity \citep[][]{Deason2016,DSouza2018}. It is difficult to produce stellar halos without invoking (at least some of) the processes that lead to formation of stars. The inclusion of baryonic physics tends to alter the shapes of the resulting stellar halos significantly. For examples, the inner portions of the stellar halos built up with semi-analytic machinery are often prolate \citep[see e.g.][]{Cooper2010}, while hydro-dynamical simulations deliver mostly oblate shapes \citep[e.g.][]{Monachesi2018}. The prevalence of the oblate shapes in the simulated stellar halos is sometimes linked to the significant contribution of so-called in-situ component \citep[][]{Benson2004,Zolotov2009,McCarthy2012,Tissera2013,Cooper2015}. Early attempts to gauge the properties of the Milky Way's stellar halo had to rely on the small number of tracers and/or sparse sky coverage \citep[][]{Preston1991,Reid1993,Sluis1998,Morrison2000,Siegel2002}. Recently, thanks to the availability of wide-area deep imaging data, the shape of the Milky Way's stellar halo has been the focus of many studies \citep[e.g.][]{Newberg2006, Bell2008, JuricVOD, Sesar2011,deasonhalo,xuehalo,Iorio18}. While surveys like the SDSS \citep[see][]{SDSSdr12} do provide a much broader view of the halo \citep[see e.g.][]{Carollo2007, Carollo2010}, large swathes of the sky are still missing, leaving portions of the inner Galaxy unmapped. Most recently, the \gaia mission \citep[see][]{Gaia} has provided the first all-sky view of the Galactic halo. By combining the variability statistics from \gaia DR1 with the color information from \gaia and 2MASS, \citet{Iorio18} built a sample of $\sim$22,000 RR Lyrae covering most of the celestial sphere, except for narrow regions close to the Galactic plane. Using these old and metal-poor pulsating stars and taking advantage of largely un-interrupted view of the Galaxy, they were able to test a wide range of stellar halo models. In this Paper, we aim to use the \gaia DR2 RR Lyrae stars to get both closer to the centre of the Milky Way and to go further beyond the reach of the \citet{Iorio18} analysis by linking the RR Lyrae density evolution with their kinematics. Our study is motivated by the recent discovery of tidal debris from what appears to be an ancient major merger event \citep[][]{BelokurovSa,MySa,Helmi18} Identified first in the Solar neighborhood, this debris cloud, sometimes referred to as the ``Gaia Sausage'' has recently been shown to dominate the Galactic stellar halo, stretching from regions in the Milky Way's bulge to near and past the halo's break radius around $20-30$ kpc \citep[see][]{Deason18,Simion18,Lancaster}. Additional evidence has been found in the studies of the detailed chemical abundances of the nearby halo stars \citep[see][]{Hayes18,Haywood2018,Mack18}. While many pieces of the ``Gaia Sausage'' have already been reported in the literature, here we attempt to provide the first comprehensive map of this {\it largest halo sub-structure}. The kinematic portion of our study is complementary to the work of \citet{Wegg18}, who recently used a sample of PanSTARRS1 RR Lyrae stars to constrain the shape of the inner portion of the Galactic gravitational potential. This Paper is organized as follows. Section~\ref{sec:sample} describes the construction of the clean sample of \gaia DR2 RR Lyrae stars. In Section~\ref{sec:slice} we show how these objects can be used to slice the Galactic halo to reveal the remnant of a large dwarf galaxy buried close to the Milky Way's centre. In Section~\ref{sec:disc} we complement the spatial analysis with an all-sky RR Lyrae kinematic map and we discuss the implications of our discovery. Finally, we summarise the conclusions of this work in Section\ \ref{sec:conclusions}. | \label{sec:conclusions} In this paper, we take advantage of the most comprehensive sample of RRL stars to date, i.e. the one supplied by the \gaia DR2, to study the shape of the Galactic stellar halo. In order to assemble a dataset with sensible and stable completeness and purity, we had to get rid of more than a half of the original total of $\sim230,000$ objects. While this may sound scary, remember that the estimated contamination of the \gaia DR2 sample shoots up to $\sim 50\%$ in the bulge area \citep[see][]{GaiaVariable}. For our investigations, we have only kept RRL stars that possess well-behaved colors and astrometry. Additionally, we do not consider objects residing in small-scale over-densities, i.e. known Milky Way satellites and globular clusters. However, even after all these cuts, we are left with nearly 93,000 RRL stars across the entire sky, from the inner several kpc to the distant outskirts - a dataset unprecedented in its richness and reach. For the very first time, we produce detailed maps of the RRL density distribution in the inner Milky Way (see Fig.~\ref{fig:Zslice}). Slicing the Galaxy at different Galactic heights, we reveal the evolution of the halo shape from nearly spherical (close to the Galaxy's centre) to clearly triaxial further out. Despite several obvious asymmetries and large-scale over-densities visible in these maps, the overall structure of the halo appears to be well-described by the SPL-TR$^{qv}$ model of \citet{Iorio18}. In this model, the major axis lies in the Galactic plane rotated by $\sim70^{\circ}$ (anti-clockwise) away from the Galactic $x$-axis, i.e. pointing approximately in the direction of the Magellanic Clouds. The ratio of the major to intermediate axis is $p=1.3$, but the ratio of the minor axis (aligned with the Galactic $z$ axis) to major one changes with distance from the Milky Way centre (from $q\sim0.5$ to $q\sim0.8$). The clearest deviations from the above model are the Virgo Over-Density and the Hercules-Aquila Cloud, which protrude far in the vertical direction on the opposite sides of the Galactic plane. As we have demonstrated in Section~\ref{sec:distribution} and Fig.~\ref{fig:View}, the SPL-TR$^{qv}$ model of \cite{Iorio18} can be adjusted slightly to encompass both HAC and VOD. This is achieved by bringing its intermediate axis out of the Galactic plane by $\sim20^{\circ}$. From the slices presented in Fig.~\ref{fig:Zslice} it is now easy to judge the whereabouts of the HAC and VOD with respect to the Milky Way's centre and to each other. These debris clouds appear to be aligned with the major axis of the triaxial structure discussed above. The first clues that HAC and VOD may actually be part of the same accretion event have already been presented by \citet{Simion18}, who calculated the orbital properties of a sub-sample of RRL stars residing in these over-densities. Given that both structures appear to be dominated by stars on extremely eccentric orbits, \citet{Simion18} conclude that HAC and VOD represent unmixed portions of an ancient massive head-on collision also known as the ``Gaia Sausage''. In an attempt to test this hypothesis, we have studied the kinematics of the inner halo RRL stars as reflected in their proper motions. We claim that across a wide range of distances from the Sun, the halo's velocity ellipsoid can be gleaned from its projection on the celestial sphere. Our results are in good agreement with an earlier analysis of the RRL proper motion data of \citet{Wegg18}. Compared to the above study, while we do not attempt to model the shape of the velocity ellipsoid, we do obtain a broader view of the global kinematic patterns in the Galactic halo. Accordingly, contrasting the observed amplitudes and directions of the RRL proper motions within $\sim30$ kpc from the Galactic centre with simple kinematic models, we show that the entire inner halo is dominated by stars on highly eccentric orbits. We interpret the stretched appearance and the extreme radial anisotropy of the inner halo as the tell-tale signs of a low angular momentum collision with a massive satellite \citep[see e.g.\ ][]{Brook03}, thus associating the bulk of the RRL stars within 30 kpc with the so-called ``Gaia Sausage'' merger event \citep[][]{BelokurovSa,MySa,Haywood2018,Helmi18}. By tracking the change in the behavior of the RRL proper motions with Galactocentric distance, we place constraints on the pericentre ($\lesssim 4$ kpc) and the apocentre (20-40 kpc) of this enormous tidal debris cloud. The fact that today it appears to be squashed vertically (in the direction perpendicular to the Galactic disc) agrees well with the predictions of numerical simulations of the Dark Matter halo evolution in the presence of baryons \citep[][]{Kaza2004,Gnedin2004,Debattista2008,Abadi2010}. In terms of local Dark Matter density, we have estimated the contribution of the ``Gaia Sausage'' to be between $10\%$ and $50\%$. A curious conundrum is starting to emerge in which a clearly triaxial stellar halo needs to be reconciled with multiple recent reports of a near spherical inner Dark Matter halo \citep[][]{Bowden2015,Bovy2016,Wegg18}, a measurement itself in tension with the results from numerical simulations which do not produce perfect sphericity \citep[e.g.][]{Kaza2010,Victor2015}. The spatio-kinematic information uncovered here will help constrain the total mass as well as the time of accretion of the ``Gaia Sausage'' progenitor, and thus understand the role this event played in the life of the Milky Way. | 18 | 8 | 1808.04370 |
1808 | 1808.03285_arXiv.txt | {The disk-outflow connection is thought to play a key role in extracting excess angular momentum from a forming protostar. HH30 is a rare and beautiful example of a pre-main sequence star exhibiting a flared edge-on disk, an optical jet, and a CO molecular outflow, making this object a case study for the disk-jet-outflow paradigm.} {We aim to clarify the origin of the small-scale molecular outflow of HH30 and its link and impact on the accretion disk.} {We present ALMA 0.25$^{\prime\prime}$ angular resolution observations of the circumstellar disk and outflow around the T Tauri star HH30 in the dust continuum at 1.33 mm and of the molecular line transitions of $^{12}$CO(2-1) and $^{13}$CO(2-1). We performed a disk subtraction from the $^{12}$CO emission, from which we analysed the outflow properties in detail in the altitudes z$\lesssim$250~au. We fit the transverse position-velocity diagrams across the $^{12}$CO outflow to derive the ring positions and projected velocity components (including rotation). We use the results of these fits to discuss the origin of the CO outflow.} {The 1.3~mm continuum emission shows a remarkable elongated morphology along PA=31.2$^{\circ}$~$\pm$~0.1$^{\circ}$ that has a constant brightness out to a radius of r=75~au. The emission is marginally resolved in the transverse direction, implying an intrinsic vertical width $\leq$~24~au and an inclination to the line-of-sight ${\rm i}~\ge~84.8^{\circ}$. The $^{13}$CO emission is compatible with emission from a disk in Keplerian rotation, in agreement with the previous findings. The monopolar outflow, detected in $^{12}$CO, arises from the north-eastern face of the disk from a disk radius r~$\le$~22~au and extends up to 5$^{\prime\prime}$ (or 700~au) above the disk plane. We derive a lower limit to the total mass of the CO cavity/outflow of $1.7\times10^{-5}$ M$_{\odot}$. The CO cavity morphology is that of a hollow cone with semi-opening angle $\sim$35$^\circ$. The derived kinematics are consistent with gas flowing along the conical surface with constant velocity of 9.3~$\pm$~0.7~\kms. We detect small rotation signatures (V$_\phi \sin{\rm i}\in[0.1;0.5]$~\kms) in the same sense as the underlying circumstellar disk. From these rotation signatures we infer an average specific angular momentum of the outflow of 38~$\pm$~15~au~\kms at altitudes z~$\le$~250~au. We also report the detection of small amplitude wiggling (1.2$^{\circ}$) of the CO axis around an average inclination to the line of sight of i=91$^{\circ}$.} {The derived morphology and kinematics of the CO cavity are compatible with expectations from a slow disk wind, originating either through photo-evaporation or magneto-centrifugal processes. Under the steady assumption, we derive launching radii in the range 0.5-7~au. In that scenario, we confirm the large minimum mass flux of 9$\times 10^{-8}$ M$_\odot$ yr$^{-1}$ for the CO wind. The wind would therefore extract a significant amount of the accreted mass flux through the disk and would likely play a crucial role in the disk evolution. If the CO flow originates from a steady-state disk wind, our ALMA observations rule out the 18~au binary orbital scenario previously proposed to account for the wiggling of the optical jet and favour instead a precession scenario in which the CO flow originates from a circumbinary disk around a close (separation $\leq$~3.5~au) binary. Alternatively, the CO outflow could also trace the walls of a stationary cavity created by the propagation of multiple bow shocks. Detailed numerical simulations are under way to fully test the entrainment hypothesis.} | A necessary prerequisite to understand the formation of stars is the comprehension of the complex processes linking the collapsing molecular core, the protostar, its circumstellar disk, and the bipolar jets and outflows that expel material. Together, these processes regulate the protostar fragmentation and the mass that the protostar(s) acquires; plus, they appear to be key for the existence and morphology of planetary systems. Among these processes, the initial amount, evolution, and re-distribution of angular momentum appear to be fundamental. Part of the excess of angular momentum may be carried away by jets and outflows and, thus, provide a solution to the angular momentum problem in star formation \citep[e.g.][]{ray07}. Yet, the exact link between jets/flows and the accretion disk is still a critical issue in contemporary physics. One attractive possibility is a transfer of angular momentum from the disk to the jets/outflows by means of magneto-centrifugal forces, such that circumstellar material may continue to accrete onto the central object \citep[e.g.][]{blandford82}. Exactly where and how this transfer occurs, and how it impacts the disk physics, is however still hotly debated \citep{ferreira06, pudritz07, shang07, romanova09, cabrit09}. Measurements of angular momentum have been reported for the jets in various evolutionary phases from Class 0 \citep{lee08} to Class I \citep{chrysostomou08}, and during the T Tauri phase \citep{bacciotti02,woitas05,coffey04,coffey07}. Under the steady mass loss assumption, these signatures imply a jet launching radius in the inner 0.1-3~au of the disk and suggest that magneto hydrodynamic (MHD) winds could fully drive the accretion in these regions. However, \cite{louvet16b} showed that for the T Tauri star Th28, the rotation sense of the disk is opposite to that of the transverse velocity shifts that were previously detected with the Hubble Space Telescope (HST) in the optical jet of this source \citep{coffey07}. That second example of counter-rotation together with RW Aur \citep{coffey04,cabrit06} suggests that the steady assumption may not hold and casts doubt on the ability to derive constraints on the launching radii of jets derived from optical rotation signatures. Slower molecular outflows may also play an important role in reducing the angular momentum from the disk/protostar system. The traditional interpretation of CO flows in terms of swept-up ambient matter has recently been challenged by the detection of small-scale, V-shaped CO cavities in evolved Class II sources. In these sources, no obvious envelope is present for entrainment and the cavity base originates from within the circumstellar disk \citep[e.g. in HH30][]{pety06}. Alternatively these small-scale cavities could trace disk winds generated either by magneto-hydrodynamical processes or by photo-evaporation of the outer disk atmosphere. The MHD disk winds are efficient at extracting angular momentum, while photo-evaporative flows have potentially a strong influence on disk gas dissipation processes. Recent studies have reported tentative rotation signatures in low-velocity Class~0 and Class~I molecular outflows at a level consistent with MHD disk winds \citep{launhardt09,zapata09,bjerkeli16,tabone17,hirota17}. In all these embedded sources however, the entrainment scenario cannot be fully excluded. In this article, we present a detailed study of the small-scale CO cavity/molecular outflow from the edge-on Class II source HH30 conducted with ALMA. The Herbig-Haro (HH) object 30 \citep{mundt83} is a young solar-type star devoid of an envelope located in the dark molecular cloud L1551 at a distance of $\sim$140 pc \citep{kenyon94} in Taurus. The HH 30 exciting source is an optically invisible star \citep{vrba85} that is highly extinguished by an edge-on disk \citep{burrows96,stapelfeldt99}, which extends up to a radius of $\sim$250 au perpendicular to the jet and divides the surrounding reflection nebulosity into two lobes. Recent interferometric observations in $^{13}$CO (J = 2-1) are consistent with a gaseous disk in Keplerian rotation around an enclosed mass of 0.45 $\pm$ 0.04 M$_\odot$ that corresponds to a typical T Tauri star with spectral class M0 $\pm$ 1 \citep[][hereafter P06]{pety06}. HH30 is considered as a prototype disk/jet/outflow system. Its impressive bipolar jet has a total angular size of 7' \citep{anglada07}. The overall HH 30 jet structure can be well described by a wiggling ballistic jet, whose knots have velocities included between 100 km s$^{-1}$ and 300 km s$^{-1}$ \citep{estalella12}. \cite{anglada07} suggested that the wiggling arises either from the orbital motion of the jet source around a primary or from precession of the jet axis because of the tidal effects of a companion. In the first scenario, the companion would be orbiting at $\sim$18 au in a 53-year period, whereas in the second scenario the companion would be orbiting at less than 1 au in less than a year. Interferometric imaging in the continuum at $\lambda$ = 1.3 mm resolved a region of reduced brightness at the centre of the system, suggesting that the disk of HH30 is truncated at an inner radius of 37$\pm$4 au \citep{guilloteau08}; this implies that the wiggling of the jet would be due to orbital motion. The molecular gas around HH30 was studied by \cite{pety06} with the Plateau de Bure interferometer (hereafter PdBI) at an angular resolution of $\sim$1.4$^{''}$. The P06 work showed that the disk of HH30 is in Keplerian rotation with its rotation vector pointing towards the north-eastern jet. Furthermore, P06 demonstrated that the outflow of HH30 is expending in the plane of the sky with a magnitude of $\sim$12 km s$^{-1}$, and that the outflowing material is mainly located on the thin edges of a cone with an opening angle of 30$^{\circ}$. The P06 authors did not detect rotation in the outflow of HH30, and set an upper limit of 1 km s$^{-1}$ at 200 au from the jet axis. \smallskip In this paper, we report the first Atacama Large Millimeter/Submillimeter Array (ALMA) band 6 CO and continuum observations at $\sim$0.25'' angular resolution (or $\sim$35 au) of the HH30 system, aimed at constraining the outflow features. We detail our observations and data reduction in Sect.~\ref{s:obs} and develop our analysis of the continuum and of the $^{13}$CO and $^{12}$CO emission lines in Sect.~\ref{s:result}. Section~\ref{s:analysis} presents our detailed analysis of the $^{12}$CO emission. The Sect.~\ref{s:discu} discusses the origin of the outflow of HH30 and give constraints on the central binary system. We summarize our conclusions in Sect.~\ref{s:concl}. | \label{s:concl} We have observed the T Tauri pre-main sequence star HH30 with ALMA during the cycle 2 campaign in Band 6 (211-275 GHz). The circumstellar disk of HH30 is detected in continuum at 1.33 mm and in $^{13}$CO($J$ 2$\rightarrow$1), while the $^{12}$CO($J$ 2$\rightarrow$1) emission is a mixture of emissions arising from the disk and from the outflow. The 1.3 mm continuum emission is fully resolved and shows an elongated morphology along PA=31.2$^{\circ}$~$\pm$~0.1$^{\circ}$ with a sharp fall-off in intensity at a radius of 75~au (0.55$^{\prime\prime}$). The emission is only marginally resolved in the transverse direction, implying an intrinsic vertical width $\leq$~24~au and an inclination to the line-of-sight ${\rm i}~\ge~85^{\circ}$. The continuum intensity profile along the disk is consistent with a constant flux of $2.4$ mJy/beam to within 3~$\sigma$. We do not detect an inner hole in the continuum image, unlike the previous finding by \cite{guilloteau08}. The $^{13}$CO emission line profile and $^{13}$CO channel maps are consistent a Keplerian disk, which agrees with the previous finding by P06. The $^{13}$CO emission is detected towards larger radii than the continuum emission, up to r=180 au. The upper and lower surfaces of the disk display very symmetric emissions with less than 15~\% discrepancy. From the $^{13}$CO integrated spectrum we derive a source $v_{\rm lsr}$ of 6.9~$\pm$~0.1~\kms. The outflow of HH30 arises from the inner parts of the north-eastern surface of the disk and is detected in $^{12}$CO out to z=5$^{\prime\prime}$, or 700~au at the distance of the source. We derive a lower limit to the total mass for the CO outflow of $1.7\times 10^{-5}$ M$_\odot$. The channel maps and pv diagrams of the $^{12}$CO emission are consistent with the conical shell morphology previously derived by P06 out to z=1.8$^{\prime\prime}$=250~au. In addition, we detect signatures of an inner knot close to the source (z~$\simeq$~0.25$^{\prime\prime}$) and of an inner shell at large distances (z~$>$~2$^{\prime\prime}$). We confirm the conical shape of the cavity and derive a semi-opening angle of 35$^{\circ}$ for 20~au~$<$~z~$<$~250~au. We constrain the base of the conical cavity at r$_0$~$<$~22~au. The derived velocity components are compatible with gas flowing along the conical surface with constant velocity V=9.3~\kms. We report detection of CO axis wiggling. The derived variation of the cone axis inclination to the line of sight shows a remarkable sinusoidal variation around 91$^{\circ}$ with amplitude 1.2$^{\circ}$ over the central z=250 au. We also detect small amplitude rotation signatures in the same sense as the underlying disk rotation sense with v$_{\phi}~\times \sin({\rm i})\in[0.1;0.7]$~\kms. We derive an average specific angular momentum $r\times v_\phi = $38$\pm$15~au~km~s$^{-1}$ for 50~au~$< z <$~250~au. The morphology and the kinematics of the CO outflow are compatible with expectations from an origin in a slow disk wind, either through photo-evaporation or magneto-centrifugal processes. For both scenarios, we confirm the large minimum mass flux of 9$\times 10^{-8}$ M$_\odot$ yr$^{-1}$ for the CO wind. In the photo-evaporated disk wind scenario, conservation of angular momentum leads to a launching radius r$_0$ of 1-7~au, which is comparable to the estimated critical radii from which the mass flux starts to originate in these models. However, the derived large mass flux is difficult to account by current photo-evaporation models. On the other hand, an origin in a magneto-centrifugal disk wind implies a magnetic lever arm of 1.6 and launching radii in the range 0.5-2.5~au. Such MHD disk winds with small magnetic levers correspond to solutions including significant entropy deposition at the base of the wind. In both models, the wind extracts a significant amount of the accreted mass flux through the disk and likely plays an important role in the gaseous disk evolution. If the CO flow arises from a disk wind, our ALMA study brings new constraints on the central binary scenario in HH30. The ALMA observations would rule out the orbital scenario previously favoured to account for the wiggling of the atomic jet, as it would predict centroid velocity variations of amplitude $1.5$~km~s$^{-1}$, much larger than observed. On the other hand, the equivalent precession scenario predicts centroid velocity and position variations much more in accordance with our ALMA observations. If the CO flow originates from one of the CS disks, unrealistically small separations of the binary are inferred. We therefore favour a precession scenario in which the CO flow originates from the CB disk around an inner non-coplanar binary with separation less than 3.5~au. Another possible origin for the CO outflow is through entrainment of surrounding matter. If the CO cavity of HH30 is due to dragged material, the dichotomy between the age of HH30 (a few Myrs) and the constant radial velocity of the outflow of 5.3 km s$^{-1}$, which implies a cavity age $\sim$500 yr, favours a stationary cavity in which the material flows along the conical shape of the outflow. Detailed simulations for the evolution of the base of jet bow shock driven cavities on spatial scales comparable to our HH30 ALMA observations are under way to fully test this scenario and in particular to account for the observed rotation and wiggling of the CO outflow. | 18 | 8 | 1808.03285 |
1808 | 1808.04977_arXiv.txt | {Broadband photometry offers a time and cost effective method to reconstruct the continuum emission of celestial objects. Thus, photometric redshift estimation has supported the scientific exploitation of extragalactic multiwavelength surveys for more than twenty years. Deep fields have been the backbone of galaxy evolution studies and have brought forward a collection of various approaches in determining photometric redshifts. In the era of precision cosmology, with the upcoming Euclid and LSST surveys, very tight constraints are put on the expected performance of photometric redshift estimation using broadband photometry, thus new methods have to be developed in order to reach the required performance. We present a novel automatic method of optimizing photometric redshift performance, the classification-aided photometric redshift estimation (CPz). The main feature of CPz is the unified treatment of all classes of objects detected in extragalactic surveys: galaxies of any type (passive, starforming and starbursts), active galactic nuclei (AGN), quasi-stellar objects (QSO), stars and also includes the identification of potential photometric redshift catastrophic outliers. The method operates in three stages. First, the photometric catalog is confronted with star, galaxy and QSO model templates by means of spectral energy distribution fitting. Second, three machine-learning classifiers are used to identify 1) the probability of each source to be a star, 2) the optimal photometric redshift model library set-up for each source and 3) the probability to be a photometric redshift catastrophic outlier. Lastly, the final sample is assembled by identifying the probability thresholds to be applied on the outcome of each of the three classifiers. Hence, with the final stage we can create a sample appropriate for a given science case, for example favoring purity over completeness. We apply our method to the near-infrared VISTA public surveys, matched with optical photometry from CFHTLS, KIDS and SDSS, mid-infrared WISE photometry and ultra-violet photometry from the Galaxy Evolution Explorer (GALEX). We show that CPz offers improved photometric redshift performance for both normal galaxies and AGN without the need for extra X-ray information.} | Looking at a single broadband image, obtained for example in the $r$ band (6000\AA), we are able to distinguish distinct sources and classify them according to their morphologies, ranging from round and smooth elliptical galaxies to the impressive grand design spiral galaxies \citep{Hubble1926}. We now know that the morphologies are linked to the type of stellar populations and the gas and dust content of the galaxy. For example, passive galaxies are known to consist of mainly old star populations, while star-forming galaxies consist of younger, bluer stars populating the galaxy's spiral arms. However, from a single image we can not say with certainty for example if a point-like source is really a star or a quasi-stellar object (QSO), or what is the cosmological distance of the source. Source classification has been subsequently enhanced by attributes both from photometric (e.g., colors) and spectroscopic (e.g., line widths) measurements. Plotting pairs of attributes has proven to be a powerful tool in identifying the parameter space occupied by each galaxy class for example separating between starforming and passive galaxies using the bimodality cloud, \citep{Bell2004}, or separating between starforming galaxies and active galactic nuclei (AGN) through the BPT diagram, \citep{Baldwin1981}. The main limitation of this approach is the dimensionality reduction of a wealthy parameter space to usually only two to four attributes and the introduction of hard limits to separate between the classes. Another approach in identifying the nature of astronomical sources is the comparison of stellar population synthesis models (SSP) to observations through spectral energy distribution (SED) fitting. SSPs demonstrate that the age and metallicity of the star population will create a distinct galaxy continuum emission which can be probed with broadband photometry which however suffers from degeneracies in color space \citep[e.g.,][]{Bruzual2003,Maraston2005}. A selection of models deemed representative of the sample at hand can be used to identify stars vs galaxies and to estimate physical properties such as the stellar mass, star-formation rate, amongst others, judged by least $\chi^2$ \citep[e.g.,][]{Bolzonella2000,Robin2007,Ilbert2009, Fotopoulou2012, Dahlen2013}. Lastly, machine-learning algorithms are very well applicable to an astronomical context and they have been embraced since the early 90's. supervised and unsupervised methods are able to identify correlations, groupings and even outliers in vast datasets that would otherwise be impossible to visualize by a human eye. Many works have explored classification in astronomy using machine-learning techniques aiming towards separating stars from galaxies \citep{Odewahn1993, Soumagnac2015}, QSO identification \citep{Brescia2015}, estimating physical parameters \citep{Ucci2017}, finding peculiar objects \citep{Meusinger2012} etc. In addition to the class of the object, multiwavelength information are useful in providing an estimate of the redshift as proposed by \citet{Baum1962}. All modern extragalactic surveys make extensive use of photometric redshift estimation as it is a cost-efficient method to determine distances of galaxies (COMBO-17, CFHTLS, CDFS and ECDFS, Lockman Hole, AEGIS, COSMOS, XXL, to name a few). However, most surveys are mainly focused on the normal galaxy population. In the presence of deep X-ray flux measurements, variability and morphology information, \citet{Salvato2009,Salvato2011} showed that the optimal photometric redshift solution can be achieved by dissecting the galaxy population in three categories containing 1) normal galaxies, 2) normal galaxy and AGN emission, 3) AGN dominated emission, which we refer to as QSO. This method has been successfully applied to other extragalactic fields such as the Lockman Hole \citep{Fotopoulou2012}, the Chandra Deep Field South \citep{Hsu2014} and AEGIS-X \citep{Nandra2015} and it is the current state of the art, used when X-ray data are available for the whole field in consideration. The core of the method is the use of independent information such as X-ray flux, morphology and variability to pin-point the SED models that will give the optimal photometric redshift solution for each population. By doing so, the degeneracies between models are reduced, thus achieving higher photometric redshift performance. However, the correct implementation of the method requires splitting the sample into point-like and varying sources and also having an estimate of X-ray flux. This information will not be available to the desired sensitivity for the majority of the source population detected by Euclid and LSST. In this paper, we generalize the idea of population-specific libraries designed for application on surveys for which X-ray fluxes and variability information is not available and the morphology is estimated by the half light radius. The classification-aided photometric-redshift estimation (CPz) utilizes machine-learning classification and spectral energy distribution (SED) fitting for photometric redshift. We show that this classification step allows the production of optimized photometric redshift for galaxies, AGN and QSO while at the same time identifying stars and catastrophic outliers. | We introduce the classification-aided photometric redshift method (CPz), an automatic method to identify stars, estimate optimal photometric redshifts for all galaxy populations including AGNs and QSO and identify photometric redshift outliers. The method consists of three stages. In the first stage, we fit star and galaxy, AGN, and QSO models to all the observations. In the second stage, we create all color combinations and pre-process the data by normalizing and whitening them. Next, we train three classifiers using a machine-learning algorithm to identify 1) stars 2) the optimal photometric redshift library setup 3) photometric redshift outliers. The final stage consists of the consolidation of the results, where the selected probability thresholds tailored to the specific science case are applied. We have shown that: \begin{itemize} \item Using a restricted set of attributes, expected to be widely available with the scheduled large surveys we successfully classify objects as stars versus galaxies. \item The best photometric redshift results are obtained when the sample is split in passive, starforming, starburst, AGN and QSO, without overlap between the classes. \item Inclusion of $W1$ and $W2$ filters of WISE photometry combined with the $u$-$K$ filters of Euclid and LSST bring a significant improvement both in accuracy and number of outliers and in the identification of stars. \item Most importantly, we able to identify AGN and QSO based on their broadband colors. \end{itemize} The sample used for this work was restricted only to sources with spectroscopic redshift information. Therefore, the classifier scores presented here should be considered only indicative since the performance achieved for a given survey will depend on the available photometry and training sample used. Thus, we refrain from making any analysis for example, on the number of objects identified per class. We defer this discussion to a future publication of the application of the method on the XXL Survey (Fotopoulou et al., in prep). Preliminary results of the CPz application on the XXL-1000-AGN sample, the 1000 brightest X-ray sources in the XXL survey, can be found in \citet{Fotopoulou2016b}. | 18 | 8 | 1808.04977 |
1808 | 1808.07079_arXiv.txt | Rapid and stepwise changes of the magnetic field are often observed during flares but cannot be explained by models yet. Using a 45 min sequence of SDO/HMI 135 s fast-cadence vector magnetograms of the X1 flare on 2014-03-29 we construct, at each timestep, nonlinear force-free models for the coronal magnetic field. Observed flare-related changes in the line-of-sight magnetic field $B_{\rm LOS}$ at the photosphere and chromosphere are compared with changes in the magnetic fields in the models. We find a moderate agreement at the photospheric layer (the basis for the models), but no agreement at chromospheric layers. The observed changes at the photosphere and chromosphere are surprisingly different, and are unlikely to be reproduced by a force-free model. The observed changes are likely to require a change in the magnitude of the field, not just in its direction. | While photospheric magnetic field measurements are readily available, measurements at the solar chromosphere and in the corona are less common and less reliable. Often fields in these higher atmospheric layers are approximated by modeling, particularly by non-linear force-free field (NLFFF) extrapolations. Our goal is to test the agreement of such extrapolations with chromospheric observations, particularly whether the models reproduce the magnetic field changes that are observed in the photosphere and in the chromosphere during a flare. The equations of the NLFFF model may be written as \begin{equation} \nabla\cdot\bb=0,\label{eq:nlfff2} \end{equation} and \begin{equation} \nabla\times\bb=\alpha\bb\label{eq:nlfff1} \end{equation} where $\bb$ is the magnetic field vector, and $\alpha$ is the force-free parameter. {{Equation (\ref{eq:nlfff2}) states the fundamental physical condition that the magnetic field must be divergence-free, while Equation (\ref{eq:nlfff1}) states our assumption that the Lorentz force in the corona is zero}}. NLFFF extrapolations use photospheric vector magnetogram data as boundary conditions to reconstruct the coronal magnetic field \citep[e.g.,][]{2012LRSP....9....5W}. {However, a given set of photospheric observations over-determine the force-free model. The data present two different choices for the boundary conditions, implying two possible solutions to the model. Hence additional choices must be made in the modeling, and the results depend to some extent on the specific choices made \citep[e.g.,][]{2015ApJ...811..107D}.} A flare is attributed to a change in the coronal magnetic field configuration, involving magnetic reconnection and leading to a release of energy. Free energy stored in the solar coronal field is converted, for example, into particle acceleration and heating of the solar atmosphere. Observations often show abrupt and permanent changes of photospheric magnetic fields during flares \citep[e.g.,][]{wang1992,wangetal1994,kosovichevzharkova1999, cameronsammis1999, kosovichevzharkova2001,sudolharvey2005,petriesudol2010}, but their mechanism is not yet fully understood. Photospheric magnetic fields preferentially change near the polarity inversion line, and the line-of-sight magnetic field is equally likely to increase or decrease \citep{castellanosetal2018}. Studies with vector magnetograms show that the horizontal field tends to increase close to the neutral line, in a direction parallel to the neutral line \citep[e.g.][]{2012ApJ...759...50P}. In contrast, chromospheric magnetic field changes are more difficult to study because of the lack of continuous space-based chromospheric polarimetric observations and because of the more complex interpretation of chromospheric spectral lines. \citet{kleint2017} recently reported observations of chromospheric magnetic field changes during the X1 flare on 2014-03-29, which demonstrated a surprising disparity between the photosphere and the chromosphere. Changes in the magnetic field at the chromosphere were observed to occur over larger areas than at the photosphere, the changes were stronger, and in many cases their locations, sign, and timing did not coincide with those at the photosphere. This leads to the question of whether NLFFF extrapolations are able to reproduce and explain photospheric and chromospheric magnetic field changes during flares. In this paper we address this question, by examining again the data from the X1 flare SOL2014-03-29T17:48. {We note that there are two basic limitations of NLFFF modeling for our purpose. First, the nonlinear force-free model does not represent accurately the photosphere-chromosphere transition region, because it excludes non-magnetic forces. Second, the static NLFFF model cannot represent the dynamic fields present during the flare. To address the second problem, we construct a long sequence of NLFFF reconstructions starting before the flare and ending after. This sequence is used to identify permanent, flare-related changes in the NLFFF models.} | Our findings can be summarized as follows: \begin{itemize} \item Using an NLFFF model, we compared synthetic and observed line-of-sight magnetogram data to examine how well the model reproduces changes in the observed field strength at both photospheric and chromospheric heights over a $>$40 min period around the time of an X1-class flare. The models are constructed from HMI photospheric vector field data, but the model $B_{\rm LOS}$ is not identical to the photospheric observations because of how the NLFFF solutions are obtained. While there is generally good agreement between the model and observed magnetograms at both heights, there are significant differences in the locations and magnitudes of changes in $B_{\rm LOS}$. \item The photospheric changes of the line-of-sight field $B_{\rm LOS}$ in the observations and NLFFF models match relatively well, especially near the neutral line. \item The chromospheric changes in $B_{\rm LOS}$ in the NLFFF models and the observations do not agree. The observations show changes concentrated along the footpoints of loops that span the neutral line, while the NLFFF models indicate broader changes closer to the neutral line. The changes also do not match in sign. \item The changes at the photosphere in the models (and to the extent that the models reproduce the data, the observations) are unlikely to be produced by a change in the orientation of the field alone. They involve changes in the magnitude of the field. \end{itemize} It is important to consider the influence of observational factors on the results. The observed chromospheric field changes appear to coincide with loop footpoints on either side of the neutral line, whereas the changes in the models are predominantly along the neutral line. This may be in part due to a reduced visibility of the \ion{Ca}{2} 8542 \AA\ line at the locations over the neutral line, where the field is nearly perpendicular to the line-of-sight. The influence of field configurations on the visibility might be tested by additional observations of flares with different locations on the disk, and also by forward modeling of the expected changes. Additionally, we are only considering a constant height in the model. During flares, the opacity of the atmosphere may change and we may be seeing different heights in the \ion{Ca}{2} 8542 \AA\ line. While we believe that this influence is not major because we fit a long time range of the observations and the intensity returns to pre-flare values during this time, we cannot fully exclude an influence. But it is known from simulations that the surface with an optical depth $\tau=1$ is corrugated even in non-flare cases, which means that our approximation of a constant height is not entirely accurate, but cannot be too far off because the observed and modeled magnetograms agree relatively well. Another observational factor is the method of determining the changes in the field associated with the flare. In principle, some of the inferred changes might be due to flux emergence or diffusion during the observing interval. However, in general these are slower processes and they are not expected to show clear jumps in $B_{\rm LOS}$ exactly at the flare time. This possibility was tested by performing the same arctan-fitting on data without any flares (the same region observed a few hours before and after this flare). The result was that no ``jumps'' larger than $150$ G were detected, and the number of small $B_{\rm LOS}$ changes was an order of magnitude lower than in the current sample. This provides confidence that most of the changes in this analysis are directly related to the flare. The observed changes in the line-of-sight field at the photosphere and the chromosphere~\citet{kleint2017} are very different. {There is general agreement between the observed and model field changes at the photosphere, but discrepancy between the observed and model changes at the chromosphere. The likely explanation is that the model behavior at the chromosphere follows the photospheric data, and the NLFFF model excludes physics needed to reproduce the chromospheric changes. It is known that} the magnetic connection between the photosphere and chromosphere is complex. The high-resolution chromospheric movie of the flare shows a very complex small-scale (subarcsecond) structure with changing loops, which do not seem to be reproduced by this global lower-resolution NLFFF model and this could be a major contributor to the observed discrepancies. Tests of a nonlinear force-free reconstruction on boundary data from a radiative magneto-hydrodynamic simulation show that the NLFFF model performs poorly in representing the field structure in the chromosphere~\citep{2017ApJ...839...30F}. The low atmosphere is not force-free, and in particular the gas pressure and gravity force are dynamically important. The change in the magnetic pressure associated with the observed change in the line-of-sight field ($\Delta B_{\rm LOS}\approx 200$ gauss) assuming a line-of-sight field $B_{\rm LOS}\approx 1000$ gauss may be estimated in cgs units as $\Delta \left(B^2/8\pi\right)\approx \Delta (B_{\rm LOS}^2/8\pi)\approx B_{\rm LOS}\Delta B_{\rm LOS}/4\pi\approx 1.6\times 10^4$ dyne/cm$^2$. This is comparable to the gas pressure at a height of $\approx 250$ km in quiet-Sun models~\citep[e.g.][]{vernazzaetal1981}, and is much smaller than the photospheric gas pressure. On this basis, non-magnetic forces may play a role in the observed changes. However, these forces may be too slow to generate the large, stepwise changes observed on the flare time scale. The dynamic process most likely requires non-zero Lorentz forces. In summary, for the purpose of reproducing the observed field changes at the photosphere and chromosphere, the force-free field model appears to be inadequate, because a NLFFF reconstruction based on photospheric boundary conditions does not include the physics of the chromosphere \citep{2017ApJ...839...30F}. A possible next step is a magneto-hydrostatic model \citep[e.g.][]{2016SoPh..291.3583G,2017SSRv..210..249W}, although this will require additional boundary conditions or simplifying assumptions. In conclusion the observed magnetic field changes in the X1 flare SOL20140329T17:48 remain a puzzle. Additional insight may also come from repeating the analysis for other well-observed flares. | 18 | 8 | 1808.07079 |
1808 | 1808.05556_arXiv.txt | We report on the 2016 outburst of the transient Galactic Black Hole candidate IGR J17091$-$3624 based on the observation campaign carried out with \emph{SWIFT} and \emph{NuSTAR}. The outburst profile, as observed with \emph{SWIFT-XRT}, shows a typical `q'-shape in the Hardness Intensity Diagram (HID). Based on the spectral and temporal evolution of the different parameters, we are able to identify all the spectral states in the q-profile of HID and the Hardness-RMS diagram (HRD). Both \emph{XRT} and \emph{NuSTAR} observations show an evolution of low frequency Quasi periodic oscillations (QPOs) during the low hard and hard intermediate states of the outburst rising phase. We also find mHz QPOs along-with distinct coherent class variabilities (heartbeat oscillations) with different timescales, similar to the $\rho$-class (observed in GRS 1915$+$105). Phenomenological modelling of the broad-band \emph{XRT} and \emph{NuSTAR} spectra also reveals the evolution of high energy cut-off and presence of reflection from ionized material during the rising phase of the outburst. Further, we conduct the modelling of X-ray spectra of \emph{SWIFT} and \emph{NuSTAR} in 0.5 - 79 keV to understand the accretion flow dynamics based on two component flow model. From this modelling, we constrain the mass of the source to be in the range of 10.62 - 12.33 M$_{\sun}$ with 90\% confidence, which is consistent with earlier findings. | Galactic Black Hole (GBH) X-ray binaries (XRBs) are mostly observed in low mass X-ray binary (LMXB) systems. Only a few of the BH XRBs (Cyg X-1, LMC X-1 and LMC X-3) are found in high mass X-ray binary (HMXB) systems \citep{MR06}. These X-ray binaries are observed to exist as either persistent or transient \citep{Chen97,2016ApJS..222...15T,2016A&A...587A..61C} in nature. The persistent sources usually show consistently high X-ray luminosity ($\sim10^{37}$ erg sec$^{-1}$;\citet{Kuz97}) for a long duration \citep{1996ARA&A..34..607T}, except for sources like GRS 1915$+$105 which has aperiodic variability. Transient/outbursting sources remain quiescent for a long time and exhibit a sudden increase in X-ray flux (from mCrabs to 12 Crab; \cite{1989ApJ...337L..81T}). The transients remain active for tens of days to a few months or a few years before returning back to quiescent phase where the X-ray flux becomes non-detectable \citep{MR06}. A detailed understanding of the X-ray emission features (i.e., spectral and temporal characteristics) of the transient BH source during its outburst, is very essential to know about the accretion dynamics around the vicinity of BH XRB. Most of the BH transients usually exhibit thermal and non-thermal emission in their X-ray spectra. Thermal emission arises from the different radii of the Keplerian accretion disc which results in a multi-color blackbody spectrum at lower energies (i.e. soft spectrum) \citep{1973A&A....24..337S}. The non-thermal emission is due to Comptonization of disc photons by a static or dynamic hot corona existing in the innermost regions. This will result in a powerlaw spectral shape at higher energies (i.e. hard spectrum) usually with a cut-off \citep{1995xrbi.nasa..126T,ST95}. Sometimes due to the illumination of the disc by this non-thermal emission, a reflection component is also observed at higher energies \citep{RF93}. In general, the ratio of flux in a higher energy band (say 6 - 20 keV) to lower energy band (e.g. 2 - 6 keV) defines the hardness ratio \citep{Belloni2005,Nandi2012,RN2014}. During the outburst, the source intensity (i.e. X-ray flux) is observed to change with hardness ratio resulting in a `q'-shape plot which is well known as Hardness-Intensity Diagram (HID) (see \citealt{2001ApJS..132..377H,Belloni2005,Nandi2012,2016A&A...587A..61C} and references therein). Temporal analysis of the observations usually suggest that the GBH sources exhibit an evolution of the fractional rms variability during the outburst. Some times there are presence of low frequency QPOs which are classified into types A, B, C, C* based on their Q-factor, significance and amplitude \citep{Casella2004,MR06,2011BASI...39..409B}. Depending upon the variation of the above mentioned spectral and temporal properties, the transient GBH sources occupy different spectral states in their HID. These states are classified as low hard (LHS), hard intermediate (HIMS), soft intermediate (SIMS) and high soft state (HSS). For details we refer to \citealt{2001ApJS..132..377H,FBG04,HB2005,Belloni2005,2006ARA&A..44...49R,Nandi2012,Motta2012} and references therein. Several works have been done based on the above spectral state classification, which has helped immensely to understand the spectral and temporal properties of BH sources and the evolution of their HID \citep{2001ApJS..132..377H,FBG04,FHB09,Belloni2005,MR06,Nandi2012,RN2014,RNVS16b}. In this paper, we refer to this general understanding of spectral state classification. In addition to these characteristics which are generally observed in BH LMXBs, some sources show different types of variabilities/oscillations. These are usually referred to as coherent variabilities which may appear in the form of quasi-periodic flares or dips which occur for time period of seconds to minutes. The BH binaries GRS 1915$+$105 \citep{2001A&A...372..551B} and IGR J17091-3624 \citep{Alt11} exhibit these oscillations/variabilities. They are usually segregated into different classes because of the difference in X-ray flux, periodicity etc. The GBH transient source IGR J17091$-$3624 was discovered by \emph{International Gamma-ray Astrophysics Laboratory (INTEGRAL)} \citep{Kuul03} during 2003. Prior to this it appeared as a moderately bright transient during the period of 1994 to 2001 \citep{2003ATel..160....1I}. Thus the source has undergone multiple outbursts (2003, 2007 and 2011) till date. Detailed study of the spectral and temporal properties of the source suggests that it is similar to GRS 1915$+$105 \citep{Alt11}. Both sources exhibit coherent X-ray variability classes (heartbeat oscillations) at lower flux values, spectral state transitions and high frequency QPOs \citep{1999ApJ...527..321M,2001A&A...372..551B,Alt11,AB2012,Cap12,Zhang2014}. IGR J17091$-$3624 had undergone state transitions during its 2011 outburst, and variabilities/oscillations in timescales of 100 sec were observed in the light curves. These X-ray variability signatures were classified into $\nu$, $\rho$, $\alpha$, $\lambda$, $\beta$, $\mu$, $\gamma$ and $\chi$ \citep{Alt11,Zhang2014,2017arXiv170309572C} and observed to be similar with GRS 1915$+$105. During the time when the light curve displayed variabilities in IGR J17091$-$3624, the source had a softer spectra but exhibited high rms variability. The evolution of the spectral states and the oscillations observed in 2011 are not similar to the previous outbursts in 2003 and 2007 where the source characteristics resembled with typical BH sources \citep{Cap12,Cap13}. Although there is no published literature which discusses about a complete HID of the source in 2011 outburst, the observations by \citealt{PahariATEL1,PahariATEL2} (ATEL 4282 and 4283) have shown a decline in source flux towards the quiescence. Since the \emph{XRT} observations had weak signal-to-noise ratio, \citealt{PahariATEL1} could not perform the detailed spectral analysis. Recently \citealt{Xu17} have studied the rising phase of 2016 outburst of this source and looked into the spectral and temporal characteristics. They have discussed about reflection features and QPOs from the {\it NuSTAR} spectra for the rising phase of the outburst. Even though IGR J17091$-$3624 is being considered as similar to GRS 1915$+$105, an estimate of its dynamical mass has not yet been obtained unlike GRS 1915$+$105. Likewise, the distance to the source IGR 17091$-$3624 and the disc inclination could not be determined due to lack of observational evidence of the nature of its binary companion. Previous attempts to estimate the mass of the source suggest the value to vary between 3 M$_{\sun}$ and 15 M$_{\sun}$ \citep{Alt11,RV2012, Rebusco12, AB2012, Pah2014}. A recent estimate points out a probable range for the mass as 8.7 M$_{\sun}$ to 15.6 M$_{\sun}$ \citep{2015ApJ...807..108I} based on spectral and temporal modelling, and 11.8 M$_{\sun}$ to 13.7 M$_{\sun}$ by modelling the broad-band energy spectra alone. The source is estimated to be at a distance of 10 kpc to 20 kpc by \cite{Alt11}. A better constraint of 11 kpc to 17 kpc is given by \cite{rodriguez2011first} for a black hole of mass 10 M$_{\sun}$ using estimated luminosity at the hard to soft state transition. The inclination of IGR J17091$-$3624 has been proposed to be between 50$\degr$ to 70$\degr$ by \cite{king2012extreme} as disc-winds are present only in systems with high inclination angles. But it has to be noted that the inclination cannot exceed 70$\degr$ due to the absence of any signature of eclipses. Most of the mass estimates depend on the assumptions of inclination and distance. This leads to the large spread in the range of possible values. Thus it is difficult to know a precise value of mass from these methods unless the inclination and distance are known accurately. However, as stated in section \ref{ss:bbspec} the mass modelling method based on two component flow has little dependency on inclination or distance. The source IGR J17091$-$3624 went into outburst during early 2016 and was detected by \emph{SWIFT-Burst Alert Telescope (BAT)} \citep{2016ATel.8742....1M}. The BAT light-curve shows a fast rise and exponential decay profile, extending from MJD 57445 (27th Feb 2016) to 57615 (15th August 2016). The INTEGRAL observations \citep{2016ATel.8761....1G} indicated the source to be in its hard state during the rising phase of the outburst. Spectral transition to the intermediate state was observed during 22nd March i.e. MJD 57469 \citep{2016ATel.8858....1C} based on \emph{SWIFT} observations. During 13th April 2016 (MJD 57491), `heartbeat' oscillations have been detected with frequency of $\sim$ 0.027 Hz, using \emph{SWIFT-X-ray Telescope (XRT)} observations \citep{2016ATel.8948....1R}. The corresponding X-ray spectrum has been understood to consist of emission due to both Keplerian disc (thermal) and Comptonized emission from the corona (non-thermal). Optical observation has found the source magnitude to be brighter by 1.5 in all the bands \citep{2016ATel.8795....1G} in comparison to the magnitude value in 2011 outburst. There has been no detection of any jet ejection in the radio band from this source during the 2016 outburst \citep{2016ATel.8821....1E}. In this paper, we consider \emph{SWIFT-XRT} and \emph{Nuclear Spectroscopic Telescope Array (NuSTAR)} observations for the 2016 outburst of the source IGR J17091$-$3624. We explore the spectral and temporal characteristics of the source, so as to look for the spectral state transitions during this outburst. The evolution of HID of the source is studied based on the phenomenological models to understand the contribution of the soft and hard components separately. We search for the evidence of coherent oscillations/variabilities in the light-curve, and how they evolve as the outburst progresses. Then we attempt to see whether these variabilities have any correlation with the different spectral states. The characteristics of PDS are also being looked into so as to understand the evolution of low frequency QPOs during the rising phase of the outburst. Finally, based on the two component accretion flow paradigm, we model the energy spectra of the four quasi-simultaneous broad-band (0.5 - 79 keV) observations using \emph{SWIFT} and \emph{NuSTAR}. Rest of the {\it XRT} data (51 in number, spanning over 172 days) and the two \emph{NuSTAR} data which are not taken simultaneously with SWIFT are also modelled separately in the same way. The procedure for modelling is based on \citealt{2015ApJ...807..108I}. From this, we understand the variations of the model parameters during the different spectral states. We generate the HID from phenomenological fits and perform a comparative study with respect to the results obtained from two component model fits. We also constrain the mass of the source from the two component model fitting of energy spectrum from different spectral states. We also construct the probability distribution function of the source mass, for having a better constrain on the mass. A summary of the procedures followed for data reduction has been given in section \ref{obs}. The methodology considered for analysis of data from \emph{XRT and NuSTAR} are discussed in section \ref{anal}. The results obtained from the spectral and temporal analysis using phenomenological and two component flow model are presented in section \ref{res}. These results have been discussed in section \ref{dis}. | \label{dis} In this paper, we have studied the spectral and temporal variabilities of the black hole source IGR J17091$-$3624 during its 2016 outburst. It has been understood very well that based on the variations of the thermal and non-thermal emission, the BHs exhibit several spectral states and form a `q'-shaped HID profile. Several studies based on theoretical models have looked into these, and explored the accretion phenomenon (\citealt{Belloni2005,2010MNRAS.403...61D,Nandi2012,RN2014} and references therein). The two component advective flow model \citep{ST95} suggests that the thermal emission is occurring from the Keplerian flow. The sub-Keplerian corona inverse Comptonize the soft photons resulting in a power-law hard photons distribution. Depending upon the contribution from Keplerian and sub-Keplerian flow during the accretion process, BH sources occupy the different spectral states. Based on this understanding of the accretion phenomenon, in this paper we have looked into the evolution of spectral and temporal characteristics of IGR J17091$-$3624 during its recent outburst in 2016. We find that during the rising phase of the outburst, the source occupies hard and hard intermediate states. During the hard state, the source exhibits a powerlaw spectrum with the hardness ratio $\sim$0.9 and high fractional rms variability in the PDS (as shown in Table \ref{tab:parameters}, Figure \ref{fig:fig3}). The broad-band fit using two component flow model implies that the values of shock location and sub-Keplerian halo rate are maximum (see Figure \ref{fig:Accrn}). In the HIMS, the contribution of thermal emission increases. This is also evident in the decrease of both the hardness ratio and fractional rms variability (right panel of Figure \ref{fig:fig3}). The shock location and halo rate have decreased while the Keplerian disc accretion rate has increased. These factors suggest the rise of thermal emission. Presence of reflection component at higher energies have been observed for a few observations in the LHS and HIMS of the rising phase (see also \citealt{Xu17}). In addition to this, we find that the value of cut-off at high energies has a decreasing trend. This is similar to that observed in a few other black hole binaries like GX 339$-$4 \citep{Motta2009}. An evolution of type C QPO frequencies is also observed from the LHS to HIMS. The QPOs observed in {\it XRT} data are weaker. But strong presence of QPOs are shown by \emph{NuSTAR} observations (see Figure \ref{fig:Nustar-PDS} and Table \ref{tab:qpo}). Although \citealt{Xu17} has reported about the detection of QPOs in {\it NuSTAR} data of this outburst of the source, we understand that they have considered only observations belonging to the rising phase of the outburst. Here, in this manuscript we have found additional QPOs for many other observations and also the mHz QPOs which have not been discussed yet. In \citealt{Sree2018} we have also further studied this evolution of QPOs using the propagating oscillation solution \citep{skc2008} of the two component flow model. Following this, we find that the source enters the SIMS as evident in the decline of disc temperature, hardness ratio and fractional rms variability (see panel h of Figure \ref{fig:fig1} and right panel of Figure \ref{fig:fig3}) w.r.t HIMS. Thus the emission is dominated by that due to the Keplerian disc. A higher ratio of Keplerian to halo accretion rate is observed (see Figure \ref{fig:Accrn}). For a very brief period on day 63 (MJD 57508), the source spectrum becomes softer with hardness ratio attaining its minimum value and also a lesser value of fractional rms variability (Figure \ref{fig:fig3}). The spectral softening is also reflected in the increase of Keplerian disc accretion rate to a maximum of 0.39 M$_{Edd}$ which is more than that during the SIMS-rise and decay phases. We understand that probably this short duration belongs to a HSS and this is unlike to typical BH sources (see \citealt{Belloni2005,MR06}). The source later decays through the SIMS, HIMS and LHS, with a reverse trend of change in the Keplerian and halo accretion rates, and shock location. The outburst under consideration has a steep rise and exponential decay pattern. Hence the states in the decay phase persists for longer duration than the corresponding states in the rising phase. Four broad-band \emph{XRT+NuSTAR} observations (0.5 - 79 keV) have been modelled using two component model during different states of the outburst. It provides a better estimation of thermal and non-thermal contributions in the spectra. The behaviour of the model parameters are consistent with state transitions as mentioned before. Also they are found to be consistent with the values obtained by two component modelling of the {\it XRT} spectra alone (see Figure \ref{fig:Accrn}). Thus based on the phenomenological and two component model fits, we understand that the source occupies all the spectral states in the HID and completes the `q'-profile. Previous publications have not been successful in producing a \emph{complete} `q'-diagram for the 2011 outburst of the source. The only published paper which has shown a `q'-diagram is \citealt{Cap12} where the profile was incomplete since the study considered only till the HSS. The Astronomer's Telegram by \citealt{PahariATEL1,PahariATEL2} discussed the source decaying towards its quiescence. But due to poor signal-to-noise ratio of the {\it XRT} data, they could not study the detailed spectral characteristics and hence the `q'-profile during decay phase. In this manuscript, for the 2016 outburst we have been able to understand that the source completes the `q'-diagram based on both phenomenological and two component flow modelling. This has been possible due to the {\it XRT} data having statistically significant count rate throughout the outburst unlike the 2011 outburst. An interesting fact is that throughout the entire rising phase of the SIMS of the 2016 outburst, we observe variabilities/oscillations in the light-curve (see Figures \ref{fig:LCPDS} and \ref{fig:Variability}) until the source entered the decay phase. The time period of oscillations suggest the presence of mHz QPOs. The extracted temporal data prove the existence of mHz QPOs for most of the days in the SIMS. Interestingly, all the observations with variability showed prominence of \textit{diskbb} in the energy spectra for the phenomenological modelling. Higher Keplerian to halo accretion rate is also exhibited as compared to the other states (see bottom panel of Figure \ref{fig:Accrn}). This implies that the cause of the variability is essentially thermal in nature. Hence linked to the presence of a Keplerian disc that reaches close to the black hole. This is consistent with smaller values of shock location during this state (top panel of Figure \ref{fig:Accrn}). The signature of variabilities during day 46.54 of the SIMS has also been reported in an Astronomer's Telegram by \citealt{2016ATel.8948....1R}. In 2011 outburst, similar oscillations were observed after the HSS only and existed for a long duration \citep{Cap12}. Apart from the variabilities during the SIMS, we observe weak signatures of variabilities during the transition from HIMS to SIMS, HSS and the initial days of SIMS-decay. There is no clear detection of variability in LHS possibly due to less source flux and hence is statistically insignificant. A weak 16 mHz QPO is observed in the \emph{NuSTAR} observation during day 31.11 while the source is transiting from HIMS to SIMS. For the observation in HSS, both the \emph{XRT} and \emph{NuSTAR} PDS show broad QPO at 21.4 mHz and 20.7 mHz respectively. A very weak peaked component at 0.16 Hz is observed in the latter. We would like to highlight that when we study outbursting sources as time dependent events, analytical models are not able to address the time evolution of the outbursting events similar to the variability signatures observed in this source. This is due to the fact that all analytical models are applicable in steady state situations only. Using numerical MHD simulations which include radiative cooling processes, might prove fruitful for this. In this paper we observed that the various types of heartbeat oscillations observed in this source are associated with intermediate states. According to two component flow model, the two types of accretion rate (Keplerian and sub-Keplerian) becomes comparable during the intermediate states. It might be possible that the radiation coupling between corona and with both types of flow (having different viscous time scale) may play a role to understand fast variabilities observed in this source. Detailed investigation of this feature using our model is at present beyond the scope of this paper. The two component spectral modelling shows that the overall mass accretion rate is only 0.39 M$_{Edd}$ during the HSS. Also, in section \ref{hssp}, we did find that the soft flux contribution to the entire spectra is only 33\%. Thus the lack of Keplerian matter might be the reason for the source to occupy a short duration of HSS. This may not be allowing the source to be in HSS for a longer period of time before transitioning into the SIMS of the decay phase. All these factors indicate that possibly the outburst is triggered due to disc instability at the outer edge. And maybe a small amount of sub-Keplerian matter can be converted into the Keplerian matter \citep{2010ApJ...710L.147M}. We also note that during the beginning of SIMS the spectral data extends only up-to 6 keV. This causes sudden absence of high energy flux suggesting that possibly a jet ejection has occurred. Unfortunately radio flares have not been observed as the system reaches the SIMS unlike the case in some outbursting sources \citep{FBG04,FHB09,MJ2012,RN2014,RNVS16a}. By means of modelling the broad-band observations by \emph{SWIFT} and \emph{NuSTAR} X-ray observatories, we estimate the mass of the black hole candidate using the two component flow model. The range of values in which the mass varies is found to be 10.62 - 12.33 M$_{\sun}$ including the systematic variation as mentioned earlier. This is consistent with the previous estimate of 11.8 - 13.7 M$_{\sun}$ using similar methodology of spectral modelling by \citealt{2015ApJ...807..108I}. It has to be clearly noted that in phenomenological models the parameters like T$_{in}$, powerlaw index are the distinct spectral signatures which can be tuned independently along with normalizations. In two-component model the parameters appear in hydrodynamic equations which self-consistently calculate the spectral features. This model has only one normalization and not separate normalizations as in diskbb and powerlaw. The advantage of this model is that mass and the accretion rate of the source self-consistently determine the density and temperature distribution of the flow. This in turn determine the spectral signatures like fraction of inverse-Comptonized black body photons, spectral index etc. So, the model chooses the correct mass of the source to match all the spectral features of all the data sets. Thus from the phenomenological and two component accretion model fits, we can summarize the following points about the 2016 outburst of IGR J17091$-$3624. \begin{itemize} \item The source occupies all the spectral states and completes the `q'-profile in HID. Variation of parameters from phenomenological fits and two component model fits corroborate the same. Spectral state evolution based on correlation between the fractional rms variability and hardness ratio, is evident from the Hardness-RMS diagram. \item The halo accretion rate dominates during the hard and hard-intermediate states while the Keplerian - disc rate dominates the softer states. \item The size of the Compton corona (shock location) is minimum during the soft state and maximum during the LHS. \item Presence of reflection component due to ionized material, and decline in cut off energy are observed during the rising phase LHS and HIMS. \item An evolution of low frequency type C QPOs from 0.15 to 2.15 Hz is observed during the rising phase of LHS and HIMS. \emph{NuSTAR} observations show strong signatures of QPOs during the LHS and HIMS. \item Coherent oscillations/variabilities are exhibited throughout the SIMS and also during the possible HSS. A very weak signature is seen during the transition from HIMS to SIMS in the rising phase. QPOs of the order of 20 mHz - 30 mHz are found during the SIMS. A 20.7 mHz broad QPO and a weak peaked component at 0.16 Hz exist during the possible HSS. \item Even in the presence of variabilities, the source completes the `q'-profile in its HID. \item Mass of the source is estimated to be in the range of 10.62 - 12.33 M$_{\sun}$. \end{itemize} | 18 | 8 | 1808.05556 |
1808 | 1808.09778_arXiv.txt | \label{sec:intro} Studies of the Milky Way are experiencing a revolution thanks to the large amount of high resolution spectral data of individual stars becoming available. This revolution has just started, with on-going spectroscopic surveys delivering thousands of spectra and future surveys planned to collect millions of them. In order to characterise large samples of survey spectra, automatic and efficient pipelines are in constant development to carry out tasks such as measuring equivalent widths or fitting models to data to pure data-driven approaches. In addition, the spectra are taken by different instruments, with surveys targeting different stellar populations. Hence, they are of different nature regarding resolution, signal-to-noise ratio and wavelength coverage. In spite of the variety of methods, the quality of the parameters obtained may be assessed in a similar way. They need to be tested against a set of reference stars, for which the parameters are known with high confidence and independently of the methodology and data employed in that particular analysis. Ideally, every survey should use the same set of reference stars, or at least have a large overlap of stars for which they can compare and scale their results. The GBS consists of a small but carefully selected set of FGK stars, with a large range in metallicity. A distinguishing feature of the sample is that for most of them the angular diameter has been measured with interferometry, which allows one to determine the effective temperature from the Stephan-Boltzmann relation provided the parallax and bolometric flux are known. Furthermore, a number of them are in wide binary systems or have asteroseismic measurements, thus helping us to constrain the mass and hence the surface gravity from dynamical or seismic relations. The GBS provide the means to calibrate spectral analysis, such that the values resulting from the simplistic assumptions in spectral line formation agree with the fundamental values. The GBS have proven to be very useful to the community, with several spectral catalogues validating and calibrating their pipelines with the GBS stellar parameters. Examples are the Gaia-ESO Survey \citep{2017A&A...598A...5P}, GALAH \citep{2018MNRAS.tmp.1218B}, AMBRE \citep[e.g.][]{2016A&A...591A..81W}, RAVE \citep{2017AJ....153...75K} and recently the Apsis pipeline of Gaia-DR2 \citep{2018arXiv180409374A}. A series of papers has been published analysing the GBS. The first sample (v1.1) is presented in \citet[Paper I]{2015A&A...582A..49H}, and a compilation of their spectra is provided in \citet[][Paper II]{2014A&A...566A..98B}. These spectra were used for the determination of metallicity in \citet[][Paper III]{2014A&A...564A.133J}. Further determination of iron-peak and $\alpha$-element abundances was presented in \citet[][Paper IV]{2015A&A...582A..81J}. With the GBS v1.1 being used by the Gaia-ESO Survey for calibration purposes it became clear that the sample was lacking stars with \feh $ \sim -1$, which we addressed in \citet[][Paper V]{2016A&A...592A..70H}. Finally, we quantified the sources of uncertainties due to methodology in \citet[][Paper VI]{2017A&A...601A..38J}. Currently we are determining new abundances of light elements. % | Here we present a consolidated sample of GBS v2.1. While the parameter values are published in Papers I--V, several tables presented in these papers are not available via CDS, making a cross-match with other catalogues less straightforward. That limits the applicability of the GBS. The summary table we present via CDS and explain in this note intend to make the GBS more accessible to the community, ensuring that the latest version is used and making their application more convenient thanks to the CDS functionalities. | 18 | 8 | 1808.09778 |
|
1808 | 1808.10613_arXiv.txt | We numerically study the radiative properties of the reverberation phase of pulsar wind nebulae. Reverberation brings a significant evolution in a short period of time. We show that even the Crab nebula, associated to the more energetic pulsar of the sample we consider, has a period in its future time evolution where the X-ray luminosity will exceed the spin-down power at the time. In fact, all nebulae in our sample are expected to have a period of radio, X-ray, and GeV superefficiency, and most will also have a period of TeV superefficiency. We analyze and characterize these superefficient phases. | Recently, \cite{Younes2016} reported the discovery of a nebula surrounding the magnetar Swift J1834.9-0846. The fact that this system has the highest efficiency of all pulsar wind nebulae (PWNe) known was considered to be highly unusual: $\sim 10\%$ of the mild spin-down power of the pulsar, $L_{sd} \sim 10^{34}$ erg s$^{-1}$, is emitted just in soft X-rays. This promoted interpretations based on a transfer, via a yet unknown mechanism, of magnetic energy into particle acceleration \citep{Granot2017}. However, we demonstrated that the multifrequency data, as well as its size, could be encompassed by a normal, rotationally-powered PWN under the condition that it is entering in reverberation \citep{Torres2017}. The latter is a relatively short but important phase in the evolution of all PWNe, produced when the reverse shock created by the supernova explosion travels back toward the pulsar, compressing the wind bubble, see, e.g., \cite{Slane2017}, for a review. This compression heats the PWN, reducing its size, and increasing the magnetic field. Such evolution leads, as we see below, to an almost complete burn-off of the electron population. Despite the obvious importance of this phase, it is not yet usual that radiative models of PWNe consider it. In fact, the effect of reverberation upon the spectral results has been dealt with only in a few scattered occasions, and with different levels of detail, see, e.g., \cite{Gelfand2009,Vorster2013,Bandiera2014,Bucciantini2011,Martin2016,Torres2017}. Here we aim at studying the radiative properties of the reverberation phase in detail. For this, we shall study the future reverberation period of well-characterized PWNe. We shall prove that the 10\% efficiency found for Swift J1834.9-0846 is not a limit at any rate, not even for this very pulsar, finding that all PWNe can have periods of superefficiency from radio to gamma-rays. | Here, we have shown that supereffiency periods in which the luminosity at a given band from radio to TeV exceeds the pulsar spin-down power, are common. They are unavoidably associated with the reverberation process. Supereffiency happens because when the PWNe are reverberating, the spin-down power is no longer the energy reservoir. In these cases, the nebulae are receiving energy from the environment, and the spin-down power is, a priori, not determinant to judge detectability at any band. Observing one such superefficient system would be amazing: a bright, small or point-like nebula, with a spatially coincident pulsar many times less energetic. The difficulty for observing them is that such systems can be maintained only for a few hundred years. For the estimate that follows, let us assume that the superefficiency period roughly lasts about 300 years in the evolution of young nebulae, of typically $<10000$ years of age (although note that as the G54 case tells, supernova with large ejected masses or low density environments can produce reverberation beyond this age). Assuming a pulsar birthrate of 3 century$^{-1}$ \citep{Faucher2006}, 300 PWNe were born within the last $10000$ years, and from these, we are interested in a period equivalent to --at most-- 3\% of their evolution. Taking into account the correspondingly shorter percentages for pulsars born at different centuries, we have a probability of $\sim 1\%$ of finding one these pulsars in the right period of their evolution. Thus we expect at most 3 PWNe in a superefficient stage in the Galaxy today. This should be taken rather as an upper limit, because it assumes it is equally probable to have reverberation at any time within the first 10000 years of a pulsar (thus neglecting that there is no reveberation in their free-expansion phases). In a future work, we shall focus on observational strategies for finding superefficient or highly efficient PWNe. Note that our model assumes no morphological shape for the PWN; they are described with a time-varying radius. If the compression is asymmetric or turbulence develops, superefficiency could be less effective, detaining the reduction in the PWN size and the increment in the field perhaps before our results indicate. This might affect less energetic nebulae in particular, such as Kes 75 or J1834, being likely unimportant for others such as G09, G21 or Crab. Magneto-hydrodynamical simulations will verify on this issue. In any case, $R_{min}$ is many orders of magnitude larger than the pulsar's radius, or even the pulsar's magnetosphere (typically at least 6 orders of magnitude larger than the size of a young pulsar's light cylinder), and thus the inner workings of the pulsed emission via synchro-curvature radiation \citep{Torres2018}, is not expected to be significantly affected even in the most severe of the compressions. | 18 | 8 | 1808.10613 |
1808 | 1808.06625_arXiv.txt | Short X-ray reverberation lags are seen across a broad Fe-K energy band in more than twenty active galactic nuclei (AGNs). This broad iron line feature in the lag spectrum is most significant in super-Eddington sources such as Ark 564 ($L/L_{\rm Edd}\sim 1$) and 1H 0707--495 ($L/L_{\rm Edd}\gtrsim 10$). The observed lag timescales correspond to very short distances of several $R_g/c$, so that they have been used to argue for extremely small `lamp-post' coronae close to the event horizon of rapidly spinning black holes. Here we show for the first time that these Fe-K short lags are more likely to arise from scattering in a highly-ionised wind, launched at $\sim 50\,R_g$, rotating and outflowing with a typical velocity of $0.2c$. We show that this model can simultaneously fit the time-averaged energy spectra and the short-timescale lag-energy spectra of both 1H 0707--495 and Ark 564. The Fe-K line in 1H 0707--495 has a strong P-Cygni-like profile, which requires that the wind solid angle is large and that our line of sight intercepts the wind. By contrast the lack of an absorption line in the energy spectrum of Ark 564 requires rather face-on geometry, while the weaker broad Fe-K emission in the energy and lag-energy spectra argue for a smaller solid angle of the wind. This is consistent with theoretical predictions that the winds get stronger when the sources are more super-Eddington, supporting the idea of AGN feedback via radiation pressure driven winds. | \label{sec1} X-ray illumination of the accretion disc in active galactic nuclei (AGN) produces a fluorescent iron line together with a reflected continuum \citep{geo91,mat91}. These scattered photons travel a longer path length than the photons directly observed, producing a time delay which is called the reverberation lag. This provides a probe of the structure and geometry of the inner accretion flow around the central black hole (e.g. \citealt{utt14}). The reverberation lag in AGNs was first seen at the soft energy band ($<1$~keV) in 1H 0707--495 \citep{fab09}. This was interpreted as the signature of a partially ionised reflector, where the multiple low-energy emission lines are smeared into a pseudo-continuum by extreme relativistic effects (e.g. \citealt{cru06}). However, this soft X-ray excess region is probably complicated, with additional components from low-temperature Comptonisation \citep{mag98,cze03,nod11b,meh11,jin13,mat14,boi16} which can make a soft lead, together with thermalisation of the reprocessed flux that contributes to the soft lag \citep{gar14}. Therefore the `soft lag' is not a clean tracer of reverberation. Instead, the iron line clearly originates in the reflected emission, so time lags in the Fe-K band are simpler to interpret. These have been reported in multiple AGNs (\citealt{kar16} and reference therein), though are generally less significant than the soft lag. These Fe-K reverberation lags are seen at high frequencies of $\sim c/100\,R_g$, where $R_g=GM/c^2$ is the gravitational radius and $c$ is the speed of light. Lag-energy spectra made at this frequency show a broad feature in the 6--9~keV band which is lagged behind the adjacent continuum bands by timescale of a few $R_g/c$. Short-amplitude reverberation lags are often interpreted as evidence for short light travel time lags, indicating reflection from the innermost regions of the accretion disc around a rapidly spinning Kerr black hole (e.g. \citealt{fab09,kar13b}). However, \citet{mil10a} pointed out that the primary component, which has no time delay, contributes a significant fraction of the flux even in the Fe K band. This significantly dilutes the reverberation time delay; if the continuum (zero time lag) contributes to half of the photons in the `Fe K' band (with lag time $t_0$), then the observed lag is $t_0/2$. Stronger dilution results in shorter lags, and \citet{mil10a,mil10b} and \citet{tur17} showed that the observed lag-frequency plots can instead be explained by more distant scattering clouds orbiting the source at $\sim100\,R_g$. \citet{leg12} directly measured the transfer function of Ark 564 and showed that scattering from circumnuclear materials at $\sim200\,R_g$ is responsible for the observed time lags. Winds from the accretion disc are the most likely source of this reprocessing material (see e.g. \citealt{kin03}), and winds typically have an outflow velocity which is of order the escape velocity from their launch radii. \citet{miz18a} (hereafter Paper 1) showed that neutral clouds located at $\sim100~R_g$ with outflow velocity of $0.14c$ (which is the typical value; \citealt{tom11}) can quantitatively explain the frequencies at which the Fe K lags are observed as well as the observed lag amplitudes. This also reproduces the width of the broad Fe K feature in the lag-energy spectra as the photons scattered on the near side of the outflow are blueshifted, whereas those on the far side are redshifted. In the present paper, we extend this analysis by considering a more physically-realistic disc wind picture. In fact, Paper 1 assumed that the wind was neutral, whereas any wind launched from the inner disc region should be ionised by the X-ray illumination. Indeed, ultrafast outflows (UFOs) are now detected as blueshifted absorption lines of highly-ionised (H- or He-like) iron ions in many AGNs (e.g.~\citealt{pou03,ree09,tom10,gof13}). Paper 1 also assumed that the material was purely radially outflowing, whereas a disc wind should be both rotating and outflowing. In addition, the wind geometry was assumed to be a section of a hemisphere, whereas a bicone geometry is physically more likely \citep{sim08,sim10a,hag15,hag16}. In this paper, we consider a realistic disc-wind geometry, in which the outflow gas is rotating, outflowing and highly-ionised. We base our calculations on the ionised biconical wind model of \citet{hag15,hag16}, which can fit the UFO features seen in the X-ray energy spectra. This uses Monte-Carlo techniques to follow the resonantly-scattered line emission in the highly-ionised gas in order to calculate both the absorption and self-consistent emission from the wind. Our goal is to construct a model that can explain both the energy spectra and reverberation lags simultaneously. In section \ref{sec2}, we explain the method and model in the Monte-Carlo simulation. Next, we show the resultant energy spectra and lag features in our calculation in section \ref{sec3}. In section \ref{sec4}, we apply our model to Ark 564 and 1H 0707--495, where the Fe-K reverberation lags are most clearly seen. We show that the wind model can explain both the observed time-averaged energy spectra and the broad Fe-K lag in the lag-energy spectra. We extend these results into a physically-based picture of radiation powered winds from super-Eddington sources in section \ref{sec5}, and state our conclusions in section \ref{sec6}. | \label{sec6} Short timescale lags around $\sim5\,R_g/c$ are widely seen over a broad Fe-K band in the lag-energy spectra of AGNs. These are most clearly seen in the super-Eddington sources Ark 564 and 1H 0707--495. We show that these short lags are likely to be produced by a fast ($0.2c$) outflowing, highly-ionised wind at $50-100\,R_g$. The wind produces a broad emission line from combination of the rotation and the outflow, and the few hundred $R_g$ size scale of the wind Fe-K reverberation lag is significantly diluted by the continuum emission underneath the iron line. We show that this model can simultaneously fit both the time-averaged energy spectra and the lag-energy spectra in Ark 564 and 1H 0707--495. These two sources show similar lag-energy spectra, but very different time average energy spectra, which we interpret as mainly due to difference in the inclination angle with respect to the wind. In Ark 564 our line of sight does not intercept the wind, while in 1H 0707--495 our line of sight does intercept the wind, resulting in a distinct blueshifted absorption line. There is also a noticeable difference that the broad iron emission line feature is stronger in 1H 0707--495, which we interpret as being due to a larger wind solid angle caused by the higher super-Eddington luminosity. Thus in Ark 564 we see the wind only via its small scattered emission, while in 1H 0707--495 we see a prominent P-Cygni profile with the strong emission and absorption. While this ionised fast wind model can explain the short lags seen from the fast variability, it does not produce the dramatic spectral changes seen in 1H 0707--495 on longer timescales. Instead, this requires that there are denser and less-ionised clumps partially occulting the central X-ray source. Simulations of the super-Eddington winds show that such clumps are produced by Rayleigh-Taylor instabilities at $\sim 500\,R_g$. Consequently, the ``hot inner and clumpy outer wind model'' we propose here can explain all the observed features; the inner hot wind produces the Fe-K emission line seen in the time-averaged spectrum and the reverberation lags, together with the absorption line along the line of sight intersecting the wind, whereas the outer cold clumps account for the longer term spectral variability as seen in the deep dips. Finally, we remark, as demonstrated in the present paper, that the reverberation provides us with a unique tool to constrain parameters of the material outside of the line of sight. Estimating the solid angle subtended by the wind is crucial to explore energetics of the AGN outflows, and hence to quantify their contribution to the AGN feedback (see e.g. \citealt{kin15}). | 18 | 8 | 1808.06625 |
1808 | 1808.06139_arXiv.txt | {The inner regions of the Galaxy are severely affected by extinction, which limits our capability to study the stellar populations present there. The Vista Variables in the V\'{i}a L\'actea (VVV) ESO Public Survey has observed this zone at near-infrared wavelengths where reddening is highly diminished.} {By exploiting the high resolution and wide field-of-view of the VVV images we aim to produce a deep, homogeneous, and highly complete database of sources that cover the innermost regions of our Galaxy.} {To better deal with the high crowding in the surveyed areas, we have used point spread function (PSF)-fitting techniques to obtain a new photometry of the VVV images, in the $ZYJHK_s$ near-infrared filters available.} {Our final catalogs contain close to one billion sources, with precise photometry in up to five near-infrared filters, and they are already being used to provide an unprecedented view of the inner Galactic stellar populations. We make these catalogs publicly available to the community. Our catalogs allow us to build the VVV giga-CMD, a series of color-magnitude diagrams of the inner regions of the Milky Way presented as supplementary videos. We provide a qualitative analysis of some representative CMDs of the inner regions of the Galaxy, and briefly mention some of the studies we have developed with this new dataset so far.} {} | \label{sec_intro} In principle, the high stellar densities in the inner regions of our Galaxy and their relative closeness should produce the kind of well populated color-magnitude diagrams (CMDs) that are ideal to study their stellar populations. In practice, however, stars located at low Galactic latitudes in the inner parts of the Milky Way are hidden behind a curtain of dust and gas that highly extinguish their emission at optical and shorter wavelengths. Near-infrared observations are better suited for studies in these regions due to the diminished effect of extinction at these wavelengths ($A_{K_s}\sim 0.1A_V$). But until recent years, the kind of wide-field, near-infrared telescopes and cameras necessary to survey these relatively big regions of sky were not available. Large surveys in the near-infrared such as 2MASS and dedicated facilities like the VISTA telescope and its imager have completely changed this situation. Nowadays, the product of 4m aperture and 0.6 square degrees sky coverage per pointing makes VISTA the fastest near-infrared survey system in the world \citep{sut15}. The Vista Variables in the V\'ia L\'actea (VVV) survey, one of the six original key ESO public surveys conducted in Paranal with the VISTA telescope \citep{min10,sai12b}, takes full advantage of this fact to provide a new view of the inner regions of our Galaxy. Our collaboration pioneered the use of the ESO public photometric catalogs available from VVV to provide a wide view of the stellar populations residing in the Galactic bulge region \citep{sai12a}, and in an adjacent Galactic disk region \citep{sot13}. However, current catalogs, based on aperture photometry, are unable to exploit the full potential of the VVV images, due to the high crowding present in the inner Galactic environments. Point spread function (PSF) photometry can provide a much more complete picture in the most crowded regions surveyed by VVV, such as the Galactic center or the inner Galactic globular clusters. But even the less crowded VVV regions can benefit from using PSF photometry by highly increasing the number of detected sources, as we show in this work. \section {Observations} \label{sec_obs} The VVV observations were taken with the VIRCAM camera on the 4.1m VISTA telescope located in Cerro Paranal Observatory, in Chile. The VVV surveyed regions include the portion of sky located between $-10\fdg0 \le l \le +10\fdg4$ and $-10\fdg3 \le b \le +5\fdg1$ for the Galactic bulge, and between $294\fdg7 \le l\le350\fdg0$ and $-2\fdg25 \le b \le 2\fdg25$ for the low-latitude Galactic disk (see Figure \ref{fig_dens}). They were observed over a six-year period (2010-2015) with the $K_s$ filter, which was used for the variability campaign, between 69 and 293 times in the Galactic bulge area, and between 48 and 52 times in the disk area. All the VVV surveyed regions were also observed at least twice in the $Z$,$Y$,$J$, and $H$ filters, a first epoch in 2010-2011, and a second one in 2015. The VVV observations are divided in 196 contiguous fields in the Galactic bulge and 152 contiguous fields in an adjacent region in the southern disk. The VIRCAM camera contains 16 detectors, each one with $2048\times2048$ pixels. The pixel size is $\sim0.34''$. The detectors in the VIRCAM camera have significant gaps between them, generating so-called pawprint images. The observing strategy of the VVV survey, described in detail in \citet{sai12b}, consists in firstly taking a set of two slightly jittered images to account for detector cosmetic effects. This jittering is $\sim20\arcsec$ in both coordinates of the detector. The combination of these two images generates the so-called stacked pawprints. Additionally, in order to have a complete coverage of the area of every field, we take six consecutive stacked pawprints, dithered following a mosaic pattern to cover all the gaps. The combination of these stacked pawprints produces a full image of the field, a so-called tile. The area covered by a single tile is $1.5\times1.1$ square degrees in the sky, and each pixel in the tile, except for the borders, have been exposed at least four times. The VVV observations are reduced, combined in stacked pawprints and tiles, astrometrized and calibrated by the Cambridge Astronomical Survey Unit (CASU; \citealt{eme04,irw04,ham04}). CASU also provides a catalog of aperture photometry, both for the stacked pawprint and for the tile images. However, as mentioned in Section \ref{sec_intro}, PSF photometry is better suited to obtain optimal results in the high-stellar-density regions VVV scanned \citep{alo15}. Still, as we show in Section \ref{sec_psf}, our PSF photometry makes use of the stacked science images produced by CASU, and the calibration of our PSF photometry relies heavily on the astrometric and photometric solutions provided by CASU. | 18 | 8 | 1808.06139 |
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1808 | 1808.08254_arXiv.txt | We find the leading-order effect of gravitational back-reaction on cosmic strings for points near kinks and cusps. Near a kink, the effect diverges as the inverse cube root of the distance to the kink, and acts in a direction transverse to the worldsheet. Over time the kink is rounded off, but only regions fairly close to the kink are significantly affected. Near cusps, the effect diverges inverse linearly with the distance to the cusp, and acts against the direction of the cusp motion. This results in a fractional loss of string energy that diverges logarithmically with the distance of closest approach to the cusp. | \label{sec:intro} Cosmic strings are one-dimensional topological defects which may form dynamically at a symmetry breaking phase transition in the early universe~\cite{Kibble:1976sj,Vilenkin:2000jqa}. Models of string theory also suggest the possibility that fundamental strings (and D1-branes) can be stretched by the cosmic expansion in the early universe and form a cosmic superstring network \cite{Dvali:2003zj,Copeland:2003bj}. As massive objects generically in motion, the strings radiate gravitational waves, and a network of cosmic string loops would produce a stochastic background (E.g., see~\cite{Blanco-Pillado:2017oxo} and references therein). They are therefore of great interest to gravitational wave observatories, many of which are actively searching for cosmic strings~\cite{Arzoumanian:2018saf,Abbott:2017mem,Lentati:2015qwp}. The emission of gravitational waves is accompanied by back-reaction: cosmic strings self-interact gravitationally, which generically changes their shape and has the potential to affect the stochastic gravitational wave background. However, owing to the complexity of a typical cosmic string loop's shape~\cite{Blanco-Pillado:2015ana}, it is generally infeasible to solve analytically for the evolution of a cosmic string undergoing gravitational back-reaction. Analytic solutions are known only for a few simple loop shapes~\cite{0264-9381-22-13-002,Wachter:2016rwc}. Instead we focus here on the self-interaction process very near features of the cosmic string loop of particular interest to its overall evolution: kinks and cusps. Kinks are persistent points on a loop where there is a discontinuity in the the tangent vector to the loop~\cite{Garfinkle:1987yw}; cusps are transient points that recur once per oscillation period where the string moves (formally) at the speed of light~\cite{Turok:1984cn}. The pioneering work in cosmic string back-reaction was done by Quashnock and Spergel~\cite{Quashnock:1990wv}. They found that there were no divergences in the gravitational back-reaction due to nearby points on a smooth string. However, in the case of kinks and cusps, the string is not smooth, so their argument does not apply, and there is the possibility of effects that become unboundedly large at points arbitrarily close to these features. Indeed, we find that points on cosmic strings very near to kinks and cusps experience a divergent self-force. This corrects the claim made by two of us (J.M.W and K.D.O) in Ref.~\cite{Wachter:2016hgi} that the back-reaction near kinks was not divergent and thus that kinks would not be rounded off. The error in the analysis of Ref.~\cite{Wachter:2016hgi} is discussed in its erratum, found in its arXiv ancillary files. In Sec.~\ref{sec:setup}, we frame the problem and establish our methodologies. In Sec.~\ref{sec:generic}, we find the self-interaction for a generic point far from kinks or cusps, reproducing a result of Ref.~\cite{Quashnock:1990wv}. In Sec.~\ref{sec:kink}, we solve for the self-interaction very near to a kink, and in Sec.~\ref{sec:cusp} for very near to a cusp. We conclude in Sec.~\ref{sec:conclusions}. We work in linearized gravity, which is accurate because the string's coupling to gravity is very small. Our metric signature is $(-+++)$, and we work in units where the speed of light is one. | \label{sec:conclusions} We have demonstrated that points on a string worldsheet near a kink or a cusp will feel a divergent acceleration due to those features. While points not located at the feature itself always have some small nearby region which looks smooth, divergent effects arise on a scale related to the distance from that point to the nearby feature. That there is a divergent acceleration as an observer approaches a kink indicates that it is possible for the kink to be rounded off by gravitational back-reaction, in contrast to the claim of Ref.~\cite{Wachter:2016hgi} that kinks are ``opened'', and may seem more similar to the ``smoothing'' of kinks used in Ref.~\cite{Blanco-Pillado:2015ana}. However, this rounding happens on small distances at early times, and it takes a significant fraction of the loop lifetime until a large length of string has been bent across the kink. So while kinks are removed rapidly, the amount of string spread across the gaps on the unit sphere is small. Thus, cusps which form as a consequence of this will be very weak. Our results on back-reaction at cusps suggest that they lose a significant amount of energy in the neighborhood of the cusp, making them weaker as time passes. The effect of back-reaction will also change the parameters that characterize the cusps, which could have important consequences for their observational signatures. These results were found using the zero-thickness string approximation. Thus, once the observer approaches a kink or a cusp to a scale comparable to the string thickness $\delta$, we expect the expressions for the accelerations to change.\footnote{At that scale one would imagine that field theory effects of the type observed in simulations~\cite{Olum:1998ag} would be the dominant contribution to back-reaction.} On the other hand, strings of cosmological and astrophysical significance always have length scales many orders of magnitude above their thicknesses,\footnote{For example: a Milky Way-scale string with $G\mu=10^{-11}$ has $L/\delta\sim10^{45}$.} so these results are applicable to all but an infinitesimal fraction of the string. More importantly, the type of analysis done here is applicable only to isolated, simple features on strings, and we can accurately calculate only the initial effect. After a significant period of back-reaction, a string will have cusps that are partly depleted and look somewhat like kinks, and kinks that are partly rounded and lead to weak cusps. To fully understand the evolution of loops under the influence of gravitational back-reaction, we need to numerically simulate back-reaction over the course of the loop lifetime. We will report on such simulations in future publications. | 18 | 8 | 1808.08254 |
1808 | 1808.08728_arXiv.txt | {The surface angular velocity evolution of low-mass stars is now globally understood and the main physical mechanisms involved in it are observationally quite constrained. However, while the general behaviour of these mechanisms is grasped, their theoretical description is still under ongoing work. This is the case for instance about the description of the physical process that extracts angular momentum from the radiative core, which could be described by several theoretical candidates. Additionally, recent observations showed anomalies in the rotation period distribution of open cluster, main sequence, early K-type stars that cannot be reproduced by current angular momentum evolution models.} {In this work, we study the parameter space of star-planet system's configurations to investigate if including the tidal star-planet interaction in angular momentum evolution models could reproduce the anomalies of this rotation period distribution.} {To study this effect, we use a parametric angular momentum evolution model that allows for core-envelope decoupling and angular momentum extraction by magnetized stellar wind that we coupled to an orbital evolution code where we take into account the torque due to the tides raised on the star by the planet. We explore different stellar and planetary configurations (stellar mass from 0.5 to 1.0 $\rm M_{\odot}$ and planetary mass from 10 $\rm M_{\oplus}$ to 13 $\rm M_{\rm jup}$) to study their effect on the planetary orbital and stellar rotational evolution.} {The stellar angular momentum is the most impacted by the star-planet interaction when the planet is engulfed during the early main sequence phase. Thus, if a close-in Jupiter-mass planet is initially located at around 50\% of the stellar corotation radius, a kink in the rotational period distribution opens around late and early K-type stars during the early main sequence phase.} {Tidal star-planet interactions can create a kink in the rotation period distribution of low-mass stars, which could possibly account for unexpected scatter seen in the rotational period distribution of young stellar clusters.} | The angular momentum evolution of young low-mass stars has been investigated for several decades \citep[e.g.][]{WD67,Sku72,Kawaler88,Keppens95,Bouvier08,RM12}. The associated theoretical efforts led to a better understanding of the main physical mechanisms at work in this evolution \citep[star-disk interaction, magnetic braking, and internal redistribution of angular momentum, see e.g.][and references therein]{Bouvier14}. Strong theoretical constraints have been added to the processes that drive angular momentum transport in stellar interiors \citep[e.g.][]{Amard15} and the extraction of angular momentum by magnetized stellar winds \citep{matt15,Reville15,See17}. The physics that controls the angular velocity evolution of low-mass stars from the pre-main sequence (hereafter PMS) up to the end of the main sequence (hereafter MS) is thus now relatively well understood \citep[see e.g.][]{MP05a,GB15,Somers15,Lanzafame15,Amard15,Johnstone15,SA17}. Despite the uncertainties about the correct physical description to use to describe the mechanisms involved in the internal transport of angular momentum between the radiative core and the convective envelope, current models grasp the main trends of stellar rotational evolution. In parallel to these theoretical developments, numerous exoplanets have been detected since 1995 \citep{MQ95} and now reach a number of confirmed objects between 2950 and 3786 (June 5 2018, see exoplanets.org and exoplanet.eu). These exoplanets can be found in a wide range of star-planet configurations that encompass a large distribution of planetary masses ranging from $10^{-4}$ to 100 $\rm M_{\rm Jup}$, orbital periods from $10^{-1}$ to $10^{5}$ days, and a (sub)stellar mass ranging from $2\times10^{-2}$ to 4 $\rm M_{\odot}$. Nevertheless, most angular momentum evolution models mainly focus on isolated stars thus neglecting the possible impact of a planetary companion on the rotational evolution of the central star. However, the presence of close-in planets ought to be included in such numerical codes as pointed out by \citet{Bolmont12}, \citet{Zhang14}, \citet{Lanza16}, \citet{Privitera2016}, and \citet{Rao18}, who show the strong impact of the stellar rotational history on the orbital evolution of massive close-in planets, and vice-versa. During the last decade, thanks to the inauguration of the Kepler satellite and most recently because of Kepler's second life mission K2, we have entered a new era of improved rotational period measurements that allows for advanced astrophysical quests. Indeed, the precision of measured stellar surface rotation periods (through photometric variation induced by the presence of magnetic stellar spots) is now good enough to detect specific features in the rotation period distribution of open clusters. This is for instance the case for the rotation period distribution of the Pleiades cluster (a 120 Myr old MS open cluster located at about 140 pc from the Earth) that has been analysed by \citet{Rebull16} and \citet{Stauffer16} using Kepler-K2 \citep{K2}. In this cluster, they found K-type stars % with a faster rotation rate than expected from current theoretical angular velocity evolution tracks (hence producing a ``kink'' in the rotational distribution). These ``classical'' rotational tracks are produced by numerical models that only invoke star-disk interaction, angular momentum extraction by stellar wind, and internal redistribution of angular momentum within the stellar interior; but this anomaly could potentially result from the presence of an exoplanet that may affect, through tidal interaction, the surface rotation rate of its host star. Indeed, \citet[][see also \citealt{Bolmont16} and \citealt{Gallet17b}]{Mathis15} showed that the tidal dissipation inside the star is maximum, during the early-MS phase, for early K-type stars due to a specific configuration of their internal structure. In the theoretical framework, tides in stars can be described by two components: the equilibrium tide, which corresponds to the large-scale hydrostatic adjustment induced by the gravitational interaction between the star and its companion \citep[of stellar or planetary nature, see][]{Zahn66,Remus2012,Ogilvie13} and which is made up of a large-scale non-wavelike/equilibrium flow; and the dynamical tides, which correspond to the dissipation of tidal inertial waves (mechanical waves that are generated inside rotating fluid bodies) due to the turbulent friction in convective regions \citep{Ogilvie07,Ivanov13} and to thermal diffusion and breaking mechanisms acting on gravito-inertial waves (gravity waves influenced by the effect of rotation through the Coriolis acceleration) in radiative regions \citep[e.g.][]{Zahn75,Terquem98,Barker10}. The dissipation of the dynamical tides thus strongly depends on the internal structure of the star \citep[see e.g.][]{Chernov13,Ogilvie14,Mathis15,Gallet17b}. Most of the studies dedicated to tidal star-planet interactions often assume solid body rotation for the whole star \citep[e.g.][]{Bolmont12,Nordhaus13,Bolmont16}. However, recent works have allowed for stellar core-envelope decoupling so as to investigate the impact of the presence of a massive planet on the surface rotation of the star. From the literature, \citet{Zhang14} used constant tidal dissipation efficiencies along the stellar evolution; \citet{Penev14} and \citet{Penev18} included core-envelope decoupling so as to add constraints on the evolution of the tidal dissipation; and \citet{Privitera2016} focused on star-planet interaction during the red giant phase. In this article, and in complement to the work of \citet{Bolmont16}, we investigate the impact of tidal dissipation evolution (controlled by the internal stellar structure during the PMS and by the surface rotation rate of the star during the MS) on the evolution of the rotation rate of the host star using a two-zone rotational model that allows for core-envelope decoupling. We explore the parameter space of star-planet systems, considering stellar mass, initial parameters (rotation, disk lifetime, and coupling timescale), planetary mass, and initial orbital distance to map the impact of star-planet interaction on the rotational evolution of low-mass stars. {{\citet{Rao18} also recently studied the impact of the equilibrium and dynamical tides on the orbital evolution of massive close-in planets. In their work they focused on the initial conditions that affect the planetary survivability around stars more massive than 1.0 $\rm M_{\odot}$ , while we are more interested in how the surface rotation rate of the host star is modified by the star-planet tidal interaction. These two works are thus very complementary.}} This paper is structured as follows. The numerical model used in this work is described in Sect. \ref{model}. In Sect. \ref{rotevol} we investigate the rotational evolution of low-mass stars in the presence of a close-in planet, and how it is impacted by the main star-planet parameters. We first study the case of a solar mass star in Sect. \ref{referencecase}, and we study the evolution of a initial rotational distribution orbiting an early-K 0.8 $\rm M_{\odot}$ type star in Sect. \ref{distribinit}. Finally we generalize these results to a broader mass range in Sect. \ref{stellarmass}. We finally compare the results of our simulations to the Pleiades data in Sect. \ref{explomass} and conclude in Sect. \ref{conclusion}. | \label{conclusion} We investigated the theoretical effect of tidal interaction on the rotation rate of stars by coupling the parametric model described in \citet{GB15}, which includes the decoupling between the core and the envelope, to the planetary orbital evolution code of \citet{Bolmont16}. We find that the stellar rotation is primarily impacted during planetary engulfment events. With this work we showed that if the planets fall into the stellar surface during the early-MS phase, then planetary accretion has a strong effect on the surface rotation rate of the star. This is especially true in the case of a massive close-in planet (one to two Jupiter-mass planet) orbiting a low-mass star. The surface rotation rate of the star can then be accelerated up to a factor of two to three. Within the right configuration, a planetary population between 1 and 5 $\rm M_{\rm jup}$ initially located around 50\% $R_{\rm co}$ can open a {rotational kink} during the early MS phase, at the age of the Pleiades cluster. This {rotational kink} is only present for stars with initial surface rotation rate around seven days and located around $\rm log~\rm P_{\rm rot,\star}=0.6$ (corresponding to $\rm P_{\rm rot,\star}= 4$ days) and stellar mass smaller than 0.8 $\rm M_{\odot}$. {In \citet{Stauffer16} this {rotational kink} is however observed around $\rm log~\rm P_{\rm rot,\star}$= 0.8 (corresponding to $\rm P_{\rm rot,\star}$= 6.3 days)}. The proposed model here thus does not allow us to exactly reproduce the location of the observed anomaly, possibly because we neglected the tidal dissipation in the stellar radiative core. However, it provides a promising direction to further investigate the influence of close-in planets on the rotational period distribution of young stars, beyond the well-known period-mass relationships, especially in the framework of the Gaia DR2 \citep{Lanzafame18} and future PLAnetary Transits and Oscillations of stars (PLATO)/Transiting Exoplanet Survey Satellite (TESS) missions \citep{Plato,TESS}. | 18 | 8 | 1808.08728 |
1808 | 1808.06735_arXiv.txt | Several recent spectroscopic investigations have presented conflicting results on the existence of Na-rich asymptotic giant branch (AGB) stars in the Galactic globular cluster M\,4 (NGC\,6121). The studies disagree on whether or not Na-rich red giant branch (RGB) stars evolve to the AGB. For a sample of previously published HERMES/AAT AGB and RGB stellar spectra we present a re-analysis of O, Na, and Fe abundances, and a new analysis of Mg and Al abundances; we also present CN band strengths for this sample, derived from low-resolution AAOmega spectra. Following a detailed literature comparison, we find that the AGB samples of all studies consistently show lower abundances of Na and Al, and are weaker in CN, than RGB stars in the cluster. This is similar to recent observations of AGB stars in NGC\,6752 and M\,62. In an attempt to explain this result, we present new theoretical stellar evolutionary models for M\,4; however, these predict that all stars, including Na-rich RGB stars, evolve onto the AGB. We test the robustness of our abundance results using a variety of atmospheric models and spectroscopic methods; however, we do not find evidence that systematic modelling uncertainties can explain the apparent lack of Na-rich AGB stars in M\,4. We conclude that an unexplained, but robust, discordance between observations and theory remains for the AGB stars in M\,4. | \label{m4_2_intro} In early GC studies stars were observed at the same evolutionary stage but with different CN strengths, which cannot be explained only with evolutionary effects \citep[e.g.][]{hesser1977,norris19816752}. These and other findings led to the general consensus that Galactic GCs contain multiple populations of stars, identified by variations in light elemental abundances that are \textit{intrinsic} -- inherited at birth -- to the stars. Variations are typically observed in the abundances of C, N, Na, and O, and sometimes Mg and Al (see the extensive reviews of \citealt{sneden1999,gratton2012} and references therein; but see \citealt{bastian2013} for an opposing view). In this paper we designate those GC stars with halo-like abundances (CN-weak, Na poor) as subpopulation one (SP1), and all stars enriched in Na (or that present as CN-strong) as subpopulation two (SP2). Over the decades since the first spectroscopic studies of Galactic GCs, stars in each evolutionary phase have been targeted to evaluate the consistency of the light-elemental abundance distributions along the stellar evolutionary tracks. While systematic observations of the asymptotic giant branch (AGB, the final phase of nuclear burning) have only been performed relatively recently, AGB stars had previously been included among the GC stellar samples of last century. The literature reviews of \citet{sneden00conf} and \citet{campbell2006} noted that the distribution of CN band strengths of AGB stars in certain globular clusters are very different to those seen in RGB stars -- most strikingly that the AGB stars of NGC\,6752 are exclusively CN-weak. This is in contradiction to the theoretical prediction that the N abundance of a star, which is traced by the CN band strength, should \textit{increase} as a result of `deep mixing' on the RGB \citep{langer1985,henkel2017}. | \label{m4_2_discussion} A significant strength of the spectroscopic results presented in this study (\S\ref{m4_2_reanalysis}--\ref{m4_2_cn}) lies in the combining of two independent methods of separating the subpopulations in chemical abundance space (using both high- and low-resolution spectra). Both of our independent sets of M\,4 results in this paper, namely (i) the re-analysed high-resolution spectra, with additional chemical abundances (Figure~\ref{fig:m4_2_mgal}), and (ii) the new CN band strengths (Figure~\ref{fig:m4_2_cn}), support the conclusions of \citetalias{maclean2016} that AGB stars in M\,4 are largely representative of SP1 stars -- namely, that there is a significant paucity of SP2 AGB stars, with an SP2 AGB deficit of $\mathscr{F} \gtrsim 65\%$ -- as evidenced by their Na and Al abundances, and CN band-strengths, compared to those of stars on the RGB. This adds M\,4 to the list of GCs that have been reported to contain significant SP2 AGB deficits, alongside NGC\,6752 \citep{campbell2013} and M\,62 \citep{lapenna2015}. A comparison of these results with those from the literature (\S\ref{m4_2_lit_comp}) indicate that this is unlikely to be an artefact of our method of abundance determination: spectroscopic M\,4 studies that included AGB stars have consistently shown the AGB to be systematically lower in Na abundance, Al abundance, and CN band strength \citep[typically indicative of N abundance;][]{cottrell1981} than the RGB -- in agreement with our original findings in \citetalias{maclean2016}. In stark contrast to this strong observational result, we predicted -- using theoretical evolutionary models representative of M\,4 stars (\S\ref{m4_2_monstar}) -- that the abundance distributions of the AGB and RGB should be \textit{identical} for all species investigated in this study (except for CN due to extra mixing of N to the stellar surface on the RGB). In an attempt to reconcile the models and observations, we found that we were unable to significantly alter our abundance results by utilising a variety of atmospheric models (\S\ref{m4_2_atmos_tests}), including those with systematically offset stellar parameters, those that included a helium enhancement, different grids of 1D atmospheric models, or 3D atmospheric models. Two recent photometric investigations of M\,4 (\citealt{lardo2017}, and \citetalias{marino2017}) have reported that their data of M\,4 AGB stars are consistent with the AGB containing both SP1 and SP2 stars. The spectroscopic results presented in this study similarly suggest that some proportion of SP2 stars may evolve to the AGB. However the photometric indices C$_{UBI}$ and C$_{F275W,F336W,F438W}$ are unlikely to be precise enough to detect whether or not the most Na-enhanced SP2 stars are missing on the AGB, as suggested by the spectroscopically-determined abundances presented in this paper. We note that our CN index results -- which are analogous to very narrow-band photometry -- agree with the conclusions drawn from high-resolution spectroscopy, and disagree with those drawn from photometric pseudo-CMDs. Na, Al, and N are all products of hydrogen burning \citep{kippenhahn1990book}, and are three of the species most commonly observed to vary among the stars of globular clusters \citep[other species include He, C, O, and Mg;][]{gratton2004}, both Galactic and extragalactic \citep{gratton2012,extragalacticgcs}. Of these, atmospheric Na and Al abundances are not predicted to change throughout the lives of individual present-day GC stars -- these abundances are typically assumed to be an intrinsic property of the star because low-mass stars do not reach temperatures high enough to activate the Ne-Na or Mg-Al H-burning chains \citep{norris1981m4,iben1984} -- while N is observed to increase on the RGB via `deep mixing' \citep{henkel2017}. In conclusion, with no viable mechanism to reduce these abundances in-situ between the RGB and AGB, and the prediction that all stars in M\,4 should evolve through to the AGB, we can see few remaining potential explanations for the consistent observations that AGB stars in M\,4 have significantly lower abundances of Na, Al, and N (inferred from CN) than RGB stars in the cluster. Avenues to consider in order to resolve this disparity are diminishing, but include investigating the effect of interstellar extinction on AGB stellar spectra (M\,4 experiences large differential reddening), and exploring differences between the atmospheric structures of AGB and RGB stars. We note, however, that any solution must simultaneously account for the observed disparity in both the elemental abundance \textit{and} CN band strength distributions, which are determined using different spectroscopic methods. | 18 | 8 | 1808.06735 |
1808 | 1808.06029_arXiv.txt | The energy dissipation mechanism in blazar jet is unknown. Blazar's flares could provide insights on this problem. Here we report statistical results of XMM-Newton X-ray flares of Mrk 421. We analyze all public XMM-Newton X-ray observations for Mrk 421, and construct the light curves. Through fitting light curves, we obtain the parameters of flare-profiles, such as peak flux ($F_{\rm p}$) and flaring time duration ($T_{\rm fl}$). It is found that both the distributions of $F_{\rm p}$ and $T_{\rm fl}$ obey a power-law form, with the same index of $\alpha_{\rm F}=\alpha_{\rm T}\approx1$. The statistical properties are consistent with the predictions by a self-organized criticality (SOC) system with energy dissipation in one-dimensional space. This is similar to solar flare, but with different space dimensions of the energy dissipation domain. This suggests that X-ray flaers of Mrk 421 are possibly driven by a magnetic reconnection mechanism. Moreover, in the analysis, we find that variability on timescale of $\sim1000\ $s frequently appears. Such rapid variability indicates a magnetic field of $\geq 2.1\delta_{\rm D}^{-1/3}$ G ($\delta_{\rm D}$ is the Doppler factor) in emission region. | \label{sec:intro} Blazars are a rather extreme class of radio-loud active galactic nuclei (AGNs), consisting of BL Lac objects (BL Lacs) and flat-spectrum radio quasars (FSRQs). Due to relativistic Doppler boosting, blazar emission is dominated by the non-thermal emission coming from its jet. Its spectral energy distribution (SED) extends from radio to $\gamma$-rays, and shows two bumps. The low-energy bump is believed to be the synchrotron radiation of relativistic electrons, while the origin of high-energy bump is under debate. A variety of emission mechanisms are proposed to explain this origin: (1) inverse Compton (IC) scattering of low-energy photons by relativistic electrons, including synchrotron self-Compton model \citep[i.e., SSC; e.g.,][]{Maraschi1992} and external Compton model \citep[i.e., EC; e.g.,][]{Dermer93,Sikora1994}; (2) relativistic proton synchrotron radiation \citep{mann92,Aharonian2000,mucke2003}; (3) synchrotron radiation of secondary particles produced in proton-photon interaction \citep{mucke2001,bottcher09,Yan15,2015MNRAS.448..910C} . According to the peak frequency of synchrotron bump ($\nu_{\rm p}$), BL Lacs are divided into three classes \citep[e.g.,][]{Padovani}: high-synchrotron-frequency peaked BL Lacs (HBLs; $\nu_{\rm p}>10^{15}\ $Hz), intermediate-synchrotron-frequency peaked BL Lacs (IBLs; $10^{14}<\nu_{\rm p}<10^{15}\ $Hz), and low-synchrotron-frequency peaked BL Lacs (LBLs; $\nu_{\rm p}<10^{14}\ $Hz). FSRQs usually have $\nu_{\rm p}<10^{14}\ $Hz. Blazars show strong variability across entire electromagnetic emission on timescales from minutes to years \citep[e.g.,][]{Aharonian2007,Dai,Ackermann,zhu}. Variability timescale can be used to constrain the size of emission region, the magnetic field in emission region, and the location of high energy emission region \citep[e.g.,][]{bottcher03, Yan17}. The correlations of variabilities in different spectral bands could carry abundant information on the emission and acceleration mechanisms of particles in blazar jet \citep[e.g.,][]{Fossati,Chen}. Although variability is important and useful for understanding blazar jet physics, the physical origin of blazar variability is not well understood. Several scenarios have been proposed to understand the production of variability \citep[see][for a review]{Aharonian2017}, like magnetospheric gap model \citep[e.g.,][]{Neronov}, jet-star interaction model \citep[e.g.,][]{Barkov}, and jet-in-jet model \citep[e.g.,][]{Giannios}. Magnetic reconnection may play an important role in the latter two models \citep[e.g.,][]{Aharonian2017}. \citet{Sironi} argued that magnetic reconnection, rather than shock, powers blazar jet emission. Statistical properties of flares could provide insights into the trigging mechanism of flares. The flares trigged by magnetic reconnection is thought to form a self-organized criticality (SOC) system, such as solar flares \citep[e.g.,][]{Lu,Aschwanden}. The SOC flare system expects that event parameters, e.g., the flux and the flaring time duration, should follow power-law distributions. The indices of these power laws are related to the effective geometric dimension of the system \citep[e.g.,][]{Aschwanden12}. Such a statistical approach has been used to investigate whether the SOC model can explain the X-ray flares of $\gamma$-ray bursts \citep[GRBs;][]{Wang13,Yi16,Yi17}, M87 \citep{Wang15}, and Sgr A$^*$ \citep{Wang15,Li,Yuan}. Here, we apply this approach to X-ray flares of Mrk 421. Mrk 421 is a HBL. It is the brightest blazar in the X-ray sky. Its X-ray emission is believed to be the synchrotron radiation of relativistic electrons, showing strong and rapid variabilities \citep[e.g.,][]{Cui,Fossati,Paliya2,Kapanadze16,Kapanadze18}. The main goal of this paper is to investigate whether the statistical properties of Mrk 421 XMM-Newton X-ray flares are consistent with the expectations of a SOC system. | We analyzed 50 XMM-Newton X-ray observations for Mrk 421, and constructed the X-ray light curves. The basic information, such as $F_{\rm var}$ and NPSD can be found in Appendix. We fitted the 17 light curves which have one complete flare-profile at least, in order to determine the flare rise and decay times as well as peak fluxes (see Fig.~\ref{fig:lcfit}). We obtained these parameters for 48 flares. Among them, 26 flares have well constrained parameters (see Table~\ref{tab:lcfit}). The flaring time duration is evaluated by using the flare rise and decay times. It is found that both the peak flux and flaring time duration distributions follow a power-law form with the same index of $\alpha_{\rm F}=\alpha_{\rm T}\approx1$. It has been argued that the behavior that event parameters obey a power-law distribution is a characteristic of SOC system \citep[e.g.,][]{Aschwanden12}. The SOC model has been used to explain astrophysical X-ray flares, such as GRB X-ray flares \citep{Wang13,Yi16,Yi17} and super massive black hole (SMBH) X-ray flares \citep{Wang15,Li}. They found that the statistical properties of the GRB and SMBH X-ray flares can be explained by a fractal-diffusive SOC model, but with different spatial dimensions $S$ ($S=1$ for GRB X-ray flares and $S=3$ for SMBH X-ray flares). However, \citet{Yuan} argued that a simple SOC model failed to explain the X-ray flares in SMBH Sgr A$^*$. The SOC model expects the index of peak flux distribution $\alpha_{\rm F}=1+(S-1)/D_S$ ($D_S$ is the fractal Hausdorff dimension, spanning from 1 to $S$), and the index of flaring time duration distribution $\alpha_{\rm T}=1+(S-1)\beta/S$ where $\beta$ is a diffusion parameter \citep[e.g.,][]{Aschwanden12}. The statistical results of Mrk 421 X-ray flares are consistent with the expectation of a SOC mode with $S=1$. This indicates that the X-ray flares of Mrk 421 are possibly driven by magnetic reconnection. Our results support the finding that magnetic reconnection is a promising process for energy dissipation in blazar jet \citep{Sironi}. The $S$ of Mrk 421 is similar to that of GRB X-ray flares, but different from that of X-ray flares in M87 and Sgr A$^*$ (i.e., the SMBH X-ray flares). M87 is a radio galaxy. It is thought that the main difference between radio galaxy and blazar is the angle of jet direction with respect to the line-of-sight. We notice that the flaring time duration for M87 in \cite{Wang15} spans from 0.2 years to several years. Such a long timescale indicates that the X-ray emissions come from a large region which locates relatively far away from the central SMBH. On the other hand, the rapid X-ray emission from blazar is believed to come from a region locating at sub-pc scale. It is possible that the results of M87 and Mrk 421 reveal the situations about magnetic field in different regions along the jet in radio-loud AGN. However, note that the uncertainties on the results of M87 are very large \citep{Wang15}. Sub-hour variabilities are presented in our analysis. Flares with $t_{\rm var}\sim t_{\rm d}\sim 1000\ $s frequently appear. Such rapid flare indicates that the magnetic field in emission region is $B' \geq 2.1\delta_{\rm D}^{-1/3}$ G. This magnetic field is much higher than the value of $B'<0.1\ $G that derived in SSC modeling of SED \citep[e.g.,][]{Yan13,Zhu}. Taking advantage of the radio core-shift-effect obtained in Very Long Baseline Array (VLBA) observations, \cite{zam} derived the magnetic field strength $B'_{\rm 1pc}$ at one pc along the jet for tens blazars, and they found $B'_{\rm 1pc}$ spanning from 0.2 G to 2 G. This is consistent with the magnetic field strength expected by a magnetically powered jet \citep[e.g.,][]{Os}. If Mrk 421 is not a outlier, the magnetic field of $B' \geq 2.1\delta_{\rm D}^{-1/3}$ G is also likely consistent with the prediction of a magnetically powered jet. For a magnetically powered jet, magnetic reconnection is a natural candidate for energy dissipation in blazar jet \citep[e.g.,][]{Sironi}. As a last remark, we note that \citet{Zub} proposed a model of tidal disruption of asteroids by the SMBH for the origin of Sgr A$^*$ X-ray flares. This model probably also can explain the power-law distributions of the parameters of Sgr A$^*$ X-ray flares \citep{Zub}. However, this scenario will not happen in blazar \citep[e.g.,][]{Komossa}, due to the SMBH with the mass of $\gtrsim10^8M_{\odot}$ in blazar, where $M_{\odot}$ is the solar mass. As far as we know, the SOC model is the only model for explaining the power-law distributions of the parameters of blazar flares. | 18 | 8 | 1808.06029 |
1808 | 1808.02116_arXiv.txt | There is now strong evidence that the close binary fraction ($P$~$<$~10$^4$~days; $a$~$<$~10~AU) of solar-type stars ($M_1$~$\approx$~0.6\,-\,1.5\,\Msun) decreases significantly with metallicity. Although early surveys showed that the {\it observed} spectroscopic binary (SB) fractions in the galactic disk and halo are similar (e.g., Carney-Latham sample), these studies did not correct for incompleteness. In this study, we examine five different surveys and thoroughly account for their underlying selection biases to measure the intrinsic occurrence rate of close solar-type binaries. We re-analyze: (1)~a volume-limited sample of solar-type stars (Raghavan et al. 2010), (2)~the SB survey of high-proper-motion stars (Latham et al. 2002), (3)~various SB samples of metal-poor giants (Carney et al. 2003; Hansen et al. 2015,\,2016), (4)~the APOGEE survey of radial velocity (RV) variables (Badenes et al. 2018), and (5)~eclipsing binaries (EBs) discovered by {\it Kepler} (Kirk et al. 2016). The observed APOGEE RV variability fraction and {\it Kepler} EB fraction both decrease by a factor of $\approx$\,4 across $-$1.0~$<$~[Fe/H]~$<$~0.5 at the 22$\sigma$ and 9$\sigma$ confidence levels, respectively. After correcting for incompleteness, all five samples / methods exhibit a quantitatively consistent anti-correlation between the intrinsic close binary fraction ($a$~$<$~10~AU) and metallicity: $F_{\rm close}$ = 53\%\,$\pm$\,12\%, 40\%\,$\pm$\,6\%, 24\%\,$\pm$\,4\%, and 10\%\,$\pm$\,3\% at [Fe/H]~=~$-$3.0, $-$1.0, $-$0.2 (mean field metallicity), and +0.5, respectively. We present simple fragmentation models that explain why the close binary fraction of solar-type stars strongly decreases with metallicity while the wide binary fraction, close binary fraction of OB~stars, and initial mass function are all relatively constant across $-$1.5~$\lesssim$~[Fe/H]~$<$~0.5. The majority of solar-type stars with [Fe/H]~$\lesssim$~$-$1.0 will interact with a stellar companion, which has profound implications for binary evolution in old and metal-poor environments such as the galactic halo, bulge, thick disk, globular clusters, dwarf galaxies, and high-redshift universe. | \label{Introduction} Variations in the close binary fraction ($a$~$\lesssim$~10~AU) with respect to metallicity have been continuously debated over the years \citep[][additional references below]{Carney1983,Latham2002,Carney2005,Machida2009,Raghavan2010,Rastegaev2010,Moe2013,Bate2014,Badenes2018}. Some observations indicate no dependence on metallicity \citep{Latham2002,Carney2005,Moe2013}, others find the close binary fraction and metallicity are positively correlated \citep{Carney1983,Abt1987,Hettinger2015}, while yet others have found that the close binary fraction decreases with metallicity \citep{Grether2007,Raghavan2010,Gao2014,Badenes2018}. Studying how the close binary fraction varies with primary mass, metallicity, age, and environment provides significant insight into the processes of protobinary fragmenation, accretion, and orbital migration \citep{Kratter2008,Kratter2010,Duchene2013,Moe2017,Moe2018}. The close binary fraction is also a crucial input parameter in population synthesis studies of blue stragglers, chemically peculiar stars, cataclysmic variables, Type Ia and Ib/c supernovae, X-ray binaries, mergers of compact objects, short gamma-ray bursts, and sources of gravitational waves \citep{Hurley2002,Eggleton2006,Belczynski2008,Sana2012,DeMarco2017} A substantial change in the close binary fraction with respect to metallicity would have dramatic consequences for the predicted rates and properties of various channels of binary evolution. The apparent discrepancies in the inferred close binary fraction as a function of metallicity must be reconciled in order to more fully understand binary star formation and to make reliable predictions for binary evolution. The primary goal of this study is to reconcile the conflicting results reported in the literature in order to accurately measure the bias-corrected close binary fraction of solar-type stars as a function of metallicity. In \S\ref{Overview}, we overview the methods, results, and potential caveats associated with previous results. In \S\ref{Spectroscopic}, we correct for incompleteness within the Carney-Latham sample and other spectroscopic binary surveys to determine if a large change in the close binary fraction with respect to metallicity is apparent in these earlier datasets. In \S\ref{APOGEE}, we analyze the \citet{Badenes2018} sample of APOGEE stars to measure precisely how the radial velocity variability fraction and bias-corrected close binary fraction change as a function of metallicity. We next measure the eclipsing binary fraction of solar-type dwarfs in the {\it Kepler} sample, providing a new and independent method for determining how the close binary fraction varies with metallicity (\S\ref{Kepler}). We combine and summarize the observational constraints in \S\ref{Summary}, where we show all five samples / methods investigated in this study exhibit a remarkably consistent anti-correlation between metallicity and close binary fraction. We also discuss the overall binary fraction and period distribution as a function of mass and metallicity, and highlight the resulting implications for binary evolution. In \S\ref{Models}, we investigate fragmentation models to explain why the close binary fraction of solar-type stars strongly decreases with metallicity while the wide binary fraction, close binary fraction of massive stars, and initial mass function are relatively constant. We conclude in \S\ref{Conclusions}. | \label{Conclusions} We have thoroughly examined the selection biases in various samples of solar-type stars and measured the intrinsic close binary fraction ($a$~$<$~10~AU) as a continuous function of metallicity. We investigated multiple samples of SBs~(\S\ref{Spectroscopic}), APOGEE RV variables~(\S\ref{APOGEE}), and {\it Kepler} EBs~(\S\ref{Kepler}), all of which exhibit the same anti-correlation between $F_{\rm close}$ and [Fe/H]~(\S\ref{Summary}). We discussed and presented our own analytic models of fragmentation that reconcile the observed trends in binary properties as a function of mass, period, and metallicity~(\S\ref{Models}). We summarize the main results in the following. \vspace*{0.2cm} \noindent {\it Spectroscopic Binaries}. Although the observed SB fraction appears to be constant with metallicity, metal-poor stars have weaker absorption lines, making it more difficult to identify SBs (Fig.~\ref{Latham_RV}). After correcting the \citet{Latham2002} sample of high-proper-motion FGK stars for incompleteness, the intrinsic close binary fraction decreases from $F_{\rm close}$~=~54\%\,$\pm$\,12\% near [m/H]~=~$-$2.7 to $F_{\rm close}$~=~17\%\,$\pm$\,6\% at [m/H]~=~+0.5 (Fig.~\ref{Latham_binfrac}). Considering only the Carney-Latham SBs with $P$~=~20\,-\,2,000~days and $K_1$~$>$~6~km~s$^{-1}$, where their survey is relatively complete (Fig.~\ref{Latham_fM}), the SB fraction of metal-poor halo stars ([m/H]~$<$~$-$1.0) is $\approx$\,1.9 times higher than metal-rich disk stars ([m/H]~$>$~$-$0.5). Similarly, the observed SB companions to metal-poor giants ($-$3.5~$\lesssim$~[Fe/H]~$\lesssim$~$-$1.5) in the \citet{Carney2003} and \citet{Hansen2015,Hansen2016a} samples are concentrated toward $K_1$~$>$~7~km~s$^{-1}$ and $P$~=~35\,-\,3,000 days (Fig.~\ref{Carney_fM}), implying the bias-corrected close binary fraction of metal-poor solar-type dwarfs is $F_{\rm close}$~$\approx$~40\%\,-\,60\%. \vspace*{0.2cm} \noindent {\it APOGEE Radial Velocity Variables}. The APOGEE RV variability fraction of GK stars decreases by a factor of 4.0\,$\pm$\,0.5 across −0.9~$<$~[Fe/H]~$<$~0.5 at the 22$\sigma$ significance level (Fig.~\ref{DeltaRV}), consistent with the conclusions of \citet{Badenes2018}. We measure the same trend independent of spectral type, surface gravity, and RV threshold, indicating both metal-poor and metal-rich binaries with $M_1$~$\approx$~0.6\,-\,1.5\,\Msun\ follow the same short-end tail of a log-normal period distribution. After correcting the APOGEE RV variability survey of GK\,IV/V stars for incompleteness, the intrinsic close binary fraction decreases from $F_{\rm close}$~=~41\%\,$\pm$\,7\% at [Fe/H]~=~$−$0.8 to $F_{\rm close}$~=~11\%\,$\pm$\,2\% at [Fe/H]~=~+0.4 (Fig.~\ref{RV_binfrac}). The median metallicities of close solar-type binaries are $\Delta$[Fe/H]~=~$-$0.13\,$\pm$\,0.03 dex lower than single stars (Fig.~\ref{cumRV}). \vspace*{0.2cm} \noindent {\it Kepler Eclipsing Binaries}. For a large sample of {\it Kepler} solar-type dwarfs in which the metallicities have been measured photometrically to $\delta$[Fe/H]~$\approx$~0.3~dex precision, the observed EB fraction decreases by a factor of 3.4\,$\pm$\,0.5 across $-$0.9~$<$~[Fe/H]~$<$~0.3 at the 9$\sigma$ confidence level (Fig.~\ref{EBfrac}). For a smaller subsample in which the metallicities have been measured spectroscopically to $\delta$[Fe/H]~$\approx$~0.1~dex precision, the observed EB fraction also decreases by a factor of $\approx$\,3.5 across the narrower interval $-$0.6~$<$~[Fe/H]~$<$~0.4 to 3$\sigma$ significance. Metal-poor and metal-rich EBs both have the same period and eclipse depth distributions (Fig.~\ref{PvsF}), implying the period and mass-ratio distributions of close solar-type binaries are metallicity invariant. After accounting for various selection biases, the corrected solar-type close binary fraction decreases from $F_{\rm close}$~=~52\%\,$\pm$\,14\% across $−$1.7~$<$~[Fe/H]~$<$~$-$1.1 to $F_{\rm close}$~=~13\%\,$\pm$\,3\% across 0.1~$<$~[Fe/H]~$<$~0.5 (Fig.~\ref{binfrac_EB}). \vspace*{0.2cm} \noindent {\it Combined Observational Constraints}. After correcting for incompleteness, all five samples of solar-type stars exhibit a quantitatively consistent anti-correlation: $F_{\rm close}$ = 53\%\,$\pm$\,12\%, 40\%\,$\pm$\,6\%, 24\%\,$\pm$\,4\% and 10\%\,$\pm$\,3\% at [Fe/H]~=~$-$3.0, $-$1.0, $-$0.2 (mean field metallicity), and +0.5, respectively (Fig.~\ref{allbin}). It is highly improbable that each of the different methods, with different biases, could conspire to produce consistent results. In contrast to close binaries, the wide binary fraction ($a$~$\gtrsim$~200~AU) of solar-type stars is relatively independent of metallicity. The close binary fraction of $M_1$~$\approx$~10\,\Msun\ primaries is quite high ($F_{\rm close}$~=~70\%\,$\pm$\,11\%) and does not vary significantly with metallicity. As solar-type stars decrease in metallicity to [Fe/H]~$\lesssim$~$-$1.0, their close binary fraction ($F_{\rm close}$ $\approx$~50\%), overall binary fraction ($F_{\rm binary}$ $\approx$~90\%), triple/quadruple star fraction ($F_{\rm triple}$~+~$F_{\rm quadruple}$~$\approx$~35\%), and companion period distribution ($a_{\rm peak}$~$\approx$~10~AU) all approach that of early-B stars (Fig.~\ref{Pdist}). \vspace*{0.2cm} \noindent {\it Fragmentation Models}. Turbulent fragmentation of molecular cores on large spatial scales is relatively independent of metallicity, which is why the overall IMF and wide binary fraction are constant across $-$1.5~$\lesssim$~[Fe/H]~$<$~0.5. Even at solar-metallicity, the disks of massive protostars are highly unstable and prone to fragmentation, explaining the high close binary fraction of massive stars. Decreasing the metallicity of massive protostars can only marginally further increase the likelihood for disk fragmentation. For solar-type protostars with log(Z/\Zsun)~=~0.5, only the small fraction of disks that attain stochastic excursions to accretion rates $\dot{M}$~$\approx$~20$\langle \dot{M}_{\rm in} \rangle$ well above the mass-weighted average infall rates are capable of fragmentation at large radii $r_d$~$\approx$~200~AU. With decreasing metallicity, (1)~the expected infall rates from hotter cores increase and (2)~the temperatures of the optically thick disks decrease, which both simultaneously drive the disk toward instability. For solar-type protostars, the probability of disk fragmentation dramatically increases from log(Z/\Zsun)~=~+0.5 to $-$1.0, consistent with the observed increase in the close binary fraction. Metal-poor low-mass disks tend to fragment on smaller scales, possibly as small as $r_d$~=~10~AU, which is consistent with the observed shift in the peak of the overall solar-type binary period distribution. \vspace*{0.2cm} \noindent {\it Implications for Binary Evolution}. Most solar-type stars with [Fe/H]~$<$~$-$1.0 will interact with a close binary companion, either through Roche lobe overflow or wind accretion. This has important consequences for binary evolution in old and metal-poor environments such as the galactic halo, bulge, thick disk, globular clusters, dwarf galaxies, and high-redshift universe. Future studies must consider the effect of a close binary fraction versus metallicity anti-correlation on the inferred rates, properties, and progenitors of blue stragglers, barium stars, planetary nebulae, evolved giants, symbiotics, cataclysmic variables, novae, and Type Ia supernovae. \vspace*{0.2cm} M.M. acknowledges financial support from NASA's Einstein Postdoctoral Fellowship program PF5-160139. K.M.K. acknowledges financial support from National Science Foundation under Grant No. AST-1410174 and NASA under Grant No. ATP-140078 and ATP-170070. We thank Andrei Tokovinin and Kevin Schlaufman for enlightening discussions that helped motivate our analysis. | 18 | 8 | 1808.02116 |
1808 | 1808.05446_arXiv.txt | {We study the effects of a reduced mass-loss rate on the evolution of low metallicity Jsolated stars, following our earlier classification for angular momentum (J) isolated stars.~By using the stellar evolution code \texttt{MESA} we study the evolution with different mass-loss rate efficiencies for stars with low metallicities of $Z=0.001$ and $Z=0.004$, and compare with the evolution with solar metallicity, $Z=0.02$.~We further study the possibility for late asymptomatic giant branch (AGB)---planet interaction and its possible effects on the properties of the planetary nebula (PN). We find for all metallicities that only with a reduced mass-loss rate an interaction with a low mass companion might take place during the AGB phase of the star. The interaction will most likely shape an elliptical PN. The maximum post-AGB luminosities obtained, both for solar metallicity and low metallicities, reach high values corresponding to the enigmatic finding of the PN luminosity function.} \keyword{late stage stellar evolution; planetary nebulae; binarity; stellar evolution} \begin{document} | {\it Jsolated stars} are stars that do not gain much angular momentum along their post main sequence evolution from a companion, either stellar or substellar, thus resulting with a lower mass-loss rate compared to non-Jsolated stars \cite{SabachSoker2018b}. As previously stated in Sabach and Soker~\cite{SabachSoker2018b,SabachSoker2018a}, the fitting formulae of the mass-loss rates for red giant branch (RGB) and asymptotic giant branch (AGB) single stars are set empirically by contaminated samples of stars that are classified as ``single stars'' but underwent an interaction with a companion early on, increasing the mass-loss rate to the observed rates. The~mass-loss rate on the giant branches has extensive effects on stellar evolution and on the resulting planetary nebula (PN) in low and intermediate mass stars. The reduced mass-loss rate of Jsolated stars results in a larger AGB radii compared to the RGB and compared to the ``traditional'' evolution with the high mass-loss rate efficiency of non-Jsolated stars. The higher AGB radii reached for Jsolated stars can lead to possible late interaction with a low mass companion. If such a Jsolated star interacts late in its evolution with a companion, thus no longer qualifying as a Jsolated star afterwards, strong interaction might cause angular momentum gain, spin up, and increase in the mass-loss rate. The role of low mass companions (brown dwarfs or planets) in shaping PNe has been long discussed over the past few decades and it has been suggested that most PNe result from binary interaction (e.g., \cite{Soker1996, SiessLivio1999a, SiessLivio1999b, DeMarcoMoe2005, SokerSubag2005, MoeDeMarco2006, VillaverLivio2007, VillaverLivio2009, Nordhausetal2010, DeMarcoSoker2011, Mustilletal2014, Villaveretal2014, Meynetetal2017}). As we have shown in \citet{SabachSoker2018b} for solar type Jsolated stars (both in mass and in metallicity), such an interaction can occur during the AGB phase of evolution, where the companion is likely to be engulfed by the star. The engulfed companion will deposit angular momentum to the primary's envelope, increasing the mass-loss rate and by that later accelerating the post-AGB evolution. This late interaction can shape an elliptical bright PN. In addition, we further found under the Jsolated framework that as the sun is a Jsolated star it will most likely engulf the earth during the AGB rather than during the RGB. We have also shown that such Jsolated stars have implications related to the puzzle of the bright end cut-off in the PN luminosity function (PNLF) of old stellar populations (\cite{SabachSoker2018b,SabachSoker2018a}; for studies on the PNLF see, e.g., \cite{Ciardulloetal1989, Jacoby1989, Ciardulloetal2005, vandeSteeneetal2006, Ciardullo2010, Davisetal2018, Gesickietal2018}). It was observed that both young and old populations have a steep bright end cut-off in the PNLF in [OIII] emission lines at $M^*_{5007}\simeq-4.5$~mag. This implies a more massive central star than expected in old populations, that reach post-AGB luminosities $L\geq 5000~L_\odot$ in order to ionize the observed bright nebulae to the desired level. Our previous results indicate that also for low mass stars the post-AGB luminosities of Jsolated stars are bright enough to account for the bright end cut-off in the PNLF of old stellar populations. In \citet{SabachSoker2018a} we focused on the implications of a reduced mass-loss rate on stellar evolution of solar-type stars and the shaping of elliptical PNe by a companion. In \citet{SabachSoker2018b} we set the term {\it Jsolated stars} and studied the possible solution for the puzzling finding of bright PNe in old stellar populations, where the stellar mass is up to $1.2~M_\odot$. Yet, we have only focused on Jsolated stars of solar metallicity, $Z=0.02$. Here we continue the research and study the evolution of Jsolated star with low metallicities. | \end{figure} | 18 | 8 | 1808.05446 |
1808 | 1808.07396_arXiv.txt | {} { We want to investigate how planet formation is imprinted on stellar surface composition using up-to-date stellar evolution models. } { We simulate the evolution of pre-main-sequence stars as a function of the efficiency of heat injection during accretion, the deuterium mass fraction, and the stellar mass, $\Mstar$. For simplicity, we assume that planet formation leads to the late accretion of zero-metallicity gas, diluting the surface stellar composition as a function of the mass of the stellar outer convective zone. We estimate that in the solar system, between $97$ and $168\,\Mearth$ of condensates formed planets or were ejected from the system. We adopt $150\,{\Mearth}(\Mstar/\Msun)(Z/\Zsun)$ as an uncertain but plausible estimate of the mass of heavy elements that is not accreted by stars with giant planets, including our Sun. By combining our stellar evolution models to these estimates, we evaluate the consequences of planet formation on stellar surface composition. } { We show that after the first $\sim0.1$ Myr during which stellar structure can differ widely from the usually assumed fully convective structure, the evolution of the convective zone follows classical pre-main-sequence evolutionary tracks within a factor of two in age. We find that planet formation should lead to a scatter in stellar surface composition that is larger for high-mass stars than for low-mass stars. We predict a spread in [Fe/H] of approximately {0.05\,dex} for stars with a temperature of $\teff\sim 6500\,$K, to $0.02$\,dex for stars with $\teff\sim 5500\,$K, marginally compatible with differences in metallicities observed in some binary stars with planets. Stars with $\teff\ge 7000\,$K may show much larger [Fe/H] deficits, by 0.6\,dex or more, in the presence of efficient planet formation, compatible with the existence of refractory-poor $\lambda$ Boo stars. We also find that planet formation may explain the lack of refractory elements seen in the Sun as compared to solar twins, but only if the ice-to-rock ratio in the solar-system planets is less than $\approx0.4$ and planet formation began less than $\approx1.3$\,Myr after the beginning of the formation of the Sun. } {} | \label{sec:intro} How does planet formation affect stellar composition? Most of the gas in protoplanetary disks eventually accretes onto the host star within several million years \citep[e.g.,][]{Haisch+01}. Materials that will eventually form planets must condense during this phase. Recent meteoritic evidence indicates that Jupiter's core should have formed rapidly, within {1\,Myr} \citep{Kruijer+17}. Disk materials accreted by the star after this time must have been poor in heavy elements\footnote{ We use ``heavy elements'' to describe all species able to condense and separate from hydrogen and helium in the protoplanetary disk.} because of the gap created by the growing giant planets \citep[e.g.,][]{Paardekooper+Mellema04, Guillot+14, Morbidelli+16}. The accretion of such a diluted gas must result in a refractory-poor composition of the stellar surface. Hereafter, we refer to this mechanism as \textit{dilution}. On the other hand, even after disk dispersal, the formation of planets can lead to the ingestion by the central star of planetesimals or even possibly planets, therefore yielding an increase in its metallicity \citep[e.g.,][]{Spina+14a,Tognelli+16}. Hereafter we refer to this mechanism as \textit{pollution}. \begin{figure}[!t] \begin{center} \includegraphics[width=7.4cm,keepaspectratio]{fig1.pdf} \caption{\small{ Schematic diagram illustrating how planet formation modifies the composition of the stellar surface. A star first accretes hydrogen, helium and heavy elements (equivalently, metals) from a protoplanetary disk of mass $M\sub{disk}(t)$. After a time $\tp$, planet formation removes refractory elements from the accreting gas flow, leading to a dilution of the stellar surface. At this point, the mass in the gas disk (to be eventually accreted by the star) is $\dMO\equiv M\sub{disk}(\tp)$. Later, after disk dispersal, the accretion of rocky objects (e.g., planetesimals) can potentially increase the stellar metallicity (pollution). }}\label{fig:pollution} \end{center} \end{figure} In solar-type stars, an outer convective zone is present and rapidly mixes the stellar {surface}. The process is extremely fast ($\sim$years) compared to evolution timescales and can be considered as instantaneous. The magnitude of the dilution depends both on the amount of heavy elements retained to form planets and on the extent of the outer convective zone of the star. Figure\,\ref{fig:pollution} illustrates how planet formation may affect stellar surface composition and shows the model that we consider in this article. The star first accretes gas with a composition that is equal to that of the molecular cloud core (mass fraction of heavy elements $\Zini$). When planetesimals begin to form, refractory-poor ($<\Zini$) gas is accreted. Accretion of planetesimals and planets then proceeds mostly later when the star is fully formed and the gas disk has dispersed. The crucial quantities involved are (i) $M\sub{disk}(t)$, the mass of the disk as a function of time $t$, (ii) $\MCZ(t)$, the mass of the outer convective zone, and (iii) $\tp$ the time at which planetesimals begin to form. In addition we define $\dMO$ as the mass of the disk at time $\tp$. Circumstellar disks are short-lived, a few to 10 Myr at most {\citep[e.g.,][]{Mamajek09}}. This implies that the dilution mechanism takes place while the central star is still on the pre-main-sequence (pre-MS) phase (for stars $\la1.5\,\Msun$). Contrary to what happens later on the main sequence (MS), on the early pre-MS, even relatively massive stars (say, $1.6\,\Msun$) possess a relatively thick outer convective zone. This convective zone shrinks with age but on a timescale of a few to tens of millions of years. In the classical picture, a $1\,\Msun$ star at 10\,Myr still has $\MCZ\approx0.4\,\Msun$ {\citep[see, e.g.,][]{Iben65,DAntona+Mazzitelli94,Stahler+Palla05}}. However, pre-MS evolution has recently been revisited \citep{BCG09,BVC12,Baraffe+17,Hosokawa+11,Vorobyov+17} and found to be more complex than previously thought: {in} particular, it appears to be sensitive to the entropy of the gas accreted by the star. \citet[][]{BC10} and \citet{Tognelli+15} showed that in this case, the evolution of the stellar internal structure may be significantly different from the classical picture (see Sect.\,\ref{sec:int-evols}). In \citet[][hereafter \citetalias{Kunitomo+17}]{Kunitomo+17}, we found that the pre-MS evolution is also sensitive to the deuterium abundance, in particular in the low-entropy accretion cases \citep[see also][]{Stahler88, Hosokawa+Omukai09, Tognelli+15}. Moreover we constrained possible accretion scenarios from the comparison with effective temperature--luminosity relations in young clusters, and showed that significant departures from the classical evolution scenario (a heat accretion efficiency of 10\% or less, see {Sect.\,\ref{sec:constraints}}) should be rare. In this article, we investigate the internal structure evolution of pre-MS stars under a variety of settings and evaluate the consequences of planet formation on stellar surface composition. We compare our predictions with some observations potentially linked to the dilution {and pollution mechanisms}: the trends in stellar metallicity versus effective temperatures in the Hyades cluster \citep{Takeda+13, Takeda+17}, the metal-poor surface compositions of $\lambda$ Boo stars {\citep{Kama+15, Murphy+Paunzen17}}, the chemical inhomogeneity in some binary systems, and the lack of refractory materials measured in our Sun when compared to solar twins {\citep[e.g.,][]{Melendez+09, Ramirez+09, Chambers10}.} This paper is organized as follows. In Sect.\,\ref{sec:background}, we describe the astrophysical background including the evolution of the metallicity of accreting materials. In Sect.\,\ref{sec:method}, we provide a brief summary of our physical model and of the computation methods. Using our up-to-date stellar evolution models, we explore the consequences of planet formation on stellar surface composition in Sect.\,\ref{sec:discussion}. In Sect.\,\ref{sec:discussion-solar}, we discuss the limits within which the dilution mechanism may explain the anomaly in the solar surface composition compared to solar twins. The results are summarized in Sect.\,\ref{sec:conclusion}. | \label{sec:conclusion} In this article, we explored the consequences of planet formation on stellar surface compositions. {We examined two opposite effects: the dilution effect due to the low-metallicity of the gas accreted in the last stages of stellar accretion, and the pollution from planetesimals and planets possibly accreted by the central star}. In order to quantify these effects, the key ingredients are the thickness of the stellar surface convective zone (CZ) and its evolution in time, the amount of heavy elements retained by the planet formation process, {and the amount and time of the accretion of planetesimals and planets.} First, following \citetalias{Kunitomo+17}, we analyzed the evolution of stellar interiors on the pre-MS, as controlled by three parameters: the efficiency with which heat is injected from the accreting flow to the star, $\xi$, the mass fraction of deuterium, $X\sub{D}$, and the stellar mass, $\Mfin$. The evolution of the CZ can be subdivided in four phases: \begin{description} \item[(1)] Initially the convective-radiative structure depends on how accretion energy is distributed within the star and can be highly variable. \item[(2)] Efficient deuterium burning starts and ensures that the interior becomes largely convective. \item[(3)] The CZ retreats and a central radiative zone grows essentially due to the progressive increase in temperature and subsequent decrease in opacity of the interior. \item[(4)] The star reaches the MS, at which point the properties of the CZ become almost time-independent. \end{description} These four phases are reached at different ages. For likely values of the heat injection parameter ($\xi\wig{>}0.1$ -- see \citetalias{Kunitomo+17}), we found that Phase\,1 lasts $\sim 0.1\,$Myr, that is, when the star is less than half of its final mass. Phase\,2 lasts for about $1\,$Myr for solar-mass stars, but $10\,$Myr for a $0.5\,\Msun$ star, and is inexistent for a $1.5\,\Msun$ star. Similarly, the end of Phase\,3 depends on stellar mass, from about $100\,$Myr for a $0.5\,\Msun$ star, $30\,$Myr for a $1.0\,\Msun$ star, and $10\,$Myr for a $1.5\,\Msun$ star. For $\xi\wig{>}0.1$ we found that after Phase\,1, the CZ evolution is relatively close to that of classical (non-accreting) evolution tracks, with a slightly faster evolution towards the MS for lower values of $\xi$ and of $X\sub{D}$. By causing changes in the composition of accreted material, planet formation will affect stellar composition but the relatively slow retreat of the stellar CZ during the first million years means that the effect will generally be small. It should be maximal for high-mass stars (smaller CZ) and {for stars hosting giant planets (requiring large amounts of solids from the early stages of protoplanetary disk evolution). } Next, we estimated that in the solar system, between $97$ and $168\,\Mearth$ of condensates formed planets or were ejected from the system. We hence adopted as a fiducial scenario the accretion of $0.03\,\Mfin$ of zero-metallicity gas in the last stages of the evolution of the circumstellar disk (dilution scenario). This is expected to be an uncertain but reasonable limit for a star with several giant planets like our Sun. Conversely, stars without planets would not show a significant metallicity change. Another mechanism, that is, planet or planetesimal engulfment during the MS phase, can increase stellar metallicity. However, this is expected to be quickly erased by thermohaline convection on a 10- to 100-Myr timescale \citep{Theado+Vauclair12}. We estimate that a significant {($\sim0.1\,\mathrm{dex}$)} increase in metallicity due to pollution by planet and planetesimal engulfment should be limited to massive stars with effective temperatures above $\sim6500\,\mathrm{K}$. With this fiducial setting (i.e., $\dMO= 0.03\,\Mfin$, $\xi=0.1$ and $X\sub{D}=28\,\mathrm{ppm}$), we found that the dilution scenario results in a decrease of [Fe/H] by up to 0.6\,dex for $\sim7000\,\mathrm{K}$ stars dropping to less than 0.05\,dex at 6500\,K and less than 0.02\,dex at 5500\,K. Given the variability of planet formation and the relative scarcity of systems with giant planets, we estimate that this is representative of the scatter in stellar composition that should be imprinted by planet formation. This scatter is smaller and has a different $\teff$ dependence than that measured in the Hyades cluster \citep{Takeda+13}, indicating either that systematic effects bias the abundance retrievals, that observational uncertainties are still too large, or that other processes such as stellar diffusion play a larger role. We examined how dilution can be used to interpret the differences in composition observed in some binary systems with planets or signs of planet formation: {several} systems with planets have stellar components differing in metallicity by 0.01 to 0.06 dex, values which are within a factor of approximately two of those estimated on the basis of planets in the solar system (i.e., $\dMO= 0.03\,\Mfin$; see Fig.\,\ref{fig:Teff-Zsurf-planetacc} and Table\,\ref{tab:feh}). Given the ambiguities of the findings, the small number of cases and the complexity and variability of planet formation itself, it is however too early to draw any conclusion at this point, except that it is a promising area of research. Other important objects are $\lambda$ Boo stars, a small fraction ($\sim2\%$) of A-type stars {with effective temperatures above 7000\,K} with a significant depletion of up to 2\,dex in refractory elements but solar compositions in volatile elements. {For such temperatures,} the CZ has shrunk rapidly enough to see very large changes in stellar composition due to planet formation, assuming relatively low values of $\xi \sim 0.1$ (see Fig.~\ref{fig:Teff-Zsurf-planetacc} and Table~\ref{tab:feh}). This however requires another ingredient, namely that planet formation preferentially favors the retention of refractory elements over volatile ones. Indeed, observations of accreting Herbig stars indicate that in systems which we expect to host giant planets, the accreting gas is depleted in refractory elements by 0.5\,dex, while the volatile elements show normal abundances \citep{Kama+15}. Planetesimal formation inside of the ice line can lead to efficient retention of refractory elements and the loss of ices \citep{Ida+Guillot16}. Finally, we looked for an explanation of the fact that our Sun is poor in refractory elements compared to the average solar twin \citep{Melendez+09, Ramirez+09, Spina+16a}. The traditional explanation is that this deficit is created by the formation of the terrestrial planets and the proto-asteroid belt \citep{Chambers10}. We showed however that this explanation is incompatible with the pre-MS evolution of the Sun and the fact that, early on, its surface CZ was much larger than it is now. Instead, the solar composition anomaly may be linked to the dilution mechanism proposed here. The early formation of a proto-Jupiter is known to have prevented the Sun from accreting material from the outer disk. If this material had a lower-than-solar ice to rock ratio, this would have led to a depletion of refractory elements in the gas accreted by the Sun in its last stage of formation. In order for this scenario to work, we found that the global ice-to-rock ratio of planets should be less than $\approx0.4$ and efficient planetesimal formation should have begun at most about 1\,Myr after the beginning of the formation of a proto-Sun (i.e., a second Larson's core). These values are much smaller than the protosolar ice-to-rock ratio of $2.04$ \citep{Lodders03} implying that planets in the solar system should be extremely rock-rich. This is not impossible \citep[see][]{Ida+Guillot16} especially given that the giant planets, whose ice-to-rock ratio is unknown, contain most of the planetary mass of heavy elements. The scenario is similar, at least qualitatively, to the one needed to explain the composition of $\lambda$ Boo stars. Planet formation thus affects stellar compositions {in a subtle and complex way. We predict that, in general, the dominant effect should be a slight decrease of the metallicity of stellar outer convective zones compared to that of their deeper interior and to the primordial value. Observations of} compositional differences in some binary stars, the composition anomalies of $\lambda$ Boo stars, and perhaps of our own Sun {do point in that direction, with multiple exceptions however}. In order to make progress, we therefore need very accurate measurements of the compositions of stars in clusters and those of binary stars and limits on the presence of planetary companions around them. We have shown that the solar composition anomaly can be explained only if planets in the solar system are extremely ice-poor. Testing this hypothesis requires much better constraints on the composition of giant planets, something Juno has started doing for Jupiter \citep[see][]{Helled+Lunine14, Bolton+17b,Guillot+18} but is eagerly awaited for the other planets, in particular Uranus and Neptune. | 18 | 8 | 1808.07396 |
1808 | 1808.06053_arXiv.txt | At present, J1819--1458 is the only rotating radio transient (RRAT) detected in X-rays. We have studied the long-term evolution of this source in the fallback disc model. The model can reproduce the period, period derivative and X-ray luminosity of J1819--1458 simultaneously in the accretion phase at ages $\sim 2 \times 10^5$~yr. We obtained reasonable model curves with a magnetic dipole field strength $B_0 \sim 5 \times 10^{11}$~G on the pole of the neutron star, which is much weaker than the field inferred from the dipole-torque formula. With this $B_0$ and the measured period, we find J1819--1458 below and close to the radio pulsar death line. Our results are not sensitive to initial period, and the source properties can be produced with a large range of disc masses. Our simulations indicate that J1819--1458 is evolving towards the properties of dim isolated neutron stars at later phases of evolution. This implies a close evolutionary link between RRATs and dim isolated neutron stars. For other RRATs with measured period derivatives and unknown X-ray luminosities, we have estimated the lower limits on the $B_0$ values in the fallback disc model. These limits allow a dipole field distribution for RRATs that could fill the $B_0$ gap between the estimated $B_0$ ranges of dim thermal isolated neutron stars and central compact objects in the same model. | \label{intro} Rotating Radio Transients (RRATs) were discovered more than a decade ago as a new neutron star population \citep{Mc2006}. Unlike normal radio pulsars, RRATs do not exhibit regular radio pulses. They show sporadic and brief radio bursts with time separations of $\sim$ minutes to a few hours. Durations of the radio bursts range from $0.5$ ms to $100$ ms with flux densities from $\sim 10$~mJy to $\sim 10$~Jy, which make these systems the brightest radio sources in the universe \citep{Mc2006, Deneva2009}. Detectable radio emission from a particular RRAT lasts for less than one second per day \citep{Mc2006}. From the analysis of burst times-of-arrival \citep{Manchester2001}, the rotational periods have been obtained in the $0.1 - 7$~s range \citep{Mc2006, Deneva2009}. Among more than 100 confirmed RRATs \citep{Taylor2016}, only J1819--1458 was detected in X-rays \citep{Mc2007}, and upper limits on the X-ray luminosity were estimated for J0847-4316 and J1846-0257 \citep{Kaplan2009}. The main reason for non-detection of the other RRATs in X-rays is the uncertainties in the positions of the sources \citep{Kaplan2009}. For J1819--1458 (hereafter J1819), the rotational period $P=4.26$~s \citep{Mc2006} and the period derivative $\dot{P} \approx 5.75 \times 10^{-13}$~s~s$^{-1}$ \citep{Keane2011} give the characteristic age $\tau_{\mathrm{c}} = P/2\dot{P} \simeq 1.2 \times 10^5$~yr and the rotational power $\dot{E} \simeq 4 \pi^2 I \dot{P} P^{-3} \simeq 3 \times 10^{32}$~erg~s$^{-1}$, where $I$ is the moment of inertia of the neutron star. Radio bursts from J1819, repeating about every four minutes, were detected in Parkers observations \citep{Mc2006}. The distance is estimated to be $d = 3.6$~kpc from the dispersion measure with an uncertainty of $\sim 25$\% \citep{Mc2006}. An unabsorbed flux of $1.5 \times 10^{-13}$~erg~s$^{-1}$~cm$^{-2}$ detected in the $0.3-5$~keV band gives an X-ray luminosity $L_{\textmd{x}} = 4 \times 10^{33}~(d/3.6~$kpc$)^2$~erg~s$^{-1}$, which is an order of magnitude higher than the rotational power of the source \citep{Rea2009}. The X-ray spectrum is thermal and can be fitted with a blackbody temperature of $kT \sim 0.14$~keV, $N_\mathrm{H} \sim 6 \times 10^{21}$~cm$^{-2}$ and absorption line at $\sim 1$~keV \citep{Mc2007, Rea2009}. If this is a cyclotron absorption line, the required field strengths are $2 \times 10^{14}$~G and $\sim 10^{11}$~G for the absorption by protons and electrons respectively \citep{Miller2013}. The reason for the transient nature of the radio emission from RRATs has not been understood yet. It was proposed that RRATs could have properties similar to the systems that show giant pulses \citep{Knight2006} or to nulling pulsars \citep{Redman2009}. Alternatively, RRATs could be the radio pulsars close to the pulsar death line in the magnetic dipole field-period plane \citep{Chen1993}. In this late phase of radio-pulsar evolution, pulsations might become rare \citep{Zhang2007}. These systems might be emitting weak, continuous radio pulses, which have not been detected yet, in addition to the observed short radio bursts \citep{Weltevrede2006}. It was also proposed that RRATs could have evolutionary links with the anomalous X-ray pulsars (AXPs), soft gamma repeaters (SGRs) \citep{Mc2006, Mc2009} or thermally emitting dim isolated neutron stars (XDINs) \citep{Popov2006}. This possibility has motivated us to study the long-term evolution of J1819 in the fallback disc model that was applied earlier to the other neutron star populations. The fallback disc model was first proposed to explain the long-term X-ray luminosity and period evolution of AXPs \citep{Chatterjee2000}. It was proposed by \citet{Alpar2001} that the observed properties of not only AXPs but also other neutron star populations, SGRs, XDINs, and possibly central compact objects (CCOs), could be explained if the fallback disc properties are included in the initial conditions in addition to the magnetic dipole moment and the initial period. To test these ideas, a long-term evolution model for neutron stars with fallback discs was developed including the effects of X-ray irradiation with contribution of the intrinsic cooling of the neutron star, and the inactivation of the disc at low temperatures on the evolution of the star \citep{ErtanE2009, Alpar2011, Caliskan2013}. Later, it was shown that the individual source properties of AXP/SGRs \citep{Benli2016}, XDINs \citep{Ertan2014}, high magnetic-field radio pulsars (HBRPs) \citep{Caliskan2013, Benli2017, Benli2018}, and CCOs \citep{Benli2018_CCOs} can be reproduced in the same long-term evolution model with very similar main disc parameters, supporting the idea proposed by \citet{Alpar2001}. In this model, estimated magnetic dipole moments of these neutron star populations range from $\sim 10^{29}$~G~cm$^3$ to a few $10^{30}$~G~cm$^3$, which are well below the values inferred from the magnetic dipole torque formula. From the numerical simulations, most AXP/SGRs are estimated to be in the accretion regime, while XDINs are found in the strong propeller regime. In line with these results, it was shown that the characteristic high-energy spectra of AXPs can be produced in the accretion column, consistently with the observed phase dependent pulse profiles \citep{Trumper2010, Trumper2013, Kylafis2014}. There are several reasons indicating that RRATs could have rather different properties in comparison with the normal radio pulsars, which also motives us to investigate RRATs in the fallback disc model. If RRATs are the neutron stars evolving in vacuum and spin down with magnetic dipole torques, they would be expected to show regular radio pulses, like many normal radio pulsars with similar rotational properties. They are bright radio emitters but with durations much shorter than their spin periods. While the continuous radio pulses are estimated to cease below the radio pulsar death line, the mechanism producing the radio bursts from RRATs, and when this behavior starts and terminates are not clear yet. These sources could be in an evolutionary phase that starts after the termination of the normal radio pulses. In this situation, they are expected to be close to the pulsar death line (below or above). This could be possible only if they are evolving with the external torques dominating the dipole torques. Because, the dipole fields inferred from the dipole torque formula places them well above the pulsar death line. If these systems are evolving with fallback discs, dipole torque formula could overestimate the actual field by one or two orders of magnitude (see e.g. \citealp{Ertan2014} for XDINs, \citealp{Benli2016} for AXP/SGRs). In this case, these systems could indeed be close to the death line in the $B~-~P$ plane. On the other hand, the thermal X-ray luminosity of J1819 can be emitted only by very young normal radio pulsars with ages less than about $10^4$~y (see Sec. \ref{secmodel}), much smaller than the characteristic age of the source ($> 10^5$~y). Results of our earlier work on the long-term evolution of XDINs show that the normal radio pulsars are not likely to be the progenitors of XDINS, and that there could be evolutionary links between RRATs and XDINs \citep{Ertan2014}. Furthermore, investigations of the statistical, rotational and X-ray properties indicate that RRATs could be progenitors of XDINs \citep{Popov2006}. Investigation of the evolution of J1819 in the fallback disc model could help us understand the evolutionary phase and the conditions that could be responsible for the RRAT behavior, if the source is indeed evolving with a fallback disc. In Section \ref{secmodel}, we briefly describe our model and give the results of the numerical simulations for J1819. We discuss and summarize our conclusions are summarized in Section \ref{secconc}. | \label{secconc} We have investigated the long-term evolution of J1819--1458 which is the only RRAT detected in X-rays. We have shown that the period, period derivative and X-ray luminosity of the source can be explained in the same model that can account for the long-term evolutions of AXP/SGRs, XDINs, HBRPs, and CCOs. The model can reproduce the properties of the source only with a narrow range of $B_0$ around $4.6 \times 10^{11}$~G, while reasonable model curves are obtained with rather different initial disc masses (($0.75 - 3.76) \times 10^{-5}~M_\odot$). The model sources reach the properties of J1819 in the accretion with spin-down (ASD) phase at an age $\sim 2 \times 10^5$~yr, when the estimated cooling luminosity of the neutron stars is a few per cent of the observed $L_\mathrm{X}$ of J1819. In the accretion phase, the mass-flow onto the neutron star is expected to switch off the radio pulses. Even if the accretion stops by some reason, we do not expect regular pulsed radio emission from J1819, since the $B_0$ indicated by our model and the measured $P$ place the source below the pulsar death line. If the absorption feature around $1$~keV is a proton cyclotron line, the required field strength is $\sim 2 \times 10^{14}$~G \citep{Miller2013}. The field close to the surface of the star could indeed be much stronger than the dipole component due to presence of local strong quadrupole fields. Alternatively, the observed absorption feature could be electron cyclotron line which could be produced in the accretion column with a field strength $ \sim 10^{11}$~G. Illustrative model curves in Fig. \ref{fig:J1819_all} imply that J1819 is currently evolving through lower part of the AXP/SGR region in the $P$~--~$\dot{P}$ diagram. Currently, the short-term timing behavior of the source seems to have been affected by the glitch effects \citep{Bhattacharyya2018}. From the model results, we estimate that J1819 will reach the XDIN properties within a few $10^5$~yr (Fig. \ref{fig:J1819_all}). The illustrative model curves in Fig. \ref{fig:J1819_all} imply that the source is evolving into the XDIN properties. This result is not very sensitive to the initial period, the disc mass and the resultant $L_\mathrm{X}$ history of the source. For the other RRATs, since the X-ray luminosities are not known, it is not possible to estimate their evolutionary paths and the $B_0$ values. Nevertheless, the lower bound, $B_{0,\mathrm{min}}$ for a given source can be estimated using the most efficient torque reached in the ASD phase and the measured $\dot{P}$ of the source (Section \ref{secconc}). In Fig. \ref{fig:B0_P}, it is seen that these lower limits on $B_0$ allow a continuous $B_0$ distribution from CCOs to AXP/SGRs in the fallback disc model. An X-ray nebula was detected around J1819--1458 \citep{Rea2009}. The size of the X-ray nebula is about $1$~ly \citep{Camero2013} which is too large to be related to the outer regions of a fallback disc that could scatter a fraction of the X-rays emitted by the star. The estimated luminosity of the point source is more than 2 orders of magnitude higher than that of the nebula \citep{Rea2009}. The extended emission might be powered by a fraction of the luminosity of the star, nevertheless the mechanism producing the extended emission is not clear yet. In any case, this extended emission with a low luminosity and a very large size could only be a secondary process that does not affect our results obtained for the point source and its interaction with the inner disc with a radius of less than about $10^9$~cm. It is expected that the pulsed radio emission is quenched by mass-flow on to the star. The behavior of RRATs could also be indicating a mechanism that tries to impede continuous pulsed radio emission, causing the observed sporadic radio emission. Alternatively, it could be the case that some mechanism could be inducing emission of these radio bursts in a sporadic way. The estimated evolution of J1819 toward the XDIN population might indicate that all known XDINs could have evolved through RRAT phase in the past. The fact that all measured RRAT periods are smaller than $7$ s, and that $5$ out of $7$ XDINs have periods greater than $7$ s could point to a maximum period (for a given $B_0$) above which RRAT behavior disappear. Considering that we have found J1819 below the death line, for a given source, there could be a certain RRAT phase that starts after the termination of the normal radio pulsations, and ends above a critical $P$ for this particular neutron star. It is not clear whether the RRAT behavior itself is related to presence or properties of fallback disc around the source. We need further detections of RRATs in X-rays to test these ideas in depth through long-term evolutionary analysis of these sources. Unlike J1819, most of the RRATs have characteristic ages greater than a few $10^6$~y. For these sources, if the actual ages are close to the characteristic ages, the cooling luminosities are estimated to be too low to be detected in X-rays. In our model, these RRATs (except very young systems) are likely to be evolving in the propeller phase at ages much smaller than their characteristic ages, similar to the case estimated for XDINs \citep{Ertan2014}. This means that these systems could have cooling luminosities much greater than those estimated for their characteristic ages, if they are indeed evolving with fallback discs. This prediction of the model can be tested by future detections of RRATs in X-rays. | 18 | 8 | 1808.06053 |
1808 | 1808.08087_arXiv.txt | The globular clusters of large spiral galaxies can be divided into two populations: one which formed in-situ and one which comprises clusters tidally stripped away from other galaxies. In this paper we investigate the contribution to the outer globular cluster population in the M31 galaxy through donation of clusters from dwarf galaxies. We test this numerically by comparing the contribution of globular clusters from simulated encounters to the observed M31 globular cluster population. To constrain our simulations, we specifically investigate the outermost globular cluster in the M31 system, MGC1. The remote location of MGC1 favours the idea of it being captured, however, the cluster is devoid of features associated with tidal interactions. Hence we separate simulations where tidal features are present and where they are hidden. We find that our simulated encounters can place clusters on MGC1-like orbits. In addition, we find that tidal stripping of clusters from dwarf galaxies leaves them on orbits having a range of separations, broadly matching those observed in M31. We find that the specific energies of globular clusters captured by M31 closely matches those of the incoming host dwarf galaxies. Furthermore, in our simulations we find an equal number of accreted clusters on co-rotating and counter-rotating orbits within M31 and use this to infer the fraction of clusters that has been accreted. We find that even close in roughly $50\%$ of the clusters are accreted, whilst this figure increases to over $80\%$ further out. | Globular clusters are believed to be an integral part in galaxy evolution, see e.g, \citet{Brodie2006, Renaud2018}, and understanding the origin of different globular clusters is essential to fully understanding their formation. There are two viable mechanisms that can populate a galaxy with clusters; either the globular clusters form {\it in-situ}, that is from gaseous material inside the galaxy itself, or they form outside and then are accreted to the total population. \citet{SearleZinn1978} suggested this twofold build-up as a hypothesis for explaining the bimodalities observed in the Milky Way cluster population \citep[see, e.g.,][]{Zinn1985,Harris1996,MarinFranch2009}, and many works has investigated this scenario since then \citep[see, e.g.,][]{Cote1998,Tonini2013,Renaud2017}. The Milky Way is not the only galaxy that shows such bimodalities, in fact bimodalities are very common in observed galaxies, see e.g. \citet{Brodie2006} for a review. Most often this is referred to as the blue and red clusters, due to the globular clusters showing a separation in colour \citep[see, e.g.,][]{GebhardtKissler-Patig1999,Larsen2001,KunduWhitmore2001,Peng2006}. Furthermore, in the Milky Way the blue clusters has been linked to a metal-poor population that is spatially extended without clear signs of rotating, whereas the red clusters are more metal-rich, spatially concentrated and shows signs of co-rotating with the galaxy, see \citet{ArmandroffZinn1988, Cote1999}. The spatial distribution and kinematics of the two populations are in favour of building the blue population by accretion, while the red population forms {\it in-situ}. A more compelling evidence for the two-fold build up is the on-going accretion of globular clusters from satellite galaxies in the Universe today. One example is the Sagittarius dwarf, which is believed to have donated multiple globular clusters to the Milky Way in the past billion years, see \citet{Layden2000, Siegel2007}. Further evidence of accretion events can also be found in the outer parts of our neighbouring galaxy Andromeda (henceforth M31), which was well studied in the Pan-Andromeda-Archaeological-Survey (PAndAS), \citep[see, e.g.,][]{Martin_et.al2006,Ibata+2007,McConnachie2008}. Using the PAndAS data, \citet{Machey_Huxor2010} found that there is a striking alignment between the position of outer globular cluster and tidal debris, such as stellar streams. By detailed investigation of the likelihood of chance alignment, \citeauthor{Machey_Huxor2010} concluded that the outer globular cluster population consists of $\goa 80\%$ accreted clusters. In this work we focus on the globular cluster MGC1, which is a globular cluster on an extremely wide orbit in M31. \citet{Martin_et.al2006} discovered this particular cluster for which they determined a position on the sky with right ascension $0^{\rm h}50^{\rm m}42.5^{\rm s}$ and declination $+32\degr54\arcmin59.6\arcsec$. This gives MGC1 a projected distance of $\approx117\,{\rm kpc}$ from the M31 centre. In another work by \citet{MackeyFerguson2010}, the authors observed MGC1 using the Gemini/GMOS observatory to determine a precise distance to the cluster. They found a distance modulus of $\mu = 23.95\pm0.06$, which gives MGC1 a radial distance from M31 of $200\pm20\,{\rm kpc}$. This makes MGC1 the most remote cluster in the Local Group with some considerable margin. Although a proper motion has not yet been determined for MGC1, several authors have measured its radial velocity, see, e.g., \citet{Galleti2007,Alves-Brito2009}. Comparing to the systematic velocity of M31 \citep{vanDerMarel2012}, the MGC1 has a radial velocity that is comfortably lower than the M31 escape velocity \citep{Chapman2007}. Thus, MGC1 is likely one of M31 {\it bona fide} members and not an intergalactic cluster. The metallicity of the cluster has been somewhat debated, where the authors of the original paper, \citet{Martin_et.al2006} determined a metallicity $[{\rm Fe/H}]\approx-1.3$ by fitting isochrones to the its colour-magnitude diagram (CMD). Using spectra from the Keck/HIRES instrument, \citet{Alves-Brito2009} argued that the metallicity for MGC1 was $[{\rm Fe/H}]\approx-1.37\pm 0.15$, which is in agreement with \citeauthor{Martin_et.al2006}. Controversially, \citet{MackeyFerguson2010} derived a significantly lower metallicity at a reported value of $[{\rm Fe/H}]\approx-2.7$. Although, said authors do not agree on the exact value, they all coincide with a metallicity that would contribute to the blue, metal-poor population of the Milky Way. For the M31 such bimodality is not clear, where both cases has been argued \citep[see, e.g.,][]{Barmby+2000,Fan+2008,Caldwell+2011}. The remote location and low metallicity of MGC1 is in favour of an accretion origin for the cluster, however there are restrictions to this scenario as well. \citet{MackeyFerguson2010} investigated this possibility by searching for signs of tidal interaction. MGC1 does coincide spatially with three satellite galaxies, however, this is due to projection where the three satellites reside significantly closer to the M31. Additionally, the three galaxies and MGC1 shows different velocities and are therefore likely on very different orbits. Another tracer for recent tidal interaction is stellar streams around the object. \citet{MackeyFerguson2010} used star counts in the vicinity of MGC1 to look for such features but could not find any. Moreover, \citeauthor{MackeyFerguson2010} found that MGC1 has an extremely extended structure, with stars that match the MGC1 stellar population out to $450\,{\rm pc}$ and possibly even $900\,{\rm pc}$. This is a significant fraction of the tidal radius at the location of MGC1, thus it must have spent some considerable time in isolation. In this work we address the question of whether it is possible that MGC1 did in fact originate from an accretion event. We test this by using numerical simulations of encounters between dwarf galaxies and the M31, in which we look at the probability of tidally stripping away globular clusters from the dwarf galaxy and place them on wide enough orbits for them to be observed as the MGC1. Furthermore, we constrain our encounters as to not leave visible traces by using an analytic expression of the tidal radius to check whether the dwarf galaxy or the clusters sustain significant damage to its luminous matter during the encounter. The report is structured with a summary of the numerical scheme and brief review of the tidal radius in Section~\ref{sec:methodology}, followed by results and their implications in Section~\ref{sec:results}, first focusing on a typical encounter in our simulation and then looking at how the likelihood of obtaining a cluster similar to MGC1 depends on the dwarf galaxy properties and orbital parameters in all encounter that where simulated. In Section~\ref{sec:building_M31_GCpop} we investigate what our results imply for the observed globular cluster population in M31 by comparing the general properties of clusters captured by M31 on orbits other than those that resemble the orbital properties of MGC1 to those observed in the accreted cluster population of M31. In Section~\ref{sec:discussion}, we discuss our results, the limitations of our model and suggest possible histories of MGC1 other than that covered in this work for future work. Finally, in Section~\ref{sec:conclusion} we list the major findings of this work. | \label{sec:conclusion} We have tested if tidally stripping a globular cluster away from a dwarf galaxy during a close encounter with M31 and leaving it on a wide orbits without leaving any visible trace is a viable mechanism for producing the MGC1 cluster. We used simple models for the M31 galaxy and the dwarf galaxy in favour of running a large set of numerical simulations to test what type of orbital properties for the dwarf galaxy gives reasonably high likelihood of leaving behind clusters observable as MGC1. The main conclusions from our study are the following: \begin{enumerate} \item We find that in certain ranges of specific orbital energy for a dwarf galaxy, there is a significant likelihood to produce isolated clusters on orbits wide enough to place them at an orbital distance comparable to that of MGC1. Regardless of mass the likelihood of producing such clusters peaks close to the specific orbital energy of MGC1 ($\approx-19\times10^3\,{\rm km}^2\,{\rm s}^{-2}$). Furthermore the amplitude of the peak varies for different masses (increasing with decreasing mass). \item In individual encounters, the clusters on prograde orbits are more likely to be tidally stripped away, in agreement with previous work for stars \citep{Read_et_al_2006}. To tidally strip away clusters and place them on orbits significantly different compared to the host dwarf galaxy (e.g. MGC1-like clusters) the angular momentum vector for the dwarf orbit around the major galaxy, $\mathbf{J}_{\rm s}$, and that of the cluster orbit around the dwarf, $\mathbf{J}_{\rm c}$, should align to as high degree as possible (quantified by $\mathbf{J}_{\rm s}\cdot\mathbf{J}_{\rm c}\approx 1$). \item We find that for the dwarf galaxies with smaller masses the likelihood of producing clusters like MGC1 decreases with increasing pericentre distance. Surprisingly, for more massive dwarf galaxies the decrease is small to negligible. Furthermore, we find that the dwarf galaxy trajectory needs a pericentre distance larger $\goa 30\,{\rm kpc}$ in order to survive the encounter regardless of mass. \item In accordance with other works investigating accretion of globular cluster \citep[see, e.g.,][]{Brodie2006}, we find that there is not any preferred orbital orientation among the accreted clusters. Assuming that accretion of clusters leaves the same number of clusters on co-rotating and counter-rotating orbits, we are able to infer the relative frequency of accreted and {\it in-situ} clusters as a function of projected radius, see equation~(\ref{eq:acc_vs_insitu}) and Table~\ref{tab:accreted_vs_insitu}. For M31, we find in the inner region roughly $50\%$ of the clusters have been accreted, whilst this figure increases to over $80\%$ further out. This agrees with the number found by \citet{Machey_Huxor2010}, whom counted accreted clusters by looking for association to stellar streams and spatial correlation between clusters. \end{enumerate} Furthermore, as a test that ties our simulations to observations of the global properties of M31, we compared the total number distribution of clusters that is accreted by M31 in our simulations to the distribution observed given that our simulations produce one cluster at the orbital distance of MGC1. We find that if we select encounters with specific orbital energy larger than the specific orbital energy of MGC1 then we tend to populate M31 with a significant number of clusters beyond $200\,{\rm kpc}$. Since MGC1 is one of the outermost cluster in M31 this implies that encounters between M31 and dwarf galaxies with specific orbital energy larger than this rarely contribute with globular clusters. Using this restriction for specific energy of the dwarf galaxy, but otherwise sampling encounters uniformly in specific energy with masses that match the subhalo mass function for a galaxy like M31, we find that the number distribution of clusters that are captured in our simulations matches the one observed in M31, with the exception of the innermost region where we do not contribute clusters. We do not populate the innermost region because our simulations do not cover encounters necessary to place clusters on such orbits. In addition, in some cases additional physics not covered in our model (for example dynamical friction) may play a role in shrinking globular cluster orbits. | 18 | 8 | 1808.08087 |
1808 | 1808.06862_arXiv.txt | {Early magnetographic observations indicated that magnetic field in the solar photosphere has unresolved small-scale structure. Near-infrared and optical data with extremely high spatial resolution show that these structures have scales of few tens of kilometres, which are not resolved in the majority of solar observations.} {The goal of this study is to establish the effect of unresolved photospheric magnetic field structure on Stokes profiles observed with relatively low spatial resolution. Ultimately, we aim to \mrk{develop methods for fast estimation of the photospheric magnetic filling factor and line-of-sight gradient of the photospheric magnetic field, which can be applied to large observational data sets}.} {We exploit 3D MHD models of magneto-convection developed using MURAM code. Corresponding profiles of Fe~I 6301.5 and 6302.5~$\ang$ spectral lines are calculated using NICOLE radiative transfer code. The resulting I and V Stokes [x,y,$\lambda$] cubes with reduced spatial resolution of 150~km are used to calculate magnetic field values as they would be obtained in observations with Hinode/SOT or SDO/HMI. } {Three different methods of the magnetic filling factor estimation are considered: the magnetic line ratio method, Stokes V width method and a simple statistical method. We find that the statistical method and the Stokes V width method are sufficiently reliable for fast filling factor estimations. Furthermore, we find that Stokes $I\pm V$ bisector splitting gradient can be used for fast estimation of line-of-sight gradient of the photospheric magnetic field.} {} | \begin{figure*}[ht!] \centerline{\includegraphics[width=0.8\textwidth,clip=]{sketch}} \caption{Sketch of a line profile, showing Stokes I profile (panel a), Stokes V (panel b), and Stokes I$\pm$V profiles (panel c) with some of their parameters used in this paper.} \label{f-sketch} \end{figure*} \begin{figure*}[ht!] \centerline{\includegraphics[width=0.7\textwidth,clip=]{fieldmap}} \caption{Magnetic field in snapshot C at different spatial resolutions. Panel (a): Magnetic field measured using Stokes V amplitudes of the 6301 line with high spatial resolution (not calibrated). Panel (b): Map of B$_\mathrm{eff}$[6301], magnetic field from the same model snapshot obtained using degraded Stokes profiles, representing low-resolution data.} \label{f-fieldmap} \end{figure*} Early observational studies indicated that photospheric magnetic field is very non-uniform on scales smaller than the spatial resolution of optical instruments. Magnetographic observations showed that the magnetic field strengths measured using two Fraunhofer lines with similar characteristics but different magnetic sensitivity ({\it i.e.} different Lande factor $g$) can differ by factor of up to $2.5$ \citep{host72,sten73}. This has been interpreted as evidence of strong horizontal field inhomogeneity. It has been suggested that most of the photospheric magnetic flux is carried by numerous intense small-scale magnetic fluxtubes, and the photospheric magnetic filling factor can be as low as 10\% \citep{frst72}. Despite a very significant progress in achieving high spatial resolution in solar observations, most existing optical solar instruments do not resolve the smallest scales in the photospheric magnetic field \cite[see e.g.][for review]{sola93,lolo94,sosc04,dewe08}. Obviously, direct high-resolution observations are the most reliable way of studying photospheric fine structure. However, very high spatial resolution (50-100~km or even less) can be achieved only in some observations using advanced instrumentation as well as advanced data-processing techniques, which are often computationally expensive. Direct high-resolution observations of small-scale photospheric magnetic elements were performed using speckle-interferometry in Fe~I~5250.2~$\ang$ line \citep{keva92,kell92}. They found magnetic elements with a field strength of a few kG and estimated their sizes at $100\,-\,200$~km. \citet{lin95} observed Stokes profiles in magneto-sensitive near-infrared Fe~I lines 15648~$\ang$ and 15652~$\ang$ and showed that there are two types of small-scale magnetic elements: stronger elements with the field of $1.4$~kG and diameters 100--1000~km located in the network boundaries, and weaker ones with fields of about $ 500$~G and diameters about $70$~km, located inside granulation cells. \citet{lage10} using IMaX magnetograph on-board Sunrise balloon mission have achieved spatial resolution of about 100~km in all Stokes components. They were able to detect small magnetic elements with the filling factor equal 1 (i.e. no unresolved structure), which have been interpreted as individual photospheric fluxtubes. The sizes of these elements are 100-500~km. Inversion of Stokes profiles observed using moderate spatial resolution (few 100~km) can be an alternative to high-resolution observations \cite[e.g.][]{vite11}. However, inversion algorithms are computationally expensive and can be applied only to rather small patches of the photosphere. Furthermore, most inversion codes oversimplify the magnetic field structure by assuming the same magnetic filling factor at different heights. Forward-modelling is another way of studying small-scale photospheric magnetic field. 3D models of magneto-convection in the photosphere developed using high-resolution 3D magnetohydrodynamic (MHD) simulations offer a unique opportunity to investigate photospheric magnetic field structure unresolved by normal solar telescopes. Combined with the radiative transfer calculations, these models make it possible to link characteristics of small- and large-scale magnetic field 3D structure with parameters inferred directly from solar observations with limited spatial and spectral resolution. Recently, \citet{smso17} used MHD models of magneto-convection combined with a radiative transfer calculations in order to investigate Stokes profiles of several photospheric lines. The focus was on using \mrk{various} pairs of lines for measuring photospheric field using the magnetic line ratio (MLR) approach. This approach makes it possible to evaluate actual field value based on the ratio of magnetic field values measured using two lines with similar thermodynamic characteristics (and, hence, similar formation depths) but different Lande factors, unlike single line measurements, which yield average field (or magnetic flux) values (see Section~\ref{s-callibr}). This study identified two new pairs of lines, one visible and another in the near-infrared, as effective diagnostic tools for magnetic field measurements using MLR approach. In the present study, \mrk{we investigate the effect of magnetic field filling factor (in a plane perpendicular to the LOS) and vertical field gradient on Stokes I and V profiles observed with relatively low spatial resolution.} We deploy techniques very similar to \citet{smso17}, however, we focus specifically on unresolved structure of photospheric field, both in horizontal and vertical (i.e. line-of-sight, LOS) directions. \mrk{Most importantly, in addition to the magnetic line ratio method, we consider two other methods (Stokes V width method and the statistical method).} The ultimate goal is to find a simple, empirical way of estimating these two parameters using large field-of-view spectropolarimetric data from telescopes such as Hinode, Gregor and future DKIST. | \label{s-con} In this study, we analyse synthetic I and V Stokes profiles of Fe~I 6301.5 and 6302.5~$\ang$ lines derived using a magneto-convection model of the photospheric magnetic field, as well as calibration curves derived for these lines. Based on this analysis, three different methods of estimating the intrinsic magnetic field and the magnetic filling factor in solar photosphere are compared. \mrk{For this pair of lines we show that}: \begin{itemize} \item The Stokes V width method appears to be quite \mrk{reliable for the intrinsic magnetic field and filling factor estimations} above 200-300~G and does not show any saturation up to at least 2~kG. Moreover, Stokes V widths seem to be less sensitive to the line width. Therefore, this method appears to be the best for the $B_\mathrm{real}$ and $\alpha$ estimation using the 6301 \mrk{line}. \item The statistical approach can be very efficient for estimating $\alpha$ values within a small patch of the photosphere when the intrinsic field is likely to be nearly constant. \mrk{Obviously, it can not be applied to large or very inhomogeneous, active photospheric areas.} \item The magnetic line ratio method \mrk{can be used} for intrinsic magnetic field \mrk{and the filling factor} using the 6301~-~6302~$\ang$ pair. However, \mrk{it appears to be the least reliable method because of the formation height difference and saturation}. Furthermore, MLR is more sensitive to the line width (Section~\ref{s-callibr}), and, hence, an error in evaluating the line width would increase the error in derived $B_\mathrm{real}$ values. This, in turn, would translate to even higher error in estimated $B_\mathrm{eff}/B_\mathrm{real}$ values. \end{itemize} However, it should be noted, that MLR approach \mrk{can be very efficient for $B_\mathrm{real}$ and $\alpha$ estimations using other line pairs, which do not saturate in a wider magnetic field range \cite[see][and references therein]{khco07,smso17}. } Finally, we find that BSG correlates with the LOS gradient of the magnetic field. Linear calibration functions $dB/dz\,(BSG)$ calculated separately for lines with positive and negative Doppler shifts provide quite reliable maps of the photospheric magnetic field gradient. | 18 | 8 | 1808.06862 |
1808 | 1808.02994_arXiv.txt | We investigate the origin of the H$\alpha$-like structure seen in late-phase nebular spectra of type IIb supernovae (SNe IIb) at $\sim 200$ days after the explosion. We compare the luminosities of emission lines in the nebular spectra with the light curve peak magnitudes to reveal their power sources. In this work, we analyze 7 SNe IIb, as well as 2 SNe Ib (SN 2007Y and iPTF 13bvn) that show the H$\alpha$-like emission in their nebular spectra. The luminosity of the H$\alpha$-like emission shows a tight correlation with the light curve peak magnitude, sharing the same behavior with other nebular lines. This result indicates that the H$\alpha$-like emission is powered by the radiative decay of $^{56}$Co. The line flux is then expected to roughly follow the mass of the emitting layer. The variation expected from the diversity of the H-rich envelope mass among SNe IIb (reaching nearly to an order of magnitude) is however not seen, suggesting that it is most likely contributed predominantly by [N II], not by H$\alpha$. While further analysis is limited by the available sample size, we find a hint that SNe IIb with a double-peak light curve, which is interpreted as an outcome of the more extended and massive hydrogen envelope, tend to show excess in the luminosity of the H$\alpha$-like feature than those with a single-peak light curve. This behavior indicates possible additional contribution from H$\alpha$. Additionally, we also find a correlation between the [Ca II]/[O I] ratio and the post-maximum decline rate, indicating that the [Ca II]/[O I] can be used as a diagnostics for the progenitor mass. | A star with zero-age main-sequence mass larger than 8 M$_{\odot}$ ends its life with a supernova (SN) explosion triggered by a collapse of its iron or oxygen-neon-magnesium core. Core collapse supernovae (CCSNe) are classified into type II SNe (SNe II, with a hydrogen envelope) and type I (SNe I, without a hydrogen envelope). Type I CCSNe are further divided into SNe Ib and Ic according to whether its helium envelope is retained. Observationally, Balmer lines shape optical spectra of SNe II, while they are (generally) not detected for SNe Ib and Ic. SNe IIb show spectroscopic properties intermediate between SNe II and Ib. Optical spectra of SNe IIb show strong hydrogen lines around the maximum light. As an SN IIb evolves, the hydrogen lines gradually fade away, eventually resembling to an SN Ib. The small amount of hydrogen retained at the time of the explosion is believed to be responsible for such a transition (\citealt{filippenko93}; \citealt{nomoto93}). The first identification of SN IIb was suggested for SN 1987K \citep{filippenko88}. The number of SNe IIb so far discovered is increasing, among which SN 1993J is the best-observed one. However, SN IIb is a relatively rare event, with the volumetric rate of about 12\% among SNe II (\citealt{li11}; \citealt{smith11}). In early phase, the emission from SNe IIb, including the hydrogen lines in their spectra, is powered by the radioactive decay chain $^{56}$Ni $\rightarrow$ $^{56}$Co $\rightarrow$ $^{56}$Fe. In nebular phase, they generally show an emission feature centered at $\sim 6500$ \AA. This may be contributed by H$\alpha$, but the line identification and the power source have not been robustly clarified. Indeed, for a fraction of SNe IIb, this feature further develops in later phases (e.g., after $\sim$300 days) and it is considered as a signature of strong interaction with circumstellar material (CSM) (\citealt{patat95}, \citealt{matheson00a}, \citealt{maeda15}). The behavior is not always seen, and thus questions remain as for what are the line identification and power source for the H$\alpha$-like feature in nebular phase but at $< 300$ days (\citealt{maurer10}, \citealt{jerk15}, \citealt{maeda15}). This is related to the still-unresolved question of the mechanism of the envelope stripping toward SNe IIb, and toward SNe Ib and Ic in general (\citealt{grafener16}; \citealt{stancliffe09}; \citealt{ouchi17}). Nebular line identification provides us with an opportunity to explore the properties of the entire ejecta structure from the core through the envelope. Although metal lines are unambiguously a result of the radioactive decay chain (\citealt{kozma98}; \citealt{houck96}), the origin of the H$\alpha$-like feature detected generally for SNe IIb already before $\sim 300$ days has not been clarified. For some SNe IIb, the H$\alpha$-like emission is relatively narrow at $< 300$ days, which is different than a flat and wide line profile predicted by the CSM interaction scenario (\citealt{cheva10}) as examplified by SN 2008ax (\citealt{tauben11}). \citet{cheva10} also argue that H$\alpha$ powered by shock-CSM interaction should be undetectable in nebular phase for relative compact objects (e.g., SN 2007Y), but this H$\alpha$-like structure still presents in their spectra. Note that while the luminosities of H$\alpha$-like structure in relatively early nebular phase are similar for SNe 1993J and 2008ax (\S 4 in this work, and \citealt{tauben11}), the mass-loss history affecting the interaction power is derived to be very different (\citealt{maund04}; \citealt{folatelli15}), questioning the shock-CSM interaction mechanism as a dominant power source at $< 300$ days. Another possibility is that this emission (before $\sim 300$ days) is powered by the radioactive decay chain. \citet{patat95} argue that the mass of hydrogen envelop of SN IIb is not massive enough to produce such luminous emission through radioactivity, however, \citet{maurer10} suggest that if some amount of hydrogen is mixed into the helium layer, the radioactive decay chain could power the H$\alpha$ emission with a broad and boxy profile, although some assumptions in their scenario remain to be discussed. \citet{jerk15} include [N II] $\lambda \lambda$ 6548, 6583 in their synthetic spectral calculations, and find that the cooling within the He/N zone by [N II] can produce the H$\alpha$-like structure seen in SNe IIb in their sample. Although various scenarios have been proposed, a model-independent (observational and phenomenological) approach, especially based on the statistic behavior of this emission, is missing. As noted before, the early light curve of SNe IIb is powered by the radioactive decay chain, and the peak magnitude is correlated with the mass of $^{56}$Ni produced at the explosion \citep{lyman16}. However, the power provided by shock-CSM interaction has no direct link to the amount of radioactive decay isotopes, as it is mainly affected by the mass-loss history. Therefore, a combined analysis of early and late phase observations will provide clear diagnostic on the power source leading to this feature. In this work, we compare early and nebular observables to distinguish shock-CSM interaction and radioactive power scenarios. We also analyze the luminosity scatter level of this feature, in order to further constrain the identity of the feature. Based on the results of this paper through the model-independent approach, we suggest this emission feature should be powered by the radioactive decay chain. It is more likely [N II] rather than H$\alpha$. This paper is organized as follows. In \S 2, we first introduce the sample of SN IIb used in this paper, together with our methods of light curve and spectrum analyses. Relations between the observables and physical parameters are also briefly summarized in \S 2, which guides the interpretations in the following sections. In \S 3, we compare the observables in early phase with those in nebular phase. The discussion part is given in \S 4, and the paper closes in \S 5. | In this work, we have analyzed the photometric data and nebular spectra compiled for 7 SNe IIb and 2 SNe Ib. We have investigated the power source of the nebular lines, including the origin of the late-time H$\alpha$-like structure seen in these objects. We have further investigated a possible origin of the diversity among these events from a statistic and model-independent approach. In previous works, several scenarios have been proposed as the origin of the H$\alpha$-like structure seen in nebular spectra of SN IIb, at $\sim 200$ days after the maximum brightness. We find a correlation between the luminosity of this emission feature and the mass of $^{56}$Ni produced in the explosion, which is not expected for the shock-CSM interaction scenario. This points to the radioactive decay of $^{56}$Co as a predominant power source of this feature. Further, our analysis clarifies that a level of the scatter in the luminosities of this feature is similar to those of the other metal lines. This is not consistent with the idea that the feature is H$\alpha$ powered by the radioactive decay, as in this case the diversity in the mass of the hydrogen envelope among SNe IIb would create a larger scatter in the luminosities of this H$\alpha$-like feature than other lines. This is further supported by the mass of the hydrogen envelope itself generally inferred for SNe IIb, which is not enough to produce such a luminous emission line \citep{patat95}. We therefore conclude that this line is mainly emitted from the inner layer, and powered by radioactive decay chain. Since [N II] in the He layer is the only candidate from simulations so far, we attribute the origin of this emission as [N II]. While we are not able to robustly exclude other possibilities from our phenomenological and observational approach, this identification provides a picture consistent with the observational constraints we have investigated in this paper. Our conclusion on the origin of this H$\alpha$-like emission, as dominated by [N II] powered by the radioactive decay of $^{56}$Co, is in line with the nebular spectral synthesis models by \citet{jerk15}. In addition to our main analyses presented in this paper, We have further investigated if the variation expected for the masses of N/He layer would be seen as a scatter in the sample of SNe IIb (plus 2 SNe Ib). We do not see such a variation, suggesting either that the progenitor mass range is relatively small for SNe IIb or that the expected variation is absorbed in the dependence on the progenitor mass, or both. Identifying the origin of this feature as [N II] thus has an interesting avenue for further investigation, i.e., a possible difference in the progenitor mass range for SNe IIb, Ib, and Ic, which we will present in a forthcoming paper (Fang et al., in prep.). The H$\alpha$-like structure is also presented in nebular spectra of some SNe Ib (e.g., SN 2007Y and iPTF 13bvn analyzed in this work, and SN 2007C, see~\citealt{tauben09}). If it is [N II] powered by the radioactive decay, whether such an emission is present can be used as an indicator of the level of the He layer stripping. We also find a possible systematic difference in the strengths of the H$\alpha$ structure between the extended SNe IIb (SNe 1993J and 2013df) and the compact ones (SNe 2008ax and 2011dh), already at $\sim 200$ days before the clear shock-CSM signature is observed for the former ($t > 300$ days). The luminosity evolution in very late stage is also compared among different objects. The logarithmic luminosities of the H$\alpha$-like structure and [Ca II] linearly decline before $\sim 250$ days. However, for SNe IIb with an extended envelope, i.e. SNe 1993J and 2013df, a transition takes place at $\sim$ 300 day where the evolution of luminosity of the H$\alpha$-like structure is significantly flattened. In contrast, such a flattening is absent for SNe IIb with a less extended envelope up to $\sim$ 400 days. The luminosities of [O I] and [Ca II] continue to drop for all SNe IIb for which the analysis is possible. The flattening of the evolution of H$\alpha$-like structure luminosity is interpreted as a result of a transition of energy source from radioactivity to shock-CSM interaction. However, the expected level of the shock-CSM contribution is not consistent with the difference between SNe eIIb and cIIb at 200 days, if we assume luminosity from the shock-CSM interaction is constant. Alternatively, the difference may simply reflect the variation of the masses in the H envelope. In any case, this work extends the intrinsic difference among SN IIb, and concludes that the two types of SNe IIb behave differently in nebular phase, which is a topic to be investigated in a forthcoming work (Fang et al. in prep). As an additional analysis, we further investigate a relation between the line ratio of [O I]/[Ca II] and the post-maximum light curve decline rate. The correlation exists, and this finding suggests that the line ratio [O I]/[Ca II] can be an indicator of the progenitor mass and ejecta mass. A systematic study of this line ratio to a sample of SNe IIb/Ib/Ic will be presented in a forthcoming paper (Fang et al. in prep). We note that our result is limited by the relatively small sample size. Our future work aims at enlarging the sample of both nebular spectra and photometric data of SNe IIb, and further extending to SNe Ib and Ic. The analyses we present in this paper can form a solid basis to apply to a larger sample of SNe IIb/Ib/Ic. | 18 | 8 | 1808.02994 |
1808 | 1808.07055_arXiv.txt | \cite{2018MNRAS.480L..28C} recently reexamined the possibility of detecting gravitational waves from exoplanets, claiming that three ultra-short period systems would be observable by LISA. We revisit their analysis and conclude that the currently known exoplanetary systems are unlikely to be detectable, even assuming a LISA observation time $T_{\rm obs}=4$~yrs. Conclusive statements on the detectability of one of these systems, GP Com b, will require better knowledge of the system's properties, as well as more careful modeling of both LISA's response and the galactic confusion noise. Still, the possibility of exoplanet detection with LISA is interesting enough to warrant further study, as gravitational waves could yield dynamical properties that are difficult to constrain with electromagnetic observations. | 18 | 8 | 1808.07055 |
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1808 | 1808.09562_arXiv.txt | By comparing {\MgII} absorption in the circumgalactic medium (CGM) of group environments to isolated galaxies, we investigated the impact of environment on the CGM. A {\MgII} absorber is associated with a group if there are two or more galaxies at the absorption redshift within a projected distance of $D=200$~kpc from a background quasar and a line-of-sight velocity separation of 500~{\kms}. We compiled a sample of 29 group environments consisting of 74 galaxies ($2-5$ galaxies per group) at $0.113<z_{\rm gal}<0.888$. The group absorber median equivalent width ($\langle W_r(2796)\rangle=0.65\pm0.13$~{\AA}) and covering fraction ($f_c=0.89_{-0.09}^{+0.05}$) are larger than isolated absorbers ($1.27\sigma$ and $2.2\sigma$, respectively) but median column densities are statistically consistent. A pixel-velocity two-point correlation function analysis shows that group environment kinematics are statistically comparable to isolated environments ($0.8\sigma$), but with more power for high velocity dispersions similar to outflow kinematics. Group absorbers display more optical depth at larger velocities. A superposition model in which multiple galaxies contribute to the observed gas matches larger equivalent width group absorbers, but overpredicts the kinematics significantly due to large velocity separations between member galaxies. Finally, galaxy--galaxy groups (similar member galaxy luminosities) may have larger absorber median equivalent widths ($1.7\sigma$) and velocity dispersions ($2.5\sigma$) than galaxy--dwarf groups (disparate luminosities). We suggest the observed gas is coupled to the group rather than individual galaxies, forming an intragroup medium. Gas may be deposited into this medium by multiple galaxies via outflowing winds undergoing an intergalactic transfer between member galaxies or from tidal stripping of interacting members. | \label{sec:intro} Extensive work has gone into investigating the role that the baryon cycle plays in forming galaxies and steering their evolution, with particular focus on gas reservoirs such as the circumgalactic medium (CGM). It is well-known that the baryon cycle regulates star formation in galaxies via a balance of inflowing and outflowing gas \citep[e.g.,][]{oppenheimer08, lilly-bathtub}, processes which must take place in and contribute material to the CGM of galaxies. The build-up of material into the CGM results in a gas reservoir with a mass comparable to the interstellar medium \citep[][]{thom11, tumlinson11, werk13, peeples14} out to large distances \citep[$D\gtrsim150$~kpc; e.g.,][and references therein]{chen10a, tumlinson11, rudie12, magiicat2}. Thus, the CGM represents an excellent laboratory for studying the processes which control galaxy evolution, containing remnants of past evolutionary processes and the fuel for future star formation. Using background quasar sightlines probing gas traced by the {\MgIIdblt} absorption doublet (and other ion tracers), we now have a simple picture of the CGM in which gas accretes onto galaxies along their major axis to feed the ISM for future star formation \citep[e.g.,][]{steidel02, ggk-sims, kcn12, stewart11, danovich12, danovich15, martin12, rubin-accretion, bouche13} and gas outflows along the minor axis to further pollute the CGM with metal-enriched gas \citep[e.g.,][]{rubin-winds, rubin-winds14, bouche12, kcn12, martin12, bordoloi14, bordoloi14-model, kacprzak14, schroetter16}. However, the large majority of this body of work has focused on an environment in which only a fraction of galaxies are found: isolated environments. Absorbers associated with groups and clusters of galaxies have often been neglected and largely removed from the analyses. Galaxy evolution is also environment-dependent. Even before the most complex parts of mergers occur, the signatures of galaxy--galaxy interactions are observable. Observations of cool {\HI} gas show a variety of structures due to galaxy interactions in group environments, including tidal streams and filaments, warped disks, and high velocity clouds \citep[e.g.,][]{fraternali02, chynoweth08, sancisi08, mihos12, wolfe13}. Using the Illustris simulations, \citet{hani18} studied the impact of a major merger on the circumgalactic medium and found that the covering fraction of the largest column density gas increases pre-merger and remains elevated for several billion years post-merger. This effect was due to merger-driven outflows rather than tidal stripping. In the FIRE simulations, \citet{angles17} also found that intergalactic transfer, particularly the transfer of gas from the outflows of one galaxy onto another nearby galaxy, is a dominant accretion mechanism of galaxies by redshift $z=0$. These structures and the hierarchical processes that place them between galaxies are an additional level of complexity on top of the isolated galaxy CGM, yet understanding the CGM in these denser environments is necessary for understanding how galaxies grow and evolve. Just as the visible (emitting) portions of galaxies become tidally stripped and disturbed, so should the diffuse (absorbing) material in the CGM undergo complex interactions, and may do so before the visible galaxy due to the large radii involved. In cluster environments, \citet{lopez08} studied {\MgII} and found an overabundance of strong {\MgII} absorbers that is more pronounced at lower impact parameters, suggesting that the halos of cluster galaxies are truncated at 10~kpc \citep[also see][]{padilla09, andrews13}. The authors also found a relative lack of weak absorbers, which are expected to be more easily destroyed in clusters where the numbers are more consistent with those associated with isolated galaxies. Also on an extreme end are ``ultrastrong'' {\MgII} absorbers with $W_r(2796)\geqslant3$~{\AA}. Without determining galaxy redshifts, \citet{nestor07} found evidence for a significant excess of galaxies around quasar sightlines hosting these absorbers compared to random fields, suggesting that group environments may give rise to some fraction of these extreme absorbers in addition to starbursts and very low impact parameter galaxies. Of the three ultrastrong {\MgII} absorbers for which galaxy redshifts have been spectroscopically determined \citep{nestor11, gauthier13}, all were found to be located in group environments and interpreted to be either outflows as the result of interaction-induced star formation, or tidal stripping. In group environments, of which several have been studied, \citet{chen10a} found that the equivalent widths of {\MgII} absorbers in groups were similar to those associated with isolated galaxies, but they did not exhibit an anti-correlation between equivalent width and impact parameter, which has long been known for isolated galaxies \citep[e.g.,][]{lanzetta90, sdp94, ggk08, chen10a, magiicat2}. Using stacked galaxy spectra probing foreground galaxies, \citet{bordoloi11} found that {\MgII} is more extended around groups, and this could be explained by a superposition of the equivalent widths of member group galaxies. Because of this superposition model, the authors suggest that the group environment (i.e., tidal stripping, interaction-induced star formation-driven outflows) does not appear to change the properties of {\MgII} absorbers for individual galaxies. Finally, \citet{whiting06}, \citet{ggk1127}, \citet{bielby17}, and \citet{peroux17} studied the absorption in one or two group environments each and concluded the gas was due to an intragroup medium or tidal interactions depending on the detailed characteristics of the sample. However, \citet{rahmani18} attributed the observed absorption to a single galaxy in the group, partially from the stellar disk and partially accretion onto a warped disk. We focus on a sample of group galaxies compiled during our work to form the {\MgII} Absorber--Galaxy Catalog \citep[{\magiicat};][]{magiicat2, magiicat1, magiicat5, magiicat4, magiicat3}. Because of this, we did not actively seek out galaxies obviously undergoing mergers/interactions and therefore, the galaxies presented here are likely pre-merger but are still expected to show the effects of residing in more dense environments. While the galaxies themselves may not be obviously merging, their CGM is likely already affected by the group environment due to the large radius of the CGM out to roughly 200~kpc, compared to the visible (in emission) portions of the galaxies. The paper is organized as follows: Section~\ref{sec:methods} describes our galaxy and quasar samples, along with our methods for creating a standardized catalog of group absorber--galaxy pairs. Section~\ref{sec:EWD} details the properties of the group sample compared to the isolated {\magiicat} sample for the anti-correlation between {\MgII} equivalent width and impact parameter while Section~\ref{sec:kinematics} examines the absorption kinematics with the pixel-velocity two-point correlation function. These sections also report the results of a superposition model in which multiple galaxies contribute to the CGM of group galaxies. We examine the absorber Voigt profile cloud column densities and velocities in Section~\ref{sec:NvsV}. Section~\ref{sec:discussion} discusses the impact of the group environment on the CGM. Finally, Section~\ref{sec:conclusions} summarizes the work. We adopt a $\Lambda$CDM cosmology ($H_0=70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_M=0.3$, and $\Omega_{\Lambda}=0.7$) and report AB absolute magnitudes throughout this paper. The group catalog presented here has been placed on-line at the NMSU Quasar Absorption Line Group website\footnote{http://astronomy.nmsu.edu/cwc/Group/magiicat} along with the previously published isolated galaxy sample. \begin{figure*}[ht] \includegraphics[width=\linewidth]{Fig1a.pdf} \caption[]{On-the-sky locations and absorption spectra for each group environment with measured {\MgII} absorption and a high-resolution HIRES/Keck or UVES/VLT spectrum. The left panel for each group shows the locations of each group galaxy (red and purple points) in physical space relative to the associated background quasar (black cross). Point sizes represent galaxy luminosity, $L_B/L_B^{\ast}$, with larger points representing more luminous galaxies. Red points represent those absorbers used in our kinematics analysis, while purple are not included in the kinematics analysis. The top panel in each spectrum panel pair shows the {\MgII}~$\lambda 2796$ line, while the bottom panel shows the {\MgII}~$\lambda 2803$ line. Black histograms are the data, red curves are the fit to the spectrum, red ticks are the individual Voigt profile components, and the green data are the error spectrum. Regions of the spectra where we use the pixel velocities for our kinematic analysis are highlighted in gray. The velocity zero points are determined by the optical depth-weighted median of absorption. Measured $W_r(2796)$ values are listed in the left panels for each group. We only have an upper limit on absorption for the J035128$-$142908 (Q0349$-$146) and J104117$+$061016 (Q1038$+$064) fields, and so there are no gray shaded regions.} \label{fig:radecspec} \end{figure*} \addtocounter{figure}{-1} \begin{figure*}[ht] \includegraphics[width=\linewidth]{Fig1b.pdf} \caption[]{(continued) The absorber in J113007$-$144927 (Q1127$-$145), $z_{\rm gal}=0.328$ does not have gray shaded regions because the equivalent width of this absorber is below our equivalent width detection threshold, which we applied to ensure a uniform kinematic sample.} \label{fig:radecspec2} \end{figure*} \begin{figure*}[ht] \centering \includegraphics[scale=0.77]{Fig2.pdf} \caption[]{On-the-sky locations of each group galaxy in physical space for those groups in which we do not have high-resolution spectra of the associated background quasar. However, equivalent widths were measured for each associated absorber and are listed in Table~\ref{tab:calcprops} (including the measurement source), as well as on each panel. Purple points represent each galaxy in the group and the black cross represents the associated background quasar. Point sizes represent galaxy luminosity, $L_B/L_B^{\ast}$, with larger points representing more luminous galaxies. Galaxies in this Figure are not included in the kinematic TPCF analysis, but are included in Figures~\ref{fig:EWD}-\ref{fig:superboot}.} \label{fig:nospecradec} \end{figure*} | \label{sec:conclusions} We presented the {\MgII} Absorber--Galaxy Catalog ({\magiicat}) group sample to complement the isolated sample presented in our {\magiicat} papers \citep{magiicat2, magiicat1, magiicat5, magiicat4, magiicat3}. The group sample consists of 29 {\MgII} absorbers associated with group environments along 27 quasar sightlines for a total of 74 foreground galaxies. The sample is located at $0.113 < z_{\rm gal} < 0.888$ and within $D=200$~kpc of a background quasar sightline. A group is defined as having two or more galaxies within a projected distance of 200~kpc and with a velocity separation of less than 500~{\kms}. With this sample, we examined the absorption properties as a function of galaxy environment and find the following: \begin{enumerate}[nolistsep] \item The median equivalent widths for the group environment sample ($0.65\pm0.13$~{\AA}) are larger than for isolated galaxies ($0.41\pm0.06$~{\AA}) ($1.7\sigma$). \item The equivalent width vs impact parameter anti-correlation may be flatter for galaxies in group environments than those in isolated environments, where a rank correlation test is marginally significant for the group environment sample at $2.9\sigma$ compared to $7.9\sigma$ for isolated galaxies. If we assign the most luminous galaxy in the group as the absorber host, then the slope of the $W_r(2796)-D$ fit is significantly flatter than for isolated galaxies. The slopes are consistent within uncertainties when the group galaxy nearest to the quasar sightline is assumed to host the observed absorption. \item The covering fraction of {\MgII} in group environments, $f_c=0.89_{-0.09}^{+0.05}$, are larger than for isolated galaxies, $f_c=0.68_{-0.03}^{+0.03}$, although this is marginally significant at the $2.2\sigma$ level. \item Using the pixel-velocity TPCF method to study absorber kinematics, we found that while the velocity dispersion of absorbers in group environments is consistent within uncertainties compared to those in isolated environments ($0.8\sigma$), the group kinematics trend towards larger dispersions with more power at $\Delta v_{\rm pixel}=200$~{\kms}. \item The type of merger activity may influence the CGM properties. Groups in which the two brightest galaxies have similar luminosities (galaxy--galaxy; $L_1/L_2<3.5$) have $1.7\sigma$ ($1.8\sigma$) larger median (median) equivalent widths and larger absorber velocity dispersions ($2.5\sigma$) than in galaxy--dwarf groups ($L_1/L_2\geq3.5$). However, their covering fractions are comparable within uncertainties, with $f_c=0.95_{-0.11}^{+0.04}$ for galaxy--galaxy groups and $f_c=0.78_{-0.22}^{+0.14}$ for galaxy--dwarf groups. \item The distribution of fitted cloud column densities are consistent within uncertainties between the group and isolated samples. Absorbers in the group sample have a comparable number of clouds but a significantly ($3.3\sigma$) larger fraction of high velocity clouds, $v\geq 100$~{\kms}, than for the isolated sample. When only galaxy--galaxy group environments are compared to the isolated sample, the fraction of high velocity clouds in groups is increased. \item A superposition of individual group galaxy CGM results in equivalent widths that are comparable to the measured values in the group sample for the strongest absorbers. The model also finds a covering fraction of $f_c=0.83_{-0.01}^{+0.03}$, which is similar to the observed values. However, the superposition model is too simplistic to explain the observed TPCF (kinematic) distributions, where a proper superposition results in absorption velocity dispersions that are much too large. \item The group absorber kinematics appear similar to the kinematics of presumably outflowing gas around face-on galaxies probed along their minor axis (see {\magiicat} V). This suggests that the gas in group environments may be agitated similarly to that entrained in outflowing winds in isolated galaxies. \item We argue that the evidence presented here supports a model where the absorption associated with group environments forms an intragroup medium in which one or more galaxies contribute material, and where galaxy interactions distribute the gas throughout the group halo. The gas may be dispersed by outflows from one galaxy entering the intragroup medium and eventually falling onto another group member galaxy (intergalactic transfer) and/or by tidal stripping from interactions that remove gas from one galaxy and place it in the intragroup medium. \item Comparing our results to {\CIV} and {\OVI} in group environments, we find that the low and higher ions behave differently compared to their respective isolated samples, presenting further evidence that these ions trace different components within the CGM and intragroup medium. \end{enumerate} To better understand the gas traced by {\MgII} absorption, it would be helpful to examine the kinematics of the gas relative to the galaxy. While we have shown that absorbers associated with group galaxies have larger velocity dispersions, we do not yet know if the gas is being stripped from galaxies, accreting, or if the gas is truly associated with a single galaxy or not. We have statistically shown that the absorption is likely coupled to the group in an intragroup medium rather than individual galaxies, but the complexity of galaxy interactions may mean this is not always the case. More accurate galaxy redshifts and rotation curves, estimates of galaxy star formation rates, and deep surface brightness, high spatial resolution imaging of the galaxies in groups will improve the situation. | 18 | 8 | 1808.09562 |
1808 | 1808.00991_arXiv.txt | In our ongoing study of $\eta$~Carinae's light echoes, there is a relatively bright echo that has been fading slowly, reflecting the 1845-1858 plateau phase of the eruption. A separate paper discusses its detailed evolution, but here we highlight one important result: the H$\alpha$ line in this echo shows extremely broad emission wings that reach $-$10,000~km~s$^{-1}$ to the blue and $+$20,000~km~s$^{-1}$ to the red. The line profile shape is inconsistent with electron scattering wings, so the broad wings indicate high-velocity outflowing material. To our knowledge, these are the fastest outflow speeds ever seen in a non-terminal massive star eruption. The broad wings are absent in early phases of the eruption in the 1840s, but strengthen in the 1850s. These speeds are two orders of magnitude faster than the escape speed from a warm supergiant, and 5--10 times faster than winds from O-type or Wolf-Rayet stars. Instead, they are reminiscent of fast supernova ejecta or outflows from accreting compact objects, profoundly impacting our understanding of $\eta$~Car and related transients. This echo views $\eta$~Car from latitudes near the equator, so the high speed does not trace a collimated polar jet aligned with the Homunculus. Combined with fast material in the Outer Ejecta, it indicates a wide-angle explosive outflow. The fast material may constitute a small fraction of the total outflowing mass, most of which expands at $\sim$600 km s$^{-1}$. This is reminiscent of fast material revealed by broad absorption during the presupernova eruptions of SN~2009ip. | The massive evolved star $\eta$ Carinae serves as a tremendous reservoir of information about episodic mass loss in the late-stage evolution of massive stars. It is uniquely valuable because it is nearby, because it underwent a spectacular ``Great Eruption'' event observed in the mid-19th century, and because we can now observe the spatially resolved shrapnel of that event with modern tools like the {\it Hubble Space Telescope} ({\it HST}). Added to this list is the recent discovery of light echoes from the 19th century eruption \citep{rest12}, which now allow us to obtain spectra of light from an event that was seen directly by Earth-based observers before the invention of the astronomical spectrograph. This is similar to studies of light echoes from historical supernovae (SNe) and SN remnants in the Milky Way and Large Magellanic Cloud \citep{rest05a,rest05b,rest08}. Spectroscopy of these light echoes provides informative comparisons between $\eta$ Car and extragalactic eruptions. Based mostly on its historical light curve \citep{sf11}, $\eta$ Car has been a prototype for understanding luminous blue variable (LBV) giant eruptions and SN impostors \citep{smith+11,vdm12}. Eruptions akin to $\eta$ Car have been discussed in the context of brief precursor episodes of extreme mass loss that create circumstellar material (CSM) of super-luminous Type~IIn supernovae \citep{smith+07,sm07}. In addition to extreme $\eta$ Car-like mass loss, several lines of evidence connect LBVs and SNe with dense CSM (see \citealt{smith14} for a review; also e.g., \citealt{gl09,groh13,groh14,justham14,kv06,mauerhan13,so06,smith07,smith+08,smith+11,trundle08}). LBVs have the highest known mass-loss rates of any stars before death, where LBV giant eruptions can lose as much as several $M_{\odot}$ in a few years (see \citealt{smith14}). The physical trigger and mechanism of these LBV-like giant eruptions are still highly uncertain. Eruptive mass loss is usually discussed in the context of super-Eddington winds \citep{davidson87,og97,owocki04,os16,q16,so06,vanmarle08}. This framework addresses how mass can be lost at such a high rate, but it does not account for where the extra energy comes from. There are also (sometimes overlapping) scenarios that have been discussed, involving binary mergers, stellar collisions, violent common envelope events, accretion events onto a companion (perhaps including compact object companions, although this has not been discussed much for $\eta$ Car), violent pulsations, extreme magnetic activity, pulsational pair instability eruptions, unsteady or explosive nuclear burning, and wave driving associated with late nuclear burning phases approaching core collapse \citep{jsg89,fuller17,gl12,hs09,ks09,pz16,piro11,qs12,sq14,smith11,sa14,smith+11,smith+16,soker01,soker04,woosley17}. In any case, a tremendous amount of mass (several $M_{\odot}$) leaves the star in a brief window of time (a few years), and observational constraints on the outflow properties provide a key way to guide theoretical interpretation. In general, quasi-steady radiation-driven winds are expected to leave a star with a speed that is within a factor of order unity compared to the escape speed from the star's surface. That is why red supergiant winds are slow (10s of km s$^{-1}$), blue supergiant winds are a few hundred km s$^{-1}$, O-type stars have winds around 1000 km s$^{-1}$, and more compact H-poor Wolf-Rayet star winds are 2000-3000 km s$^{-1}$ (see \citealt{smith14} for a review). For example, line-driven winds of hot O-type stars have a ratio of their terminal wind to the star's escape speed of $v_{\infty}/v_{\rm esc} \approx 2.6$, and cooler stars below about 21,000 K have $v_{\infty}/v_{\rm esc} \approx 1.3$ \citep{lamers95,vink99}. Line driven wind theory and observations indicate that $v_{\infty}/v_{\rm esc} \approx 2.6$ is expected to become lower as the star's temperature drops \citep{cak,abbott82,pauldrach86,pp90,lamers95,vink99}. For a strongly super-Eddington wind in an LBV, where $\Gamma$ substantially exceeds 1, the effective gravity is low, the stellar envelope may inflate, the wind may show a complicated pattern of outflow and infall, and material may ultimately leak out slowly. The atmosphere may be porous \citep{owocki04}, perhaps leading to a range of outflow speeds, but we don't expect a steady wind-driven outflow with a high mass-loss rate to be many times faster than a star's escape speed \citep{owocki04,vanmarle08,owocki17}. Numerical simulations of super-Eddington continuum-driven winds predict terminal wind speeds below the star's surface escape speed \citep{vanmarle08,vanmarle09}. Observationally, a wide range of outflow speeds are seen in the $\eta$ Car system. The bulk outflow of the present-day wind is around 400-500 km s$^{-1}$ \citep{hillier01}, although with some faster speeds up to around 1000 km s$^{-1}$ in the polar wind \citep{smith+03}. The bipolar Homunculus nebula, which contains most of the mass ejected in the 19th century eruption \citep{morse01,smith17} has a range of speeds that vary with latitude from 650 km s$^{-1}$ at the poles to about 50 km s$^{-1}$ in the pinched waist at the equator \citep{smith06}. However, there is also faster material in the system. Hard X-ray emission from the colliding-wind binary suggests that a companion star has a very fast wind of 2000-3000 km s$^{-1}$ \citep{corcoran01,pc02,parkin11,russell16}. In spectra of the central star system, speeds as fast as $-$2000 km s$^{-1}$ are only seen in absorption at certain phases, attributed to the companion's wind shocking the primary star's wind along our line of sight \citep{groh10}. So far, the fastest material associated with $\eta$ Car has been seen in the Outer Ejecta, where filaments have speeds based on Doppler shifts and projection angles as high as 5000 km s$^{-1}$ \citep{smith08}. (Most of the Outer Ejecta seen in images are slower, moving at a few hundred km s$^{-1}$; \citealt{kiminki16,weis12}.) This fast material, combined with the high ratio of kinetic energy to total radiated energy in the eruption \citep{smith03}, has led to speculation that the Great Eruption may have been partly caused by a hydrodynamic explosion \citep{smith06,smith08,smith13}. Spectra of $\eta$ Car's light echoes \citep{rest12,prieto14} also seemed inconsistent with traditional expectations for a simple wind pseudo-photosphere \citep{davidson87}, although \citet{os16} showed that proper treatment of opacity and radiative equilibrium in such a wind may lead to cool temperatures around 5000~K. Well-developed models for sub-energetic and non-terminal explosive events do not yet exist, but an explosive ejection of material and a surviving star might arise if energy is deposited in the star's envelope that is less than the total binding energy of the core, but enough to unbind the outer layers. \citet{dessart10} explored how stellar envelopes might respond to such energy deposition, and found some cases with partial envelope ejection and model light curves reminiscent of SN impostors. \citet{rm17} argued that any deep energy deposition at a rate that substantially exceeds the steady luminosity of the star is likely to steepen to a shock. For the specific case of $\eta$~Car's eruption, \citet{smith13} argued that an explosive ejection of fast material interacting with a previous slow wind could account for the historical light curve and several properties of the Homunculus, where CSM interaction leads to efficient radiative cooling as in SNe~IIn. In this paper, we present evidence based on Doppler shifts in light echo spectra from the Great Eruption, which show that there was in fact an explosive ejection of very fast material relatively late in the eruption. The observed speeds in excess of 10,000 km s$^{-1}$ suggest that a small fraction of the mass was accelerated to very high speeds by a blast wave, confirming similar conclusions based on fast nebular ejecta observed around the star at the present epoch \citep{smith08,smith13}. \begin{table}\begin{center}\begin{minipage}{3.1in} \caption{Optical Spectroscopy of Light Echo EC2} \scriptsize \begin{tabular}{@{}lcccccc}\hline\hline UT Date &Tel./Intr. &grating &$\Delta\lambda$ (\AA) &slit &PA \\ \hline 2014 Nov 03 &Gemini/GMOS &R400 &5000-9200 &1$\farcs$0 &293$^{\circ}$ \\ 2015 Jan 20 &Baade/IMACS f4 &1200 &5500-7200 &0$\farcs$7 &293$^{\circ}$ \\ 2015 Jan 20 &Baade/IMACS f4 &300 &4000-9000 &0$\farcs$7 &293$^{\circ}$ \\ \hline \end{tabular}\label{tab:spec}\end{minipage} \end{center} \end{table}% | This paper presents spectra of light echoes from $\eta$~Carinae that correspond to the time period of the main plateau of the eruption during the late 1840s through the 1850s. The full spectral evolution, photometry, and other details of this echo will be discussed in a forthcoming paper (S18). Here we focus on one important aspect that is significant on its own, which is the discovery of extremely broad emission wings of H$\alpha$ that represent the fastest material ever detected in an LBV-like eruption. The main results from this work are summarized as follows. 1. In addition to a relatively narrow (600 km s$^{-1}$) line core, H$\alpha$ displays extremely broad wings in emission, reaching to approximately $-$10,000 km s$^{-1}$ to the blue and $+$20,000 km s$^{-1}$ or more on the red wing. 2. We demonstrate that the broad wings are not instrumental. They are not present in a nearby field star included in the same slit, and moreover, the same broad wings are seen in spectra obtained with different instruments on different telescopes as well as two different gratings on the same spectrograph. The strength of the broad wings changes with time, and the broad emission is not seen in a different echo that traces earlier epoch in the eruption seen from a similar direction. Correcting for the telluric B-band absorption, the red wing clearly extends to $+$20,000 km s$^{-1}$ or more. 3. The shape of the broad wings is inconsistent with electron scattering wings, and we argue that the broad emission must trace Doppler shifts from bulk expansion velocities. Therefore, these are the highest outflow speeds discovered yet in an LBV or any non-terminal eruptive transient. 4. The high velocities are too fast for any previously conceived escape velocity in the system, but similar to outflow speeds from accreting compact objects or expansion speeds of SN ejecta. The expanding material probably does not arise in a steady wind, but instead likely indicates a shock-accelerated outflow. 5. The broad wings are seen in echo spectra that view $\eta$~Car from the equator, so these high speeds are probably not indicative of a polar jet (even one from a compact object). The high speeds in echoes seen from the equator combined with fast polar speeds in the Outer Ejecta seen today \citep{smith08} suggest a wide-angle explosion rather than a highly collimated jet. 6. The viewing angle of this echo could be special, however, since it is looking from a similar direction as the ``S Condensation'' in the Outer Ejecta. This is also a special direction in the present day binary system, since it is situated preferably to view the wide companion plunge into a putative common envelope, for example (see text). 7. Regardless of the physical interpretation, the dual presence of fast and slow speeds (10,000-20,000 km s$^{-1}$ and 600-1000 km s$^{-1}$, respectively) point to CSM interaction at work in the eruption. They are also similar to slow and high velocities seen in spectra of the eruptive progenitor of SN~2009ip. Therefore, the high velocities in $\eta$ Car provide yet another interesting possible link between LBVs and SNe~IIn. | 18 | 8 | 1808.00991 |
1808 | 1808.05099_arXiv.txt | Asteroid mining offers the possibility to revolutionize supply of resources vital for human civilization. Preliminary analysis suggests that Near-Earth Asteroids (NEA) contain enough volatile and high value minerals to make the mining process economically feasible. Considering possible applications, specifically the mining of water in space has become a major focus for near-term options. Most proposed projects for asteroid mining involve spacecraft based on traditional designs resulting in large, monolithic and expensive systems. An alternative approach is presented in this paper, basing the asteroid mining process on multiple small spacecraft. To the best knowledge of the authors, only limited analysis of the asteroid mining capability of small spacecraft has been conducted. This paper explores the possibility to perform asteroid mining operations with spacecraft that have a mass under 500 kg and deliver 100 kg of water per trip. The mining process considers water extraction through microwave heating with an efficiency of 2 Wh/g.The proposed, small spacecraft can reach NEAs within a range of $\sim 0.03$ AU relative to earth's orbit, offering a delta V of 437 m/s per one-way trip. A high-level systems engineering and economic analysis provides a closed spacecraft design as a baseline and puts the cost of the proposed spacecraft at \$ 113.6 million/unit. The results indicate that more than one hundred spacecraft and their successful operation for over five years are required to achieve a financial break-even point. Pros and cons of using small spacecraft swarms are highlighted and the uncertainties associated with cost and profit of space related business ventures are analyzed. | Asteroids are celestial bodies that are of fundamental scientific importance for uncovering the formation, composition and evolution of the solar system \cite{badescu2013asteroids}. Moreover, mining an asteroid for useful resources is a concept that even predates modern space programs, as an idea initially proposed in the early $20^{th}$ century by Konstantin Tsiolkovsky. More recent analysis suggests that specifically Near-Earth Asteroids (NEAs) are close enough and could contain trillions of dollars worth of precious metals and minerals, potentially making the endeavor feasible \cite{hellgren2016asteroid,sanchez2011asteroid,ASTRA2010}.Useful reservoirs of important substances may be found, such as water, metals and semiconductors \cite{sanchez2012assessment}. The extraction of volatiles is currently the most realistic near-term asteroid mining application. Therefore, several concepts for extraction and supply of water were developed recently \cite{badescu2013asteroids}. These concepts consider water extraction for refueling of spacecraft, radiation shielding, and potable water for life support systems in outer space \cite{hellgren2016asteroid}. In the last twenty years, a vast amount of data and results from space missions have been collected. Observations from spacecraft are mainly used to complement theories and findings which were deduced from ground based asteroid data \cite{badescu2013asteroids}. Although a full scale exploitation of space resources has not been achieved yet, some minimal asteroid samples have been retrieved for analysis and testing on earth. The number of discovered NEAs goes beyond 15000, with an average of 30 new asteroids discovered per week \cite{JPL-CNEOS}. However, estimates from ground based observations do not guarantee the accurate composition of asteroid candidates. Therefore, spacecraft are required for in-situ measurements complementing the data and establishing a clear candidate for exploitation. Current missions for asteroid mining consider spacecraft prospection as a first step before the extraction process. Prospection itself usually falls into three different phases \cite{badescu2013asteroids}: discovery, remote characterization, local characterization. These last two characterization phases are endeavors currently pursued by asteroid mining companies using small spacecraft\cite{PlanetRes}. However, recent advances in the miniaturization of spacecraft components and mining equipment may allow for a more cost effective and reliable approach to mine NEAs overall. We propose and analyze a mission architecture focusing on the utilization of small spacecraft for the asteroid mining cycle. This includes local prospecting, mining, and return of relevant substances. Focusing on the extraction of volatiles as a first step, we conduct a survey of water mining techniques, other relevant technologies, and past missions. Using standard space systems engineering techniques a trade-off analysis is conducted to select a suitable mission architecture and spacecraft design. We identify the high level challenges facing asteroid mining, highlight where technological improvements are required, and present a road map for implementation. Conducting an analysis of the costs involved in establishing mining operations, constraints are derived on the economic feasibility of asteroid mining using the proposed architecture. The constraints reveal that the number of spacecraft and the target market for the retrieved volatiles is essential to achieve a break-even point. | For the presented asteroid mining architecture, utilizing spacecraft designed to be below 500 kg in weight, the maximum distance to asteroid rendezvous from LEO is approximately 0.03 AU. From the corresponding delta-V of 437 m/s the NEAs that can be reached contain more than one million liters of water. The economic analysis shows that using swarms of smaller spacecraft around 200 units are required to achieve an economically feasible operation within 10 years of operation. The concept has the advantages that it allows for rapid scaling up of mining operations and implements redundancy on the system level. Even for the 200 spacecraft fleet required to reach break-even in less than 10 years the up-front investment of $\approx \$7$ billion is below major acquisitions currently happening in our terrestrial economy, e.g. Amazon bought Whole Foods for \$13.7 billion in 2017 and the Vision Fund acquired \$93 billion during their 2017 funding round. Finally, the sensitivity analysis has shown that the mass-produced spacecraft cost is only weakly dependent on rising launch costs, thus allowing for maximization of profits from potentially rising water prices. On the other hand, the concept does not become profitable in less than 8 years and does not significantly profit from decreasing launch prices, within the parameter space explored. The sensitivity analysis also indicates that using a very large number of spacecraft can lead to a non-linear increase in overall cost for unexpectedly low benefits from mass production (as embodied by the learning curve slope parameter $S$). Therefore, an intermediate number of spacecraft seems a ideal, at which break-even is possible within 10 years but the cost dependence on $S$ is still linear. In the work presented, this number lies between 200 and 350 spacecraft. Lowering the launch cost by using rideshare opportunities does not make the proposed mission architecture profitable within 10 years for small numbers of spacecraft. This assumes that ridesharing should not be pursued once its cost per spacecraft exceeds the cost of booking a full heavy launcher. With regard to target markets, the analysis identified cis-lunar space as the use-case most likely to make steroid water mining economically feasible. Customers in this sector include lunar and lunar-orbit bases, transiting Astronauts, so-called deep space gateways (space stations), and operations in the L2 Lagrange point of the Earth-Moon system. The analysis makes it obvious that further development and research is required to make asteroid mining more attractive for investors and more likely to succeed in general. The authors identified several areas that, if improved, would contribute to this goal: \begin{itemize} \item Further miniaturization of spacecraft components will reduce component and launch cost significantly for a large number of spacecraft. \item Water extraction techniques need to be explored further and qualified for usage with actual asteroid material. Water needs to be extracted in an efficient and effective manner, as that directly impacts spacecraft power requirements and the amount of water that can be extracted in a given time frame. \item Water and water-derived fuel propulsion systems need to reach higher efficiency levels and achieve a sufficient TRL. \item Much larger, monolithic mining spacecraft, including asteroid capturing concepts, represent alternative mission architectures for asteroid mining. Inter-comparison of economic feasibility between small, medium, and large spacecraft concepts will provide important information regarding the most promising path to take in the future. \end{itemize} | 18 | 8 | 1808.05099 |
1808 | 1808.07780_arXiv.txt | M dwarfs are prime targets in the hunt for habitable worlds around other stars. This is due to their abundance as well as their small radii and low masses and temperatures, which facilitate the detection of temperate, rocky planets in orbit around them. However, the fundamental properties of M dwarfs are difficult to constrain, often limiting our ability to characterise the planets they host. Here we test several theoretical relationships for M dwarfs by measuring 23 high precision, model-independent masses and radii for M dwarfs in binaries with white dwarfs. We find a large scatter in the radii of these low-mass stars, with 25 per cent having radii consistent with theoretical models while the rest are up to 12 per cent over-inflated. This scatter is seen in both partially- and fully-convective M dwarfs. No clear trend is seen between the over-inflation and age or metallicity, but there are indications that the radii of slowly rotating M dwarfs are more consistent with predictions, albeit with a similar amount of scatter in the measurements compared to more rapidly rotating M dwarfs. The sample of M dwarfs in close binaries with white dwarfs appears indistinguishable from other M dwarf samples, implying that common envelope evolution has a negligible impact on their structure. We conclude that theoretical and empirical mass-radius relationships lack the precision and accuracy required to measure the fundamental parameters of M dwarfs well enough to determine the internal structure and bulk composition of the planets they host. | The discovery of a super-Earth orbiting the nearby (14.6\,pc) M4.5 dwarf GJ\,1214 \citep{charbonneauetal09-1} via photometric follow-up of individual M-dwarfs \citep{nutzman08} and the recent radial-velocity detection of an Earth-mass planet at Proxima Centauri \citep{anglada-escude16-1} demonstrates the enormous potential of planet searches focusing on low-mass stars, as their small radii and low masses substantially facilitate the discovery of smaller planets compared to planet searches at FGK stars. Consequently, M-dwarfs are now key targets of many transit and radial surveys, e.g. NGTS \citep{wheatley18}, SPECULOOS \citep{delrez18} and CARMENES \citep{reiners18}. In particular, TESS will survey the brightest and closest M-dwarfs for transiting planets \citep{rickeretal15-1}, substantially increasing the number of known exoplanets orbiting low-mass stars \citep{ballard18-1}. The identification of several temperate Earth-sized planets orbiting low-mass stars \citep{dittmannetal17-1, gillonetal16-1, gillonetal17-1}, combined with the fact that M-dwarfs are the most numerous stars in the Milky Way, has led to considerable interest in the habitability of these worlds \citep{seager13-1, wandel18-1, kopparapuetal17-1}. A fundamental limitation in the characterisation of exoplanets is that the derived bulk parameters, including masses, radii, and densities, require accurate knowledge of the planet host properties. Accurate planet radii and masses (which require accurate stellar radii and masses) are required to gauge insight into their internal structure and bulk composition. \citet{valenciaetal07-1} argued that planet radius measurements to better than 5\% and mass measurements to better than 10\% are necessary to distinguish between rocky and icy bulk composition, and even then, details of the interior composition are model-dependent \citep{rogers+seager10-1, dornetal15-1}. It has been well established that the measured radii of low-mass stars ($<$0.6\,\MSUN) are larger than predicted by evolutionary models, by up to 10-20 per cent \citep{lopezmorales05}. This is thought to be caused by the fact that virtually all precise mass-radius measurements of low-mass stars come from stars in close binaries\footnote{While accurate parallaxes help to constrain stellar radii of single stars if their effective temperature can be empirically constrained, their masses require additional information, such as an independent measure of their surface gravity from planet transits \citep{stassunetal17-1, southworthetal07-6}, or from their granulation-driven variability \citep{stassunetal18-1} and hence remain limited in their accuracy.}. These stars are tidally locked and are hence rapid rotators and magnetically active. This activity is thought to lead to a cooler and larger star \citep{morales08} and can therefore explain the over-inflation, an idea supported by the fact that the interferometrically-measured radii of isolated, inactive low-mass stars appear more consistent with evolutionary models \citep{demory09}. Magnetic activity can also explain the 14 per cent larger radii of young low-mass stars in the Pleiades cluster \citep{jackson18}. However, the reality is more complicated than this, as there are several relatively inactive nearby low-mass stars with interferometric radii more than 15 per cent too large \citep{berger06} and there are stars in long period, slowly rotating binaries that are also oversized \citep{doyle11,irwin11}. Conversely, there are rapidly rotating low-mass stars in close binaries that have radii consistent with evolutionary models \citep{blake08}, and some binaries where one component has a consistent radius and its companion is oversized \citep{kraus17}, implying that there are a number of different factors that affect the over-inflation beyond enhanced magnetic activity. Recent work from \citet{kesseli18} also shows that neither rotation nor binarity is responsible for the inflated radii of low-mass stars. The number of precisely characterised low-mass stars is still low, due mainly to their faintness. Pairs of eclipsing low-mass stars are still the benchmark systems for such measurements \citep{lopezmorales07}, but few are known and fewer still are bright enough to be studied at high precision. Moreover, the effects of starspots on both stars makes modeling their light curves complex. Low-mass stars in eclipsing binaries with more massive solar-type stars are more numerous and brighter, but the large brightness contrast between the two stars often means that the M star is essentially undetectable spectroscopically, meaning that not only are these single-lined binaries (making them less ideal for testing evolutionary models), but precise temperature measurements for the M star are extremely challenging. Interferometric studies of isolated low-mass stars can yield very precise radii, but lack the mass precision provided by binary systems and are limited to a few nearby bright stars. One type of system that is often overlooked is low-mass stars in detached eclipsing binaries with white dwarfs. More than 3000 white dwarf plus main-sequence star binaries are known \citep{rebassa16,ren18}, including more than 70 eclipsing systems \citep{parsons15}. The small size of the white dwarf (roughly Earth sized) results in very sharp eclipse features that can be used to measure radii to very high precisions (1-2 per cent in the best cases, e.g. \citealt{parsons10}). Moreover, in most cases both the white dwarf and low-mass star are visible in optical spectra, making these double-lined binaries. Low-mass stars are roughly 10 times larger than white dwarfs, meaning that the eclipse of the white dwarf is total and a clean spectrum of the low-mass star can be obtained without contamination from the white dwarf. Finally, the cooling of white dwarfs is well understood, making them ideal objects for constraining the ages of their low-mass stellar companions. It should be noted that these systems have experienced a brief common envelope phase in their past evolution, when the progenitor star of the white dwarf evolved off the main-sequence. During the common envelope phase (or rather shortly prior to it) mass was transferred to the low-mass star. However, this phase is extremely short ($10^3-10^4$\,years) compared to the thermal timescale of a low-mass star ($10^8-10^9$\,years) and so has a negligible effect on the star. The common envelope itself possesses much higher specific entropy than the surface of the M dwarf, meaning that the star is thermally isolated from the common envelope and hence essentially no accretion takes place \citep{hjellming91}. In this paper we present 16 high precision mass and radius measurements for M dwarfs in eclipsing binaries with white dwarfs. Along with another 7 previously studied systems we also determine the effective temperatures, metallicities and ages of these stars and compare these to the predictions of evolutionary models. | \begin{figure} \begin{center} \includegraphics[width=\columnwidth]{PvR.eps} \caption{The over-inflation of M dwarfs as a function of their orbital period. Note that many stars in systems with periods longer than a few days are not synchronously rotating (usually rotating slower than the binary period) and generally have moderately eccentric orbits.} \label{fig:period} \end{center} \end{figure} We have presented high-precision mass, radius, effective temperature and age measurements for 23 M dwarfs in eclipsing binaries with white dwarfs, 16 of which are new results. We have also determined the metallicities for 13 of these objects. On average the radii of these stars are $6.2\pm4.8$ per cent larger than theoretical models predict, although they show a large amount of scatter, and around a quarter of them have measured radii consistent with models. No difference is seen between partially and fully convective stars. The fact that all of these stars are rapid rotators means that enhanced activity leading to the suppression of convection cannot be the only cause of the discrepancy in the radii of low-mass stars. We find that the measured temperatures of very low-mass M dwarfs ($< 0.2$\MSUN) are in agreement with theoretical models, but more massive stars are systematically cooler than models predict by $\sim$100\,K. Finally, we find no clear trend in the over-inflation of M dwarfs as a function of age or metallicity, but do find that M dwarfs rotating slower than $\sim$5 days have on average radii more consistent with models, although there is a similar amount of scatter compared to more rapidly rotating M dwarfs. The results presented in this paper demonstrate the difficulty in determining reliable parameters for low mass stars and by extension any planets that they may host. The use of theoretical or empirical relations may still lead to errors of 5--10 per cent in the radii of exoplanets around M dwarfs, generally insufficient to constrain their internal structure and bulk composition. | 18 | 8 | 1808.07780 |
1808 | 1808.02670_arXiv.txt | In this work, we report on the detection of enhanced TeV $\gamma$- ray emission from the high synchrotron-peaked blazar Mrk 421 with the TACTIC telescope on the night of December 28, 2014 (MJD 57019). We use data from the TACTIC observations of Mrk 421 for one week during December 25-31, 2014 (MJD 57016-57022) in this study. The TACTIC observation on December 28, 2014 (MJD 57019) alone results in the detection of 86$\pm$17 $\gamma$- ray like events from Mrk 421 with a statistical significance of 5.17$\sigma$ in a livetime of $\sim$ 2.2 hours above an energy threshold of 0.85 TeV. The high statistics (higher than three Crab Units) of TeV photons enables us to study the very high energy (VHE) $\gamma$- ray emission from the source at shorter timescales. A minimum variability timescale of $\sim$ 0.72 days is obtained for the TeV $\gamma$- ray emission from Mrk 421 during the above flaring activity of the source. The intrinsic VHE spectrum is described by a power law with spectral index of 2.99$\pm$0.38 in the energy range 0.85--8.5 TeV. The integral VHE $\gamma$- ray flux above 0.85 TeV is determined to be (3.68$\pm$0.64)$\times$10$^{-11}$ ph~cm$^{-2}$~s$^{-1}$ from the TACTIC observations of Mrk 421 on the night of December 28, 2014 (MJD 57019). Near simultaneous measurements by the HAWC observatory give an integral flux of (2.90$\pm$0.40)$\times$10$^{-11}$ ph~cm$^{-2}$~s$^{-1}$ above 2 TeV from Mrk 421 observations on December 29, 2014 (MJD 57020.33-57020.58). We have also analyzed the contemporaneous data from \emph{Fermi}-LAT to study the high energy (HE) $\gamma$--ray emission during the high activity state of the source. The HE $\gamma$--ray emission is observed to be increasing after the TeV flaring activity detected with the TACTIC. We also use other near simultaneous archival data available from the \emph{Swift}-BAT in hard X-rays and from SPOL at Steward Observatory in optical V and R bands to characterize the multi-wavelength emission of Mrk 421 during the high activity state observed at TeV energies. The TeV $\gamma$- ray emission observed on December 28, 2014 (MJD 57019) is found to be more prominant than the emissions in lower energy bands during the same period. The TeV $\gamma$- ray observation of Mrk 421 in high activity state with the TACTIC telescope is also used to understand the physical mechanism for blazar emission under the frame work of the leptonic single zone synchrotron self Compton process. | Mrk 421 is a relatively nearby blazar located at a distance of $\sim$ 135 Mpc (redshift z=0.031) in the extragalactic sky [1]. It has been classified as the high synchrotron-peaked (HSP) blazar on the basis of the position of synchrotron peak frequency ($\nu_{syn}^p \ge 10^{15}$Hz) in the spectral energy distribution (SED) of blazars, which is generally characterized by a double hump structure [2]. Mrk 421 is one of the well studied and strongest TeV $\gamma$- ray sources in the northern hemisphere. Motivated with the detection of high energy (HE) $\gamma$- ray emission from Mrk 421 above 100 MeV by \emph{EGRET} for the first time in 1991 [3], the source was selected as a prime TeV candidate for very high energy (VHE) $\gamma$- ray observation with the ground based Whipple telescope. In March-June 1992, the Whipple telescope discovered the first unambiguous VHE $\gamma$- ray emission from Mrk 421 with a statistical significance of 6$\sigma$ above 0.5 TeV and an integral flux of 30$\%$ of the Crab Nebula flux [4]. After Whipple observations, Mrk 421 became the first extragalactic source detected at TeV energies. Since its discovery at TeV energies, Mrk 421 has been observed to exhibit episodes of strong flaring activities over the entire electromagnetic spectrum from TeV $\gamma$- rays to radio energies on several occasions. During 1993-2004, the Whipple telescope detected many dramatic outbursts at TeV energies from Mrk 421 with doubling timescales from hours to less than 15 minutes [5,6] and for the first time spectral hardening of TeV $\gamma$- ray emission during the flare was observed in a blazar [7,8]. The MAGIC telescope observed TeV $\gamma$- ray emission from this source in 2004 [9] followed by first simultaneous observation of X-ray and TeV flares in 2006 [10]. Subsequently, this blazar had been regularly monitored by all the ground based $\gamma$- ray telescopes with the detection of various flaring activities from the source [11,12,13]. Again, a major outburst at all energies was observed from Mrk 421 in February 2010 by various ground and space based instruments. At TeV energies, this flaring activity was detected by VERITAS, HESS, TACTIC, HAGAR and ARGO-YBJ detectors [14,15,16,17,18,19,20]. Apart from the detection of multiple short-term flaring activities from Mrk 421 during the last two decades, many long term multi-wavelength observations of the source are also reported in the literature by various telescopes including TACTIC [21,22,23,24,25,26,27,28,29,30]. An integral baseline flux of 33$\%$ of the Crab Nebula flux above 1 TeV has been derived for Mrk 421 using a combination of data collected during 1991-2009 [31]. \par Blazars are radio-loud active galactic nuclei (AGNs) powered by accretion on to the supermassive black holes in the Universe. They are characterized by the relativistic jets originating from the region close to the central engine and pointed towards the line of sight from the Earth. The relativistic effects like Doppler boosting of the non-thermal radiation emitted from the blazar-jet are more pronounced and the emission is observed to be variable over the entire eletromagnetic spectrum from radio to VHE $\gamma$- rays. Mrk 421 has also been an important blazar to investigate correlations in TeV $\gamma$- ray and X-ray fluxes measured during low and high activity states. A tentative positive and strong correlation between X-ray and TeV $\gamma$- ray fluxes is found during multi-wavelength campaign of several flaring episodes [32,33]. However, VHE $\gamma$- ray flares without any X-ray activity have also been observed [8,34]. Such flaring activities are referred to as \emph{orphan} TeV flares. A positive correlation in X-ray and TeV $\gamma$- ray emission during quiescent state of Mrk 421 is also reported [35]. The connection between the variations in TeV energy bands and lower energy bands has not been clearly understood for blazars like Mrk 421 and detailed time-dependent emission models are being developed to study the complex correlations among different energy bands [36,37,38]. \par Because of its proximity and high degree of multi-wavelength variability at different timescales, Mrk 421 has been a good extragalactic TeV source for understanding the physical mechanisms involved in the blazar emission during the quiescent as well as flaring states. The low energy emission from blazars is attributed to the relativistically beamed incoherent synchrotron radiation whereas high energy emission in GeV-TeV regime has not yet been well understood. Different models have been proposed in the literature to explain the $\gamma$- ray emission from blazars in quiescent as well as flaring states. In the leptonic synchrotron self Compton (SSC) model, the high energy $\gamma$- ray photons are produced by the inverse Compton (IC) scattering of the low energy synchrotron photons by the same population of relativistic electrons that emit the synchrotron photons [39,40,41]. In another leptonic model, the target photons for IC enter from outside regions like accretion disk [42], broad-line region and dusty torus [43]. This is referred to as the External Compton (EC) model for $\gamma$- ray emission in blazars. On the other hand, hadronic models have also been proposed in which $\gamma$- ray photons are produced by proton synchrotron emission [44,45] and by the secondary particles of the proton-initiated cascades [46,47]. \par Motivated by the observation of frequent flaring activities of Mrk 421, we study the sudden increase in the TeV $\gamma$- ray emission on the night of December 28, 2014 (MJD 57019) observed with the TACTIC. In order to characterize the short term enhanced TeV $\gamma$- ray emission from the source, we have used data from TACTIC observations of Mrk 421 collected during December 25-31, 2014 including the high activity state. In Section 2, we describe the observations and data analysis procedures followed in different energy bands for the period December 25-31, 2014 (MJD 57016-57022). The results from the TACTIC observations on the night of December 28, 2014 (MJD 57019) are presented in Section 3. In Section 4, results from broad-band near simultaneous observations during December 25-31, 2014 in multi-wavelength context are reported. Finally, we conclude our study in Section 5. We have adopted $\Lambda$CDM cosmology with parameters H$_0$ = 70 km s$^{-1}$ Mpc$^{-1}$, $\Omega_m$ = 0.27 and $\Omega_{\Lambda} $= 0.73 throughout this paper. | We have performed a detailed study of the short term TeV flare of high synchrotron peaked blazar Mrk 421 detected with the TACTIC telescope on the night of December 28, 2014 (MJD 57019) using the data collected during December 25-31, 2014 (MJD 57016-57022). The TACTIC telescope has detected 86$\pm$17 TeV $\gamma$--ray photons with a statistical significance of 5.17$\sigma$ in a short livetime of 2.2 hours on December 28, 2014. The time averaged VHE $\gamma$--ray rate detected with the TACTIC during this period corresponds to the source activity at the level of $\sim$ 3-times the emission from the Crab Nebula. The main focus of this work is to analyze and study this short duration TeV flare of Mrk 421 observed with the TACTIC and near simultaneous activity of the source in other wave-bands. The observed and intrinsic differential energy spectra of TeV photons detected with the TACTIC are described by power law with spectral indices 3.18$\pm$0.38 and 2.99$\pm$0.38 respectively in the energy range 0.85-8.5 TeV. The corresponding integral flux measured with the TACTIC telescope above 0.85 TeV is obtained to be (3.68$\pm$0.64)$\times$ 10$^{-11}$ ph~cm$^{-2}$~s$^{-1}$. The quasi-simultaneous measurements of the integral flux from Mrk 421 with the TACTIC and HAWC observatory characterize the relatively high activity state of the source at TeV energies during observations on December 28, 2014. \par We have also used near simultaneous observations available in other wave-bands from HE $\gamma$- ray to optical observations. From the analysis of the multi-wavelength light curves, it is found that the TeV $\gamma$- ray flare observed with the TACTIC on December 28, 2014 is detected without any significant change in lower energy bands. However, this can not be termed as an orphan flare because observations of soft X-rays and radio are not available during this period. We have applied the null hypothesis for constant flux to characterize the varaibility of the source in different energy bands in the first step. The goodness of fit ($\chi_r^2$/dof and probability) obtained corresponding to the null hypothesis indicates that the emission in TeV band is significantly variable whereas other wave-bands do not show significant variability. We have estimated various amplitude parameters in order to further quantify the variability present in the multi-wavelength light curves of Mrk 421 during the period December 25-31, 2014. We find that the TeV light curve exhibits relatively high values of variability parameters and implies strong variability during the above period. However, the highest value of $RVA=0.59$ is obtained for hard X-rays which implies that the maximum flux is approximately three times the minimum flux in the light curve. But the large fluctuations in the individual flux measurements reduce its intrinsic varability with large error bar. The daily HE $\gamma$- ray photon spectral indices also do not show any significant change during this period. The overall behaviour of the intrinsic fractional varaiability is found to be consistent with the general trend of high synchrotron peaked blazars where variability amplitude increases with energy [70] and highest variability with F$_{var}\sim$0.52 occurs in TeV flux points measured with the TACTIC. This also indicates that the VHE emission originates from a very compact region in the jet and it can be attributed to the change in electron injection or turbulance in the jet [71]. The lower values of variability amplitudes for optical and \emph{Fermi}-LAT observations can be attributed to the fact that variability amplitude is higher at frequencies beyond the synchrotron and inverse Compton peaks in blazar SED. Also, in high synchrotron peaked blazars like Mrk 421 the optical emission lines are weak and therefore the synchrotron photons at X-ray energies are the dominant targets for the inverse Compton scattering to produce the TeV $\gamma$--rays. Therefore, correlated variability at X-ray and TeV energies is expected from the single zone leptonic SSC model. The temporal analysis of TeV light curve gives a conservative estimate of the minimum variability timescale of $\sim$ 0.69 days in the source frame. However, the minimum variability timescale estimated from the analysis of near simultaneous multi-wavelength light curves with flaring activities will give the strongest possible upper-limit on the size of the active region in the jet taking into account the light travel time effects. The data statistics available during this period is not sufficient to perform such detailed temporal analysis of the emission from the source. \par The one day broad-band spectral energy distribution of the source using near simultaneous observations on December 28, 2014 can be broadly reproduced by simple one zone leptonic SSC model. The model parameters estimated from the best fitting of the SED are found to be in agreement with the values recently reported in the literature for Mrk 421 [72,11,16]. The difference between the electron spectral indices $p$ and $q$ is more than the expected value for the pure radiative/synchrotron cooling break in the electron spectrum. This can be attributed to the energy dependent acceleration and escape timescales [73,74] which have not been explicitly modelled in the present work. The kinetic energy or power of the jet is estimated from the derived model parameters by assuming that the hadrons in the emission region are cold and do not contribute in the radiative process. Under this approximation, the kinetic power of the jet in the source frame is given by [75] \begin{equation} P_{jet} \approx \pi R^2 \Gamma^2_j \beta_j c(U_e + U_B + U_p) \end{equation} where $U_e$, $U_B$ are $U_p$ are comoving energy densities corresponding to leptons, magnetic field and cold protons respectively. Using the best fit model parameters given in Table \ref{tab:Tab3}, the jet power is estimated to be 7.44$\times$10$^{44}$ erg~s$^{-1}$ which is consistent with the value generally assumed for blazars. The model parameters derived in this work represent one of the probable parameter set for Mrk 421, however they may considerably differ from the values estimated using the multi-zone emission models [17] and because of their inherent degeneracy. The fact that strictly simultaneous multi-wavelength observations are not available during the TeV flaring activity of Mrk 421 detected with the TACTIC telescope on the night of December 28, 2014, it is difficult to provide any firm conclusion about the emission processes involved in the source. However, given that Mrk 421 is known to exhibit frequent flaring activities in all energy bands from radio to TeV with short variability timescales, future contemporaneous multi-wavelength observations of short duration flaring activities will help in constraining the parameter space in a relatively better way. | 18 | 8 | 1808.02670 |
1808 | 1808.10071_arXiv.txt | Observations of low-frequency gravitational waves will require the highest possible timing precision from an array of the most spin-stable pulsars. We can improve the sensitivity of a pulsar timing array (PTA) to different gravitational-wave sources by observing pulsars with low timing noise over years to decades and distributed across the sky. We discuss observing strategies for a PTA focused on a stochastic gravitational-wave background such as from unresolved supermassive black hole binaries as well as focused on single continuous-wave sources. First we describe the method to calculate a PTA's sensitivity to different gravitational-wave-source classes. We then apply our method to the 45 pulsars presented in the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11-year data set. For expected amplitudes of the stochastic background, we find that all pulsars contribute significantly over the timescale of decades; the exception is for very pessimistic values of the stochastic background amplitude. For individual single sources, we find that a number of pulsars contribute to the sensitivity of a given source but that which pulsars contribute are different depending on the source, or versus an all-sky metric. Our results seem robust to the presence of temporally-correlated red noise in pulsar arrival times. It is critical to obtain more robust pulsar-noise parameters as they heavily affect our results. Our results show that it is also imperative to locate and time as many high-precision pulsars as possible, as quickly as possible, to maximize the sensitivity of next-generation PTA detectors. | As the detection of low-frequency gravitational waves (GWs) nears \citep{Taylor+2016}, pulsar timing array (PTA) collaborations must begin looking towards the future characterization of the GW sky. As with ground-based detectors, we must begin planning for the next-generation of PTA detectors, one optimized for these observations. The North American Nanohertz Observatory for Gravitational Waves \citep[NANOGrav;][]{McLaughlin2013} collaboration, one of several efforts worldwide \cite[e.g.,][]{IPTADR1,Desvignes+2016,Reardon+2016}, is currently observing over 70 high-precision millisecond pulsars (MSPs) in its PTA detector for the purpose of low-frequency GW detection from both a stochastic background and from single sources. Without a detection, we have placed constraints on the environments of supermassive black hole binary (SMBHB) mergers, cosmic strings, and inflationary era GWs \citep{NG5BWM,NG5CW,NG11GWB}. Detector sensitivity depends on the GW signal we wish to observe. A stochastic background requires observations of many MSPs \citep{Siemens+2013,vs2016} whereas the sensitivity to single sources such as from a single binary or merger event requires the highest timing precision from a few of the best-timed MSPs \citep{Ellis+2012}. PTA observations require years to decades of a timing baseline to detect nanohertz-regime GWs and therefore large amounts of telescope time are required. In theory with enough observing time we could observe enough pulsars with adequate timing-precision to cover both science targets (stochastic background versus single source) but practical limitations apply. NANOGrav currently observes its pulsars on a monthly cadence except for a handful of the highest-precision pulsars which are observed weekly, with the goal of covering both stochastic background and single continuous wave (CW) source characterization. However, the efficacy of the approaches to maximizing GW sensitivity has been unclear so far. In \citet{optimalfreq}, we examined pulse arrival-time uncertainty for MSPs as a function of the radio frequencies observed by specific telescopes taking into account a wide variety of effects. The requirements per pulsar vary but large bandwidths covering much of the radio spectrum typically used for high-precision pulsar timing ($\sim$GHz) are needed to obtain the best possible arrival-time estimates. In this work, we will consider the time-allocation optimization for various pulsars in the array to maximize overall GW sensitivity. \citet{KJ+2012} examined this problem first by considering a simplified PTA and providing the methodology to optimize a specific stochastic-background detection statistic given observing constraints from one or several telescopes. Here we will develop the methodology for time optimization for the goals of detecting and characterizing both the stochastic background and single CW sources. We apply this formalism to the 45 pulsars presented in the NANOGrav 11-year data set \citep[NG11;][]{NG11yr}, providing specific prescriptions for allocating the observing time per pulsar depending on the two science goals. In \S\ref{sec:statistic}, we describe the cross-correlation statistic used as our GW sensitivity metric. We apply our formalism to the NG11 pulsars in \S\ref{sec:application} and describe future directions in \S\ref{sec:future}. | 18 | 8 | 1808.10071 |
|
1808 | 1808.07331_arXiv.txt | {} {A strong X-ray outburst was detected in HE\,1136-2304 in 2014. Accompanying optical spectra revealed that the spectral type has changed from a nearly Seyfert 2 type (1.95), classified by spectra taken 10 and 20 years ago, to a Seyfert 1.5 in our most recent observations. We seek to investigate a detailed spectroscopic campaign on the spectroscopic properties and spectral variability behavior of this changing look AGN and compare this to other variable Seyfert galaxies.} {We carried out a detailed spectroscopic variability campaign of HE\,1136-2304 with the 10 m Southern African Large Telescope (SALT) between 2014 December and 2015 July.} {The broad-line region (BLR) of HE\,1136-2304 is stratified with respect to the distance of the line-emitting regions. The integrated emission line intensities of H$\alpha$, H$\beta$, \ion{He}{i}\,$\lambda 5876$, and \ion{He}{ii}\,$\lambda 4686$ originate at distances of $15.0^{+4.2}_{-3.8}$, $7.5^{+4.6}_{-5.7}$, $7.3^{+2.8}_{-4.4}$, and $3.0^{+5.3}_{-3.7}$ light days with respect to the optical continuum at 4570\,\AA{}. The variability amplitudes of the integrated emission lines are a function of distance to the ionizing continuum source as well. We derived a central black hole mass of $3.8 \pm 3.1 \times 10^{7} M_{\odot}$ based on the linewidths and distances of the BLR. The outer line wings of all BLR lines respond much faster to continuum variations indicating a Keplerian disk component for the BLR. The response in the outer wings is about two light days shorter than the response of the adjacent continuum flux with respect to the ionizing continuum flux. The vertical BLR structure in HE\,1136-2304 confirms a general trend that the emission lines of narrow line active galactic nuclei (AGNs) originate at larger distances from the midplane in comparison to AGNs showing broader emission lines. Otherwise, the variability behavior of this changing look AGN is similar to that of other AGN.} {} \keywords {Galaxies: active -- Galaxies: Seyfert -- Galaxies: nuclei -- Galaxies: individual: HE\,1136-2304 -- (Galaxies:) quasars: emission lines } | About a dozen Seyfert galaxies are known to have significantly changed their optical spectral type: for example, NGC\,3515 (Collin-Souffrin et al.\citealt{souffrin73}), NGC\,4151 (Penston \& Perez\citealt{penston84}), Fairall\,9 (Kollatschny et al.\citealt{kollatschny85}), NGC\,2617 (Shappee et al.\citealt{shappee14}), Mrk\,590 (Denney at al.\citealt{denney14}), and references therein. Further recent findings are based on spectral variations detected by means of the Sloan Digital Sky Survey (e.g., Komossa et al.\citealt{komossa08}; LaMassa et al.\citealt{lamassa15}; Runnoe et al.\citealt{runnoe16}; MacLeod et al.\citealt{macleod16}). These galaxies are considered to be changing look active galactic nuclei (AGNs). However, most of these findings are based on only a few optical spectra. HE\,1136-2304 ($\alpha_{2000}$ = 11h 38m 51.1s, $\delta_{2000}$ = $-23^{\circ}$ 21$^{'}$ 36$^{''}$) was classified as a changing look AGN based on spectroscopy performed after a strong increase in the X-ray flux was detected by XMM-Newton in 2014 in comparison to an upper limit based on the ROSAT All-Sky Survey taken in 1990 (Parker et al.\citealt{parker16}). The increase in the X-ray flux came with an increase in the optical continuum flux and with a change of the Seyfert type. HE\,1136-2304 was of Seyfert 2/1.95 type in early spectra taken in 1993 and 2002. However, its spectral type changed to a Seyfert 1.5 type in 2014 (Zetzl et al.\citealt{zetzl18}, Paper 1). This notation of Seyfert subclasses was introduced by Osterbrock \cite{osterbrock81}. Long-term and detailed optical variability studies exist for many AGN such as NGC\,5548 (Peterson et al.\citealt{peterson02}; Pei et al.\citealt{pei17} and references therein), 3C120 (Peterson et al.\citealt{peterson98}; Kollatschny et al.\citealt{kollatschny00}; Grier at al.\citealt{grier13}), NGC\,7603 (Kollatschny et al.\citealt{kollatschny00}), and 3C\,390.3 (Shapovalova et al.\citealt{shapovalova10}). Corresponding detailed follow-up studies have not yet been reported for the type of changing look AGN mentioned above. We carried out a detailed spectroscopic and photometric variability study of HE\,1136-2304 between 2014 and 2015 after the detection of the strong outburst in 2014. We presented the optical, UV, and X-ray continuum variations of HE\,1136-2304 from 2014 to 2017 in a separate paper (Paper 1). We verified strong continuum variations in the X-ray, UV, and optical continua. We showed that the variability amplitude decreased with increasing wavelength. The amplitude in the optical varied by a factor of three after correcting for the host galaxy contribution. No systematic trends were found with regards to the variability behavior following the outburst in 2014. A general decrease in flux would have been expected for a tidal disruption event. The Seyfert type did not change between 2014 and 2017 despite strong continuum variations. We describe the results of the spectroscopic variability campaign taken with the 10 m Southern African Large Telescope (SALT) for the years 2014 to 2015. Throughout this paper, we assume $\Lambda$CDM cosmology with a Hubble constant of H$_0$~=~70~\kms Mpc$^{-1}$, $\Omega_{\text{M}}$=0.27, and $\Omega_{\Lambda}$=0.73. Following the cosmological calculator by Wright et al. (\citealt{wright06}) this results in a luminosity distance of 118 Mpc. | \subsection {Optical variability} We thoroughly investigated the spectroscopic variability behavior of HE\,1136-2304 by taking 16 spectra over a period of six months between February to August 2015. The fractional variability F$_{\text{var}}$ was on the order of 0.1 in the optical continuum without correcting for the host galaxy flux. After correcting for the host galaxy contribution, the fractional variability F$_{\text{var}}$ of the continuum amounted to $0.25-0.3$ (see Paper I). The integrated Balmer and Helium lines showed F$_{\text{var}}$ values of 0.1 to 0.5 and the higher ionized lines originating closer to the center varied with stronger amplitudes. These results describing the continuum and emission line variability are similar to those detected in other variable Seyfert galaxies such as NGC\,5548 (Peterson et al.\citealt{peterson04}), Mrk\,110 (Kollatschny et al.\citealt{kollatschny01}), or 3C\,120 (Kollatschny et al.\citealt{kollatschny14}). This confirms that the variability behavior of this changing look AGN is similar to that of other Seyfert galaxies. \subsection {Balmer decrement variability} The Balmer decrement \Ha{}/\Hb{} of the narrow components has a value of 2.81. This corresponds exactly to the expected theoretical line ratio (Case B) without any reddening. However, the Balmer decrement \Ha{}/\Hb{} of the broad components varies with the continuum and/or Balmer line intensity. For example, the broad line Seyfert galaxy NGC~7693 showed the same behavior based on long-term variability studies over a period of 20 years (Kollatschny et al.\citealt{kollatschny00}): the Balmer decrement decreased with increasing H$\beta$ flux. Heard \& Gaskell\cite{heard16} proposed a model \text{with} additional dust reddening clouds interior to the narrow-line region causing higher Balmer decrements in the BLR. In contrast to this model, there might be important optical depth effects in the BLR itself explaining the observations. This is consistent with the finding that H$\alpha$ originates at twice the distance of H$\beta$. A similar radial stratification as seen in HE\,1136-2304 has been observed in, for example, Arp~151 (Bentz et al.\citealt{bentz10}) as well. It has been discussed by Korista and Goad\cite{korista04} that the radial stratification is a result of optical-depth effects of the Balmer lines: the broad-line Balmer decrement decreases in high continuum states and steepens in low states exactly as observed in HE\,1136-2304 (see Fig.~\ref{balmerdek_vs_cont4570.ps}). The continuum varied by a factor of nearly two during our campaign in 2015. However, we did not detect simultaneous variations of the Seyfert subtype during our observing period of seven months. A variation of Seyfert subtypes might be connected with stronger continuum amplitudes and/or longer timescales as has been seen before, for example, in Fairall\,9 (Kollatschny et al.\citealt{kollatschny85}). \subsection {H$\beta$ lag versus optical continuum luminosity} Now we want to test whether HE\,1136-2304 follows the general trend in the radius-luminosity relationship for AGN (Kaspi et al.\citealt{kaspi00}; Bentz et al.\citealt{bentz13}). We determined a continuum luminosity $\log \lambda \text{L}_{\lambda}$ of 42.6054 erg\,s$^{-1}$ ($0.47 \times 10^{-15}$\,erg\,s$^{-1}$\,cm$^{-2}$\,\AA$^{-1}$) in the optical at 5100\,\AA{} after correction for the contribution of the host galaxy (Zetzl et al.\citealt{zetzl18}). Furthermore, we derived a mean radius of 7.5 light days for the H$\beta$ line-emitting region based on the delay of the integrated H$\beta$ line variability curve with respect to the optical continuum light curve. Fig.~\ref{hblag_vs_loglambda_L_lambda_v2.ps} shows the optical continuum luminosity and H$\beta$-optical lags for HE\,1136-2304 (red), for NGC\,5548 based on different variability campaigns (black; Pei et al.\citealt{pei17} based on Kilerci-Eser et al.\citealt{kilerci15} and Denney et al.\citealt{denney09}), and a sample of other AGN excluding NGC\,5548 (green; Bentz et al.\citealt{bentz13}). The black line is the linear least-squares fit to the NGC\,5548 data as presented by Pei et al.\cite{pei17}. The $R-L$(5100\AA{}) relationship is given by \begin{equation} \log \Bigg[\frac{R_\text{BLR}}{ 1\,\text{light-day}}\Bigg] = K +\beta \log\Bigg[\frac{\lambda L_{\lambda}(5100\AA)}{{10^{44}\, \text{erg\, s}}^{-1}}\Bigg], \end{equation} where K is the origin and $\beta$ is the slope. The red solid line gives the best-fit linear regression to the whole AGN sample. The data of HE\,1136-2304 is in very good accordance with the general H$\beta$ lag versus the optical continuum luminosity relation. \begin{figure} \centering \includegraphics[height=9cm,angle=-90]{hblag_vs_loglambda_L_lambda_v2.ps} \caption{Optical continuum luminosity and H$\beta$-optical lags for HE\,1136-2304 and other AGN.} \label{hblag_vs_loglambda_L_lambda_v2.ps} \end{figure} The red solid line has a slope $\beta$ of 0.53, which is therefore identical to the best-fit slope of $0.533^{+0.035}_{-0.033}$ of Bentz et al.\cite{bentz13}. This value is very close to the value of 0.5 expected from simple photoionization arguments, i.e., \begin{equation} R \sim L^{1/2} \end{equation} (e.g., Kaspi et al.\citealt{kaspi00}; Bentz et al.\citealt{bentz13} and references therein). We tested whether the $\beta$ slope approaches values even closer to 0.5 or whether the Pearson correlation coefficient becomes higher if we add a few light days to the H$\beta$ radius. Such an additional delay might be caused by the fact that the optical continuum is generally delayed by a few light days with respect to the driving X-ray light curve (Zetzl et al.\citealt{zetzl18}, Shappee et al.\citealt{shappee14}; Fausnaugh et al.\citealt{fausnaugh16}). We added additional lags of one to eight light days to all H$\beta$-optical lags to take into account a systematic delay of the optical bands with respect to the driving X-ray flux. A time delay of eight light days is an upper limit based on the correlation of the optical band light curves with respect to the XRT light curve (Zetzl et al.\citealt{zetzl18}). Figs.~\ref{hblag_vs_loglambda_L_lambda_v2_plus1days.ps} and \ref{hblag_vs_loglambda_L_lambda_v2_plus4days.ps} show the H$\beta$ lag versus optical continuum luminosity diagrams with an additional lag of one and four days, respectively, taking into account the optical-X-ray lag. \begin{figure} \centering \includegraphics[height=9cm,angle=-90]{hblag_vs_loglambda_L_lambda_v2_plus1days.ps} \caption{Optical continuum luminosity and H$\beta$-optical lags for HE\,1136-2304 and other AGN (plus 1 day additional lag for optical-X-ray lag).} \label{hblag_vs_loglambda_L_lambda_v2_plus1days.ps} \end{figure} \begin{figure} \centering \includegraphics[height=9cm,angle=-90]{hblag_vs_loglambda_L_lambda_v2_plus4days.ps} \caption{Optical continuum luminosity and H$\beta$-optical lags for HE\,1136-2304 and other AGN (plus 4 days additional lag for optical-X-ray lag).} \label{hblag_vs_loglambda_L_lambda_v2_plus4days.ps} \end{figure} \begin{table} \centering \leavevmode \tabcolsep5mm \newcolumntype{d}{D{.}{.}{-2}} \newcolumntype{p}{D{+}{\,\pm\,}{-1}} \newcolumntype{K}{D{,}{}{-2}} \caption{ Pearson correlation coefficient for the relation between optical continuum luminosities and H$\beta$-optical lags. The H$\beta$ lags have been modified assuming additional lags (in units of days) for the optical lag with respect to the driving X-ray source. Additionally, we give the gradient $\beta$.} \begin{tabular}{cdK} \htopline \hspace{0mm}Offset delay & \mcc{Pearson CC} & \mcc{$\beta$}\\ \hspace{0mm} [days] & & \\ \hmidline \noalign{\smallskip} 0 & 0.8870 & 0.529,\pm0.032\\ 1 & 0.8903 & 0.496,\pm0.029\\ 2 & 0.8919 & 0.469,\pm0.027\\ 3 & 0.8926 & 0.447,\pm0.026\\ 4 & 0.8928 & 0.428,\pm0.025\\ 5 & 0.8927 & 0.411,\pm0.024\\ 6 & 0.8923 & 0.396,\pm0.023\\ 7 & 0.8918 & 0.383,\pm0.022\\ 8 & 0.8911 & 0.371,\pm0.022\\ \noalign{\smallskip} \hbotline \end{tabular} \label{pearsoncc_lag} \end{table} Tab.~\ref{pearsoncc_lag} gives the Pearson correlation coefficient for the relation between optical continuum luminosities and H$\beta$-optical lags. The H$\beta$ lags have been modified assuming additional lags (in units of days) for the optical lag with respect to the driving X-ray source. Furthermore, we present the $\beta$ values for the additional delays that have been assumed. We get the highest correlation coefficient for an additional delay of four days. We reached a $\beta$ slope of exactly 0.5 for an additional delay of one day. \\ \subsection{Structure and kinematics in the BLR} \subsubsection{Mean and rms line profiles} The mean and rms line profiles of the broad emission lines give us information about the kinematics and structure of the line-emitting BLR region. Differences in the broad-line widths of the rms and mean profiles (see Figs.~\ref{velo_meanrms_ha.ps} to \ref{velo_meanrms_he1.ps}) might be caused by a radial stratification of optical depth effects in these lines (Korista and Goad\citealt{korista04}). Especially the rms profiles of the Balmer lines in HE\,1136-2304 show an asymmetric triple structure. Aside from a central component there were additional blue and red components at $+/-$1\,400~\kms{} (see Fig.~\ref{velo_rms_hahb.ps}). These components are barely visible in the mean profiles. The additional component in the red wing is by far stronger than that in the blue wing. An additional weak blue component, which is nearly symmetrical to the red component, is apparent in the rms profile of H$\beta$ (Fig.~\ref{velo_rms_hahb.ps}). Furthermore, this red rms component varies relatively stronger in the H$\beta$ line than in H$\alpha$. The additional blue and red components in the line profiles -- in addition to the central component -- are an indication that the line-emitting region is connected to the accretion disk. Such double-peaked profiles are considered to be ubiquitous signatures of accretion disks (e.g., Eracleous \& Halpern\citealt{eracleous03}; Gezari et al.\citealt{gezari07}; Shapovalova\citealt{shapovalova13}; Storchi-Bergmann et al.\citealt{storchibergmann17}, and references therein). In some cases these double-peaked profiles become only visible in the rms line profiles as in NGC4593, for example (Kollatschny \& Dietrich\citealt{kollatschny97}). The variable Seyfert galaxy Akn~120 is another example of a very strong red component showing up in the H$\beta$ wing within one year (Kollatschny et al.\citealt{kollatschny81}). Similar to the line profiles in NGC4593 (Kollatschny \& Dietrich\citealt{kollatschny97}), the rms line profiles of H$\alpha$ and H$\beta$ in HE\,1136-2304 show a steeper red wing and a flatter outer blue wing indicating an additional outflow component (see Fig.~\ref{velo_rms_hahb.ps}). The outer blue wing is even more pronounced in the higher ionized Helium lines in comparison to the Balmer lines (see Fig.~\ref{velo_rms_he.ps}), indicating a stronger outflow in the inner BLR. \subsubsection{Velocity delay maps} The 2D-CCFs or velocity-delay maps shown in Figs.~\ref{ccf2d_ha.ps} to \ref{ccf2d_he2.ps} contain additional information about the structure and kinematics of the BLR. We compare the derived velocity delay maps of HE\,1136-2304 with theoretical models for the structure and kinematics of the BLR (Welsh et al.\citealt{welsh91}; Horne et al.\citealt{horne04}; Goad et al.\citealt{goad12}; Grier et al.\citealt{grier13}) and with velocity delay maps of other AGN. All the velocity delay maps are very symmetric with respect to their line centers at $v=0$ \kms{}. The delays in the wings are by far shorter than in the line center. Such behavior is typical for thin Keplerian disk BLR models (Welsh et al.\citealt{welsh91}; Horne et al.\citealt{horne04}; Grier et al.\citealt{grier13}). There is an indication in the velocity delay maps of the Balmer lines that the response in the red wing (at v = 3000 to 5000\,\kms) is slightly stronger and that it shows a shorter delay than in the blue wing. This might be caused by an additional inflow component (Welsh et al.\citealt{welsh91}), by hydro-magnetically driven wind (Horne et al.\citealt{horne04}), or by an additional turbulent component (Goad et al.\citealt{goad12}). The velocity delay maps of other Seyfert galaxies in general show two different trends: a more symmetrical velocity delay map that is typical for Keplerian disks or a velocity delay map showing a strong red component caused by strong inflow or hydro-magnetically driven wind, and a combination of both. NGC\,4593 (Kollatschny et al.\citealt{kollatschny97}), 3C\,120 (Kollatschny et al.\citealt{kollatschny14}), Mrk\,50 (Barth et al.\citealt{barth11}), and NGC\,5548 (Pei et al.\citealt{pei17} and references therein) show a more symmetrical velocity delay map. NGC\,3516 (Denney et al.\citealt{denney10}), Mrk1501, PG\,2130+099 (Grier et al.\citealt{grier13}) and Mrk\,335 (Du et al.\citealt{du16}) show a dominant red component. Velocity delay maps of other galaxies indicate a combination of dominant Keplerian motion and an additional red component, such as Mrk\,110 (Kollatschny et al.\citealt{kollatschny01}) and Arp\,151 (Bentz et al.\citealt{bentz10}). However, there are three exceptions (Mrk\,817, NGC\,3227, and Mrk\,142) in which only a strong blue component is present in the velocity delay maps (Denney et al.\citealt{denney10}; Du et al.\citealt{du16}). The velocity delay map of the changing look AGN HE\,1136-2304 is similar to that of most other AGN. It shows a dominant Keplerian motion component with a slightly more intense red component. \subsection{Vertical BLR structure in a sample of AGN} The higher ionized broad emission lines originate at smaller radii as shown in section 3.3. Furthermore, the integrated H$\alpha$ originates at a distance of 15 light days and therefore at twice the distance of H$\beta$ (see Tab.~\ref{CCF_1D}). Moreover, it has been shown that the higher ionized lines originate closer to the midplane of the accretion disk in comparison to the lower ionized lines. We presented the BLR structure as a function of distance to the center and height above the midplane (Fig.~\ref{disc_he1136.ps}). The \ion{He}{ii}\,$\lambda 4686$ line originates closest to the midplane. H$\alpha$ originates at a larger distance from the midplane in comparison to H$\beta$. Such a trend has been observed before in other galaxies as NGC~7469 (Kollatschny \& Zetzl\citealt{kollatschny13c}) and 3C~120 (Kollatschny et al.\citealt{kollatschny14}). A second trend has been found when comparing the H$\beta$ distances above the midplane for different active galaxies: galaxies showing the broadest H$\beta$ linewidths originate closest to the midplane, while galaxies showing the narrowest H$\beta$ linewidths originate at the largest distance to the midplane (Kollatschny et al.\citealt{kollatschny14}). The linewidths (with respect to the individual lines) are therefore a characteristic for the height of the line-emitting regions above the midplane. We present the height-to-radius ratio and FWHM of H$\beta$ for a sample of AGN (Kollatschny et al.\citealt{kollatschny14}) and for HE\,1136-2304 in Tab.~\ref{height_to_radius}. \begin{table} \centering \leavevmode \tabcolsep7mm \newcolumntype{d}{D{.}{.}{-2}} \newcolumntype{p}{D{+}{\,\pm\,}{-1}} \newcolumntype{K}{D{,}{}{-2}} \caption{ Height-to-radius ratio and FWHM of H$\beta$ for a sample of AGN. } \begin{tabular}{lKK} \htopline \hspace{3mm} Campaign & \mcc{FWHM} & \mcc{$H_{\text{obs}}/R$}\\ \hspace{3mm} &\mcc{[\kms{}]}& \\ \hmidline \noalign{\smallskip} NGC 7469 &2169,^{+459}_{-459}&0.36,^{+0.14}_{-0.14}\\ 3C 120 p04 &2205,^{+185}_{-185}&0.19,^{+0.03}_{-0.03}\\ 3C 120 g12 &2539,^{+466}_{-466}&0.31,^{+0.07}_{-0.07}\\ 3C 120 k14 &3252,^{+67}_{-67}&0.27,^{+0.03}_{-0.03}\\ NGC 3783 &3093,^{+529}_{-529}&0.33,^{+0.10}_{-0.10}\\ HE 1136-2304 &3791,^{+150}_{-150}&0.22,^{+0.06}_{-0.06}\\ NGC 5548 T1 &4044,^{+199}_{-199}&0.16,^{+0.03}_{-0.03}\\ NGC 5548 T2 &7202,^{+392}_{-392}&0.25,^{+0.06}_{-0.06}\\ NGC 5548 \Hb{}&5957,^{+224}_{-224}&0.06,^{+0.02}_{-0.02}\\ \dots &8047,^{+1268}_{-1268}&0.22,^{+0.13}_{-0.13}\\ \dots &5691,^{+164}_{-164}&0.18,^{+0.03}_{-0.03}\\ \dots &7202,^{+392}_{-392}&0.25,^{+0.06}_{-0.06}\\ \dots &6247,^{+343}_{-343}&0.10,^{+0.04}_{-0.04}\\ \dots &5776,^{+237}_{-237}&0.11,^{+0.03}_{-0.03}\\ \dots &5706,^{+357}_{-357}&0.10,^{+0.03}_{-0.03}\\ \dots &5541,^{+354}_{-354}&0.09,^{+0.03}_{-0.03}\\ \dots &4664,^{+324}_{-324}&0.16,^{+0.04}_{-0.04}\\ \dots &4044,^{+199}_{-199}&0.16,^{+0.03}_{-0.03}\\ \dots &6142,^{+289}_{-289}&0.13,^{+0.05}_{-0.05}\\ \dots &6377,^{+147}_{-147}&0.03,^{+0.01}_{-0.01}\\ \dots &4596,^{+505}_{-505}&0.12,^{+0.05}_{-0.05}\\ 3C 390.3 &9958,^{+1046}_{-1046}&0.06,^{+1.26}_{-1.26}\\ \noalign{\smallskip} \hbotline \end{tabular} \label{height_to_radius} \end{table} \begin{figure} \centering \includegraphics[width=6.5cm,angle=-90]{korr_h_obs_r_fwhm.ps} \caption{Height-to-radius ratio for the H$\beta$ line-emitting regions for a sample of AGN showing different H$\beta$ linewidths (FWHM).} \label{korr_h_obs_r_fwhm.ps} \end{figure} The height-to-radius ratio for H$\beta$ is largest for galaxies showing narrow emission lines and smallest for galaxies with broad lines. The overall picture we derived for the BLR region structure previously in Kollatschny \& Zetzl\cite{kollatschny13c} and Kollatschny et al.\citealt{kollatschny14} is confirmed by the additional emission line data of HE\,1136-2304. The derived height-to-radius ratio for HE\,1136-2304 confirms the general trend (see Fig.~\ref{korr_h_obs_r_fwhm.ps}). Again, the HE\,1136-2304 data support the picture that the broad emission line geometries of AGN are not simply scaled-up versions depending only on the central luminosity (and central black hole mass). | 18 | 8 | 1808.07331 |
1808 | 1808.02272_arXiv.txt | { A large filament composed principally of two sections erupted sequentially in the southern hemisphere on January 26 2016. The central, thick part of the northern section was first lifted up and lead to the eruption of the full filament. This event was observed in H$\alpha$ with the Global Oscillation Network Group (GONG) and Christian Latouche IMageur Solaire (CLIMSO), and in ultraviolet (UV) with the Atmospheric Imaging Assembly (AIA) imager on board the Solar Dynamic Observatory (SDO). } {The aim of the paper is to relate the photospheric motions below the filament and its environment to the eruption of the filament. } {An analysis of the photospheric motions using Solar Dynamic Observatory Helioseismic and Magnetic Imager (SDO/HMI) continuum images with the new version of the coherent structure tracking (CST) algorithm developed to track granules, as well as large-scale photospheric flows, has been performed. Following velocity vectors, corks migrate towards converging areas.} {The supergranule pattern is clearly visible outside the filament channel but difficult to detect inside because the modulus of the vector velocity is reduced in the filament channel, mainly in the magnetized areas. The horizontal photospheric flows are strong on the west side of the filament channel and oriented towards the filament. The ends of the filament sections are found in areas of concentration of corks. Whirled flows are found locally around the feet. } { The strong horizontal flows with an opposite direction to the differential rotation create strong shear and convergence along the magnetic polarity inversion line (PIL) in the filament channel. The filament has been destabilized by the converging flows, which initiate an ascent of the middle section of the filament until the filament reaches the critical height of the torus instability inducing, consequently, the eruption. The $n$ decay index indicated an altitude of 60 Mm for the critical height. It is conjectured that the convergence along the PIL is due to the large-scale size cells of convection that transport the magnetic field to their borders.} | The physical conditions leading to filament eruptions and coronal mass ejections (CMEs) have been recently reviewed by \citet{Schmieder2013}. They are based on the existence of flux ropes in the corona submitted to increasing electric currents. The decrease of the magnetic tension that restrains the flux rope favors its eruption. Twist motions, shears, and canceling flux are observed or involved in the magnetohydrodynamics MHD models as producing instabilities of the filament flux rope. Commonly it is found that eruptions are due to converging flows and canceling polarities along the polarity inversion lines (PIL). A filament consists of a magnetic structure aligned along the PIL with untwisted magnetic field lines anchored at both ends in opposite magnetic photospheric polarities of the network as linear force-free field extrapolations suggest \citep{Aulanier98,Aulanier2002}. The cool filament material is suspended in the dips. Along an H$\alpha$ filament or prominence, footpoints or legs are observed with an equidistant distance of about 30Mm, which we also call barbs when observed on the disk. A filament barb is directly related to a parasitic polarity close to the PIL \citep{Aulanier98,Martin94}. If the parasitic polarity is canceled by merging with opposite sign polarities, the barb disappears and the filament is no longer anchored in place. Material may be falling along the field lines, which transforms the dips to loops as was suggested in an MHD simulation \citep{Schmieder06}. This explains the counter streaming often observed in rising filaments before eruptions \citep{Zirker98,Schmieder08}. In MHD models, it is shown that canceling flux, twist, or rotation of sunspots induce a strong shear along the PIL. Progressively a flux rope is formed by reconnection of low magnetic field lines in a region of convergence \citep{vanBallegooijen1989,Aulanier2010}. The reconnection is driven by the diffusion of the photospheric magnetic field. It allows the flux rope to rise progressively in the upper atmosphere. When the flux rope reaches a critical height, a torus-type instability starts accelerating the rise of the flux rope and leading to eruption \citep{Tend1978,Kliem2006}. The critical altitude is estimated by the computation of the decay index ($n= - dlnB/dlnz$) , which represents the decay of the background magnetic field in the vertical direction. The critical height is defined as the height where the decay index reaches a critical value slightly dependent on the model of the flux rope used. For a thin straight current channel the critical value of the decay index is equal to unit \citep{Tend1978,Filippov2001}. \citet{Torok2007} found that for a thin circular current channel a torus instability of the flux rope is initiated when $n$ is larger than 1.5. From an observational point of view, \citet{Filippov2001} and \citet{Filippov2008} performed a statistical study of quiescent prominences and concluded that prominences were more prone to erupt when they approach a height where the decay index of the external field was close to 1. \citet{Zuccarello2016} computed the decay index for different MHD configuration models and derived a possible range for the critical decay index between 1.3 and 1.5 when the apex of the flux rope is considered, otherwise it can be lower. The difference referred to in these works between the values of the critical index 1 and 1.4 can be considered unimportant, while the decay index in regions with filaments changes from $\ll$ 1 to 3. The exact value of the critical decay index depends on the shape of the flux-rope axis and the properties of the flux-rope cross-section as was shown by \cite{Aula2010}. In the model simulations of Zuccarello et al. (2016), the axis of the flux rope is more curved, which is more appropriate for three-dimensional (3D) modeling. However, even in this model the topmost part of the distribution of magnetic dips, where filament material sits, is located at n = 1.1 when the instability starts. Since in the works of Filippov and colleagues the relationship between decay indexes and filament top heights was studied, there is no discrepancy with the results of Zuccarello et al. (2016). Surface motion on long-term as well on short-term scales is important for the formation and the stability of filaments. Photospheric motions are due to the coupling of the convection with the diffusion of the magnetic field at the solar surface. It is important to be able to quantify the horizontal flows in the photosphere and follow their evolution. A few analyses of surface motions have been done with high cadence and high spatial resolution. Mainly the local correlation tracking (LCT) method is applied to magnetic field polarities in order to explain eruptions or flares with Michelson Doppler Imager (MDI) data, with a spatial resolution of 1.96 arc sec, and only recently with Helioseismic and Magnetic Imager (HMI) data, with a resolution of 0.5 arc sec \citep{Ahn10,Zhou06,Green11,Liu12}. The techniques of correlation tracking (LCT) \citep{November88,Chae08} have been developed in two ways: either by tracing the surface flows with the differential affine velocity estimator for vector magnetograms (DAVE4VM) \citep{Schuck08} or by tracking coherent structures (CST) on various scales (spatial and temporal) \citep{Roud2012}. \citet{Roudier08} studied the flow pattern in a filament channel in a bipolar region using LCT, from MDI magnetograms and Dopplergrams supergranular flow pattern. It was found that the flow field changes significantly during the eruption phase, measuring an increase of the shear below the point where the eruption starts and a decrease after it \citep{Roudier08}. They found a pattern in the large scale horizontal flows at the solar surface that interacts with the differential rotation. The local photospheric flows were also measured with a higher spatial resolution (0.5 arc sec) in the filament channel during its eruption phase using Transition Region and Coronal Explorer (TRACE) 1600 \AA\ to show the coupling between convection and magnetic field \citep{Rondi07}. Apparently along the PIL both parasitic and normal polarities were continuously swept by the diverging supergranular flow and canceled, which leads to the filament eruption. \citet{Schmieder2014} computed the proper horizontal flows in a filament channel using the CST method and conjectured that the shear flows were responsible for the counterstreaming along the filament axis and finally for the eruption. Flux cancellation and magnetic shear were already proposed to play a major role in the filament eruption based on observations \citep{Martin1986,Litvinenko1999,Hermans1986,Martin1998} and models \citep{Priest1987,vanBallegooijen1989,Priest1994}. Still now, similar measurements are done using magnetograms showing the disappearance on a single bipole by flux cancellation as responsible for a filament eruption \citep{Wang2013,Yardley2016}. The action of large-scale flows on the filament (formation and eruption) has not yet been quantified. In the present study, we take advantage of the CST method applied to the full Sun data (SDO/HMI) to get flow fields over the whole of the Sun's surface at high and low spatial and temporal resolutions. In particular the CST method allows us to get large-scale flows such as solar differential rotation, meridian circulation, and supergranulation flows \citep{Chian2014,Roudier2018}. Previous works use LCT and many other methods for detecting approaching bipoles (see the benchmark paper of \citet{Welsch2007}), but no detection of large-scale inflow or shear has been done. Therefore, the measurement of large-scale flow such as differential rotation or supergranular flow is fundamental with regards to this question of filament eruption. We propose in this paper to correlate the horizontal photospheric flows, the H$\alpha$ (see Movie 1), and the UV dynamics (see Movies 2 and 3) of the filament before its eruption. In Sect. 2 we describe the observations of the filament and its dynamics observed with space- and ground-based instruments. We pay particular attention to the ends or anchorages of the filament in the network and the progressive lift up of the main body of the filament until it reaches the critical height for developing the torus instability. In Sect. 3 the new CST method that allows us to compute the horizontal photospheric flows in the filament channel and its environment is described. The results are presented in Sect. 4 and discussed in the conclusion from the perspective of the coupling between magnetic field and convection. (Sect. 5). \begin{figure*} \centerline{ \includegraphics[width=0.9\textwidth,clip=]{Figure_roudier_1.jpg}} \caption{Huge filament starting to lift up observed on January 26 2016 at 16:30 UT with SDO/AIA (before the eruption; left panel): combined image of three filters (211 \AA, 193 \AA, 171 \AA; right panel) HMI longitudinal magnetogram showing the magnetic channel of the filament. A, B, C, D are the places in the network where the magnetic field lines supporting the filament are anchored. The filament consists of two sections or two filaments (Filament one: AB and Filament two: CD). The temporal evolution of the left panel showing the huge filament eruption is available as a movie online. } \label{SDO} \end{figure*} | We analyzed the dynamics of the photosphere below a long filament during 24 hours on January 26 2016 before its eruption. Counterstreamings along the filament before its eruption are observed in H$\alpha$ , as well as moving brightenings in 304 \AA\ along its spine during all this time period. The main results of the Coherent Structure Tracking (CST) analysis concerning the flows in the photosphere are the following:\\ \begin{itemize} \item Supergranules with diverging flow pattern have a similar size in and outside the filament channel but have a lower amplitude in the magnetized areas. In the same way, the modulus of the horizontal velocity is reduced in the filament channel, particularly in the magnetized region where the field lines of the flux rope of the filament are anchored (A, B, C) \item The ends of the two filament sections (A, B, C) are between supergranules in regions of convergent flows nearly perpendicular to the axis of the filament. \item Whirled flows are found locally around points A, B, and C. \item Corks meet in magnetized areas (convergence areas) and consequently are associated to the filament ends. \item Large zones of flows lie at the western border of the filament channel according to the analysis of large-scale coherent structures. \item Strong flows from west to east reduce the differential rotation velocity in the central part of the filament where the anchorage of the field lines are in B and C. That difference in flows creates a stronger shear flow experienced by the filament feets. \end{itemize} There is a strong coupling between convection and magnetic field in the photosphere. Large convection cells transport the magnetic field and form between them a magnetic polarity inversion line. We have seen convergence of the flows towards the inversion line PIL. We conjectured that the different loops or arcades over the magnetic PIL are sheared and reconnection is possible due the convergence motions like in the model of {\citet{vanBallegooijen1989}. Through the reconnections, a twisted flux rope is formed like in the simulation \citep{Aulanier2010}. It could correspond to the filament that we have observed. If the convergence motion continues, then the convection cells are continuing to roll one against to each other; material in the photosphere is going down along the PIL. We have effectively measured downflow velocities between - 0.100 and - 0.200 km/s while the filament was rising. When it reaches the height of the torus instability threshold, it could erupt. The horizontal photospheric motions that we have measured explain the formation and the eruption of the filament. The CST method could be also generalized and applied systematically to full disk HMI magnetograms. | 18 | 8 | 1808.02272 |
1808 | 1808.05664_arXiv.txt | We present results from general relativistic calculations of the tidal disruption of white dwarf stars from near encounters with intermediate mass black holes. We follow the evolution of 0.2 and $0.6 M_\odot$ stars on parabolic trajectories that approach $10^3$ - $10^4 M_\odot$ black holes as close as a few Schwarzschild radii at periapsis, paying particular attention to the effect tidal disruption has on thermonuclear reactions and the synthesis of intermediate to heavy ion elements. These encounters create diverse thermonuclear environments characteristic of Type I supernovae and capable of producing both intermediate and heavy mass elements in arbitrary ratios, depending on the strength (or proximity) of the interaction. Nuclear ignition is triggered in all of our calculations, even at weak tidal strengths $\beta \sim 2.6$ and large periapsis radius $R_P \sim 28$ Schwarzschild radii. A strong inverse correlation exists between the mass ratio of calcium to iron group elements and tidal strength, with $\beta \lesssim 5$ producing predominately calcium-rich debris. At these moderate to weak interactions, nucleosynthesis is not especially efficient, limiting the total mass and outflows of calcium group elements to $< 15$\% of available nuclear fuel. Iron group elements however continue to be produced in greater quantity and ratio with increasing tidal strength, peaking at $\sim 60$\% mass conversion efficiency in our closest encounter cases. These events generate short bursts of gravitational waves with characteristic frequencies 0.1-0.7 Hz and strain amplitudes $0.5\times10^{-22}$ - $3.5\times10^{-22}$ at 10 Mpc source distance. | Tidal disruptions (TD) of white dwarf (WD) stars by intermediate mass black holes (IMBH) are complex and violent cosmic events capable of generating significant electromagnetic and potentially observable gravitational wave energies. A star passing by a black hole can be disrupted (elongated and torn apart) while also suffering compression when the black hole tidal force exceeds the star's self-gravity. The debris from disrupted stars will either dispense unbound materials into the surrounding medium, or accrete onto the black hole and produce flares and jets that can be observed electromagnetically \citep{Rees88, Haas12, Macleod16}. Unlike their supermassive counterparts, observational evidence for IMBHs in their likely host environments, dwarf galaxies or globular clusters, is tentative at best \citep{Gerssen02, Gerssen03, Gebhardt02, Gebhardt05, Dong07}, fueling efforts to identify signatures from IMBHs like those that might come from tidal disruption events (TDE). Supermassive black holes (greater than $10^5 ~M_\odot$), such as are observed at the centers of many large galaxies, are not likely to disrupt a WD substantially before swallowing it entirely. IMBHs, on the other hand, can be effective disruptors, leading to accretion rates up to $\sim 10^4 ~M_\odot$ yr$^{-1}$ \citep{Haas12} (henceforth referred to as HSBL12), producing strong bursts of radiation useful for detecting these events. The mass function of IMBHs is uncertain but anticipated to be about $2\times10^7$ to $4\times10^8$ Gpc$^{-3}$ \citep{Baumgardt04,Macleod16}. WDs for their part, represent the final stellar evolution of stars ranging from about 0.07 to 10 solar masses, and are commonly found in spiral galaxies and globular clusters \citep{Reid05, Gerssen02}. Less common of course are WD-IMBH interactions, but recent estimates place expected disruption rates at 500 yr$^{-1}$ Gpc$^{-3}$ \citep{Haas12}. One especially intriguing aspect of TDEs that concerns this work is the possibility that tidal compression perpendicular to the orbital plane could trigger explosive thermonuclear reactions and create heavy-ion nuclei if the temperature is raised above $\sim 3\times10^8$ K for He burning or $\sim 3\times10^9$ K for C/O \citep{Luminet89, Rosswog09, Haas12, Tanikawa17, Kawana17}. This is a likely outcome if the WD is massive enough and tidal compression strong enough. The compression strength in turn is affected by the periapsis radius and black hole mass. If sufficient amounts of radioactive nuclei, e.g. $^{56}$Ni, are synthesized and dispersed along with the unbound debris, their decay (through the $^{56}$Ni $\rightarrow$ $^{56}$Co $\rightarrow$ $^{56}$Fe chain, which releases $\sim 1$ MeV gamma-rays) supplies nuclear energy to the ejecta, much of which is absorbed and reprocessed as optical/UV photons. The resulting transient emissions might appear similar to Type Ia supernovae with comparable energy release \citep{Macleod16}. These optical transients are accompanied by small ejecta mass ($\lesssim 1 M_\odot$) and fall-back accretion signatures producing flares and jet emissions that emerge at high X-ray and gamma-ray energies, similar to gamma-ray bursts, but softer in spectrum and longer in time. \cite{Shcherbakov13}, for example, suggest that GRB060218 from the {\it Swift} GRB catalog might be a viable candidate for a TDE involving a WD and a $10^4 M_\odot$ black hole. If confirmed, the appearance of GRB060218 in a dwarf galaxy at a distance of 150 Mpc would indicate IMBHs are more abundant in the local universe than previously thought, by about an order of magnitude. On the other hand, less massive WDs or weaker tidal interactions may lead to low-luminosity explosions with incomplete radioactive synthesis, or may not explode at all. Incomplete burning can result in relatively large mass fractions of intermediate mass elements (IMEs) such as $^{40}$Ca, $^{44}$Ti, and $^{48}$Cr. \cite{Holcomb13} demonstrated how these elements might be a natural outcome from helium detonations in certain conditions typical of WD-IMBH encounters, with calcium production generally increasing with decreasing stellar density. \cite{Sell15} used these results to propose the possibility that the disruption of a light WD composed mainly of $^{4}$He can be a progenitor of calcium-rich gap transients. These systems, typically found in the outskirts of known galaxies, exhibit features similar to Type Ia supernovae, but are faint with high velocities and large calcium abundances \citep{Kasliwal12}. Disruption from some subset of TDEs involving white dwarfs might produce large quantities of IMEs, offering a possible production mechanism for calcium-rich transients. Observational evidence for the existence of TDE transients (including heavy iron-group elements, IMEs, fall-back accretion flares) remains uncertain, as does the very existence of IMBHs. Identifying distinguishing features of WD tidal events and providing detailed estimates of the properties of these transients might help constrain the highly uncertain nature of the black hole mass function for masses between stellar and supermassive, and place meaningful constraints on the density of IMBHs in the universe. In this work we consider the disruption and explosion of 0.2 and 0.6 $M_\odot$ WDs approaching to within a few Schwarzschild radii of $10^3$ - $10^4 ~M_\odot$ non-rotating IMBHs, performing a series of parameter studies in an effort to clarify under what conditions thermonuclear reactions are activated in these near encounter scenarios. Modeling all of the relevant physics in these systems remains a challenging undertaking, requiring substantial computational resources and fidelity modeling of not just hydrodynamics, but also more generally magnetic fields \citep[as recently reported in][]{Guillochon17}, radiation, and nuclear reactions. Near encounters, such as those considered here, additionally require general relativity. We do not consider magnetic fields or radiation in this work. We do however include general relativistic hydrodynamics, a full relativistic treatment of the black hole gravitational field, and a coupled thermonuclear reaction network with self-consistent burn energy feedback. Nearly all numerical work to date associated with TDEs has relied on Newtonian hydrodynamics and gravity (in many cases augmented by central potentials approximating relativistic corrections). Very few incorporate general relativity which is needed to accurately model ultra-close encounters \citep{Laguna93, Kobayashi04}, but none of that body of work includes nuclear reactions. Our goals are to extend previous work \citep[e.g.][]{Rosswog09} (henceforth referred to as RRH09) to the general relativistic regime, scope the strength parameter ranges which result in nuclear burning from close encounters, calculate the synthesis of intermediate to heavy mass elements, and explore disruptions of helium-rich WDs to address whether such events are viable candidates for calcium-rich gap transients. We begin in Section \ref{sec:methods} with a brief discussion of our numerical methods, physical models (hydrodynamics, equation of state, nucleosynthesis), and dynamical mesh strategy needed to approach the high spatial resolution required for nucleosynthesis, particularly along the vertical scale height. Initial data for the WD stellar profiles and their locations, trajectories, and tidal strength parameters for all of the case studies conducted in the course of this work are specified in Section \ref{sec:initial}. Our results follow in Section \ref{sec:results}, and we conclude with a brief summary in Section \ref{sec:conclusions}. Unless otherwise noted, standard index notation is used for labeling spacetime coordinates: repeated indices represent summations, raising and lowering of indices is done with the 4-metric tensor, and Latin (Greek) indices run over spatial (4-space) dimensions. | \label{sec:conclusions} We have developed a novel numerical methodology based on a combination of moving mesh and adaptive mesh refinement, and applied it to simulate the tidal disruption of white dwarf stars from near encounters with non-rotating, intermediate mass black holes. We solve the general relativistic hydrodynamics equations in a Kerr-Schild background spacetime, to account for relativistic tidal forces. The AMR/moving mesh hybrid approach allows us to move the base grid along Lagrangian fluid lines, while at the same time refining on the densest parts of the white dwarf as it compresses and stretches from tidal forces. This is critical in order to achieve sufficient zone resources in the central plane regions and provide the necessary scale height coverage to resolve internal shock and ignition features, which in turn are critical to approach convergent nuclear reactive solutions. A comprehensive study by \cite{Tanikawa17} suggests a resolution of $\le 10^6$ cm is needed to properly resolve nuclear flows for moderate tidal strength interactions ($\beta \approx 5$). Previous three dimensional calculations, (e.g. RRH09, HSBL12) fell short of that standard by about an order of magnitude. The calculations presented here, to our knowledge, thus represent the highest resolution 3D studies of these systems to date, achieving vertical resolution of slightly better than $10^6$ cm. However, we caution that even this resolution is almost certainly inadequate at high interaction strengths. In addition to improved spatial resolution, this work expands on previous investigations by accounting for general relativistic hydrodynamics coupled with nuclear reactions composed of a larger isotopic network and more accurate energy production estimates. The combination of high resolution and inline nuclear reactions makes these calculations computationally expensive. Nuclear reactions by themselves increase run times by about a factor of a few compared to pure hydrodynamics, depending on local state conditions and reactive response times. As a consequence our calculations are terminated between one to two seconds after the white dwarfs pass periapsis along parabolic trajectories. However, this is more than enough time for nucleosynthesis to complete at 1\% relative energy production levels ($\delta e_\mathrm{nuc}/(e~\delta t) < 0.01$). Our choice of parameters is motivated by a desire to sample WD mass, BH mass, and periapsis radius to elucidate the effects of relativity, compression ratios, and thermodynamic response on nuclear reactions. Options for a 0.2 or 0.6 $M_\odot$ WD brings in different initial hydrodynamic conditions (density, pressure, temperature), but also different isotopic compositions (predominately either helium or a carbon-oxygen mixture initializing isotopic mass fractions with trace amounts of minor isotopics). BH mass of $10^3$ or $10^4 M_\odot$ affects tidal compression, elongation, and crossing/compression timescales. The periapsis radius modulates relativistic effects and proximity to the BH. Collectively, these combinations define a tidal strength parameter $\beta=R_T/R_P$ (ratio of tidal to perihelion radii) which is critically important for predicting conditions necessary for nuclear ignition. We find all of our calculations ignite, even at tidal strengths as low as $\beta =2.6$, creating a wide variety of environments capable of converting tidal debris into arbitrary combinations of intermediate and high mass elements (or mass ratio of burn products) simply by adjusting the tidal strength parameter. In a crude sense, considering the debris is far from spherical, stellar matter assembles into compositions resembling SN Ia models in that the densest parts are composed mostly of iron-group elements (or otherwise heaviest possible nuclei depending on the interaction strength), surrounded by IMEs and an outer layer of unburned fuel. Stronger interactions (greater $\beta$) of course give rise to systematically greater energy release and nuclear production of iron group elements. At tidal strengths $\beta \gtrsim 4.5$ the amount of released nuclear energy exceeds the binding energy of the stars. This result is consistent with RRH09, as are predictions of the released energy (to about a factor of two) when we compare runs with comparable interaction strengths. However, our calculations tend to produce significantly greater amounts of iron group elements, with differences ranging from factors of three to orders of magnitude. A peak conversion efficiency, defined by the ratio of iron-group products to the initial stellar mass, of about 60\% is observed in our closest encounter scenarios, most of which is in the form of $^{56}$Ni. These differences are not surprising considering the sensitivity of element production to spatial resolution, the strong dependence of reaction rates on temperature and therefore the equation of state, and the limitations of small $\alpha$-chain networks to calculate heavy element production. It is unclear how much of the observed differences from previous work is due to improvements made in this paper (general relativity, increased grid resolution, and extended network model), to different initial stellar conditions (density, temperature, isotopic distributions), or to the approximation made for the equation of state and therefore the temperature that is critical for nucleosynthesis. Any combination of these possibilities could contribute to the factor of two differences observed in the total energy production diagnostic. However the much greater differences in iron-group production are not as easily explained and requires further study. We have additionally investigated whether tidally disrupted WDs might be viable sources of observed calcium-rich gap transients \citep{Sell15}. These gap transient systems are characterized by relatively large calcium abundances compared to iron or nickel, by factors of ten or more, and are thus representative of incomplete burning environments generally incapable of sustaining chain reactions through to iron-group production. Idealized one-dimensional calculations performed by \cite{Holcomb13} suggest these regimes do exist and might be within the realm of conditions produced by tidal disruption events, particularly for low mass white dwarfs at densities between $10^5$ and $10^6$ g cm$^{-3}$ and temperatures $\sim 10^9$ K. \cite{Kawana17} in their investigations did not observe calcium-rich products, but noted densities found in their calculations were slightly higher than $10^6$ g cm$^{-3}$. We point out that conditions appropriate for producing Ca-rich transients are achieved through moderate to weak tidal interactions, $\beta \lesssim 5$, where scale height resolution requirements are less demanding and marginally resolved with current methods. Our investigations show Ca-group elements do dominate over iron and nickel masses at tidal strengths producing relatively low density cores, with a clear trend for increasing calcium to iron abundance ratio with decreasing $\beta$. However, we also find nuclear reactions at these conditions are inefficient, converting less than 15\% of available fuel to burn products, the precise composition of which is a strong function of tidal strength. So, although we have demonstrated that Ca-rich debris can be produced from the tidal disruption of WDs by IMBHs, the associated cooler, low density environments produce corresponding outflows with limited amounts of IMEs ($\lesssim 0.03$ $M_\odot$). Mass accretion rates are strongly dependent on the interaction strength and proximity to the BH, but invariably well above Eddington-limited rates. We can reasonably expect these interactions to emit x-ray and $\gamma$-ray transients and shine at Eddington luminosity for more than a year. Rates are generally characterized by a large prompt burst (for sufficiently close $R_P \lesssim 12$ encounters) lasting between 0.5 to 1 second during periapsis approach, followed by a quasi-static phase with a shallower decay profile that scales roughly as $\dot{M} \propto 10^{-0.9t}$ during the onset of the circularization phase. At larger perihelion radius, the prompt accretion rate is weak, so the quasi-static phase is the only distinguishable feature of distant encounters. The amplitude of the prompt burst is strongly influenced by tidal strength, and peaks between $10^6$ - $10^7 M_\odot$ yr$^{-1}$ for ultra-close encounters. Quasi-static accretion rates do not vary as much with tidal strength and are typically confined to a much smaller and narrower range $10^2$ - $10^4 M_\odot$ yr$^{-1}$ at $R_P \lesssim 12$. We find nuclear burning enhances the mass accretion rate, but only by a modest 10\%. Finally, the encounter scenarios considered here generate burst-like gravitational waves with amplitudes that are not sensitive to nuclear burning, and that scale nonlinearly with tidal strength and vary between $0.5\times10^{-22}$ - $3.5\times10^{-22}$ at 10 Mpc source distance. Their characteristic frequencies fall in the range 0.1 - 0.7 Hz, just below LIGO's frequency band but potentially observable with LISA for admittedly rare events at source distances within 10-100 kpc. | 18 | 8 | 1808.05664 |
1808 | 1808.09483_arXiv.txt | The discovery of quasi-periodic brightness oscillations (QPOs) in the X-ray emission accompanying the giant flares of the soft gamma-ray repeaters SGR~1806--20 and SGR~1900+14 has led to intense speculation about their nature and what they might reveal about the interiors of neutron stars. Here we take a fresh look at the giant flare data for SGR~1806--20, and in particular we analyze short segments of the post-peak emission using a Bayesian procedure that has not previously been applied to these data. We find at best weak evidence that any QPO persists for more than $\sim 1$ second; instead, almost all the data are consistent with a picture in which there are numerous independently-excited modes that decay within a few tenths of a second. This has interesting implications for the rapidity of decay of the QPO modes, which could occur by the previously-suggested mechanism of coupling to the MHD continuum. The strongest QPOs favor certain rotational phases, which might suggest special regions of the crust or of the magnetosphere. We also find several previously unreported QPOs in these data, which may help in tracking down their origin. | \label{sec:introduction} Quasi-periodic X-ray brightness oscillations in the 2004 December giant flare from SGR 1806$-$20 were first reported by \citet{2005ApJ...628L..53I}. They detected a strong QPO at 92.5~Hz in Rossi X-Ray Timing Explorer (RXTE) data and found evidence for lower frequency QPOs at about 18 and 30~Hz. They suggested the QPOs could be related to torsional modes excited during the flare. Motivated by this \citet{2005ApJ...632L.111S} investigated the RXTE data obtained during the 1998 August event from SGR 1900+14. They found a sequence of rotation-phase-dependent QPOs at 28, 54, 84 and 155~Hz, and suggested an identification with a sequence of low-order torsional modes with different $l$ values. These authors also re-examined the RXTE data from the SGR 1806$-$20 giant flare, and found evidence for additional oscillations at 150 and 625 Hz \citep{2006ApJ...653..593S}. They suggested that the 625~Hz QPO could be identified with torsional oscillation modes with at least one radial node in the crust, and that this could lead to a probe of the crust thickness. These observational findings touched off a plethora of theoretical investigations. \citet{2006MNRAS.368L..35L} noted that the coupling of the crust to the core by a strong vertical magnetic field should lead to damping of the crustal oscillations within a few tenths of a second. Subsequent investigations explored the magnetic coupling of the crust to the core in more realistic scenarios \citep{2007MNRAS.377..159L,2007Ap&SS.308..607G,2007ApJ...661.1089V,2008arXiv0812.1570G,2009MNRAS.396.1441C,2011MNRAS.410.1036V,2011MNRAS.410L..37G,2012MNRAS.420.3035V,2013MNRAS.430.1811G}, and also explored how torsional mode identifications could be used to constrain the properties of the neutron star, including its mass and radius \citep{2007MNRAS.374..256S,2007MNRAS.375..261S,2011MNRAS.414.3014C,2016NewA...43...80S,2016EPJA...52...63M,2017MNRAS.464.3101S}, as well as its internal composition \citep{2007MNRAS.379L..63W}. Other authors have explored emission and X-ray modulation mechanisms for the QPOs \citep{2008ApJ...680.1398T,2012ApJ...751L..41D}, and the role of superfluidity in modifying the torsional oscillation spectrum of neutron stars \citep{2013MNRAS.429..767P,2014MNRAS.438..156P}. A focus of current theoretical modeling is the relative importance of magnetic and shear stresses, and to what extent the crustal torsional oscillation spectrum is present in the excitation spectrum, if at all \citep{2014AN....335..240G,2016MNRAS.460.4242G,2016MNRAS.463.1173P,2016ApJ...823L...1L,2016ApJS..224....6L,2016MNRAS.459.4144R,2017PhRvC..95a5803T}. Most of the data analysis and theoretical attention has focused on the frequencies of the QPOs. The attraction of this focus is that, potentially, particular oscillation modes can be associated with particular QPO frequencies, and those associations can reveal aspects of the interiors of the oscillating neutron stars. But the {\it duration} of the signals also contains useful information, particularly about the expected damping mentioned above. Indeed, \citet{2014ApJ...793..129H} found evidence of such damping of the $\sim 625$~Hz QPO from SGR~1806$-$20. However, there has not yet been a systematic study of these QPOs over short intervals. Here we perform a comprehensive analysis of QPOs from the SGR~1806$-$20 giant flare. We divide the data into intervals of one second, which is roughly one eighth of the rotation period, to explore whether there are short-lived QPOs, or whether instead most QPOs are long-lived. This also allows us to determine whether there are QPOs that are present for many rotational periods, but only in some range of rotational phases. Somewhat surprisingly, we find that there is little evidence for long-lived QPOs; instead, there are many QPOs that come and go over times that are likely to be a few tenths of a second. This could provide further support for the idea that coupling of crustal modes to the core MHD continuum damps the modes rapidly. In Section~\ref{sec:methods} we describe the data set that we analyze, as well as our analysis method (which is a new Bayesian approach not previously used in this context). In Section~\ref{sec:results} we present our results, and we conclude with a discussion of the results in Section~\ref{sec:discussion}. | \label{sec:discussion} Now we explore the implications our results could have for a model of the source star, the nature of the oscillations, and the mechanism responsible for the emission, that is, in what way the stellar oscillations can be coupled to the radiation emitted by the star and observed on Earth. The results presented in Figure~\ref{fig:phases} show that the emission happened predominantly in two nearly opposite rotational phases labeled 4 and 7 in our notation; one full period goes from phases 0 to 7 in our analysis). \footnote{It is also worth noting that this phase dependence in the appearance of the QPOs is distinct from the phase dependence observed in the number of counts (see Figure~\ref{fig:lightcurve}), indicating that it should be a real effect, and not a bias resulting from the detection of more or less counts.} A possible way of obtaining this symmetry would be by means of a slightly off-center dipolar magnetic field. The physical mechanism for the emission is not yet clearly understood (but see the models proposed by \citealt{2008ApJ...680.1398T,2012ApJ...751L..41D,2014AN....335..240G}). Whether it comes from the crust or from the magnetosphere, the QPOs appear to be strong mostly in those two phases. If the giant flare indeed comes from a rearrangement of the magnetic field, the crust at the magnetic poles of the star could be the regions more likely to break; at the same time, the magnetosphere above the poles would have the largest magnetic energy density. Both conditions could amplify the signal in a way such that it would be mostly visible at these two phases, making it seem more beamed, even if it is a broad (thermal) emission. Perhaps our most striking result is the indication that there are no obviously persistent oscillations in the tail of the giant flare. This is expected from theoretical studies of the properties of the crustal oscillations, which indicate that the crustal modes will couple to a continuum of MHD modes excited below the crust, which quickly damp the crustal oscillations. If, as we discussed in Section \ref{sec:freq_id}, we estimate the damping time $\tau$ of the oscillations by the inverse of the frequency width $\Delta f$, our results in Table~\ref{tab:QPOs} imply $\tau \approx 0.2 - 2$ s. This is consistent with the findings of \cite{2014ApJ...793..129H} for a higher frequency QPO ($\tau \approx 0.5$ s), and also roughly consistent with the expectations of \cite{2006MNRAS.368L..35L} ($\tau$ at most 1 s), which takes into account the damping resulting from the coupling with the continuum spectrum of MHD modes. More sophisticated theoretical analysis have introduced the possibility that there are gaps in the continuous spectrum of MHD modes, which could allow for longer-lived oscillations at least for the lower frequencies detected in the QPOs. Gaps in the continuum could be a consequence of more complicated magnetic field geometries (for example including a toroidal component or a tangled magnetic field, which can actually produce a discrete spectrum of MHD modes: see \cite{2016ApJ...823L...1L,2016ApJS..224....6L}). However, our analysis shows no compelling evidence for persistent oscillations in any part of the spectrum. This therefore suggests that the QPOs are independent oscillations with distinct but close frequencies (see Figure~\ref{fig:strong}). This could be understood as evidence of the existence of the continuous spectrum of MHD modes that was theoretically predicted. If the models for the continuum gap are correct, then the lack of persistent oscillations provides further support for a simple magnetic field configuration that is relatively close to a pure dipole. Note, however, that smooth dipoles are not stable (e.g., \citealt{2006A&A...450.1077B,2009MNRAS.397..763B}), so our findings will need to be reconciled with previous studies of magnetic stability. Another consequence of this picture is the need for a continued re-excitation of the modes after the giant flare. If the initial shock causes a starquake, then perhaps aftershocks in the crust provide the energy for the subsequent excitations. This could provide constraints on the nature of the crust, but other unknown mechanisms, perhaps including interactions with the perturbed magnetosphere, could be responsible for the continued input of energy. Finally, we have not attempted to perform an identification of the modes we have obtained in our analysis. Even in the simplest scenario in which the QPOs are explained as torsional crustal oscillations, the exact frequencies will depend on the mass, compactness, equation of state, crust composition and shear modulus, magnetic field strength and geometry, and so on. This multitude of parameters makes it extremely challenging to identify the modes and to solve the inverse problem, particularly given that there is a lack of relevant analytical expressions or universal relations for these frequencies (work on these issues is in preparation by G. de Souza and C. Chirenti). Nonetheless, the detailed data available for these QPOs means that they can still serve as a rich source of information that can be used to constrain many aspects of the interiors of neutron stars. | 18 | 8 | 1808.09483 |
1808 | 1808.10184_arXiv.txt | In this study, we present and validate a variation of recently-developed physically motivated sub-grid prescriptions for supernova feedback that account for the unresolved energy-conserving phase of the bubble expansion. Our model builds upon the implementation publicly available in the mesh-less hydrodynamic code \textsc{gizmo}, and is coupled with the chemistry library \textsc{krome}. Here, we test it against different setups, to address how it affects the formation/dissociation of molecular hydrogen (H$_2$). First, we explore very idealised conditions, to show that it can accurately reproduce the terminal momentum of the blast-wave independent of resolution. Then, we apply it to a suite of numerical simulations of an isolated Milky Way-like galaxy and compare it with a similar run employing the delayed-cooling sub-grid prescription. We find that the delayed-cooling model, by pressurising ad-hoc the gas, is more effective in suppressing star formation. However, to get this effect, it must maintain the gas warm/hot at densities where it is expected to cool efficiently, artificially changing the thermo-chemical state of the gas, and reducing the H$_2$ abundance even in dense gas. Mechanical feedback, on the other hand, is able to reproduce the H$_2$ column densities without altering the gas thermodynamics, and, at the same time, drives more powerful outflows. However, being less effective in suppressing star formation, it over-predicts the Kennicutt-Schmidt relation by a factor of about 2.5. Finally, we show that the model is consistent at different resolution levels, with only mild differences. | According to the current cosmological model, baryons cool down and fall within the potential well of dark matter haloes, fragmenting and forming stars (and galaxies). From simple arguments, star formation (SF) should occur on a free-fall time--scale, consuming very quickly all the available gas supply \citep[e.g.,][]{bournaud10,dobbs11}. However, the typical observed time--scale for SF is much longer than that expected from these simple arguments. One of the possible reasons behind this difference is stellar feedback, which evacuates the gas from the SF sites, suppressing the actual SF efficiency. One of the most important feedback processes to be considered is supernova (SN) feedback, i.e. the explosion of massive stars ($M_{\rm s} > 8\,\msun$) and accreting white dwarfs in binary systems (as type Ia SNe). Although an accurate physical description of the SN explosion mechanism is still missing, at pc scales SN events can be simply modelled as an instantaneous injection into the surrounding medium of mass, metals, and energy. In the last few decades, many authors investigated the evolution of the SN-driven bubble, with both analytical calculations and numerical simulations \citep[e.g.,][]{chevalier74,mckee77,cioffi88,kimostriker15,martizzi15,geen16}. However, to properly capture this evolution in numerical simulations, in particular the initial energy conserving phase \citep[the Sedov--Taylor phase;][]{taylor50,taylor50b,sedov59}, when radiative losses are still unimportant, extreme mass and spatial resolution are needed. Unfortunately, this is currently not achievable in galaxy-scale simulations, and it gets even worse in cosmological ones. In this case, a simple thermal energy injection would result in efficient radiative losses and negligible feedback effect, hence ad-hoc sub-grid prescriptions are necessary to overcome this problem. At very low resolution, when the inter-stellar medium (ISM) is unresolved, empirical models are usually employed, like in (i) \citet{navarro93}, where energy is injected in the kinetic form, (ii) \citet{springel03,keller14}, where the gas is described via a sub-grid multi-phase model, (iii) \citet{stinson06}, where cooling is shut off for some time to allow the blast-wave to expand following the energy-conserving solution, and (iv) \citet{dallavecchia12}, where many SN events are stochastically grouped together to produce more energetic explosions. Despite the success of these models, at higher resolution, when the multi-phase structure of the ISM can be resolved, a more physically motivated model is desirable. Recently, several authors put an effort to implement a new sub-grid supernova feedback model, so-called mechanical feedback, in different hydrodynamic codes \citep{hopkins13sf,kimm14,smith18,hopkins18}, where the feedback deposition takes into account the possibly unresolved Sedov--Taylor phase, injecting 1) the initial ejecta momentum/thermal energy if this phase is resolved, or 2) the terminal momentum of the bubble otherwise. Recently, \citet{martizzi15} investigated the evolution of SN bubbles in homogeneous and inhomogeneous media with very high resolution, in order to properly model the Sedov--Taylor phase. With their simulations, the authors were able to fit an analytic formula to properly describe the thermal energy and the momentum of the SN bubble at different stages of the evolution. This prescription, so far implemented only by \citet{semenov17}, allows a more accurate estimation of the amount of thermal energy and momentum to be injected as a function of the `coupling radius', i.e. the resolution of the simulation. Here, we implement the same prescription in the numerical code \textsc{gizmo} \citep{hopkins15}, as a variation of the already implemented mechanical feedback model by \citet[][H18 hereafter]{hopkins18b}, and we validate it against different tests, i.e. a single explosion in a uniform medium, and an isolated galaxy. Here, we follow the evolution of a single galaxy with a complete non-equilibrium reduced network of H$_2$ and a physically motivated SN feedback, similarly to what is done in \citet{hu18} in the case of a dwarf galaxy, \footnote{Although \citet{kimm17} performed radiation-hydrodynamics cosmological simulations including non-equilibrium H$_2$ chemistry, their model does not have a full out-of-equilibrium treatment, since they do not directly follow H$^-$ and H$_2^+$. In particular, they assume that H$^-$ is in collisional equilibrium and that H$_2^+$ is instantaneously dissociated, and this is different from what we employ here.} to assess whether the correlation between H$_2$ and star formation rate (SFR) surface densities can still be naturally reproduced without assuming a priori dependence of SF on the H$_2$ abundance \citep{lupi18a}. The manuscript is organised as follows: in Section~\ref{sec:model}, we describe the model and its implementation in the code; in Section~\ref{sec:test} we validate it by means of a single SN explosion test in a pseudo-uniform medium; in Section~\ref{sec:setup}, we describe the sub-grid model employed in the galaxy simulations; in Section~\ref{sec:results}, we present our results; in Section~\ref{sec:conclusions}, we discuss the limits of the model and we draw our conclusions. | \label{sec:conclusions} We presented here a variation of the physically motivated SN feedback model presented in H18, that is able to deposit the right amount of energy and momentum into the ISM, according to the results of high-resolution, small-scale simulations. Most of the numerical details closely follow H18, but with some significant modifications, which include the maximum coupling radius, the effective face shared by particles, and the momentum/thermal energy deposition. After validating the model using isolated SN explosions in a uniform medium at different resolutions as done in H18, we applied the model to a Milky Way-like galaxy at $z\sim 0.1$ in isolation, to assess its ability to reproduce the observed correlation between SF and H$_2$. We compared this new model with the delayed-cooling SN feedback model employed in \citet{lupi18a}, which showed very good agreement with observations \citep[see also][]{capelo18}, despite the unphysical temperature of the gas kept hot by SNe, and we also tested the resolution dependence of the model. We summarise here our findings: \begin{itemize} \item Terminal momentum in a uniform medium: the mechanical feedback model almost perfectly reproduces the terminal momentum of a single SN event, independent of resolution. However, to achieve this convergence, the proper swept-up fraction of the particle mass should be employed for the momentum deposition, otherwise the terminal momentum would be overestimated at high resolution. The delayed-cooling prescription, on the other hand, overestimates the terminal momentum by up to an order of magnitude, at low resolution, because of the cooling shut-off that draws the evolution closer to the fully energy-conserving case. \item Model comparison -- SF in the galaxy: the delayed-cooling model more effectively suppresses SF, because of the artificial pressurisation of the gas, that completely inhibits SF for some time. When the shut-off time is short, the SF is not dispersed like in the mechanical feedback case, but it stays warm and not SF. In the opposite case, when the shut-off time is long enough, the SF region is destroyed, but the gas is kept hot, and it does not collapse efficiently when shocks occur with the surrounding medium. On the other hand, mechanical feedback more effectively sweeps the gas away, because of the kick imparted to the gas, but is not able to properly describe the hot, low-density cavity produced ( the gas remains cold and moves super-sonically, resulting in shocks and subsequent cooling that trigger new SF, yielding a slightly too high SF rate. \item Model comparison -- KS relation: the H$_2$ KS relation and the H$_2$ column density fraction are consistent between the two models, with only mild differences, suggesting that these correlations are reasonably robust against different sub-grid models, as already stated in \citet{lupi18a} for the SF prescription. On the other hand, the total KS relation is higher in the mechanical feedback run, because of the overall higher SFR relative to the delayed-cooling case, although the slope in the high surface density regime is consistent with observations. \item Model comparison -- galaxy outflows: close to the galaxy, the delayed-cooling model produces slightly stronger outflows ($\beta_{\rm out}$ is slightly larger than with mechanical feedback, but with a less than a factor of two difference), whereas the opposite occurs at larger distances. In all cases, the outflows never exceed the escape velocity from the halo, hence resulting in galactic fountains rather than proper outflows. This is consistent with previous results from \citet{rosdahl17}, where they find that only kinetic feedback is able to produce very powerful outflows. However, the idealised setup of our experiment does not allow to conclude whether mechanical feedback can explain the missing baryons in a cosmological context or not. \item Resolution dependence: the mechanical feedback model is not strongly resolution-dependent. In particular, the outflows close the galactic plane (2~kpc) are similar among the runs, with only the low-resolution cases producing slightly stronger outflows because of the typically larger volumes of each cell and the SN--gas interaction that extends to larger distances from the disc plane. At larger distances, the variations increase up to one or two order of magnitudes among the different runs, but a clear trend cannot be observed, suggesting that the outflow rate evolution becomes very sensitive to the actual dynamical evolution of the galaxy and the location of the stellar particles, but not necessarily to the resolution itself. All the other properties, instead, are consistent among the five resolutions, with only larger fluctuations at lower resolutions because of the poorer sampling of the gas properties. \end{itemize} In the delayed-cooling model, one of the problems is the overshooting of the H$_2$ KS relation at high density. As already stated in \citet{lupi18a}, this could be related to (i) the fact that, at high densities, the SF prescription converts gas into stars very quickly, removing all the molecular hydrogen available for the converted gas particle, hence reducing its surface density, or (ii) to the numerical diffusion close to the resolution limit which slightly reduces the turbulent support of the gas. A possible solution to avoid (ii) is to include a sub-grid model for the turbulent cascade, as in \citet{semenov17}. However, from the comparison with the mechanical feedback, an alternative explanation could be that the high-density gas is kept warm by SNe, and H$_2$ is dissociated too efficiently. For the mechanical feedback model, instead, the higher SFRs observed can be the result of missing additional feedback processes like HII regions, young stellar winds, and cosmic rays, that could help provide additional energy/pressure able to more efficiently suppress SF. In the delayed-cooling runs, the empirical choice of shutting off radiative cooling could probably mimic (despite not in a completely physical fashion) these additional processes not present in the mechanical feedback model. An alternative explanation for the too high SFR in the mechanical feedback model is that the momentum injected is too low compared to reality \citep[see, e.g.][]{keller14,gentry17}, probably because of numerically enhanced mixing \citet{gentry18}. If this is the case, then the terminal momentum should be higher, the shocks in the swept-away gas should be stronger and the gas heating more effective. As a consequence, this could lead to larger mass loading factors and in a more effective suppression of SF, as shown by \citet{semenov18b} where their fiducial boost to the momentum is enough to perfectly match the KS relation (in both total and molecular gas). However, a thorough investigation of these effect is beyond the scope of this study. Concluding, although the delayed cooling has many advantages that make it suitable for galaxy-scale simulations, it is unable to properly reproduce all the galaxy properties observed, especially those dependent on the thermochemical state of the gas. On the other hand, the mechanical feedback, despite not being as effective as the delayed cooling in suppressing the SF, better reproduces the thermo-chemical state of the gas, the H$_2$ column densities observed, and is also able to drive more powerful outflows. Although further investigations are certainly necessary to fully assess the limitations of the mechanical feedback model, its physical motivation and ability to accurately reproduce the terminal momentum independent of resolution represent a step forward compared to the empirical delayed cooling mode. Thanks to the general effort of the community in improving the sub-grid modelling, mechanical feedback, coupled with other state-of-the-art prescriptions for processes like SF, chemistry, and enrichment will definitely help us to better understand how galaxies self-regulate during their evolution. | 18 | 8 | 1808.10184 |
1808 | 1808.05208_arXiv.txt | We present predictions for the UV-to-mm extragalactic background light (EBL) from a recent version of the \galform\ semi-analytical model of galaxy formation which invokes a top-heavy stellar initial mass function (IMF) for galaxies undergoing dynamically-triggered bursts of star formation. We combine \galform\ with the \grasil\ radiative transfer code for computing fully self-consistent UV-to-mm spectral energy distributions for each simulated galaxy, accounting for the absorption and re-emission of stellar radiation by interstellar dust. The predicted EBL is in near-perfect agreement with recent observations over the whole UV-to-mm spectrum, as is the evolution of the cosmic spectral energy distribution over the redshift range for which observations are available ($z\lesssim1$). We show that approximately 90~per~cent of the EBL is produced at $z<2$ although this shifts to higher redshifts for sub-mm wavelengths. We assess whether the top-heavy IMF in starbursts is necessary in order to reproduce the EBL at the same time as other key observables, and find that variant models with a universal solar-neighborhood IMF display poorer agreement with EBL observations over the whole UV-to-mm spectrum and fail to match the counts of galaxies in the sub-mm. | The extragalactic background light (EBL) provides a record of the production of photons since (re)combination, and thus contains a wealth of information regarding various astrophysical processes over the history of the Universe. In the $0.1-1000$~$\muup$m (UV-to-mm) wavelength range it is dominated by the redshifted emission from galaxies, including the absorption and re-emission by interstellar dust of photons produced in stars. It also includes minor ($\lesssim10$~per~cent) contributions from active galactic nuclei \citep[AGN e.g.][]{Almaini99,Silva04}, intra-halo light (IHL) from diffuse halo stars no longer associated with a host galaxy \citep[e.g.][]{Zemcov:2014} and redshifted Lyman~$\alpha$ emission from the epoch of reionization \citep[e.g.][]{MitchellWynne:2015}. As such, the EBL provides strong constraints on the cosmic star formation history and on models of galaxy formation and evolution \citep[e.g.][]{Fardal:2007,Franceschini:2008,Finke:2010,Somerville:2012,Inoue:2013,Andrews:2018,Baes:2019}. Historically, two methods have been used to observationally estimate the EBL: (i) direct detection with instruments such as the diffuse infrared background explorer \citep[DIRBE, ][]{Silverberg:1993} and the far-infrared absolute spectrophotometer \citep[FIRAS, ][]{Mather:1993} flown on the Cosmic Background Explorer satellite \citep[\emph{COBE} e.g.][]{Puget96, Fixsen98, Wright:2004}; and (ii) integrating galaxy number counts \citep[e.g.][]{MadauPozzetti:2000,Berta:2011,Bethermin12,Driver:2016}. The former requires accurate removal of foregrounds, most notably that of zodiacal light \citep[solar emission scattered by interplanetary dust e.g. ][]{Bernstein:2002, Mattila:2006} and emission from the Milky Way \citep[e.g.][]{Bernard:1994, Arendt:1998}, which have put a limit on the accuracy with which the EBL can be measured directly. The second method requires an extrapolation to faint fluxes as is discussed in more detail below. Integrating galaxy number counts has, until relatively recently, suffered from insufficiently deep data, particularly at far-IR wavelengths, to fully resolve the EBL. In this wavelength regime confusion noise introduced by the coarse angular resolution [$\sim20$~arcsec full width at half maximum (FWHM)] of single-dish telescopes commonly used for imaging at these wavelengths and the high surface density of detectable objects (e.g. Nguyen et al. \citeyear{Nguyen:2010}) meant that only a small fraction ($\sim15$~per~cent) of the far-IR EBL could be resolved \citep[][]{Oliver10}. The use of techniques such as gravitational lensing \citep[e.g.][]{Smail97, Knudsen08, Chen13}, stacking \citep[e.g.][]{Bethermin12, Geach13} and high resolution interferometry \citep[e.g.][]{Hatsukade13,Carniani15} has allowed galaxy number counts to be statistically estimated at fluxes fainter than the traditional confusion limit. This has resolved a much higher proportion of the EBL, and results from direct detection and from integrated number counts are now in good agreement over mid- to far-IR wavelengths. There exists a general discrepancy between integrated counts and direct measurements at optical/near-IR wavelengths however, with direct observational estimates typically being factors of $\sim2-5$ higher than those obtained from the integrated counts. This could indicate that sources of light not associated with individual galaxies (e.g. IHL) form a significant component of the EBL at these wavelengths, or that the models used in foreground removal require revision. Recently, a third, independent, method of estimating the EBL has shed some light on this issue. Measurements of the attenuation of high-energy (TeV) photons from blazars, which are assumed to be emitted with a well-defined power law spectrum, as they scatter with EBL photons could reveal the spectrum of the EBL. This was first illustrated by the High Energy Stereoscopic System \citep{HESS:2006}, and detailed measurements have since been performed over the full UV-to-mm range \citep[][]{BiteauWilliams:2015, MAGIC:2016}. These independent measurements all favour the estimates from integrated number counts (though some caveats do remain e.g. their dependence on the assumed intrinsic shape of the blazar spectrum), suggesting that current zodical light models may require some revision, and that light not associated with galaxies e.g. IHL, makes a minimal contribution (see also the discussion in Driver et al. \citeyear{Driver:2016}). For this reason, throughout we take the observed EBL as being equivalent to what is obtained from integrating galaxy number counts at all UV-to-mm wavelengths. Here we present predictions for the EBL from the well-established semi-analytical model for galaxy formation, \galform\ \citep[e.g.][]{Cole00,Lacey16}. This provides a physical calculation of galaxy formation from high redshift ($z\gtrsim15$) to the present day ($z=0$), accounting for the main physical processes involved (e.g. gravitational collapse, gas cooling, star formation and feedback) implemented within the cold dark matter (CDM) cosmological model. Simulated galaxy spectral energy distributions (SEDs) are computed using the radiative transfer code \grasil\ \citep{Silva98}. This means the absorption, scattering and re-emission of stellar radiation by interstellar dust is calculated completely self-consistently from the physical properties of galaxies predicted by \galform\ (e.g. gas-phase metallicity, size) and the assumed geometry and composition of the interstellar dust. The model thus provides a consistent physical framework for interpreting multi-wavelength observations over the history of the Universe. This combined modelling represents a significant advantage over empirical models that employ arbitrary phenomenological recipes to reproduce key observational constraints \citep[and thus forgo a physical interpretation of their predictions e.g.][]{Franceschini:2008,Dominguez:2011,Andrews:2018}, and over models that rely on empirical SED templates for calculating galaxy spectra over some (e.g. far-IR) or all of the UV-to-mm spectrum \citep[as their predicted luminosities are not necessarily internally self-consistent with the underlying galaxy formation model e.g.][]{Gilmore:2012,Somerville:2012}. Additionally, the flexibility of the semi-analytical method means that variant models in which some modelling assumptions are varied can be calculated quickly to assess their impact on reproducing various observations. This type of parameter exploration is not generally possible with the current state-of-the-art hydrodynamical cosmological galaxy formation simulations \citep[e.g.][]{Vogelsberger14, Schaye15, Nelson:2018} due to their prohibitive computational expense. One of the key features of the version of the \galform\ model used in this work \citep[and described fully in][]{Lacey16} is that it incorporates a top-heavy initial mass function (IMF) during periods of dynamically-triggered star formation. This feature was incorporated into the model so that it could simultaneously reproduce the number counts and redshift distribution of sub-mm galaxies observed at $850$~$\muup$m and the present day (i.e. $z=0$) optical and near-IR galaxy luminosity functions \citep{Baugh05}. The IMF used in the \cite{Lacey16} model is much less top-heavy, however, than the one implemented by Baugh et al. We investigate whether this feature is required in order for the model to reproduce the EBL at far-IR wavelengths in conjunction with other constraints such as the $K$-band luminosity function at $z=0$ and the evolution of the cosmic star formation rate density. In doing so we reassess the argument of \cite{Fardal:2007}, who suggest that these three observational datasets are incompatible with a universal IMF of the form observed in the solar neighbourhood. Fardal et al. integrated simple parametrizations of the cosmic star formation history and found that it was not possible to find histories that could reproduce the local $K$-band luminosity density and the EBL simultaneously whilst assuming a Salpeter (\citeyear{Salpeter55}) IMF (see e.g. their Figure~5). We note that \cite{Somerville:2012}, using a semi-analytical galaxy formation model assuming a universal IMF, found a reasonable match to the EBL, cosmic star formation history and present-day $K$-band luminosity function, but under-predicted the number counts of galaxies at $850 \,\mu $m. Other galaxy formation studies have considered IMF variations, such as \cite{Gargiulo:2015} and \cite{Fontanot:2017}, who invoked a top-heavy IMF in regions of high star formation in semi-analytical models, and \cite{Barber:2018}, who imposed a pressure dependent IMF in an {\tt EAGLE} hydrodynamical simulation; these studies did not consider the EBL. This paper is structured as follows: in Section~\ref{sec:Model} we introduce the theoretical model, which incorporates a semi-analytical model of galaxy formation implemented within halo merger trees derived from a Millennium-style dark matter only $N$-body simulation \citep{Springel05,Baugh:2019} and the radiative transfer code, \grasil\ \citep{Silva98}, for computing the absorption and re-emission of stellar radiation by interstellar dust. In Section~\ref{sec:Results} we present the predictions of the model for the EBL and show how this is built up over the history of the Universe\footnote{Some of the model data presented here will be made available at \url{http://icc.dur.ac.uk/data/}. For other requests please contact the first author.}. We also present predictions from variant models with a universal solar-neighbourhood IMF and discuss how critical this feature is for reproducing the EBL. We summarise in Section~\ref{sec:Conclusion}. Throughout we assume a flat $\Lambda$CDM cosmology with cosmological parameters consistent with recent \emph{Planck} satellite results \citep{PlanckCollaboration:2014}\footnote{$\Omega_{\rm m}=0.307$, $\Omega_{\Lambda}=0.693$, $h=0.678$, $\Omega_{\rm b}=0.0483$, $\sigma_{8}=0.829$}. | \label{sec:Conclusion} We have investigated the extragalactic background light (EBL) predicted by the semi-analytical galaxy formation model \galform. The model is implemented in halo merger trees from the P--Millennium, a large ($800$~Mpc)$^{3}$ cosmological $N$-body simulation \citep{Baugh:2019} run with cosmological parameters consistent with the \emph{Planck} satellite data, and is calibrated to reproduce an unprecedentedly large set of observational data at $z\lesssim6$ \citep{Lacey16}. For computing simulated galaxy SEDs accounting for the absorption and re-emission of stellar radiation by interstellar dust we combined \galform\ with the fully self-consistent radiative transfer code \grasil\ \citep{Silva98}. The predicted EBL is in remarkable agreement with available observations over the whole of the UV-to-mm range investigated. We show that most (c. $90$~per~cent) of the EBL is produced at $z\lesssim2$, although far-IR EBL photons tend to be produced at slightly higher redshifts. Comparing the model predictions for galaxy number counts with observations, we find that the model can generally reproduce the observed distribution of fluxes well over the whole range of wavelengths. We also find that the redshift distribution of the EBL is in good agreement with observational estimates at far-IR wavelengths, and this is also the case if $24$~$\muup$m and near-IR flux limits on stacked data are considered. We show the predicted evolution of the cosmic SED, the luminosity density as a function of wavelength at a given epoch in the Universe's history. We find that this is in good agreement with available observational data at $z\lesssim1$, although the predicted UV continuum slopes appear to be too `blue' at these redshifts, and the luminosity density in the optical ($\lambda_{\rm rest}\sim0.3-4$~$\muup$m) portion of the spectrum appears to be mildly over-predicted, perhaps as a consequence of having slightly too much star formation at higher redshifts. Finally, we investigated the necessity of a top-heavy IMF during dynamically-triggered star formation for reproducing the EBL, simultaneously with the $K$-band luminosity function at $z=0$, the cosmic star formation history and the number counts and redshift distribution of galaxies at $850 \, \mu $m, by examining the predictions of variant models with a universal IMF and comparing these with the predictions of our fiducial model. We find that variant models with a universal solar-neighbourhood IMF struggle to reproduce these observational constraints to the same level of accuracy. In particular, the universal IMF variants do not reproduce the sub-mm ($850$~$\muup$m) galaxy number counts as well as our fiducial model, failing by over an order of magnitude. This is a challenge shared by other physical galaxy formation models. Whilst we have only investigated a small number of variant models with a universal IMF it is difficult to see how simple parameter variations in current models can alleviate this {\it mismatch whilst simultaneously} reproducing constraints such as the $K$-band luminosity function at $z=0$. Similar conclusions were reached by \cite{Somerville:2012} who, using a different semi-analyical model of galaxy formation, were unable to reproduce the counts of galaxies at $850 \, \mu$m using a model with a universal IMF. Thus it seems that these data favour a top-heavy IMF in highly star-forming galaxies, a feature which remains controversial but for which there is mounting evidence from independent observational probes \citep[e.g.][]{Zhang18}. The overall excellent agreement of the predictions of our pre-existing galaxy formation model with EBL data is a remarkable success of the model. These data encode multiple aspects of the galaxy formation process and are distinct from the data originally used to calibrate the fiducial model originally. No model parameters were adjusted for the comparisons presented in this study. This work highlights the predictive power and realism of this self-consistent multi-wavelength physical model and underlines its utility as a powerful tool for interpreting and understanding multi-wavelength observational data over a broad range of redshifts. | 18 | 8 | 1808.05208 |
1808 | 1808.00107_arXiv.txt | We investigate acceleration of cosmic rays by shocks and accretion flows in galaxy clusters. Numerical results for spectra of accelerated particles and nonthermal emission are presented. It is shown that the acceleration of protons and nuclei in the nearby galaxy cluster Virgo can explain the observed spectra of ultra high energy cosmic rays. | Clusters of galaxies are considered as a possible candidate for the origin of ultra-high energy cosmic rays (UHECRs) (see e.g. \cite{brunetti14} for a review). Primordial density fluctuations are amplified via gravitational instability in the expanding Universe and result in the appearance of different coherent density structures at the present epoch. The galaxy clusters are formed at the latest times and continue to grow presently due to accretion of the cicumcluster gas and dark matter. The inflow of matter is accompanied by an accretion shock at a distance several Mpc from the cluster center. Virgo cluster of galaxies with the total mass of $\sim 10^{15}M_{\odot }$ at the distance $d\sim 15-20$ Mpc \cite{ade16} from the Milky Way is the nearest large galaxy cluster. It is located at the center of the Local super cluster of galaxies. Because of its proximity Virgo has been proposed as the source of observed UHECRs within a phenomenological diffusive model \cite{giler80}. The diffusive shock acceleration (DSA) process \cite{krymsky77,bell78,axford77,blandford78} is believed to be the principal mechanism for the production of galactic cosmic rays (CR) in supernova remnants (SNRs). Over the last decade the excellent results of X-ray and gamma-ray astronomy have been providing evidence of the presence of multi-TeV energetic particles in these objects (see e.g. \cite{lemoine14}). Since the accretion shocks are very large they can accelerate particles to significantly higher energies compared to SNRs and produce a significant fraction of observable UHECRs \cite{norman95,kang96,kang97}. In this paper we describe the modifications of our non-linear DSA model \cite{zirakashvili12} designed for the investigation of DSA in SNRs and apply it for the investigation of particle acceleration in clusters of galaxies. In particular we apply the model for the Virgo cluster of galaxies. | We show that almost all UHECRs can be accelerated in the nearby Virgo cluster of galaxies. Our consideration is close to the earlier pure proton model of Kang et al. \cite{kang96}. Note that we used more realistic value of the magnetic field strength that is 10 times lower. The corresponding decrease of the maximum energy is compensated by the presence of heavier nuclei in UHECR spectrum. The drawback of the model is its sensitivity to adjusted parameters to fit UHECR data. As mentioned before we observe an exponentially small part (10$^{-4}$) of the highest energy particles accelerated at the accretion shock. That is why modest variations of the magnetic field strength result in the significant change of UHECR intensity. Probably more massive and more distant clusters like Coma or another astrophysical sources (e.g. active galactic nuclei) also might give some contribution at highest energies. The particles accelerated in distant astrophysical objects can reach the Local supercluster propagating in the cosmological voids where the magnetic fields are very weak. The adjusted maximum energy of background cosmic rays $E_{IG}=cp_{IG}= 8 \ Z$ Pev is not far from the "knee" energy. It is not excluded that this is not a coincidence. The value of $E_{IG}$ is rather well constrained by available UHECR data. For lower values of $E_{IG}$ we would observe a large dip in the spectrum between 0.1 and 1 EeV. For higher values of $E_{IG}$ we would observe heavy UHECR composition at 1 EeV. \ack The work was supported by Russian Foundation of Fundamental Research grant 16-02-00255. The paper was presented at the 26th European Cosmic Ray Symposium, Barnaul, July 6 - 10, 2018. \bigskip % | 18 | 8 | 1808.00107 |
1808 | 1808.05365.txt | In Zhang $\&$ Showman (2018, hereafter Paper I), we developed an analytical theory of 1D eddy diffusivity $K_{zz}$ for global-mean vertical tracer transport in a 3D atmosphere. We also presented 2D numerical simulations on fast-rotating planets to validate our theory. On a slowly rotating planet such as Venus or a tidally locked planet (not necessarily a slow-rotator) such as a hot Jupiter, the tracer distribution could exhibit significant longitudinal inhomogeneity and tracer transport is intrinsically 3D. Here we study the global-mean vertical tracer transport on tidally locked planets using 3D tracer-transport simulations. We find that our analytical $K_{zz}$ theory in Paper I is validated on tidally locked planets over a wide parameter space. $K_{zz}$ strongly depends on the large-scale circulation strength, horizontal mixing due to eddies and waves and local tracer sources and sinks due to chemistry and microphysics. As our analytical theory predicted, $K_{zz}$ on tidally locked planets also exhibit three regimes In Regime I where the chemical and microphysical processes are uniformly distributed across the globe, different chemical species should be transported via different eddy diffusivity. In Regime II where the chemical and microphysical processes are non-uniform---for example, photochemistry or cloud formation that exhibits strong day-night contrast---the global-mean vertical tracer mixing does not always behave diffusively. In the third regime where the tracer is long-lived, non-diffusive effects are significant. Using species-dependent eddy diffusivity, we provide a new analytical theory of the dynamical quench points for disequilibrium tracers on tidally locked planets from first principles. | As stated in Paper I (\citealt{zhang2018kzz}), atmospheric transport can drive the atmospheric chemical species out of chemical equilibrium and greatly influence the observations (e.g., \citealt{prinn1976chemistry}, \citealt{prinn1977carbon}, \citealt{smith1998estimation}, \citealt{cooper-showman-2006}, \citealt{visscher-moses-2011}). Currently, the dominant approach of simulating the global-mean vertical distributions of chemical species and clouds on atmospheres of tidally locked planets is solving a 1D diffusive system with an effective eddy diffusivity and chemical/microphysical source and sinks (e.g., \citealt{moses-etal-2011}, \citealt{line2011thermochemical}, \citealt{tsai2017vulcan}, \citealt{helling2008dust}, \citealt{gao2014bimodal}, \citealt{lavvas2017aerosol}, \citealt{powell2018formation}). In the 1D chemical-diffusion framework, the strength of the vertical diffusion is characterized by a parameter called eddy diffusivity or eddy mixing coefficient $K_{zz}$. The physical underpinning of this key parameter is obscure. In Paper I, we constructed a first-principles theory of $K_{zz}$ and provided analytical expression for $K_{zz}$ in a 3D atmosphere under idealized assumptions about the nature of the chemical source/sink and other simplifications. We further validated the theory using 2D numerical simulations on fast-rotating planets. However, for tidally locked exoplanets or slow-rotating planets that exhibit significant day-night contrast such as Venus, a 2D model is not sufficient to simulate the intrinsically 3D tracer transport process in those planetary atmospheres. This is our focus in this paper. On these planets, the global circulation pattern could vary from a substellar-to-anti-stellar circulation in the upper atmosphere to a fast zonal-jet circulation in the lower atmosphere (e.g., \citealt{bougher1997venus} for Venus, \citealt{showman-etal-2013} and \citealt{cooper-showman-2005} and \citealt{zhang2017effects} for tidally locked planets). Tracer transport with a substellar-to-anti-stellar wind pattern cannot be treated in a 2D zonal-symmetric system as we described in Paper I. Even in the zonal-jet regime, the existence of longitudinally varying dynamical structures (eddies) plays a critical role in both the dynamics and the mixing of chemical tracers. Moreover, the day-night temperature and insolation gradients imply that, for many tracers, there will exist large day-night variations in chemical sources and sinks that further exacerbate the longitudinal asymmetry and amplify the overall 3D nature of the problem. For instance, photochemically produced tracers on a slowly rotating planet or a tidally locked planet could develop substantially different chemistry and equilibrium tracer distributions between the dayside and nightside, a canonical example being sulfur species from photochemistry on Venus (e.g., \citealt{zhang2010venus}, \citealt{zhang2012sulfur}). For another example, transport of haze and cloud particles on a tidally locked planet is essentially 3D because their formation and destruction are greatly affected by the local temperature and condensable gas abundance which might have a large zonal variation (\citealt{powell2018formation}). To investigate the global-mean vertical tracer transport on tidally locked exoplanets, a 3D dynamical model is needed (e.g., \citealt{cooper-showman-2006}, \citealt{parmentier20133d}). There have been several studies of 3D chemical-transport on tidally locked exoplanets with simplified chemical and cloud schemes (e.g., \citealt{cooper-showman-2006}, \citealt{parmentier20133d}, \citealt{charnay20153d2}, \citealt{lee2016dynamic}, \citealt{drummond2018effect}, \citealt{lines2018simulating}). However, how to parameterize the the 3D transport processes in a 1D global-mean tracer transport model is still an open question. Especially, if one adopts the 1D chemical-diffusion framework, a thorough theoretical link between the 3D tracer transport and the effective 1D eddy diffusivity $K_{zz}$ on these planets has not been well established. For example, \citet{parmentier20133d} studied simple passive cloud tracers using a 3D dynamical model, and showed that the 1D effective eddy diffusivity on hot Jupiters does not exhibit a significant dependance on tracer sinks. This seems contradictory to our findings as well as previous terrestrial studies such as \citet{holton1986dynamically} that the $K_{zz}$ should be species-dependent. This puzzle has not been satisfactorily solved. Here we will apply our analytical $K_{zz}$ theory in Paper I and 3D tracer-transport simulations to the photospheres on tidally locked planets where most of the chemical tracers and haze/clouds are observed. In the following sections, we will first recap the analytical $K_{zz}$ theory in Paper I and further develop it for tidally locked planets. A 3D general circulation model (GCM) with passive tracers is then used to understand the atmospheres on tidally locked exoplanets under two typical scenarios: tracers that are transported from the deep atmosphere and that are produced in the upper atmospheres via photochemistry or ion chemistry. We will also study the effects of our $K_{zz}$ theory on the dynamical quenching of disequilibrium tracers on tidally locked planets. We conclude this study with several take-home messages. | In this study we investigated tracer transport on tidally locked planets using a simple chemical source/sink scheme. Using the analytical vertical velocity theory from \citet{komacek2016atmospheric} and \citet{zhang2017effects}, we constructed a first-principles theory for the 1D eddy diffusivity $K_{zz}$ on this type of planet. We performed 3D tracer simulations using a GCM and derived the $K_{zz}$ from the globally averaged vertical transport flux from the model. We showed that the $K_{zz}$ derived from the 3D simulations agree with our analytical predictions. Therefore this study can serve as a theoretical foundation for future work on estimating or understanding the effective eddy diffusivity for global-mean vertical tracer transport on tidally locked exoplanets and slow-rotating planets with strong day-night contrast such as Venus. Our detailed analytical and numerical analysis for 3D tidally locked planets basically agree with the conclusions we have drawn in Paper I (1-8 in the Conclusion Section) for fast-rotating planets. We also confirm that all three typical regimes in our $K_{zz}$ theory exist on tidally locked planets. Since this is the first time to validate these conclusions in a 3D model with a strongly 3D circulation in a tidally locked configuration, we briefly recap all the points here. (1) Larger vertical velocities lead to a larger global-mean vertical tracer mixing. (2) Efficient horizontal eddy mixing reduces the horizontal variations of tracer and decreases the global-mean eddy diffusivity. (3) Global-mean eddy diffusivity depends on the tracer sources and sinks due to chemistry and microphysics. The effective eddy diffusivity increases with the chemical lifetime in the case with linear chemical relaxation. (4) In regime I, short-lived species exhibit a similar spatial pattern as the vertical velocity field. But the resulting tracer distribution is complicated in other regimes. (5) The diffusive assumption is generally valid in regime I and the effective eddy diffusivity is always positive using our idealized chemical schemes. But non-diffusive effects can be important in regime II if there is a good correlation between the equilibrium tracer field and the vertical velocity field. (6) Non-diffusive behavior could occur in regime III when the tracer chemical lifetime is much longer than the atmospheric dynamical timescale. (7) We derived the analytical species-dependent eddy diffusivity for tracers for the tracers on tidally locked planets, the theoretical predictions generally agree with our 3D simulations in all regimes. (8) In the 3D planetary atmospheres under tidally locked configuration, the widely used assumption in current 1-D chemistry and cloud formation models---a single profile of vertical eddy diffusivity for all species---is generally invalid. In this study, based on the species-dependent eddy diffusivity theory, we also provide a new analytical theory of the global-mean departure ``quench" point of the tracer from its chemical equilibrium profile. Because the species-dependent eddy diffusivity is smaller than the conventional species-independent value, the departure point estimated in our theory is located at lower pressure than the previous estimate if the tracer chemical timescale increases with decreasing pressure. For tracers on close-in tidally locked exoplanets, the departure point estimated from our theory assuming $L_v\sim H$ agrees with the numerical simulations for longer-lived species. For shorter-lived species, using the equilibrium chemical scale height $H_{ceq}$ as $L_v$ provides a better estimate. How to better approximate the 3D tracer transport in a 1D model for real atmospheres? We emphasize that it is the correlation between the horizontally varying tracer fields and horizontally varying vertical velocity field along an isobar that determines the the vertical transport efficiency. Here we propose two approaches. First, from a theoretical point of view, it is necessary to perform 3D tracer transport simulations with more realistic chemical and microphysical schemes for a specific atmospheric situation (e.g., \citealt{lee2016dynamic}, \citealt{lines2018simulating}) and analyze how to better parameterize the 1D effective tracer transport in that atmospheric regime. Taking close-in tidally locked planets as an example, one could include simplified dayside photochemistry and ion chemistry to study a chemically active species, and/or include nightside haze/cloud condensation and dayside particle evaporation to study cloud particle transport. \citet{parmentier20133d} and this study represent an initial step in this direction. Second, from an observational point of view, it would be interesting to perform a correlation analysis between the observed tracer fields and the vertical velocity field (or the simulated vertical velocity field if the vertical velocity is not easy to determined from observations). Even for exoplanets, observations are starting to reveal horizontal gas distributions (\citealt{stevenson2017spitzer}) and the cloud distribution from the light curve data (e.g., \citealt{parmentier2016transitions}). A correlation analysis between the tracer fields and the velocity field estimated from the atmospheric models (e.g., \citealt{dobbs-dixon-lin-2008}; \citealt{showman-etal-2009}; \citealt{rauscher-menou-2010}; \citealt{heng-etal-2011}; \citealt{perna-etal-2010}; \citealt{mayne2014unified}) may shed light on how the vertical tracer transport operates on those planets and lead to a better understanding of global-mean vertical eddy mixing for future chemical models and cloud models. | 18 | 8 | 1808.05365 |
1808 | 1808.06983_arXiv.txt | We present results obtained from spectroscopic observations of red giants located in the fields of the Large Magellanic Cloud (LMC) globular clusters (GCs) NGC\,1928 and NGC\,1939. We used the GMOS and AAOmega+2dF spectrographs to obtain spectra centred on the Ca\,II triplet, from which we derived individual radial velocities (RVs) and metallicities. From cluster members we derived mean RVs of RV$_{\rm NGC\,1928}=249.58\pm$4.65 km/s and RV$_{\rm NGC\,1939}=258.85\pm$2.08 km/s, and mean metallicities of [Fe/H]$_{\rm NGC\,1928}=-1.30\pm$0.15 dex and [Fe/H]$_{\rm NGC\,1939}=-2.00\pm$0.15 dex. We found that both GCs have RVs and positions consistent with being part of the LMC disc, so that we rule out any possible origin but that in the same galaxy. By computing the best solution of a disc that fully contains each GC, we obtained circular velocities for the 15 known LMC GCs. We found that 11/15 of the GCs share the LMC rotation derived from $HST$ and $Gaia$ DR2 proper motions. This outcome reveals that the LMC disc existed since the very early epoch of the galaxy formation and experienced the steep relatively fast chemical enrichment shown by its GC metallicities. The four remaining GCs turned out to have circular velocities not compatible with an {\it in situ} cluster formation, but rather with being stripped from the SMC. | Only fifteen old GCs (GCs, ages $\ga$ 12 Gyr) are known to survive in the Large Magellanic Cloud (LMC) \citep{pg13}, of which NGC\,1928 and NGC\,1939 have only recently been added by \citet[][hereafter D99]{detal99}. Their first colour-magnitude diagrams come from $HST$ photometry \citep{mg04}, confirming their old ages. As far as we are aware, neither NGC\,1928 nor NGC\,1939 have published accurate metallicity or radial velocity (RV) measurements. The orbital motions of LMC ancient GCs are satisfactorily described by a disc-like rotation with no GC appearing to have halo kinematics \citep{shetal10}. \citet{s92} found that these clusters form a disc that agrees with the parameters of the optical isophotes and inner H\,I rotation curve. There are some other galaxies that appear to have GC systems with kinematic properties related to the H\,I discs \citep[e.g.][]{olsenetal2004}, which might suggest a benign evolutionary history, such as might be expected if the LMC has evolved in a low density environment. However, the destruction of a GC system that is on a coplanar orbit about a larger galaxy could also produce such a disc-like rotation geometry \citep{leamanetal2013}. Furthermore, \citet{vdbergh2004} showed that the possibility that the LMC old GCs formed in a pressure-supported halo, rather than in a rotating disc, should not be discarded. In this sense, \citet{carreraetal2008} argued that the lack of evidence of such a hot stellar halo in the LMC is related to a low contrast of the halo population with respect to that of the disc, particularly at the innermost galactocentric radii where NGC\,1928 and NGC\,1939 are located. On the other hand, \citet{carpinteroetal2013} modelled the dynamical interaction between the Small Magellanic Cloud (SMC) and the LMC, and found that at least some of the oldest clusters observed in the LMC could have originated in the SMC. The LMC old GCs have also been compared to those of the Milky Way (MW). \citet{brocatoetal1996}, \citet{mucciarellietal2010} and \citet{wagnerkaiseretal2017}, among othes, showed that the old LMC GCs resemble the MW ones in age and in many chemical abundance patterns. In contrast, \citet{johnsonetal2006} found that many of the abundances in the LMC old GCs are distinct from those observed in the MW, while \citet{pg13} suggested that the most likely explanation for the difference between the old GC and field star age-metallcity relationships is a very rapid early chemical enrichment traced by the very visible old GCs. Indeed, the integrated spectroscopic metallicities obtained by \citet{detal99} suggest that NGC\,1928 is one of the most metal-rich ([Fe/H] $\sim$ -1.2 dex) old GCs, whereas NGC\,1939 one of the most metal-poor ([Fe/H] $\sim$ -2.0 dex) old GCs. In Section 2 we describe the spectroscopic observations performed with the aim of deriving for the first time accurate mean cluster RVs (Section 3) and metallicities (Section 4). These quantities are considered in Section 5 to investigate whether NGC\,1928 and NGC\,1939 have been born in the LMC disc, or have other origins. Finally, a summary of the results is presented in Section 6. | With the aim of investigating the origin of the LMC GCs NGC\,1928 and 1939, we carried out spectroscopic observations of giant stars located in their fields with the GMOS and the AAOmega+2dF spectrographs of the Gemini South and the Australian Astronomical Observatories, respectivey. The targets were selected bearing in mind their positions along the red giant branch or red clump in $HST$ cluster CMDs, the only available photometric data set at the moment of preparing the observations. Some few candidates without $HST$ photometry were also selected. The resulting high S/N spectra centred on the Ca\,II infrared triplet allowed us to measure accurate individual RVs for 11 and 15 stars in the fields of NGC\,1928 and 1939, respectively. The RVs were obtained through cross-correlation of the observed spectra with template spectra. We also measured equivalent widths of the three Ca\,II lines and derived individual metallicities ([Fe/H]) for those stars with available photometry using a previous well-established calibration. The accuracy in the individual [Fe/H] values ranges 0.1-0.3 dex. By considering as membership probability criteria the position of the observed stars in the cluster CMDs, and their position in the RV and metallicity distribution functions, we concluded that 7 and 9 observed stars are probable cluster members of NGC\,1928 and 1939, respectively. The combined three criteria resulted to be a robust approach to assess the cluster membership of the observed stars. From the adopted cluster members we estimated for the first time accurate mean cluster RVs and metallicities. We found that NGC\,1928 is one of the most-metal rich GCs ([Fe/H]=-1.3 dex), and NGC\,1939 is one of the most metal-poor ones ([Fe/H]=-2.0 dex). Both GCs are located in the innermost region of the LMC (deprojected distance < 1 kpc) and have RVs consistent with being part of the LMC disc. Therefore, we rule out any possible origin but that in the same galaxy. Indeed, we computed the best solution for a rotation disc that fully contains each GC, separately, and found that the resulting circular velocities at the deprojected cluster distances very well match the rotation curves fitted from $HST$ and $Gaia$ DR2 proper motions, respectively. We extended our kinematics analysis to all the 15 LMC GCs by obtaining also circular velocities. The outcomes show that most of the GCs share the LMC rotation curve. Since they span the whole LMC GC metallicity range with no evidence of a metallicity gradient, we concluded that the LMC disc has existed since the early epoch of the galaxy formation and has also experienced the abrupt chemical enrichment seen in its GC populations in an interval of time of $\sim$ 3 Gyr. Four objects out of the fifteen GCs (NGC\,1835, 1898, 2210 and Reticulum) have estimated circular velocities which notably depart from the LMC rotation curve. We think that they are witnesses of having been stripped by the LMC from the SMC, an scenario predicted from numerical simulations of the galaxy dynamical interactions and confirmed from observation of field star populations. | 18 | 8 | 1808.06983 |
1808 | 1808.00476_arXiv.txt | {} {We use {Gaia Data Release 2 (DR2)} to place {252} Herbig Ae/Be stars in the HR diagram and investigate their characteristics and properties.} {For all known Herbig Ae/Be stars with parallaxes in {Gaia DR2}, we collected their atmospheric parameters and photometric and extinction values from the literature. To these data we added near- and mid-infrared photometry, collected H$\alpha$ emission line properties such as equivalent widths and line profiles, and their binarity status. In addition, we developed a photometric variability indicator from {Gaia's DR2} information.} {We provide masses, ages, luminosities, {distances}, {photometric variabilities} and infrared excesses homogeneously derived for the most complete sample of Herbig Ae/Be stars to date. We find that high mass stars have a much smaller infrared excess and have much lower optical variabilities compared to lower mass stars, with the break at around 7M$_{\odot}$. H$\alpha$ emission is generally correlated with infrared excess, with the correlation being stronger for infrared emission at wavelengths tracing the hot dust closest to the star. The variability indicator as developed by us shows that {$\sim$25\%} of all Herbig Ae/Be stars are strongly variable. We observe that the strongly variable objects display doubly peaked H$\alpha$ line profiles, indicating an edge-on disk.} { The fraction of strongly variable Herbig Ae stars is close to that found for {A-type} UX Ori stars. It had been suggested that this variability is in most cases due to asymmetric dusty disk structures seen edge-on. The observation here is in strong support of this hypothesis. Finally, the difference in dust properties occurs at 7M$_{\odot}$, while various properties traced at UV/optical wavelengths differ at a lower mass, 3M$_{\odot}$. The latter has been linked to different accretion mechanisms at work whereas the differing infrared properties and {photometric variabilities} are related to different or differently acting (dust-)disk dispersal mechanisms. } | \label{sec:intro} Herbig Ae/Be stars (HAeBes) are Pre-Main Sequence stars (PMS) of intermediate mass, spanning the range between low mass T-Tauri stars and the embedded Massive Young Stellar Objects (MYSOs). They are optically bright so they are much easier to observe and to study than MYSOs and it is expected that within the mass range of HAeBes a change in accretion mechanism from the magnetically controlled accretion acting for T-Tauri stars (see \citealp{Bouvier}) to an, as yet, unknown mechanism for high mass stars occurs. Indeed, there is evidence that the magnetically driven accretion model is valid for Herbig Ae stars but not for several Herbig Be stars (\citealp{Fairlamb}; \citealp{Ababakr}; \citealp{Oudmaijer2}; \citealp{Grady}; \citealp{Scholler}). Moreover, there are multiple evidences that Herbig Ae and T-Tauri stars behave more similarly than Herbig Be stars, and Herbig Ae and Herbig Be stars have different observational properties. Examples of this are the different outer gas dispersal rates (higher for Herbig Be stars, \citealp{Fuente}), the higher incidence of clustering scenarios for Herbig Be stars (\citealp{Testi}), and the evidences of Herbig Be stars hosting denser and larger inner gaseous disks (\citealp{Ilee}; \citealp{Monnier}) that may suggest a different accretion scenario with the disk reaching directly into the star (\citealp{Kraus2}). Other spectro-photometric (\citealp{Mendigutia4}; \citealp{Cauley} and \citealp{Patel}) and spectro-polarimetric studies (\citealp{Vink2}) also point in the direction that the accretion physics change within the Herbig Ae/Be stars mass range. In addition, Herbig Be stars are more likely to be found in binaries than Herbig Ae stars (\citealp{Baines}). An important indicator of their PMS nature, {together with emission lines}, is the infrared (IR) excess that also traces the Herbig Ae/Be forming environment. The IR excess profile have been classified into two groups differentiated by a flat or rising shape of the continuum (\citealp{Meeus}). This difference has a geometric origin depending on the presence of flaring outer disks and puffed-up inner disks (\citealp{Dullemonda}, 2004b, 2005), and the presence of gaps in the disk (\citealp{Maaskant}; \citealp{Honda}). The IR excess of HAeBes is expected to be characteristic and different from the IR excess of other similar objects like for example, ordinary Be stars \citep{Finkenzeller}. Herbig Ae/Be stars are known to present irregular photometric variations, with a typical timescale from days to weeks (\citealp{Eiroa}; \citealp{Oudmaijer5}) and of the order of one magnitude in the optical. This variability is typically understood as due to variable extinction, due to for example rotating circumstellar disks, or as an effect of rotation on cold photospheric spots and also pulsation due to the source crossing the instability strip in the HR diagram (\citealp{Marconi}). An extreme case of large non-periodic photometric and polarimetric variations is observed in UX Ori type stars (UXORs) with amplitudes up to $2-3$ mag. Many of them are catalogued as HAeBes and their extreme variability is explained by eclipsing dust clouds in nearly edge-on sources and the scattering radiation in the circumstellar environment (see \citealp{Grinin} and references therein; \citealp{Natta} and \citealp{Natta2}). Infrared photometric variability, related to disk structure variations, is not always correlated with the optical variability (\citealp{Eiroa}) which implies that different mechanisms regarding both the disk structure and accretion underlie the final observed variability. Spectroscopic variability is also present in Herbig Ae/Be stars (\citealp{Mendigutia3}). With the advent of the {second} data release of Gaia (DR2, \citealp{Gaia Collaboration2016}, \citealp{Gaia Collaboration2018}), providing parallaxes to over {1.3 billion} objects ({\citealp{Lindegren_new}}), including the majority of known Herbig Ae/Be stars, the time is right for a new study on the properties of the class. {Gaia DR2} contains a five dimensional astrometric solution ($\alpha$, $\delta$, $\mu_\alpha$, $\mu_\delta$ and parallax ($\varpi$)) up to $G\lesssim21$ (white G band, described in {\citealp{Evans}}). {Almost all} of the known Herbig Ae/Be stars have parallaxes {in Gaia DR2}, which allowed luminosities to be derived and {252} HAeBes to be placed in the HR diagram, a {tenfold} increase on earlier studies using Hipparcos data alone. The paper is organized as follows: In Sect. \ref{sec:Data_acq}, we describe the data acquisition of not only the parallaxes, but also optical and infrared photometry, effective temperatures, extinction values, H$\alpha$ emission line information and binarity. In Sect. \ref{sec:Der_cuantities} we derive the stellar luminosities and place the objects in an Hertzsprung-Russell (HR) diagram, while we also present a method to derive a statistical assessment of the objects' variability in Gaia's database. In addition, we homogeneously derive masses and ages for all the sources, together with near- and mid-infrared excesses. In Sect. \ref{sec:Data_analysis} we carry out an analysis of the data and present various correlations and interdependencies, which we discuss in the context of intermediate mass star formation in Sect. \ref{sec:Discussion}. We conclude in section Sect. \ref{sec:Conclusions}. | \begin{enumerate} \item The Gaia photometric variability indicator as developed here indicates that {48/193} or $\sim$25\% of all Herbig Ae/Be stars are strongly variable. We find that the presence of variability correlates very well with the H$\alpha$ line profile. The variable objects display doubly peaked profiles, indicating an edge-on disk. It had been suggested that this variability is in most cases due to asymmetric dusty disk structures seen edge-on. The observation here is the most compelling confirmation of this hypothesis. {Most sources catalogued as UXORs in the sample appear as strongly variable with double-peaked profiles. The fraction of strongly variable A-type objects is close to that found for the A-type objects with the UXOR phenomenon.} \item High mass stars do not display an infrared excess and show no strong photometric variability. Several suggestions have been put forward to explain this. These include fast evolutionary timescales and fast dust dispersion timescales for high mass objects. We do note that the break is around 7~M$_{\odot}$, which is intriguingly similar to other statistical studies related to dusty disks around Herbig Ae/Be stars which signpost a different or more efficient disk dispersal mechanism for high mass objects. \item Whereas the break in IR properties {and photometric variabilities} occurs at 7~M$_{\odot}$, various H$\alpha$ line properties including mass accretion rates, spectropolarimetric properties and emission line variability seem to differ at a lower mass, 3~M$_{\odot}$. The latter has been linked to different accretion mechanisms at work; magnetospheric accretion for the A-type objects and another mechanism, possibly boundary layer accretion, for the B-type objects. The differing IR and variability properties are related to different or differently acting (dust-)disk dispersal mechanisms, which occurs at much larger size scales than the accretion traced by hydrogen recombination line emission. \end{enumerate} Finally, the findings presented in this paper signal just the beginning in unveiling the formation of intermediate mass stars using Gaia. Gaia presents us with an excellent opportunity to search and identify new Herbig Ae/Be stars, resulting in a well-selected and properly characterized sample. The results presented here will assist greatly in identifying new Herbig Ae/Be objects from the more than a billion stars with astrometric parameters in Gaia. This is the subject of our follow-on study, the STARRY project. | 18 | 8 | 1808.00476 |
1808 | 1808.04720.txt | { We investigated 64 pairs of interacting-CME events identified by the simultaneous observations of SOHO and STEREO spacecraft from 2010 January to 2014 August, to examine the relationship between the large SEP events in the energy of $\sim25-\sim60$MeV and the properties of the interacting CMEs. We found that during CME interactions the large SEP events in this study were all generated by CMEs with the presence of enhanced type II radio bursts, which also have wider longitudinal distributions comparing to events with the absence of type II radio burst or its enhancement (almost associated with small SEP events). It seems that the signature of type II radio bursts enhancement is a good discriminator between large SEP and small or none SEP event producers during CME interactions. The type II radio burst enhancement is more likely to be generated by {CME interactions}, with the main CME having larger speed ($v$), angular width (WD), mass ($m$) and kinetic energy ($E_k$), that taking over the preceding CMEs which also have higher $v$, WD, $m$ and $E_k$, than those preceding CMEs in CME pairs missing the type II radio bursts or enhancements. Generally, the type-II-enhanced events typically have higher values of these properties than that of non-type-II or non-type-II-enhanced cases for both the main and the preceding CMEs. Our analysis also revealed that the intensities of associated SEP events %, especially for large SEP events, correlate negatively with the intersection height of the two CMEs. Moreover, the overlap width of two CMEs is typically larger in type-II-enhanced events than in non-type-II or non-type-II-enhanced events. Most of type-II-enhanced events and SEP events are coincidentally and almost always made by the fast and wide main CMEs that sweeping fully over a relatively slower and narrower preceding CMEs. We suggest that a fast CME with enough energy completely overtaking a relatively narrower preceding CME, especially in low height, can drive more energetic shock signified by the enhanced type II radio bursts. The shock may accelerate ambient particles (likely provided by the preceding CME) and lead to large SEP event more easily. | Solar energetic particle (SEP) is one of the serious radiation hazard for the spacecraft and the astronauts in space. The relationship between SEP and solar activities is also a central topic in space physics and space weather. SEP events are usually classified to two types according {to} their different acceleration processes: impulsive and gradual events, thought to be produced by solar flare and coronal mass ejection (CME)-driven shock respectively \citep{Reames95a, Reames99a}. The gradual SEP events usually present the distinctive features, such as high peak flux intensity, high energy, long duration, and et al, comparing to impulsive events \citep[e.g.][]{Reames95a, Reames99a, Kahler96, Kahler05b}. However, in many cases \citep[e.g.][]{Cane.etal03,Li.etal07b,Li.etal07a,Ding.etal16}, gradual and impulsive SEP components are mixed, which can not be distinctively classified to these two types. {So the solar source of energetic particles in the large SEP events is still a popular issue. Some statistical results implied that the higher energetic particles (e.g. $>30$MeV) are dominantly accelerated by the concurrent solar flares, while the CME-driven shock is generally as an effective accelerator mainly for SEPs within lower energies }\citep[e.g.][]{Le.etal17,Le.Zhang17}. {The spectra rigidity of GLE also revealed that the flare plays an important role in large gradual SEP event }\citep{Wu.Qin18}. {Case study presented the evidence that the first arriving relativistic and non-relativistic protons and electrons are accelerated by the concurrent flare according to the timing analysis in an individual SEP event, and then these particles may be further accelerated by the associated CME-driven shock }\citep{Zhao.etal18}. In general, a large SEP events, e.g. $I_p>10$pfu (pfu=$proton/cm^2~s~sr$) at $>10$MeV in GOES observations, are always almost associated with fast and wide CME eruptions, but inversely not all fast and wide CMEs can produce SEP events. So a number of mechanisms of CME generating SEPs were proposed, such as coronal waves, CME lateral expansion, CME-CME interaction, and so on \citep{Desai.Giacalone16, Lugaz.etal17}. The intensity of large gradual SEP event is positively correlated with the speed of associated CME, but the scatter is very large \citep{Kahler96, Kahler.etal00}. This suggested that the number of ambient energetic particles may be another %\del{deciding} factor {determining the intensity of the associated SEP event} besides of associated CME-driven shock speed \citep[e.g][]{Kahler01,Kahler.Vourlidas14}. These seed particles may be from solar flares \citep{Mason.etal99, Mason.etal00} or from the preceding CMEs \citep{Gopalswamy.etal02, Gopalswamy.etal04, Li.etal12}. CME {interaction} is a frequent phenomenon in solar corona and interplanetary (IP) space. Usually CME ``cannibalism'' or collision can happen in the process of two CMEs interaction \citep[e.g.][]{Gopalswamy.etal01, Temmer.etal14, Shanmugaraju.etal14}. \citet{Shen.etal12} presented a case of two CMEs colliding in IP space and revealed that these two magnetized plasmoids collided as if they were solid-like objects, with a likelihood of 73\% that the collision was super-elastic. In a study of the first ground level enhancement event (GLE) of solar cycle 24, which occurred on 17 May 2012, \citet{Shen.etal13} reported two CME erupting from a complicated active region separated by only $3$ minutes using the observations of STEREO and SOHO. Successive CMEs can also cause an extreme space weather storm in IP space via interaction and pre-conditioning of the interplanetary medium at the CMEs \citep{Liu.etal14}. \citet{Gopalswamy.etal02, Gopalswamy.etal03} suggested that CME interaction is an important aspect of SEP production, which can be as a good discriminator between SEP-poor and SEP-rich CMEs. However, \citet{Richardson.etal03} {argued that this interaction do not play a fundamental role in determining whether a wide and fast CME is associated with an SEP event.} \citet{Gopalswamy.etal04} showed that there exists a strong correlation between high particle intensities and the presence of preceding CMEs with $24$ hours. And it is interpreted that seed particles may be trapped in the closed field lines of the preceding CMEs or associated turbulence so that they are subject to repeated acceleration by the shock driven by the second CME. However, this time {interval between two CME eruptions} is too long to {make sure that} direct CME(shock)-CME interaction {is responsible for} the observed {large} SEP events, because most large SEPs are believed to occur below $\sim10R_s$ ($R_s$ is solar radius) \citep{Kahler03}. Later, \citet{Li.Zank05a} suggested that two consecutive CMEs may provide a favorable environment for particle acceleration. Subsequently, \citet{Li.etal12} proposed the ``twin-CME'' scenario, where two CMEs erupt in sequence from the same or nearby active regions within a short period of time, the preceding CME or its shock can increase the turbulence level and/or seed population ahead of the main CME-driven shock. Thereby the enhanced turbulence level and seed population favor a more efficient particle acceleration at the main CME shock comparing to a single CME. \citet{Ding.etal13} extended the work of \citet{Li.etal12} and found that CMEs having a preceding CME with speed $>300$km/s within $9$ hours from the same active region have larger probability of leading to large SEP events than CMEs that do not have preceding CMEs. A subsequent case study showed that the SEP release time near the Sun is consistent with the time of the main CME leading edge overtaking the tailing edge of the preceding CME, as well as the radio enhancement \citep{Ding.etal14}. Type II radio bursts have been often used as a diagnostic of the CME-driven shock in studying SEP events \citep[e.g.][]{Kahler82, Gopalswamy.etal05b, Cho.etal08}. Metric type II radio bursts are generated when the shock is close to the Sun (e.g. $\leq3R_s$) \citep{Gopalswamy.etal09a}. While many SEP events have metric type II bursts associated with them, the signature of metric type II bursts do not necessarily lead to a large SEP event \citep{Kahler82}. \citet{Cliver.etal04} argued that the presence of the decameter-hectometric (DH) type II radio emissions may be used as a marker to distinguish between SEP-rich and SEP-poor metric type II radio bursts. Later, \citet{Gopalswamy.etal05b} found that CME tend to be more energetic if radio bursts appear from metric to DH wavelength. Usually, shock that survive beyond $3R_s$, indicated by the signature of type II radio emission from metric drifting to DH wavelength, are more stronger and broader \citep[e.g.][]{Cliver.etal04}. {CME interaction} can lead to radio enhancement following an IP type II burst when a fast CME overtaking a slow one, which may imply a strengthened shock \citep{Gopalswamy.etal01}(also see \citet{Shen.etal13, Ding.etal14, Temmer.etal14}). The result of \citet{Temmer.etal14} indicated that the interaction process is strongly position angle (PA) dependent in terms of timing as well as kinematical evolution, and the timing for the enhanced type II bursts may be related to shock streamer interaction. In previous statistical works of CME interaction and its role on SEP production by, e.g., \citet{Gopalswamy.etal02, Gopalswamy.etal03, Gopalswamy.etal04, Ding.etal13}, the observations of CMEs and SEPs were all made only by spacecraft near the Earth. However, the CME projection effect and the longitude dependence of SEP flux detection are always inevitable, especially in the study of CME interaction. In this paper, we make use of multiple spacecraft observations, and focus on the effect of {CME interactions} on the association with SEP events and radio enhancement by using SOHO and STEREO-A/B data. STEREO A and B spacecraft are advancing ahead of or lagging Earth at $\sim1$~AU in the heliocentric orbits respectively, and separating slowly from the Earth by $\sim22^\circ~year^{-1}$. During the study period from January 2010 to August 2014, the separation between STEREO-A(B) and Earth increases from $\sim64^\circ(68^\circ$) to $\sim166^\circ(161^\circ)$. Our paper is organized as follows: Section 2 presents the dataset; Section 3 shows our statistical results; and Section 4 contains the discussion and the conclusion. | In this paper, we focused on 64 interacting CME pairs, and investigated what properties of the main and preceding CMEs best correlate with the enhancement of type II radio burst and whether the presence or absence of such enhancement is related to SEP events. %including their interaction can effect distinctly on the acceleration of SEPs. Various properties, such as CME speed, angular width, mass, kinetic energy, intersection height, and overlap WD, were examined in detail. We approximated a comparative flux threshold of large SEP event to the value of 0.0114(0.01)/($cm^2ssr$MeV) for the observations of STEREO-A/B HET (SOHO/EPHIN) instrument in the energy range of $\sim25-\sim60$MeV, by which a large SEP event is defined equivalently to the event identified usually using $>10$pfu at $>10$MeV in GOES observations. %The intensities of all large SEP events show positive correlations with the speed, kinetic energy and the mass of the main CMEs, but no association with the preceding CMEs. However, some properties of the main CMEs and the preceding CMEs may control the generation of (large) SEP events during the interaction of two CMEs. For events in this sample, a vast majority of SEP events, including all individual large events, occur when the main CME overtakes the preceding CME and the accompanying type II radio burst shows enhancement. In contrast, only a few small SEP events occur for CME pairs without type II or enhancement. The en-type-II SEP events usually have wide longitudinal distribution, comparing to the noen-type-II SEP events. In all 64 interacting CME pairs, the probability of the SEPs occurrence for en-type-II events is higher than that of noen-type-II events. It suggests that the presence of type-II radio enhancement can be used as a distinct signature of whether the interaction of CME pairs can produce a SEP event or not, especially large SEP event. We suggested that the presence of the signature of enhanced type II radio may be treated as a discriminator between SEP-rich and SEP-poor {CME interactions}. %\red{which is important for space weather.} The statistical results show that the speed, WD, mass and kinetic energy of both main CMEs and preceding CMEs positively correlate with the probability of the presence of type II radio burst enhancement {during CME interactions}. The en-type-II events usually have higher speed, WD, mass and kinetic energy than the noen-type-II cases. These features imply that the main and preceding CMEs are more intense and energetic, which can more easily drive a stronger shock signified by type II radio bursts and enhancement. %If enough seed particles can be provided, the shock is thereby expected to accelerate particles to high energy and generate large SEP event easily. In our study, the intersection height and the overlap WD are roughly used to quantify the extent of the interaction of the two CMEs. The intersection height seems to show no distinct difference between the presence and absence of radio enhancement. But the intensity of SEP events was found to correlate inversely with the intersection height. This result indicates that if two CMEs interact in the lower corona during their propagation, due to perhaps a higher speed of the main CME, they can produce larger SEP events more easily. %, which agrees with the fact that many large SEP or GLE events were accelerated and released at very low height \citep[e.g.][]{Reames09, Gopalswamy.etal12a, Ding.etal15}. The overlap WD of en-type-II events is obviously larger than noen-type-II events. The portion of en-type-II events increases when the overlap WD becomes larger. All but one en-type-II events are associated with main CMEs having wider WD than that of the preceding CMEs. However, it must be pointed out that most of main CMEs with radio enhancement are halos. The result also shows that most of SEP events (20/24) are accelerated by the main CMEs widely overtaking the preceding CMEs or with largest overlap in the plane-of-sky. A possible interpretation may be that when {a} fast and wide CME widely sweeps up {a narrower and slower} preceding CME, particle acceleration of the shock can become more efficiently either because of the enhanced seed particles injected into the shock surface or because of the trapping and acceleration of the energetic particles in the closed flux loop of pre-CMEs intersecting with the shock surface. We therefore suggested that if an energetic fast and wide CME overtakes its preceding CME fully in the low height, with the presence of enhanced type II radio emissions, then the CME pair generally can generate a high intensity SEP event. These results can help us to further understand the relationship between CME interaction and the large SEP events, and the mechanism of large SEP event that triggered by CME-driven shock. %% If you wish to include an acknowledgments section in your paper, %% separate it off from the body of the text using the | 18 | 8 | 1808.04720 |
1808 | 1808.09282_arXiv.txt | {During single clock inflation, hidden fields (i.e. fields coupled to the inflaton only gravitationally) in their adiabatic vacua can ordinarily only affect observables through virtual effects. After renormalizing background quantities (fixed by observations at some pivot scale), all that remains are logarithmic runnings in correlation functions that are both Planck and slow roll suppressed. In this paper we show how a large number of hidden fields can partially compensate this suppression and generate a potentially observable running in the tensor two point function, consistently inferable courtesy of a large $N$ resummation. We detour to address certain subtleties regarding loop corrections during inflation, extending the analysis of \cite{SZ}. Our main result is that one can extract bounds on the hidden field content of the universe from bounds on violations of the consistency relation between the tensor spectral index and the tensor to scalar ratio, were primordial tensors ever detected. Such bounds are more competitive than the naive bound inferred from requiring inflation to occur below the strong coupling scale of gravity if deviations from the consistency relation can be bounded to within the sub-percent level. We discuss how one can meaningfully constrain the parameter space of various phenomenological scenarios and constructions that address naturalness with a large number of species (such as `N-naturalness') with CMB observations up to cosmic variance limits, and possibly future 21cm and gravitational wave observations.} | Observations strongly indicate that the Universe underwent an early phase of primordial inflation. Such an inflationary phase not only solves the horizon and flatness problems ~\cite{Guth,Linde:1981mu}, it also naturally produces a nearly scale invariant spectrum of density fluctuations~\cite{Mukhanov:1981xt} consistent with what has been observed in the cosmic microwave background (CMB). These fluctuations originated as quantum vacuum fluctuations that were forced out of the horizon by the quasi-exponential expansion of the Universe and subsequently squeezed, resulting in their phase coherence. The inflationary background also amplifies vacuum fluctuations of the transverse traceless part of the metric, leading to the generation of primordial gravitational waves~\cite{Starobinsky:1979ty} as well as fluctuations of all other fields present in the quantum vacuum whether they couple directly to the inflaton or not. In this paper we consider the effects of fields that one would ordinarily be tempted to ignore during inflation: hidden fields, defined as fields that couple only to gravity and have no direct couplings to the inflaton. In their adiabatic vcauum, such fields would only serve to renormalize background quantities\footnote{Whose effects therefore would simply be absorbed into physical measurements of quantities such as $\epsilon := -\dot H/H^2$ (e.g. through the detection of primordial tensors) and its derivatives or the ratio $H^2/\mpl^2$, all of which denote renormalized quantities.} and induce unobservably small (i.e. Planck and slow roll suppressed) logarithmic runnings in cosmological correlation functions. However, in large enough numbers, their effects can add up to an observable running of the spectral index of the two point function of the tensor perturbation, consistently inferable via a "large $N$" expansion that allows us to resum a restricted class of diagrams. The running induced for correlation functions of the curvature perturbation on the other hand remains feeble, since the relative suppression of the interaction vertices by factors of $\epsilon$ is too great to be overcome by large $N$ and still consistent with being below the strong coupling scale of gravity. One can thus use this observation to convert bounds on the violation of the tensor to scalar consistency relation to a bound on the possible number of hidden fields present in the universe with masses below the scale of inflation, \textit{were primordial tensors ever to be observed}\footnote{Although fields with masses much greater than the Hubble scale during inflation also contribute to the running of the tensor spectrum, their effects are very suppressed at long wavelengths and so will not contribute to the bounds derived here. Fields with masses $m \sim H$ (cf. \cite{Chen:2009we,Chen:2009zp}) do not affect the running of two point functions, although they can imprint on higher order (cross-)correlation functions with additional interactions not considered here \cite{Saito:2018omt}.}. For simplicity, we focus on hidden scalars, although our argument generalizes straightforwardly to particles of other spin \cite{DDP}. We find that any bound from above (to some confidence level) on deviations from the tensor to scalar consistency relation \eq{}{n_t + \frac{r_*}{8} \lesssim \xi} for some positive $\xi$, translates into a bound on the number of hidden species as \eq{final0}{N\lesssim 8.5\times 10^2 \frac{\xi}{r_*^2} \Delta_\zeta^{-1}} Where $\Delta_\zeta \approx 2.44 \times 10^{-9}$ \cite{Aghanim:2015xee} is the amplitude of the spectrum of the curvature perturbation at the pivot scale where we determine the tensor to scalar ratio $r_*$, with $n_t$ being the tilt of the tensor spectrum. If we presume the most optimistic case that $r_* \sim 0.06$ then the best we can hope to bound $N$ through CMB measurements is by \eq{}{N \lesssim \frac{3.5 \times 10^{11}}{r_*^2}\xi \sim 10^{14}\times \xi} We note that this bound is only interesting if it is stronger than the bound coming from the requirement that we stay below the scale at which gravity becomes strongly coupled \cite{Dvali:2007hz, Dvali:2007wp} (cf. eq (\ref{lqg}), reviewed in appendix \ref{a:sc}): \eq{sc0}{N \lesssim \frac{16\pi^2\mpl^2}{H^2}= \frac{32 \Delta_\zeta^{-1}}{r_*} \approx \frac{1.3\times10^{10}}{r_*} \sim 10^{11}.} In order to infer a stronger bound from (\ref{final0}) than from consistency imposed by being below the strong coupling scale (\ref{sc0}), we would need to bound $\xi$ one order of magnitude better than we the accuracy with which we measure $r_*$. As we shall elaborate upon further, cosmic variance limits us to bounds on $\xi$ no better than the percent level (were $r \sim 0.06$) from CMB observations alone, allowing only marginally to bound the parameter space of a variety of models that attempt to address the hierarchy problem with a large number of sectors \cite{Dvali:2009ne, Arkani-Hamed:2016rle}. However, as we discuss further, observations of the stochastic background at very different comoving scales through future 21cm and space based gravitational wave interferometer observations could allow us to entertain significant improvements upon these constraints. We begin this paper with an outline of our calculation with details deferred to the appendix. It behoves us to elaborate upon various subtleties encountered in the calculation of loop corrections to cosmological correlation functions relevant to this calculation \cite{SZ,Adshead}. In particular, we extend the analysis of Senatore and Zaldarriaga \cite{SZ} which pointed out that dimensional regularization had only been partially implemented in previous calculations (e.g. \cite{weinberg} and subsequent studies), where it was found that loop corrections induced a running of the form $\log (k/\mu)$ in the two point function of the curvature perturbation, with $\mu$ some arbitrary renormalization scale. Including previously neglected corrections to the mode functions and to the integration measure in $D = 3 + \delta$ spatial dimensions\footnote{A conclusion independently arrived at by working in a \textit{mass dependent} regularization scheme (a hard cutoff in physical momenta).}, it was found that loops instead induce a correction of the form $\log (H/\mu)$ \cite{SZ}. At first glance this appears to preclude any running of the loop correction, which cannot be the case in general as quantum corrections typically induce scale dependence unless we are at a fixed point of the theory, e.g. in the dS (de Sitter) limit where an exact dilatation (i.e. scale) invariance is realized -- implicitly assumed in \cite{SZ}. Since corrections to the correlation functions are being forged as modes exit the horizon during single clock inflation, it must be the case that what appears inside the log is in fact $H_k$ -- the Hubble scale at the time the $k$-mode exits the horizon. We demonstrate this explicitly in appendix \ref{a:tensor}, where we show how additional slow roll corrections to the mode functions and the integration measures within the loop integrals indeed result in a correction of the form $\log (H_k/\mu)$. Upon fixing the renormalization conditions at some (pivot) scale $\mu = H_*$, one reintroduces a running as one moves away from this scale, but now of the form $\log (H_k/H_*) \to -\epsilon\, \log(k/k_*)$. This contribution to the running is far too feeble to ever be observed for the curvature perturbation\footnote{In section \ref{s:disc}, we discuss the possible implications of the running of the two point function of the curvature perturbation for whether or not a given model of inflation is eternal according to criteria derived in \cite{eternal}.}, but does have a potentially observable effect on the tilt of the tensor spectrum. In Section~\ref{s3} we derive the modifications of the tensor and scalar spectral indices due to the presence of hidden fields and in Section~\ref{s:disc}, we discuss possible observational bounds on $N$ and generalizations of our results. \\ \noindent {\bf Notation:} In what follows, we shall consider a spatially flat FRLW universe with line element in Cartesian coordinates \be ds^2 = a^2(\tau)\left[-d\tau^2 +\de_{ij}dx^idx^j\right] = g_{\mu\nu}dx^\mu dx^\nu \,, \label{e:Fried}\ee where $\tau$ denotes conformal time and physical time is given by $dt=ad\tau$. Derivatives w.r.t. $\tau$ are denoted by a prime and those w.r.t. $t$ by an overdot. The physical Hubble parameter is $H=\dot a/a$. % | } For the purposes of the following, we frame the discussion in terms of an observational challenge for bounding $\xi$ in the context of (\ref{final}) as a null test. We will abuse our privileges as theorists to contemplate the possibility that one could bound $\xi$ past CMB cosmic variance limits to the level of $10^{-3}$ or beyond. That this may be plausible with a combination of future space based interferometry \cite{Danzmann:2003tv} and ground based arrays \cite{Janssen:2014dka} can be appreciated from the fact that the tilt for the tensor spectrum is no longer as negative as $\lambda$ approaches its upper bound (\ref{ub}), so that at comoving scales $k \sim 10^{14}k_* \sim 10^{11}$ Mpc$^{-1}$ (corresponding to peak interferometer sensitivities in the mHz range) the power will be enhanced by about 20\% relative to the standard case. One might conceive improved prospects for constraining deviations from the consistency relation from combining observations sensitive enough to detect the stochastic primordial background \cite{Bartolo:2016ami} at widely separated scales, with CMB observations and space-based interferometry sensitive to modes 14 orders of magnitude apart\footnote{One might be concerned that higher order corrections might need to be incorporated in order to extrapolate the running over such a large range of scales. However, such corrections only become important when considering scales such that $\log k/k_* \sim \frac{1}{\lambda\epsilon_*} \gtrsim \frac{1}{\epsilon_*} = \frac{16}{r_*} \gtrsim 160$, which is safely beyond anything accessible to observations.}, with SKA like surveys interpolating between them with sensitivity at the nHz frequencies ($k \sim 10^{8}k_* \sim 10^{5}$ Mpc$^{-1}$). Ultimate 21 cm observations also offer the possibility to measure primordial gravitational wave background through large scale structure fossils, allowing for an in principle sensitivity to $r$ down to the $ \sim 10^{-6}$ level \cite{Masui:2010cz}, however, the question of whether foregrounds can be understood to the required level is far from settled at the present moment. For now, we merely state the obvious corollary that follows from (\ref{final}) that (for $r_* \sim 0.06$) \eq{pmtest}{N \lesssim \xi\cdot 10^{14} \sim 10^{9}-10^{12}} for $\xi$ ranging from $10^{-5} \lesssim \xi \lesssim 10^{-2}$ where the latter corresponds to CMB cosmic variance bounds, and the former corresponds to us rather speculatively entertaining bounds that could be obtained by other means -- combinations of next generation space and ground based gravitational wave observations or ultimate 21cm observations. \subsection{Implications for BSM/ string models} The idea of invoking a large number of hidden sectors to address the electroweak hierarchy problem was considered in \cite{Dvali:2007hz, Dvali:2007wp, Dvali:2009ne} -- the observation being that a large number of species can be used to make the scale of quantum gravity $\Lambda_{\rm QG}$ parametrically lower than the Planck mass (cf. appendix C)\footnote{\label{scg bound}This bound is often stated as $\Lambda_{\rm QG} \sim \frac{\mpl}{\sqrt N}$ where $\mpl$ is the reduced Planck mass and an order unity pre-factor is understood. As reviewed in the appendix, repeating the various arguments presented in \cite{Dvali:2007hz, Dvali:2007wp} suggests that the bound is \textit{at least} (\ref{lqg}).} \eq{lqg}{\Lambda_{\rm QG} \sim \frac{4\pi\mpl}{\sqrt N}.} Far from being an ad hoc construction, \cite{Dvali:2007wp, Dvali:2009ne} argue that such a large number of hidden sector arise naturally as Kaluza-Klein copies of the standard model in scenarios with extra dimensions, although their origin needn't be extra dimensional in general (see \cite{DSV} for an interesting speculation that these extra species could constitute dark matter). As discussed above, any observation of primordial tensors in the context of single field inflation immediately implies that in order for inflation to have occurred below the strong coupling scale, one must necessarily live in a universe with less than $N \lesssim \frac{16\pi^2\mpl^2}{H^2} \approx \frac{10^{10}}{r_*}$ hidden fields (\ref{sc}), with tests of deviations from the tensor to scalar consistency relation to better than the percent level allowing us more constraining power than the strong coupling bound. More recently, the authors of \cite{Arkani-Hamed:2016rle} proposed an alternative solution to the hierarchy problem that necessarily invokes inflation, initially dubbed `$N$-naturalness'. The idea is that we live in a universe with $N$ copies of the standard model each hidden from the other, with all coupled to a reheating field (the reheaton), not necessarily the inflaton. The mass of the Higgs fields in any of the $N$ copies of the standard model is drawn from a uniform distribution that interpolates between $-\Lambda^2 \leq m^2_H \leq \Lambda^2$. Given that reheating will preferentially produce particles in the lightest sector (with masses set by the Higgs expectation value), one dynamically explains why the universe that emerges from inflation will have a naturally small Higgs mass. A significant parameter space of interest lies within the range $N \sim 10^4 - 10^{16}$, for which tests of the tensor to scalar consistency relation at the per-mille level or better (\ref{pmtest}) could significantly constrain. \subsection{Generalization to higher spin} In general, hidden sectors in string or BSM constructions possess a spectrum that is not restricted to scalar fields. An obvious question therefore is how our results generalize when including higher spins. Leaving aside the precise nature of the running of the two point function (the primary concern of this investigation), one can immediately infer the relative importance of the contributions from particles of different spins by consulting the one loop effective action obtained from integrating them out over a fixed background \cite{HK}. For a particle of a given spin, the effective action is given by (\ref{hkea}) (see appendix \ref{a:sc} for a discussion of the interpretation of the quantity below) \eq{effact}{\calL_{\rm eff} = \frac{\mpl^2}{2}R + \frac{1}{2880\pi^2}\left[a_s R_{\mu\nu}R^{\mu\nu} + b_s R^2\right] + ...} where the coefficients $a_s, b_s$ depend on the spin of the particle integrated out, and where we have used the Gauss-Bonnet relations in 4D to eliminate redundant operators. The relative contributions of the terms from which we have extracted our tree level result and our loop contributions can be determined from the ratio of the two contributions in (\ref{effact}). From the table in Appendix~\ref{a:sc} and eq.~(\ref{hkea}), we can read off the coefficients $a_s$ and $b_s$ for different spins to obtain for maximally symmetric backgrounds (where $R_{\mu\nu} = g_{\mu\nu}R/4$) \begin{eqnarray} \label{spinw} \frac{\calL_{\rm 1-loop}}{\calL_{\rm tree}} &=& \frac{9/4}{1440\pi^2}\frac{R}{\mpl^2};~~ {\rm spin~ 0},\\ \nn &=& \frac{3/2}{1440\pi^2}\frac{R}{\mpl^2};~~ {\rm spin~ 1/2},\\ \nn &=& \frac{-3}{1440\pi^2}\frac{R}{\mpl^2};~~ {\rm spin~ 1}. \end{eqnarray} From this, we can conclude that in a universe with a spectrum of particles consisting of $N_\phi$ scalars, $N_\psi$ Dirac fermions and $N_V$ $U(1)$ gauge fields, the actual quantity one is bounding with (\ref{final}) is the relevant spin weighted sum indicated in (\ref{spinw}). We leave the explicit computation of this index and the running induced by higher spin fields for a future study \cite{DDP}. We note in passing that on a dS background, $R = 12H^2$, so that for $N$ scalar fields we have \eq{}{2\times \frac{\calL_{\rm 1-loop}}{\calL_{\rm tree}} = \frac{2N\cdot 9/4}{1440\pi^2}\frac{R}{\mpl^2} = \frac{N}{16\pi^2}\frac{3}{5}\frac{H^2}{\mpl^2}} where the factor two is to count the two independent polarizations that contribute to the tensor power spectrum. This is exactly the relative ratio of the loop contribution to the tree level result calculated in (\ref{resumans4}), providing a non-trivial check on our results. \subsection{Possible implications for eternal inflation} Although not the primary focus of this investigation, having to come to terms with the precise nature of the slow roll corrections to the loop integrals (and correctly implementing dimensional regularization on a quasi dS spacetime) has potential implications for eternal inflation\footnote{Recently, the authors of \cite{Agrawal:2018own} have proposed a conjecture motivated from string `swampland' considerations \cite{Obied:2018sgi} that suggest obstacles for accomplishing inflation at all within string theory. Insofar as our study takes a viable inflating background for granted, the presence of additional hidden fields with no potential terms is no more problematic than assuming an inflationary background in the first place. }. Recalling the discussion of \cite{SZ}, who discovered by using a \textit{mass dependent} regularization scheme (a hard cutoff in physical momentum) that logarithmic corrections to the the two point function of the curvature perturbation of the form $\log H_*/\mu$ resulted. This was in contradiction with the $\log k/\mu$ form of the loop correction derived elsewhere in the literature when applying dimensional regularization. Senatore and Zaldarriaga reasoned that the former could not be the final answer -- taking the result \cite{weinberg} at face value, \eq{}{\calP_\zeta = \frac{H^2_*}{8\pi^2\mpl^2\epsilon_*}\left[1 - \epsilon_* \frac{N}{16\pi^2} \frac{4}{15}\frac{H_*^2}{\mpl^2 } \log \frac{k}{\mu}\right]} one finds upon Fourier transforming back to position space, that the variance of the inflaton fluctuation $\delta \phi = -\frac{\dot{\phi_0}}{H_*}\zeta$ is given by \eq{weinc}{\langle \delta\phi^2 \rangle_{{\rm 1-loop}} = - \frac{\epsilon_* N}{15\pi} \frac{H_*^2}{\mpl^2 }\int^{\Lambda a(t)} d^3k \frac{H^2_*}{k^3}\log k \sim - \frac{\epsilon_* N}{15\pi} \frac{H_*^2}{\mpl^2 } H_*^2 (\log a)^2 \sim - \frac{\epsilon_* N}{15\pi} \frac{H_*^2}{\mpl^2 } H_*^4 t^2 } implying that the fluctuations of the inflaton field decay monotonically over time, implying that \textit{no model of inflation is eternal} were the form of the correction (\ref{weinc}) to be trusted\footnote{A more thorough treatment is provided in \cite{eternal} where it is shown that the reheating volume diverges above the critical inflaton velocity $\dot\phi^2_{\rm cl}/H^4 > 3/(2\pi^2)$. Here, $\phi_{\rm cl}$ is to be understood as the field around which one implements background field quantization -- i.e. the field that minimizes the \textit{effective action}. For the purposes of the present discussion, we content ourselves with observing the growth or decay of the variance, which after repeating the steps of \cite{eternal} can be shown to result in crossing this critical velocity or not.}, which clearly cannot be the case. The resolution pointed out by \cite{SZ} was that the $\log k/\mu$ corrections found previously were merely the first of several logarithmic contributions that had to be supplemented with corrections to the dimensionally deformed mode functions and integration measures that went as $\log(-H_*\tau_k)$, where $\tau_k$ is the time of crossing of the comoving $k$-mode. Adding up all such corrections resulted in a dependence of the form \eq{}{\log k/\mu + \log (-H_*\tau_k) = \log H_*/\mu,} in agreement with the results obtained with a hard cutoff, which suggest that the correlation functions do not run at this order. However as we have shown, this is not the final story either, since the only possibility for which correlation functions of an interacting theory remain independent of scale is if we are at a fixed point of the theory, where a scale symmetry is realized. This is indeed the case in the strict dS limit, where $H$ is constant and one has an exact dilatation invariance. Therefore, moving away from the strict dS limit must reintroduce a running calculated in appendix B (to next to leading order in slow roll) with the result (\ref{hk}): \eq{}{\log k/\mu + (1 + \epsilon)\log (-H_*\tau_k) = \log H_k/\mu,} Upon fixing renormalization conditions at a particular pivot scale $\mu = H_*$, this implies that correlation functions will run as (\ref{htok}) \eq{}{\log \frac{H_k}{H_*} = -\epsilon \log \frac{k}{k_*}} Therefore, repeating the calculation for the corrections to the curvature two point function, one finds that a $\log k$ running is reintroduced, but of the opposite sign and with additional slow roll suppression. Retracing the argument leading to (\ref{weinc}) seems to imply that our results imply that all models of inflation in the presence of hidden fields are eternal. However this is too naive, as we have to factor in corrections from the background as well. If the sign of the net log correction $\log H_k/H_*$ generated from background corrections and cubic self interactions of the curvature perturbation alone were always positive, one would then be able to conclude that \textit{indeed, all models of inflation were eternal}, as argued to be the case in \cite{Ijjas:2015hcc}. However, it is very likely that loop corrections do not always compete with classical logarithmic corrections from the background evolution, and the precise conclusion one arrives at depends on the given background model. This is an important issue which deserves a thorough separate investigation. | 18 | 8 | 1808.09282 |
1808 | 1808.10116_arXiv.txt | NGC1052-DF2 was recently discovered as the dark-matter deficient galaxy claimed by~\citet[][vD18]{vD2018a}. However, large uncertainties on its dynamical mass estimate have been pointed out, concerning the paucity of sample, statistical methods and distance measurements. In this work, we discuss the effects of the difference in modeling of the tracer profile of this galaxy on the dynamical mass estimate. To do this, we assume that the tracer densities are modeled with power-law and S\'ersic profiles, and then we solve the spherical Jeans equation to estimate the dynamical mass. Applying these models to kinematic data of globular clusters in NGC1052-DF2, we compare 90 per cent upper limits of dynamical mass-to-light ratios estimated between from this analysis and from vD18. We find that the upper limit obtained by the power-law is virtually the same as the result from vD18, whilst this limit estimated by the S\'ersic is significantly greater than that from vD18, thereby suggesting that NGC1052-DF2 can still be a dark-matter dominated system. Consequently, we propose that dynamical mass estimate of a galaxy is largely affected by not only small kinematic sample but the choice of tracer distributions, and thus the estimated mass still remains quite uncertain. | Owing to recent deep photometric observations, ultra diffuse galaxies~(UDGs) have been discovered in clusters and groups of galaxies~\citep[e.g.,][]{vanetal2015a,vanetal2015b,Kodetal2015,Yagetal2016,vandetal2017,Truetal2017}. These galaxies have commonly the typical luminosity of a dwarf galaxy, but they are similar to Milky-Way-sized galaxies in physical size. Therefore, UDGs are characterized as an extremely low surface brightness galaxies. From dynamical analysis for kinematic data of globular clusters~(GCs) within UDGs, they are, in general, thought to be largely dominated by dark matter as well as the the Galactic dwarf spheroidal galaxies~\citep[e.g.,][]{vanetal2016}, but how these diffuse galaxies are formed and evolved in their dark matter halo is still ongoing debate~\citep[e.g.,][]{vanetal2015a,vanetal2015b,AL2016,DiCetal2017}. Interestingly enough, however, \citet[][hereafter vD18]{vD2018a} have recently discovered a dark matter deficient the UDG that is deficient in dark matter, NGC1052-DF2, which is a satellite of NGC1052~elliptical galaxy. They adopted mass tracer estimator~(MTE) constructed by~\citet{Watetal2010} to estimate the dynamical mass within a given radius, and applied it to the kinematic data of the 10 GCs of the galaxy. Then, they estimated the dynamical mass to be only $<3.4\times10^8M_{\odot}$ (at 90\% confidence) within 7.6~kpc from its centre, even though the stellar mass of this galaxy is estimated to be $2\times10^8M_{\odot}$. If their mass estimation is correct, this UDG is a certainly exciting galaxy in terms of the deficit of dark matter and understanding its formation~\citep[e.g.,][]{Ogi2018}. However, previous studies have pointed out uncertainties of this mass estimation due to the paucity of kinematic sample, statistical methods and distance measurements~\citep{Lapetal2018,Maretal2018,Truetal2018}. All of them argued that the mass estimate of NGC1052-DF2 still remains largely uncertain, hence it is difficult to conclude that the UFD is a galaxy laking dark matter. In this paper, we point out uncertainties of tracer models assumed in dynamical mass estimations. In particular, we show that the dynamical mass of NGC1052-DF2 might be affected by tracer distribution models assumed in analysis. As mentioned above, vD18 utilized MTE to determine the dynamical mass. This mass estimator is based on the projected virial theorem and a spherical Jeans equation. Moreover, this estimator assumes that the density profile of the tracers is modeled with single power-law form because of requirement from their analytic treatment in the MTE modelling. However, a power-law profile is only acceptable to have a diverged profile at the centre of system without any apparent physical motivation or evidence. Furthermore, since vD18 reported that the stellar system of NGC1052-DF2 is fitted with a S\'ersic profile, which has cored profile in inner parts, it may be natural to expect that GC tracers might follow a similar profile. Therefore, in order to investigate the effects of model differences on mass estimate, especially tracer distribution, we calculate dynamical masses of NGC1052-DF2 with two models: S\'eric and power-law tracer density profiles. In addition, to estimate dynamical mass, we do not utilize MTE but use line-of-sight velocity dispersion derived from the spherical Jeans equation. Thus, we set constraints on dark halo parameters from the information of positions and line-of-sight velocities of tracers, and then we estimate the dynamical mass using these best-fitting parameters. However, in principle, both methods should result in virtually similar results if there is not significant statistical uncertainty in the tracer distribution. This Letter is organized as follows. In Section 2 we introduce the method of dynamical mass estimation based on our analysis. In Section 3, we show the results of mass estimation and then comparison with vD18's estimation. Summary and conclusion are shown in Section 4. | 18 | 8 | 1808.10116 |
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1808 | 1808.00530_arXiv.txt | We study the effect of inclination on the apparent brightness of star-forming galaxies in spectral passbands that are commonly used as star-formation indicators. As diagnostics we use mass-to-light ratios in three passbands: the UV continuum at 280~nm, the H$\alpha$ emission line, and the FIR 24$\mu$-band. We include a study of inclination trends in the IR/UV ratio (``IRX'') and the IR/H$\alpha$ ratio. Our sample comprises a few hundred galaxies from the region around the clusters Abell 901/902 with deep data and inclinations measured from outer disks in {\it Hubble Space Telescope} images. As a novelty, the H$\alpha$- and separately the NII-emission are measured by tunable-filter imaging and encompass galaxies in their entirety. At galaxy stellar masses above $\log M_*/M_\odot \ga 10$ we find trends in the UV and H$\alpha$ mass-to-light ratio that suggest an inclination-induced attenuation from face-on to edge-on of $\sim 1$ mag and $\sim 0.7$ mag in UV and H$\alpha$, respectively, {\refbf implying that star-formation rates of edge-on galaxies would be underestimated by $\sim 2.5\times$ in UV and $\sim 2\times$ in H$\alpha$}. We find the luminosities in UV and H$\alpha$ to be well correlated, but the optical depth of diffuse dust that causes inclination dependence appears to be lower for stars emitting at 280~nm than for gas clouds emitting Balmer lines. For galaxies with $\log M_*/M_\odot \la 9.7$, we find no measurable effect at $>0.1$~mag. The absence of an inclination dependence at 24$\mu$ confirms that the average galaxy is optically thin in the FIR. | The appearance of galaxies is largely determined by their luminous components, i.e. stars and ionised gas clouds. A second factor is extinction of galaxy light due to dust inside them, where geometry and amount of dust determine how a galaxy appears from different viewing angles. Star-forming disk galaxies are the most common type of galaxy, and they contain a fair amount of dust, mostly in a disk thinner than the stellar disk \citep{Xilouris99}, at least in galaxies that are large enough to be ordered by significant rotation \citep{Dalcanton04}. Disk galaxies viewed edge-on usually display impressive dust bands that clearly obscure much of a galaxy's stars and gas clouds, while those seen face-on show their dust more as a filigree pattern woven subtly into their spiral arms. This difference in prominence and optical depth of the dust is even clearer when considering viewing points inside the dust disk, e.g. the Earth's location inside the Milky Way. When we look out of our Galaxy's disk at steep angles, only a few percent of the light is absorbed before arriving at Earth. But when we look along a line-of-sight running within the disk itself, the view is quickly blocked; visual light from the centre of the Milky Way arrives at Earth only after being diminished by a factor of up to one trillion \citep{Catchpole90}. For a while, a debate has raged about whether disk galaxies are optically thin or thick \citep{Holmberg58,Disney89,Valentijn90,Xilouris99,Holwerda05}, but it seems there is convergence to the view that disks are optically thick only when viewed edge-on or in their innermost parts, see \citet{Calzetti01} for a review, and also \citet{Wild11}. Many details of the spatial distribution between luminous components and absorbing dust are important for the appearance of a galaxy in different spectral passbands, as discussed e.g. by \citet{Popescu11}. However, the viewing angle of a galaxy, or inclination, is still an obvious primary ordering parameter that can be easily measured. Hence, several past works have considered the effect of inclination on the apparent sizes, concentration, brightness and colour of galaxies \citep[e.g.][]{Holmberg58, Giovanelli94, Tully98, Masters03, Driver07, ChoPark09, Maller09, M10, Wild11, Devour16, Devour17, Battisti17}. It is found that the inclination of a galaxy affects estimates of its physical properties, such as the population mix and total mass of its stars \citep[see review by][]{Conroy13}; when considering samples of galaxies it causes an underestimation of the average cosmic matter density \citep[e.g.][]{Driver07}; it complicates attempts to understand galaxy evolution from comparisons with simulations \citep[e.g.][]{SomPrim99, McKinnon17}; and it causes apparently random, flux-limited samples of galaxies to suffer from selective incompleteness that even affects cosmological studies; finally, measurements of the star-formation rate are affected by inclination \citep{Morselli16,Leslie18}. On the other hand, changes in galaxy appearance with inclination are an opportunity to learn about the dust itself. A first step towards a more structured picture of dust is a two-component model \citep[e.g.][]{LonsdalePerssonHelou87,CF00,Tuffs04} with diffuse dust and clumpy dust: diffuse cirrus-like dust pervades the disk of the Milky Way and other galaxies with a high fill factor at low density, while high-density dust clumps enshroud the birth clouds of stars with high optical depth but moderate and constantly evolving covering factors as the radiation from the new-born stars blows away the dust within less than ten million years. Most observations to date appear consistent with this two-component picture \citep[e.g.][]{Wild11}, including the fact that Balmer emission from star-forming regions is more extinguished than the stellar continuum of older stars by a factor of two or more \citep{Kennicutt83,Calzetti94,Yip10,Hao11,Wild11} due to high optical depth of the dusty birth clouds. When galaxies are inclined in the two-component model, the line-of-sight through cirrus becomes longer and the optical depth of dust larger; however, the total extinction of new-born stars embedded in birth clouds increases less in relative terms than the extinction of older stars, whose face-on extinction by the low-density cirrus is expected to be mild. As the extinction of stars depends not only on inclination but also age, the effective attenuation curves of the integrated stellar population in a galaxy may change with inclination. Effective attenuation curves are light-weighted and thus susceptible to changes in the apparent mix of stellar populations in the integrated light of a galaxy, even when the local composition and extinction law of the dust is constant throughout the galaxy \citep{Calzetti94,Wild11,Battisti17}. Previous studies have shown that dust opacity in galaxy disks has (i) a radial dependence, where centres are more extinguished than outskirts of disks \citep{Valentijn94,Peletier95,Holwerda05,Tacchella17}; (ii) a type dependence, where early-type spirals have higher opacities than late-type disks \citep{deVau91,Han92,M10}; (iii) a luminosity dependence, where the mean extinction of the disk increases towards more luminous galaxies \citep{Giovanelli95,Tully98,Masters03}, but turns over at the highest luminosities, where the specific star formation rate drops \citep{M10,Devour16}; and (iv) spiral arms are more opaque than inter-arm regions \citep{Beckman96, White00, Holwerda05}. \citet{ChoPark09} found that extinction changes with concentration of the galaxy, and \citet{Grootes13} note that the central face-on $B$-band dust optical depth in a galaxy is correlated with its mean stellar mass surface density. Previous work has mostly addressed the effects of inclination on the appearance of galaxies in the stellar continuum light of UV-optical and near-infrared passbands. Generally, it is observed that measuring additional extinction as galaxy orientation changes from face-on to edge-on is easier than assessing total extinction, although approaches exist for the latter \citep[e.g.][]{Driver07}. For instance, \citet{M10} find that the average extinction added from face-on to edge-on in the passbands of Sloan Digital Sky Survey \citep[SDSS,][]{SDSS} ranges from 0.4~{\refbf mag} in $i$-band to 0.7~{\refbf mag} in $u$-band for the integrated light of a galaxy, and \citet{Devour16} find similar values but can distinguish trends with mass and star formation. Studies of integrated light of course average over a range of behaviour from negligible extinction in the outer parts to high obscuration in galaxy centres. Some work has considered trends in the extinction of Balmer lines, but such data was mostly drawn from SDSS fibre spectra, which concentrate on small central areas in galaxies and thus fail to represent their disks \citep[e.g.][]{Yip10,Wild11,Battisti17}. In this paper, we look specifically at the inclination-dependence of total galaxy luminosity in passbands that are used as star-formation indicators, notably the UV~280~nm continuum, the integrated H$\alpha$-line luminosity and the far-infrared continuum in the {\it Spitzer} 24$\mu$ band. Specifically, the {\refbf 24$\mu$} luminosity is a star-formation indicator that should be largely independent of inclination, such that the ratio of UV-to-IR and H$\alpha$-to-IR luminosity can {\refbf directly reflect UV- and H$\alpha$-extinction}. We work with a comparatively small sample of a few hundred galaxies, but compared to SDSS {\refbf our spatial resolution is larger, and also our multi-band images have vastly deeper surface brightness sensitivity; this allows fitting the outer disk contours as opposed to relying on inner axis ratios that are more easily biased by bulges and bars; finally, our deep H$\alpha$ and [N{\sc ii}] line imaging captures H$\alpha$ light from across the entire galaxy disk, thus matching the H$\alpha$-footprint consistently to the other passbands and avoiding aperture biases}. We use a volume-limited sample of galaxies around a cluster at a fixed distance (redshift $z\approx 0.16$) and thus avoid a dispersion of K corrections within the sample. In Section~\ref{s-data-sample}, we describe our multi-wavelength data and the sample, including inclination biases in stellar-mass determination. In Section~\ref{results} we measure the slopes of our $M_*/L_{\rm band}$ ratios in UV, H$\alpha$ and FIR versus stellar mass and inclination, and consider in particular the infrared excess over UV and H$\alpha$. This is followed by a discussion and summary. We adopt a flat $\Lambda$ cold dark matter cosmology with $\Omega_\Lambda=0.7$ and $H_0=70$~km~s$^{-1}$~Mpc$^{-1}$, which fixes the luminosity distance to our target cluster at $D_L=791$~Mpc. We use Vega magnitudes throughout the paper, and a bolometric luminosity for the Sun of $L_{\odot,\rm bol} = 3.823 \times 10^{33}$~erg~s$^{-1}$. | \label{discussion} \subsection{Stellar-mass estimates} A study of inclination effects based on mass-to-light ratios depends crucially on their freedom from inclination biases. The literature contains conflicting statements on the reliability of mass-to-light ratios from \citet{BdJ01}: \citet{Maller09} consider their masses to be the least biased among a choice of three alternatives, and describe them as essentially unbiased even at the highest inclinations; in contrast, \citet{Driver07} consider them to be unbiased at $i<60\degr$, but find them to be biased at higher inclinations. Our results appear in between, as we find these masses acceptable up to $\log a/b=0.6$, which is $i>75\degr$, or indeed $i\approx 80\degr$ for an intrinsic thickness of $q=0.18$. At higher inclinations, all the way to the edge-on case at $i=90\degr$, we find an underestimation of the mass by potentially up to a factor of $\sim 2$. This underestimation can be explained by attenuation levels that increase faster than the reddening at the highest inclinations, such that the declining apparent brightness of the galaxy is not sufficiently compensated by an increased mass-to-light ratio. {\refbf \citet{Xilouris99} noted that dust disks have larger scale lengths than stellar disks in galaxies and may extend beyond the edges of the visible stellar disks; if that were the case, such dust would not contribute while inclination changes from face-on to $i\ga80\degr$, but its effect, although presumably weak, could kick in edge-on, when it is moved into the lines-of-sight to the thick disk of a galaxy.} \subsection{Attenuation of stellar continuum and line-emitting gas} Our measurement for the attenuation of the UV stellar continuum at 280~nm from face-on to edge-on can be best compared with the results in the SDSS $u$-band by \citet{M10} and in the GALEX FUV-band by \citet{Leslie18}: \citet{M10} found an extinction contribution going from face-on to edge-on of $\Delta A_u=0.7$ in the SDSS $u$-band. Our value of $\Delta A_{280}=0.97$ translates into $\Delta A_u = 0.68$, if we assume a Milky Way extinction law with $R_V=3.1$. We note that \citet{M10} find an attenuation curve, going from $\Delta A_u=0.7$ to $\Delta A_i=0.4$, that is greyer than a Milky Way extinction law, but still consistent with $\Delta A_{280}\approx 1$ within the errors. The results are equally compatible with the slope measurements for the SDSS $u$-band by \citet{Devour16}. \citet{Leslie18} find $\gamma_{\rm FUV}=0.79\pm 0.09$ with a different parametrisation of inclination, suggesting $\Delta A_{\rm FUV}=1.97\pm 0.2$, where we would expect $\Delta A_{\rm FUV}=1.29\pm 0.45$ if we assume a \citet{F99} attenuation curve with $R_{\rm FUV}=8.02$. In contrast, our results are {\refbf incompatible with the trends suggested by \citet{Maller09}. On this matter, \citet{Devour16} present an excellent discussion suggesting that all} our studies are consistent in terms of data, but lead to inconsistencies due to the analysis, and we have nothing to add to their assessment. Our value for the attenuation from face-on to edge-on in H$\alpha$ is $\Delta A_{{\rm H\alpha}}=0.72$. This means that the 280~nm-emitting stars are attenuated by less diffuse dust than the Balmer line-emitting gas, most likely with a factor of $\Delta E(B-V)_{\rm stars} \approx 0.52 \times \Delta E(B-V)_{\rm H\alpha}$, but the deviation from equality is only significant at the 2$\sigma$ level. We note, that for the overall extinction ratio \citet{Calzetti00} report $E(B-V)_{\rm stars} = 0.41 \times E(B-V)_{\rm H\alpha}$ in star-bursting galaxies, but this combines the diffuse and the clumpy dust and refers to the population of stars more generally. In a simplistic two-component model with a thin disk of diffuse dust and isotropic clumps of thick dust around star-forming regions, we would naively expect no difference in the $\Delta E(B-V)$ of stars and gas caused by inclination, although the face-on $E(B-V)$ values for the two would be very different. This result is indeed found by \citet{Yip10}, whose Fig.~16 shows no inclination trend in the ratio of the equivalent width between H$\alpha$ and H$\beta$ within the errors; this is consistent with the stellar continuum changing with inclination by the same attenuation curve as the Balmer emission lines as this will keep line equivalent widths unchanged\footnote{Note, that the discussion in \citet{Yip10} is misled by a confusion of line fluxes and equivalent widths in their equation 10 for the optical depth; consequently their Fig. 18 is mislabelled on the y-axis as $\tau$ is not really an optical depth, and the diagonal line for the model of dust optical depth being identical for stars and gas should be a horizontal line for their chosen y-axis instead, which would also match their data beautifully. As a consequence, the authors fail to acknowledge that they actually measure a consistent trend in the attenuation of stars and gas with inclination.}. Still, a marginally higher extinction for the gas could be plausible in a mixed gas-dust-star geometry \citep[and would be consistent with][]{Yip10}, where more stars than gas are seen with low or no attenuation; this would be the case, if either gas is in a thinner disk than the stars and some stars are above the dusty volume and thus less attenuated. An alternative explanation stems from the nature of our cluster sample, which includes some galaxies with more centrally concentrated star formation than is typical in field samples. The loss of star formation in the outer parts of the disks might have gone hand in hand with a loss of gas and dust, such that the outer stellar disks in our galaxies are actually seen with lower-than-typical attenuation that is mixed into our integral values representing galaxies as a whole. Inclination trends in the attenuation of the line-emitting gas have also been measured by \citet{Battisti17}, who find a mild inclination trend in Balmer decrement, but they consider mostly low-mass galaxies ($\log M_*/M_\odot<10$), and study only the central regions of galaxies through fibre spectra. Interpreting and comparing their results is challenged by the fact that the dust line-of sight in fibre spectra increases with inclination not only by $1/(\cos i)$, but by more as the fibre footprint on the galaxy becomes elliptical and finally cylindrical within the galaxy plane once an edge-on view is reached: thus face-on only the dust within the fibre aperture contributes, while towards edge-on a whole cylinder across the full diameter of the galaxy moves into the fibre aperture. \subsection{Trends in far-infrared emission} In this paper we use the far-infrared luminosity as a reference measurement that we expect to be minimally affected by inclination. We find indeed no significant trend in the $M_*/L_{\rm IR}$-ratio with inclination. The same is found by \citet{Leslie18}, who studied WISE W4 data for low-redshift field galaxies in the SDSS. Due to the restricted dynamic range in mass we find only a weak trend of the $M_*/L_{\rm IR}$-ratio with mass, which is furthermore dominated by a few massive galaxies that have high ratios above trend in all passbands we consider. These are likely to have their masses of $\log M_*/M_\odot\approx 11$ estimated correctly, while having unusually low luminosities in the star-formation indicators because they {\refbf have moved off the star-forming main sequence already}. \citet{M10} and \citet{Devour16} have used a much larger parent sample, which allowed a careful analysis of the highest-mass end of the disk galaxy distribution at $\log M_*/M_\odot\approx 11$. They found that the declining star formation is accompanied also by a declining dust density, although this is inferred from the visual extinction and not the infrared emision. The reason is most likely that dust gets produced in the context of star formation, but it also gets destroyed rapidly afterwards and disappears with time if not replenished by sufficient star formation. However, discussions of the life of dust are beyond the scope of this paper. According to \citet{Calzetti07} and \citet{Calzetti13} a very good star-formation indicator is the sum of star formation seen in H$\alpha$ and 24$\mu$, as it captures both unobscured star formation and dust-reprocessed light from obscured star formation. In the context of our inclination study, we note that such an indicator still shows an inclination trend, as the isotropically emitting 24$\mu$-band is combined with the inclination-dependent H$\alpha$. While the combined indicator is intended to be a best-case estimate in an ensemble average, it will of course still overestimate individual star-formation rates in face-on galaxies and underestimate them at high inclination. \subsection{Trends of dust extinction with mass} {\refbf \citet{Brinch04} and \citet{GarnBest10} measured the mass-dependency of H$\alpha$ extinction for SDSS galaxies. Unfortunately, we are not able to measure trends with mass independently, e.g. using our $24\mu$ data, because the luminosity at $24\mu$ depends not only on star-formation rate but also on mass itself, as evidenced by non-linear calibrations for star-formation rate as a function of 24$\mu$ luminosity; this non-linearity has been studied in great detail and probably results from a mass dependence of metallicity and dust-star geometry \citep[e.g.][]{Calzetti07,Davies16,Brown17}. If we use a mean calibration from \citet{Brown17} to convert 24$\mu$-luminosity into predicted dust-corrected H$\alpha$-luminosity, and derive extinction by comparison with the observed H$\alpha$-luminosity, then we find results compatible with those of \citet{Brinch04} and marginally lower than \citet{GarnBest10}, but the uncertainties are too large to be conclusive.} \subsection{Impact of the galaxy cluster on the results} A valid question is, whether the results we find for our sample of cluster galaxies resembles properties of field galaxies or not. \citet{Tully98} have used cluster samples before, but their disk galaxies from the relatively low-density Ursa Major and Pisces Clusters are expected to be similar to field spirals. The properties of Abell 901/2, our cluster, are more similar to those of the Virgo Cluster than Ursa Major and Pisces; indeed, \citet{Boesch13} found that in A901/2 many of the red spirals in particular have more centrally concentrated and more asymmetric emission-line disks than field spirals. Differences in the radial distribution of young stars, compared to field spirals, propagate into differences in the integrated effect of dust and inclination on star-formation indicators. Our sample contains roughly half-and-half galaxies that are inside and outside of the projected virial radius of the four sub-clusters in the Abell 901/2 system \citep[see e.g.][]{Heymans08,OMEGA3}, but projection effects alone will wash out clear signatures. Qualitatively, we expect that ram-pressure stripping or thermal evaporation could have removed some gas and dust from the outer disks of galaxies, especially those that are now seen as less star-forming as a consequence. This effect has been shown to be present in A901/2 by \citet{Boesch13}, and the affected galaxies would now show less average extinction on their stellar population. How the persisting, more centrally located star-forming regions are extinguished in comparison to normal galaxies is not obvious. Central attenuation in normal galaxies is known to be higher than attenuation in outer disks, but ram pressure could have changed the dust-star geometry and models are not refined enough to reliably investigate populations of transitioning galaxies that are not in a known equilibrium configuration. | 18 | 8 | 1808.00530 |
1808 | 1808.04125_arXiv.txt | The astrophysical S-factor and reaction rate of the direct capture process $\alpha+d$ $\rightarrow$ $^6$Li + $\gamma$, as well as the abundance of the $^6$Li element are estimated in a three-body model. The initial state is factorized into the deuteron bound state and the $\alpha+d$ scattering state. The final nucleus $^6$Li(1+) is described as a three-body bound state $\alpha+n+p$ in the hyperspherical Lagrange-mesh method. Corrections to the asymptotics of the overlap integral in the S- and D-waves have been done for the E2 S-factor. The isospin forbidden E1 S-factor is calculated from the initial isosinglet states to the small isotriplet components of the final $^6$Li(1+) bound state. It is shown that the three-body model is able to reproduce the newest experimental data of the LUNA collaboration for the astrophysical S-factor and the reaction rates within the experimental error bars. The estimated $^6$Li/H abundance ratio of $(0.67 \pm 0.01)\times 10^{-14}$ is in a very good agreement with the recent measurement $(0.80 \pm 0.18)\times 10^{-14}$ of the LUNA collaboration. | \par There are two open astrophysical problems related to the abundance of lithium elements in the Universe. First, the Big Bang nucleosynthesis (BBN) model predicts for the $^{7}$Li/H ratio an estimate about three times larger than the recent astronomical observational data from metal-poor halo stars \cite{sbor10,MSB16}. The second lithium puzzle is related to the estimation of the primordial abundance ratio $^{6}$Li/ $^{7}$Li of the lithium isotopes. For this ratio the BBN model \cite{serp04} yields a value about three orders of magnitude less than the astrophysical data \cite{asp06}. In the BBN model the abundance of the $^7$Li element is estimated on the basis of two key capture reactions $\alpha(^3$He,$\gamma)^7$Be and $\alpha(^3$H,$\gamma)^7$Li (see \cite{neff,navratil,tur18} and references therein). For the estimation of the $^6$Li/$^7$Li ratio the BBN model includes as input parameters the reaction rates of the direct radiative capture process \begin{eqnarray} \label{1} \alpha+d\rightarrow {\rm ^6Li}+\gamma \end{eqnarray} at low energies within the range $30 \le E_{\rm cm} \le 400$ keV \cite{serp04}. The data set of the LUNA collaboration at two astrophysical energies E=94 keV and E=134 keV \cite{luna14} was recently renewed with additional data at E=80 keV and E=120 keV \cite{luna17}. These data sets were obtained as results of the direct measurements of the astrophysical S-factor at the underground facility. The new data are lower than the old data of nondirect measurements from Ref. \cite{kien91}. Based on the new data set, the thermonuclear reaction rate of the process has been estimated by the LUNA collaboration. The results for the reaction rates turn out to be even lower than previously reported. This further increases the discrepancy between prediction of the BBN model and the astronomical observations for the primordial abundance of the $^6$Li element in the Universe \cite{luna17}. Until recently all the theoretical estimations of the astrophysical S-factor of the above direct capture reaction at low astrophysical energies were based on the so-called exact mass prescription, in the both potential models \cite{dub951,dub952,type97,desc98,mukh11,tur15,MSB16} and microscopic approaches \cite{lang86,noll01,TBL91}. Within this prescription the matrix elements of the isospin forbidden E1-transition were estimated by using the exact experimental mass values of the colliding nuclei $^2$H and $^4$He. As was shown recently in Ref. \cite{bt18} in details, this way has no microscopic background at all and cannot be used, for example in the description of the capture process $d(d,\gamma)^4$He of two identical nuclei. Of course, the estimated in this way cross sections and S-factors of the $\alpha(d,\gamma)^6$Li capture reaction can be fortituously close to the experimental data, however this method does not yield a relevant energy dependence of the S-factor and cross section and correct predictive power for future $\it ab-initio$ studies \cite{bt18}. An alternative approach to the description of the capture processes is based on solving the three-body Faddeev equations \cite{shub16} using quasi-separable potentials. An advantage of this method is that it allows an easier treatment of non-local effects that can be extended to three-body problems. Realistic three-body models are based on the isovector E1 transition from the initial $T_i=0$ (isosinglet) states to the $T_f=1$ (isotriplet) components of the final $^6$Li$(1^+)$ bound state, or from the initial isotriplet components to the main isoscalar part of the final $^6$Li$(1^+)$ nucleus bound state \cite{bt18}. First attempt to estimate in a correct way the matrix elements of the isospin-forbidden E1- transition together with the E2-transition for the $^4$He$(d,\gamma)^6$Li direct capture process has been done in the three-body model \cite{TKT16}. The formalism of the model has been developed in a consistent way and correct analytical expressions have been obtained for the matrix elements of the E1- and E2-transitions, including the isovector transition matrix elements. The numerical results were obtained on the basis of the final three-body wave function $^6$Li$=\alpha+p+n$ in hyperspherical coordinates \cite{desc03,tur06}, which had a small isotriplet component with the norm square of 1.13 $\times 10^{-5}$. Due to smallness of the isotriplet component of the final three-body bound state the corresponding numerical calculations in Ref. \cite{TKT16} have reproduced the existing experimental data for the S-factor only in the frame of the exact mass prescription and with the help of additional spectroscopic factor. Further studies in Ref. \cite{bt18} have demonstrated that the quality of the final three-body wave function $^6$Li$=\alpha+p+n$ can be improved and convergent isotriplet component can be reached with the norm square of 5.3$\times 10^{-3}$, which is larger than the old number by two orders of magnitude. This led to the fact that the E1 S-factor also increased by two orders of magnitude. Additionally, as was shown in that paper, the E2 S-factor can be improved owing to the correction of the asymptotics of the overlap integral of the $^6$Li and deuteron wave functions at a distance 5-10 fm. The aim of present study is to estimate the reaction rates of the $\alpha(d,\gamma)^6$Li direct capture process and the primordial abundance of the $^6$Li element in the Universe within the improved realistic three-body model \cite{TKT16,bt18}. The initial wave function is factorized into the deuteron bound-state and the $\alpha-d$ scattering-state wave functions. The final $^6$Li(1+) state is described as a $\alpha+p+n$ three-body bound system. The wave function on the hyperspherical Lagrange mesh basis available for the $^6$Li(1+) bound state \cite{desc03,tur06} will be employed. In Sec. II we describe the model, in Sec. III we discuss obtained numerical results and finally, in the last section we draw conclusions. | The astrophysical direct capture process $\alpha+d\rightarrow ^6$Li$+\gamma$ has been studied in the three-body model. The reaction rates, E1 and E2 astrophysical S-factors as well as the primordial abundance of the $^6$Li element have been estimated. The asymptotics of the overlap integral in the S- and D-waves have been corrected. This increased the E2 S-factor by an order of magnitude at low astrophysical energies. Together with the corrected E2 S-factor, the contribution of the E1-transition operator to the S-factor from the initial isosinglet states to the small isotriplet components of the final $^6$Li(1+) bound state is shown to be able to reproduce the new experimental data of the LUNA collaboration within the experimental error bars. The theoretical reaction rates have the same temperature dependence at low temperatures as the newest direct 2017 data of the LUNA collaboration. For the abundance ratio $^6$Li/H we have obtained an estimation $(0.67 \pm 0.01)\times 10^{-14}$ , consistent with the new estimation of the LUNA collaboration and much lower than the results of the models based on the exact mass prescription. Further improvement of the theoretical estimations of the reaction rates and $^6$Li abundance is expected with the help of NN-tensor forces within {\it ab-initio} calculations. | 18 | 8 | 1808.04125 |
1808 | 1808.04852_arXiv.txt | Cosmic rays are predominantly accelerated in shocks associated with star formation such as supernova remnants and stellar wind bubbles, so the cosmic-ray flux and thus cosmic-ray ionization rate, $\zeta_{\rm H}$, should correlate with the star-formation rate in a galaxy. Submillimeter bright galaxies (SMGs) are some of the most prolific star forming galaxies in the Universe, and gravitationally lensed SMGs provide bright continuum sources suitable for absorption line studies. Abundances of OH$^+$ and H$_2$O$^+$ are useful for inferring $\zeta_{\rm H}$ when combined with chemical models, and have been used for this purpose within the Milky Way. At redshifts $z\gtrsim2$ transitions out of the ground rotational states of OH$^+$ and H$_2$O$^+$ are observable with ALMA, and we present observations of both molecules in absorption toward the lensed SMGs SMM~J2135$-$0102 and SDP~17b. These detections enable an exploration of $\zeta_{\rm H}$ in galaxies with extreme star formation and high supernova rates, both of which should significantly enhance cosmic-ray production. The observed OH$^+$ and H$_2$O$^+$ absorption is thought to arise in massive, extended halos of cool, diffuse gas that surround these galaxies. Using a chemical model designed to focus on the reaction network important to both species, we infer cosmic-ray ionization rates of $\zeta_{\rm H}\sim10^{-16}$--$10^{-14}$~s$^{-1}$ in these extended gaseous halos. As our estimates come from gas that is far away from the sites of cosmic-ray acceleration, they imply that cosmic-ray ionization rates in the compact regions where star formation occurs in these galaxies are orders of magnitude higher. | \label{sec_intro} The star formation rate (SFR) density has varied throughout the history of the Universe, peaking around a redshift of $z\approx2$ \citep{madau2014}. Submillimeter-bright galaxies (SMGs) observed during this epoch of peak star formation outshine even ultra-luminous infrared galaxies (ULIRGs) and starburst galaxies, and it has been speculated that they are the progenitors of the massive elliptical galaxies seen in the local Universe \citep[e.g.,][and references therein]{simpson2014}. Characterizing the physical conditions in SMGs is thus important for better understanding star formation in and evolution of massive galaxies. Star formation is regulated by the molecular gas content in a galaxy \citep{wong2002}, and in turn, the newly formed stars influence the physical and chemical conditions in the interstellar medium (ISM) through various feedback mechanisms. Many atomic and molecular species are useful in constraining properties of the ISM such as density, temperature, and radiation field since the relative population in different quantum states is controlled by radiative and collisional (de)-excitation. As a result, observations of emission and absorption from species such as CO, H$_2$O, C, and CH$^+$ can and have been used to infer properties of SMGs \citep[e.g.,][]{swinbank2011,falgarone2017,yang2017}. One property of SMGs that has received minimal study thus far is the cosmic-ray ionization rate, and the underlying cosmic-ray flux. Because photons capable of ionizing hydrogen ($E>13.6$~eV) do not penetrate very far into molecular clouds, cosmic rays represent the dominant ionization mechanism in cloud interiors. Interstellar gas phase chemistry is primarily driven by fast ion-molecule reactions, so this ionization source is vital to increasing chemical complexity. Cosmic rays are accelerated in shocks associated with massive stars---most notably in supernova remnants, but also in the termination shocks of stellar wind bubbles---so it follows that the cosmic-ray flux should be correlated with the star formation rate. Indeed, estimates of the cosmic-ray ionization rate increase from the Galactic disk \citep[$10^{-16}$~s$^{-1}$;][]{indriolo2012,indriolo2015oxy} to the Galactic center \citep[$10^{-15}$--$10^{-13}$~s$^{-1}$; e.g.,][]{yusefzadeh2013,goto2014,lepetit2016} to nearby star-forming galaxies \citep[$10^{-13}$--$10^{-12}$~s$^{-1}$;][]{gonzalez-alfonso2013,gonzalez-alfonso2018arxiv}. Our goal is to infer the cosmic-ray ionization rate in SMGs at $z\sim2.3$ to better understand the impact of prolific star formation on the gas reservoirs in these massive galaxies, and to trace the relation between star formation and ionization rate in the early Universe. Multiple studies of OH$^+$ and H$_2$O$^+$ in the Milky Way have demonstrated that these oxygen-bearing ions are useful in constraining the cosmic-ray ionization rate of atomic hydrogen, $\zeta_{\rm H}$ \citep{gerin2010,neufeld2010,porras2014,indriolo2015oxy,zhao2015}. This is because the formation, and thus abundances, of these species is closely linked to the ionization of atomic hydrogen through the following chemical reactions: \begin{equation} {\rm H} + {\rm CR} \rightarrow {\rm H}^+ + e^- + {\rm CR'}, \label{reac_CR_H} \end{equation} \begin{equation} {\rm H}^+ + {\rm O} + \Delta E \longleftrightarrow {\rm O}^+ + {\rm H}, \label{reac_Hp_Op} \end{equation} \begin{equation} \mathrm{O^+ + H_2 \rightarrow OH^+ + H}, \label{reac_Op_H2} \end{equation} \begin{equation} \mathrm{OH^{+} + H_{2} \rightarrow H_{2}O^{+} + H}. \label{reac_OH+_H2} \end{equation} The reaction network surrounding these species is, of course, more complicated than these four reactions \citep[see, e.g.,][]{hollenbach2012,indriolo2015oxy}, and the reactions shown above are only intended to demonstrate how the production of OH$^+$ and H$_2$O$^+$ is a few steps removed from the ionization of H. Given our success with inferring cosmic-ray ionization rates from OH$^+$ and H$_2$O$^+$ in the Galaxy, we have targeted transitions from the ground rotational states of both species in a small sample of SMGs at $z\sim2.3$ with the same goal in mind. Throughout this paper we will refer to the cosmic-ray ionization rate of atomic hydrogen, $\zeta_{\rm H}$, which accounts for ionization by both cosmic rays and energetic secondary electrons produced via ionization. Estimates of the primary ionization rate of atomic hydrogen, $\zeta_p$, which does not include ionization by secondary electrons, and the ionization rate of molecular hydrogen, $\zeta_2$, can be made via the relations $\zeta_{\rm H}=1.5\zeta_p$ and $\zeta_2=2.3\zeta_p$ \citep{glassgold1973,glassgold1974}. | \label{section_discussion} The different model grids shown in Figure \ref{fig_zetaH} demonstrate that the inferred cosmic-ray ionization rate is dependent upon the adopted strength of the UV radiation field for $\chi_{\rm UV}/n_{50}\leq10$. It is difficult to determine the strength of the UV radiation field in the gas where the OH$^+$ and H$_2$O$^+$ absorption occurs, but we can attempt to make some rough estimates. \citet{danielson2011} report a UV field over 1000 times\footnote{This study describes the UV flux in terms of the Habing field, $G_0$. At $\chi_{\rm UV}=1$, $G_0=1.7$.} stronger in SMM~J2135$-$0102 than in the Milky Way based on the luminosity ratios of various CO, C, and C$^+$ emission lines. This estimate applies to the dense ($n_{\rm H}\sim10^4$~cm$^{-3}$) gas in close proximity to the starburst regions though, and likely not the gas with $n_{\rm H}\sim50$~cm$^{-3}$ where we see CH$^+$, OH$^+$ and H$_2$O$^+$ absorption. The $\chi_{\rm UV}/n_{50}=1000$ model (panel e in Figure \ref{fig_zetaH}) suggests cosmic-ray ionization rates in SMM~J2135$-$0102 are on the order of $10^{-16}$~s$^{-1}$, several orders of magnitude below the $\zeta_2\sim10^{-13}$--$10^{-11}$~s$^{-1}$ estimate of \citet{danielson2013} for the same gas component were they find the high UV field. This discrepancy suggests that OH$^+$ and H$_2$O$^+$ absorption does not come from gas close to the starburst regions, reaffirming the idea that it instead is located in the same extended halo where CH$^+$ absorption is seen. The fact that the SMM~J2135$-$0102 results occupy the same location in $\log_{10}[N({\rm OH}^+)/N({\rm H})]$ vs. $N({\rm OH}^+)/N({\rm H_2O}^+)$ parameter space as Galactic diffuse clouds \citep{indriolo2015oxy,neufeld2017} also supports this picture. Even if we assume that the UV field is highly attenuated in this extended halo and use the model with $\chi_{\rm UV}/n_{50}=0.1$ (panel a in Figure \ref{fig_zetaH}), ionization rates in SMM~J2135$-$0102 are still only on the order of a few times $10^{-15}$~s$^{-1}$. However, a decrease in the cosmic-ray ionization rate between the starburst regions and an extended halo is in fact expected, since the underlying cosmic-ray flux will decrease with propagation into a much larger volume and due to losses as particles interact with the ambient medium. Assuming the underlying cosmic-ray spectrum does not vary in shape, and that particles propagate away from the star-forming regions isotropically, the cosmic-ray flux and ionization rate at large distances will decrease as $d^{-2}$. The low-energy ($\sim$MeV) particles most efficient at ionization (due to larger interaction cross sections), will be removed from the particle spectrum more quickly due to energy losses \citep{cravens1978,padovani2009} and may be preferentially confined both near the star-forming regions and within the galaxy by magnetic fields \citep[see review by][]{cesarsky1980}, so the underlying cosmic-ray spectrum is expected to change. As a result, the cosmic-ray ionization rate should decrease even faster than $d^{-2}$, and our estimate of $\zeta_{\rm H}\approx10^{-15}$~s$^{-1}$ in the extended gaseous halo around SMM~J2135$-$0102 can be reconciled with the $\zeta_2\sim10^{-13}$--$10^{-11}$~s$^{-1}$ estimate of \citet{danielson2013} in the star-forming region. There are no previous estimates of the cosmic-ray ionization rate or the strength of the UV radiation field in SDP~17b, and observations of CO and H$_2$O do not resolve the emitting region \citep{omont2011,omont2013,yang2017}. If we again assume that the OH$^+$ and H$_2$O$^+$ absorption arises in an extended halo where the UV field is weak, we find ionization rates on the order of $10^{-15}$--$10^{-14}$~s$^{-1}$. As for SMM~J2135$-$0102, the cosmic-ray ionization rate in the more compact star-forming regions of SDP~17b where CO and H$_2$O emission have been observed would likely be a few orders of magnitude above our estimates in the extended halo. Cosmic-ray ionization rates have been inferred in a variety of regions both within and beyond the Milky Way. Diffuse gas in the Galactic ISM has an average ionization rate of about $3\times10^{-16}$~s$^{-1}$ \citep{gerin2010,neufeld2010,indriolo2012,indriolo2015oxy}. Dense gas shows a lower ionization rate of about $3\times10^{-17}$~s$^{-1}$ \citep[e.g.,][]{caselli1998,maret2007}, while gas in the Galactic center shows a higher ionization rate around 10$^{-15}$--10$^{-13}$~s$^{-1}$ \citep[e.g.,][]{yusefzadeh2013,goto2014,lepetit2016}, demonstrating that $\zeta_{\rm H}$ can vary by a few orders of magnitude within a single galaxy. This is not surprising given that the cosmic-ray spectrum at any given location is dependent on proximity to cosmic-ray accelerators, particle propagation effects, and losses via interactions with the ambient medium. Observations of OH$^+$ and H$_2$O$^+$ that probe the nuclear regions of ULIRGs suggest ionization rates of $\zeta_{\rm H}\gtrsim10^{-13}$~s$^{-1}$ \citep{gonzalez-alfonso2013,gonzalez-alfonso2018arxiv}, while OH$^+$ and H$_2$O$^+$ observed in the disks of starburst galaxies give an average value of $\zeta_{\rm H}\approx4\times10^{-16}$~s$^{-1}$ \citep{vandertak2016}. \citet{muller2016} detected OH$^+$ and H$_2$O$^+$ absorption in the disk of the Milky Way-like absorber at $z=0.89$ toward PKS~1830$-$211, and inferred ionization rates in the range $3\times10^{-15}$~s$^{-1}\lesssim \zeta_{\rm H}\lesssim 2\times10^{-14}$~s$^{-1}$. Clearly, there is large variation in cosmic-ray ionization rates inferred in different regions, but the general trend is that $\zeta_{\rm H}$ is larger in regions of more copious star formation. The intent of our study was to investigate this relationship in SMGs, which show some of the highest star-formation rates in the Universe. Note that while we have referred to an ionization rate of $10^{-13}$--$10^{-11}$~s$^{-1}$ in SMM~J2135$-$0102 \citep{danielson2013}, that estimate is based on the galaxy's star-formation rate, and so should not be used when investigating the relationship between the two parameters. Although we have not directly determined $\zeta_{\rm H}$ in the star-forming regions of SMGs, the ionization rates of $10^{-16}$--$10^{-14}$~s$^{-1}$ that we infer in the extended gaseous halos around SMM~J2135$-$0102 and SDP~17b are interesting. The fact that the ionization rate is expected to decrease faster than $d^{-2}$ with increasing distance from the site of particle acceleration suggests that cosmic-ray ionization rates in the star-forming regions of SMM~J2135$-$0102 and SDP~17b may be orders of magnitude larger than in the gas probed by our observations. This is an extremely rough estimate, but it is consistent with the trend of increasing $\zeta_{\rm H}$ with increasing SFR. | 18 | 8 | 1808.04852 |
1808 | 1808.06585_arXiv.txt | The Tarleton Observatory's 0.8m telescope and CCD photometer were used to obtain 1298 observations of the short period eclipsing binary star {\astrobj}. The observations were obtained in Johnson's BVR filters. The light curves show that {\astrobj} is an eclipsing binary star with a period of 0.26376886 days. Further analysis showed that the period of {\astrobj} is changing at the rate of $0.17\, sec/year$. The photometric solutions were obtained using the 2015 version of the Wilson-Devinney model. The solutions show that {\astrobj} is an eclipsing binary star of W UMa type. Our analysis suggests that the system has a light curve of W-subtype contact system. Its spectral type of K0/K1, as estimated from its color, places it in the Zero-Age contact zone of the period-spectral type diagram. Luminosity from the solutions indicates that it is a double-line spectroscopic system and therefore, spectroscopic observations are recommended for further detail study. | W Ursae Majoris (W UMa) stars are short period eclipsing binary stars (EB) in which there is a common envelope around both stars due to overflowing Roche lobes of the stars. Inspection of All-Sky Survey data indicates that W UMa systems are very common \citep{2006Malkov}. Our understanding of their origin, structure, and evolution is vastly incomplete and as such, it has been difficult to develop a satisfactory theory for their occurrence. It is not known for sure whether the systems are born as Siamese twins or are formed from detached binaries through Angular Momentum Loss (AML) \citep{1981Vilhu}, or through Kozai Cycle because of a third component \citep{1962Kozai}. More work needs to be done in this respect \citep{2006Paczynski}. Their lifetimes are also not very well known and various numbers from 1.0 Gyr to $>$ 5.68 Gyr are quoted in literature by different authors \citep{1992deLoore,1967Kraft}. Observational data shows that the light curve of the W UMa can be classified either as an A-type system (primary minimum due to eclipse of the larger more massive component) or a W-type system (primary minimum due to eclipse of the smaller less massive component). It has been suggested that in W-type systems, the primary component is an un-evolved main-sequence star, with later spectral type, smaller mass, lower luminosity, larger mass ratio, and a thick common envelope, while in A-type systems the primary component is approaching terminal age of the main-sequence state with earlier spectral type, larger mass, higher luminosity, smaller mass ratio, and a shallow convective envelope. Further detailed discussion on A-type and W-type can be found in various literature \citep[see for example][]{1982VanHamme,1988Hilditch,1985Rucinski}, but in short, whether they originate from the same base system, or they form from one type to the other and what will be their final fate remain unanswered questions.\\ Data on well-determined parameters of W UMa systems are few and limited while there is no shortage of known W UMa systems from All-Sky Surveys. The problem is that for many of these systems, there is no detailed and comprehensive spectroscopic and photometric data available for the determination of absolute parameters. In addition, spectroscopic observations of faint systems, magnitude $>$ 14 require 1.5 m or larger telescopes, and considering that large telescope time is hard to secure for binary star work, it becomes much more important to first obtain photometry data to analyze the light curve and to obtain preliminary parameters of the binary system. For this reason, we have embarked on a project to obtain UBVRI photometry data on 14 and fainter magnitude W UMa systems. \\ In this paper, we present the photometric data analysis and modeling of {\astrobj}. The General Catalog of Variable Stars (GCVS) \citep{2017GCVS} lists {\astrobj} as a possible W UMa contact system. SIMBAD \citep{2000Wenger} search show that there are only eight references as of this writing. The available references \citep{2014Drake,2012Paschke,2006Otero} discusses the light elements of {\astrobj} only and none contain detailed photometric and modeling analysis. The references contained therein also do not provide any further information about photometric parameters. No other literature review resulted in any additional information. Therefore, we selected this system in our list of targets to observe. | \citet{1985Maceroni} from their study of 42 W UMa system have shown W UMa stars evolve from high to low mass ratio. A-type and W-type systems are believed to be in slightly different states of evolution. \citet{1988Hilditch} proposed that W-type systems evolve into A-type systems, while \citet{2006Gazeas} proposed the opposite. {\astrobj} show W-type light curve at present, with evolve components. With the current data, it is not possible to predict its future evolution.\\ Period changes in contact binaries is attributed to three different causes: 1) mass exchange and/or mass loss, 2) apsidal motion, and 3) the possibility of a third body. Inspection of Table \ref{parameters} show no presence of a third body or apsidal motion, therefore the period decrease in the system is most likely due to mass exchange and/or mass loss. The intense magnetic field as evident by presence of star spots control the mass flow and magnetic breaking \citep{1988Guinan}. {\astrobj} contains star spot on each star so this further supports mass exchange or loss. \\ According to the popular view of the stellar evolution and structure of contact binary stars contact system evolve from detached systems to semi-detached and then finally to contact state \citep{1992deLoore, 1993RealmofInteractingBinary, 2018newmechanismforWUMa, 1996goderyaV719Her}. Mass transfer can occur during the core H-burning phase (Case A type mass transfer) or during the shell H-burning phase (Case B type mass transfer). Detailed discussion on mass transfer can be found elsewhere \citep{1967Kippenhahn, 1968Palvec, 1971Paczynski}. Most contact systems are thought to be main sequence stars however, considering the spectral type of {\astrobj} and its position in the period-spectral type diagram for contact binaries \citep{1995goderyaV508Cyg, 1975Yamasaki}, it appears that {\astrobj} is a Zero-Age contact system with case A-type mass transfer. \\ From our study of {\astrobj}, we conclude that it is a high mass ratio contact binary system in zero age contact phase and currently going through a period change of 0.17 sec/year. The luminosity of each component is about the same, indicating the possibility of double-lined spectroscopic system. We therefore propose that radial velocity data for this system should be obtained to accurately determine the temperature from its spectral class and compute the absolute dimensions from the combined analysis of photometric and radial velocity data. Very few zero age contact binary systems have been discovered so far and for this reason it becomes a very interesting candidate to choose for future studies. | 18 | 8 | 1808.06585 |
1808 | 1808.07195_arXiv.txt | { We investigate the properties of the ionized gas irradiated by an active galactic nucleus (AGN) based on our ``radiation-driven fountain" model for the nearest type-2 Seyfert galaxy, the Circinus galaxy \citep{wada2016}. We conducted ``quasi-three dimensional" spectral analysis using the spectral synthesis code C{\scriptsize LOUDY} and obtained the surface brightness distributions of lines, such as H$\alpha$, H$\beta$, \oiii, \nii, and \sii for the central 16-parsec region. The ionized regions observed based on these lines show a conical morphology around the rotation axis, even if we do not phenomenologically postulate the presence of an optically thick ``torus". This region also shows non-uniform internal structures, reflecting the inhomogeneous structure of fountain flows. Using ionization diagnostic diagrams, we investigated the spectral properties of the ionized gas. The diagrams based on the line ratios of \niiha and \siiha show that most regions of the cone have the same properties as those in the narrow line regions (NLRs) in AGNs, whereas using \oiha, the central 10-pc regions are rather LINER-like. The gas density, temperature, and ionizing parameter in regions identified as ``NLR" are typically $n \sim 300-1500$ cm$^{-3}$, $T \sim 1-3\times 10^4 $ K, and $ U \sim 0.01$, respectively. The morphology and \oiii intensity are similar to the base of the observed \oiii cone in the Circinus galaxy, implying some physical connections with the origin of the $\sim100$ parsec scale NLR. } | { In the standard picture of active galactic nuclei (AGNs), % an AGN hypothetically consists of an accretion disk around a supermassive black hole, a broad emission line region, a dusty ``torus", and a narrow emission line region (NLR). NLRs are spectroscopically characterized by narrow (several 100 km s$^{-1}$) emission lines, and they spatially extend from tens of parsecs to a few kiloparsecs from the nucleus. Therefore, these regions can be spatially resolved in nearby AGNs, which are characterized by conical structures with clumpy internal morphologies \citep[e.g.][]{marconi1994, schmitt1996, veilleux2001,sharp2010, muller2011}. It has been determined that NLRs are gases photo-ionized by a power-law spectrum from the nucleus \citep{davidson1979, evans1986, binette1996,komossa1997, nagao2006}, showing characteristic lines, such as H$\alpha$, H$\beta$, \oiii$\lambda$5007, \nii$\lambda$6583, and \sii$\lambda\lambda$6716,6731\footnote{ Shock excitation should be also considered to explain some lines, such as [FeII] and [PII], that form NLRs in some Seyfert galaxies \citep{mouri2000, oliva2001, storchibergmann2009, terao2016}. See also \citet{kraemer2000b} for modeling the origin of emission lines in NGC 1068.}.} { The structures of the ISM in NLRs on the parsec scale are still not resolved, even in nearby AGNs. Various theoretical models of the emitting gas have been proposed, in which the ISM is assumed to consist of single- or multi-component clouds illuminated by nuclear radiation \citep[e.g.]{baldwin1995, ferguson1997, murayama1998, nagao2003, groves2004} (See also a review by \citet{groves2007}). Imaging observations and long-slit spectra acquired by the Hubble Space Telescope/WFPC2 and STIS have been used to study the fundamental three-dimensional geometry and conditions of the NLR gases in some nearby AGNs, such as NGC 1068, NGC 4151, Mrk 3, and Mrk 573 \citep[e.g.][]{kraemer2000a, crenshaw2000, das2005, das2006, das2007, fischer2010, crenshaw2010}. These studies suggest that the gases in NLRs form intrinsically biconical outflows consisting of multiple components, whose conditions are determined by the central radiation propagating through the media around AGNs. } { However, the origin of such outflowing, multi-component gas is not clear, and the reason why the conical and clumpy morphology of NLRs is formed is still an open question. The conical shape suggests that the radiation from the central source is spatially limited by the optically thick ``torus", that the distribution of the outflowing gas is intrinsically conical, or both. Instead of assuming phenomenological models, in which the geometry and properties of the ``torus" and outflowing gas are postulated, here we use a physics-motivated, three-dimensional hydrodynamic model. Recently, we proposed a novel, dynamic picture of the ISM in the central tens of parsecs of AGNs, based on three-dimensional radiation-hydrodynamic calculations, i.e., a radiation-driven fountain \citep{wada2012}. In this picture, the outflowing, multi-phase gas with dust is naturally formed, and we found that it is not necessary to postulate a donut-like ``torus" to explain type-1 and -2 dichotomies in the spectral energy distribution (SED) \citep{schartmann2014} . In this paper, we focus on the spectral properties of the fountain flows illuminated by the AGN, to determine whether they show the properties of the observed NLRs. One should note that our current hydrodynamic model is still spatially limited, i.e. $r \leq16$ pc, therefore it may not be used to explain the general morphology of NLRs extended to several hundred parsecs; however, it can be compared with the central part of the NLR in the nearest ($D=$ 4.2 Mpc, \citet{tully2009}) type-2 Seyfert galaxy, the Circinus galaxy. } The structure of this paper is as follows. In \S 2, we briefly describe the input hydrodynamic model, i.e., the radiation-driven fountain \citep{wada2016}, and the model set-up for {\it quasi-multi-dimensional} C{\scriptsize LOUDY} simulations. Numerical results are shown in \S 3, and their implications are discussed with respect to the observed NLR in \S 4. A summary is given in \S 5. | \subsection{Comparison with observations} \begin{figure}[h] \centering \includegraphics[width = 8cm]{figure7.pdf} % \caption{Comparison of Fig. \ref{wada_fig: oiii}a with observed \oiii \citep{wilson2000, sharp2010} and CO(3-2) \citep{izumi2018} in the Circinus galaxy.} \label{wada_fig: 7} \end{figure} { In Fig. \ref{wada_fig: 7}, our \oiii map (Fig. \ref{wada_fig: oiii}a) is compared with the one obtained by the Integral Field Unit observation using the Anglo-Australian Telescope \citep{sharp2010} and the Hubble Space Telescope/WFPC2 \citep{wilson2000}. A CO(3-2) map obtained by ALMA \citep{izumi2018} is also shown to elucidate the multi-phase structures in the central region of Circinus. The IFU observations by \citet{sharp2010} show a conical ionizing region extending to $r \sim 400-500$ pc by observing \oiii, H$\alpha$, H$\beta$, \nii, and \sii lines (see their Figs. 19 and 20). Their observed resolution was 0.7 arcsec ($=14.3$ pc), which is ten times larger than our model. The innermost region of the observed ionizing cone ($< 50$ pc) is mostly categorized as ``NLR" in their ionization diagnostic diagram, but direct comparison with Fig. \ref{wada_fig: 4} is not relevant.} \citet{wilson2000} presented images of \oiii $\lambda 5007$ and H$\alpha$ with 0.046 arcsec (0.9 pc) angular resolution in the central 20-pc region of the Circinus galaxy using the Hubble Space Telescope/WFPC2. The observed \oiii ionizing cone ($< 20$ pc) has clumpy internal structures, and this is also the case in our model. The surface brightness of the brightest spots in the \oiii cone are approximately $10^{-16}$ erg s$^{-1}$ cm$^{-2}$ pixel$^{-1}$ $\sim 10^{-14}$ erg s$^{-1}$ cm$^{-2}$ arcsec$^{-2}$, which is comparable with that shown in Fig. \ref{wada_fig: oiii}a. { The origin of the knot-like structures of the NLR seen in \citet{sharp2010} is still an open question. Its morphology shows some self-similarity to the innermost structures seen in \citet{wilson2000} and also in our simulations. Our model presented here cannot follow the evolution of the AGN-driven outflows on such a large scale. Still, one should note that the outflows driven by AGNs can be intrinsically non-uniform and non-steady; therefore, it would be natural to see the knot-like structures in the emission lines. The radiative transfer effect (e.g., Fig. \ref{wada_fig: 6}) and time variation of the AGN activity itself could also enhance the non-uniform nature in the emission lines. It is also notable that the physical conditions of the ``NLR" gases in our model (\S 3.3) are consistent with those that have been inferred for the observed narrow line regions.} \subsection{Multi-phase nature in the central region} Recently, mid-infrared (MIR) interferometric observations showed that the bulk of the MIR emission comes from dust in the polar region, rather than from the dusty ``torus" \citep{tristram2014, asmus2016}. The polar infrared emission is naturally predicted from our radiation-fountain picture \citep{schartmann2014}. The present results suggest that the fountain flows can be a source of MIR polar emission and line emission from NLRs. Both the ionizing cone presented here and the MIR polar emission extend perpendicular to the molecular ``disk" observed by CO (3-2) using ALMA \citep{wada2018, izumi2018} (see also Fig. \ref{wada_fig: 7}). The radiation-driven fountain can naturally explain the multi-phase gas structures around the nucleus, at least for the central region of the Circinus galaxy. Investigating the generality of this picture for other nearby Seyfert galaxies would be an interesting subject for future theoretical and observational studies. | 18 | 8 | 1808.07195 |
1808 | 1808.05968_arXiv.txt | Foregrounds with polarization states that are not smooth functions of frequency present a challenge to \hi Epoch of Reionization (EoR) power spectrum measurements if they are not cleanly separated from the desired Stokes I signal. The intrinsic polarization impurity of an antenna's electromagnetic response limits the degree to which components of the polarization state on the sky can be separated from one another, leading to the possibility that this frequency structure could be confused for \hi emission. We investigate the potential of Faraday rotation by the Earth's ionosphere to provide a mechanism for both mitigation of, and systematic tests for, this contamination. Specifically, we consider the delay power spectrum estimator, which relies on the expectation that foregrounds will be separated from the cosmological signal by a clearly demarcated boundary in Fourier space, and is being used by the Hydrogen Epoch of Reionization Array (HERA) experiment. Through simulations of visibility measurements which include the ionospheric Faraday rotation calculated from real historical ionospheric plasma density data, we find that the incoherent averaging of the polarization state over repeated observations of the sky may attenuate polarization leakage in the power spectrum by a factor of $10$ or more. Additionally, this effect provides a way to test for the presence of polarized foreground contamination in the EoR power spectrum estimate. | \label{sec:intro} Experiments seeking to observe the redshifted \hi signal from the Epoch of Reionization (EoR) must contend with foregrounds that are $\sim10^4$ times brighter than the cosmological signal by employing foreground removal or avoidance strategies \citep[e.g.][]{Santos05, Bernardi.09, Bernardi.10, Pober13, Dillon14}. These techniques rely on the smooth frequency structure of the foreground emission, in contrast to the spectrally structured cosmological signal \citep[e.g.][]{Datta.10, Morales.12,Trott.12, Pober.14, Liu.14a, Liu.14b, Nithya.15a, Nithya.15b}. While the total intensity (Stokes I) of foreground radiation is spectrally smooth, Faraday rotation during propagation through our galaxy produces frequency structure in the linear polarization state (Stokes $Q$ and $U$) at low frequencies \citep{jelic2010}. Although extra-galactic point-sources appear largely depolarized, the large scale synchrotron emission within the Milky Way appears to retain a significant level of polarization by the time it reaches an observer on Earth \citep{bernardi13, lenc16}. The cosmological signal is expected to be effectively unpolarized given current experimental sensitivities \citep{BabichLoeb2005, Hirata.17} and thus will be detected by measurements of Stokes I on the sky. On its own, frequency structure in the polarization state would not seem to be a concern when the objective is a measurement of the total intensity. However, the dipole antenna elements used in low radio frequency interferometers generally have significant sensitivity over the full sky when compared to the faintness of the EoR emission - bright foreground emission off of boresight in the instruments beam may still be relatively bright compared to the cosmological emission along the antenna's boresight. Additionally, these dipole antennae are necessarily imperfect polarimeters over the full sky, and do not naturally produce measurements of the incident radiation field in an orthogonal basis - a necessary condition to properly measure Stokes I. This imperfection in the measurements, commonly referred to as "polarization leakage", means that even though we would like to make obtain a pure measurement of the the Stokes I intensity field on the sky, the measured visibilities will always involve a coupling to the polarization state of incident radiation. Although the sky is thought to be largely depolarized in the low frequency radio spectrum \citep{Farnes.14}, even a polarization fraction of $p\approx 10^{-2}$, which implies a polarized brightness that is "small" compared to total intensity, is not necessarily negligible compared to the cosmological signal, and therefore has the potential to produce contamination that is comparable to the EoR signal. This coupling must be understood and appropriately addressed to ensure that frequency structure in the polarization state of astrophysical foregrounds will not be mistaken for the cosmological power spectrum. As a successor to the PAPER experiment \citep{Parsons.10} the HERA experiment \citep{deBoer17} plans to use a delay spectrum based estimator \citep{parsons2012} to make measurements of the EoR power spectrum. In contrast to other efforts to observe the EoR that pursue imaging-based methods, the delay spectrum analysis approach does not involve precision imaging and thus has not included detailed modeling and subtraction of polarized foregrounds. This makes potential contamination due to polarization leakage particularly concerning for the HERA experiment. However, in \citet{Moore17} it was proposed that the natural density fluctuations of the plasma in the Earth's ionosphere will produce a kind of polarization filter that can attenuate the coupling of visibility measurements to the polarization state of the sky. In this paper we seek to understand the magnitude of this ionospheric attenuation effect in visibility measurements and the derived power spectra. We simulate interferometric visibilities based on models that include the wide-field effect of the ionosphere on the polarization state of diffuse foregrounds, and the full-polarizaion instrumental response of an early HERA antenna design. This paper is organized as follows: in Section~\ref{sec:theory}, we review the relevant mathematical description of polarization in interferometric measurements including ionospheric Faraday rotation, and present a pedagogical picture of its attenuating effect on the measured polarized power. In Section~\ref{sec:numerical}, we discuss our implementation of this formalism which involves modeling of the instrumental response, the diffuse polarized foreground emission on the sky, and calculations using archival data of Faraday rotations based on real ionospheric behavior. Section~\ref{sec:results} presents the results of our simulations and analysis of the effect of ionospheric behavior on HERA observations. We conclude in Section~\ref{sec:conc}. | \label{sec:conc} \begin{enumerate} \item Ionospheric attenuation cannot be counted on to suppress polarization leakage in the power spectrum. Given what little is known about the level of polarized power on the sky in the 100-200 MHz frequency band, even at solar maximum it seems as likely as not that this attenuation might suppress polarization leakage to a negligible level. This increases the importance of precise modeling of this systematic, either to show that it will indeed be small relative to the EoR signal, or for the purpose of subtraction. \item Our simulations suggest a definitive test for polarization leakage in the power spectrum. This test comprises the following: \begin{enumerate} \item \label{SubsetSelection} From the set $S$ of $N_d$ available sidereal days select a collection $\mathfrak{C}$ of subsets $S_k \subset S$ with the number $N < N_d$ of elements in each $S_k$ held fixed. The number $N_d$ must be large enough to allow significant ionospheric variation over $S$. Additionally, the fraction $N/N_d$ must be chosen to strike a balance between allowing the ionospheric attenuation to vary significantly between subsets, while also ensuring that each subset represents sufficient integration time on the thermal noise. \item Compute the power spectra $P_I(S_k)$ and $P_L(S_k)$ for each of the subsets. This produces a distribution of power spectra over $\mathfrak{C}$. \item \label{ISame} If the Vokes-I power spectrum estimator is dominated by Stokes-I on the sky, then the changing ionospheric Faraday rotations between different subsets will have no effect and each subset will produce the same spectrum up to an expected distribution due to the thermal noise. \item \label{LChange} The distribution of $P_L$ should be significantly and obviously inconsistent with the expected thermal noise distribution. \item The null test is passed when both \ref{ISame} and \ref{LChange} are satisfied, as \ref{LChange} demonstrates that the effective polarized power on the sky has an observable variation over $\mathfrak{C}$, while \ref{ISame} shows that there is no corresponding variation of what is supposed to be Stokes-I. \end{enumerate} The method by which the elements of $\mathfrak{C}$ should be chosen remains open to further investigation. We have shown that a simple proxy function for ionospheric attenuation can reliably bias the sampling toward subsets with relatively high or low attenuation factors. Additional consideration could produce an improved method. The sensitivity of this test as a function of the thermal noise level is explored in a schematic way in Appendix \ref{sec:NoiseAppendix}, but detailed consideration should be the subject of further simulations and analysis that can explore in detail the parameter space of cosmological signal level, thermal noise level, and polarized foreground power level. Additionally, the method of quantifying the consistency of these distributions with an expected thermal noise distribution need not be limited to simply computing the variance. For example, we showed that using our simple proxy function to select subsets can often produce distinctly bimodal distributions. The difference in the mean of the high-attenuation collection to the low-attenuation collection could be a useful discriminating statistic. More generally, an advanced subset selection method may go hand-in-hand with a more robust way of distinguishing the resulting distributions from the expected thermal noise. \item The simulations we have used of the polarized sky are intended to be reasonably accurate representations of the expected sky, but their fidelity could certainly be improved. This is necessary for accurate prediction, since we have shown that the level of leakage is sensitively dependent on the correlated structure in the sky model and its alignment with the polarized antenna response, and this does produce large variations in the potential level of leakage. Given this uncertainty, we have purposely avoided considerations of the details of the absolute level of polarization leakage by considering ratios, and demonstrate that these do show systematic trends independent of the details of the sky model. \item Averaging over sidereal days at fixed LST may still be a useful method for suppressing polarized foregrounds even in the situation in which one tries to model and subtract them directly from the visibilities, as the residual (unmodeled) polarization leakage will be attenuated by averaging over many days. This may ease the requirements on the completeness of the polarized model. On the other hand, an increasing level of ionospheric attenuation goes hand-in-hand with increasing complexity of the ionosphere, and thus increasing complexity of the model that must be constructed in order to perform the subtraction. It remains to be seen whether the global model of the ionospheric Faraday rotation which we have presented here would be adequate for such a task. \item The variance in the visibility and resulting power spectrum can be quite large when the polarization angle on the sky is not constrained. While preliminary, the results of our simulations suggest that a statistical foreground model which does not constrain the orientation of the polarization on the sky may be inadequate for predicting polarization leakage levels to the accuracy required for HERA, and possibly other EoR experiments. Determining the extent to which this is true or not through more careful consideration of the parameterization the sky model and the mapping into the visibility will require further research. Obviously, it is necessary to determine the polarization angle accurately to be able to subtract a model from the visibilities. \end{enumerate} | 18 | 8 | 1808.05968 |
1808 | 1808.09188_arXiv.txt | Microlensing of multiply imaged quasars is a unique probe of quasar structure, down to the size of the accretion disc and the central black hole. Flux ratios between close pairs of images of lensed quasars can be used to constrain the accretion disc size and temperature profile. The starting point of any microlensing model is the macromodel of the lens, which provides the convergence and shear values at the location of the multiple images. Here I present a new approach of microlensing modelling independently of the macromodel of the lens. The technique is applied to the close pair of images $A_1$ and $A_2$ of \mg, for a set of flux ratios with large variation with respect to wavelength. The inferred accretion disc size and temperature profile measurements, as well as the smooth matter fraction at the location of the images, are quite robust under a wide range of macromodel variations. A case of using purely microlensing data (flux ratios) to constrain the macromodel is also presented. This is a first application of the technique on a fiducial system and set of flux ratios; the method is readily applicable to collections of such objects and can be extended to light curve and/or imaging data. | \label{sec:intro} Cosmological microlensing observations constitute a unique probe of the structure of lensing galaxies and lensed quasars. Understanding the dark (smooth) and stellar (compact) matter components in galaxy-scale systems is an open issue and has many implications for studying their formation and evolution scenarios \citep[e.g.][]{Conroy2009,Moster2010,Behroozi2010}. To this end, using strong gravitational lenses has been valuable \citep[e.g.][]{Treu2010,Oguri2014,Leier2016}. In the case of the lensed source being a quasar, microlensing can be employed to unveil the structure of the accretion disc and the geometry of the emitting regions in the vicinity of the supermassive black hole \citep[e.g.][]{Dai2010,Morgan2010,Guerras2013,ODowd2015}. This, in turn, can be used to understand the growth of the black hole \citep[e.g.][]{Rosas-Guevara2015,Terrazas2017} and its relation to the quasar host galaxy and its environment via feedback mechanisms \citep[e.g.][]{Bourne2017,Cowley2018}. For any quasar to be microlensed, it has to be first multiply imaged by a foreground lensing galaxy (the `macrolens', or just `lens'). The positions of the images, any extended lensed features of the background quasar host galaxy, and other available data (e.g. time delays or flux ratios between the images) can be used to construct a mass model for the lens \citep[e.g. see][]{Keeton2001a}. Such models describe the total mass of the lens, and provide the convergence, $\kappa$, and shear, $\gamma$, fields. However, the degeneracy between its baryonic and dark matter components remains. To lift this degeneracy, the light profile of the lens can be used to measure the smooth matter fraction, $s$ (equation \ref{eq:smf}), as a function of radius \citep{Oguri2014,FoxleyMarrable2018}. This approach, however, is accompanied by the large uncertainty in the stellar initial mass function, used to convert the light into the mass distribution. The individual values of $\kappa$, $\gamma$, and $s$, at the locations of the multiple images are the primary parameters for setting the microlensing properties. Incoming light rays from the background quasar are further deflected by several stellar-mass microlenses existing within the lens and lying along the line of sight to the quasar images. The presence of such collective deflections creates a network of caustics which can be described by a magnification map \citep{Kayser1986}. The properties of these maps (e.g. the caustic density, orientation, etc) depend mainly on $\kappa$, $\gamma$, and $s$, which set the mass density of the essential grainy (i.e. stellar in this case) mass component. The final result is a microlensing-induced time-dependent magnification on the source, uncorrelated between its observed (macro) images. Analyzing observations using microlensing techniques can provide a measurement for $s$ \citep{Schechter2002}, which can otherwise be only approximated as explained in the previous paragraph. This has been done using microlensing light curve data \citep[e.g.][]{Chartas2009,Dai2010,MacLeod2015} or microlensing flux ratios \citep[e.g.][]{Bate2011,Pooley2012,Jimenez2015a}. Besides $\kappa$, $\gamma$, and $s$, the size of the source with respect to the caustics plays an important role: the smaller the background source, the more prominent the microlensing induced brightness variations will be. It is currently thought that quasar accretion discs are hotter in their innermost regions and cool down further from the central supermassive black hole. The standard thin-disc model \citep[][]{Shakura1973} predicts a power-law dependence of the temperature as a function of radius, with the power-law index fixed to 3/4. This is easily transformed into a size-wavelength relation, making discs appear bigger in long (red) and smaller in short (blue) wavelengths. This wavelength-dependent microlensing effect has been used to constrain quasar accretion discs \citep{Bate2008,Floyd2009,Jimenez2014,Rojas2014,Bate2018}. All microlensing studies so far have employed the `traditional' two-stage modeling approach. Firstly, a lens mass model is fitted to the imaging data and the individual values of $\kappa$, $\gamma$ are extracted for each image. Secondly, a set of microlensing magnification maps is produced as a function of $s$ (or other parameters like the microlens masses, proper motions, etc). A series of flux ratios or light curves are produced from the maps for different accretion disc profiles and compared to the observations (in the case of light curves, the time delay between the macro-images has to be used to correct the data first). The very high computational cost associated with generating magnification maps for different parameters \citep{Bate2012}, and the adequately constrained lens mass models from imaging data justify the choice of using fixed values for $\kappa$, $\gamma$. The possibility of inferring microlensing constraints, and their robustness, on the lens mass model has not been investigated before. Conversely, studies of the effect of lens model variations/uncertainties on accretion disc constraints, or $s$, inferred by microlensing have been very limited \citep[e.g. see][]{Vernardos2014c}. The main reason behind this is the computationally demanding task of producing magnification maps for many different combinations of $\kappa$, $\gamma$, and $s$. The new approach presented in this work assesses the robustness of the derived $s$ and accretion disc constraints with respect to the lens mass model (i.e. the $\kappa$, $\gamma$). The feasibility of using purely microlensing data and methods in providing constraints to the lens mass model is also examined. Any constraints on $\kappa$, $\gamma$ coming from the macromodel (i.e. having them as fixed parameters) are therefore dropped, and they are treated as free parameters instead. Although a computationally more intensive task as a whole, the bulk of the effort, which is computing magnification maps, can be avoided by using the GERLUMPH\footnote{\tt http://gerlumph.swin.edu.au} collection of maps \citep{Vernardos2014a,Vernardos2014b}, whose uniform and extensive coverage of the $\kappa$, $\gamma$, and $s$ parameter space makes it ideal for such an application. The model and its implementation, as well as the choice of a fiducial system to apply it, are described in Section \ref{sec:method}. Results are presented in Section \ref{sec:results}, followed by discussion and conclusions in Section \ref{sec:discuss}. | \label{sec:discuss} Despite the extreme variations in $\kappa$, $\gamma$, leading to dramatically different magnification maps with respect to caustic structure and magnification probability distribution, in all the examined cases the same accretion disc constraints are derived, as shown in the last two rows of Table \ref{tab:means_sdevs} and in Fig. \ref{fig:disc_corner}. This apparent independence of the accretion disc on the macromodel supports the findings of \citet{Bate2018}: the derived accretion disc properties appear to be tightly connected to the observed data, in this case, the large chromatic variations of the flux ratios. The macromodel seems to be playing an insignificant role, at least for \mg~examined here and the given extreme chromatic variation of the flux ratios \citep{Bate2018}. The accretion disc constraints of Table \ref{tab:means_sdevs} are consistent with \citet{Bate2008} for the size and the slope parameters of equation (\ref{eq:profile}), while for the slope the agreement with \citet{Bate2018} is marginal. The main reason for this is that they used maps with a width of $100 R_{\rm Ein}$, much wider than the $25 R_{\rm Ein}$ maps used here, allowing for the inclusion of larger sources ($>16 R_{\rm Ein}$) in calculating the likelihood surface of Fig. \ref{fig:disc_corner}. This and a number of other effects have been identified to influence the derived accretion disc constraints to a smaller or larger extent: the size of the effective map, the value of the baseline ratio, $f_{\rm base}$, and its uncertainty, the number of simulated ratios between maps, and the way these were selected (from pixels on a fixed grid, in random locations, etc). These potential sources of bias will be examined in future work. More than half of the matter at the location of the examined image pair is found to be in the form of a smooth component, regardless of the macromodel. This is not surprising because the multiple images form at the outskirts of the lensing galaxy, where the stellar density is expected to be low. In fact, higher smooth matter fractions can be invoked to explain the observed flux ratio anomaly, usually manifesting itself as a demagnified saddle-point \citep{Schechter2002,Vernardos2014a}. The value of $s$ from \citet{Bate2018} is $0.5^{+0.3}_{-0.3}$ (N. Bate, private communication), consistent with the values of Table \ref{tab:means_sdevs}. \citet{Bate2011} find a value of 0.8 for \mg, \citet{Pooley2012} find a higher value of 0.93, while \citep{Jimenez2015a} find a value of 0.8 by examining a collection of 27 image pairs of lensed quasars. However, the uncertainty on $s$ (Table \ref{tab:means_sdevs}) is quite large in all cases, indicating basically flat distributions. Based purely on the microlensing observations, without using any other kind of data, is there anything to be said about the lens mass model? The inferred values of \kmin,\gmin, and \ksad,\gsad, more often disagree with the macromodel of \citet{MacLeod2013} than agree. Of course, one has to take into account the largely underconstrained nature of the problem: the model has 7 free parameters and the result sets CON6, CON7, and CON8 use 6, 7, and 8 constraints respectively. Therefore, the values and confidence intervals derived for $\kappa,\gamma$ in Table \ref{tab:means_sdevs} should be taken cautiously. In general, for the observed flux ratios in Table \ref{tab:ratios}, and without any information on the macromodel (derived from imaging data), it seems that steeper mass distributions than isothermal are favoured, leading to lower $\kappa$ and higher $\gamma$ values at the location of the close pair of images (see Figs. \ref{fig:min_sad_corner} and \ref{fig:pairs}). It is interesting to investigate the convergence of the solutions of the model as more observational constraints are used. The method introduced in this paper would be straightforward to apply by adding more terms in equation (\ref{eq:chi2}) and assuming the flux ratios from different observational epochs are uncorrelated\footnote{This means that the source will have to move across the sky by a distance corresponding to at least its own size. \citet{Mosquera2011b} calculate a median source crossing timescale of 7.3 months based on a sample of 87 lensed quasars.}. Additionally, the effectiveness of using flux ratios with different (smaller) chromatic variations should be tested. In fact, if each close pair image configuration can be associated with distinct flux ratio properties, then the solutions should converge to the correct $\kappa,\gamma$. This will be investigated in future work using mock data for several systems with different $\kappa,\gamma$ \citep[similarly to what is suggested in][]{Bate2018}. A similar ansatz, i.e. finding the macromodel parameters based on microlensing observables, can be suggested and tested in the case of light curves. The method presented here can be modified accordingly to use light curve data, and the model expanded to include additional parameters such as the velocities of the observer, source, and lens, etc. However, this would require a careful selection of priors on the new parameters and an understanding of their effect in the interpretation of the results. This is another path of exploration spurring from this work. Finally, it is relatively straightforward to combine the analysis presented here with techniques that fit the macromodel to imaging data; it would be a simple addition of flux ratio and image position $\chi^2$ terms. Such an approach would be meaningful if the solutions of the method presented here are indeed shown to converge to useful values of $\kappa,\gamma$, and could be proven valuable in disentangling microlensing effects from the presence of substructure in the lens. Combining this method with imaging data would be easier than with light curves. In this paper, a joint analysis of the lens macromodel and the accretion disc was performed for the first time, driven solely by microlensing flux ratio data. The derived accretion disc constraints were proven to be quite robust under broad variations of the $\kappa,\gamma$ for each image. With the method and machinery presented in this study, one can envisage simultaneous analysis of different kinds of available observations, deriving constraints on the lens mass and accretion disc models of a lensed quasar. The cornerstone for such multi-component modelling approaches is a readily available collection of magnification maps, like GERLUMPH, which removes the need of the huge amount of computations associated with generating them. The future for lensing studies driven by a variety of available observational data modelled in the same framework looks promising. | 18 | 8 | 1808.09188 |
1808 | 1808.09231_arXiv.txt | Binary stars are of course more than two stars, but they are also at least two stars. In this chapter we will review some aspects of the physics governing the evolution of single massive stars. We will also review the uncertainties of key physical ingredients: mass loss, rotation and convection. | \label{Georgy_basics} Massive stars\index{massive star} are stars more massive than about $8-10\,M_\odot$, that are bound to die in the explosion of a supernova or collapsing directly into a black hole \citep{Heger2003b,Jones2013a}. Their life is marked by the succession of all burning stages up to silicon burning. The modelling\index{modelling} of massive stars is done by the mean of one-dimension (1d) stellar evolution codes (see below), which solve the four equations of stellar structure \citep[see][for a classical textbook]{Kippenhahn1990a}, coupled with a network of nuclear reactions providing the energy generation rate inside the stellar model, and the time evolution of the chemical content of the star. On top of that, various effects can be accounted for, such as rotation\index{rotation} or mass loss\index{mass loss}, particularly important in the context of the evolution of massive stars. An important aspect of massive star evolution that became prominent during the past decade is that a significant fraction of massive stars are found in multiple systems. Large surveys in different environments suggest that $50\%$ to $70\%$ of all massive stars \citep{Sana2012a,Sana2013a} are in binary (or multiple) systems where components are sufficiently close to interact at least once during their lifetime. Evolution of massive stars in multiple systems can be very different from single star evolution \citep[][among others]{vandenHeuvel1975a,Vanbeveren1991a,Podsiadlowski1992a,Vanbeveren1998a,Eldridge2008a,deMink2013a}. Taking multiplicity into account is thus extremely important when dealing with massive star populations. It is however important to keep in mind that it is utopian to model correctly multiple stellar systems without being able to accurately describe the evolution of a single star. In this chapter, we discuss uncertainties of key physical processes taking place in single star models and their consequences. These shortcomings should be kept in mind by anybody using results from stellar evolution computations or from population synthesis. | \label{Georgy_conclu} In this chapter, we have discussed some of the uncertainties inherent to the modelling of single massive stars. In the first section, we have shown how the inclusion of various mass-loss rates prescription can affect the evolution of massive stars. In particular, the mass loss during the red supergiant phase, which is still largely unknown, plays a key role for the subsequent evolution of the star and its final location in the Hertzsprung-Russell diagram. Another key ingredient of stellar modelling is the treatment of convection. Here again, the difficulties of a correct treatment in classical 1d stellar evolution codes are a source of major shortcomings in our understanding of massive star life. The hopes for a better understanding and an improved modelling of convection come nowadays from multi-dimensional hydrodynamics simulations. Finally, the implementation of rotation, which is suspected to play an important role as a mixing process inside massive stars, also suffers from uncertainties. The various possible ways of implementing rotation in stellar evolution codes make the prediction of simulations largely uncertain. All of the uncertainties discussed above, related to single star evolution, also appear in the modelling of multiple systems, and they should be kept in mind when considering the results of any simulations involving stars. \copyrightline{This material has been published in \textit{The Impact of Binaries on Stellar Evolution}, Beccari G. \& Boffin H.M.J. (Eds.). This version is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. \copyright\ 2018 Cambridge University Press.} | 18 | 8 | 1808.09231 |
1808 | 1808.05703_arXiv.txt | The observation of the shadows cast by the event horizon of black holes on the light emitted in its neighborhood is the target of current very-long-baseline-interferometric observations. When considering supermassive black holes, the light source is the black hole's accretion disk, and therefore, the observation of the shadow may reveal information about the black hole and the accretion flow. We here study the shadows cast by stellar-mass black holes that are illuminated not by an accretion disk but by a stellar companion in a wide binary orbit. We calculate the shadows produced in such a configuration for the first time and show snapshots of the time-dependent shadow ``movie'' that is generated. We also study the minimal criteria for detecting and resolving such shadows with very-long-baseline-interferometric observations. We find that one would need telescopes capable of resolving apparent magnitudes greater than $33$ with baselines larger than $10^{6}$ km. Therefore, although very-long-baseline-interferometric efforts such as the Event Horizon Telescope would not be able to detect these shadows, their detection is possible with future telescopes in the next few decades. | In April 2017, the Event Horizon Telescope~\cite{2009astro2010S..68D} (EHT) collaboration undertook a week long observing campaign of Sagittarius A*, the supermassive black hole (BH) at the center of our Milky Way Galaxy. EHT, through the use of very long baseline interferometry techniques (VLBI), joins together telescopes around the world into a telescope that is effectively as large as the Earth. Thus, this literally world-wide telescope has an unprecedented observing resolution of about 20 $\mu$as, allowing it to resolve features on the scale of an orange on the Moon as seen from Earth. For EHT and similar projects such as BlackHoleCam~\cite{Goddi:2017pfy} and GRAVITY~\cite{2008SPIE.7013E..2AE}, the goal is to resolve features near to and on the scale of the event horizon of Sagittarius A* and other supermassive BHs. An observation of particular interest to EHT and similar projects is what is known as the BH shadow, a dark region that exists on any observation of a BH caused by photons falling into the BH event horizon. Unlike any other object in the universe, photon orbits exist around a BH. But these orbits are unstable and demarcate the boundary between photons that will escape the gravitational well of the BH and those that will be forever lost inside the event horizon. This boundary, the conglomeration of all the spherical unstable photon orbits, is known as the photon sphere and when observed far from the BH it is the boundary between the light and dark regions of the BH shadow image. The shape of the boundary depends on the properties of the BH and thus the shadow observation can be used to determine these properties. Currently, only supermassive BHs are the targets of BH shadow observation campaigns. The radius of the photon sphere is on the order of 1 km for a BH the mass of the Sun and scales linearly with mass; thus, it is easy to see why supermassive BHs, with shadows on the order of $10^{6}$ km in radius, are the only current targets. Attempting to image the shadows of stellar-mass BHs, which have masses on the order of 10 $M_{\odot}$, and are typically found at distances of thousands of parsecs from Earth is impossible with current observational capabilities. Even so, with advances in technology and the construction of new telescopes, it may be possible in the coming future to achieve observations of shadows of stellar-mass BHs. Generally, when discussing electromagnetic observations of BHs the primary source of the electromagnetic radiation near the BH is an accretion disk, i.e.~a disk of gas orbiting the BH. In the case of stellar-mass BHs, these disks form when gas from a companion star is pulled into an orbit around the BH. This most commonly occurs when the star overflows its Roche lobe, i.e.~the region within which the star's gravitational pull dominates. In more massive stars that are more widely separated, a disk can also form if the stellar wind of the star is large enough to send a significant amount of gas towards the BH. When the orbital separation is large enough and the stellar wind of the companion star is relatively small, an accretion disk will not form or will be scarce enough that the electromagnetic radiation of the companion star will dominate the spectrum. In this case, the primary source of illumination for the BH shadow observation will be the stellar companion, a scenario that has not been studied to date. In this paper, we perform the first calculations of BH shadows produced by stellar-mass BHs in binary systems in which the companion star is the primary source of electromagnetic radiation. We calculate these shadows as follows: we employ a general relativistic ray-tracing code to solve for the trajectories of photons near a Kerr BH, and sub-select those that would have originated from a companion star, as a function of the physical properties of the binary. The end result are images of the BH shadow at different points in the orbit, which can, in principle, be combined to create a BH shadow movie. We find that the shadows are quite complex and can provide a wealth of information about the BH, the companion star, and the system as a whole, provided they are detected and a proper model is used to filter the data. This paper is, in some sense, related to work done by Cunningham and Bardeen in 1973~\cite{1973ApJ...183..237C, Dokuchaev:2018fze}. In this previous work, the system modeled was that of a star in a very close (at most 10 gravitational radii) circular orbit around a supermassive extremal Kerr BH. The main results were the analytic calculation of the apparent position and energy flux of the star in different locations in its orbit. To perform these calculations the star was treated as a point source of electromagnetic radiation, although the leading order effects of an extended source were taken into account. Recently, Cunningham's and Bardeen's work was corrected and redone using the physical properties of Sagittarius A*~\cite{Dokuchaev:2018fze}, and the leading order effects on the image of the star were calculated and made into images and a movie. Our work also deals with the calculation of the image of a star orbiting a BH, but there are significant differences in the systems being studied and the method of calculation. We here focus on a binary system composed of a BH and a star, so the separation between the two bodies is several orders of magnitude larger than in previous work and the masses are within an order of magnitude. Our method for calculating the images is to solve the photon equations of motion numerically rather than using an analytic method. While our method introduces some numerical error, it is an exact calculation in the sense that we do not truncate the equations at a finite order. Due to these differences, our work and results are not directly comparable to the work of Cunningham and Bardeen~\cite{1973ApJ...183..237C, Dokuchaev:2018fze}. In addition to calculating these shadows, we also discuss the feasibility of observing them with future instruments. Using some simplifying assumptions, we make rough estimates of the apparent magnitude and angular size of the shadow. We then evaluate these magnitudes for the three nearest BH-stellar binary systems~\cite{1986ApJ...308..110M, 2010ApJ...710.1127C, Ziolkowski:2005ag, 2011ApJ...742...84O, Parker:2015fja, 1994MNRAS.271L..10S, 1994MNRAS.271L...5C, Bernardini:2016mub} and the only non-interacting BH-stellar binary candidate~\cite{Thompson:2018ycv} and compare them to the capabilities of current telescopes. As expected, we find that current telescopes cannot detect or resolve the BH shadows of stellar-mass BHs, but we argue that given what is currently possible and what is planned for the very near future, it is not unreasonable to think that imaging these shadows will be possible in the next few decades. Such observations will require a VLBI telescope that is at least a few orders of magnitude more sensitive than the proposed Large UV/Optical/Infrared Surveyor~\cite{LUVOIR} (LUVOIR) and is placed at least $\sim10^{7}$ km from Earth. We suggest that the Lagrange points $L_{4}$ and $L_{5}$, located $\sim10^{8}$ km from Earth, would be ideal for such a new telescope to carry out these BH-stellar shadow observations. As the telescope requirements for observing the shadow of a BH-stellar binary will not be fulfilled for at least several decades, we perform a secondary study of the light curves produced by these shadows. To observe the light curves, a VLBI is no longer required and many of the other requirements are relaxed, making such an observation more feasible in the near future. We calculate the light curves by integrating the photons from each image generated by the general relativistic ray-tracing code at many points along the binary's orbit. The number of photons is then normalized and plotted as a function of the position in the orbit, providing a light curve of the shadow. Such light curves could be extracted from observations of BH-stellar binary systems and could be used to determine the properties of the BH and the system as a whole. The remainder of this paper presents the details pertaining to these results. Section~\ref{sec:Kerr} presents the Kerr BH and properties that are relevant to the BH shadow observation. Section~\ref{sec:shadow} discusses the BH shadow, ideally and as it may be seen in nature. Section~\ref{sec:algo} details the algorithm and setup we use to calculate the shadow of a BH-stellar system. Section~\ref{sec:res} presents the BH shadow images produced for four configurations of interest. Section~\ref{sec:feas} discusses the feasibility of observing a BH-stellar binary system shadow and estimates the observing capabilities required. Section~\ref{sec:curves} presents an alternative observation using the light curve of the system and the variations due to the shadow. Section~\ref{sec:conc} concludes by summarizing our results and discussing the implications. Throughout this paper, we use the following conventions: the metric signature is $(-,+,+,+)$; Latin letters in index lists stand for spacetime indices; we use geometric units with $G=1=c$ (e.g.~$1 M_\odot$ becomes 1.477 km by multiplying by $G/c^2$ or $4.93\times10^{-6}$ s by multiplying by $G/c^3$), except where otherwise noted. | \label{sec:conc} We have performed the first study of BH shadows produced by BH-star binary systems, where the companion star is the primary source of electromagnetic radiation. We produced images of what the BH shadows would look like to some future VLBI telescope with four configurations, one of which is similar to the Cygnus X-1 system and another to the A0620-00 system. We argue that due to the complexity of the shadows and their predictable time-dependence, their observations could be used to estimate the parameters of the BH, the star, and the system as a whole. We estimated the apparent magnitude and angular size of three of the nearest BH-star binary systems~\cite{1986ApJ...308..110M, 2010ApJ...710.1127C, Ziolkowski:2005ag, 2011ApJ...742...84O, Parker:2015fja, 1994MNRAS.271L..10S, 1994MNRAS.271L...5C, Bernardini:2016mub} and the only non-interacting BH-star binary candidate~\cite{Thompson:2018ycv} and compared those quantities to the capabilities of current and upcoming telescopes. We argued that given current and upcoming capabilities it is not unreasonable to think that observing the BH shadows of BH-star binary systems will be possible within the next century, if not sooner. We also calculated the light curves of BH shadows as a more feasible alternative to imaging and resolving the shadows themselves. We found that, even though light curves are a simpler observation, they could still be used to estimate parameters of the BH, the star, and the system. Since to our knowledge this is the first study of its kind, our analysis of BH shadows has been qualitative, but much more work could be done to explore their scientific case more thoroughly for a wider range of configurations. In particular, our claim that observations of these shadows could be used to estimate parameters of the system could be studied more carefully with an actual data analysis investigation. Perhaps shadow observations of such systems would be well suited for tests of GR, seeing as the shadows of supermassive BHs are already a prime target for such studies~\cite{Psaltis:2014mca, Vincent:2016sjq, 2017RvMP...89b5001B}. In producing our shadow images we made a number of simplifying assumptions that could also be relaxed in future work. One such simplification is our treatment of the star as a source of electromagnetic radiation. Through our algorithm the star is effectively a two-dimensional, monochromatic, and isotropically emitting source. A more realistic model of emission could be implemented as well as a ray-tracing algorithm that actually traces rays to the star's surface. The simplification of using monochromatic light also extends to the final images we produced and the calculations for determining the feasibility of these shadow observations. In our calculations, we work with the bolometric luminosity, but stars do not emit at a single wavelength and telescopes have a limited range of observable wavelengths. Extending the ray-tracing code and feasibility calculations to include the effects of non-monochromatic light and non-ideal telescopes would provide more realistic images and capability requirements for observing the shadows of BH-star binary systems. \ack NY, DA, and HG acknowledge support from the NSF CAREER grant PHY-1250636. NY and HG also acknowledge support from NASA grants NNX16AB98G and 80NSSC17M0041. DA also acknowledges support from the National Natural Science Foundation of China (NSFC), Grant No. U1531117, and Fudan University, Grant No. IDH1512060. We would also like to acknowledge the support of the Research Group at Montana State University through their High Performance Computer Cluster \emph{Hyalite}. | 18 | 8 | 1808.05703 |
1808 | 1808.08237_arXiv.txt | {The quantum effective action for the electromagnetic field in an expanding universe has an anomalous dependence on the scale factor of the metric arising from virtual charged particles in the loops. It has been argued that this Weyl anomaly of quantum electrodynamics sources cosmological magnetic fields in the early universe. We examine this long-standing claim by using the effective action beyond the weak gravitational field limit which has recently been determined. We introduce a general criteria for assessing the quantumness of field fluctuations, and show that the Weyl anomaly is not able to convert vacuum fluctuations of the gauge field into classical fluctuations. We conclude that there is \textit{no} production of coherent magnetic fields in the universe from the Weyl anomaly of quantum electrodynamics, irrespective of the number of massless charged particles in the theory.} \begin{document} | Cosmic inflation freezes the quantum fluctuations of the inflaton field into classical fluctuations which source the large-scale structures in the universe. While such a processing of field fluctuations happens generically both for nearly massless scalars and gravitons, the situation is different for gauge fields. This is a simple consequence of the classical Weyl invariance of the Yang-Mills action. The dynamics of a gauge field governed by a Weyl invariant action in a Friedmann-Robertson-Walker spacetime is independent of the scale factor, and hence naively unaffected by the expansion of the universe. However, the classical Weyl invariance of the Yang-Mills action is violated in the quantum theory because of the need to regularize the path integral. These Weyl anomalies, or equivalently the nontrivial beta functions of the theory, imply that the quantum effective action obtained after integrating out massless charged particles is no longer Weyl invariant. This is expected to lead to an anomalous dependence on the scale factor under a fairly mild assumption that the masses of the charged particles that contribute to the quantum loops are negligible compared to the Hubble scale during the cosmological era of interest. For the Maxwell theory, the violation of Weyl invariance can lead to gauge field excitations in the early universe, and thus to the generation of electromagnetic fields. In our universe, magnetic fields are observed on various scales such as in galaxies and galaxy clusters. Recent gamma ray observations suggest the presence of magnetic fields even in intergalactic voids. In order to explain the origin of the magnetic fields, theories of primordial magnetogenesis have been studied in the literature, where most models violate the Weyl invariance explicitly at the classical level by coupling the gauge field to some degrees of freedom beyond the Standard Model of particle physics~\cite{Turner:1987bw, Ratra:1991bn}. See e.g. \cite{Kronberg:1993vk, Grasso:2000wj, Widrow:2002ud, Barrow:2006ch, Kulsrud:2007an,Ryu:2011hu,Durrer:2013pga, Subramanian:2015lua} for reviews on magnetic fields in the universe from different perspectives. It was pointed out in~\cite{Dolgov:1993vg} that the Weyl anomaly of quantum electrodynamics itself should also induce magnetic field generation. If true, this would be a natural realization of primordial magnetogenesis within the Standard Model. Moreover, since the anomaly is intrinsic to the Standard Model, its contribution to the magnetic fields, if any, is irreducible. Hence it is important to evaluate this also for the purpose of identifying the minimum seed magnetic fields of our universe. Since~\cite{Dolgov:1993vg}, there have indeed been many studies on this topic. However, there is currently little consensus on the effect of the Weyl anomaly on magnetic field generation. One of the main difficulties in proceeding with these computations is that the quantum effective action in curved spacetime is in general very hard to evaluate. In principle, it is a well-posed problem in perturbation theory. One can regularize the path integral covariantly using dimensional regularization or short proper-time regularization and evaluate the effective action using the background field method. However, explicit evaluation of the path integral for a generic metric is not feasible. For instance, to obtain the one-loop effective action it is necessary to compute the heat kernel of a Laplace-like operator in an arbitrary background, which amounts to solving the Schr\"odinger problem for an arbitrary potential. One could evaluate the effective action perturbatively in the weak field limit using covariant nonlocal expansion of the heat kernel developed by Barvinsky, Vilkovisky, and collaborators \cite{Barvinsky:1984jd,Barvinsky:1985an}. The effective action in this expansion has been worked out to third order in curvatures \cite{Barvinsky:1988ds,Barvinsky:1994hw,Barvinsky:1994cg,Barvinsky:1995it}. Similar results have been obtained independently by Donoghue and El-Menoufi \cite{Donoghue:2015xla,Donoghue:2015nba} using Feynman diagrams. Some of the earlier works on primordial magnetogenesis from anomalies, e.g.~\cite{El-Menoufi:2015ztk}, relies on the effective action derived in this weak field approximation. The weak field expansion is valid in the regime $\cR^{2} \ll \nabla^{2} \cR $, where $\cR$ denotes a \textit{generalized} curvature including both a typical geometric curvature $R$ as well as a typical gauge field strength $F$. During slow-roll inflation, one is in the regime of slowly varying geometric curvatures, $R^{2} \gg \nabla^{2} R$, whereas during matter domination, one has $R^{2} \sim \nabla^{2} R$. Thus, during much of the cosmological evolution, the curvatures are not weak compared to their derivatives. Therefore, to study primordial magnetogenesis reliably over a long range of cosmological evolution, it is essential to overcome the limitations of the weak field approximation. It was shown recently in \cite{Bautista:2017enk}, that one can go beyond the weak field approximation for Weyl flat spacetimes. In this case, one can exploit Weyl anomalies and the symmetries of the background metric to completely determine the dependence of the effective action on the scale factor at one-loop even when the changes in the scale factor are large. The main advantage of this approach is that Weyl anomalous dimensions of local operators can be computed reliably using \textit{local} computations such as the Schwinger-DeWitt expansion \textit{without} requiring the weak field approximation $\cR^{2} \ll \nabla^{2} \cR $. The resulting action obtained by integrating the anomaly is necessarily nonlocal and essentially resums the Barvinsky-Vilkovisky expansion to all orders in curvatures albeit for the restricted class of Weyl-flat metrics. A practical advantage is that one can extract the essential physics with relative ease using only the local Schwinger-DeWitt expansion which is computationally much simpler. In this paper we use the quantum effective action of \cite{Bautista:2017enk} beyond the weak field limit, and present the first consistent computation of the effect of the Weyl anomaly on cosmological magnetic field generation. We study $U(1)$~gauge fields originating as vacuum fluctuations in the inflationary universe, and analyze their evolution during the inflation and post-inflation epochs. Our main conclusion is that there is {\it no} production of coherent magnetic fields from the Weyl anomaly of quantum electrodynamics, contrary to the claims of previous works. Our results hold independently of the details of the cosmological history, or of the number of massless charged particles in the theory. We show, in particular, that even if there were extra charged particles in addition to those of the Standard Model, the Weyl anomaly with an increased beta function still would not produce any magnetic fields. Since the time-dependence introduced by the Weyl anomaly is unusually weak, the analysis of the (non)generation of magnetic fields requires careful consideration of the nature of the field fluctuations, in particular whether they are classical or quantum. For this purpose, we introduce general criteria for assessing the quantumness of field fluctuations. Using these criteria, we find that the quantum fluctuations of the gauge field actually do {\it not} get converted into classical fluctuations. The paper is organized as follows. In $\S\ref{Action}$ we review the derivation \cite{Bautista:2017enk} of the one-loop quantum effective action for a Weyl-flat metric. In $\S\ref{sec:quant}$ we canonically quantize the gauge fields using this action and introduce the criteria for quantumness. In $\S\ref{sec:cosmo}$ we analyze the evolution of the gauge field in the early universe and show that there is no production of coherent magnetic fields. In $\S\ref{Discussion}$ we comment on the relation of our work to earlier works and conclude with a discussion of possible extensions. | } We have analyzed cosmological excitation of magnetic fields due to the Weyl anomaly of quantum electrodynamics. Despite the anomalous dependence of the quantum effective action on the scale factor of the metric, we showed that the vacuum fluctuations of the gauge field do not get converted into classical fluctuations, as long as inflation happens at scales below the Landau pole. In particular, the number of photons with a comoving momentum~$k$ produced within a comoving volume~$k^{-3}$ was found to be at most of order unity, for generic~$k$. With such a small number of created photons, we conclude that the Weyl anomaly does not give rise to coherent magnetic fields in the universe. Our conclusion is independent of the details of the cosmological history, or the number of massless charged particles in the theory. For obtaining this result, which disproves the claims of many previous works, there were two key ingredients. The first was the quantum effective action beyond the weak gravitational field limit. We saw that, especially for cases where the beta function of quantum electrodynamics was large in the early universe, one could draw dramatically incorrect conclusions from inappropriate assumptions about the effective action. The essential point is that the anomalous dependence of the effective action on the metric is associated to the renormalization group flow of the gauge coupling, and therefore the dependence is only logarithmic in the scale factor, cf.~(\ref{action2}) and (\ref{Delta}); this is in contrast with the case of massless scalar fields having power-law dependences on the scale factor at the classical level. The second element was a proper evaluation of the nature of the gauge field fluctuations, which we discussed quantitatively in terms of the photon number~(\ref{beta-amp}) and the quantumness parameter~(\ref{kappa}). Focusing on these quantities, we explicitly showed that the logarithmic dependence on the background metric induced by the Weyl anomaly does not lead to any generation of coherent classical magnetic fields. We now briefly comment on some of the earlier works on Weyl anomaly-driven magnetogenesis. The original works~\cite{Dolgov:1981nw,Dolgov:1993vg} approximated the effect from the Weyl anomaly as a power-law~$I^2$ for a generic beta function, and thus arrived at the incorrect conclusion that a large beta function gives rise to observably large magnetic fields. On the other hand, the recent work~\cite{El-Menoufi:2015ztk} relies on the effective action derived in the weak gravitational field limit. The Weyl factor in an inflationary background is computed using the curvature expansion of~(\ref{Omegaweak}), which yields $\Omega \sim (2/3) \log a$ in the asymptotic future, instead of the exact answer of $\log a$. At any rate, a logarithmic~$I^2$ is obtained with a form similar to~(\ref{I2}) up to numerical coefficients. However, the fact that a logarithmic~$I^2$ cannot produce enough photons to support coherent magnetic fields was overlooked. Our considerations can also be applied to quantum chromodynamics. The effective action is analogous to \eqref{ouraction} with $\tilde{\beta}$ given by the beta function of quantum chromodynamics coupled to massless quarks. One main difference from electrodynamics is that the beta function is negative, yielding asymptotic freedom; hence the theory goes into the strongly coupled regime in the late universe. The time evolution of the mode function can further be altered by the nonlinearities of the Yang-Mills action. Here, since the dependence of the effective action on the scale factor is anyway logarithmic, it may turn out that color magnetic fields are also not generated by the Weyl anomaly; however, it would be worthwhile to analyze systematically the range of possibilities that can arise for $SU(N)$ Yang-Mills fields. With such analyses, one should also be able to evaluate the effect of the possible mixing of the $SU(2)$ gauge field fluctuations into the photons upon the electroweak phase transition, which we did not consider in this paper. The study of the effects of the Weyl anomaly in the strongly coupled regime, for instance electrodynamics with inflation scales higher than the Landau pole (thus with a very large beta function), or chromodynamics near the confinement transition is very interesting but would require nonperturbative methods. Even though the Weyl anomaly does not generate coherent magnetic fields in the universe, it can produce a small number of photons in the squeezed state. The squeezed light from the Weyl anomaly may have interesting consequences for astrophysical observations~\cite{Grishchuk:1990bj,Allen:1999xw}. Our criteria for quantumness could also be useful for studying field excitations in other processes with weak time dependence. | 18 | 8 | 1808.08237 |
1808 | 1808.01120_arXiv.txt | Gravity-induced non-Gaussianity in the large-scale structure of the Universe, characterised by higher-order statistics such as the bispectrum (three-point cumulant), is expected to contain rich cosmological information. A measurement of the bispectrum will not only improve the cosmological constraints, but also give us the possibility to probe gravity on cosmological scales. In this paper, we present a framework to numerically calculate the one-loop matter bispectrum based on standard perturbation theory (SPT). This approach allows general modifications to the standard $\Lambda$CDM model to be easily implemented. We demonstrate the performance of the bispectrum calculation in three representative cases, namely the Vainshtein-screened Dvali-Gabadadze-Porrati (DGP) model, the chameleon-screened Hu-Sawicki $f(R)$ model and the phenomenological dark scattering (DS) momentum-exchange model. The predicted bispectra are then compared with measured results from a set of cosmological $N$-body simulations, and the impact of possible systematics arising from simplified or approximate treatments in the perturbative calculation is studied in detail. We find that the one-loop bispectrum calculation offers significantly more information on general screening and momentum exchange effects than the leading-order bispectrum calculation. Further, the accuracy of the one-loop prediction is shown to be comparable to non-linear fitting formulas over a wide range of wavenumbers ($k\lesssim0.3\,h$$\mbox{Mpc}^{-1}$) even at lower redshifts, $z\lesssim 1$. | \label{sec:intro} The concordance model of cosmology, i.e. general relativity (GR) with constant dark energy ($\Lambda$) and cold dark matter (CDM) components, is now widely accepted as the most successful cosmological model. Indeed, with only $6$ parameters the model consistently describes both cosmic expansion and structure formation and accommodates not only the high-precision data set of the cosmic microwave background (CMB) \cite{Planck:2015xua} but also various measurements made of the late-time universe such as cluster counts \cite{Hamana:2015bwa}, baryon acoustic oscillations (BAO) \cite{Anderson:2013zyy} and supernovae data \cite{Lampeitl:2009jq}. However despite its great success our understanding of the Universe is still limited. The concordance model implies that the Universe's geometry is close to flat and that it is filled with the hypothetical CDM, together with a small fraction of baryons. Moreover, the $\Lambda$CDM model assumes an unknown energy component called dark energy which is the underlying cause of the observed late time acceleration of the Universe \cite{Riess:1998cb,Perlmutter:1998np}. The dark energy may be explained by the non-zero cosmological constant $\Lambda$, but its smallness leads to the biggest fine-tuning problem in fundamental physics \cite{Weinberg:1988cp,Martin:2012bt}. Further, several tensions in cosmological parameters between local/low-$z$ measurements and CMB data have been recently advocated, specifically with respect to the present-day Hubble constant $H_0$ \cite{Efstathiou:2013via,Zhang:2017aqn,Riess:2009pu} and amplitude of density fluctuations $\sigma_8$ \cite{Abbott:2017wau,Beutler:2016arn} (see \cite{Lin:2017bhs} for a review). These problems may suggest that the underlying assumption of GR in the $\Lambda$CDM model is wrong and gravity is modified at cosmological scales (see \cite{Koyama:2015vza} for a review). Also, as an alternative scenario, the cosmological constant may be replaced with a dynamical dark energy with potential interactions with the dark matter sector (see \cite{Yoo:2012ug} for a review). Modified gravity (MG) has been often invoked in order to explain the accelerated expansion, introducing extra degrees of freedom. Most of MG models involve a scalar field which generally results in additional forces and hence modifies the gravitational force predicted by GR. A crucial point is that in order for such models to be viable, so-called screening mechanisms, by which the theory recovers GR at small scales, need to be self-consistently implemented. Hu-Sawicki $f(R)$ gravity \cite{Hu:2007nk} and Dvali-Gabadadze-Porrati (DGP) \cite{Dvali:2000hr} models are prototypical examples having such mechanisms. Recently, larger classes of healthy models has been uncovered, referred to as the Horndeski class \cite{Horndeski:1974wa}, beyond Horndeski \cite{Gleyzes:2014dya} and extended scalar-tensor theories \cite{Crisostomi:2016czh}. On the other hand, if we choose to accept the idea of dark energy instead of MG, there is no reason to stop us from considering departures from a pure cosmological constant. Such modifications are again described by introducing free parameters, and one simple example is the equation-of-state parameter which changes the cosmic expansion at late times. One may also consider the interaction within the dark sector, and introduce energy or momentum exchange between dark matter and dark energy in a parametric form \cite{Simpson:2010vh,Lesgourgues:2015wza,Pourtsidou:2016ico,Baldi:2016zom,Buen-Abad:2017gxg}. These theories must retain all the observational successes of the $\Lambda$CDM model. A particularly interesting alternative to the cosmological constant may be the case of momentum exchange between dark energy and dark matter which has a general formulation at the Lagrangian level \cite{Pourtsidou:2013nha}. This has been shown to explain the CMB as well as to weaken the tensions in the $\sigma_8$ parameter \cite{Pourtsidou:2016ico}. There are thus various possible alternatives to $\Lambda$CDM which should be tested against future precision observations, especially at cosmological scales. In this respect, galaxy redshift surveys and weak lensing experiments offer nearly ideal testing grounds, and with future stage-IV class surveys such as EUCLID \footnote{\url{www.euclid-ec.org}} \cite{Laureijs:2011gra}, WFIRST \footnote{\url{https://wfirst.gsfc.nasa.gov/}} \cite{Spergel:2013tha}, DESI\footnote{\url{http://desi.lbl.gov/}} \cite{Aghamousa:2016zmz} and LSST\footnote{\url{https://www.lsst.org/}} \cite{Chang:2013xja}, we will be able to falsify or detect any deviation from $\Lambda$CDM at an unprecedented level. To make the best use of the statistical precision data, theoretical descriptions of the large-scale structure must be improved, accounting for any observational systematics including non-linear gravitational evolution. This is indeed essential to extract vital and non-degenerate information about the gravitational potential \cite{Baker:2014zba} and is the subject of active research \cite{Baumann:2010tm,Perko:2016puo,Lewandowski:2016yce,Schneider:2010gv,Heitmann:2006hr,Hashimoto:2017klo,Schmittfull:2016yqx}. If we are to move toward unbiased and improved tests of gravity and dark energy, future high-precision data not only requires us to carefully quantify the accuracy of theoretical templates \cite{Bose:2018orj,Bose:2017myh,Barreira:2016ovx,Taruya:2010mx,Taruya:2016jdt,Lewandowski:2017kes}, but also prompts us to use higher-order statistics such as the bispectrum or the three-point correlation function as informative cosmological signals, which will be measured at high-statistical significance. On top of the traditional method using two-point statistics, adding a bispectrum measurement is expected to improve the constraints on gravity and cosmology \cite{Child:2018klv,Byun:2017fkz,Song:2015gca}. Also in \cite{An:2017kqu} the authors show that weak lensing tomography is very sensitive to energy exchange in the dark sector and that the bispectrum can provide tighter constraints over the conventional convergence power spectrum. Further, \cite{Namikawa:2018erh} shows that the CMB lensing bispectrum can be used to get clean constraints on general MG theories. Note, however, that while there have been numerous works on modeling the bispectrum in alternative theories of gravity \cite{Hirano:2018uar,GilMarin:2011xq,Yamauchi:2017ibz,Bellini:2015wfa,An:2017kqu,Dinda:2018eyt}, most of the analytic works are restricted to a leading-order calculation only valid at very large scales. On the issue of moving to the non-linear small scales, numerical simulations are still a computationally expensive and impractical approach in the context of survey data analyses. In this paper, we try to fill the gap between the leading-order analytic calculation and fully non-linear simulations by employing the next-to-leading order perturbative calculation in alternatives to $\Lambda$CDM. To be precise, employing the numerical algorithm described in \cite{Taruya:2016jdt}, we extend the power spectrum code presented in \cite{Bose:2016qun} to compute the matter bispectrum at one-loop order. Based on the newly developed code, we demonstrate the one-loop predictions of the bispectrum in three representative models: Vainshtein screened DGP \cite{Dvali:2000hr} model, the Hu-Sawicki $f(R)$ chameleon screened model \cite{Hu:2007nk} and the dark scattering (DS) momentum exchange model \cite{Simpson:2010vh,Baldi:2016zom}. The present code can be easily extended to a wide class of alternative models, for example the Horndeski class of MG theories with a generalised potential \cite{Bose:2016qun} or general dark energy models. We also highlight the power of the bispectrum for distinguishing between alternatives and $\Lambda$CDM. In particular we investigate the signal of one-loop contributions from screening or interaction effects. Further, we will compare the one-loop computation with another promising non-linear prescription for the matter bispectrum in order to identify optimal theoretical frameworks for next generation analyses pipelines. This paper is organised as follows: Sec.II presents the generalised evolution equations for the density perturbations and the expressions for the one-loop statistics. We describe modifications coming from three representative non-standard models, namely DGP, $f(R)$ and the DS model. Further, we highlight the numerical treatment of the perturbations used in this work. In Sec.III we test the perturbative predictions against sets of numerical simulations. We also compare our numerical PT approach against common approximations and other non-linear prescriptions for the bispectrum. In Sec IV we investigate the non-linear signal of MG's dependence on bispectrum shape and redshift. Finally, Sec.V gives a summary of the results and discusses future work. | In this paper we have presented an extension of Ref.~\cite{Bose:2016qun} to three-point statistics, specifically a tool to numerically calculate the standard perturbation theory (PT) prediction for the one-loop matter bispectrum. We considered four representative models, namely $\Lambda$CDM, nDGP, $f(R)$ and the phenomenological dark scattering momentum exchange model. In the latter case we consider the phantom model with equation of state parameter of dark energy $w=-1.1$. We have validated the code for standard PT (SPT) calculations against a set of N-body simulations. In the $\Lambda$CDM and nDGP cases, these numerical PT results are also compared with analytic PT predictions involving approximations and/or simplifications as well as fitting formulas. Our results are consistent with those previously obtained in $\Lambda$CDM for one-loop bispectra (e.g. \cite{Hashimoto:2017klo}) and for one-loop power spectra (e.g. \cite{Bose:2018orj,Fasiello:2016qpn}). \newline \newline Our important findings for one-loop bispectra are summarized as follows: \begin{itemize} \item Including one-loop contributions offers a large gain in accuracy over the leading-order (tree-level) predictions in all models considered. The accuracy of one-loop bispectra is comparable to the fitting formulas at higher redshift ($z\gtrsim0.5$) in the quasi linear regime ($k \lesssim 0.15$ - $0.25\,h$\,Mpc$^{-1}$) and the one-loop SPT bispectrum prediction reproduces well the simulations at a relatively wider range than that of the power spectrum. \item Analytic PT treatment involving approximations/simplifications generally produces a percent level deviation from the numerical PT approach. While the Einstein-de Sitter approximation just gives a sub-percent error and hence can be safely applied, the omission of screening effects at higher-order can produce an error that reaches the percent level, which may be of concern to upcoming surveys, although the actual impact would depend on survey errors and other nuisance parameters. \item Characteristic shape dependence seen in modified gravity models, which appears at tree-level order, tends to be erased as we move to lower redshift in the one-loop SPT prediction. For instance, in nDGP, taken as a representative model of the Horndeski class, the tree-level bispectrum exhibits a clear maximal deviation from GR in the equilateral configuration. This is qualitatively the same in $f(R)$ gravity. At one-loop order, however, the shape dependence drastically changes, and becomes similar in both nDGP and $f(R)$ gravity, although the magnitude of the deviation depends on the specific model. Interestingly, the equilateral shape still shows the maximal deviation, and its magnitude is up to $4$ times as large as the signal exhibited in the tree-level prediction, indicating that one-loop bispectrum could be a promising probe of modified gravity. \end{itemize} The numerical PT framework presented here naturally finds many extensions available to PT. For example, one can include prescriptions that improve the poor-convergence properties in SPT calculation. One example would be the inclusion of resummation such as multi-point propagator expansion \cite{Bernardeau:2008fa,Bernardeau:2011dp,Taruya:2012ut}. Also, the effective field theory of large scale structure \cite{Baumann:2010tm,Carrasco:2012cv} has been extended to the bispectrum \cite{Angulo:2014tfa,Baldauf:2014qfa}, which could be useful in extracting valuable information from small scales. In confronting observations, CMB lensing can offer a relatively clean probe of gravity \cite{Namikawa:2018erh}, for which application of our pipeline is rather straightforward. As a first step, in a future work, we shall examine simulated lensing data to further investigate some of the claims proposed here. Further, the redshift-space bispectrum has recently been measured in the BOSS survey \cite{Pearson:2017wtw,Sugiyama:2018yzo} and a promising redshift-space bispectrum model has also been proposed at one-loop order in \cite{Hashimoto:2017klo}. Extending our treatment to redshift space is thus another interesting avenue. However, this would involve some severe numerical optimisations to the code used in this paper, since an additional two-dimensional integral would need to be performed to obtain the bispectrum multipoles (e.g., \cite{Sugiyama:2018yzo}). Further, substantial optimisations are also needed in order to apply our numerical one-loop bispectrum to the parameter estimation analysis, typically using the Markov Chain Monte Carlo technique. One may also consider gravitational and dark energy effects on the 3 point correlation function (see \cite{Slepian:2016weg} for a recent model for GR). Recently progress has been made in methods to estimate and measure this in redshift space \cite{Slepian:2017lpm,Friesen:2017acf}, making it another interesting statistic relevant for upcoming surveys, especially as it provides a means of overcoming systematics typical of the bispectrum. These points are currently within the authors' focus. On top of this we have the issue of tracer bias. Recently a fully comprehensive bias model for the one-loop bispectrum has also been derived based on the bias expansion approach \cite{Desjacques:2018pfv}. This primes an investigation into the constraining power of the one-loop redshift space galaxy bispectrum for non-standard models of cosmology, and if moving beyond consistency tests of $\Lambda$CDM can be achieved with future spectroscopic surveys. On this note, there is still the major issue of the covariance between redshift-space multipoles which has been mostly studied for the Gaussian case \cite{Scoccimarro:1997st,Scoccimarro:2003wn} and has been restricted to GR \cite{Takada:2003ef,Kayo:2012nm,Sato:2013mq,Chan:2016ehg}. We leave the study of this in theories beyond $\Lambda$CDM to a future work. \newpage | 18 | 8 | 1808.01120 |
1808 | 1808.04828_arXiv.txt | The next decade will see two large-scale space-based near-infrared surveys, Euclid and WFIRST. This paper shows that the subtle differences between the filters proposed for these surveys and those from ground-based photometric systems will produce a ground-space colour term that is dependent on water absorption in the spectra of astronomical objects. This colour term can be used to identify free-floating planets in star forming regions, mimicing a successful ground-based technique that uses a filter sensitive to water absorption. This paper shows that this colour term is an effective discriminant between reddened background stars and ultracool dwarfs. This represents just one science justification for a Galactic Plane survey in the event of an extension to the Euclid mission beyond its original timeframe. | Since the end of the 1990s, near-infrared surveys have transformed our view of the universe, from high-redshift quasars \citep{Mortlock2011} and early galaxy formation \citep{Foucaud2007,Bouwens2015,Finkelstein2015} to ultracool dwarfs in our own Galactic back-yard \citep{Burgasser2002,Burningham2011}. To date, most wide-field surveys short of two and a half microns have been conducted from the ground. Hence surveys such as 2MASS \citep{Skrutskie2006}, UKIDSS \citep{Lawrence2007} and VISTA\footnote{http://casu.ast.cam.ac.uk/surveys-projects/vista/technical/filter-set} use filter sets which avoid wavelengths dominated by telluric water absorption. The next decade will see two large infrared surveys of the sky conducted from space. The Euclid NISP instrument \citep{Laureijs2011} will map one third to one half of the sky in $Y$, $J$ and $H$ with the goal of measuring the acceleration of the universe. WFIRST \citep{Spergel2015}, which focusses both on measuring cosmic acceleration and detecting extrasolar planets, will use similar near-infrared filters to survey large areas of the sky. Ultracool dwarfs are objects with spectral types later than M7. These are known to have significant water absorption in their atmospheres at similar wavelengths to telluric water absorption. Indeed indices based on water absorption provide a useful tool for determining the spectral classification of late M \citep{Allers2013}, L \citep{McLean2003,Allers2013} and T \citep{Burgasser2006} dwarfs. L dwarfs have red colours in the near-infrared, most probably due to dust clouds in their photospheres; whilst the cooler T dwarfs have blue infrared colours due to methane absorption and a lack of photospheric dust clouds. The transition between these two spectral classes produces a rapid change in spectral type and is often associated with photometric variability \citep{Radigan2014a}. Substellar objects lack a stable internal energy source from hydrogen fusion. Thus, unlike main sequence stars there is a degeneracy between mass and age. Free-floating planetary mass objects have masses under the deuterium-burning dividing line between planets and brown dwarfs and yet move through space without a parent star. These can exist both as field objects \citep{Liu2013} and as members of young star forming regions \citep{AlvesdeOliveira2012}. At young ages, giant free-floating planets can be warm enough to have M, L and T spectral types, similar to many field brown dwarfs.These free-floating planets have lower observed surface gravity than field brown dwarfs and (based on their ages and temperatures) are predicted to have masses below the deuterium-burning limit by theoretical models \cite{Saumon2008}. Star forming regions are often found within regions of the sky with high amounts of background reddening. This means that photometrically it is hard to distinguish red L type free-floating planetary mass objects from highly reddened background stars. \cite{Allers2007} present a novel method to solve this problem. They proposed a specialist $W$ band filter sandwiched between the ground-based $J$ and $H$ bands at around 1.4 microns. M, L and T dwarfs have significant water absorption around this wavelength with methane also contributing to absorption in T dwarfs. Reddened background stars will be dominated by continuum emission in this wavelength range. As this filter covers a wavelength range with telluric water absorption it is best used from the driest, most stable sites. Recently a $W$ band filter has been installed on CFHT on Mauna Kea. Ground-based near-infrared filter sets avoid wavelength regions with significant telluric water absorption, leaving gaps between the $J$ and $H$ and $H$ and $K$ filters (see for example the MKO photometric system \citealt{Tokunaga2002}). Space-based surveys such as Euclid and WFIRST are not affected by telluric water absorption. Hence there is no need for their near-infrared filters to avoid wavelengths where water absorption occurs. This means that space-based filters will sample spectral regions where ultracool dwarfs have significant water absorption whilst ground-based filters will not. This paper shows that this difference in wavelength coverage leads to near-infrared colour terms between ground-based and space-based filter, mimicing the effect of observations with a specialist $W$ band filter. In this paper synthetic photometry is used to determine that a combination of space-based and ground-based filters gives a colour term that distinguishes L-type objects from reddened stars. A short discussion then follows on how this technique could be used in both the planned Euclid and WFIRST surveys and how future surveys with these missions could be informed by this technique. | This work shows that the different passbands of ground-based and proposed space-based photometric systems produce a colour term dependent on water absorption in astronomical objects. In a decade it will be possible to use this colour term to mimic the powerful water imaging technique for detecting young free-floating planets. Euclid and WFIRST will concentrate on surveys at high galactic latitude for their core science goals. This technique is one possible justification for future Galactic plane surveys using these spacecraft. | 18 | 8 | 1808.04828 |
1808 | 1808.04533_arXiv.txt | Accurate stellar properties are crucial for determining exoplanet characteristics. Gaia DR2 presents revised distances, luminosities, and radii for 1.6 billion stars. Here, we report the calculation of revised radii and densities for 320 \edit1{non-Kepler} exoplanets using this data and present updated calculations of the incident flux received by 690 known exoplanets. This allows the likelihood that those planets orbit in the habitable zone of their host stars to be reassessed. As a result of this analysis, three planets can be added to the catalogue of potentially habitable worlds: HIP~67537~b, HD~148156~b, and HD~106720~b. In addition, the changed parameterisation of BD~+49~898 means that its planet, BD~+49~898~b, now receives an incident flux that places it outside the optimistic habitable zone region, as defined by \citep{Kopparapu2013,Kopparapu2014}. We find that use of the new \textit{Gaia} data results in a mean increase in calculated exoplanet radius of 3.76\%. Previously, CoRoT-3 b had been reported as having the highest density of all known exoplanets. Here, we use updated information to revise the calculated density of CoRoT-3~b from 26.4$g\:cm^{-3}$ to 16.1$\pm3.98g\:cm^{-3}$. We also report the densest exoplanet in our dataset, KELT-1~b, with a density of 22.1$^{+5.62}_{-9.16}g\:cm^{-3}$. Overall, our results highlight the importance of ensuring the the parameterisation of known exoplanets be revisited whenever significant improvements are made to the precision of the stellar parameters upon which they are based. | \label{sec:intro} Over the three decades since the discovery of the first planets around other stars marked the dawn of the Exoplanet Era \citep{GammaCeph,Latham,psr1257,51peg}, we have come to realise that planets are ubiquitous, and that the variety of planetary properties and system architectures is far greater than we ever imagined \citep[e.g.][]{kepler36,20782,kelt9,trappist1}. Aside from the unexpected worlds found orbiting the pulsar PSR1257 +12 \citep{psr1257}, the first exoplanets found were all behemoths, comparable in size to Jupiter \citep[e.g.][]{lathamsworld,47uma,70vir}. Those first planets included the first surprise of the Exoplanet Era -- the 'Hot Jupiters' -- planets the mass of Jupiter moving on orbits with periods measured in hours, or just a few days \citep[e.g.][]{51peg,HotJ2,HotJupiters}. In the decades since those first discoveries, the surprises have kept coming. A great diversity of alien worlds has been revealed. Some planets move in tightly packed planetary systems \citep[e.g.][]{Pack1,Pack2,Trapp}, whilst others move on extremely elongated orbits \citep[e.g.][]{80606,ecc2,ecc3}. In the early years of the Exoplanet Era, the predominant method used to find exoplanets was the radial velocity technique \citep[e.g.][]{RV1, RV2, RV3}. Using that technique, it is possible to constrain the orbit and mass of newly discovered planets, but with radial velocity observations alone, we can learn nothing more about the planet's physical nature. The advent of large scale transit surveys, such as the Wide Angle Search for Planets \citep[WASP;][]{wasp1,HotJ2,wasp3}, the Hungarian Automated Telescope Network \citep[HATnet][]{HAT1,HAT2,HAT3} and the Kilodegree Extremely Little Telescope \citep[KELT][]{kelt1,KELT2,KELT3} offer a solution to this problem. If a planet is known to transit its host star, then its diameter can be determined. Simply - a larger planet will block more light than a smaller one, resulting in a deeper, more pronounced transit. Spectroscopic observations carried out during an exoplanet's transit can yield information on the atmospheric scale and even composition of that planet's atmosphere \citep[e.g.][]{atmos1,atmos2,atmos3}. In addition to such observations, measuring the radial velocity variations of the transiting planet's host star will yield its mass. As a result, it is possible to more fully characterise the planet - calculating its bulk density. Such observations have revealed an incredible breadth of potential planetary densities, ranging from planets less dense than cotton candy \citep[e.g.][]{Candy} to others denser than Osmium \citep[e.g.][]{kelt1,dense1}. In the coming years, the focus of planet search programs will shift from primarily finding large planets to the search for potentially habitable, Earth-like worlds \citep[e.g.][]{ExoEarth1,ExoEarth2,ExoEarth3}. NASA's Transiting Exoplanet Survey Satellite \citep{TESS} should yield hundreds of such worlds over the coming years, and the race will be on to determine which, if any, could be potentially suitable as targets for the search for life beyond the Solar system \citep[e.g.][]{HabReview,Hab2,Hab3}. A key component of that characterisation effort will be attempts to quantify the incident flux a given planet will receive from its host star, to see whether it falls in the putative 'habitable zone', and could therefore have a reasonable likelihood of hosting liquid water upon its surface \citep[though a variety of other factors will also have to be taken into account - see e.g.][]{HabReview,FoF3,FoF4}. To address this, \citet{Kopparapu2013,Kopparapu2014} propose the concepts of the 'optimistic' and 'conservative' habitable zones, whose inner boundaries are defined as the limits where a planet would resemble a younger Venus, potentially harboring liquid water, and where a planet would lose its water oceans entirely to evaporation, respectively. Using these boundaries, researchers are already proposing potential systems that are worthy of attention with the next generation of radial velocity facilities as potential hosts of habitable worlds \citep[e.g.][]{Matt1,Matt2} The characterisation of the density and potential habitability of newly discovered exoplanets depends strongly on the precision with which the host star can be characterised. The measurement of the planet's diameter, for example, relies on an accurate value for the star's size, whilst the investigation of the planet's potential habitability (in terms of the insolation received) depends critically on an accurate measurement of the star's luminosity \citep[e.g.][]{Kopparapu2014}. For this reason, when new and improved data become available allowing planet host stars to be better characterised, it is vital that the catalog of known exoplanets be revisted, in order to ensure that the parameters available to researchers are as accurate and up-to-date as possible. The {\it Gaia} spacecraft is currently undertaking a five-year program of observations, through which it will obtain exquisitely precise measurements of several billion stars \citep[e.g.][]{Gaia,GaiaDR1}. {\it Gaia's} observations will yield precise distances, luminosities and effective temperatures for its target stars that represent a vast improvement on the data previously available. The second {\it Gaia} data release was made available on April 25, 2018, and contains data for a total of almost two billion sources\footnote{Details of the {\it Gaia} Data Release 2 can be found at https://www.cosmos.esa.int/web/gaia/dr2}, of which over 1.3 billion include parallax determinations, allowing the distances to those stars to be accurately determined. In this work, we take advantage of the recent {\it Gaia} Data Release 2 \citep{BigGaia,MoreGaia,GaiaPhotometry,GaiaSpectroscopy,GaiaParallax} to update the calculated sizes, densities, and incident fluxes for a large sample of known exoplanets. Our paper is structured as follows: in Section ~\ref{Methods}, we describe our methodology, before presenting and discussing our results in Section ~\ref{results}. Finally, in Section ~\ref{conclusion}, we draw our conclusions, and highlight the important role that surveys such as {\it Gaia} will play in the development of exoplanetary science in the coming years. | \label{conclusion} Since derived planetary properties are so heavily dependent on the properties of their stellar hosts, which are in turn dependent on an accurate measurement of the distance to that % star, it is critical for our understanding of the variety of exoplanets to have accurately determined distances for planet host stars. The recently released \textit{Gaia} DR2 database provides accurate parallaxes and stellar parameters for billions of stars, and represents a great improvement over the parameterisations previously available. We have used these to obtain better distance estimates for many of the stars that are known to host exoplanets, and used this to obtain updated radii and densities for many of the aforementioned exoplanets. In addition, we have used the \textit{Gaia} data to reassess whether known exoplanets orbit within the habitable zone of their host stars. Such improved characterisation will prove vital, in the coming years, in helping to determine which planets are the most promising targets for the detailed follow-up observations that will be necessary if we are to search for any evidence of life beyond the Solar system \citep[e.g.][]{HabReview}. \\ In summary, our key results are as follows: \begin{itemize} \item The updated stellar parameters from {\it Gaia} DR 2 result in an average change in planetary radius of +3.76 \% and a median change in planetary radius of +2.56 \%, across the whole sample. \item The calculated density of CoRoT-3 b, once considered the most dense planet detected to date, is reduced from $26.4 \pm 5.6 g cm^{-3}$ to $17.3 \pm 2.9 g cm^{-3}$. \item We report a new densest exoplanet, KELT-1 b. Its revised density was calculated to be 23.7$\pm4.0$ $g$ $cm^{-3}$. \item We report a revised density for WASP-103 b. WASP-103 b showed the largest change in radius of our entire sample, with the new value some 87 \% larger than that published in previous work. As a result of this increase in radius, the density of WASP-103 b was calculated to be 0.085$\pm 0.011$ $g$ $cm^{-3}$, making it one of the lowest density exoplanets of our sample. \item We report an average percentage change in incident flux of +8.92 \% as well as a median percentage change in incident flux of +1.05 \%. \item We report three new planets in the habitable zone based on incident flux: HIP 67537 b, HD 148156 b, and HD 106270 b. We also report one exoplanet, BD+49 898 b, being removed from the habitable zone, on the basis of a significant increase in the calculated luminosity of its host star. \item We observed a clear prevalence of hot Jupiters in our sample, characterized by low semi-major axis, low period, and high planetary radius. This reflects a selection bias generated by picking only stars for which we had transits. Further observational studies are needed to confine the masses of these exoplanets to then provide more accurate densities. \end{itemize} Our work reveals the critical importance of missions such as {\it Gaia} to our ongoing attempts to better understand the variety of planets orbiting other stars. In particular, the future identification of potential targets for the search for life beyond the Solar system will rely on precise knowledge of the stars that host those planets. As {\it Gaia} continues its work, it will yield still more precise measurements of billions of stars, which will play a vital role in exoplanetary science for years to come. | 18 | 8 | 1808.04533 |
1808 | 1808.04369_arXiv.txt | \noindent The circumgalactic medium (CGM), i.e.\ the gaseous haloes around galaxies, is both the reservoir of gas that fuels galaxy growth and the repository of gas expelled by galactic winds. Most cosmological, hydrodynamical simulations focus their computational effort on the galaxies themselves and treat the CGM more coarsely, which means small-scale structure cannot be resolved. We get around this issue by running zoom-in simulations of a Milky Way-mass galaxy with standard mass refinement and \emph{additional uniform spatial refinement} within the virial radius. This results in a detailed view of its gaseous halo at unprecedented (1~kpc) uniform resolution with only a moderate increase in computational time. The improved spatial resolution does not impact the central galaxy or the average density of the CGM. However, it drastically changes the radial profile of the neutral hydrogen column density, which is enhanced at galactocentric radii larger than 40~kpc. The covering fraction of Lyman-Limit Systems within 150~kpc is almost doubled. We therefore conclude that some of the observational properties of the CGM are strongly resolution dependent. Increasing the resolution in the CGM, without increasing the resolution of the galaxies, is a promising and computationally efficient method to push the boundaries of state-of-the-art simulations. | \label{sec:intro} Cosmological, hydrodynamical simulations have seen dramatic advances in recent years, producing well-resolved stellar disks with sizes, scale lengths, and stellar masses in reasonable agreement with observations of late-type galaxies \citep[e.g.][]{Schaye2015, Grand2017, Garrison2017, Genel2018}. These simulations have wildly different feedback models, suggesting that galaxy properties may not discriminate between them. The circumgalactic medium (CGM; i.e.\ the gaseous haloes around galaxies) will enable us to study how galaxies' gas reservoirs are replenished and how galactic winds alter the galaxies and their environments. Studying this regime can also help test theoretical models by comparing them to available observations of the CGM \citep[e.g.][]{Putman2012, Tumlinson2017}. It is often assumed that the hydrodynamical processes outside the galaxy's interstellar medium (ISM) are well-resolved. However, the resolution in state-of-the-art simulations is generally adaptive in a (quasi-)Lagrangian sense, such that the mass resolution is kept fixed. The spatial resolution therefore drops quickly with galactocentric radius in the CGM, in lock-step with the much lower densities there. Worryingly, many idealized studies (which give up the cosmological context in favour of much higher spatial resolution) found that the properties of `halo gas' change considerably with improved resolution \citep[e.g.][]{Scannapieco2015, Schneider2017, Mandelker2018, McCourt2018, Sparre2018}. This suggests that the CGM in cosmological simulations is under-resolved, which could affect our ability to predict or reproduce CGM observables and also have major consequences for the amount of gas accretion on to galaxies and for the mixing of metals. Questions surrounding the physical and observable properties of the CGM, the role of feedback, the re-accretion of previously expelled gas, and the distribution of heavy elements would greatly benefit from simulations that offer higher spatial resolution in the CGM than permitted by standard simulation techniques. We therefore present zoom-in simulations centred on a Milky Way-mass galaxy taken from the `Auriga' project \citep{Grand2017}, resimulated with fixed spatial resolution within the gaseous haloes of all galaxies within the zoom-in region. A similar approach was taken by \citet{Miniati2014} to study turbulence in a merging galaxy cluster at fixed spatial resolution, achieving 10~kpc uniform spatial resolution in the intracluster medium. In this letter, we present properties of the halo gas around a simulated Milky Way analogue with direct implications for observations of atomic hydrogen (also called ``neutral hydrogen'' or ``H\,\textsc{i}'') around the Milky Way. The new simulation refinement method is described in Section~\ref{sec:sim}. In Section~\ref{sec:results} we present our results on the density and H\,\textsc{i} structure in the CGM and we conclude in Section~\ref{sec:concl}. | \label{sec:concl} We have presented a new refinement technique to simulate the CGM at uniform spatial resolution. This enables us to achieve much higher resolution at relatively low cost. We ran three cosmological simulations of the same Milky Way-mass halo: one with standard mass refinement, one with mass refinement and additional 2~kpc spatial refinement within $1.2R_\mathrm{vir}$, and one with additional 1~kpc spatial refinement. We find that the global properties of the galaxy are not affected by the better sampling of the halo gas. Similarly, the median density profile and its $1\sigma$ scatter are also robust to changes in the resolution of the halo gas. However, we find a large impact on the H\,\textsc{i} column density in the CGM. The median $N_\mathrm{H\,\textsc{i}}$ 2D radial profile is substantially higher (by up to 1.6~dex) in the simulation with additional 1~kpc spatial refinement as compared to the simulation with only mass refinement. As a result, the covering fraction of LLSs within 150 kpc from the galaxy centre increases from 18 to 30 per cent when including 1~kpc spatial refinement. The large reservoirs of cool CGM detected in observations \citep[e.g.][]{Werk2014} arise naturally in cosmological simulations. However, there are some uncertainties remaining that affect the normalization of our results. The correction due to self-shielding as given in \citet{Rahmati2013} was derived from simulations with much lower resolution and may not be applicable to the small clouds we can resolve here. Therefore, we repeated our calculations in the optically thin regime. This reduces the column densities in $N_\mathrm{H\,\textsc{i}}\gtrsim10^{16}$~cm$^{-2}$ systems and strongly affects the normalization. However, qualitatively our results are unchanged and the simulations with 1~kpc spatial resolution have substantially higher $N_\mathrm{H\,\textsc{i}}$. The H\,\textsc{i} fraction would also be lower across the density range if our simulations used ionization and recombination rates given by \citet{Hui1997}, as done by \citet{Rahmati2013}, instead of following \citet{Katz1996}. This again affects the absolute normalization of our H\,\textsc{i} column density results, but none of the reported relative differences between our simulations. We conclude that the growth of the central galaxy and the bulk properties of the halo gas are not strongly affected by improved spatial resolution in the CGM. Simulations with only mass refinement therefore seem adequate to capture these aspects of galaxy evolution. However, observables that probe the extremes of the halo gas distribution, such as the low-temperature CGM, are strongly resolution dependent. Cosmological, hydrodynamical simulations with additional spatial refinement in the CGM can help bridge the gap between simulations with a realistic cosmological environment and high-resolution idealized simulations. Our results suggest that future observations with telescopes such as ASKAP, MeerKAT, and SKA are likely to detect more H\,\textsc{i} 21~cm emission than predicted by low-resolution cosmological simulations. In combination with observations, a well-resolved CGM will allow us to test, refine, and potentially rule out feedback models. In future work, we will study the impact of our improved uniform spatial resolution on metal-line emission and absorption in the CGM. | 18 | 8 | 1808.04369 |
1808 | 1808.08371_arXiv.txt | Classification of young stellar objects\\ (YSOs) into different evolutionary stages helps us to understand the formation process of new stars and planetary systems. Such classification has traditionally been based on spectral energy distribution (SED) analysis. An alternative approach is provided by supervised machine learning algorithms, which can be trained to classify large samples of YSOs much faster than via SED analysis. We attempt to classify a sample of Orion YSOs (the parent sample size is 330) into different classes, where each source has already been classified using multiwavelength SED analysis. We used eight different learning algorithms to classify the target YSOs, namely a decision tree, random forest, gradient boosting machine (GBM), logistic regression, na\"ive Bayes classifier, $k$-nearest neighbour classifier, support vector machine, and neural network. The classifiers were trained and tested by using a 10-fold cross-validation procedure. As the learning features, we employed ten different continuum flux densities spanning from the near-infrared to submillimetre wavebands ($\lambda = 3.6-870$~$\mu$m). With a classification accuracy of 82\% (with respect to the SED-based classes), a GBM algorithm was found to exhibit the best performance. The lowest accuracy of 47\% was obtained with a na\"ive Bayes classifier. Our analysis suggests that the inclusion of the 3.6~$\mu$m and 24~$\mu$m flux densities is useful to maximise the YSO classification accuracy. Although machine learning has the potential to provide a rapid and fairly reliable way to classify YSOs, an SED analysis is still needed to derive the physical properties of the sources (e.g. dust temperature and mass), and to create the labelled training data. The machine learning classification accuracies can be improved with respect to the present results by using larger data sets, more detailed missing value imputation, and advanced ensemble methods (e.g. extreme gradient boosting). Overall, the application of machine learning is expected to be very useful in the era of big astronomical data, for example to quickly assemble interesting target source samples for follow-up studies. | % An essential part of the star formation studies is to try to classify the young stellar objects (YSOs) into different evolutionary stages, and construct a coherent YSO evolutionary sequence. Also, by determining the relative percentages of YSOs in different stages, the statistical time spent in each stage can be constrained, which in turn helps to quantify the overall timescale of the stellar birth process in different molecular cloud environments (e.g. \citealp{evans2009}; \citealp{dunham2015}). Considering the formation of low-mass, solar-type stars, the YSOs have traditionally been classified into distinct stages on the basis of their infrared (IR) spectral slopes (e.g. \citealp{lada1984}) or bolometric temperatures (\citealp{myers1993}). In particular, the spectral energy distribution (SED) of a YSO, which is characterised by the bolometric temperature and luminosity, is commonly used to determine the evolutionary stage of the source, that is whether it is a so-called Class~0 or I protostar, or Class~II or III pre-main sequence (PMS) star (e.g. \citealp{lada1987}; \citealp{adams1987}; \citealp{andre1993}; see also \citealp{andre2000} for a review). Indeed, an SED analysis is very useful, not just for the purpose of source classification, but to derive some of the key physical properties of the source, such as the dust temperature and dust mass. However, modelling the source SEDs can be fairly time consuming, and hence, to quickly determine the evolutionary classes for a large sample of YSOs, an automated procedure that employs the observed source properties (i.e. the flux densities) would be very useful. In this regard, machine learning has the potential to yield a fast way to classify sources (as compared to an SED analysis) as long as the algorithm(s) in question can be trained with data sets composed of relevant flux densities and corresponding evolutionary classes of the target YSOs. So far, machine learning based classification of astrophysical objects has mostly been applied in extragalactic research (e.g. \citealp{krakowski2016}; Aniyan \& Thorat 2017; \citealp{sreejith2018}; \citealp{beck2018}; Pashchenko et al. 2018; \citealp{hui2018}; Lukic et al. 2018; \citealp{an2018}; see also \citealp{lochner2016}), while Galactic machine learning studies have been relatively few in number (e.g. \citealp{marton2016}; \citealp{yan2018}). Hence, pilot studies about using machine learning in YSO classification, which the present work represents, are warranted. In this paper, we report the results of our protostellar classification test using several different supervised machine learning algorithms. The data set used in this study is described in Sect.~2, while the data analysis is presented in Sect.~3. The results are presented and discussed in Sect.~4, and in Sect.~5 we summarise the key results and conclusions of this work. | We used eight different supervised machine learning algorithms to classify the Orion protostellar objects from FFA16 into Class~0, Class~I, and flat-spectrum sources. On the basis of PCA, we employed only the IR and submm continuum photometric data from FFA16. The training and testing of the classifiers were performed by using a 10-fold CV technique. Using the SED-based classifications of FFA16 as the benchmark, we found that the highest classification accuracy is reached by a GBM algorithm (82\% of the cases were correctly classified with $\gtrsim80\%$ purity and an MCC of 0.73), while the poorest performance was that of na\"ive Bayes classification (47\% accuracy). Our analysis suggests that among the ten continuum emission bands used in the classification, the \textit{Spitzer} 3.6~$\mu$m and 24~$\mu$m flux densities are the most informative features in terms of the source classification accuracy. Hence, these two wavelength bands would be useful to include in a panchromatic YSO classification study, especially if the other bands available are comparable to those analysed in the present work (i.e. 4.5, 5.8, 8.0, 70, 100, 160, 350, and 870~$\mu$m). Larger data sets, detailed missing value imputations, and more sophisticated learning algorithms have the potential to improve the classification accuracies. Overall, machine learning algorithms can provide a fast (at least compared to an SED analysis) way to classify large samples of sources into different evolutionary stages, and hence estimate the statistical lifetimes of the sources, and also pick up subsamples of interesting sources for targeted follow-up studies. However, an obvious challenge of supervised machine learning classification is the creation of training data sets, which requires classification of large numbers of YSOs into different evolutionary stages on the basis of their measured flux densities at the observed wavelengths. Because the latter is based on SED fitting, which itself requires knowledge of the source distance and assumptions about the underlying dust grain model, an SED analysis might be a prerequisite to the usage of machine learning classifiers on new survey data sets. | 18 | 8 | 1808.08371 |
1808 | 1808.06646_arXiv.txt | The distribution of the absorption line broadening observed in the Ly$\alpha$ forest carries information about the temperature, $T$, and widths, $\lambda_{\rm F}$, of the filaments in the intergalactic medium (IGM), and the background hydrogen photo-ionization rate, $\Gamma_{\rm HI}$. In this work, we present and test a new method for inferring $T$ and $\lambda_{\rm F}$ and $\Gamma_{\rm HI}$ from combining the distribution of the absorption line broadening and the median flux. The method accounts for any underlying degeneracies. We apply our method to mock spectra from the reference model of the EAGLE cosmological simulation, and we demonstrate that we are able to reconstruct the IGM properties. | 18 | 8 | 1808.06646 |
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1808 | 1808.06193_arXiv.txt | {The $R^2$ term in the Starobinsky inflationary model can be regarded as a leading quantum correction to the gravitational effective action. We assume that parity-preserving and parity-violating (axial) non-minimal couplings between curvature and electromagnetic field are also present in the effective action. In the Einstein frame, they turn into non-trivial couplings of the scalaron and curvature to the electromagnetic field. We make an assessment of inflationary magnetogenesis in this model. In the case of parity-preserving couplings, amplification of magnetic field is negligibly small. In the case of axial couplings, magnetogenesis is hampered by strong back-reaction on the inflationary process, resulting in possible amplification of magnetic field at most by the factor $10^5$ relative to its vacuum fluctuations.} | Magnetic fields are present in our universe on a broad range of spatial scales. Spiral galaxies similar to Milky Way host regular magnetic fields of the order of $\mu$G, while distant galaxies exhibit fields of the order of $100~\mu$G \cite{Bernet:2008qp, Wolfe:2008nk}. There is a strong evidence for the presence of magnetic fields in intergalactic medium, including voids \cite{Tavecchio:2010mk, Ando:2010rb, Neronov:1900zz, Dolag:2010}, with strengths $\gtrsim 10^{-16}$~G\@. All this suggests a cosmological origin of magnetic fields, which are subsequently amplified in galaxies, probably by the dynamo mechanism (see reviews \cite{Grasso:2000wj, Widrow:2002ud, Kandus:2010nw, Durrer:2013pga, Subramanian:2015lua}). Various mechanisms of the cosmological origin of magnetic fields have been under consideration in the literature (for reviews, see \cite{Grasso:2000wj, Widrow:2002ud, Kandus:2010nw, Durrer:2013pga, Subramanian:2015lua}). This paper will be concerned with inflationary scenario of magnetogenesis. Two of its classical versions are based on coupling either the inflaton field $\phi$ or the metric curvature to the electromagnetic field in order to violate the conformal invariance of the latter. In the seminal paper \cite{Turner:1987bw}, Turner and Widrow considered gravitational couplings of the (symbolic) type $R A^2$ and $R F^2$, while Ratra \cite{Ratra:1991bn} introduced coupling of the form $e^{\alpha \phi} F^2$ with constant $\alpha$. In the subsequent development of these ideas, numerous generalizations of the form $ f( \phi ) F^2$ and axial couplings of the form $f ( \phi ) F \tilde F$ as well as their combinations $f(\phi, R) F^2$ and $f(\phi, R) F\tilde F$ were under investigation (see \cite{Durrer:2013pga, Subramanian:2015lua} for recent reviews). Such inflaton couplings to electromagnetic field are usually introduced ad hoc. On the other hand, couplings to metric curvature, as noted already in \cite{Turner:1987bw}, are naturally expected due to one-loop vacuum polarization in curved space-time. In this paper, we point out that the vacuum-polarization corrections that are used in the curvature-based models of inflation also naturally generate inflaton coupling to the electromagnetic field. The seminal inflationary model of this kind is the Starobinsky model \cite{Starobinsky:1980te}, for which we illustrate this idea. We consider parity-preserving couplings of the form $R F^2$ as well as parity-violating (axial) couplings $R F \tilde F$ as present in the original (Jordan) frame along with the lowest-order correction to the gravitational action proportional to $R^2$. In the Einstein frame, such terms naturally produce additional non-trivial couplings between the scalaron and the electromagnetic field. We then make an assessment of inflationary magnetogenesis in the arising model. In the case of parity-preserving couplings, magnetic field of considerable strength might be generated only by fine tuning of the coupling constants, while, in the axial case, generation of magnetic field is easier. However, in both cases, magnetogenesis is hampered by strong back-reaction on the inflationary process. Our paper is structured as follows. Section~\ref{sec:Starobinsky} describes the Starobinsky model and its inflationary regime. Section~\ref{sec:parity} introduces parity-preserving couplings to curvature and explores magnetogenesis in the arising model, while section~\ref{sec:axial} does this for parity-violating (axial) couplings. Section~\ref{sec:both} briefly considers the presence of both types of couplings. We discuss our results in section~\ref{sec:discuss}. | \label{sec:discuss} In this work, we investigated the possibility of primordial magnetogenesis in one of the curvature-based inflationary models\,---\,the Starobinsky model. The idea is that, just as one can consider the $R^2$ term as a leading quantum correction in a low-energy effective field theory expansion, one can also include in this expansion all possible couplings between the electromagnetic field and curvature. After proceeding to the Einstein frame by conformal transformation of the metric, these terms generate nontrivial couplings of the electromagnetic field and the inflaton, with the form of interaction completely determined by the original model without further arbitrariness. This idea can be realized also in other inflationary models with non-minimal couplings to curvature, such as the Higgs inflation \cite{Bezrukov:2007ep}. We studied the most general terms of the smallest dimension six in the effective action, which can be regarded as the lowest-order loop corrections to electromagnetism in curved spacetime. In a general case, these couplings involve both parity-preserving and axial parts, with the axial part leading to helicity-dependent evolution of electromagnetic field. Considering electromagnetic field as a test field that does not influence the cosmological expansion or the dynamics of the inflaton, we analyzed the evolution equations for the mode functions during inflationary regime and preheating. In the parity-preserving case, amplification of the magnetic field is negligibly small for the values of couplings allowed by the requirement of stability of electromagnetic field during and after inflation. In the axial case, one can get a significant amplification in a natural range of parameters. However, back-reaction considerations, based on the requirement that the generated electromagnetic field should not spoil the usual inflationary evolution, lead to a strong constraint $W \lesssim M/m \sim 10^5$ on the amplification factor of the vacuum fluctuations, resulting in the spectrum $B_\lambda \lesssim 10^{-52} \left({\rm Mpc}/\lambda \right)^2$~G today all the way down to the cosmic diffusion scale $\lambda_{\rm diff} \sim 1\,{\rm AU} \approx 5 \times 10^{-6}\,{\rm pc}$ \cite{Grasso:2000wj}, at which one would have $B \lesssim 10^{-30}$~G\@. This is apparently not enough to explain the observed large-scale magnetic fields. Such a strong constraint can be traced back to the fact that, in all cases, due to the flatness of the Starobinsky potential, the coupling functions change very slowly during inlfation, so that the form of the power spectrum of electromagnetic field in the amplification domain is not essentially modified with respect to the vacuum case. As we have established, the back-reaction of the generated electromagnetic field in this model is two-fold. Firstly, the stress--energy contribution from the new coupling terms in the action modifies the dynamics of the universe expansion, threatening to halt inflation. Secondly, the same new terms in the action modify the dynamics of the inflaton. Both effects turned out to be of the same level of importance for the estimation of back-reaction effects in the model under consideration. The specific flatness of the scalar-field potential in models of this type leads to an interesting question about possible existence of a self-consistent regime whose inflationary property is modified but not completely destroyed by the presence of generated electromagnetic field, and which might be free from the back-reaction constraint. We leave this as a subject of future investigation. | 18 | 8 | 1808.06193 |
1808 | 1808.04182_arXiv.txt | { The origin of the first magnetic fields in the Universe is a standing problem in cosmology. Intergalactic magnetic fields (IGMFs) may be an untapped window to the primeval Universe, providing further constrains on magnetogenesis. We demonstrate the feasibility of using ultra-high-energy cosmic rays (UHECRs) to constrain the helicity of IGMFs by performing simulations of cosmic-ray propagation in simple magnetic field configurations. We show that the first harmonic moments of the arrival distribution of UHECRs may be used to measure the absolute value of the helicity and its sign. } \begin{document} | Intergalactic magnetic fields (IGMFs) may be fossil records of some cosmological process taking place in early phases of the Universe, thereby carrying imprints of the processes from whence they originated. For instance, phase transitions such as the quantum chromodynamics (QCD)~\cite{PhysRevLett.51.1488,1989ApJ...344L..49Q,PhysRevD.55.4582,Tevzadze:2012kk} and the electroweak (EW)~\cite{Vachaspati:1991nm,Enqvist:1993np,PhysRevD.53.662,Grasso:1997nx,Fujita:2016igl} one, as well as inflation~\cite{PhysRevD.37.2743,Ratra:1991bn,Byrnes:2011aa,Ferreira:2014hma}, have been suggested as mechanisms for magnetogenesis. Alternative explanations postulate their origin much later in time, for example during structure formation~\cite{Kulsrud:1996km}. These fields are believed to have served as seeds for structures to acquire their current magnetisation. We define IGMFs as pervasive fields filling the whole Universe, not bound to any particular structure. The strength of IGMFs is believed to be $B \lesssim 1 \; \text{nG}$~\cite{PhysRevD.80.123012,Ade:2015cva}, thereby not being measurable inside any structures such as filaments and galaxy clusters. Furthermore, they are prone to contamination by feedback and magnetohydrodynamical processes in the immediate vicinity of structures. For this reason, the measurement of IGMFs should ideally be carried out in cosmic voids, the low-density regions of the cosmic web that fill most of the volume of the Universe. This is, however, rather difficult, and requires indirect measurement techniques. Upper limits on the strength of IGMFs have been available for some time and were obtained using a variety of methods including Faraday Rotation~\cite{PhysRevD.80.123012,han2017a} and anisotropies of the cosmic microwave background (CMB) (see \cite{Jedamzik:2018itu} and the references therein). Lower limits, on the other hand, are much harder to derive. A promising method proposed over two decades ago consists in the observation of gamma-ray-induced electromagnetic cascades in the intergalactic medium~\cite{Aharonian:1993vz,Plaga:1995ins,Coppi:1996ze}. Nevertheless, it was not until recently, with the advent of imaging air Cherenkov telescopes such as H.E.S.S., VERITAS, and MAGIC, combined with space telescopes such as Fermi, that we were able to study individual sources of high-energy gamma rays with high enough precision to attempt to constrain IGMFs with gamma rays. A number of such works has been done in the past decade~\cite{JETPLett.85.10.473,PhysRevD.80.123012,2010ApJ...722L..39A,2010MNRAS.406L..70T,Taylor:2011bn,Takahashi:2013lba,2014arXiv1410.7717C}. The fundamental idea is to observe electromagnetic cascades triggered by TeV gamma rays from extreme blazars. The charged leptonic component of these cascades is deflected away from the line of sight, resulting in a suppression of the observed signal in the GeV range. This signal would be clearly visible in blazar spectra under ideal conditions. A similar effect could also be seen in the arrival directions by observing the so-called blazar pair haloes. Moreover, the distribution of arrival times of gamma rays from flaring sources could provide us hints of the strength and coherence length of the intervening field (see~\cite{PhysRevD.80.123012} for further details). Electromagnetic cascades provide lower limits for the strength of IGMFs of the order of $B \gtrsim 10^{-17}\, \text{G}$. These results are, however, still disputed, due to claims~\cite{0004-637X-752-1-22,0004-637X-758-2-102,Schlickeiser:2013eca,SavelievIGM,Chang:2014cta,Broderick:2018nqf} that plasma instabilities could provide similar signatures even in the absence of IGMFs, thus rendering the inferred limits invalid. Another astroparticle approach to obtain information on IGMFs is to use ultra-high-energy cosmic rays (UHECRs), since they may carry imprints of the intervening fields~\cite{Ryu:2009pf}, including anisotropies in their angular distributions~\cite{Takami:2012uw,Mollerach:2016mko,Hackstein:2016pwa}, or, if individual UHECR sources can be identified, specific morphological features in their arrival directions~\cite{Harari:2015mal}. Another possibility, similar to the case of electromagnetic cascades, is to look at the UHECR flux suppression~\cite{Mollerach:2013dza,Batista:2014xza}. Finally, it is also possible to constrain IGMFs using spectra of secondary particles produced by UHECR such as gamma rays~\cite{Essey:2009ju,Essey:2010nd}. One should bear in mind that, in the case of UHECRs, disentangling the IGMF signal from those due to, for example, fields in filaments, clusters, and galaxies would be extremely difficult. Besides the strength and coherence length of IGMFs, their topological properties are equally important. A proxy to describe the overall geometry of the field is the magnetic helicity $\mathcal{H}$, defined as \begin{equation} \label{HelDef} \mathcal{H} = \int \mathbf{A} \cdot \mathbf{B} \, {\rm d}^{3}r \,, \end{equation} where $\mathbf{A}$ is the magnetic vector potential and $\mathbf{B}=\nabla \times \mathbf{A}$ is the magnetic field. Magnetic helicity is a crucial quantity for understanding the (intergalactic) magnetic fields as it connects their geometrical structures and time evolutions in a unique way. As mentioned above, it describes the topological properties of the field, which follows from the fact that Eq.~\ref{HelDef} contains both the vector field $\mathbf{A}$ and its curl, which describes rotations. Thus, the scalar product between these two quantities gives a measure of how strongly the vector potential follows a helical structure. Formally, one can establish this connection by proving that magnetic helicity is strongly related to the linking number of infinitisimally thin magnetic flux tubes -- a formal description of magnetic field lines~\cite{Moffatt1969,0741-3335-41-12B-312}. In general, helicity is defined for magnetic fields for which no field lines are crossing the boundary\footnote{Note, however, that there are suggestions on how to drop this condition~\cite{JFluidMech_147.133}).} as this ensures invariance under electromagnetic gauge transformations. In addition, for ideal magnetohydrodynamics, i.e.~with electrical conductivity tending to infinity ($\sigma \rightarrow \infty$), one can show that the overall helicity is conserved, which is also known as the First Woltjer Theorem \cite{1958PNAS...44..489W}. The fact that helicity is virtually conserved\footnote{Magnetic helicity is conserved for infinite conductivities. In reality, conductivity is very large but finite.} is also responsible for different regimes of time evolution for the IGMFs depending whether it has a zero value or not. In particular, it might be responsible for the so-called inverse cascade of the magnetic spectrum~\cite{Sigl:2002kt,0004-637X-640-1-335,Saveliev:2013uva}, i.e.~an efficient transport of energy from small to large scales, even though a non-helical inverse cascade may also be possible~\cite{Brandenburg:2014mwa}. Thus, one possible approach for measuring magnetic helicity would be to compare theoretical models for the IGMF evolution with actual measurements of the spectral features. Another possibility, which has gained some interest recently, is again to use electromagnetic cascades, since depending on its magnitude, helicity might leave some specific imprints on blazar pair haloes~\cite{PhysRevD.87.123527,Tashiro:2013ita,Tashiro:2014gfa,Long:2015bda,Chen11072015,AlvesBatista:2016urk,Duplessis:2017rde}. Following the considerations above, it is reasonable to assume that UHECRs, too, may be used to determine the helicity content of IGMFs. However, up to the present day, to the best of our knowledge, there has been only one work~\cite{Kahniashvili:2005yp} addressing this possibility. The authors of the aforementioned work claim that for specific configurations of sources imprints of the helicity of the intervening field may be found, and propose a method to obtain this information. Conversely, helical magnetic fields may significantly affect the propagation of UHECRs leaving specific signatures on their spectrum, composition, or arrival distributions. A detailed understanding of magnetic fields is essential when building phenomenological models to interpret the measurements and, most importantly, when attempting to use UHECRs for particle astronomy. A number of works~\cite{Hackstein:2016pwa,AlvesBatista:2017vob,Hackstein:2017pex} has discussed the effects of extragalactic magnetic fields on the propagation of UHECRs, though with conflicting conclusions due to the different assumptions and owing to our lack of knowledge about magnetic field distributions in the Universe. Nevertheless, even in extreme scenarios in which voids are highly magnetised ($B \sim 1 \; \text{nG}$), UHE proton astronomy may be possible in most of the sky for typical magnetic field configurations~\cite{AlvesBatista:2017vob}. In this paper we study the effect of helical magnetic fields on the propagation of UHECRs, and show that such particles may be used to constrain the helicity of IGMFs. The paper is structured as follows: in Sec.~\ref{sec:HelSources} we present an analytical treatment of the influence of magnetic helicity on the propagation of UHECRs; in Sec.~\ref{sec:Simulations} we describe the Monte Carlo simulations of UHECR propagation, and derive constraints on the magnetic helicity in Sec.~\ref{sec:Constraints}, before discussing the results in Sec.~\ref{sec:discussion}; finally, in Sec.~\ref{sec:CO} we draw our conclusions and present the prospects for detecting IGMFs using the presented method or a derivation thereof. | \label{sec:CO} In this paper we have shown, as a proof of principle, that it may be possible to constrain the helicity of magnetic fields using UHECRs. We have outlined a methodology to look for the imprints of helical fields in the arrival directions of UHECRs. By performing a harmonic analysis of simulated data sets, we have demonstrated that the direction to which the dipole points correlates with the sign of the helicity. We have also suggested that the ratio between the dipole and quadrupole amplitudes may be used to constrain the absolute value of the helicity. The galactic magnetic field does not compromise the measurement of the sign of the helicity. However, it may compromise the value of the absolute value of the helicity, depending on the orientation of the helical magnetic field with respect to the galactic plane. In our analysis we have discussed in detail the case of IGMFs, but similar ideas can be applied to measure the helicity of magnetic fields in clusters or filaments, for example. Nevertheless, the conclusions that could be drawn would strongly depend upon the distribution of sources, which is unknown. We have demonstrated the impact of magnetic helicity on UHECR propagation, and how this may affect UHECR arrival distributions. Given the elongation in the trajectory described by a cosmic ray in the presence of a helical magnetic field, it is not unreasonable to expect this to have an impact on observables other than the arrival directions, namely the spectrum and inferred composition. We will defer this investigation to future works. If UHECR sources are ever found, the observation of energy-ordered multiplets could also be used to constrain the helicity of intervening magnetic fields, provided that enough events are detected. With this study we have laid the foundations for constraining magnetic helicity with UHECRs. In the future we intend to extend our analysis to more realistic cases of helical turbulent magnetic fields and source distributions. Then, by comparison with data collected by the two largest UHECR observatories, the Pierre Auger Observatory and the Telescope Array, it might be possible to constrain not only the sign, but also the absolute value of the magnetic helicity. | 18 | 8 | 1808.04182 |
1808 | 1808.08962_arXiv.txt | Effective field theory methods suggest that some rather-general extensions of General Relativity include, or are mimicked by, certain higher-order curvature corrections, with coupling constants expected to be small but otherwise arbitrary. Thus, the tantalizing prospect to test the fundamental nature of gravity with gravitational-wave observations, in a systematic way, emerges naturally. Here, we build black hole solutions in such a framework and study their main properties. Once rotation is included, we find the first purely gravitational example of geometries without $\mathbb{Z}_2$-symmetry. Despite the higher-order operators of the theory, we show that linearized fluctuations of such geometries obey second-order differential equations. We find nonzero tidal Love numbers. We study and compute the quasinormal modes of such geometries. These results are of interest to gravitational-wave science but also potentially relevant for electromagnetic observations of the galactic center or $X$-ray binaries. | \subsection{$\epsilon_1$ corrections} For $\epsilon_2=\epsilon_3=0$, the perturbed field equations take the following form, \be \frac{d^2\Psi_\pm^{\epsilon_1}}{dr_*^2}+\left(\omega^2-\sqrt{f_t^{\epsilon_1}f_r^{\epsilon_1}}\left(V_\pm^{\rm GR} +\epsilon_1 V_\pm^{\epsilon_1}\right)\right)\Psi_\pm^{\epsilon_1} =0\,,\label{eq:epsilon1mastereq} \ee where $dr/dr_*=\sqrt{f_t^{\epsilon_i}f_r^{\epsilon_i}}$. We should stress that these equations are valid only up to $O(\epsilon_1)$. For odd parity perturbations, the master variable and potential are \beq \Psi_-^{\epsilon_1} &=& \frac{i \sqrt{f_t^{\epsilon_1}f_r^{\epsilon_1}} h_1}{\omega r} \left(1 + \frac{1152 M^8 \epsilon_1 (13 M - 7 r)}{r^9}\right),\\ V_-^{\epsilon_1} &=& -\frac{256M^8}{r^{12}}\times \Big(15561M^2+Mr(146\ell(\ell+1)\nonumber\\ &-& 13509) +9r^2\left(324-8\ell(\ell+1)+7r^2\omega^2\right)\Big)\,. \eeq For even parity perturbations, \beq \Psi_+^{\epsilon_1} &=&\frac{i \sqrt{f_t^{\epsilon_1}f_r^{\epsilon_1}} H_1}{\omega r^8 ((\ell (\ell+1)-2) r+6 M)^2}\nonumber\\ &\times &\Big[r^9 ((\ell (\ell+1)-2) r +6 M)\nonumber\\ &-&128 M^8 \epsilon_1 \Big((23 \ell (\ell+1) +98) M r\nonumber\\ &+& 3 (\ell-1) \ell (\ell+1) (\ell+2) r^2-162M^2\Big)\Big]\nonumber\\ &+& \frac{K}{r^7 ((\ell (\ell+1)-2) r+6 M)^2}\nonumber\\ &\times & \Big[r^9 ((\ell (\ell+1)-2) r+6 M) \nonumber\\ &-& 384 M^8\epsilon_1 \Big(3(\ell^2+\ell+14) M r\nonumber\\ &+& (\ell-1) \ell (\ell+1) (\ell+2) r^2 -82 M^2\Big)\Big].\\ V_+^{\epsilon_1} &=& \frac{128 M^8}{r^{12} ((\ell^2+\ell-2) r+6 M)^3}\nonumber\\ &\times & \Big[-126 r^4 \omega ^2 ((\ell^2+\ell-2) r+6 M)^3\nonumber\\ &+& 230688 M^5 + 144 (1984 \ell (\ell+1)-4643) M^4 r\nonumber\\ &+&36 (\ell-1) (\ell+2) (2249 \ell (\ell+1)-10132) M^3 r^2\nonumber\\ &+&18 (\ell-1) (\ell+2) (\ell (\ell+1) (321 \ell (\ell+1)-4982)\nonumber\\ &+& 10696) M^2 r^3-10 (\ell^2+\ell-2)^2 (\ell (\ell+1) (13 \ell (\ell+1)\nonumber\\ &+& 469)-2502) M r^4+9 (\ell^2+\ell-2)^3 (\ell (\ell+1) (\ell^2+\ell\nonumber\\ &+& 14)+144) r^5 \Big] \eeq Re-write Eq.~\eqref{eq:epsilon1mastereq} in the form \beq && \frac{d^2\Psi_\pm^{\epsilon_1}}{dr_*^2}+\bigg(\omega^2 \left(1 + \epsilon_1 \sqrt{f_t^{\epsilon_1}f_r^{\epsilon_1}} \frac{16128 M^8}{r^8} \right) \nonumber \\ &&-\sqrt{f_t^{\epsilon_1}f_r^{\epsilon_1}}\Big(V_\pm^{\rm GR} +\epsilon_1 \tilde{V}_\pm^{\epsilon_1}\Big)\bigg)\Psi_\pm^{\epsilon_1} =0\,. \nonumber \eeq The potential $V_\pm^{\rm GR} +\epsilon_1 \tilde{V}_\pm^{\epsilon_1}$ is frequency-independent, and positive-definite outside the horizon for small positive $\epsilon_1$ (other arguments imply that $\epsilon_1,\epsilon_2$ are positive~\cite{Endlich:2017tqa}). It is possible to change $r_*$ coordinate and to transform the master equation into a manifestly positive-definite potential. Thus, mathematically, one can show mode stability of the above equation for {\it any} positive $\epsilon_1$~\cite{Kodama:2003kk}. Notice however that on physical grounds, large enough couplings (that might change the positive-definite character of the GR potential) are probably outside the regime of validity of the EFT. \subsection{$\epsilon_2$ corrections} Set now $\epsilon_1=\epsilon_3=0$. Then $f_t^{\epsilon_2} = f_r^{\epsilon_2} = f = 1- 2M/r$, and the master equations take the form \be \frac{d^2\Psi_\pm^{\epsilon_2}}{dr_*^2}+\left(\omega^2-f \left(V_\pm^{\rm GR}+\epsilon_2 V_\pm^{\epsilon_2}\right)\right)\Psi_\pm^{\epsilon_2} =0\,, \ee where $dr/dr_*=f$. Defining functions $\Psi_\pm^{\epsilon_2}$ \beq && \Psi_-^{\epsilon_2} = \frac{i f h_1(r)}{r \omega }\,,\\ && \Psi_+^{\epsilon_2} = \frac{1}{(\ell^2+\ell-2) r+6 M}\left[-r^2 K+\frac{i f r H_1}{\omega }\right]\,, \eeq we find \beq V_-^{\epsilon_2} &=& \frac{4608M^8(\ell-1)\ell(\ell+1)(\ell+2)}{r^{10}}\,,\\ V_+^{\epsilon_2} &=& 0\,. \eeq The equation for even parity is the same as in GR. Since $V_-^{\epsilon_2}$ is clearly positive definite the system is linearly mode stable for positive $\epsilon_2$ as long as higher order corrections are negligible. \subsection{$\epsilon_3$ corrections} For $\epsilon_1=\epsilon_2=0$ we find that $\epsilon_3$ couples odd and even modes together. Defining the master variables \beq \tilde{\Psi}_-^{\epsilon_3} &=& \Psi_-^{\epsilon_3} +\epsilon_3 \frac{64 M^8 \Psi_+^{\epsilon_3}}{r^9 ((\ell^2+\ell-2) r+6 M)}(-63 (\ell^2+\ell-2) r^2\nonumber\\ &+&2 (56 \ell (\ell+1)-355) M r+888 M^2)\nonumber\\ &+& \epsilon_3 \frac{1152 M^8}{r^7}\frac{d\Psi_-^{\epsilon_3}}{dr_*}\,,\\ \tilde{\Psi}_+^{\epsilon_3}&=& \Psi_+^{\epsilon_3} +\epsilon_3 \frac{64 M^8 \Psi_-^{\epsilon_3}}{r^9 ((\ell^2+\ell-2) r+6 M)} (2 (70 \ell (\ell+1)\nonumber\\ &-& 383) M r+3 (\ell-1) (\ell+2) (2 \ell (\ell+1)-21) r^2 \nonumber\\ &+& 1056 M^2)-\epsilon_3 \frac{1152 M^8}{r^7} \frac{d\Psi_-^{\epsilon_3}}{dr_*}\,, \eeq with \beq && \Psi_-^{\epsilon_3} = \frac{i f h_1(r)}{r \omega }\,,\\ && \Psi_+^{\epsilon_3} = \frac{1}{(\ell^2+\ell-2) r+6 M}\left[-r^2 K+\frac{i f r H_1}{\omega }\right]\,, \eeq the perturbed field equations can be written in the form \beq && \frac{d^2\tilde{\Psi}_-^{\epsilon_3} }{dr_*^2}+(\omega^2- fV_-^{\rm GR})\tilde{\Psi}_-^{\epsilon_3}-\epsilon_3 f V^{\epsilon_3} \tilde{\Psi}_+^{\epsilon_3} =0\,,\\ && \frac{d^2\tilde{\Psi}_+^{\epsilon_3} }{dr_*^2}+(\omega^2- fV_+^{\rm GR})\tilde{\Psi}_+^{\epsilon_3}-\epsilon_3 f V^{\epsilon_3} \tilde{\Psi}_-^{\epsilon_3} =0\,, \eeq where $dr/dr_*=f$, and $V^{\epsilon_3}$ is given by \beq && V^{\epsilon_3} = -\frac{384 M^8}{r^{12} ((\ell^2+\ell-2) r+6 M)^2}\nonumber\\ && \times\Big[ 203280 M^4+ 2400 (31 \ell (\ell+1)-132) M^3 r\nonumber\\ && +4 (\ell (\ell+1) (1743 \ell (\ell+1)-22394)+46321) M^2 r^2\nonumber\\ && + 36 (\ell-1) (\ell+2) (\ell (\ell+1) (\ell^2+\ell-162)+671) M r^3\nonumber\\ && + 3 (\ell^2+\ell-2)^2 ((\ell-1) \ell (\ell+1) (\ell+2)+396) r^4\Big]. \eeq It is easy to check that $V^{\epsilon_3}/(V_-^{\rm GR}-V_+^{\rm GR})$ is not a constant, and hence decoupling of the above equations is not possible~\cite{Chuan:1992}. We can see that $\epsilon_3$ appears only in terms coupling even and odd modes, i.e., non-diagonal parts of the equations. For the potential matrix \be \bm{V}_{(\epsilon_3)} = f \begin{pmatrix} V_-^{\rm GR} & \epsilon_3 V^{\epsilon_3} \\ \epsilon_3 V^{\epsilon_3} & V_+^{\rm GR}\,. \end{pmatrix} \ee the determinant, $\det(\bm{V}_{(\epsilon_3)}) = f^2 V_-^{\rm GR}V_+^{\rm GR} + {\cal O}(\epsilon_3^2)$, is positive in $r>2M$. It is easy to check that both eigenvalues of $\bm{V}_{(\epsilon_3)}$ are positive in the far region. Thus, following the argument in Ref.~\cite{Kimura:2018nxk}, mathematically this system is mode-stable for any coupling (within the small coupling regime of the effective field theory). The $\epsilon_3$ parameter couples odd and even modes, and introduces non-trivial effects in the tidal deformability. Consider static, quadrupolar ($\ell = 2$) perturbations, for which the general solution regular at the horizon is \beq H_0 &=&-r^2 (1-2 M/r) {\cal E}_2-\frac{384 M^5 {\cal B}_2 \epsilon_3}{35 r^8}\times \Big(420 M^5\nonumber \\ &-& 280 M^4 r-135 M^3 r^2+50 M^2 r^3+ 21 M r^4+7 r^5\Big)\,,\nonumber\\ h_0 &=&\frac{1}{3} r^3 {\cal B}_2 (1-2 M/r)+\frac{64 M^5 {\cal E}_2 \epsilon_3 (r- 2M)}{105 r^7}\nonumber \\ &\times & (980 M^4+630 M^3 r-540 M^2 r^2-210 M r^3-63 r^4)\,, \nonumber \eeq where ${\cal E}_2,\,{\cal B}_2$ are the strength of the external gravitational quadrupolar moment, polar and axial, respectively. Thus, an external {\it axial} quadrupolar field, induces a {\it polar} quadrupolar moment in the spacetime. New TLNs seem to be needed to describe this scenario, but we will not dwell on this any further. | 18 | 8 | 1808.08962 |
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1808 | 1808.06378_arXiv.txt | Systems of identical particles possessing non-local interactions are capable of exhibiting extra-classical properties beyond the characteristic quantum length scales. This letter derives the dynamics of such systems in the non-relativistic and degenerate limit, showing the effect of exchange symmetry and correlations on structure both in and out of equilibrium. Such descriptions may be crucial to understanding systems ranging from nuclei to dark matter. Appropriate limits for restoring the mean-field description are also discussed. | Introduction} Identical particles with non-local interactions are common in non-relativistic quantum mechanics. Many intriguing systems in atomic and nuclear physics, condensed matter, astrophysics, and cosmology may fundamentally be understood by many-body quantum mechanics subject to non-local and sometimes infinite-range inter-particle forces \cite{CMMBbook,Dobaczewski2011,Fiolhais2003,Marsh2016}. Degenerate systems are particularly interesting as their coherence can bring quantum behavior into prominence. The effects of degeneracy often permits significant simplification and, on occasion, almost innumerable possible configurations are able to be described straightforwardly with only a single degree of freedom. Mean field theory (MFT) is among the most popular approaches to studying such systems. Often relying on conditions of separability among bodies, diffusion, or other means of ensuring uncorrelated motion, such models can describe entire systems with very simple equations, such as Vlassov's \cite{Vlasov1968,Eby2016,Levkov2017}. However, such conditions restrict solutions to a small portion of the system's domain, with no guarantee that the sub-space intersects the region of interest. These constraints may then influence the dynamics of the system in an un-physical way. \begin{figure}[h] \begin{center} \includegraphics[width=9cm]{sph_coll.pdf} \caption{\textbf{Demonstration of XC dynamics on gravitational collapse}: Radial trajectories of collapsing condensed self-gravitating spherical shells of QCD axion dark matter. Shells start from rest. The color gradient is logarithmic in XC strength $\lambda_+$, which is left as a free constant parameter, running from the near-classical limit of $\lambda_+=-10^{-10}$ at the top to the much stronger contribution of $\lambda_+=-10^{-5}$ at the bottom, evaluated in units of R$^{3/2}$M$^{1/2}$G$^{-1/2}$. The XC physics obviously alters the infall of the shell, generally increasing the attraction and making the collapse more violent. The locations where XC physics dominates over classical gravity are shaded in gray. Details of the model are covered in Section \ref{sec:Example}.} \label{sph_shell_coll} \end{center} \end{figure} Identical-particle quantum mechanics has its own constraints, principally permutation symmetry or anti-symmetry according to the nature of the intrinsic spin degrees of each particle. The permutation constraint on these boson (symmetric) and fermion (anti-symmetric) systems are also expected to influence dynamics \cite{Beinke2018}. The scale independence of this constraint suggests the range of this dynamics change may extend beyond the standard quantum length scales. One may expect such effects to be most visible in the system's degenerate phases. Together, the degeneracy and permutation influences are referred to as exchange-correlation (XC) effects. This letter shows that the dynamics of non-locally interacting identical particles, both bosonic and fermionic, have a concise description beyond the de Broglie scale in the degenerate limit. The description presents exchange-correlation effects naturally via an extremal inter-particle correlation function. The standard mean-field description is recovered in the homogeneous limit. An example calculation is performed on a self-gravitating degenerate Bose fluid. | Conclusions} This communication derives the dynamics of non-relativistic condensed fluids with non-local inter-particle forces. It is found that the (anti-)symmetric condensed state accumulates sufficient strength to alter the system's dynamics on macroscopic scales. This model is related to the standard mean-field theory in the separable limit. A simple example of the model applied to QCD axion dark matter demonstrates notable deviation from classical gravitational collapse. There are many other potential applications of this technique. The authors' own interests are in using the model for axion structure formation, but other fields such as condensed matter, nuclear astrophysics, cold atomic physics, and many others may find the above description helpful. An extension from the condensed limit to mixed systems of identical particles may be needed to describe axion dynamics. A letter detailing the expansion to fermions as well as bosons with non-local interactions is in preparation. | 18 | 8 | 1808.06378 |
1808 | 1808.01628_arXiv.txt | We use our state-of-the-art semi analytic model for GAlaxy Evolution and Assembly (GAEA), and observational measurements of nearby galaxies to study the influence of the environment on the gas content and gaseous/stellar disc sizes of star forming galaxies. We analyse the origin of differences between physical properties of satellites and those of their central counterparts, identified by matching the $V_{\rm max}$ of their host haloes at the accretion time of the satellites. Our model reproduces nicely the differences between centrals and satellites measured for the HI mass, size of the star forming region, and stellar radii. In contrast, our model predicts larger differences with respect to data for the molecular gas mass and star formation rate. By analysing the progenitors of central and satellite model galaxies, we find that differences in the gas content arise after accretion, and can be entirely ascribed to the instantaneous stripping of the hot gas reservoir. The suppression of cold gas replenishment via cooling and star formation lead to a reduction of the cold gas and of its density. Therefore, more molecular gas is lost than lower density HI gas, and model satellites have less molecular gas and lower star formation rates than observed satellites. We argue that these disagreements could be largely resolved with the inclusion of a proper treatment for ram-pressure stripping of cold gas and a more gradual stripping of the hot gas reservoir. A more sophisticated treatment of angular momentum exchanges, accounting for the multi-phase nature of the gaseous disc is also required. | \label{sec:introduction} It has long been known that galaxy properties correlate with their environment: galaxies in dense regions of the Universe are redder, more passive and more concentrated than those in regions with `average' density \citep[e.g.][]{dressler1980,balogh1999,poggianti1999,lewis2002,gomez2003, kauffmann2004,bamford2009,peng2012}. Complementary trends are found if one focuses on the abundance of gas in galaxies \citep{bothun1980,chamaraux1980,giovanelli1985, solanes2001,boselli2002,boselli2006,koopmann2004,kenney2004,chung2009,odeken2016,jaffe2016}. HI deficiencies (i.e. the lack of HI with respect to isolated galaxies of similar morphological size and optical size) are typically ascribed to environmental effects. This hypothesis, however, is difficult to test as it would require, in principle, the identification of the progenitors of galaxies observed today, at a time when they were residing in similar environments. Theoretically, there are a number of physical processes that can effectively reduce the cold gas content of galaxies in dense environments: (i) `strangulation', i.e. the removal of the hot diffuse gas reservoir associated with galaxies falling into denser structures \citep{larson1980}; (ii) `ram-pressure stripping' of cold gas suffered by galaxies travelling at large velocities through the diffuse intra-cluster medium \citep{gunn1972}; (iii) `tidal stripping' due to the gravitational interaction with the parent halo or with other galaxies \citep{merritt1983}. (iv) `galaxy harassment', i.e. the effect associated with repeated high-velocity encounters, which is believed to play a role in the formation of dwarf ellipticals or the destruction of low surface brightness galaxies in clusters \citep{moore1996}. The efficiency of these processes at different scales has been studied extensively using detailed numerical simulations \citep[e.g.][]{tonnesen2009,tecce2010,guo2011,steinhauser2016,emerick2016,stevens2017}. Their relative importance in driving the observed environmental trends remains, however, debated. Recent studies have combined observational measurements with simulated accretion histories to constrain the timescales for the suppression of star formation in satellite galaxies (related to the timescale necessary to significantly deplete their cold gas reservoir). These are rather long ($\sim$ 3-8 Gyr in the local Universe), with a dependence on both galaxy stellar mass and redshift \citep[e.g.][]{delucia2012,wetzel2013,hirschmann2014,fossati2017}. Although these results should be interpreted in a `probabilistic' sense (not all galaxies will shut off simultaneously, and the scatter in quenching timescale is likely correlated with the orbital distribution of infalling galaxies), these long timescales are difficult to reproduce in theoretical models of galaxy formation \citep[e.g.][]{hirschmann2014,bahe2015,luo2016,brown2017}. The ratio between the sizes of the star forming and stellar discs ($R_{\rm SFR}/R_{\star}$) of satellite galaxies can provide important information about environmental processes: ram-pressure is expected to remove first low-density gas at large distance from the galaxy centre. The stellar disc would be unaffected, at least until tidal stripping of stars becomes effective. Therefore, `weak' ram-pressure stripping should cause a decrease of the HI size but would likely not affect significantly the molecular and stellar disks, leading to no significant evolution of the $R_{\rm SFR}/R_{\star}$ size ratio. `Strong' ram-pressure stripping can affect the low-density HI and also the denser molecular gas in the disk, causing a decrease of the $R_{\rm SFR}/R_{\star}$ size ratio, up until the point at which the galaxy is completely quenched (i.e. no longer forms stars, even in the centre). In case of strangulation, the density of cold gas is expected to decrease at all radii, due to star formation and stellar feedback, so that the ratio between the sizes of the gaseous and stellar disc should remain approximately constant initially. The decreasing gas density leads to a lower molecular-to-atomic gas ratio and therefore a lower star formation efficiency, that becomes negligible at large radii. The shrinking star forming region therefore leads to an increase of the size ratio between the HI and the stellar or molecular disc. Statistical studies focusing on the size-mass relation have so far mainly focused on stellar disc sizes. These have indicated that late-type galaxies in dense environments are slightly more concentrated (have smaller sizes) than those in the field \citep{weinmann2009,kuchner2017,spindler2017}. Multi-wavelength surveys have allowed us to gather important information on how the gas content of individual galaxies is affected by the environment. Based on studies of galaxies in nearby clusters, \citet{cortese2012} and \citet{fossati2013} showed that HI-deficient galaxies have star forming discs smaller than stellar discs, and that the size ratio decreases with HI-deficiency. A large fraction of HI-deficient late type galaxies are also depleted in molecular hydrogen, i.e. the star forming reservoir \citep{boselli2002,fumagalli2009}. The depletion of HI is, however, more efficient than that of star forming gas \citep{fabello2012,catinella2013}. Because of stripping galaxies in a dense environment can have truncated HI density profiles \citep{cayatte1990,cayatte1994}, molecular profiles \citep{fumagalli2009,boselli2014c} dust profiles \citep{cortese2010}, and H$_{\alpha}$ profiles \citep{kenney2004,koopmann2006,fossati2013,schaefer2017}. In some cases, a tail of HI and ionised gas is observed \citep{gavazzi1995,chung2009,jachym2017,bellhouse2017}, which can be interpreted as a consequence of ram-pressure \citep{tonnesen2010}. Semi-analytic models of galaxy formation have been crucial to improve our understanding of the correlation between galaxy properties and their evolving environment. \citet{xie2015} found that the size-mass relation of early-type central galaxies correlates tightly with the formation time of their host haloes: $R_{\star}\approx H(z(t_f))^{-2/3}$. On the basis of this result, we argued that the evolution of the stellar size, at fixed stellar mass, can be explained by differences in the halo assembly histories. These are expected to be large when comparing central and satellite galaxies: host haloes of satellite galaxies have likely formed earlier than those hosting central galaxies of the same stellar mass, and have suffered significant stripping after being accreted. In this work, we will combine observational estimates with state-of-the-art semi-analytic models to explore the origin of the observed size differences between centrals and satellite star forming galaxies today. This paper is organized as follows: Section~\ref{sec:modelanddata} introduces the semi-analytic model used in this study and the observational samples considered. In Section~\ref{sec:gas}, we compare observed and predicted integrated properties of central and satellite galaxies at $z=0$, and explain the differences between centrals and satellites by studying their evolution histories. In Section~\ref{sec:size}, we review the prescriptions adopted to model disc sizes, and compare observational measurements and model predictions for the sizes of central and satellite galaxies. In Section~\ref{sec:discussion}, we discuss our results, that are then summarized in Section~\ref{sec:conclusion}. | \label{sec:conclusion} We use the state-of-art semi-analytic model GAEA, together with observational measurements from the HRS, xGASS and HAGGIS surveys to study the gas content and SF/stellar disc sizes of star forming galaxies (these are selected according to their offset from the model/observed main sequence). In particular, we focus on the differences between central and satellite galaxies with the aim to determine when and how these differences arise. The overall distributions of HI and H$_2$ masses, SFRs, SF and stellar radii of model galaxies agree relatively well with those of observed galaxies. Comparing the median scaling relations of central and satellite star forming galaxies separately, we find that the different data-sets considered are consistent with each other. The model reproduces reasonably well the measured HI mass-stellar mass relation, stellar size-stellar mass relations for both central and satellite galaxies, while predicting a lower normalization for the H$_2$ mass-stellar mass, SFR-stellar mass, and SF size-stellar mass relations. For the HI mass, H$_2$ mas, SFR, and SF radii, the measured differences between central and satellite galaxies are $\sim 0.2$, $\sim 0.5$, $\sim 0.5$, $\sim 0.1$, respectively. No significant difference is measured for the stellar radii. The model agrees well with the observational data for the differences in HI mass, and SF/stellar radii, while over-predicting significantly the differences in H$_2$ mass and SFR. For our model galaxies, we use the available galaxy merger trees to verify if differences between central and satellite galaxies result from environmental processes or originate before environment starts playing a role. We find that all differences considered can be ascribed to environmental effects, which reduces to stripping of the hot-gas reservoir in our model. The stellar and gaseous sizes of satellite galaxies in our model are comparable to those of their central counterparts at both accretion time and present time. This is due to the similar assembly history of their host haloes, that is a result of the selection/matching adopted for central-satellite pairs. In our model, the size growth of star forming-galaxies is dominated by cooling in the case of the gaseous stellar discs, and by subsequent star formation for the stellar discs. Mergers and disc instabilities play a minor role in the size growth of our model galaxies. After accretion (i.e. the time when a central galaxy is accreted onto a larger halo, becoming a satellite galaxy), sizes stop growing because of the suspension of cooling and of the low fraction of stars formed. Meanwhile, central galaxies grows very little at late time. Including only strangulation, our model reproduces well the median observed HI masses, SF radii, and stellar radii for both central and satellite main sequence (star forming) galaxies. In contrast, it tends to over-predict the depletion of molecular gas and the related suppression of the star formation activity. We argue that this could be largely resolved with the inclusion of a proper treatment for ram-pressure stripping of the cold gas and for non-instantaneous stripping of hot gas. A treatment of angular momentum balance that accounts for the multi-phase nature of the gaseous disc is also required. We plan to work on these aspects in the future. | 18 | 8 | 1808.01628 |
1808 | 1808.10208_arXiv.txt | We investigate the onset of the classical magnetohydrodynamic (MHD) tearing instability (TI) and focus on non-modal (transient) growth rather than the tearing mode. With the help of pseudospectral theory, the operators of the linear equations are shown to be highly non-normal, resulting in the possibility of significant transient growth at the onset of the TI. {This possibility increases as the Lundquist number $S$ increases.} In particular, we find evidence, numerically, that the maximum {possible} transient growth, {measured} in the $L_2$-norm, for the classical setup of {current sheets unstable to} the TI, scales as $O(S^{1/4})$ on time scales of $O(S^{1/4})$ {for $S\gg 1$}. This behaviour is much faster than the time scale $O(S^{1/2})$ when the solution behaviour is dominated by the tearing mode. {The size of transient growth obtained is dependent on the form of the initial perturbation.} Optimal initial conditions for the {maximum possible} transient growth are determined, which take the form of wave packets and can be thought of as noise concentrated at the current sheet. We also examine how the structure of the eigenvalue spectrum relates to physical quantities. | In magnetohydrodynamics (MHD), the tearing instability (TI) occurs in highly sheared magnetic field configurations called {current sheets}. In a current sheet there is a thin (compared to larger length scales outside the current sheet) layer of intense current density where the magnetic field changes direction rapidly. If the conditions of the TI are met, the current sheet begins to `tear' or, to be more precise, the topology of the magnetic field changes to form multiple islands (or plasmoids in three dimensions) of magnetic flux. Since the seminal work of \cite{furth63}, the onset of the TI has been traditionally studied using normal mode analysis, to the extent that the terms `tearing instability' and `tearing mode' are often used synonymously. {Recent studies that address the linear onset of TI in high aspect ratio current sheets, also known as the plasmoid instability (PI), \citep[e.g.][]{loureiro07, bhattacharjee09,pucci14,uzdensky16,tenerani16} do so from the point of view of normal mode analysis. For the TI (and the PI), however, normal mode analysis cannot give a complete picture of its linear onset.} The operators in the equations describing the onset of the TI are non-normal. This means that eigenmodes are not orthogonal and for the application in hand are heavily ill-conditioned \citep{borba94}. Therefore, although eigenmodes may be damped as $t\rightarrow\infty$, they can result in significant transient (or algebraic) growth within a finite time. Performing normal mode analysis on equations with non-normal operators results in the translation to a later time when the transient growth has been damped away. {Therefore, if significant transient growth is possible, it is ignored in normal mode analysis}. Although stability theory in plasma physics is dominated by normal mode (eigenvalue) analysis, studies of non-modal behaviour are on the increase. In the MHD literature, one early suggestion that subcritical behaviour may be important for the tearing instability was made by \cite{dahlburg83}, although the mechanism was thought to be nonlinear rather than linear. Later, \cite{dahlburg94} studied the algebraic growth of current sheets in ideal MHD as a possible route to turbulent reconnection through the creation of smaller length scales. \cite{borba94} investigated the eigenmodes of resistive MHD using pseudospectra but did not focus on the TI. They argue that the non-orthogonality of the eigenmodes implies that normal mode analysis can only describe instability growth on a long time scale (of $O(S^{1/2})$, where $S$ is the Lundquist number that will be defined later). Other researchers have recognized the importance of non-modal growth in other MHD applications, including kinematic dynamo theory \citep[e.g.][]{farrell991,farrell992,livermore06,chen18}, the magnetorotational instability \citep[e.g.][]{squire14a,squire14b} and the tearing instability \citep{dmac17}. There is also a growing interest in the subcritical transition to turbulence in tokamak plasmas \citep[e.g.][]{landremann15,vw16} and the non-modal consequences of shearing on microinstabilities \citep[e.g.][]{newton10}. The purpose of this article is to investigate the non-modal transient growth at the onset of the classical TI. In particular, our aim is to determine the dependence of the {maximum possible} transient growth on the Lundquist number and to understand the relationship between the eigenvalue spectrum and the underlying physics. We solve the linearized equations numerically and use pseudospectral theory to help us understand how the spectrum relates to (a) the transient growth and (b) the optimal initial conditions that give rise to the maximum possible transient growth. | \subsection{Summary} In this article we have studied the non-modal onset of the classical tearing instability for visco-resistive MHD. We have paid particular attention to the eigenvalue spectrum of the linearized MHD equations. We demonstrate that the branching structure of the spectrum, which exists in the `damped half plane' of $\mathbb{C}$, is important for transient growth. We reveal this behaviour through the calculation of pseudospectra and by finding the maximum {possible} transient growth due to subsets of the spectrum. The spectrum branches are also closely linked to the Lorentz force, which is needed for strong transient growth. The importance of the Lorentz force in driving transient growth is also found from considering the energy balance of the system. A simple scaling law is determined {for tearing-unstable wavenumbers}, revealing that the maximum {possible} transient growth, {measured} in the $L_2$-norm, can grow to $O(S^{1/4})$ in a time of $O(S^{1/4})$. Optimal initial conditions which produce the maximum transient growth are shown to take the shape of wave packets and can be interpreted as noise in the system. {Although significant transient growth is possible during the linear onset of the TI for $S\gg 1$, it will only occur if the form of the initial perturbation allows it. Both non-modal and modal growth are required to give a complete description of the linear onset of the TI.} \subsection{Discussion} \subsubsection{Tearing-stable cases} {In this article we have focussed on wavenumbers for which the current sheet is unstable to the TI $(0<k<1)$. For wavenumbers $k>1$, transient growth is also possible and its maximum possible size increases with increasing $S$. There does not, however, appear to be a simple scaling law as we derived for tearing-unstable values of $k$. Figure \ref{stable_plot} displays the optimal initial conditions that produce the maximum size of transient growth at $t=50$ for $S=10^4$ and $k=1.01$ (the size of this optimal transient growth is 11.94).} \begin{figure} \centering {\includegraphics[scale=0.65]{fig11.eps}} \caption{The optimal initial conditions that produce the maximum transient growth at $t=50$ for $S=10^4$ and $k=1.01$.} \label{stable_plot} \end{figure} {In this example, the optimal initial conditions take the form of two wave packets on either side of the current sheet. Perturbations such as those shown in Figure \ref{stable_plot} should be used as initial conditions in non-linear MHD simulations in order to determine the non-linear consequences of linear transient growth. It may be the case that optimal initial conditions, through transient growth, can excite the tearing instability for values of $k$ which are linearly stable in normal mode analysis.} \subsubsection{Choice of norm} {Unlike asymptotic stability, the size of transient growth is dependent on the norm used to measure it. Optimizing with respect to different norms will give different results. Therefore, in calculations of transient growth, it is important to choose a norm with a clear physical meaning. In this article, we have focussed on the $L_2$-norm, which can be thought of as the `root mean square' of the variables and measures typical size that the variables can be amplified to. Other useful norms are the infinity norm, which measures the maximum amplitude of the perturbation and the energy norm. For a given $k$, the energy norm (disturbance kinetic plus magnetic energies) can be written as \citep[e.g.][]{dmac17} \be\label{energy_norm} \|\vv\|_E^2 = \frac{1}{2k^2}\int_{-d}^{d}(|Du|^2 + k^2|u|^2 + |Db|^2 + k^2|b|^2)\,{\rm d}x = \frac{1}{2k^2}\|D\vv\|_2^2 + \frac12\|\vv\|_2^2. \en where use has been made of (\ref{mhd3})$_1$ and (\ref{mhd3})$_2$. Notice from equation (\ref{energy_norm}) that if a certain value of transient growth is found in the $L_2$-norm, this is a lower bound of the resulting energy measure. {The converse is not generally true, however, as a large measure in the energy norm need not imply a large $L_2$-norm. With regard to transient growth in the TI, however, there is still the possibility of increasing transient growth with increasing $S$, optimized with respect to the energy norm. This result was first looked at in \cite{dmac17}. Using the technique described in \cite{dmac17} we present, in Figure \ref{energy_plots}, numerical estimates of the maximum growth envelopes for different values of $S$. As in our previous analysis using the $L_2$-norm, we take $k=0.5$ and consider the contribution from asymptotically stable modes with eigenvalues in the range $-0.5<{\rm Im}(\sigma)<0$. The resolution is $N=1600$. \begin{figure} \centering {\includegraphics[scale=0.65]{fig12.eps}} \caption{The maximum energy growth envelopes for different $S$.} \label{energy_plots} \end{figure} Although the shapes and maxima of the transient growth envelopes in Figure \ref{energy_plots} are different compared to those in Figure \ref{tcurves}, there is still an increasing possibility of significant transient growth as $S$ increases. Further work is required, using both the $L_2$-norm and the energy norm, to investigate transient growth at very high (astrophysical) values of $S$. } \subsubsection{Transient growth in other TI research?} {Simulations of the TI have generally skipped directly to the non-linear phase of the instability, e.g. the GEM Magnetic Reconnection Challenge \citep{gem1,gem2}, or have been interpreted in terms of the tearing mode. In some high-Lundquist number simulations, such as \cite{samtaney09} with $S=10^4$, transient growth is not reported. However, significant transient amplification will only occur if the initial condition (perturbation) is of a suitable form. It is therefore possible for transient growth not to be detected in simulations if the initial condition is not one that leads to significant transient growth. We have shown that optimal initial conditions take the form of wave packets, which can be interpreted as noise. Interestingly, recent simulations by \cite{huang17} clearly show that different levels of noise in the initial condition affect when current sheet disruption occurs {(see their Figure 12)}. It is not unreasonable to suggest that different noise patterns could lead to different transient growth, affecting when current sheet disruption takes place. A systematic study of how initial conditions, transient growth and non-linear consequences are related in MHD simulations will be carried out in future work. } | 18 | 8 | 1808.10208 |
1808 | 1808.09225_arXiv.txt | With a decade of $\gamma$-ray data from the {\it Fermi}-LAT telescope, we can now hope to answer how well we understand the local Universe at $\gamma$-ray frequencies. On the other hand, with $\gamma$-ray data alone it is not possible to directly access the distance of the emission and to point out the origin of unresolved sources. This obstacle can be overcome by cross-correlating the $\gamma$-ray data with catalogs of objects with well-determined redshifts and positions. In this work, we cross-correlate {\it Fermi}-LAT skymaps with the 2MPZ catalog to study the local $z<0.2$ $\gamma$-ray Universe, where about 10\% of the total unresolved $\gamma$-ray background is produced. We find the signal to be dominated by AGN emissions, while star forming galaxies provide a subdominant contribution. Possible hints for a particle DM signal are discussed. | \label{sec:intro} The extragalactic \g-ray background (EGB) is defined as the the \g-ray emission remaining after the subtraction of all Galactic sources from the \g-ray sky. It should be sourced by various classes of extragalactic \g-ray emitters, including the common star-forming galaxies, Active Galactic Nuclei such as blazars, and cascades of high-energy particle propagation (for a recent review, see Ref.~\cite{Fornasa:2015qua}). Exotic sources, such as dark matter annihilation or decay, can also contribute to this signal. In the era of the {\it Fermi}-LAT satellite, much has been revealed about the origins of the EGB. Some $\sim$3,000 extragalactic \g-ray sources, dominantly blazars, have been resolved \cite{Acero:2015hja}, which explain up to half of the EGB \cite{TheFermi-LAT:2015ykq}, and the number will almost double with the upcoming FL8Y point source catalog. Removing these extragalactic point sources from the EGB leaves a residual, the so-called unresolved (or isotropic) \g-ray background (UGRB) \cite{Ackermann:2014usa}, whose origins remain debated and is the focus of this analysis. The large numbers of EGB point sources detected have enabled increasingly sophisticated predictions for their contributions to the UGRB \cite{Ackermann:2011bg,Ajello:2011zi,Ajello:2013lka,DiMauro:2013xta,DiMauro:2013zfa}. Often, these utilize extrapolations of multi-wavelength observations to predict the source behaviors in the faint unresolved end. In parallel, a number of new and complementary techniques have been developed to study the UGRB in a more direct way. These uniquely exploit the sub-threshold information in the spatial distribution of \g-ray photons, and include the techniques of anisotropy \cite{Ando:2005xg,Ackermann:2012uf,Harding:2012gk,Cuoco:2012yf,Fornasa:2012gu,Ando:2013ff,DiMauro:2014wha,Fornasa:2016ohl,Ando:2017alx}, pixel statistics \cite{Dodelson:2009ih,Malyshev:2011zi,Lisanti:2016jub,Zechlin:2016pme,Zechlin:2015wdz,DiMauro:2017ing}, and spatial cross-correlation with tracers of large-scale structure \cite{Xia:2011ax,Camera:2012cj,Ando:2013xwa,Ando:2014aoa,Fornengo:2014cya,Shirasaki:2014noa,Camera:2014rja,Cuoco:2015rfa,Regis:2015zka,Xia:2015wka,Shirasaki:2015nqp,Feng:2016fkl,Troster:2016sgf,Shirasaki:2016kol,Branchini:2016glc,Cuoco:2017bpv,Shirasaki:2018dkz,Hashimoto:2018ztv}. Galaxies provide abundant opportunities that allow powerful probes of the local large-scale structure of the Universe. In recent works, {\it Fermi}-LAT data were cross-correlated with a variety of galaxy catalogs, including the SDSS-DR6 quasars, SDSS-DR8 main galaxies, SDSS-DR8 luminous red galaxies, SDSS-DR12 photo-$z$ galaxies, NVSS radiogalaxies, WI$\times$SC galaxies, the 2MASS galaxies, and the 2MPZ subsample of 2MASS galaxies. Positive correlations (at the level of $3$--$5 \sigma$) were detected on angular scales of $\lesssim 1^\circ$ with all but the luminous red galaxy catalogs \cite{Xia:2015wka,Cuoco:2015rfa,Regis:2015zka,Shirasaki:2015nqp}, providing valuable information on the sources behind the UGRB and constraints on dark matter contributions. Tomographic analyses, whereby depth (redshift) information is also utilized in unraveling the sources of the correlation signals \cite{Camera:2014rja}, have been successful in increasing the significance of the measured correlations with some galaxy catalogs to $\sim 10 \sigma$ \cite{Cuoco:2017bpv}. In this work, we perform new analyses of the cross-correlation that focus on disentangling the astrophysical and exotic contributions to the UGRB at low redshift. Galaxy observables, e.g., in the $B$- and $K$-bands, provide proxies for the amount of astrophysical activity and dark matter, respectively. Thus they can be used to predict astrophysical background and dark matter signal strengths. In order to capture this information, we exploit the plethora of multi-wavelength data available on galaxies and perform new position cross-correlation analyses using galaxies divided into multiple quadrants of astrophysical and dark matter signal expectations. We work with the 2MASS Photometric Redshift catalog (2MPZ), which consists of cross-matching 2MASS XSC, WISE and SuperCOSMOS all-sky samples, which provide multi-wavelength data in 8 wavelengths (B, R, I, J, H, Ks, W1, W2) for over a million galaxies with distribution peaked at $z=0.07$. Simply put, one expects dark matter to correlate most cleanly with massive yet astrophysically inactive targets, and also in nearby galaxies since competing astrophysical processes peak at higher redshifts. The fact that dark matter peaks at low-$z$ stems from three competing effects: stronger clustering (namely, higher concentration for dark matter halos) as $z$ decreases, higher average dark matter density as $z$ increases (scaling as $(1+z)^3$), and dilution of the observed radiation as $z$ (i.e., distance) increases. The first and the latter effects win over the second (see, e.g., \cite{Camera:2014rja}), and the different redshift distribution of the dark matter signal compared to astrophysical backgrounds is one of the most important features making cross-correlation analyses relevant for constraining the particle dark matter nature. Generically speaking, the method can probe weakly interacting massive particle (WIMP) dark matter with annihilation cross section around the thermal value (depending on the mass and type of analysis~\cite{Cuoco:2015rfa}), as confirmed also by the work presented here. This paper is organized as followed. In Section \ref{sec:data}, we describe the \g-ray data and galaxy catalogs used. In Section \ref{sec:measur}, we describe our analysis procedure. In Section \ref{sec:inter} we present our results and provide discussions for the origins of the UGRB. Section \ref{sec:concl} concludes. We provide details of our various validation checks in Appendix \ref{sec:xck}, and treatment of source modeling in Appendices \ref{sec:hod} and \ref{sec:cp}. Throughout, we adopt the Planck cosmology with parameters from Ref.~\cite{Ade:2015xua}. | \label{sec:concl} In this work, we have made an attempt to characterize the unresolved \g-ray emission of the Local Universe. To this aim, we employed {\it Fermi}-LAT skymaps with detected sources being masked and performed the measurement of their angular cross-correlation with the \twoMPZ catalog. The latter contains about one million of galaxies with a median redshift of 0.07. The cosmological volume probed by \twoMPZ\ powers only about 10\% of the total unresolved \g-ray background. Despite this small fraction, the technique adopted here enables us to study the composition of such emissions. The null hypothesis, i.e., the absence of correlation between the two datasets, is excluded at a statistical confidence larger than $99.99\%$. To understand the origin of this correlation, we considered a few different subsamples of the \twoMPZ\ catalog by splitting it into redshift, K-band luminosity (taken as a tracer of the object mass) and B-band luminosity (taken as a tracer of the star formation rate of the object) bins. We found misaligned AGNs to be the most likely contributor of the bulk of the signal. The normalization of this contribution is such that the extrapolation to higher redshift makes mAGN emission compatible with explaining the majority of the UGRB at GeV energies. On the other hand, star forming galaxies appear to be a subdominant component in our measurement. Nevertheless, the derived bounds allow them to still be a significant component of the UGRB at higher redshift. The energy spectrum of the APS somewhat favors the presence of a blazar-like component at high-energies. On the other hand, the contribution is rather featureless, being driven by the shot-noise term. In order to fully establish the fraction of their contribution, an improvement in the link between IR and \g-ray luminosity for faint blazars is crucial. Finally, we evaluated the possible contribution of a particle DM signal. The $95\%$ C.L. bounds on the DM annihilation rates reach close to the ``thermal'' rate for DM mass of 10 GeV for $b\bar b$, $\tau^+\tau^-$ and $W^+W^-$ annihilation channels (while an order of magnitude weaker bound is found for $\mu^+\mu^-$) and then increasing with a nearly linear trend for higher masses. Interestingly, when considering samples where the DM evidence is expected to increase (namely, correlation with objects at low-$z$, with high-mass, and low level of star formation), we see a slightly more pronounced peak in the DM likelihood for the DM contribution. Currently, the statistical significance of this effect is low, and it prevents us from deriving any firm conclusions on the presence of a DM signal. Nevertheless, this result motivates to deepen the investigation of cross-correlations between suitable galaxy catalogs (especially low redshift ones, like 2MRS) and multiwavelength observations, to probe the potential contribution of DM. | 18 | 8 | 1808.09225 |
1808 | 1808.05651_arXiv.txt | The observation of IceCube-170922A event from the direction of TXS 0506+056 when it was in its enhanced $\gamma$-ray emission state offers a unique opportunity to investigate the lepto-hadronic processes in blazar jets. Here, the observed broadband emission of TXS 0506+056 is explained by boosted synchrotron/synchrotron self Compton emission from the jet whereas the $\gamma$-ray data observed during the neutrino emission- by inelastic interactions of the jet-accelerated protons in a dense gaseous target. The proton energy distribution is $\sim E_{p}^{-2.50}$, calculated straightforwardly from the data obtained by Fermi-LAT and MAGIC and if such distribution continues up to $E_{c,p}=10$ PeV, the expected neutrino rate is as high as $\sim0.46$ events during the long active phase of the source or $\sim0.15$ if the activity lasts 60 days. In this interpretation, the energy content of the protons above $>$ GeV in blazar jets can be estimated as well: the required proton injection luminosity is $\simeq2.0\times10^{48}\:{\rm erg\:s^{-1}}$ exceeding $10^3$ times that of electrons $\simeq10^{45}\:{\rm erg\:s^{-1}}$ which are in equipartition with the magnetic field. As the required parameters are physically realistic, this can be an acceptable model for explanation of the neutrino and $\gamma$-ray emission from TXS 0506+056. | \label{sec:1} Recently, IceCube detected Very High Energy (VHE; $>100$ GeV) neutrinos from extragalactic sources \citep{neutrino1,neutrino2}, \citep{neutrino3}. This opens new perspectives for investigation of nonthermal processes in astrophysical objects even though no sources emitting these neutrinos have been identified so far. As neutrinos are not absorbed when interacting either with a photon field or the matter, unlike the \grays{}, they can be detected from distant sources which are "Terra Incognita" for \gray{} observations.\\ Different types of objects are proposed as potential sources for VHE neutrino emission among which the most prominent are Active Galactic Nuclei (AGNs). AGNs, being powered by supermassive black holes, are among the most luminous and energetic extragalactic objects. When the jet of an AGN is aligned with an observer's line of sight, they appear as blazars \citep{urry} which, based on the observed emission lines, are commonly sub-divided into BL Lacertae (BL-Lac) objects and Flat-Spectrum Radio Quasars (FSRQs). Blazars are characterized by high luminosity (e.g., $10^{48}-10^{49}\:{\rm erg\:s^{-1}}$ in the \gray{} band) and variable nonthermal emission in the radio to the VHE \gray{} bands. As blazar emission is dominating in the extragalactic \gray{} sky, it is natural to consider them as the most probable sources of the observed neutrinos. In fact, \citet{padovani1, padovani2}, have recently found a correlation between High Energy (HE) peaked BL Lacs (emitting $> 50$ GeV) detected by Fermi Large Area Telescope (Fermi-LAT) and the VHE neutrino sample detected by IceCube. Also, remarkable is the possible association of the highest-reconstructed-energy ($\sim2$ PeV) neutrino event with the exceptionally bright phase of FSRQ PKS B1414-418 \citep{kadler}. Recently, \citet{aartsenB} showed that the maximum contribution of the known blazars to the observed astrophysical neutrino flux in the energy range between 10 TeV and 2 PeV is less than 27 \%, but in principle significant neutrino emission from a particularly bright blazar can be detected.\\ There are proposed different mechanisms for VHE neutrino production in blazar jets (e.g., \citet{man, bednarekneutrino, prot, yoshida, tavec}, \citep{ 2016PhRvL.116g1101M, 2016PhRvD..93h3005W, 2016MNRAS.455..838K}). These relativistic jets are ideal laboratories where the leptons (electrons) and hadrons (protons) can be effectively accelerated, which interacting with the magnetic and/or photon fields can produce emission across the whole electromagnetic spectrum. Even if the leptonic emission alone can explain the observed features of some blazars, the energetic protons co-accelerated with electrons might contribute to the observed emission. As the protons probably carry a significant fraction of the total jet power, the exact estimation of their content in the jet is crucial for understanding the jet launching, collimation and dynamics. In general, only HE \gray{} observations alone are not sufficient to differentiate between the contribution of protons and electrons; this can be done only by neutrino observations.\\ The lack of a high-confidence association of a neutrino event with a particular blazar significantly complicates the interpretation of hadronic emission from blazar jets. The best association to date is that between IceCube-170922A neutrino event with the \gray{} bright BL Lac object \bl{} \citep{IceCubeFermi}. The Fermi LAT and MAGIC observations reveal that \bl{} was in the active state in MeV/GeV and above 100 GeV bands when the neutrino event was observed on September 22, 2017; the evolution of its multiwavelegth emission in time around the neutrino event can be seen here \href{https://youtu.be/lFBciGIT0mE}{\nolinkurl{youtu.be/lFBciGIT0mE}} \citep{sah}. At the redshift of $z=0.336$ \citep{paiano} \bl{} is among the brightest BL Lacs detected by Fermi LAT. Moreover, IceCube detected a $3.5\sigma$ excess of neutrinos from the direction of \bl{} in 2014-2015 \citep{IceCube1}. Further detailed spatial and temporal analyses of the complex \gray{} region around \bl{} showed that the emission from the nearby flaring blazar PKS 0502+049 is dominating at low energies, but \bl{} is brighter above a few GeV, making it the most probable neutrino source \citep{sah}.\\ The data available from the observations of \bl{} makes it a unique object for testing the lepto-hadronic emission scenarios in blazar jets. For example, in \citet{magic} the one-zone lepto-hadronic model based on the interaction of both accelerated electrons and protons (photo-meson reaction) with the external photons (from a slow-moving external layer) can successfully explain the observed multiwavelength SED and neutrino rate if the proton energies are in the range from $10^{14}$ eV to $10^{18}$ eV. In this and other similar models it is impossible to estimate the relative contribution of low-energy protons ($>1$ GeV) which carry a significant portion of the jet power. An alternative modeling of the multiwavelength emission from \bl{} is applied in the current paper; it is assumed that the protons accelerated in the jet of \bl{} interact with a dense target crossing the jet and produce the observed HE and VHE \gray{} emission from the decay of neutral pions. This is done within widely discussed jet-target interaction models which were successfully applied for modeling the emission from different AGNs (e.g., M87 \citep{barkov, 2012ApJ...755..170B}, Cen A core \citep{araudo10}, Mrk 421 \citep{dar}, 3C454.3 \citep{2013ApJ...774..113K}, etc.). The initial proton distribution is estimated by normalizing the expected \gray{} flux from proton-proton ($pp$) interactions to the Fermi LAT and MAGIC data, then the neutrino spectra are estimated straightforwardly. There is no contradiction between this and other discussed models involving photo-meson reactions as, again, the cascade initiated from the interaction of ultrahigh-energy protons might be still responsible for the emission in the X-ray band. By interpreting that the observed HE and VHE \gray{} emission originates from $pp$ interactions, the main purpose of the current paper is to estimate {\it i)} the total luminosity of protons ($>$ GeV) and compare it with that of electrons and {\it ii)} the expected detection rate of neutrinos produced from $pp$ inelastic collisions.\\ The paper is structured as follows: the model adopted here is described in Section \ref{sec:2}. The modeling of broadband emission from \bl{} is presented in Section \ref{sec:3}. The results are discussed in Section \ref{sec:4} and summarized in Section \ref{sec:5}. | \label{sec:5} In blazar studies, one of the long-standing and unclear questions is whether the protons are effectively accelerated in their jets and if they have a significant contribution to the observed emissions. The \gray{} observations solely are not sufficient to differentiate between the emission from electrons and protons not allowing to estimate their content in jets exactly. The recent association of \bl{} with the neutrino events allowed to measure the total energy of the jet carried by electrons and protons.\\ When the observed \grays{} and neutrinos from a blazar are due to $pp$ interactions, the energy of protons is mostly released in the GeV band allowing straightforward measurement of the proton spectra based on the observed \gray{} data. A simplified scenario of lepto-hadronic emission from \bl{} is discussed assuming that beside the constant boosted electron synchrotron/SSC emission from the jet compact region, a significant radiation in the \gray{} band is produced when a target (cloud, star envelope, etc.) crosses the jet and the inelastic $pp$ interactions produce pions which then decay into \grays{}. If only the emission from the leptons is considered, the electrons and magnetic field are in equipartition and the observed low-energy and time-averaged \gray{} data can be explained for the jet luminosity of $L_{\rm jet}\simeq 10^{45}\:{\rm erg\:s^{-1}}$. The \gray{} data when the neutrino was observed, can be modeled if the protons are distributed as $\sim E_{p}^{-2.50}$ and their energy extends up to $E_{c,p}=10$ PeV. The expected neutrino rate is $\simeq0.13-0.46$ during the long active phase of the source and $\sim 0.04-0.15$ events if the activity lasts 60 days. The synchrotron emission of electrons directly accelerated in the jet is significant up to the X-ray band, whereas the synchrotron emission of newly injected fresh pairs (from $pp$ interactions) in a dense target dominates afterwards explaining the observed X-ray data obtained during the low VHE \gray{} emission state of \bl{}. Within this scenario, the energy content of the protons (above $>$ GeV) in the blazar jet is estimated for the first time: the required proton injection luminosity should be $\simeq2.0\times10^{48}\:{\rm erg\:s^{-1}}$ which exceeds $10^{3}$ times that of electrons. This implies that a significant fraction of the jet kinetic energy is carried by the protons but still involvement of hadrons acceleration in the jet will not dramatically (unreasonably) increase its luminosity. Considering the applied model can satisfactorily reproduce the observed multiwavelegth emission spectrum of \bl{} and predicts a sufficient neutrino production rate, it provides an acceptable explanation for the hadronic emission from the \bl{} jet. | 18 | 8 | 1808.05651 |
1808 | 1808.02889_arXiv.txt | We discuss how to constrain new physics in the neutrino sector using multimessenger astronomical observations by the IceCube experiment. The information from time and direction coincidence with an identifiable source is used to improve experimental limits by constraining the mean free path of neutrinos from these sources. Over the coming years, IceCube is expected to detect neutrinos from a variety of neutrino-producing sources, and has already identified the Blazar TXS 0506+056 as a neutrino-producing source. We explore specific phenomenological models: additional neutrino interactions, neutrinophilic dark matter, and lepton-number-charged axion dark matter. For each new physics scenario, we interpret the observation of neutrinos from TXS 0506+056 as a constraint on the parameters of the new physics models. We also discuss mergers involving neutron stars and black holes, and how the detection of neutrinos coincident with these events could place bounds on the new physics models. | \label{sec:introduction} The neutrino sector is the least known sector of the standard model -- the absolute value of their masses, the mass generation mechanism itself, and the Dirac or Majorana nature of neutrinos are a few of many open questions. Besides, long standing discrepancies in short baseline oscillation experiments~\cite{Aguilar:2001ty, Ko:2016owz, Aguilar-Arevalo:2018gpe, Alekseev:2018efk, Almazan:2018wln} are still to be understood, possibly pointing towards novel interactions secluded to the neutrino sector. In fact, current experimental constraints still allow relatively sizable new neutrino interactions, specially in scenarios where new physics is light and weakly coupled (see, e.g. Refs.~\cite{Gninenko:2009ks, Cherry:2014xra, Bai:2015ztj, Asaadi:2017bhx, Chu:2018gxk, Bertuzzo:2018itn}). As neutrinos interact very weakly with matter, exploring this sector is a challenging task, requiring non-trivial search strategies ranging from man made neutrino beams to astrophysical neutrino sources. Since the discovery of ultra-high energy extraterrestrial neutrinos (UHE$\nu$) by IceCube~\cite{Aartsen:2013jdh}, a great deal of attention has been devoted to what can be learned about neutrino physics from these events. The underlying features that prompt such question are essentially the extreme conditions of UHE$\nu$ that are otherwise inaccessible at collider experiments: multi-PeV neutrinos traversing Gigaparsecs of cosmic neutrino and dark matter backgrounds to arrive at the Earth. The observation of the UHE$\nu$ spectrum provides an invaluable probe of physics beyond the standard model. For instance, the flavor composition of UHE$\nu$ can be used to probe non-standard neutrino interactions, mixing with sterile neutrinos and neutrino decays~\cite{Athar:2000yw, Keranen:2003xd, Blennow:2009rp, Mehta:2011qb, Hollander:2013im, Chatterjee:2013tza, Mena:2014sja, Palladino:2015zua, Arguelles:2015dca, Pagliaroli:2015rca, Bustamante:2015waa, Gonzalez-Garcia:2016gpq, Brdar:2016thq, Rasmussen:2017ert,Denton:2018aml}, as well as CPT violation~\cite{Ando:2009ts, Barenboim:2003jm, Klop:2017dim,Ellis:2018ogq}; the shape of UHE$\nu$ energy spectrum can probe interactions between neutrinos and leptoquarks~\cite{Anchordoqui:2006wc, Barger:2013pla, Dutta:2015dka, Dey:2015eaa, Mileo:2016zeo, Chauhan:2017ndd, Dey:2017ede, Becirevic:2018uab}; and the arrival of extragalactic events is an indication that the universe is not opaque to neutrinos, constraining new interactions in the neutrino sector~\cite{Ioka:2014kca, Ng:2014pca, Cherry:2014xra, Shoemaker:2015qul, Araki:2015mya, DiFranzo:2015qea, Marfatia:2015hva, Davis:2015rza, Cherry:2016jol,Arguelles:2017atb,Chianese:2018ijk}. In this paper, we will focus on the opacity of the universe to neutrinos, and how multimessenger astrophysics can be used to extract additional information from IceCube UHE$\nu$. Our motivation relies on the following recent observations. First, the IceCube collaboration recently detected a high-energy neutrino event in time and directional correlation with a gamma ray flare from the blazar TXS 0506+056~\cite{IceCube:2018dnn,IceCube:2018cha}. Additionally, the IceCube collaboration, upon analyzing data from 2014-2015, has measured an excess of $13\pm 5$ events from the direction of TXS 0506+056 with $\sim$ TeV-PeV energy neutrinos. Measurements of TXS 0506+056 constrain its redshift to be $z = 0.3365 \pm 0.0010$~\cite{Paiano:2018qeq}, corresponding to a distance of $1.3$ Gpc, implying that the mean free path of neutrinos is larger than $1.3$ Gpc. Second, the LIGO collaboration has recently begun detecting gravitational waves (GW) from the merger of compact objects. The first such observation that detected GW coincident with electromagnetic (EM) followup from a wide range of frequencies~\citep{Evans:2017mmy,Goldstein:2017mmi,Savchenko:2017ffs,Pozanenko:2017jrn,Fermi-LAT:2017uvi,Coulter:2017wya,Chornock:2017sdf,Tanvir:2017pws,Nicholl:2017ahq,Soares-Santos:2017lru,Verrecchia:2017hck,Hu:2017tlb} was the event GW170817~\cite{TheLIGOScientific:2017qsa}. This has allowed the LIGO collaboration to estimate that there exists a non-zero rate of binary neutron star (NS-NS) mergers in the universe~\cite{TheLIGOScientific:2017qsa}of $1540^{+3200}_{-1220}$ Gpc$^{-3}$ yr$^{-1}$. While EM followup was detected for this, no neutrinos were detected coincident with GW170817 by a variety of neutrino detectors~\cite{ANTARES:2017bia}. Many have speculated about the possibility of high-energy neutrino emission from NS-NS mergers, and in the next generation of neutrino experiments, these types of events should be detectable~\cite{Dermer:2003zv, Waxman:1997ti, Murase:2013ffa, Moharana:2016xkz, Kimura:2017kan}. Neutrinos may also be emitted from Neutron Star-Black Hole (NS-BH) mergers, the rate of which in the universe is estimated to be between $0.5$ and $1000$ Gpc$^{-3}$ yr$^{-1}$~\cite{Abadie:2010cf}. Our aim is to evaluate how much more one can learn about the neutrino sector using multimessenger astrophysics, that is, using the information from the coincidence between a high energy neutrino signal and GW/EM observations. This coincidence bears valuable information, allowing to further assess the opacity of the universe to neutrinos as the direction, timing and distance of the neutrino source is identified. While the predicted neutrino fluxes from NS mergers and blazars vary based on a number of assumptions, making it hard to predict an event yield at a neutrino experiment, we may still use the possibility of detection to probe new physics in the neutrino sector. For example, if new neutrino interactions exist, there is the possibility that a neutrino emitted from an identified source can scatter off a neutrino from the Cosmic Neutrino Background (C$\nu$B), causing it to go undetected at Earth, or to have a neutrino signal delayed with respect to the optical one. In this manuscript, we will focus on the detection of neutrinos coincident with the blazar TXS 0506+056 as a means of probing specific new physics scenarios. Additionally, we will discuss the future ability of IceCube Generation 2 (IceCube-gen2) and its sensitivity to NS mergers in probing these new physics scenarios. We analyze the existence of neutrino secret interactions ($\nu$SI), in which there exists a new massive particle coupling to neutrinos, the possibility of neutrinophilic dark matter, and the existence of a lepton-number-charged axion. We provide a recipe for setting limits on these scenarios given the detection of one neutrino event or more, and we discuss the possibility of discovering new physics in the neutrino sector in the absence of detecting neutrinos in particular regimes. | We have discussed how new physics in the neutrino sector can be probed with multimessenger astronomical observations in IceCube and its upgrade, Generation 2. By identifying the neutrino-producing source with time and direction coincidence with gravitational wave and/or electromagnetic observations, we may improve on constraints on the opacity of the universe to neutrinos. To exemplify this method, we have performed an analysis of the neutrino events detected coincident with the blazar TXS 0506+056 and interpreted their detection in several simplified models: neutrino secret interactions, neutrinophilic dark matter, and axion-neutrino couplings. For the first two models, a more thorough analysis than ours would improve the bounds from the CMB and $\tau$/meson decays. For the axion case, we derive complementary constraints to cosmological bounds. IceCube could also place strong bounds for sub-micro-eV axions, if the right-handed neutrinos are in the keV-MeV scale. Briefly, we offer some remarks on new neutrino physics scenarios in which utilizing the large distances traveled by ultra-high energy extraterrestrial neutrinos is not advantageous compared with other methods of neutrino detection. Famously, the observation of neutrinos from Supernova 1987A has been used to place constraints on new physics models, such as the existence of a neutrino magnetic moment~\cite{Barbieri:1988nh}, neutrinos with nonzero electric charge~\cite{Barbiellini:1987zz}, or new particle interactions~\cite{Raffelt:1987yt}. Unlike the scenarios studied in this work, these specific models are more easily probed by low-energy ($E_\nu \sim$ several MeV) neutrinos. As an explicit example, if one were to attempt to constrain the lifetime of neutrino decay, the Lorentz factor $\gamma = E_\nu/m_\nu$ makes probes with ultra-high energy extraterrestrial neutrinos feeble in comparison to those from distant supernovae. Having identified specific new neutrino physics models that are better probed by high-energy neutrinos, we emphasize the importance of multimessenger astronomy in searching for this new physics. Of critical importance here is the ability to pinpoint the sources of neutrinos, both in terms of time and direction. Then, and only then, can one be confident that the mean free path of travel is greater than the distance of the observation of gravitational waves and/or electromagnetic signature detection. Over the next decades, the joint effort of these probes will be able to explore a wide variety of new physics models in the neutrino sector. | 18 | 8 | 1808.02889 |
1808 | 1808.02840_arXiv.txt | We present a $3^{\circ} \times 3^{\circ}$, 105-pointing, high-resolution neutral hydrogen (\HI) mosaic of the M81 galaxy triplet, (including the main galaxies M81, M82 and NGC 3077, as well as dwarf galaxy NGC 2976) obtained with the Very Large Array (VLA) C and D arrays. This \HI synthesis mosaic uniformly covers the entire area and velocity range of the triplet. The observations have a resolution of $\sim 20''$ or $\sim 420$ pc. The data reveal many small-scale anomalous velocity features highlighting the complexity of the interacting M81 triplet. We compare our data with Green Bank Telescope (GBT) observations of the same area. This comparison provides evidence for the presence of a substantial reservoir of low-column density gas in the northern part of the triplet, probably associated with M82. Such a reservoir is not found in the southern part. We report a number of newly discovered kpc-sized low-mass \HI clouds with \HI masses of a few times $10^6$ \msun. A detailed analysis of their velocity widths show that their dynamical masses are much larger than their baryonic masses, which could indicate the presence of dark matter if the clouds are rotationally supported. However, due to their spatial and kinematical association with \HI tidal features, it is more likely that the velocity widths indicate tidal effects or streaming motions. We do not find any clouds that are not associated with tidal features down to an \HI mass limit of a few times $10^4$ \msun. We compare the \HI column densities with resolved stellar density maps and find a star formation threshold around $3-6 \cdot 10^{20}$ cm$^{-2}$. We investigate the widths of the \HI velocity profiles in the triplet and find that extreme velocity dispersions can be explained by a superposition of multiple components along the line of sight near M81 as well as winds or outflows around M82. The velocity dispersions found are high enough that these processes could explain the linewidths of Damped-Lyman-$\alpha$ absorbers observed at high redshift. | The evolution of galaxies is affected by their environment. Galaxy interactions and mergers are probably the most obvious examples of this. These processes can severely alter or completely transform a galaxy's properties. Signs of galaxy interactions are most easily detected in the component of the galaxy that is the most sensitive to them, namely the extended reservoirs of circum-galactic neutral hydrogen (\HI) (although evidence for interactions can also be seen in extended stellar envelopes; for an early example see \citealt{ferguson02}). The M81 triplet (with M81, M82 and NGC 3077 as the main galaxies) is often presented as a prime example of the complexity of interactions, their impact on the circum-galactic medium and, therefore, galaxy evolution (see \citealt{yun94}). The three main galaxies in the triplet each highlight different aspects of galaxy evolution. The inner disk of the grand spiral galaxy M81 seems largely unaffected by the interaction. Studies of the disk have been instrumental in developing the theory of density waves and formation of (grand) spiral structure (e.g., \citealt{rots75} for an early example). The starburst galaxy M82 is a unique target for studying interaction-triggered star formation feedback processes in essentially all wavelength bands (e.g., H$\alpha$, X-rays, dust, \HI, molecular gas, see \citealt{walter02a,leroy15} and references therein). The third galaxy is NGC 3077, an optically smooth galaxy with an actively starforming core, which has been stripped of most of its \HI (e.g., \citealt{walter02b}). Much of this \HI is now found immediately to the east of the main galaxy as part of the ``Garland'' feature (e.g., \citealt{yun93a,walter11}). The triplet is surrounded by at least 20 dwarf galaxies (including a few tidal dwarfs) that together form the greater `M81 group' (e.g., \citealt{karachentsev02}). One of the more prominent of these dwarf galaxies is NGC 2976, an actively star-forming, gas-rich dwarf galaxy. Very Large Array (VLA) D-array \HI observations of the M81 triplet, obtained by \citet{yun94}, have played a critical role in shaping our understanding of how interactions between galaxies affect the distribution of the atomic gas (see also \citealt{yun93a} and early work by \citealt{vanderhulst79} and \citealt{appleton88}). The 12 pointing ($\sim 2.8$ square degrees) mosaic presented in \citet{yun94} (which was later extended to 24 pointings [$\sim 5.6$ square degrees], \citealt{yun00}) demonstrated that the extended \HI emission in the triplet is dominated by filamentary structures of many tens of kpc connecting the main galaxies and containing most of the \HI in the system. These structures are mostly due to the effects of the tidal interactions. No such signs are visible in shallow optical imaging of the triplet. However, recent star count analyses of the triplet, which are sensitive to very low surface brightness emission, have revealed that the stellar component is also affected by the interaction \citep{okamoto15}. Green Bank Telescope (GBT) \HI observations \citep{chynoweth08} of the M81 triplet covered a larger area ($3^{\circ} \times 3^{\circ}$) down to low column densities, albeit at a spatial resolution ($\sim 10$ kpc) that is insufficient to resolve the sub-kpc giant atomic complexes that are present in nearby galaxies and that are key to our understanding of star formation (e.g., \citealt{leroy08, bigiel08}). However, the GBT observations clearly demonstrated that there is almost twice as much \HI present in the system than detected in the \citet{yun94, yun00} observations. Here, we use the dramatic increase in VLA capabilities over the last two decades to completely map at high resolution (spatially and spectrally) the \HI in the entirety of the M81 triplet and its immediate surroundings. We present a 105-pointing (7.6 square degrees out to the 50 percent sensitivity level) C- and D-array mosaic, covering the same area as the \citet{chynoweth08} GBT observations. These new data form the most complete high-resolution and high-sensitivity census of atomic gas in the M 81 triplet so far. Our highest-resolution data set has a resolution of $\sim 24''$ (420 pc at $D = 3.63$ Mpc, the distance of the M81 triplet; \citealt{karachentsev04}), or close to a factor of three higher spatial resolution than the earlier 12-pointing data presented in \citet{yun94}. These earlier data were limited by the capacities of the correlator at the time, with different pointings observed over different, fairly narrow velocity ranges. In our new data, all pointings cover the entire velocity range of the triplet, at a much higher velocity resolution. These data thus form the currently most complete and comprehensive view of the atomic gas in the M81 triplet and its immediate surroundings. A data set of this size with this level of detail has many applications. Here, apart from presenting the data, we focus on the following aspects. Our $\sim 400$ pc resolution observations reach a limiting \HI mass of $\sim 10^4$ \msun and constrain the numbers of individual \HI clouds in the group down to very low masses and sizes. This will provide a link to the missing satellite problem, i.e., satellites with clumps of cool \HI, but no star-formation. A second important topic is the connection to high-redshift \HI through measurements of the \HI probability distribution function. Linking high-redshift \HI absorption measurements to local emission properties is important as our high-$z$ \HI knowledge is based on absorption measurements. If the M81 triplet were by chance observed in the foreground against a high-redshift quasar, it would be classified as either a Lyman Limit System (LLS), or a Damped Lyman-$\alpha$ absorber (DLA), depending on where exactly the quasar's sightline would appear through the \HI distribution. Our covered area measures about 0.2 Mpc $\times$ 0.2 Mpc, large enough to include typical impact parameters between quasars and DLAs at high redshift (e.g., \citealt{rahmati14}). We can therefore directly compare the \HI linewidths in the triplet with those seen in DLA systems at high redshift. Finally, we address the link between star formation and \HI in the triplet. Empirical descriptions of this link often treat star formation as dependent on (amongst others) local conditions (such as the gas column density; \citealt{skillman87}, or the cooling time; \citealt{schaye01}) or assume a more global dependency on the galaxy dynamics (e.g., Toomre-$Q$ or shear; \citealt{kennicutt89, hunter98}). Our high-resolution data will allow a direct comparison with maps of the (resolved) stellar distribution of young stars. In Sect.\ 2 we describe the observations, data reduction and data products. Section 3 compares the data with previous observations and highlights the new aspects of this data set. We also compare our data with the \citet{chynoweth08} deep Green Bank Telescope observations, and discuss a number of low-mass \HI clouds visible in these data sets. In Sect.\ 4 we compare the \HI column densities with stellar density maps and relate the profile velocity width in our data with those found in DLAs. Finally, we summarise our results in Sect.\ 5. | \subsection{Moment maps and position-velocity slices\label{sec:moms}} The zeroth moment map (Fig.\ \ref{fig:mom0}) shows features not visible in the \citet{yun94} and \citet{yun00} data, such as the full length of the arm between M81 and NGC 2976, emission between NGC 2976 and M81 and the presence of clouds to the SE of the triplet. The existence of the northern part of the NGC 2976 arm was already known from observations by \citet{appleton81} and \citet{appleton88}, as well as from the 24-pointing mosaic by \citet{yun00}. The zero-spacing corrected moment map convincingly shows that this arm forms with one part extending down to NGC 2976, as was also shown in the GBT observations in \citet{chynoweth08}. Also visible close to the northernmost edge of the mosaic is dwarf galaxy M81dwB (UGC 5423) at $10^h05^m30^s, +70^{\circ}21'52''$. One striking result is that the observed area away from the triplet is mostly empty. We do not find a large population of small \HI clouds that are not associated with the tidal features, even though the 5$\sigma$ \HI mass limit for an unresolved cloud is $\sim 10^4$ \msun for a velocity width of $\sim 10$ \kms. Even taking into account that clouds may be resolved by a few beams, or have velocity widths that are a factor of few larger, this still implies upper limits below $\sim 10^5$ \msun for a hypothetical population of free-floating \HI clouds. It is often thought that these free-floating clouds could be embedded in mini-dark-matter halos, with implications for cosmological problems such as the ``missing satellites'' problem (e.g., \citealt{kauffmann93}). A more extensive discussion on cloud masses is given in Sect.\ \ref{sec:clouds}. The velocity field of M81 (Fig.\ \ref{fig:mom1}) shows a regularly rotating inner disk. The outer disk is more disturbed. The transition occurs at approximately the Holmberg radius. The largest deviations from regular rotation occur to the east of the center, along the minor axis, and are visible as strong kinks in the velocity contours. This region corresponds to the location of dwarf galaxy Holmberg IX. This is also visible in the position-velocity slices in Fig.\ \ref{fig:slices}. Slice 10 and 11 cross this location, and the presence of the extra \HI is clearly visible at an offset of $\sim -0.1^{\circ}$. The orientation of the kinematical minor axis of M82 seems to be almost perpendicular to its optical minor axis. It is likely that this is caused by the gas outflows in M82 (e.g., \citealt{yun93b, walter02a,leroy15,martini18}) affecting the velocity field. Slices 6 and 7 in Fig.\ \ref{fig:slices} show that in these regions \HI is present with a velocity spread of close to 400 \kms. NGC 3077 is hardly visible kinematically, and the dynamics of the gas in that region are dominated by the interaction. It also does not stand out in slices 1--5 (Fig.\ \ref{fig:slices}) which cross this area. Note that the smaller clumps and stream fragments surrounding the main body of the triplet all have velocities close to those of the nearby parts of the triplet, indicating they are probably all associated with the observed tidal features. The second-moment map (Fig.\ \ref{fig:mom2}) shows a north-south gradient in velocity dispersion, with lower values of around 5--10 \kms mainly found towards the south-west, while high values of 20 \kms and higher are found towards the north-east. Many of these high values are associated with M82, and inspection of the data cube shows that this is indeed diffuse gas that is spread over a large range in velocity, as shown by slices 6--8 (Fig.\ \ref{fig:slices}). The situation is different in the northern part of M81 and the connection with M82. Here the high values indicate the presence of multiple components at different velocities along the line of sight. This is explains the extremely high second-moment values of $>100$ \kms found about $10'$ to the north of the center of M81. Here, multiple, separate components with a maximum separation of $\sim 260$ \kms are present. Slices 12--14 (Fig.\ \ref{fig:slices}) show this region at offsets between $\sim +0.1^{\circ}$ and $\sim +0.3^{\circ}$. To disentangle these multiple components, most likely different physical structures along the same line of sight, requires a full 3D structural and kinematic model of all the \HI, both the rotating disk of M81 and the various tidal filaments wrapping around M81 and its satellite galaxies. Athough the features just discussed are the most prominent, similar structures can be found at many places within the group; see, e.g., slice 9 at $-0.4^{\circ}$ and slice 7 at $0.0^{\circ}$. Some of the high second-moment value clumps seen in the bridge between M81 and NGC 3077 are caused by \HI clouds at different velocities from the main \HI bridge features. These clouds are in the tidal structures, well away from the main galaxies. In contrast, the high values in the immediate proximity of NGC 3077 are intrinsic again, and indicate the presence of a gas component spread over a large range in velocity, as shown by the feature in slice 4 (Fig.\ \ref{fig:slices}) at $\sim -0.55^{\circ}$. In addition to the larger-scale phenomena described above, several interesting individual smaller-scale features can be made out in the position-velocity slices. One example is the high-velocity feature visible in slice 16 at an offset of $+0.14^{\circ}$ with anomalous velocities of up to $\sim 100$ \kms. It is located in the interarm region just south of the inner of the two prominent northern \HI spiral arms of M81. Ultra-violet GALEX \citep{gildepaz07} and H$\alpha$ \citep{greenawalt98} data, as well as the stellar density map discussed in Sect.\ \ref{sec:sf}, show the presence of star formation in the area, and it is likely that the feature is associated with a recent star formation event. Several similar, but less prominent features are visible in the same area. \subsection{Comparison with GBT data\label{sec:GBT}} As noted in the Introduction, the survey area presented here was also observed with the GBT, as published in \citet{chynoweth08}. In Sect.\ \ref{sec:zero} we described using the GBT data to correct for the missing spacings in the VLA data. As the zero-spacing corrected cube is a combined data set with the resolution of the interferometry data and the flux of the single-dish data, it in principle contains no new information that is not already present in the two source data sets. It is therefore instructive to compare these original data sets to get a understanding of where the various features visible in the moment maps originate. Figure \ref{fig:GBT} displays an overlay of the \citet{chynoweth08} data on top of our D-array mosaic. The GBT beam size is $10.1' \times 9.4'$, with a major axis position angle of $53^{\circ}$. This translates to a physical size of $10.7 \times 9.9$ kpc. The column density sensitivities of both data sets are similar. \citet{chynoweth08} quote a $1\sigma$, 1 channel (5.2 \kms) sensitivity of $2.5 \cdot 10^{17}$ cm$^{-2}$. Smoothing our D-array data to the same velocity resolution yields a sensitivity of $3.5 \cdot 10^{17}$ cm$^{-2}$. In Fig.\ \ref{fig:GBT}, we therefore chose identical contour levels for both data sets. We see a good correspondence between the \HI distribution as observed by the VLA and the GBT. The only major discrepancy is immediately to the south-west of M81, where the GBT data show an extended north-south trough that is not visible in the VLA data. This trough is artificial and entirely due to the interpolation over the blanked Galactic emission that was used in the \citet{chynoweth08} paper to construct the moment map. \begin{figure*} \centering \includegraphics[width=0.9\hsize]{m81na_DplusGBT_mom0_ref.pdf} \caption{Comparison of our natural-weighted D-array zeroth-moment map with the GBT zeroth-moment map from \citet{chynoweth08}. The D-array data are shown as grayscale and black contours, the GBT data as dark-blue contours. The grayscale runs from 0 (white) to 8 (black) Jy beam$^{-1}$ \kms. The GBT contour levels are shown at 1500 (thick contour), 3000, 7500, 15000, 30000, 75000, 150000 and 300000 kJy beam$^{-1}$ \kms which corresponds to $(4.5, 9.0, 22.5, 45, 90, 225, 450, 900) \cdot 10^{18}$ \cm. The D-array mosaic contour values were chosen to have the same column densities, and are shown at $0.0329 \cdot (1, 2, 5, 10, 20, 50, 100, 200)$ Jy beam$^{-1}$ \kms. The full GBT survey area is shown. The mosaic 50 percent sensitivity contour is shown as the dotted curve. The VLA beam is indicated in the bottom-left corner, the GBT beam in blue in the bottom-right corner. Numbers and letters indicate the cloud complexes described in Sect.\ \ref{sec:GBT} and Sect.\ \ref{sec:clouds}. \label{fig:GBT}} \end{figure*} The low-column density filament seen in the GBT data near $10^h06^m$, $+68^{\circ}00'$, which is resolved into clumps with the VLA, extends to the edge of the GBT survey area, suggesting there may be additional HI clouds beyond the VLA survey area. We will return to this in Sect.\ \ref{sec:clouds}. The feature in the GBT data located near $10^h11^m$, $+69^{\circ}30'$ has a velocity of $\sim -110$ \kms as detected in the original GBT data cube. At this position and velocity it is also marginally visible in the VLA mosaic. It is not included in the VLA moment map as its peak flux is below $3\sigma$ and its location close to the 50 percent sensitivity contour makes identification more uncertain based on the VLA data alone. The reverse situation is true for M81 Dw B (UGC 5423), a dwarf galaxy which is clearly detected in the VLA mosaic (at $10^h05^m30^s, +70^{\circ}21'52''$), but is not visible in the GBT moment map. Inspection of the GBT data cube shows a marginal detection at the correct position and velocity, but it is located in the edge region of the GBT map where the noise is enhanced and many artificial features of similar extent and brightness are present. It is striking that, especially towards the south, the low-column density arms and streams detected by the GBT break up in clouds and clumps as observed by the VLA. An interesting question is whether these clouds represent all the \HI seen in the lower-resolution GBT data, or whether they form the high column density tip of the iceberg in a surrounding lower column density component. To address this, we compare the \HI masses of a number of these clouds, selecting only objects that are far enough away spatially and spectrally from bright \HI emission that may affect the object fluxes. As noted above, we consider the VLA and GBT data sets separately to better trace the origin of emission features. The zero-spacing corrected data is (for individual low-flux objects) less suited due to the various contributions from, amongst others, flux scale factors, masking and difference in velocity resolution that are difficult to quantify. One example of a low-mass \HI cloud is the isolated cloud to the NW of M82, which \citet{chynoweth08} denote as ``Cloud 1'' (indicated as ``1'' in Fig.\ \ref{fig:GBT}). We find an \HI mass of $3.2 \cdot 10^6$ \msun, which is a factor 4.6 less than found by \citet{chynoweth08}. (The other clouds discussed in that paper are affected by Galactic emission and therefore not discussed here.) Other examples can be found to the south of the triplet. These are indicated in Fig.\ \ref{fig:GBT} as ``A'' and ``B''. Complex A consist of two small clouds in the VLA data, and corresponds to single overdensity in the GBT map. Cloud B is a single cloud in the VLA data, corresponding with a single overdensity in the GBT map. The two clouds A have a total mass of $4.8 \cdot 10^6$ \msun. The mass of the corresponding GBT peak is $1.2 \cdot 10^7$ \msun, or a factor 2.5 higher. Cloud B has a mass of $3.2 \cdot 10^6$ \msun in the VLA data, and a mass of $1.2 \cdot 10^7$ \msun in the GBT map. This is a factor 3.6 different. For completeness, we did check the combined data, and for the \HI clouds discussed here found masses intermediate to the GBT and VLA masses. In these particular comparisons we can be confident that the GBT is detecting excess \HI not seen in the VLA data. This indicates that the low-column density filaments seen in the GBT data are not simply the VLA \HI clouds observed at low resolution, but that they consist of substantial amounts of low-column density \HI in which the clouds are embedded. \subsection{Comparison of HI masses: GBT vs.\ VLA\label{sec:masses}} \subsubsection{Total \HI mass} The previous section established that some of the isolated clouds seen in the VLA data are embedded in a low-column density \HI component detected by the GBT. We can check if this is more generally the case by comparing the respective \emph{total} \HI masses found in both data sets. As discussed above, we compare the individual VLA and GBT sets, rather than the zero-spacing-corrected data. We use the moment maps to determine the total \HI mass detected in the mosaic area. For the VLA C+D natural-weighted data we find a total flux of 2234.4 Jy \kms. Using the assumed distance of 3.63 Mpc, this gives a total HI mass of $6.94 \cdot 10^9$ \msun. The D-array data gives a slightly higher value of 2489.0 Jy \kms. This translates into an HI mass of $7.74 \cdot 10^9$ \msun. These values are $\sim 35$ percent higher than the total \HI masses given in \citet{yun99} and \citet{appleton81}. This discrepancy is likely due to a combination of different survey volumes, column density sensitivities and Galactic foreground corrections. We show below that the latter alone can already amount to differences of $\sim 30$ percent in the total fluxes. For the GBT data of the M81 triplet, \citet{chynoweth08} report a total \HI mass of $10.46 \cdot 10^9$ \msun. This is substantially higher than the previous literature values, but also $\sim 35$ percent higher than the value derived from our D-array data. \begin{figure} \centering \includegraphics[width=0.9\hsize]{fieldflux.pdf} \caption{Comparison of integrated intensity profiles of the observed area. The thick full profile shows the integrated flux based on our D-array mosaic. The thin dashed profile show the integrated flux derived from the \citet{chynoweth08} GBT observations. The light-gray area indicates the velocity range over which \citet{chynoweth08} have interpolated their data. The dark-gray areas indicate the velocity ranges which we omitted from our data due to the Galactic emission. Note the different behavior of the profiles at positive velocities, probably indicating the presence of diffuse gas associated with M82. \label{fig:fieldflux}} \end{figure} \citet{chynoweth08} note that their data were affected by Galactic foreground emission between $-85$ and $+25$ \kms. They replaced the data in these velocity channels with a linear interpolation based on the channels immediately adjacent to this range. From the global \HI profile of the full area as shown in Fig.\ 2 of \citet{chynoweth08}, and also reproduced in Fig.\ \ref{fig:fieldflux}, we find that this interpolated part of the spectrum constitutes 29 percent of total flux they report. The higher velocity resolution of our data allows us to gauge the accuracy of this correction. We overplot the global profiles of the full mosaic area in Fig.\ \ref{fig:fieldflux}. The D-array fluxes in the interpolated region of the GBT spectrum are $\sim 30$ percent lower than the GBT interpolations. It is, however, not trivial to correct the GBT \HI mass on the basis of this. Fig.\ \ref{fig:fieldflux} shows that at negative velocities the GBT and D-array fluxes agree very well with each other, whereas at positive velocities the GBT has detected substantially more flux than the D-array. Note that, as discussed in Sect.\ \ref{sec:deconv}, the behaviour of detected flux as a function of clean depth is identical for channel maps with positive and negative velocities, so that the difference is not due to different relative importance of uncleaned flux in these channel maps. In other words, at negative velocities the D-array observations have managed to detect almost all of the \HI flux (mostly associated with the southern part of M81), while the extra GBT flux at positive velocities (associated with the very northern part of M81, with M82, and with the transition region in between) indicates the presence of an extended low-column density HI component that is not present in the southern part of the triplet. Fig.\ \ref{fig:fieldflux} shows that the difference between the integrated spectra is largest around the peak at $\sim 125$ \kms, and the ``missing'' gas is thus most likely associated with the already detected diffuse \HI around M82. For a full synthesis observation, the largest angular scale the VLA is sensitive to at 1.4 GHz is $\sim 16'$, while for a single snapshot observation this is $\sim 8'$. This range of scales is mostly larger than the GBT beam. So while the length of the integration time per pointing may have some influence on the recovery of structures larger than $\sim 10'$, it is more likely that the difference between the integrated spectra is due to surface brightness sensitivity limitations. We also considered the integrated spectrum of the zero-spacing corrected C+D data, and found a good match with the GBT profile at positive velocities. However, at negative velocities this profile overestimates significantly overestimates the flux compared to the GBT profile. The situation is reverse when using D-array corrected data. We did test the combination using various different velocity ranges to determine the scale factor, but found this did not affect the outcomes. Due to the uncertainty in relative flux scales of these combined data, we therefore do not consider the zero-spacing corrected data further in this context. A full study of the relative fluxes found in the VLA and GBT data as a function of resolution is beyond the scope of this paper. The presence of extra \HI at positive velocities and its absence at negative velocities, with the transition happening exactly in the region affected by Galactic emission, makes deriving a more accurate correction for Galactic foreground correction difficult. Fig.\ \ref{fig:fieldflux} suggests that, with various extra components and corrections cancelling each other, the \emph{total} \HI mass estimate given in \citet{chynoweth08} is probably an overestimate, but likely by not more than $\sim 5-10$ percent. Taking all this into account, we can therefore conclude that the GBT data shows the presence $\sim 25$--30 percent more \HI than our VLA D-array mosaic. \subsubsection{\HI masses of the triplet galaxies} The \HI masses of the major triplet galaxies are more difficult to determine and compare, as the extent of their \HI disks cannot be well determined due to the presence of the tidal \HI component. \citet{chynoweth08} compare the \HI masses of the three major triplet galaxies as derived from the GBT data, the \citet{yun99} data and the \citet{appleton81} data. The latter are also based on single-dish data. \citet{appleton81} define the \HI masses of the galaxies as the mass measured within the Holmberg ellipse of the respective objects and \citet{chynoweth08} follow that definition. As noted by \citet{appleton81}, this choice of radius likely underestimates the \HI masses. In M81 the Holmberg radius only encompasses the inner, high-density spiral arms; in M82 it misses much of the extra-planar gas, while in NGC 3077 the main \HI component falls outside the Holmberg radius. Nevertheless, in the absence of any clear physical indicators, other choices would be equally arbitrary. We here apply the same procedure to our D-array data, using the parameters given in Table 1 of \citet{appleton81}. To get an estimate of the uncertainty in the masses, we also derive the \HI masses within a radius of $2R_{25}$, with the $R_{25}$ values taken from HyperLEDA, but still adopting the orientations given in \citet{appleton81}. Larger radii are impractical as the disks of M81 and M82 start overlapping at $\sim 2.5R_{25}$. The masses are listed in Table \ref{tab:masses} and compared with the \citet{chynoweth08}, \citet{yun99} and \citet{appleton81} masses. For M81, an alternative definition for the HI mass could be made by using the transition radius between the ordered motion of the inner disk and the more disturbed motion beyond that (cf.\ the velocity field in Fig.\ \ref{fig:mom1}). This radius turns out to be almost exactly equal to the Holmberg radius, so this mass is equal to the one already listed in Table \ref{tab:masses}. There is a large spread in \HI mass values for each galaxy. We have already established that Galactic foreground corrections introduce an extra uncertainty in the \citet{chynoweth08} data, mostly due to the lower velocity resolution. It is likely that a similar uncertainty applies to the \citet{yun99} and \citet{appleton81} masses as well. A full and proper determination of the ``true'' \HI masses of the three main galaxies would thus require a further in-depth analysis and comparison of all these effects. \begin{deluxetable}{lrrrrr} \tabletypesize{\scriptsize} \tablewidth{0pt} \tablecaption{Comparison of \HI masses\label{tab:masses}} \tablehead{\colhead{Galaxy} & \colhead{$M_{\rm HI}$} & \colhead{$M_{\rm HI}$} & \colhead{$M_{\rm HI}$} & \colhead{$M_{\rm HI}$}& \colhead{$M_{\rm HI}$} \\ \colhead{} & \colhead{(Ho)} & \colhead{($2R_{25}$)} & \colhead{(Ch08)} & \colhead{(Y99)} & \colhead{(Ap81)}\\[2pt] \colhead{} & \multicolumn{4}{c}{$(\times 10^9\,M_{\odot})$}} \startdata M81 & 2.29 & 2.79 & 2.67 & 2.81 & 2.19 \\ M82 & 0.44 & 0.75 & 0.75 & 0.80 & 0.72 \\ NGC 3077 & 0.23 & 0.31 & 1.01 & 0.69 & 1.00 \\ Total\tablenotemark{a} & 7.74 & --- & 10.46 & 5.6\phantom{0} & 5.4\phantom{0}\\ \enddata \tablenotetext{a}{Value refers entire observed area.} \tablecomments{(Ho): \HI mass within Holmberg radius from D-array mosaic; ($2R_{25}$): \HI mass within $2R_{25}$ radius from D-array mosaic; (Ch08): \HI mass from \citet{chynoweth08}; (Y99): \HI mass from \citet{yun99}; (Ap81): \HI mass from \citet{appleton81}.} \end{deluxetable} \subsection{The South-East clouds\label{sec:clouds}} In Sect.\ \ref{sec:GBT}, we compared the \HI masses of the overdensities ``A'' and ``B'' seen in the GBT map in Fig.\ \ref{fig:GBT}. These overdensities correspond with a number of more compact clumps as observed with the VLA. The GBT map also shows that the \HI filament containing the overdensities extends all the way to the south-east corner of the observed area. Our VLA mosaic does not extend this far, but we can use additional observations to explore this area at higher resolution. We use the data from project AW683 which consists of a 16-pointing mosaic observed in C- and D-array and partly overlapping with the SE corner of our mosaic. A description of these data is given in Sect.\ \ref{sec:se-data}. \begin{figure*} \centering \includegraphics[width=0.9\hsize]{m81na_SEclouds_mom0.pdf} \caption{Comparison of emission detected in the D-array AW683 mosaic, the GBT observations and our D-array mosaic. Grayscale shows the emission detected between $-120$ and $-80$ \kms in the AW683 mosaic. The grayscale runs from 0 (white) to 0.65 (black) Jy beam$^{-1}$ \kms. The corresponding black contour shows the $1.2 \cdot 10^{19}$ \cm column density level. Red and blue contours show the GBT and VLA emission at identical repective column density levels of $(4.5,22.5,90,225,450)\cdot 10^{18}$ cm$^{-2}$ (cf.\ Fig.\ \ref{fig:GBT}). The different \HI distribution in the M81-NGC 3077 bridge is due to the different velocity ranges displayed. The blue dotted curve indicated the 50 percent sensitivity level of our mosaic, the black curve that of the 15-pointing AW683 mosaic. The red dashed lines show the extent of the GBT survey area. Beams are indicated at the bottom using the respective contour colours. The letters indicate the cloud complexes described in Sect.\ \ref{sec:clouds}. \label{fig:clouds}} \end{figure*} Inspection of the AW683 data cube clearly shows the presence of clouds A and B. We show the zeroth-moment map derived from these data in Fig.\ \ref{fig:clouds}, in combination with the corresponding maps from the GBT and our mosaic. It is clear that the low-column density structure detected by the GBT at the edge of the survey area coincides with a clump of \HI in the extended area mosaic. For this clump, we find a mass of $6.3 \cdot 10^6$ \msun, comparable to that of the A and B clumps. The velocities of these clumps are all close to that of the more prominent \HI features in this general area, suggesting that they are tidal debris from the triplet interactions. There are no other new \HI clumps of comparable flux in this area. We find a number of marginal detections of smaller clumps, but deeper observations will be needed to confirm whether these are real. The \HI masses of the SE clumps are larger than those of the smallest dwarf galaxies that have been detected in \HI in the Local Volume. An example is Leo P, a low-mass, gas-dominated galaxy with an \HI mass of $8.1 \cdot 10^5$ \msun \citep{mcquinn15}. It, and other galaxies like it, are known to contain dark matter \citep{bernstein15}, and potentially could help solve some of the problems that exist in small-scale $\Lambda$CDM, such as the ``missing satellites'' problem (see, e.g., \citealt{kauffmann93} for an early discussion). Similarly, ultra-compact high-velocity clouds (UHVCs), which have similar \HI masses and sizes as the SE clouds, are thought to be candidate low-mass galaxies harbouring dark matter halos \citep{adams16}. An interesting question to explore is whether the SE clumps have properties consistent with low-mass galaxies or UHVCs. We extract integrated velocity profiles of clouds A and B from the D-array cube, where we treat cloud A as two separate objects, hereafter ``A east'' and ``A west''. We use the D-array zeroth-moment map as a mask to define the area over which to extract the profiles. We extracted profiles from both the masked cube (used to create the moment maps) and the unmasked cube. The three sets of profiles are shown in Fig.~\ref{fig:profs}. The profiles are narrow and well-defined. For the A-clouds, the masked and unmasked profiles agree well with each other. For the B-cloud, the unmasked profile is significantly wider than the masked profile. Inspection of the cube shows that this extra emission is due to a nearby diffuse \HI feature, though it is not clear whether this emission belongs to the cloud (and is extra confirmation that these clouds do not exist in isolation). We measure the velocity widths $W_{20}$ and $W_{50}$ of the masked and unmasked profiles at 20 percent and 50 percent of the peak flux. These are listed in Table \ref{tab:mdyn}. We use these widths to calculate indicative dynamical masses $M_{\rm dyn}\sin i = (W/2)^2 R / G$ of these clouds, where $W$ is the velocity width $W_{20}$ or $W_{50}$, $R$ is the radius of the cloud, $G$ is the gravitational constant and $i$ the inclination of the cloud. For the radius we simply use half of a cloud's extent along its major axis. These radii are also listed in Table \ref{tab:mdyn}, along with the resulting indicative dynamical masses. These values assume the clouds are fully gravitationally (rotationally) supported. Other estimates for the dynamical mass, which assume that the clouds are fully or partially pressure supported, tend to give higher values for $M_{\rm dyn}$, so the values given in Table \ref{tab:mdyn} are lower limits. Comparing the \HI masses with the indicative dynamical masses (we find no evidence for a stellar component in SDSS images), we find that the dynamical to \HI mass ratios are high: for the $W_{20}$ values we find an average ratio of $59.8 \pm 21.7$ (where we have omitted the value of the unmasked B-cloud profile), and for the $W_{50}$ values we find a ratio of $23.7 \pm 11.4$. Using the GBT \HI masses instead, would decrease these ratios by a factor $\sim 3$ (cf.\ Sect.\ \ref{sec:clouds}), but this would still give ratios substantially larger than unity. At first glance, these results would indicate that the clouds are dark-matter-dominated, and good candidates for low-mass galaxies. Indeed, the velocity widths, \HI masses and dynamical masses are fully consistent with those of the UHVC candidates and the dwarf galaxies Leo T and P, as described in \citet{adams16}. \begin{figure} \includegraphics[width=0.8\hsize]{cloudprofs.pdf} \caption{Velocity profiles of clouds A east, A west and B, integrated over their area as shown in Fig.\ \ref{fig:GBT}. Full profiles are derived from the unmasked D-array cube, dashed profiles from the masked version. The peak at $\sim -50$ \kms is due to Galactic foreground emission. \label{fig:profs}} \end{figure} \begin{deluxetable*}{llccccrr} \tabletypesize{\scriptsize} \tablewidth{0pt} \tablecaption{Comparison of properties of \HI clouds\label{tab:mdyn}} \tablehead{\colhead{Cloud}&\colhead{Type} & \colhead{$M_{\rm HI}$} & \colhead{$R_{\rm HI}$} & \colhead{$W_{20}$} & \colhead{$W_{50}$}& \colhead{$M_{\rm dyn}^{W20}\sin i$} & \colhead{$M_{\rm dyn}^{W50}\sin i$}\\[2pt] \colhead{} & \colhead{} & \colhead{$(\times 10^6$\,\msun)} & \colhead{(kpc)} & \colhead{(\kms)} & \colhead{(\kms)} & \colhead{($\times 10^6$\,\msun)} & \colhead{$(\times 10^6$\,\msun)}} \startdata A east & masked & 2.0 & 2.4 & 25 & 15 & 87.2 & 31.4\\ & unmasked & 2.0 & 2.4 & 34 & 24 & 161.3 & 80.3\\ A west & masked & 2.8 & 3.1 & 22 & 14 & 87.2 & 35.3\\ & unmasked & 2.8 & 3.1 & 32 & 20 & 184.5 & 72.1\\ B & masked & 3.2 & 3.3 & 36 & 17 & 248.6 & 55.4\\ & unmasked & 3.2 & 3.3 &(58)\tablenotemark{a}& 24 & 645.2 & 110.5 \\ \enddata \tablenotetext{a}{This value is probably affected by emission not belonging to the cloud.} \end{deluxetable*} There is, however, one big difference. The clouds discussed here are not isolated, but part of a larger, tidal structure. In contrast, the UHVC candidates and Leo T and P galaxies are isolated. Interpreting their velocity width is therefore less ambiguous than for clouds A and B whose velocity widths could also be explained by processes other than rotation. For example, the tidal arm in which the clouds are embedded shows a north-south velocity gradient of $\sim 50$ \kms, and part of this gradient could be reflected in the clouds. Streaming motions of the gas in the arm are a possibility as well. Finally, as discussed earlier, it is not clear whether the clouds are separate, isolated physical entities. More likely they are density enhancements in the tidal arm that could possibly evolve into tidal dwarfs. The fact that the clouds are only observed in or near tidal structures, and not in the rest of the mosaic volume (which has after all been observed to the same depth and sensitivity) is another argument against the interpretation of the velocity widths as evidence for these clouds being dark-matter-dominated objects. We therefore find no unambiguous evidence for dark-matter dominated clouds in our survey volume. We have presented a new, high-resolution, 105-pointing \HI mosaic of $3^{\circ} \times 3^{\circ}$ centered on the M81 triplet, M81, M82 and NGC 3077 obtained with the VLA in its C- and D-configurations. This is the first radio synthesis data set that maps the entire volume of the triplet at high spatial and spectral resolution. These data can serve as input for further sophisticated modeling of the interaction and evolution of the triplet (e.g., \citealt{oehm17}). Our main results are summarized as follows: \begin{itemize} \item We do not find a large population of free-floating \HI clouds down to an \HI mass limit of $\sim 10^4$ \msun. While small clouds and \HI complexes are detected they only occur close (spatially and spectrally) to the main \HI tidal features of the triplet, suggesting they are all debris of the interaction that shaped the triplet. A detailed investigation of the \HI masses of these clouds show that they are likely embedded in extended low-column density tidal features. \item Comparison with a sensitive GBT \HI mosaic of the same area by \citet{chynoweth08} shows that the VLA mosaic has detected most of the \HI in the southern part of the mosaic (i.e., the southern part of M81 and NGC 3077). In the northern part of the mosaic (M82 and the the M81-M82 transition region) the GBT has detected a significant excess of flux most likely associated with M82. This probably indicates the presence of a low-column density \HI component associated with the M82 outflows. \item Using additional data we show that low-column density features detected by the GBT beyond the south-eastern edge of our VLA mosaic are resolved into clouds. In turn, we detect a small \HI cloud beyond the extent of the GBT mosaic, suggesting that a low-column density \HI tail resulting from the interaction may extend further south-east beyond the areas mapped by the VLA and GBT. \item A comparison of the velocity widths and \HI masses of these clouds seems consistent with them being dominated by dark matter. Their properties are, in that regard, very similar to those of UHVCs or the smallest gas-rich dwarf galaxies. However, given their association with tidal features it is more likely that the velocity widths should not be interpreted in terms of gravitational support. It is possible that these clouds will eventually evolve in tidal dwarf galaxies. \item We compare the observed \HI column densities with a Subaru Suprime-Cam map of the resolved young stellar population of the triplet. The majority of the OB star distribution is found within the $6 \cdot 10^{20}$ cm$^{-2}$ contour. After taking projection effects into account, this is consistent with theoretical predictions for the star formation threshold surface density value. \item We derive the distribution of $\Delta V_{90}$ of the \HI profiles and compare these with that observed for DLAs to investigate whether the triplet can be regarded as a local version of the high-$z$ objects that cause the DLA absorption. We find that the peaks of the distributions coincide at low $\Delta V_{90}$ values, consistent with the interpretation that the low $\Delta V_{90}$ values occur in objects that will evolve in neutral gas disks. High $\Delta V_{90}$ values are found around M82, and these cover the entire range in $\Delta V_{90}$ found in DLAs up to 200 \kms. This is consistent with high $\Delta V_{90}$ values being caused by feedback, outflows or multiple components along the line of sight. For the triplet to also reproduce the relative fraction of high- versus low- $\Delta V_{90}$ values found in DLAs, the frequency of the values found near M82 needs to be increased by a factor 2-5, presumably indicating that in DLAs the relative importance of feedback and outflow effects is somewhat more important than in the triplet. \end{itemize} | 18 | 8 | 1808.02840 |
1808 | 1808.10452_arXiv.txt | The radio and far-infrared luminosities of star-forming galaxies are tightly correlated over several orders of magnitude; this is known as the far-infrared radio correlation (FIRC). Previous studies have shown that a host of factors conspire to maintain a tight and linear FIRC, despite many models predicting deviation. This discrepancy between expectations and observations is concerning since a linear FIRC underpins the use of radio luminosity as a star-formation rate indicator. Using \lofar \lofarfreq, \first \firstfreq, and \herschel infrared luminosities derived from the new \lofarhatlas catalogue, we investigate possible variation in the monochromatic (250\,\micron) FIRC at low and high radio frequencies. We use statistical techniques to probe the FIRC for an optically-selected sample of 4,082 emission-line classified star-forming galaxies as a function of redshift, effective dust temperature, stellar mass, specific star formation rate, and mid-infrared colour (an empirical proxy for specific star formation rate). Although the average FIRC at high radio frequency is consistent with expectations based on a standard power-law radio spectrum, the average correlation at \lofarfreq is not. We see evidence for redshift evolution of the FIRC at \lofarfreq, and find that the FIRC varies with stellar mass, dust temperature and specific star formation rate, whether the latter is probed using \magphys fitting, or using mid-infrared colour as a proxy. We can explain the variation, to within $1\sigma$, seen in the FIRC over mid-infrared colour by a combination of dust temperature, redshift, and stellar mass using a Bayesian partial correlation technique. | \label{sec:intro} The far-infrared luminosities of star-forming galaxies have long been known to correlate tightly and consistently with synchrotron radio luminosity across many orders of magnitude in infrared and radio luminosities, independent of galaxy type and redshift \citep{Kruit1971Observations,Jong1985Radio,Condon1991Correlations,Yun2001Radio,Bell2003Estimating,Bourne2011Evolution}. The existence of some relation should not be surprising since the basic physics relating emission in each waveband to the presence of young stars is well understood. Young stars heat the dust within their surrounding birth clouds, which radiate in the infrared \citep{Kennicutt1998Star,Charlot2000Simple}. The supernovae resulting from the same short-lived massive stars accelerate cosmic rays into the galaxy's magnetic field thereby contributing non-thermal radio continuum emission over $\approx 10^8$ years \citep{Blumenthal1970Bremsstrahlung,Condon1992Radio,Longair2011High}. However, the fact that the Far-Infrared Radio Correlation (FIRC) has consistently been found to have low scatter \citep{Helou1985Thermal,Jong1985Radio,Condon1992Radio,Lisenfeld1996FirRadio,Wong2016Determining} is surprising. Such tight linearity is consistent with a simple calorimetry model \citep{Voelk1989Correlation}, whereby cosmic ray electrons lose all of their energy before escaping the host galaxy and where all UV photons are absorbed by dust and re-radiated in the infrared. This results in synchrotron radiation being an indirect measure of the energy of the electron population and infrared luminosity being proportional to young stellar luminosity. Therefore, assuming calorimetry, the ratio of these two measures will remain constant as they are both dependent on the same star formation rate. The FIRC can therefore be used to bootstrap a calibration between a galaxy's star formation rate and its radio luminosity \citep[\eg][]{Condon1992Radio,Murphy2011Calibrating} -- but only if there is no additional contribution from AGN. The physics required to model the FIRC is complex. For example, the timescale of the electron synchrotron cooling that produces the radio emission is thought to be longer than the timescale for the escape of those electrons \citep{Lisenfeld1996Quantitative,Lacki2010Physics} for normal spirals, and starlight is only partially attenuated in the UV \citep{Bell2003Estimating}. Therefore, it is reasonable to suppose that the calorimetry interpretation must be at least partially inaccurate and that there should be some observable variation in the FIRC over the diverse population of star-forming galaxies. In particular, due to their strong magnetic fields, we expected starburst galaxies to be good calorimeters and therefore have a correlation with a slope that is much closer to one than other star-forming galaxies \citep{Lacki2010Physics}. However, since synchrotron emission depends strongly on magnetic field strength, the assumption about how this changes with galaxy luminosity is crucial to explain the correlation. Alternatives to the calorimetry model have also been proposed, \eg (i) the model of \citet{Niklas1997New}, where the FIRC arises as the by-product of the mutual dependence of magnetic field strength and star-formation rate upon the volume density of cool gas, and (ii) \citet{Schleicher2016StarForming}, where the FIRC is based on a small-scale dynamo effect that amplifies turbulent fields from the kinetic turbulence related to star formation. There are a number of reasons to expect the FIRC to vary with the parameters that control synchrotron and dust emission, but it seems that infrared and radio synchrotron must both fail as star formation rate indicators in such a way as to maintain a tight and linear relationship over changing gas density. The model detailed by \citet{Lacki2010Physicsa} and \citet{Lacki2010Physics} suggests that although normal galaxies are indeed electron and UV calorimeters, conspiracies at high and low surface density, $\Sigma_g$, contrive to maintain a linear FIRC. At low surface density, many more UV photons escape (and therefore lower observed infrared emission) due to decreased dust mass but at the same time, because of the lower gravitational potential, more electrons escape without radiating all their energy, decreasing the radio emission. Meanwhile, at high surface densities, secondary charges resulting from cosmic ray proton collisions with ISM protons become important \citep{Torres2004Theoretical,Santamaria2005High}. Synchrotron emission from those electrons and positrons may dominate the emission from primary cosmic ray electrons. However, the FIRC is maintained due to the increased non-synchrotron losses from bremsstrahlung and inverse Compton scattering at higher densities. These conspiracies rely on fine tuning of many, sometimes poorly known, parameters in order to balance the mechanisms that control the linearity of the FIRC. If we expect variation over star-forming galaxies due to differences in gas density, stellar mass, and redshift (to name a few), then we should probe the FIRC over known star-forming sequences such as those found in colour-magnitude \citep{Bell2004Nearly} and mid-infrared colour-colour diagrams \citep[\eg][]{Jarrett2011SpitzerWise,Coziol2015Comparing}, and the star formation rate -- stellar mass relation \citep{Brinchmann2004Physical,Noeske2007Star,Peng2010Mass,Rodighiero2011Lesser}. Naively, we might also expect some variation of the FIRC with redshift. At the very least, radio luminosity should decrease with respect to infrared luminosity due to inverse Compton losses from cosmic microwave background (CMB) photons \citep{Murphy2009FarInfraredRadio}. The CMB energy density increases proportional to $(1+z)^4$ \citep{Longair1994High}, so the ratio of infrared to radio luminosity should noticeably increase with redshift even at relatively local distances, assuming a calorimetry model and that CMB losses are significant. However, this is one of the key areas of dispute between different observational studies. While the many works find no evidence for evolution \citep[\eg][]{Garrett2002FirRadio,Appleton2004Far,Seymour2009Investigating,Sargent2010VlaCosmos}, there are exceptions \citep[\eg][]{Seymour2009Investigating,Ivison2010FarInfraredRadio,Michaowski2010Rapid,Michaowski2010Cosmic,Basu2015RadioFarInfrared,Rivera2017Lofar,Delhaize2017VlaCosmos}. Particular among those studies, \citet{Rivera2017Lofar} find a significant redshift trend at both \lofarfreq and \firstfreq when using the \textit{Low Frequency Array} \citep[\lofar,][]{Haarlem2013Lofar} data taken over the Bo{\"o}tes field. The FIRC has been studied extensively at \firstfreq \citep{Jong1985Radio,Condon1991Correlations,Bell2003Estimating,Jarvis2010HerschelAtlas,Bourne2011Evolution,Smith2014Temperature} but rarely at lower frequencies. These low frequencies are particularly important, since new radio observatories such as \lofar are sensitive in the $15-200\,\mathrm{MHz}$ domain, where at some point the frequency dependence of optical depth results in the suppression of synchrotron radiation by free-free absorption \citep{Schober2017Tracing}, causing the radio SED to turn over. As a result, there will be some critical rest-frame frequency below which we can expect a substantially weaker correlation between a galaxy's radio luminosity and its star formation rate.\footnote{This frequency at which a galaxy's radio SED turns over will depend heavily upon gas density and ionisation, and so we expect it to vary from galaxy to galaxy.} Moreover, at the higher frequencies probed by \textit{Faint Images of the Radio Sky at Twenty centimetres} \citep[\first,][]{Becker1995First} (\firstfreq), there may be a thermal component present in the radio emission \citep{Condon1992Radio}, which tends to make the correlation between infrared and higher radio frequencies more linear. However, due to the poor sensitivity of \first to star-forming galaxies with low brightness temperatures (galaxies with $T_{\textrm{bright}}<10\mathrm{K}$ will not be detected by \first), we cannot expect the thermal components of detected sources to help linearise the FIRC at \firstfreq. At low frequencies, these effects become less important and so the perspective they provide is useful in disentangling the effect of thermal contributions and lower luminosity galaxies on the FIRC. Given the potential ramifications for using low-frequency radio observations as a star formation indicator, this possibility must be investigated. Indeed, \citet{Gurkan2018LofarHAtlas} have found that a broken power-law is a better calibrator for radio continuum luminosity to star-formation rate, implying the existence of some other additional mechanism for the generation of radio-emitting cosmic rays. Furthermore, lower radio frequencies probe lower-energy electrons, which take longer to radiate away their energy than the more energetic electrons observed at 1.4\,GHz, and this results in a relationship between the age of a galaxy's electron population and the radio spectral index \citep{Scheuer1968Radio,Blundell2001Spectral,Schober2017Tracing}. Therefore, even if the FIRC is linear at high frequencies due to some conspiracy, this will not necessarily be the case at low frequencies. An investigation of the FIRC at low frequency will test models of the FIRC which rely on spectral ageing to maintain linearity \citep[\eg][]{Lacki2010Physics}. Combined with the fact that radio observations are impervious to the effects of dust obscuration, this makes low-frequency radio observations a very appealing means of studying star formation in distant galaxies, providing that the uneasy reliance of SFR estimates on the FIRC can be put on a more solid footing. The nature of the FIRC conspiracies varies over the type of galaxy and its star formation rate \citep{Lacki2010Physicsa}. The detection of variation in the FIRC over those galaxy types, or lack thereof, will provide important information about the models that have been constructed \citep[\eg][]{Lacki2010Physicsa,Schober2017Tracing}. Several methods are used to distinguish galaxy types for the purposes of studying the FIRC, particularly to classify these into star-forming galaxies and AGN such as BPT diagrams \citep{Baldwin1981Classification}, panchromatic SED-fitting with AGN components \citep{Berta2013Panchromatic,Ciesla2016Imprint,Rivera2016Agnfitter}, and classification based on galaxy colours. Among these, galaxy colours provide a readily accessible method to distinguishing galaxy types or act as proxies for properties such as star formation rate. Diagnostic colour-colour diagrams are commonplace in galaxy classification; infrared colours in particular have been widely used to distinguish between star-forming galaxies and AGN \citep{Lacy2004Obscured,Stern2005MidInfrared,Jarrett2011SpitzerWise,Mateos2012Using,Coziol2015Comparing}. In order to investigate the potential difference in the FIRC over normal galaxies as well as in starbursts we use the mid-infrared diagnostic diagram, (MIRDD, \citealt{Jarrett2011SpitzerWise}) . Constructed from the \textit{Wide-field Infrared Survey Explorer} \citep[\wise,][]{Wright2010WideField} \wisex and \wisey colours, SWIRE templates \citep{Polletta2006Chandra,Polletta2007Spectral} and GRASIL models \citep{Silva1998Modeling} can be used to populate the MIRDD with a range of galaxy types spanning a redshift range of $0 < z < 2$. This MIRDD not only distinguishes AGN and SFGs but also describes a sequence of normal star-forming galaxies whose star formation rate increases to redder colours. Past \firstfreq surveys such as \first and the \textit{NRAO VLA Sky Survey} \citep[NVSS, ][]{Condon1998Nrao} have been extremely useful in studying star formation, though there are inherent problems in using them to do this. NVSS is sensitive to extended radio emission on the scale of arcminutes. However, its sensitivity of $\sim 0.5$ m\jybeam and resolution of 45\,\asec means that it has trouble identifying radio counterparts to optical sources and its flux limit means that it will peferentially detect bright or nearby sources. \first has both a higher resolution and a higher sensitivity than NVSS (5\,\asec with $\sim 0.15$ m\jybeam). However, due to a lack of short baselines, \first resolves out the extended emission frequently present in radio-loud AGN and in local star-forming galaxies \citep{Jarvis2010HerschelAtlas}. This makes it difficult to remove galaxies dominated by AGN and to directly compare star-forming galaxies over different wavelengths. Meanwhile, \lofar offers the best of both worlds: a large field of view coupled with high sensitivity on both small and large scales and high resolution \citep{Haarlem2013Lofar} at frequencies between 30 and 230\,MHz. Operating at \lofarfreq, \lofar contributes a complementary view to the wealth of data gathered at higher frequencies. The sparsely examined low-frequency regime offered by \lofar combined with its increased sensitivity and depth relative to other low-frequency instruments allows us to probe the FIRC in detail, and to test predictions of its behaviour relative to relations at higher frequencies that we measure with \first. This study will analyse the nature of the FIRC at low and high frequencies and over varying galaxy properties. How does the FIRC evolve with redshift? Does it vary as a function of \wise mid-infrared colour? Do the specific star-formation rate (as fit by \magphys) and stellar mass impact these questions? We answer these questions for our data set and compare these metrics with those found at higher frequencies and with literature results using different selection criteria. This work uses the same base dataset as \citet{Gurkan2018LofarHAtlas}. The same aperture-corrected fluxes extracted from \herschel , \lofar, and \first images are used here. Our investigation differs from theirs in that we concentrate on the observed variation of the FIRC over dust properties whereas \citet{Gurkan2018LofarHAtlas} focus on the direct characterisation of radio star-formation rates. In Section~\ref{sec:data}, we describe our data sources and the method of sample selection. In Section~\ref{sec:methods} we outline our methods for calculating \kcorrection s, luminosities, and the methods used to characterise the variation of the FIRC. We present and discuss the results of these procedures in Section~\ref{sec:results}, and summarise our conclusions in Section~\ref{sec:conclusions}. We assume a standard $\Lambda$CDM cosmology with $H_0 = 71$\,km\,s$^{-1}$\,Mpc$^{-1}$, $\Omega_M = 0.27$ and $\Omega_\Lambda = 0.73$ throughout, and for consistency with \citet{Jarrett2011SpitzerWise}, all magnitudes are in the Vega system. | \label{sec:conclusions} We have used a catalogue of optically selected, BPT-classified star-forming galaxies from \citet{Gurkan2018LofarHAtlas} to study variation in the far-infrared radio correlation over redshift and other parameters. We calculate the monochromatic far-infrared radio correlation, parametrised as \q, for \lofarfreq and compare it to that found for \firstfreq, using forced aperture photometry. We obtained the photometry (fluxes were measured using 10 arcsec radius circular apertures centred on the optical positions) for all of these sources -- including those which are not formal detections at \lofar, \first, and \herschel wavelengths. To avoid introducing bias to our findings, we make no significance cuts on infrared or radio fluxes. Knowing about possible variation in the FIRC is of great importance, since a constant FIRC underpins the use of radio luminosity estimates as a star formation rate indicator. Our main results are summarised as follows: \begin{itemize} \item \q at \firstfreq for our sample is found to be consistent with previous studies \citep{Jarvis2010HerschelAtlas,Ivison2010FarInfraredRadio,Smith2014Temperature}. \item The FIRC for \lofarfreq is found not to be consistent with that for \firstfreq assuming a standard power law with spectral index of $-0.71$ (0.1 dex lower). \item We find evidence for a decreasing \q with redshift at \lofarfreq (gradient of $-1.0^{+0.2}_{-0.3}$). By comparing to the results of \citet{Molnar2018InfraredRadio}, we also find tentative evidence that the slope of this evolution becomes shallower with increasing frequency. An increase in radio luminosity of star-forming galaxies with redshift will be useful for high-redshift SFG detection, assuming that this evolution is maintained above $z=0.5$, as has also been suggested by FIRC studies conducted with \lofar at higher redshifts \citep[\eg][]{Rivera2017Lofar}. \item We corroborate the \q-temperature variation discovered by \mbox{\citet{Smith2014Temperature}} at high frequency. We find that this relation also applies at low frequency to within $1\sigma$, but only at temperatures above 20K. \item We find that \q varies across a two-dimensional mid-infrared colour-colour space, at both radio frequencies, and within the star-forming region defined by \citet{Jarrett2011SpitzerWise}. By using a hierarchical correlation model, we find that all of the correlation between \q with \wisex and \wisey colours can be attributed to the combined effects of the correlations that we measure between \q and stellar mass, redshift, and isothermal temperature, to within $1\sigma$. We note that the variation is not explained by redshift, temperature, or stellar mass alone but by all three in conjunction. \item Using the indicative locations of different galaxy types within the WISE colour-colour plot from \citet{Jarrett2011SpitzerWise} -- \eg spirals etc -- we see that the trend to lower \q appears to reflect the transition from spirals to LIRGs to starbursts. \q decreases with redder \wisex colour and with increasing specific star formation rate. Indeed, the lowest values of \q are seen in the region of the MIRDD occupied by the \citet{Polletta2007Spectral} starburst templates. Moreover, the region where LIRGs overlap with normal spirals ($3 < [4.6] - [12] < 4$) is the region where the largest gradient in \q (relative to WISE colour) is seen. \item To test the possible influence of AGN contamination on our results, we re-ran our analysis but this time included the BPT-classified AGN. The only significant change in our results was at the lowest dust temperatures, and lowest specific star formation rates; the other regions of parameter space, and therefore our conclusions, are unchanged. We can be confident, therefore, that our results are robust to the inclusion of detectable AGN, and it is tempting to attribute this variation to hitherto unknown physics of the FIRC. However, we cannot totally rule out the possibility that widespread low-level AGN have some influence (though we see no evidence of high ionisation and\slash or broad emission lines indicative of their presence in stacked rest-frame optical spectroscopy for subsets of our BPT-classified SFG sample). We also test for residual AGN contamination by analysing the radio images for \wise-red and \wise-blue sub-samples, finding no clear evidence for obvious AGN jet structure in either group. We also test that our choice of aggregate statistic (the mean) of the parameter \q is not affected by outliers by performing the same analysis with the median. We find that the trends that we report of \q over redshift, sSFR, temperature, and mid-infrared colours remain unaffected by the choice of aggregate statistic with only the global value of \q changing. \end{itemize} Taken together, these results indicate that the monochromatic FIRC varies strongly across the full range of BPT-classified star-forming galaxies in a manner dependent upon their mid-infrared colours (which are widely used as an empirical probe of galaxies' star formation properties), even at fixed redshift. We do not draw conclusions from our results alone about the efficacy of using the FIRC to calibrate radio star-formation rates, however \citet{Gurkan2018LofarHAtlas} used the same sample of galaxies, along with a full analysis of energy-balance derived stellar mass and star formation rate estimates, to investigate the low frequency radio luminosity star-formation rate relation directly. The broken power law relation between SFR and 150\,MHz luminosity found in that work -- which they suggest may indicate the presence of an additional mechanism for the generation of radio-emitting cosmic rays -- is consistent with the possibility of residual low-level AGN contamination, and the FIRC behaviour we observe at low specific star formation rates. Indeed, this suggests that calibrations such as those proposed in \citet{Brown2017Calibration} may need to be more nuanced than they currently are. Though our results underline the exquisite combined power of \herschel and \lofar for studying star-forming galaxies (and in particular the high quality of the maps produced by the LoTSS pipeline), it will be of great interest to investigate the star-formation and AGN content of galaxies in more detail with even more sensitive, high resolution data in the coming years, as we enter the era of the Square Kilometre Array. | 18 | 8 | 1808.10452 |
1808 | 1808.03657_arXiv.txt | A potential resolution for the generation of coherent radio emission in pulsar plasma is the existence of relativistic charge solitons, which are solutions of nonlinear Schr\"{o}dinger equation (NLSE). In an earlier study, Melikidze et al. (2000) investigated the nature of these charge solitons; however, their analysis ignored the effect of nonlinear Landau damping, which is inherent in the derivation of the NLSE in the pulsar pair plasma. In this paper we include the effect of nonlinear Landau damping and obtain solutions of the NLSE by applying a suitable numerical scheme. We find that for reasonable parameters of the cubic nonlinearity and nonlinear Landau damping, soliton-like intense pulses emerge from an initial disordered state of Langmuir waves and subsequently propagate stably over sufficiently long times, during which they are capable of exciting the coherent curvature radiation in pulsars. We emphasize that this emergence of {\em stable} intense solitons from a disordered state does not occur in a purely cubic NLSE; thus, it is {\em caused} by the nonlinear Landau damping. | \label{intro} Radio pulsars are rotationally powered neutron stars where the radio emission arises well within the neutron star magnetosphere. Observations of pulsar wind nebula suggest that the pulsar wind is composed of a dense electron position pair plasma outflowing from the pulsar. The problem of solving the pulsar magnetosphere equations to obtain estimates of the radiation and pulsar wind from a pulsar, is nontrivial and is a matter of intense research (see, e.g., \citealt{2011ASSP...21..139S}; \citealt{2016JPlPh..82e6302P}). The region around a strongly magnetized ($\mathbf{B}\sim 10^{12}$ G) and fast-spinning neutron star generates enormous electric fields $\mathbf{E}$ and cannot be maintained as vacuum (\citealt{1969ApJ...157..869G}). Most theories follow the idea that the region around the neutron star is a charge-separated magnetosphere that is force-free, meaning that the electromagnetic energy is significantly larger than all other inertial, pressure, and dissipative forces. To maintain co-rotation in the magnetosphere, the condition $\mathbf{E}\cdot\mathbf{B}=0$ should be satisfied, and this corresponds to a charge number density equal to the Goldreich--Julian density $n_{GJ} = \Omega\,B/(2\pi c e)$, where $\Omega = 2\pi/P$, $P$ is the rotational period of the pulsar, $c$ is the velocity of light, and $e$ is the electron charge. The magnetosphere is initially charge-starved, and a supply of charged particles can come from the neutron star or due to pair creation in strong magnetic fields. It was first suggested by \citet{1971ApJ...164..529S} that the region above the polar cap is the most likely place of electron--positron pair generation by magnetic field, and an electromagnetic cascading effect can multiply the pairs to reach density of about $10^{4}-10^{5} n_{GJ}$ (see, e.g., \citealt{2015ApJ...810..144T}). This value agrees very well with the evidence available from observations of pulsar wind nebula (see, e.g., \citet{2011ASSP...21..624B} for a recent review). Thus, pair creation in the polar cap is an essential feature of any pulsar model. In the last few decades, significant progress has been made in understanding the global force-free magnetosphere physics. In the presence of a copious supply of pair plasma and for the commonly assumed dipolar magnetic field configuration, the steady state global current distribution, the pulsar wind, and the resultant magnetic field structure can be found numerically. A large number of studies has been devoted to finding the global magnetospheric structure (e.g. \citealt{1999ApJ...511..351C};\citealt{2006ApJ...648L..51S}; \citealt{2006MNRAS.368.1055T};\citealt{2009A&A...496..495K}), and hence the global current distribution is considered to be known. However, most of these global magnetosphere studies do not include the effect of how the plasma is generated in the polar cap. To address this shortcoming, \citet{2013MNRAS.429...20T} and \citet{2010MNRAS.408.2092T} revisited two earlier models by \citet{1979ApJ...231..854A} and \citet{1975ApJ...196...51R}, where charges can and cannot, respectively, be extracted from the neutron star surface. They combined properties of the global force-free magnetosphere and the local mechanism of pair creation and obtained the solution for the plasma generation in the polar cap numerically. Importantly, \citet{2013MNRAS.429...20T} and \citet{2010MNRAS.408.2092T} found that the plasma flow along the open dipolar field lines is non-stationary, as it was suggested by \citet{1975ApJ...196...51R}. Radio emission from pulsar is thought to arise from the development of plasma instabilities in the electron--positron plasma streaming relativistically along open dipolar magnetic field lines in the pulsar magnetosphere. However, identifying the physical process that can explain the radio emission {\em properties} in pulsars is a challenging problem in astrophysics. The key issues here are: \ (i) \ to explain the problem of coherency, which manifests itself as observed pulsar radio emission with unrealistically high brightness temperatures $\sim 10^{28}\ldots\;10^{30}$K; and \ (ii) \ to explain the range of pulsar phenomena, such as micropulses, subpulse drift, nulling/moding, pulsar profile stability, polarization properties, etc.. Generally, the coherent pulsar radio emission can be generated by means of either a maser or a coherent curvature mechanism (e.g., \citealt{1975ARA&A..13..511G}; \citealt{1975ApJ...196...51R}; \citealt{1980Ap.....16..104M}; \citealt{1984Ap.....20..100M}; \citealt{1991MNRAS.253..377K}; \citealt{2000ApJ...544.1081M}) emitted in strongly magnetized electron--positron plasma well inside the light cylinder. However, as we will discuss in section~\ref{sec2} (see also \citet{2017JApA...38...52M} for a recent review), a large body of observations appear to suggest that the pulsar radio emission is excited via a mechanism of coherent curvature radiation. This radiation emerges from regions of about 500 km above the neutron star surface. The high brightness temperature of this coherent radiation can be explained only if it is excited by charge bunches containing a very large number of charged particles rather than by a single charge. The physics of how these charge bunches are formed and how they emit coherent radio emission is still poorly understood. In this work we will focus on the problem of formation of charge bunches and their stability, and will also address the problem of coherency in pulsar radio emission. We will rely on a commonly used approximation whereby the non-stationary flow of the plasma along open dipolar field lines is one-dimensional. This approximation is justified because of the strong confinement of the plasma along those lines. We also note that the recent time-dependent model of \citet{2010MNRAS.408.2092T} qualitatively reproduces the non-stationary plasma flow that was proposed in the classical radio pulsar emission model of \citet[hereafter RS75]{1975ApJ...196...51R}. While the RS75 model does not solve for the detailed time-dependent effect of pair creation, it does give a prescription of how to estimate the plasma parameters in the radio emission region. Since we are primarily interested in simple estimates of the plasma parameters, we will use the RS75 model as the starting point of our study. RS75 were amongst the first to propose a model that attempted to explain the overall aspect of the pulsar emission, i.e., both coherency and radio pulsar observational phenomenology. In their model, there exists an inner acceleration region close to the polar cap, where a relativistic non-stationary flow of the electron--positron pair plasma can be established. To address the problem of coherent radio emission, RS75 suggested that charge bunches could be formed due to development of a two-stream instability that results from the overlap between fast-moving and slow-moving particles of the non-stationary plasma. This instability leads to the formation of linear electrostatic Langmuir waves, whose frequency is the plasma frequency. As the Langmuir wave propagates along the magnetic field, each type of particles is subject to the sinusoidal electric field, where for half of its period the field bunches together charges of one sign, while for the next half-period it bunches together charges of the opposite sign. RS75 proposed that these charge bunches can excite the coherent radio emission. However, the explanation of coherent emission as occurring from such charge bunches has the following fundamental difficulty, as was pointed out by \citet{1986FizPl..12.1233L} and \citet{2000ApJ...544.1081M} (hereafter MGP00). On one hand, the spatial dimension $\Lambda_b$ of an emitting bunch (along the magnetic field lines) should be smaller than the period of the coherently emitted wave $\lambda_c$: \bsube \be \lambda_c > \Lambda_b. \label{contr1a} \ee Indeed, if $\lambda_c<\Lambda_b$, then different regions of the bunch would emit independently and hence incoherently. As described above, the bunching is caused by linear Langmuir waves (having wavelength $\lambda_l$), and the size of a bunch is about half of the wave's period; i.e., $\Lambda_b\approx \lambda_l/2$. Since Langmuir waves have an approximately vacuum dispersion relation, $\omega = 2\pi c/\lambda$, the condition \eqref{contr1a} that the emission be coherent amounts to \be \omega_c < 2\omega_l, \label{contr1b} \ee \label{contr1} \esube where $\omega_c$ and $\omega_l$ the characteristic frequency of the emitted waves and the Langmuir waves, respectively. On the other hand, the temporal period of the emitted wave, i.e. $\mathcal{T}_c=2\pi/\omega_c$, cannot exceed the time window over which the emitting bunch exists; this time window is half of the period of the Langmuir wave, i.e. $\mathcal{T}_b=\pi/\omega_l$. Indeed, if the condition \bsube \be \mathcal{T}_c < \mathcal{T}_b \label{contr2a} \ee does not hold, the charge bunch would disperse away before it has the chance to emit a radio wave. Equivalently to \eqref{contr2a}, one must have \be \omega_c > 2\omega_l\,. \label{contr2b} \ee \label{contr2} \esube Clearly, the above two conditions: \eqref{contr1b} (coherency of the emission) and \eqref{contr2b} (non-dispersal of the charge bunch) are in contradiction with each other. In the last few decades, significant refinement of the basic physical ideas that were postulated by RS75 has been achieved both theoretically and observationally (e.g., MGP00; \citealt{2004ApJ...600..872G}; \citealt{2009ApJ...696L.141M}; \citealt{2014ApJ...794..105M}). To circumvent the fundamental difficulty described in the previous paragraph, MGP00 accounted for nonlinear effects due to sufficiently strong two-stream instability in the relativistic plasma. Their theory led to the nonlinear Schr\"{o}dinger equation (NLSE) with a nonlinear Landau damping term, which describes propagation of the {\em slowly varying envelope} of Langmuir waves. It is important to clarify that the same mechanism --- the interaction between packets of Langmuir waves and charged particles in the plasma --- leads to the appearance of both the local and nonlocal nonlinear terms in the NLSE (see section 4 for details). Therefore, strictly speaking, both these terms are to be kept in a comprehensive analysis of the problem. However, no analytical solution of the NLSE with the nonlocal nonlinear Landau damping term is known. Thus, by way of approximation, MGP00 neglected the nonlinear Landau damping term, assuming it to be small, and showed that for reasonable pulsar parameters, the solution of the NLSE leads to formation of a nonlinear solitary wave, i.e., a soliton, which carries an effective charge. Unlike the ``half-period" charge bunches in the linear RS75 theory, the charge solitons can exist for times much longer than $\pi/\omega_l$. Thus, since $\mathcal{T}_b$ is no longer related to $\pi/\omega_l$, condition \eqref{contr2b} can no longer be deduced from condition \eqref{contr2a}. (Let us note, in passing, that for solitons, condition \eqref{contr1b} also does not follow from condition \eqref{contr1a}, because the soliton's length is much greater than the spatial period of the carrier Langmuir wave.) Hence, the bunch non-dispersal condition \eqref{contr1b} no longer contradicts the coherency condition \eqref{contr1a}, and therefore charge solitons, at least in principle, can excite coherent radio emission in the plasma. Yet, an explanation of the coherent emission relying on solitons of the ``pure" NLSE without a nonlinear Landau damping term has a shortcoming of its own. A stably propagating soliton (or a few solitons) is known to emerge only from a certain class of initial conditions --- a localized one. However, there is no reason to assume that such an initial state actually occurs in a magnetospheric plasma; rather, the initial condition there is likely to be a nonlocalized Langmuir wave with a randomly modulated envelope.\footnote{ As we discuss in detail in section 5, the random variation of the field's envelope occurs over a spatial scale that is much larger than the Langmuir period. } A solution developing from such an initial condition is known to be a disordered ensemble of solitons and a non-solitonic part of the solution (so-called linear dispersive waves). In this disordered state, solitons continuously appear and disappear as a result of their interaction with one another and with linear dispersive waves; see, e.g., \citet{2007Natur.450.1054S}; \citet{2010PhFl...22c6601F}; \citet{2015PhLA..379.1821L}; \citet{15_AgafontsevZakharov}; \citet{18_GelashAgafontsev}. Consequently, such ``flickering" solitons do not exist for times long enough that would let conditions \eqref{contr2a} and \eqref{contr1a} hold simultaneously. Thus, a mechanism that would preserve a soliton's individuality for a sufficiently long time, is required for the MGP00 theory to become a strong contender in explaining the pulsar coherent radio emission. In this paper we demonstrate that taking into account the effect of nonlinear Landau damping in the MGP00 theory provides such a soliton-stabilizing mechanism. The main part of this paper is organized as follows. In section~\ref{sec2} we briefly describe the observational evidence from radio pulsars that motivates invoking the charge soliton model. In section~\ref{sec3} we briefly outline the generation mechanism and features of the radio emitting plasma based on the polar-cap RS75 class of models. In section~\ref{sec4} we introduce the concept of the NLSE in pulsar plasma, and in section ~\ref{sec5} we discuss the range of parameters which are reasonable to expect in charge bunches of plasma near a pulsar. In section~\ref{numsim} we present the main results: a numerical observation of an intense long-living electrostatic pulse with an internal structure, which is formed in the NLSE model {\em due to} the nonlinear Landau damping. In section~\ref{sec6} we summarize the results. Appendix A contains a description of the numerical method, Appendix B discusses the appropriateness of using periodic boundary conditions in the numerical simulations, and Appendix C lists definitions of notations used in this work. | \label{sec6} We have addressed the open problem of explaining a mechanism of coherent curvature radio emission by the electron--positron plasma in pulsar magnetosphere. As the mathematical model of this phenomenon we considered the generalized nonlinear Schr\"odinger equation (NLSE) proposed by \citet{2000ApJ...544.1081M} (MGP00), which includes effects of group velocity dispersion, nonlinearity of electric susceptibility, and resonant interaction between Langmuir waves and plasma particles (nonlinear Landau damping). In the absence of nonlinear Landau damping, the purely cubic NLSE can, in principle, support solitons, which in the plasma would be manifested as charge bunches that propagate stably and therefore are capable of emitting coherent radiation. However, formation of solitons in the purely cubic NLSE requires that initially, the Langmuir wave have the envelope that is either localized or consists of several well-separated localized ``bumps". It is only then that the emerging charge solitons can maintain their shape for a sufficiently long time to radiate coherently. There is no reason to expect that such a special initial condition of Langmuir waves would exist in a disordered pulsar plasma. Then, it is known (see section 6.1.1) that evolution of a {\em disordered initial state} in the purely cubic NLSE leads to an ensemble of strongly interacting pulses, which constantly appear, disappear, and change their shape due to the interaction. Such a disordered, in both time and space, ensemble of pulses cannot be expected to emit coherently. Motivated by this inability of the purely cubic NLSE to identify a candidate mechanism of coherent emission, we numerically solved the NLSE {\em with the nonlinear Landau damping} term, as derived by MGP00. We found that for a range of realistic values of pulsar parameters, the presence of nonlinear Landau damping leads to the formation of an intense, soliton-like pulse out of an initially disordered Langmuir wave. Such a stable pulse can emit coherently and thus is a reasonable candidate as a source of coherent radio emission. However, an analytical explanation of this emergence of a long-living intense pulse remains an open problem. Let us point out a key difference between this result and the results of earlier studies (\citealt{78_NLS_SolPertNonlinLD}; \citealt{89_DNLS_MHD_NonlinLD}; \citealt{09_NLS_Dusty_NonlinLD}; \citealt{15_NLS_CollisionlessElectronPositron_NonlinLD}; \citealt{17_NLS_Degenerate_NonlinLD}; \citet{18_NLS_RelatElectronIon_NonlinLD}), which considered the effect of nonlinear Landau damping on an {\em isolated} soliton. Those earlier studies found that such a soliton will experience decay and a frequency shift of the carries. Both of these phenomena are consequences of the fact that the nonlocal term in the NLSE \eqref{NLSwdamp} describes energy transfer from one side of the pulse spectrum to the other. In contrast, in our simulations, a pulse emerges from an initially disordered state and, during its ``maturation" stage, appears to absorbs energy from the surrounding field. Two important notes about this pulse formation are in order. First, the nonlinear Landau damping coefficient has to fall in a certain range (namely, the lower part of \eqref{tn_06}). If it is too high, then the intensity of the emerging pulse is lower, or a stable pulse may even not form at all; see section 6.3. On the other hand, if the nonlinear Landau damping is too low, the pulse may not have the time to form during the stage when the charge density in the plasma cloud is sufficiently large to produce strong radiation; see section 5. Second, the intense pulse, formed for appropriate values of the nonlinear Landau damping coefficient, has an internal structure whose spatial scale can be about an order of magnitude smaller than the spatial extent of the pulse itself; see Fig.~\ref{fig_t2b}(b). In this work we did not undertake an actual {\em calculation} of the coherent emission by such stable pulses, containing a large number of charged particles; this clearly requires a separate study. Without such a calculation, one cannot tell to what extent each of these structures: the ``bulk" solitonic pulse itself and the finer ``ripple" on top of it, contribute to the coherent emission. It appears intuitively plausible that frequencies in the lower end of the observed spectrum (tens to hundreds of MHz) are generated by the pulse as a whole, while frequencies from the higher end (up to several GHz) are generated by the ``ripple". This is because the spatial scale of the pulse is about an order of magnitude greater than that of the ``ripple"; see sections 6.1.2 and 6.2. However, a {\em calculation} of the spectrum emitted by such a {\em two-scale} structure of charges remains an open problem. Let us now demonstrate that while the ``ripple" on top of the solitonic pulse keeps changing its shape on a time scale that is small compared to the time scale where such a pulse exists, those changes are still ``slow enough" to allow the ``ripple" to emit coherently in the range of frequencies estimated in section 6.1.2 (several GHz), and even at lower frequencies. To that end, note that in order for the ``ripple" to be a source of coherent radiation, it must exist long enough to guarantee condition \eqref{contr2a}. Namely, the time ${\mathcal T}_b$ over which the shape of this ``ripple" remains mostly unchanged must be much greater than the period ${\mathcal T}_c$ of the coherent radio emission. Let us demonstrate, using the illustrating example of Fig.~\ref{fig_t2b}, that this is indeed the case. In Fig.~\ref{fig_t5} we show that the profiles of both the electric field's intensity $|u|^2$ and the ponderomotive force $|u|^2_{xx}$ are mostly preserved over $t\approx 0.01$. Now, if $t\sim 100$ corresponds to $500$ km (see section 5), then ${\mathcal T}_b\sim 0.01$ corresponds to about $50$ m. Then, condition \eqref{contr2a} implies that the lower limit of frequencies $\omega_c$ is about $c/(50\;{\rm m})\sim 10$ MHz. This is consistent (within a two-order of magnitude margin) with the value of several GHz mentioned after estimate \eqref{e2_02b}. \begin{figure}% \begin{minipage}{7.5cm} \hspace*{-0.1cm} \includegraphics[height=6cm,width=7.5cm,angle=0] {figpap_tn5a.eps} \end{minipage} \hspace{0.5cm} \begin{minipage}{7.5cm} \hspace*{-0.1cm} \includegraphics[height=6cm,width=7.5cm,angle=0] {figpap_tn5b.eps} \end{minipage} \caption{(Color online) \ Same quantities as in Fig.~\ref{fig_t2b}(b),(c), respectively, but for $t=66.00,\,66.01,\,66.02$. Line colors and styles are as shown in the legend in panel (a). The $x$-window is smaller than in Fig.~\ref{fig_t2b}(b),(c) in order to make the details appear more clearly. In both panels, the centers of the pulses at the different times are manually superimposed in order to clearly show the changes of the profile. (If a pulse moves without changing its shape, its does not affect its ability to emit coherently.) We also observed that at $t=66.10$ the profile of the ``ripple" has changed completely relatively to that at $t=66.00$; the corresponding curves are not shown in order not to clutter the picture. } \label{fig_t5} \end{figure} Note that since the solitonic pulse itself stably propagates over $t>O(10)$ nondimensional units, there is, for practical purposes, no lower limit from condition \eqref{contr2a} on the frequencies that it, as a whole, can emit coherently. Finally, let us note that since we had to use periodic boundary conditions in our numerical simulations (see the preamble to section 6), we always observed that only one intense pulse forms as a result of many collisions with smaller pulses. In an actual plasma cloud, where the pulse passes through it only once rather than repeatedly, many well-separated and long-living solitonic pulses may form. Then, taking into account emission by this ensemble of stable charge bunches, as opposed to by a single charge bunch, is yet another open problem. | 18 | 8 | 1808.03657 |
1808 | 1808.04241_arXiv.txt | A newly-born magnetar is thought to be central engine of some long gamma-ray bursts (GRBs). We investigate the evolution of the electromagnetic (EM) emission from the magnetic dipole (MD) radiation wind injected by spin-down of a newly-born magnetar via both quadrupole gravitational-wave (GW) and MD radiations. We show that the EM luminosity evolves as $L_{\rm em}\propto (1+t/\tau_c)^{\alpha}$, and $\alpha$ is $-1$ and $-2$ in the GW and MD radiation dominated scenarios, respectively. Transition from the GW to MD radiation dominated epoch may show up as a smooth break with slope changing from $-1$ to $-2$. If the magnetar collapses to a black hole before $\tau_c$, the MD radiation should be shut down, then the EM light curve should be a plateau followed by a sharp drop. The expected generic light curve in this paradigm is consistent with the canonical X-ray light curve of {\em Swift} long GRBs. The X-ray emission of several long GRBs are identified and interpreted as magnetar spin-down via GW or MD, as well as constrain the physical parameters of magnetar. The combination of MD emission and GRB afterglows may make the diversity of the observed X-ray light curves. This may interpret the observed chromatic behaviors of the X-ray and optical afterglow light curves and the extremely low detection rate of a jet-like break in the X-ray afterglow light curves of long GRBs. | The energy reservoir of a newly-born magnetar is its total rotation energy, which reads as \begin{eqnarray} E_{\rm rot} = \frac{1}{2} I \Omega^{2} \simeq 2 \times 10^{52}~{\rm erg}~ M_{1.4} R_6^2 P_{-3}^{-2}, \label{Erot} \end{eqnarray} where $I$ is the moment of inertia, $\Omega$, $P$, $R$, and $M$ are the angular frequency, rotating period, radius, and mass of the neutron star. The convention $Q = 10^x Q_x$ is adopted in cgs units. It may spin down by losing its rotational energy through two channels, magnetic dipole torques ($L_{\rm EM}$) and gravitational wave radiation ($L_{\rm GW}$) (e.g., Shapiro \& Teukolsky 1983; Zhang \& M{\'e}sz{\'a}ros 2001; Fan et al. 2013; Lasky \& Glampedakis 2016), i.e., \begin{eqnarray} -\frac{dE_{\rm rot}}{dt} = -I\Omega \dot{\Omega} &=& L_{\rm EM} + L_{\rm GW} \nonumber \\ &=& \frac{B^2_{\rm p}R^{6}\Omega^{4}}{6c^{3}}+\frac{32GI^{2}\epsilon^{2}\Omega^{6}}{5c^{5}}, \label{Spindown} \end{eqnarray} where $\dot{\Omega}$ is time derivative of angular frequency, $B_p$ is the surface magnetic field at the pole, and $\epsilon=2(I_{\rm xx}-I_{\rm yy})/(I_{\rm xx}+I_{\rm yy})$ is the ellipticity in terms of the principal moments of inertia. One can find that for a magnetar with given $R$ and $I$, its $L_{\rm EM}$ depends on $B$ and $\Omega$, and $L_{\rm GW}$ depends on $\epsilon$ and $\Omega$. We derive the evolution of $L_{\rm EM}$ in the phases of that $L_{\rm EM}$ and $L_{\rm GW}$ dominates the rational energy lost in the following. (I) $L_{\rm EM}$ dominated scenario: In this scenario, one has \begin{eqnarray} L_{\rm EM}\simeq -I\Omega \dot{\Omega}=\frac{B^2_{\rm p}R^{6}\Omega^{4}}{6c^{3}}. \label{EM_dominated} \end{eqnarray} The full solution of $\Omega(t)$ in Eq.(\ref{EM_dominated}) can be written as \begin{eqnarray} \Omega(t) &=& \Omega_{0}(1+\frac{t}{\tau_{\rm em}})^{-1/2} \nonumber \\ &\simeq&\cases{ \Omega_0, & t $\ll \tau_{\rm c,em}$ \cr \Omega_{0}(\frac{t}{\tau_{\rm c,em}})^{-1/2}, & t $\gg \tau_{\rm c,em}$ \cr } \label{Omega_EM} \end{eqnarray} where $\Omega_{0}$ is initial angular frequency at $t=0$, and $\tau_{\rm c,em}$ is a characteristic spin-down time scale in this scenario. $\tau_{\rm em}$ can be given by \begin{eqnarray} \tau_{\rm c,em}&=&\frac{3c^{3}I}{B_{p}^{2}R^{6}\Omega_{0}^{2}} \nonumber \\ &\simeq&2.05 \times 10^3~{\rm s}~ (I_{45} B_{p,15}^{-2} P_{0,-3}^2 R_6^{-6}), \label{spintau_em} \end{eqnarray} where $P_0$ is the initial period of the magnetar (e.g., $P_0=2\pi/\Omega_0$). The evolution of $L_{\rm EM}$ with time can be expressed as \begin{eqnarray} L_{\rm EM}(t) &=& L_{\rm em,0}(1+\frac{t}{\tau_{\rm c,em}})^{-2} \nonumber \\ &\simeq&\cases{L_{\rm em,0}, & t $\ll \tau_{\rm c,em}$ \cr L_{\rm em,0}(\frac{t}{\tau_{\rm c,em}})^{-2}, & t $\gg \tau_{\rm c,em}$ \cr } \label{Luminosity_EM} \end{eqnarray} where $L_{\rm em,0}$ is the initial kinetic luminosity of electromagnetic dipole emission at $t_0$, given by \begin{eqnarray} L_{\rm em,0}&=&\frac{B^2_{p}R^6\Omega^{4}_{0}}{6c^3} \nonumber \\ &\simeq&1.0 \times 10^{49}~{\rm erg~s^{-1}} (B_{p,15}^2 P_{0,-3}^{-4} R_6^6), \label{spinlu_em} \end{eqnarray} (II) $L_{\rm GW}$ dominated scenario: In this scenario, one has \begin{eqnarray} L_{\rm GW}\simeq -I\Omega \dot{\Omega}=\frac{32GI^{2}\epsilon^{2}\Omega^{6}}{5c^{5}}. \label{GW_dominated} \end{eqnarray} The full solution of $\Omega(t)$ in Eq.(\ref{GW_dominated}) can be written as \begin{eqnarray} \Omega(t) &=& \Omega_{0}(1+\frac{t}{\tau_{\rm c,gw}})^{-1/4} \nonumber \\ &\simeq&\cases{ \Omega_0, & t $\ll \tau_{\rm c,gw}$ \cr \Omega_{0}(\frac{t}{\tau_{\rm c,gw}})^{-1/4}, & t $\gg \tau_{\rm c,gw}$ \cr } \label{Omega_GW} \end{eqnarray} where $\tau_{\rm c,gw}$ is a characteristic spin-down time scale in this scenario, which reads as \begin{eqnarray} \tau_{\rm c,gw}&=&\frac{5c^{5}}{128GI\epsilon^2\Omega^4_0} \nonumber \\ &\simeq&9.1 \times 10^3~{\rm s}~ (I^{-1}_{45}\epsilon_{-3}^{-2} P_{0,-3}^4 ). \label{spintau_gw} \end{eqnarray} The evolution of $L_{\rm GW}$ with time thus can be expressed as \begin{eqnarray} L_{\rm GW}(t) &=& L_{\rm gw,0}(1+\frac{t}{\tau_{\rm c,gw}})^{-3/2} \nonumber \\ &\simeq&\cases{L_{\rm gw,0}, & t $\ll \tau_{\rm c,gw}$ \cr L_{\rm gw,0}(\frac{t}{\tau_{\rm c,gw}})^{-3/2}, & t $\gg \tau_{\rm c,gw}$ \cr } \label{Luminosity_GW} \end{eqnarray} where $L_{\rm GW,0}$ is the luminosity of gravitational-wave quadrupole emission at $t=0$, given by \begin{eqnarray} L_{\rm gw,0}&=& \frac{32GI^{2}\epsilon^{2}\Omega_0^{6}}{5c^{5}} \nonumber \\ &\simeq&1.08 \times 10^{48}~{\rm erg~s^{-1}}(I_{45}^2 \epsilon_{-3}^{2} P_{0,-3}^{-6}). \label{spinlu_gw} \end{eqnarray} Within this scenario, the evolution of $\Omega(t)$ is different from the $L_{\rm EM}$ dominated scenario, and the evolution of $L_{\rm EM}$ is replaced by \begin{eqnarray} L_{\rm EM}(t) &=& L_{\rm em,0}(1+\frac{t}{\tau_{\rm c,gw}})^{-1} \nonumber \\ &\simeq&\cases{L_{\rm em,0}, & t $\ll \tau_{\rm c,gw}$ \cr L_{\rm em,0}(\frac{t}{\tau_{\rm c,gw}})^{-1}, & t $\gg \tau_{\rm c,gw}$ \cr } \label{Luminosity_GWEM} \end{eqnarray} Based on Eq.(\ref{Luminosity_EM}) and Eq.(\ref{Luminosity_GWEM}), and following the method of Lasky \& Glampedakis (2016), one can obtain the transition time ($\tau_{\ast}$) which point is from gravitational-wave quadrupole dominated to electromagnetic dipole dominated emission (Zhang \& M{\'e}sz{\'a}ros 2001; Lasky \& Glampedakis 2016), \begin{eqnarray} \tau_{\ast}=\frac{\tau_{\rm c,em}}{\tau_{\rm c,gw}}(\tau_{\rm c,em}-2\tau_{\rm c,gw}) \label{transition_time} \end{eqnarray} One can observe $\tau_{\ast}<0$ if $\tau_{\rm c,em}<2\tau_{\rm c,gw}$, indicating that no time is found for making $L_{\rm EM}(t)=L_{\rm GW}(t)$ and the rotational energy lost is always dominated by electromagnetic dipole emission, and the $L_{EM}$ evolves with time as Eq. (\ref{Luminosity_EM}). If $\tau_{\rm c,em}>2\tau_{\rm c,gw}$, one has $\tau_{\ast}>0$, suggesting that the spin-down is dominated by gravitational-wave quadrupole early and electromagnetic dipole emission later. In this case, the luminosity evolves with time as \begin{eqnarray} L(t)&\propto&\cases{(1+\frac{t}{\tau_{\rm c,gw}})^{-1}, & t $\leq\tau_{\ast}$ (GW dominated) \cr t^{-2}, &t $>\tau_{\ast}$ (EM dominated). \cr } \label{L_EMGW} \end{eqnarray} Moreover, Usov (1992) proposed that the spin-down of the neutron star is dominated by gravitational-wave quadrupole radiation when the angular velocity $\Omega$ of magnetar is larger than the critical value $\Omega_{cr}$ (also see Blackman \& Yi 1998; Zhang \& M{\'e}sz{\'a}ros 2001). Here, the $\Omega_{cr}$ ranges in $(0.4\sim 1.2)\times 10^{4}\rm~s^{-1}$ that depended on the equation of state of neutron star. | We have presented the temporal evolution feature of the EM emission during the spin-down of a newly-born magnetar (the remnant of massive star collapse) in the scenarios that the GW quadrupole and magnetic dipole emission dominate the rotational energy lost, respectively. We show that the EM emission light curve of the magnetic dipole radiation is described as $F\propto (1+t/\tau_c)^{\alpha}$, where $\tau_c$ is the characteristic spin-down timescales, and $\alpha=-1$ in the GW emission dominated scenario and $\alpha=-2$ in the magnetic dipole radiation dominated scenario. Transition from a GW emission dominated epoch to a magnetic dipole radiation dominated epoch may show up as a smooth break with a decaying slope from $-1$ to $-2$. In case of that the magnetar collapses to a black hole before $\tau_c$, the light curve of EM emission should be a plateau followed by a sharp drop being due to the immediate shut down of the magnetic dipole radiation. In a generic scenario, the magnetar coherently spins down by both the GW emission and magnetic dipole radiation, the EM emission lightcurve may be a shallow-to-normal decay segment with a slope changing from 0 to $-1\sim -2$. Our result presents a new paradigm for physical origin to explain the X-ray data of long GRBs observed with XRT. The expected generic light curve in this framework resembles the canonical XRT light curve of {\em Swift} GRBs presented by Zhang et al. (2006). Analysis of XRT data for a large sample of long GRBs and cases study are also consistent with our paradigm (e.g., Zou et al. 2018). We propose that the early shallow-decaying X-ray afterglows in long GRBs may be dominated by the magnetic dipole emission but not external shock mission of GRB fireballs. The combination of the magnetic dipole radiation and GRB fireball afterglows may make the diversity of the observed X-ray light curves. As shown in Liang et al. (2010, 2013) and Li et al. (2012), a clear onset bump, which may be a signature of the deceleration of GRB fireballs, is observed in the optical afterglows of some GRBs. Their XRT light curves in the according time interval are usually a shallow-decay segment. It is possible that the X-ray emission is dominated by the magnetic dipole radiation and the optical emission is dominated by the GRB afterglows. This may interpret the observed chromatic behaviors of the X-ray and optical afterglow light curves and the extremely low detection rate of a jet-like break in the X-ray light curves (Uhm \& Beloborodov 2007; Genet et al. 2007; Liang et al. 2008). Moreover, we present four long GRBs (070306, 060807, 070110, and 101225A) which X-ray light curves are likely contributed from magnetar spin-down via gravitational wave quadrupole emission and magnetic dipole radiation. Such as GRB 070306, the X-ray emission is likely originated from magnetar spin-down with magnetic dipole emission dominated; or magnetar spin-down via gravitational wave quadrupole emission and magnetic dipole radiation (e.g., GRB 060807); or magnetar collapse into black hole before its spin down (GRB 070110); or collapse of a supra magnetar during its spinning down period via gravitational wave quadrupole emission (GRB 101225A). Within this scenario, the physical parameters of magnetar can also be constrained via the observed properties of X-ray emission, e.g., $B_p$, $P_0$ and $\epsilon$. Especially, the derived value of $\epsilon$ for long GRBs 060807 and 101225A are consistent with the constraints of Lasky \& Glampedakis 2016 by adopting short GRBs. On the other hand, the origin of some peculiar (e.g., soft-long lasting $\gamma$-ray emission) Ultra-long GRBs may be consistent with our scenario. For example, the possible origin of GRB 101225A may be consistent with the hypothesis magnetar spin-down with GW emission dominated and collapses to a black hole at later time, e.g., long-soft $\gamma$-ray emission may be of energy injection from magnetar wind within off-axis observations, the early segment of normal decay in XRT light curve is consistent with spin-down magnetar wind with gravitational-wave quadrupole radiation dominated, and the later phase of steeper decay in XRT light curve is the signature of magnetar collapse into black hole. However, due to lack of smoking gun evidence, catching this possible interpretation is expected by observing more events of GW and EM associated with LIGO and high energy instruments in the future. | 18 | 8 | 1808.04241 |
1808 | 1808.04900_arXiv.txt | {Star-forming galaxies have been found to follow a relatively tight relation between stellar mass ($M_{*}$) and star formation rate (SFR), dubbed the `star formation sequence'. A turnover in the sequence has been observed, where galaxies with $M_{*} < \SI{e10}{\solarmass}$ follow a steeper relation than their higher mass counterparts, suggesting that the low-mass slope is (nearly) linear. In this paper, we characterise the properties of the low-mass end of the star formation sequence between $7 \leq \log M_{*}[\si{\solarmass}] \leq 10.5$ at redshift $\samplezmin < z < \samplezmax$. We use the deepest MUSE observations of the \emph{Hubble} Ultra Deep Field and the \emph{Hubble} Deep Field South to construct a sample of \samplesize\ star-forming galaxies with high signal-to-noise emission lines. Dust-corrected SFRs are determined from \Hbeta\ and \Halpha. We model the star formation sequence with a Gaussian distribution around a hyperplane between $\log M_{*}$, $\log \text{SFR}$, and $\log (1+z)$, to simultaneously constrain the slope, redshift evolution, and intrinsic scatter. We find a sub-linear slope for the low-mass regime where $\log \text{SFR}[\si{\solarmass\per\year}] = \corrslope\log M_{*}[\si{\solarmass}] + \corrzevol \log (1+z)$, increasing with redshift. We recover an intrinsic scatter in the relation of \corrsigtext\ dex, larger than typically found at higher masses. As both hydrodynamical simulations and (semi-)analytical models typically favour a steeper slope in the low-mass regime, our results provide new constraints on the feedback processes which operate preferentially in low-mass halos.} | \label{sec:introduction} How galaxies grow is one of the fundamental questions in astronomy. The picture that has emerged is that a galaxy builds up its stellar mass mainly through star formation, which is triggered by gas accretion from the cosmic web \citep[e.g.][]{DekelA_09a,VandeVoort2012}, while mergers with other galaxies play only a minor role \citep[except for massive systems;][]{Bundy2009}. In the past decade, star-forming galaxies have been found to form a reasonably tight quasi-linear relation between stellar mass ($M_{*}$) and star formation rate (SFR) \citep{Brinchmann2004, Noeske2007a, Elbaz2007, Daddi2007, Salim2007} over a wide range of masses and out to high redshifts \citep{Pannella2009, Santini2009, Oliver2010, PengY_10a, Rodighiero2010, Karim2011, Bouwens2012, Whitaker2012, StarkD_13a, Whitaker2014, Ilbert2015, Lee2015, Renzini2015, Schreiber2015, Shivaei2015, Salmon2015, Tasca2015, Gavazzi2015, Kurczynski2016, Tomczak2016, Santini2017,Bisigello2017}, which is often referred to as the `main sequence of star-forming galaxies' or the `star formation sequence'. In contrast, galaxies that are undergoing a starburst or have already quenched their star formation respectively lie above and below the relation. This main sequence is close to a similar scaling relation for halos \citep{BirnboimY_07a,NeisteinE_08a, GenelS_08a, FakhouriO_08a,Correa2015a, Correa2015b} where the growth rate increases super-linearly~\footnote{There is a tension between the shallow slope of the observed main sequence with the super-linear slope expected in models, which is set by the index of the initial dark matter power spectrum~\citep{BirnboimY_07a, NeisteinE_08a,Correa2015a,Correa2015b}.} with halo mass, and this has been interpreted as supporting the picture where galaxy growth is driven by gas accretion from the cosmic web \citep[e.g.][]{BoucheN_10a, Lilly2013, Rodriguez-PueblaA_16a, Tacchella2016a}. This interpretation is supported by hydrodynamical simulations of galaxy formation \citep{Schaye2010, Haas2013a, Haas2013b, Torrey2014, Hopkins2014, Crain2015, Hopkins2016}, where a global equilibrium relation is found between the inflow and outflow of gas and star formation in galaxies. In this picture the star formation acts as a self-regulating process, where the inflow of gas, through cooling and accretion, is balanced by the feedback from massive stars and black holes \citep[e.g.][]{Schaye2010}. Furthermore, semi-analytical models \citep[e.g.][]{DuttonA_10a,Mitchell2014,Cattaneo2011,Cattaneo2017} and relatively simple analytic theoretical models which connect the gas supply (from the cosmological accretion) to the gas consumption can also reproduce the main features of the main sequence rather well \citep[e.g.][]{BoucheN_10a, Dave2012, Lilly2013, DekelA_13a, DekelA_14a, MitraS_15a, Rodriguez-PueblaA_16a, Rodriguez-PueblaA_17a}~\footnote{For an alternative interpretation, cf. \cite{Gladders2013, Kelson2014, Abramson2016}.}. The parameters of the $M_{*}$-SFR relation (i.e. slope, normalisation, and scatter) are thus important, as they provide us with insight into the relative contributions of different processes operating at different mass scales, in particular when comparing the values of the parameters to their counterparts in dark matter halo scaling relations. The normalisation of the star formation sequence is governed by the change in cosmological gas accretion rates and gas depletion timescales. The slope can be sensitive to the effect of various feedback processes acting on the accreted gas, which prevent (or enhance) star formation. The intrinsic scatter around the equilibrium relation is predominantly determined by the stochasticity in the gas accretion process \citep[e.g.][]{ForbesJ_14a, MitraS_17a}, but can also be driven by dynamical processes that rearrange the gas inside galaxies \citep{Tacchella2016a}. The $M_{*}$-SFR relation is observed to be reasonably tight, with an intrinsic scatter of only $\approx 0.3$ dex \citep[][though we caution against a blind comparison as different observables probe star formation on different timescales]{Noeske2007a, Salmi2012, Whitaker2012, Guo2013, Speagle2014,Schreiber2015,Kurczynski2016}. Yet, it has proven to be challenging to place firm constraints on the intrinsic scatter as one needs to deconvolve the scatter due to measurement uncertainty \citep[e.g.][]{Speagle2014, Kurczynski2016, Santini2017}. Observationally, the slope has been difficult to measure, particularly at the low-mass end, as most studies have been sensitive to galaxies with stellar masses above $\log M_*[\si{\solarmass}]\sim 10$ and often lack dynamical range in mass. In addition, while it is well known that there is significant evolution in the normalisation of the sequence with redshift, most studies have measured the slope in bins of redshift. For a flux limited sample this could introduce a bias in the slope because overlapping populations at different normalisations are not sampled equally in mass within a single redshift bin. The slope may also be mass dependent and indeed recent studies have observed that the relation turns over around a mass of $M_{*} \sim \SI{e10}{\solarmass}$ \citep{ Whitaker2012, Whitaker2014, Lee2015, Schreiber2015, Tomczak2016} and shows a steeper slope below the turnover mass. In the low-mass regime, a (nearly) linear slope has generally been expected \citep[e.g.][]{Schreiber2015, Tomczak2016}, motivated also by the fact that there is very little evolution in the faint-end slope of the blue stellar mass function with redshift \citep{Peng2014}. \cite{Leja2015} showed that the sequence cannot have a slope $a < 0.9$ at all masses because this would lead to a too high number density between $10 < \log M_{*}[\si{\solarmass}] < 11$ at $z = 1$. In addition to the observational challenges, careful modelling is required to get reliable constraints on the parameters (slope, normalisation, scatter) of the star formation sequence. It is important to properly take selection effects into account as well as the uncertainties on both the stellar masses and star formation rates (and, if spectroscopy is lacking, also on the photometric redshifts). The latter in particular, due to the fact that there is intrinsic scatter in the relation that needs to be deconvolved from the measurement errors. Common statistical techniques do not take these complications into account self-consistently, which leads to biases in the results. Putting the existing observations in perspective, it is clear that a large dynamical range in mass is necessary to measure the slope of the star formation sequence in the low-mass regime. Deep field studies, that can blindly detect large numbers of galaxies down to masses much below $\SI{e10}{\solarmass}$, are invaluable in this regard \citep[e.g.][]{Kurczynski2016}. Yet, such studies are challenged by having to measure all observables, distances as well as stellar masses and star formation rates, from the same photometry. This can lead to undesirable correlations between different observables. At the same time the measurements suffer from the uncertainties associated with photometric redshifts. Spectroscopic follow up is crucial in this regard, but can suffer from biases due to photometric preselection. With the advent of the \emph{Multi Unit Spectroscopic Explorer} (MUSE; \citealt{Bacon2010}) on the VLT it is now possible to address these concerns. With the deep MUSE data obtained over the \emph{Hubble} Ultra Deep Field \citep[HUDF;][]{Bacon2017} and \emph{Hubble} Deep Field South \citep[HDFS;][]{Bacon2015}, we can `blindly' detect star-forming galaxies in emission lines down to very low levels ($\sim \SI{e-3}{\solarmass \per \year}$) and obtain a precise spectroscopic redshift estimate at the same time \citep{Inami2017}. These data provides a unique view into the low-mass regime of the star formation sequence. In this paper we present a characterisation of the low-mass end of the $M_{*}$-SFR relation, using deep MUSE observations of the HUDF and HDFS. We characterise the properties of the $M_{*}$-SFR relation down stellar masses of $M_{*} \sim \SI{e8}{\solarmass}$ and SFR $\sim \SI{e-3}{\solarmass \per \year}$, out to $z < 1$, and trace the SFR in individual galaxies with masses as low as $M_{*} \la \SI{e7}{\solarmass}$ at $z\sim0.2$. We model the relation using a self-consistent Bayesian framework and describe it with a Gaussian distribution around a plane in (log mass, log SFR, log redshift)-space. This allows us to simultaneously constrain the slope and evolution of the star formation sequence as well as the amount of intrinsic scatter, while taking into account heteroscedastic errors (i.e. a different uncertainty for each data point). The structure of the paper is as follows. In \Sec{sec:observations-methods} we first introduce the MUSE data set and outline the selection criteria used to construct our sample of star-forming galaxies. We then go into the methods used to determine a robust stellar mass and a SFR from the observed emission lines. Before looking at the results, we discuss the consistency of our SFRs in \Sec{sec:cons-sfr-indic}. We then introduce the framework of our Bayesian analysis used to characterise the $M_{*}$-SFR relation (\Sec{sec:modelling}) and present the results in \Sec{sec:results}. We discuss the robustness of the derived parameters in \Sec{sec:selection-function-completeness}. Finally, we discuss our results in the context of the literature and models, and the physical implications (\Sec{sec:discussion}). We summarise with our conclusions in \Sec{sec:conclusions}. Throughout this paper we assume a \cite{Chabrier2003} stellar initial mass function and a flat $\Lambda$CDM cosmology with $H_0 = \SI{70}{km.s^{-1}.Mpc^{-1}}$, $\Omega_m = 0.3$ and $\Omega_{\Lambda} = 0.7$. \begin{figure} \centering \includegraphics[width=\columnwidth]{./Images/fig1.pdf} \caption{\label{fig:redshift-sfct} Redshift distribution of our galaxies plotted against their (dust-corrected) SFR (1$\sigma$ error bars are in grey). The colour denotes the stellar mass. The solid line depicts the lowest uncorrected SFR from \Hbeta\ we can detect in the HUDF at each redshift (which is effectively determined by the requirement that S/N$(\Hgamma) > 3$; see \protect\Sec{sec:star-formation-rates}).} \end{figure} | \label{sec:conclusions} We have exploited the unique capabilities of the MUSE instrument to investigate the star formation sequence for low-mass galaxies at intermediate redshift ($\samplezmin < z < \samplezmax$). From the large number of sources detected with MUSE in the HUDF and HDFS we have constructed a sample of \samplesize\ star-forming galaxies down to $M_{*} \sim \SI{e8}{\solarmass}$, with a number of objects at even lower masses (\Fig{fig:mass-histogram}). The accurate spectroscopic redshifts from MUSE are combined with the deep photometry available over the HUDF and HDFS to determine a robust mass estimate for the galaxies in our sample through stellar population synthesis modelling. With MUSE we can detect star-forming galaxies down to SFR $\sim \SI{e-3}{\solarmass \per \year}$ (\Fig{fig:m*-sfr}). We show that we can determine robust, dust-corrected SFR estimates from \Halpha\ and \Hbeta\ recombination lines, by comparing the SFRs from different tracers (\Fig{fig:sfr-consistency}). A dust-corrected star formation rate is inferred from the \Halpha\ and \Hbeta\ emission lines observed with S/N > 3 in the MUSE spectra. We characterise the star formation sequence by a Gaussian distribution around a plane (\Eq{eq:linear}). This methodology is chosen to maximally exploit the data set taking into account heteroscedastic errors. We constrain the slope, normalisation, intrinsic scatter, and evolution with redshift from the posterior probability distribution via MCMC methods (\Fig{fig:triangle}). We analyse the robustness of our model and the influence of the MUSE detection limit on the derived properties of the star formation sequence, by determining how well we can recover the parameters from a sample of simulated relations (detailed in \autoref{sec:simulations}). Using the results, we correct our inferred parameters for observational biases. We report a best-fit description of the low-mass end of the galaxy star formation sequence of $\log \mathrm{SFR} = \corrslope \log M_{*} \corrintercpt + \corrzevol \log(1+z)$ between $\samplezmin < z < \samplezmax$, shown in \Fig{fig:m*-z-sfr}. The full description of our parameters, including errors and normalisation, is found in \Eq{eq:best-fit-corr}. The intrinsic scatter around the sequence is found to be \corrsigtext\ dex (in log SFR). This is notably higher than the average value reported in literature ($\sim 0.3$ dex), which could be attributed to a combination of the Balmer lines probing star formation on shorter timescales and the star formation histories of low-mass galaxies being more diverse. Excluding massive galaxies (with $M_{*} > \SI{e9.5}{\solarmass}$) has no significant effect on the best-fit parameters, indicating we are primarily sensitive to low-mass galaxies. Notably though, we find that the slope steepens when splitting our sample into one or multiple redshift bins, with the values going up to $\log \mathrm{SFR} [\si{\solarmass\per\year}] = \twodslope \log M_{*}[\si{\solarmass}]$. This shows the importance of taking into account the evolution with redshift when deriving the properties of the star formation sequence. The slope of the star formation sequence is an important observable as it provides information on the processes that regulate star formation in galaxies. Our slope is shallower than most simulations and (semi-)analytical models predict, which find a (super-)linear slope essentially due to the growth rate of dark matter halos. Feedback processes operating specifically in the low-mass regime, which affect the accretion of gas onto galaxies and/or subsequent star formation, are required to reconcile these differences. Models suggest that supernova feedback or a decreased star formation efficiency do not affect the slope of the star formation sequence. Instead, processes that prevent the accretion of gas onto low-mass galaxies are thought to play an important role in determining the slope of the star formation sequence in the low-mass regime. | 18 | 8 | 1808.04900 |
1808 | 1808.06628_arXiv.txt | \citet{2017A&A...605A..58A} identified seventy six candidate supernova remnants (SNRs) using data from The HI, OH, Recombination line survey of the Milky Way (THOR). The spectral index and polarization \edit2{properties } can help distinguish between SNRs and H\begin{small}II\end{small}regions, which are often confused. We confirm \edit1{two } SNR candidates using spectral index data and morphology. However, we observe that the fractional linear polarization cannot distinguish between SNRs and H\begin{small}II\end{small}regions, \edit1{likely due to contamination by diffuse Galactic synchrotron emission}. We also comment on the association of SNR candidates with pulsars \edit1{through geometric and age considerations.} | The list of nearly 300 Galactic Supernova Remnants (SNRs) compiled by \citet{2014BASI...42...47G} is thought to be incomplete because it was estimated that there must be upwards of 1000 SNRs in the Milky Way \edit1{\citep{1991ApJ...378...93L,1994ApJS...92..487T}}. Even including recent TeV $\gamma$-ray SNRs detected by the H.E.S.S. collaboration does not increase this number greatly \citep{2017AIPC.1792d0030G}. Though the lack of detections at radio and X-ray wavelengths supports the arguments of \citet{2006MNRAS.371.1975Y} that there could be several SNRs with no radio, optical, ultraviolet or X-ray emissions, \citet{2006ApJ...639L..25B} have shown that the deficiency is primarily due to the lack of sensitivity to observe low surface brightness SNRs and due to low angular resolution that prevents the detection of small angular size SNRs. Galactic SNRs are routinely identified in radio wavelengths. The emission (or the lack of it) at different wavelengths depends on intrinsic factors such as the progenitor's history and also on external conditions such as the properties of surrounding medium. H\begin{small}II\end{small}regions, which are bright at radio wavelengths due to thermal emission, are frequently confused with SNRs. SNRs have a significantly smaller ratio of flux at Mid Infrared (MIR) wavelengths to flux at radio wavelengths than H\begin{small}II\end{small}regions \edit1{\citep{2001MNRAS.325..531C}}. This feature led to the proposal of 76 candidate SNRs by \citet{2017A&A...605A..58A} who have used radio continuum data from The HI, OH, Recombination line survey of the Milky Way \citep[THOR;][]{2016A&A...595A..32B} and the Karl G. Jansky Very Large Array (VLA) 1.4 GHz Galactic Plane Survey \citep[VGPS;][]{2006AJ....132.1158S}, and MIR wavelength data from Spitzer GLIMPSE, Spitzer MIPSGAL and WISE surveys. We propose to confirm the \edit1{identification of the candidate SNRs} by measuring the fractional linear polarization and spectral index of the total \edit1{continuum} emission. We \edit1{measured these parameters for} known SNRs and known H\begin{small}II\end{small}regions in the THOR survey region ($|b| <$ 1.25\degree, 17.5\degree $< l <$ 67.4\degree; \citealp[see][]{2016A&A...595A..32B}) \edit1{and compared them with the data from candidate SNRs.} The list of known H\begin{small}II\end{small}regions was taken from The WISE Catalog of Galactic H\begin{small}II\end{small}regions \citep{2014ApJS..212....1A} through an interactive website \citep{2014AAS...22331201A}. We leave out candidate H\begin{small}II\end{small}regions and use only known H\begin{small}II\end{small}regions with sizes greater than $1'$, so that the comparison with known and candidate SNRs is appropriate. Pulsars near the SNR candidates with associations to high energy sources could \edit1{be indicative of a positive identification. However, to ensure a clear identification, distances to the SNR and pulsar should be compatible with age and proper motion of the pulsar.} The Australia Telescope National Facility (ATNF) pulsar catalog \citep{2005AJ....129.1993M} provides the list of pulsars and their association with other sources. H\begin{small}II\end{small}regions are expected to have no linearly polarized emission at radio wavelengths because their emission is thermal. They have flat radio spectra ($\alpha \approx 0$)\footnote{Spectral index $\alpha$ is defined by $S_\nu \propto \nu^{\alpha}$, for a flux density $S_\nu$ and a frequency $\nu$} for optically thin and $\alpha \gtrsim 0.5$ for optically thick regions. On the other hand, SNRs are strong synchrotron sources, which are highly linearly polarized. For synchrotron emission in a uniform magnetic field, fractional linear polarization is related to the spectral index by \citep{2013tra..book.....W}: \begin{equation} \Pi \equiv \frac{\sqrt{Q^2 + U^2}}{I} = \frac{3-3\alpha}{5-3\alpha} \end{equation} Synchrotron emission usually has $-2 < \alpha < 0$, so we expect fractional linear polarizations of above 0.6. However, we rarely observe $\Pi > 0.25$. This is due to the Faraday depolarization effect \citep{2007EAS....23..109F}. Varying rotation measure within the resolution element causes different Faraday rotations of the polarization vector, leading to reduced polarization fraction being observed. As the polarization data from THOR is not fully processed yet \citep{2016A&A...595A..32B}, we use the polarization data from the 1.4 GHz Northern VLA Sky Survey \citep[NVSS;][]{1998AJ....115.1693C}. We use the publicly available spectral index map presented by \citet{2018MNRAS.474.5008D}, which is based on data from 150 MHz TIFR GMRT\footnote{TIFR -- Tata Institute of Fundamental Research; GMRT -- Giant Metrewave Radio Telescope} Sky Survey (TGSS) \citep{2017A&A...598A..78I} and the NVSS. \edit2{RRLs are indicative of thermal processes, but the lines are often broad and weak.} \edit1{\citet{2016A&A...595A..32B} have detected RRLs in THOR survey only in some H\begin{small}II\end{small}regions. Hence, while a detection of RRLs in THOR might imply thermal emission, a non-detection does not imply non-thermal emission, and it cannot be used to confirm the SNR candidates.} | We have shown that the statistics of SNR candidates follows the sample of known SNRs more closely than that of H\begin{small}II\end{small}regions in spectral index and linear polarization. \edit2{However, the fractional polarization could not be used to discriminate between SNRs and H\begin{small}II\end{small}regions because of contamination by diffuse polarized emission in the Galactic Plane.} Compact sources and overlaps with known or candidate SNRs account for most of the steep negative spectra in H\begin{small}II\end{small}regions. There is only one H\begin{small}II\end{small}region G050.317$-$00.421 with an apparent non-thermal spectrum that needs to be explained. Despite the above shortcomings, spectral index data, along with morphology, confirmed the status of G27.06+0.04 and G51.26+0.11 as SNRs. \edit1{There are three other candidate SNRs with non-thermal spectral indices (G18.76$-$0.07, G58.70$-$0.75 and G59.68+1.25) but no shell morphology. High energy emissions and a high degree of polarization might confirm their nature. Ongoing work on the THOR survey includes a careful analysis of the polarization data (Stil et al. in prep). Though THOR data are not ideal for deriving the spectra of large structures, they work well for compact sources \citep[][Wang et al. submitted]{2016A&A...588A..97B}. Candidate SNRs G28.56+0.00 and G47.15+0.73 are such sources (angular size $< 3'$). They are detected in 1.4 GHz NVSS but not in 150 MHz TGSS. Future spectral index information from THOR could be used to study these candidates.} \edit2{Using optical emission lines could help to distinguish SNRs since they have elevated values for [S II]:H$\alpha$ compared with H\begin{small}II\end{small}regions and the lines are often broader \citep{2018ApJ...855..140L}.} \edit2{We have been able to confirm the identification of only two candidates out of 76 using spectral index and morphology. Several candidates have not been detected in TGSS, some not in NVSS as well. Both these data are from snapshot surveys, which are not well suited to study low surface brightness emissions. On the other hand, compact candidate SNRs -- despite favorable spectral index measurements -- could not be confirmed because of confusion with background sources (AGNs). The low rate in confirming the identification of candidate SNRs underlines the importance of future Galactic plane surveys with better sensitivity and high angular resolution.} \edit2{We could not find any pulsar associations with candidate SNRs. More data on proper motions of pulsars, age and distance measurements of candidate SNRs can be used to argue for or against an association.} \edit1{Proper motions of pulsars can be measured by comparing their current positions with the positions in the ATNF pulsar catalog. Distances to pulsars can be estimated from dispersion measure and an electron density model \citep{2017ApJ...835...29Y}, or through the \textit{kinematic} method. Astrometric observations by Very Long Baseline Array also can be used to measure parallaxes and proper motions of pulsars \citep{2009ApJ...698..250C}. } | 18 | 8 | 1808.06628 |
1808 | 1808.10758_arXiv.txt | We study the perturbations of scalar, vector, and tensor fields in a slowly rotating Kerr-(Anti-)de Sitter black hole spacetime, presenting new and existing Schr{\"o}dinger style master equations for each type of perturbation up to linear order in black hole spin $a$. For each type of field we calculate analytical expressions for the fundamental quasi-normal mode frequencies. These frequencies are compared to existing results for Schwarzschild-de Sitter, slowly rotating Kerr, and slowly rotating Kerr-de Sitter black holes. In all cases good agreement is found between the analytic expressions and those frequencies calculated numerically. In addition, the axial and polar gravitational frequencies are shown to be isospectral to linear order in $a$ for all cases other than for \textit{both} non-zero $a$ and $\Lambda$. | Black holes are among the most captivating aspects of Einstein's Theory of General Relativity (GR) \cite{Einstein:1916vd,Schwarzschild:1916uq,Finkelstein:1958zz,Kerr:1963ud,Misner:1974qy}, and their properties have been studied extensively since the dawn of GR in the early 20th century. Of great interest to physicists and mathematicians alike is the response of black holes to perturbations. Notably, perturbed black holes `ring', emitting gravitational waves at a characteristic set of frequencies known as the quasi-normal mode (QNM) frequencies \cite{1975RSPSA.343..289C,0264-9381-16-12-201,Kokkotas:1999bd,Berti:2009kk,Konoplya:2011qq}. These QNM frequencies are dependent on the background properties of the black hole (e.g. mass or angular momentum), acting like a `fingerprint' for a given black hole. Furthermore, the presence of a cosmological constant, or a modification to the theory of gravity itself, can and will affect the spectrum of frequencies that a black hole will emit gravitational waves at. Thus studying the QNM frequencies of black holes (and other fields propagating on the black hole spacetime) provides a window from which to observe not only the properties of the black hole itself, but also of the wider universe and indeed of the fundamental laws governing gravity \cite{Dreyer:2003bv,Berti:2005ys,Berti:2015itd,2018PhRvD..97d4021T,Berti:2018vdi,Barack:2018yly,Brito:2018rfr}. From an observational point of view, given the dawn of the gravitational wave era of astronomy (with multiple direct observations of gravitational waves from mergers of highly compact objects, i.e. black holes or neutron stars, having now been made by advanced LIGO and VIRGO \cite{2016PhRvL.116f1102A,2016PhRvL.116x1103A,2017PhRvL.118v1101A,Abbott:2017oio,PhysRevLett.119.161101}), determining and detecting the QNM frequencies of the remnant black holes left perturbed after the merger of compact objects is an interesting and important area of study. In this paper, we will study the responses a variety of fields to linear perturbations on a black hole spacetime, and present analytical expressions for the QNM frequencies that each type of field characteristically `rings' at. The black holes we will consider will possess angular momentum and be embedded in a universe with a cosmological constant that can be positive or negative (i.e. the spacetime will be either asymptotically de Sitter or Anti-de Sitter). For the case of a positive cosmological constant, the black holes studied here will represent the kind of astrophysical black holes that we expect to observe in our universe (assuming the $\Lambda$CDM paradigm of cosmology \cite{Akrami:2018vks}). For a negative cosmological constant, on the other hand, the AdS/CFT correspondence provides an interesting motivation to study the QNMs of asymptotically Anti-de Sitter black holes as a method of gaining insight into certain conformal quantum field theories \cite{Maldacena:1997re,Nunez:2003eq,Son:2007vk,Hartnoll:2009sz,Herzog:2009xv}. \textit{Summary}: In section \ref{background}, we will present the background spacetime of the black holes that are to be studied in this work. In section \ref{perturbations}, we will review aspects of black hole perturbation theory before presenting second order Schr{\"o}dinger-style master equations for perturbations of massive scalar (spin $s=0$), massive vector ($s=-1$), and massless tensor ($s=-2$) fields. Some of the master equations presented are known from the literature, with others (to the author's best knowledge) being new results. In section \ref{qnmsection} we will then present analytic expressions for the QNM frequencies that satisfy each of the master equations present in section \ref{perturbations}, and compare these analytic expressions to previously obtained numerical results. Finally, in section \ref{conclusion}, we will discuss the results presented and make some concluding remarks. Throughout we will use units such that $G=c=1$. | In this paper we have presented Schr{\"o}dinger style master equations for the perturbations of massive scalar, massive vector, and gravitational fields on a slowly rotating Kerr-(A)dS black hole. These represent generalisations of the Regge-Wheeler and Zerilli equations (for fields of spin $0,-1,$ or $-2$) to include the effects of both a non-zero cosmological constant $\Lambda$ \textit{and} of slow rotation (i.e. to linear order in dimensionless black hole spin $a$). Some of these equations have been presented before in their entirety (e.g. eq.~(\ref{scalareq}) and (\ref{procaeq}) in \cite{2012PhRvD..86j4017P}), whilst versions of the equations with either $a=0$ or $\Lambda=0$ have been presented in, for example, \cite{Pani:2013pma,Cardoso:2001bb}. The generalisation of the gravitational perturbation equations to include both the effects of rotation and of a cosmological constant presented here should, however, prove useful given the wealth of knowledge accumulated to address such Schr{\"o}dinger style equations. We have also presented, following the method of \cite{2009CQGra..26v5003D}, analytical expressions for the QNM frequencies that satisfy each of the perturbation master equations present in section \ref{perturbations} (eq.~(\ref{scalareq}), (\ref{procaeq}), (\ref{gravaxial}), and (\ref{gravpolar})). The expressions given in appendix \ref{coeff} are intended as a compliment to existing methods of QNM calculation, with the equations presented in section \ref{perturbations} of course being amenable to being solved via one's preferred method. Given that there are relatively few numerical results for QNM frequencies in the literature for some categories of black holes (e.g. Kerr-de Sitter), numerically investigating the perturbation master equations presented in this paper and elsewhere is worthy of further attention. In addition, a natural extension of this work would be to consider black holes possessing non-zero electric charge \cite{doi:10.1063/1.1704350,doi:10.1063/1.1704351}. In section \ref{qnmsection} we find that the analytic expressions calculated in this paper agree well with the QNM frequencies calculated via other methods for a Schwarzschild-dS black hole \cite{Zhidenko:2003wq}, for a slowly rotating Kerr black hole \cite{Berti:2009kk}, and for a slowly rotating Kerr-de Sitter black hole \cite{PhysRevD.81.044005,Dyatlov:2011jd}. They are not, however, valid for asymptotically AdS spacetimes (as explained in \cite{2009CQGra..26v5003D}). The frequencies calculated in this paper support the numerically observed isospectrality of gravitational modes to linear order in spin for Kerr black holes \cite{Pani:2013wsa}, whilst the axial and polar gravitational spectra are shown to split for $a\neq0$ \textit{and} $\Lambda \neq0$. Given the good agreement with numerical results, the analytic expressions for QNM frequencies presented here provide a useful addition to those techniques already in the modern physicist's toolbox, allowing one to see the explicit dependence of the QNM frequencies on the parameters of the black hole and/or field. The study of gravitational QNM frequencies is, of course, of great interest in the context of gravitational wave observations. Properties of black hole merger remnants can be inferred from the observation of the QNM ringing, as well as tests of GR and of the `no-hair hypothesis' \cite{Dreyer:2003bv,Berti:2005ys,Berti:2015itd,0264-9381-33-17-174001,2018PhRvD..97d4021T,Berti:2018vdi,Barack:2018yly,Brito:2018rfr}. Meanwhile, the study of the QNM frequencies of massive bosons (e.g. the scalar and vector cases considered here) propagating on rotating black hole backgrounds finds great relevance in the study of black hole superradiance \cite{Brito:2015oca}. Furthermore, the AdS/CFT correspondence continues to provide motivation for studying QNMs in asymptotically AdS spacetimes \cite{Maldacena:1997re,Nunez:2003eq,Son:2007vk,Hartnoll:2009sz,Herzog:2009xv}. The technique of recasting the complicated, multidimensional, equations of motion governing black hole perturbations in GR into decoupled one-dimensional Schr{\"o}dinger style equations is an incredibly useful one that has allowed great advances in the understanding and numerical calculation of QNM frequencies. The ability to execute such a simplification of the equations of motion, and in particular to include the effects of rotation, in theories of gravity \textit{beyond} GR is in many cases still a work in progress \cite{Tattersall:2018nve,Konoplya:2001ji,Cardoso:2009pk,Molina:2010fb,Lasky:2010bd,Brito:2013wya,Brito:2013yxa,Babichev:2015zub,Blazquez-Salcedo:2016enn,Blazquez-Salcedo:2017txk,Dong:2017toi,2018arXiv180709081B,Zhang:2014kna}. Given that the strong gravity regime of black hole mergers is likely to be one of the best `laboratories' available to us to probe any potential deviations from Einstein's theory, continuing the analysis of black hole perturbations for a variety of fields in alternative theories of gravity will remain an important avenue of research as gravitational wave astronomy matures in the coming years. | 18 | 8 | 1808.10758 |
1808 | 1808.02698_arXiv.txt | {It has been suggested that the well-studied giant HII regions M16 and M17 may have had a common origin, being an example of large-scale triggered star formation. While some features of the distribution of the interstellar medium in the region support this interpretation, no definitive detection of an earlier population of massive stars responsible for the triggering has been made thus far.} {We have carried out observations looking for red supergiants in the area covered by a giant shell seen in HI and CO centered on galactic coordinates $l \sim 14^\circ 5$, $b\sim +1^\circ$ that peaks near the same radial velocity as the bulk of the emission from both giant HII regions, which are located along the shell. Red supergiants have ages in the range expected for the parent association whose most massive members could have triggered the formation of the shell and of the giant HII regions along its rim.} {We have obtained spectroscopy in the visible of a sample of red stars selected on the basis of their infrared colors, whose magnitudes are consistent with them being red supergiants if they are located at the distance of M16 and M17. Spectroscopy is needed to distinguish red supergiants from AGB stars and RGB stars, which are expected to be abundant along the line of sight.} {Out of a sample of 37 bright red stars, we identify four red supergiants that confirm the existence of massive stars in the age range between $\sim 10$ and $\sim 30$~Myr in the area. At least three of them have Gaia DR2 parallaxes consistent with them being at the same distance as M16 and M17.} {The evidence of past massive star formation within the area of the gaseous shell lends support to the idea that it was formed by the combined action of stellar winds and ionizing radiation of the precursors of the current red supergiants. These could be the remnants of a richer population, whose most massive members have exploded already as core-collapse supernovae. The expansion of the shell against the surrounding medium, perhaps combined with the overrun of preexisting clouds, is thus a plausible trigger of the formation of a second generation of stars currently responsible for the ionization of M16 and M17.} | \label{intro} The close proximity in the sky of M16 and M17, two of the nearest giant HII regions of our galactic neighbourhood lying at a similar distance from the Sun, naturally leads to the question of whether they are physically related, and whether they may share a common origin \citep{Moriguchi02,Oliveira08, Nishimura17}. Both giant HII regions are projected on the contour of a giant bubble-shape structure, outlined in the distribution of HI and CO emission as first noted by \citet{Moriguchi02}. This suggests that the formation of M16 and M17 could have been triggered by the expansion of the bubble, powered by a previous generation of massive stars near its center, thus representing an example of triggered star formation at the scale of several tens of parsecs \citep{Elmegreen98}. Given the ages of the giant HII regions, the timescale of expansion of a wind-blown bubble, and the short lifetimes of massive stars, it is to be expected that the most massive members of that previous generation may have exploded as supernovae several Myr ago. The spatial dispersion of the members of the association that must have taken place progressively during its existence, combined with the distance of 2~kpc to the M16/M17 complex and the large amount of unrelated foreground and background stars in that general direction, would make it extremely difficult to identify even its currently hottest members still remaining on the main sequence. \citet{Moriguchi02} noted the presence of O and early B stars in the area and proposed them to be part of a massive star population responsible for having caused the bubble, but a review of their properties shows them to be generally too bright to be at the distance of the bubble and the giant HII regions, most likely being instead members of a foreground population. Red supergiants stars offer a venue to circumvent this problem. They are the descendants of stars with initial masses between 7 and 40~M$_\odot$ \citep{Hirschi10}, which reach this phase after leaving the main sequence at ages ranging from 5~Myr to 50~Myr, the precise value depending on both the initial mass and the initial rotation velocity \citep{Ekstroem12}. The duration of the red supergiant phase ranges from several hundred thousands of years to about 2~Myr. Although relatively short-lived, red supergiants are found in significant numbers in rich stellar aggregates with ages extending up to a few tens of Myr, and their luminosity makes them stand out at near infrared wavelengths, therefore making them suitable and easily accessible probes of past massive star formation in regions where O-type stars have already completed their lifecycles \citep{Davies07,Clark09,Messineo14,Negueruela16,Alegria18}. Here we present the results of a search for the vestiges of the massive stellar association that could have triggered the formation of the shell containing M16 and M17 through the identification of red supergiants in the area. We present our target selection criteria and our findings, through which we produce a crude estimate of the overall massive star content of the association and the mechanical energy deposited in the bubble, which suggest that the scenario of triggered formation of M16 and M17 is indeed plausible. | } We have developed the interpretation of the presence of four red supergiants in the interior of the shell in whose rim M16 and M17 are located as an indication for the past existence of a rich OB association in the region. The association, which formed massive stars over an extended period lasting from $\sim 30$~Myr to $\sim 10$~Myr ago, may have hosted several tens of O stars and the precursors of around one hundred supernovae up to the present time. Such an extended period of star formation may not be an anomalous feature of large, rich OB associations, based on similar recent findings on the younger, more nearby Cygnus OB2 association \citep{Hanson03,Comeron12,Comeron16,Berlanas18}. Our estimates about the richness of the association and its supernova history involve some grossly oversimplifying assumptions, and should not be taken as a quantitative proof of the hypothesis. However, we have shown that the injection of mechanical energy into the bubble by the postulated association could have produced a substantial rearrangement of the gas over hundred parsec-long scales, accounting for the current size of the shell, and an expansion at supersonic speeds up to the present, thus being able to compress the swept-up gas or previously existing gas concentrations encountered along the path of expansion, ultimately triggering further star formation. The origin and location of M16 and M17, two giant HII regions much younger than the estimated age of the old association, as a consequence of triggered star formation along the rim of the shell thus becomes a plausible scenario. A more realistic modeling should take into account at least a time-variable energy input consistent with the assumed star formation rate of the association and the expansion of the shell in a vertically stratified medium. Proposed examples of triggered star formation abound in the literature over a variety of scales. In particular, the high quality infrared observations from the {\sl Spitzer} and {\sl Herschel} space observatories over the last decade and a half have provided abundant support for the actual existence of triggered star formation along the edges of bubble-like HII regions \citep{Deharveng11, Samal14,Liu16,Gama16,Cichowolski18}. Examples at larger scales where star formation appears to have been caused by expanding supershells seen in HI in the disk of our Galaxy also exist \citep{Megeath03,Oey05,Arnal07,Lee09}, although the evidence is more elusive, largely due to confusion and crowdedness along the line of sight. Cleaner examples exist in the Magellanic Clouds \citep{Oey95,Efremov98} and other nearby galaxies with resolved populations \citep{Egorov14,Egorov17}, where the evidence for large-scale triggered star formation is more compelling. The hints reported here of an old association having caused the large molecular shell and possibly having triggered the formation of M16 and M17 along its rim, based on just four red supergiant stars, make it difficult to further confirm the proposed scenario. A prediction that may be validated in the near future is the existence of large amounts of early B-type stars, the still unevolved lower-mass counterparts of the red supergiant precursors, near the main sequence turn-off of the association. The location of those stars near the galactic equator makes it nearly impossible to identify them at present against the overwhelming foreground and background contamination. However, the final Gaia data release, with parallaxes of substantially better quality than the already excellent ones available at present, may make it possible to produce samples within precise distance boundaries in which early-type stars could be easily distinguished. The coincidence at a similar distance of two young giant HII regions, an evolved supershell, and the remnants of an old, rich association in its interior might not be the ultimate proof of the triggered common origin of M16 and M17, but would strongly support it. | 18 | 8 | 1808.02698 |
1808 | 1808.05247_arXiv.txt | We present measurements of the large-scale ($\approx 40$ comoving Mpc) effective optical depth of \ion{He}{2} \lya\ absorption, \teff, at $2.54<z<3.86$ toward 16 \ion{He}{2}-transparent quasars observed with the Cosmic Origins Spectrograph (COS) on the \textit{Hubble Space Telescope} (\textit{HST}), to characterize the ionization state of helium in the intergalactic medium (IGM). We provide the first statistical sample of \teff\ measurements in six signal-to-noise ratio $\ga 3$ \ion{He}{2} sightlines at $z>3.5$, and study the redshift evolution and sightline-to-sightline variance of \teff\ in 24 \ion{He}{2} sightlines. We confirm an increase of the median \teff\ from $\simeq 2$ at $z=2.7$ to $\mteff\ga 5$ at $z>3$, and a scatter in \teff\ that increases with redshift. The $z>3.5$ \ion{He}{2} absorption is predominantly saturated, but isolated narrow ($\Delta v<650$\,km\,s$^{-1}$) transmission spikes indicate patches of reionized helium. We compare our measurements to predictions for a range of UV background models applied to outputs of a large-volume (146 comoving Mpc)$^3$ hydrodynamical simulation by forward-modeling our sample's quality and size. At $z>2.74$ the variance in \teff\ significantly exceeds expectations for a spatially uniform UV background, but is consistent with a fluctuating radiation field sourced by variations in the quasar number density and the mean free path in the post-reionization IGM. We develop a method to infer the approximate median \ion{He}{2} photoionization rate \gheii\ of a fluctuating UV background from the median \teff, finding a factor $\simeq 5$ decrease in \gheii\ between $z\simeq 2.6$ and $z\simeq 3.1$. At $z\simeq 3.1$ a $\mgheii=\left[9.1^{+1.1}_{-1.2}\,\mathrm{(stat.)}\,^{+2.4}_{-3.4}\,\mathrm{(sys.)}\right]\times 10^{-16}$\,s$^{-1}$ corresponds to a median \ion{He}{2} fraction of $\simeq 2.5$\%, indicating that our data probe the tail end of \ion{He}{2} reionization. | The epoch of helium reionization marked the final baryonic phase transition to substantially influence the thermal and ionization state of the IGM. While hydrogen reionization occurred at $z\ga 6$ \citep[e.g.,][]{fan06,becker15,davies18b,planckcollab18}, the completion of \ion{He}{2} reionization was likely delayed to $z\sim 3$ when quasars became numerous enough to supply the required hard ($E=h_\mathrm{P}\nu>54.4$\,eV) UV photons \citep[e.g.][]{madau94,miralda-escude00,mcquinn09a,compostella13,compostella14}. The current picture of a quasar-driven \ion{He}{2} reionization process extending over $\sim 1$\,Gyr is supported by most measurements of the $z>3$ quasar luminosity function \citep[e.g.,][]{hopkins07,mcgreer13,jiang16,kulkarni18}, which yield a total quasar emissivity sufficient to complete \ion{He}{2} reionization by $z\sim 3$ \citep{madau99,miralda-escude00,wyithe03,furlanetto08,haardt12,laplante16,khaire17,puchwein19,kulkarni18}. However, such photon budget arguments only provide rough constraints on the \ion{He}{2} reionization history due to their simplified treatment of the gas density distribution, in particular the gradual reionization of optically thick absorbers near the end of reionization \citep{bolton09,madau17}. Semianalytic models and detailed cosmological radiative transfer simulations that self-consistently include the physics governing \ion{He}{2} reionization both predict that the bulk of intergalactic \ion{He}{2} was reionized by the emerging quasar population at $z\la 5$, and ended with the percolation of the \ion{He}{3} zones around quasars at $z\sim 3$ \citep{fardal98,miralda-escude00,sokasian02,gleser05,furlanetto08,tittley07,furlanetto09,faucher09,mcquinn09a,furlanetto10,tittley12,compostella13,compostella14}. However, there remains significant uncertainty in the precise timing and morphology of \ion{He}{2} reionization, as the detailed conditions of the intergalactic gas during and after \ion{He}{2} reionization depend on several poorly constrained parameters of the high-redshift quasar population (e.g.\ their duty cycle, spectral energy distribution and opening angle), and the frequency and structure of self-shielding absorbers. Typically, several generations of quasars are required to fully reionize a given region, resulting in a rich thermal and ionization structure of the gas \citep{compostella13,compostella14}. Over the last two decades much theoretical and observational work has focused on the thermal state of the IGM during and after \ion{He}{2} reionization. During \ion{He}{2} reionization supersonic quasar ionization fronts impulsively heat the IGM which subsequently relaxes to a tight post-reionization power-law temperature-density relation governed by adiabatic (Hubble) cooling and photoheating by a quasi-homogeneous UV background \citep[e.g.][]{hui97,haehnelt98b,furlanetto08b,bolton09b,mcquinn09b,becker11,compostella13,compostella14,puchwein15,mcquinn16,laplante17}. The exact amount of injected heat ($\Delta T= 5,000$--$10,000$\,K) depends on the duration of \ion{He}{2} reionization, the spatial clustering of the sources, and their typical spectral energy distribution \citep{tittley07,bolton09,mcquinn09b,compostella13,compostella14,puchwein15}. Information on the thermal state of the IGM has been extracted from the \ion{H}{1} Ly$\alpha$ forest by decomposing it into individual absorption lines \citep{schaye00,ricotti00,bryan00,mcdonald01b,rudie12,bolton14,rorai18,hiss18} or by treating it as a continuous field using various transmission statistics, i.e.\ the probability distribution function \citep{bolton08,viel09,calura12,lee15,rorai17a}, the power spectrum \citep{zaldarriaga01,walther18,walther19}, the transmission curvature \citep{becker11,boera14}, wavelet decomposition \citep{theuns02a,theuns02c,lidz10,garzilli12}, and the quasar pair phase angle distribution \citep{rorai17b}. Despite large statistical errors and some remaining tension between the measurements, these studies indicate an extended heating of the IGM from $z\simeq 6$ \citep{bolton10,bolton12} to $z\simeq 2.8$ \citep{schaye00,becker11,boera14,hiss18} expected from an extended \ion{He}{2} reionization process. Very recent results from \citet{walther19} show a rise in the IGM temperature from $z=5$, peaking at $z\sim 3.4$, and subsequent cooling to $z=1.8$, which can only be explained as being a result of extended \ion{He}{2} reionization. The \ion{He}{2} reionization epoch can be studied directly via spectroscopy of intergalactic \ion{He}{2} Ly$\alpha$ absorption ($\lambda_\mathrm{rest}=303.78$\,\AA) toward far-UV (FUV)-bright quasars at $z>2$. The discovery and systematic study of the \ion{He}{2} Ly$\alpha$ forest at $z\ga 2.7$ has been a science driver for \textit{HST} since its inception \citep{bahcall79}. However, despite extensive efforts during the first 15 years of \textit{HST} operations, only seven \ion{He}{2} sightlines had been successfully probed, because for most $z_\mathrm{em}>2.7$ quasars the spectral range covering the \ion{He}{2} Lyman series is blacked out by optically thick \ion{H}{1} Lyman limit systems in the foreground IGM \citep{picard93,worseck11}. Early \textit{HST} spectra of varying spectral resolution and quality revealed strong evolution of the \ion{He}{2} Ly$\alpha$ effective optical depth \teff\ from Gunn-Peterson troughs ($\mteff\ga 3$) measured toward four $z_\mathrm{em}>3$ quasars \citep{jakobsen94,hogan97,anderson99,heap00,zheng04b,zheng08} to fluctuating \ion{He}{2} absorption at $2.7\la z\la 2.9$ \citep{reimers97,reimers05,heap00,smette02}. High-resolution spectra taken with the \textit{Far Ultraviolet Spectroscopic Explorer} (\textit{FUSE}, $R=\lambda/\Delta\lambda\approx 20,000$) resolved the \ion{He}{2} Ly$\alpha$ forest in two sightlines \citep{kriss01,shull04,zheng04,fechner06,fechner07}. Inferences on the \ion{He}{2} reionization history, however, were severely limited by sample variance and data quality \citep{mcquinn09a,furlanetto10}. The first panoramic FUV imaging surveys by the \textit{Galaxy Evolution Explorer} \citep[\textit{GALEX},][]{martin05,morrissey07} enabled the efficient photometric selection of likely \ion{He}{2}-transparent quasar sightlines \citep{syphers09a,syphers09b,worseck11}. \textit{HST} follow-up spectroscopy with the FUV-sensitive Cosmic Origins Spectrograph \citep[COS,][]{green12} yielded a sample of 11 new science-grade (signal-to-noise ratio S/N$\ga 3$) \ion{He}{2} Ly$\alpha$ absorption spectra covering $2.7\la z\la 3.8$ \citep{worseck11b,syphers12,zheng15,worseck16}. Together with high-quality COS spectra of the previously known sightlines \citep{shull10,syphers13,syphers14}, these new sightlines enabled statistical studies of the intergalactic \ion{He}{2} Ly$\alpha$ opacity and constraints on the \ion{He}{2} reionization history. The diminishing sightline-to-sightline variance in the large-scale ($\sim 40$ comoving Mpc) \ion{He}{2} effective optical depth indicates that \ion{He}{2} reionization completed at $z\simeq 2.7$ \citep{worseck11b}. In \citet[][hereafter \citetalias{worseck16}]{worseck16} we presented first results of the Helium Reionization Survey (HERS), a comprehensive campaign to study the epoch of \ion{He}{2} reionization with \textit{HST} \ion{He}{2} absorption spectra. Our analysis of 17 sightlines revealed a gradual increase in the \ion{He}{2} effective optical depth from $z=2.3$ ($\mteff\simeq 1$) to $z=3.4$ ($\mteff\ga 4.5$) with strong sightline-to-sightline variance at $z>2.7$, consistent with a predominantly ionized IGM with large UV background fluctuations \citep[][hereafter \citetalias{davies17}]{davies14,davies17}. Numerical simulations of quasar-driven \ion{He}{2} reionization struggle to reproduce the observed distribution of \ion{He}{2} effective optical depths at $z\simeq 3.4$ \citep{mcquinn09a,compostella13}, suggesting a very extended epoch of \ion{He}{2} reionization \citepalias{worseck16}. However, this apparent tension may be due to the limited number of quasar models run in limited simulation volumes \citep{daloisio17}, or due to the small number of four \ion{He}{2} sightlines covering $z\simeq 3.4$ \citep{compostella14}. A large population of faint quasars may accomplish \ion{He}{2} reionization at $z>4$ \citep{madau15}, but underpredicts the observed \ion{He}{2} effective optical depths at $2.7<z<3$\citep{worseck16,mitra18,puchwein19,garaldi19} unless the post-reionization UV background is strongly fluctuating on large scales (\citealt{furlanetto10,mcquinn14,davies14}; \citetalias{davies17}). Likewise, an early \ion{He}{2} reionization would prematurely heat the IGM \citep{daloisio17,mitra18,puchwein19,garaldi19}. Similarly, the \ion{H}{1} effective optical depths display a large sightline-to-sightline variance at $z>5.5$ \citep{becker15}, possibly persisting to $z\simeq 5.2$ \citep{bosman18,eilers18}. These may be explained by relic temperature fluctuations from patchy \ion{H}{1} reionization \citep{daloisio15,keating18} and/or large UV background fluctuations that are either sourced by clustered galaxies and a short mean free path to ionizing photons \citep{davies16,davies18a,daloisio18,becker18} or rare bright sources, such as quasars \citep{chardin15,chardin17}. While quasars are likely not abundant enough to substantially contribute to the $z\ga 5$ \ion{H}{1}-ionizing UV background and \ion{H}{1} reionization \citep[e.g.][but see \citealt{giallongo15}]{jiang16,ricci17,mcgreer18,parsa18,matsuoka18,kulkarni18,wang18}, it may be necessary to include them in reionization models in order to explain the fluctuations in the effective optical depths of \ion{H}{1} at $z>5.5$ \citep[although see \citealt{kulkarni18b}]{chardin15,chardin17} and of \ion{He}{2} at $z\simeq 3.4$ \citep{compostella14}. In light of this heated debate on the duration of \ion{He}{2} reionization, the sources of reionization, and the high-redshift UV background, it is timely to extend the sample of \ion{He}{2} absorption measurements, particularly at $z>3$. In this manuscript we present \textit{HST}/COS spectra of eight additional \ion{He}{2}-transparent quasars (Section~\ref{sect:obsdatared}) that more than double the redshift pathlength sensitive to $\mteff\sim 5$ at $3<z<3.5$, and provide a statistically meaningful sample of six \ion{He}{2} sightlines probing $z>3.5$ (Section~\ref{sect:he2zpath}). With an enlarged sample of measured \ion{He}{2} effective optical depths (Section~\ref{sect:he2tauevol}) and using realistic forward-modeled mock spectra from a large-volume hydrodynamical simulation \citep{lukic15}, we test recent models of the \ion{He}{2}-ionizing background \citep[\citetalias{davies17};][]{puchwein19}, and provide measurements of the evolving \ion{He}{2} photoionization rate and the corresponding \ion{He}{2} fraction at $2.3<z<3.86$ (Sections~\ref{sect:he2uvb} and \ref{sect:discussion}). We conclude in Section~\ref{sect:conclusions}. We adopt a flat cold dark matter cosmology with dimensionless Hubble constant $h=0.685$ ($H_0=100h$\,km\,s$^{-1}$\,Mpc$^{-1}$) and density parameters $\left(\Omega_\mathrm{m},\Omega_\mathrm{b},\Omega_\Lambda\right)=(0.3,0.047,0.7)$ for total matter, baryons, and cosmological constant, consistent with \citet{planckcollab18}. In this cosmology $\Delta z=0.04$ -- the standard interval that we will use for our \teff\ measurements -- corresponds to a distance interval of $\approx 40$ comoving Mpc (hereafter cMpc) at $z=3$. The object designations of quasars discovered by SDSS will be abbreviated to SDSS~J\texttt{HHMM$\pm$DDMM}. | \label{sect:conclusions} We have conducted a systematic survey to characterize the ionization state of intergalactic helium at $2.3<z<3.8$ with \textit{HST} \ion{He}{2} Ly$\alpha$ absorption spectra. Building on earlier results \citepalias{worseck16}, we have analyzed \textit{HST}/COS spectra of eight additional \ion{He}{2}-transparent $z_\mathrm{em}>3$ quasars, six of which had been discovered in our dedicated survey for FUV-bright high-redshift quasars (dubbed HE2QS, Figure~\ref{fig:he2newspc}). These spectra increase the redshift pathlength sensitive to high \ion{He}{2} effective optical depths $\mteff\sim 5$ by more than a factor of two at $3<z<3.5$, and provide the first statistically meaningful sample of six \ion{He}{2} sightlines at $z>3.5$. Adding archival higher-quality high-resolution spectra of four known \ion{He}{2}-transparent quasars, we have constructed a total sample of 25 science-grade (S/N$\ga 3$) \textit{HST} \ion{He}{2} Ly$\alpha$ absorption spectra, available from our survey data repository \footnote{\url{https://archive.stsci.edu/prepds/hers/}}. Our main results can be summarized as follows: \begin{enumerate} \item At $z>3.5$ \ion{He}{2} Ly$\alpha$ absorption is predominantly saturated with some isolated narrow ($\Delta v<650$\,km\,s$^{-1}$) transmission spikes, most of which are unresolved and/or impacted by Poisson noise in our \textit{HST}/COS G140L spectra (Figure~\ref{fig:he2spczoom2}). At $z<3.5$ these features become more numerous and broader (Figure~\ref{fig:he2spczoom1}), but the \ion{He}{2} Ly$\alpha$ absorption is still patchy at $2.7<z<3.3$ with significant sightline-to sightline variance. \item The \ion{He}{2} effective optical depth on a scale $\Delta z=0.04$ ($\approx 40$\,cMpc at $z=3$) increases from $\mteff\simeq 2$ at $z=2.7$ to a sensitivity limit $\mteff\ga 5$ at $z>3$, but with significant sightline-to-sightline variance at $z>2.7$ that increases with redshift (Figure~\ref{fig:he2tau_model}). At $z>3$ regions with $\mteff<5$ gradually disappear as a result of the diminishing number and significance of \ion{He}{2} transmission spikes. At $z\simeq 3.4$ our larger sample yields a lower fraction of statistically significant $\mteff\la 5$ values ($26.1$\%) than in \citetalias{worseck16} (50\%), bringing the data into better agreement with numerical models of the fluctuating \ion{He}{2}-ionizing radiation field at the tail end of \ion{He}{2} reionization (\citealt{compostella14}; \citetalias{davies17}). Still, 6/38 $\Delta z=0.04$ regions at $z>3.5$ show statistically significant \ion{He}{2} transmission. \item We have compared our \teff\ measurements to predictions for a range of UV background models applied to outputs of a large ($100h^{-1}$\,cMpc) high-resolution ($25h^{-1}$\,ckpc) hydrodynamical simulation, forward-modeling variations in data quality and sample size. At $z>2.74$ the observed variance in \teff\ cannot be reproduced by a spatially uniform redshift-dependent \ion{He}{2}-ionizing background (Figure~\ref{fig:he2gammavar1}), strictly confining the applicability of common UV background synthesis models to $z<2.74$ \citep[e.g.][]{faucher09,haardt12,puchwein19}. Instead, the observed \teff\ distributions closely agree with predictions of the \citetalias{davies17} fluctuating post-reionization UV background that is due to the varying quasar number density and the mean free path to \ion{He}{2}-ionizing photons. This suggests an extended overlap epoch of \ion{He}{3} zones around quasars at $2.7\la z\la 3.3$ that is captured by the \citetalias{davies17} model without deliberately tuning its parameters. However, at $z>3.3$ we cannot distinguish between this scenario and ongoing \ion{He}{2} reionization due to limited sensitivity to $\mteff\sim 5$ and model assumptions (\citealt{davies14}; \citetalias{davies17}). \item We have developed a method to infer the characteristic \ion{He}{2} photoionization rate by matching the median \teff\ of observed and mock data, respectively. Tests with mock data confirmed that our procedure approximately recovers the median value of a \gheii\ distribution with sightline-to-sightline variance but spatial coherence on the adopted scale $\Delta z=0.04$. The inferred \gheii\ decreases by a factor $\simeq 5$ between $z\simeq 2.6$ and $z\simeq 3.1$ (Figure~\ref{fig:he2gammacomp}), in very good agreement with the median $\mgheii\left(z\right)$ by \citetalias{davies17}. At $3.06<z<3.26$ our inferred $\mgheii=\left[9.1^{+1.1}_{-1.2}\,\mathrm{(stat.)}\,^{+2.4}_{-3.4}\,\mathrm{(sys.)}\right]\times 10^{-16}$\,s$^{-1}$ translates to a median \ion{He}{2} fraction $\mxheii\simeq 0.025$, confirming that our sample of \ion{He}{2} sightlines probes the tail end of \ion{He}{2} reionization that is well approximated by the \citetalias{davies17} fluctuating UV background model. At $z>3.3$ our constraints are limited by saturation in \ion{He}{2} \lya\ due to IGM density evolution, decreasing instrument sensitivity, and a small sample size. \end{enumerate} In summary, our sample of \ion{He}{2} sightlines probes the extended end phase of \ion{He}{2} reionization and the build-up of the \ion{He}{2}-ionizing background with gradually diminishing fluctuations, in good agreement with recent models (\citealt{compostella14}; \citetalias{davies17}). At $z>3$ the observed \teff\ distributions are consistent with models of \ion{He}{2} reionization primarily driven by the observed quasar population at $z>4$ \citep{compostella14}. At face value, our six $\mteff\la 4$ values at $z>3.5$ indicate mild tension with these models, which may be due to the few specific quasar models run on limited simulation volumes \citep[e.g.][]{daloisio17}. Future progress requires large-volume \ion{He}{2} reionization simulations with accurate radiative transfer (see \citealt{laplante17} for a recent effort) but also more and higher-quality data. Our forthcoming \textit{HST} program (PID~15356, PI Worseck) aims at resolving the \ion{He}{2} Ly$\alpha$ absorption toward the two UV-brightest $z>3.5$ \ion{He}{2}-transmitting quasars discovered in our dedicated survey, to verify and resolve isolated narrow \ion{He}{2} transmission spikes. In the near future, optical slitless prism spectroscopy currently obtained by the \textit{Gaia} satellite will provide a complete census of bright quasars on the full sky \citep[e.g.][]{proft15} that does not exhibit the specific bias against UV-bright $z_\mathrm{em}>2.7$ quasars in optical color-selected samples \citep{worseck11}. Correlation of the \textit{Gaia} quasar catalog to \textit{GALEX} photometry will reveal further likely \ion{He}{2}-transparent quasars to complete \textit{HST}'s legacy on \ion{He}{2} absorption spectroscopy. The physical interpretation of these data will require dedicated efforts to run large-volume radiative transfer simulations of \ion{He}{2} reionization that use updated quasar luminosity functions \citep{kulkarni18} and the latest constraints on the distribution of quasar lifetimes \citep{eilers17,schmidt18,khrykin19}. These simulations will also make detailed predictions for the early stages of \ion{He}{2} reionization at $z>4$ that may be studied with sensitive \ion{He}{2} absorption spectroscopy obtained with a next-generation large-aperture UV space telescope. | 18 | 8 | 1808.05247 |
1808 | 1808.03632_arXiv.txt | We study the chaotic properties of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is measured for simulations with varying Reynolds number and magnetic Prandtl number. We extend the Ruelle theory of hydrodynamic turbulence to magnetohydrodynamic turbulence as a working hypothesis and find broad agreement with results. In other simulations we introduce magnetic helicity and these simulations show a diminution of chaos, which is expected to be eliminated at maximum helicity. We also find that the difference between two initially close fields grows linearly at late times, which was also recently found in hydrodynamics. This linear growth rate is found to be dependent on the dissipation rate of the relevant field. We discuss the important consequences this linear growth has on predictability. We infer that the chaos in the system is totally dominated by the velocity field and connect this work to real magnetic systems such as solar weather and confined plasmas. | Introduction} Turbulence displays chaotic dynamics. A small change in initial conditions will result in a large difference in the state at later times, with this difference growing exponentially. This exponential growth of error puts limits on the predictability of the system, and understanding these limits is important for forecasting the evolution of fluids governed by turbulence. Turbulence, or its underlying equations, is interesting from a dynamical systems point of view. In this context, it is just another dynamical system of which we wish to know the chaotic properties. In homogeneous isotropic turbulence (HIT), recent results have shown a relationship between the Reynolds number, Re, and the maximal Lyapunov exponent, $\lambda$, for chaos in an Eulerian (considering the difference between two fields) description \cite{Berera2018,Boffetta2017} consistent with theoretical predictions by Ruelle \cite{Ruelle1979,Crisanti1993}. In these simulations, two initially close fields were evolved concurrently and their difference quantified. Surprisingly, a limit was found on the growth of this difference which is proportional to the dissipation rate. This paper presents analysis of a set of simulations of magnetohydrodynamic (MHD) turbulence, also known as hydromagnetic turbulence. This is the first analysis of chaos in MHD turbulence in an Eulerian context. Within this first analysis, we produce a dataset for chaotic behavior in MHD in the range of Prandtl number that is comparable to all the simulation data to date on MHD spectra. The analysis of these simulations and presentation of the data from them is the main work of this paper. We develop a working hypothesis that the level of chaos primarily depends on quantities dependent on the velocity field only. This hypothesis is found to show reasonable consistency with the results from our simulations. There is room for further theoretical consideration but that is beyond the scope of this paper which is only focussed on the measurements of the Lyapunov exponents. Our simulations also show a growth limit analogous to that in hydrodynamics, but for MHD the value of this limit differs for the magnetic versus velocity fields. The evolution of an uncharged fluid is described by the Navier-Stokes equation, whilst the evolution of an electrically conducting fluid is described by the MHD equations. The incompressible MHD equations are \begin{align} \label{eq:MHD} \partial_t \vec{u} &= - \frac{1}{\rho}\nabla P -(\vec{u}\cdot \nabla)\vec{u} + \nu \Delta \vec{u} + \frac{1}{\rho}(\nabla \times \vec{b}) \times \vec{b} \ , \\ \partial_t \vec{b} &= (\vec{b} \cdot \nabla) \vec{u} - (\vec{u} \cdot \nabla) \vec{b} + \eta \Delta \vec{b} \ , \ \nabla \cdot \vec{u} = \nabla \cdot \vec{b} = 0 \ , \end{align} with velocity field $\vec{u}$, magnetic field $\vec{b}$, density $\rho$, pressure $P$, viscosity $\nu$, and magnetic diffusivity $\eta$. Like the Navier-Stokes equations which they modify, they also display turbulence \cite{Biskamp2003}. In the equations above, the incompressible assumption is made. In many real world applications, such as at laboratories and space plasma systems, the incompressible assumption is made merely for convenience, and it is known that compressible effects can be of importance. As well, there may be complications from the reduced MHD limit, where there are very large guide magnetic fields \cite{Kadomtsev1974,Strauss1976}. The velocity perpendicular to the guide field is incompressible, but the parallel component can be far from incompressible, and in fact sound waves can play an important role \cite{Zank1993}. However, as the simulations analysed in this paper use the incompressible MHD equations, they are presented here in the above form. The MHD equations contain three ideal inviscid invariants which should hold within the inertial range. These are total energy, magnetic helicity, and magnetic cross helicity. The magnetic helicity, although not positive definite, can undergo an inverse transfer from the small to large length scales \cite{Brandenburg2001,Alexakis2006}. This transfer itself is considered to not be a proper cascade since it vanishes in the limit of infinite magnetic Reynolds number \cite{Alexakis2018}. Whilst these are the invariants for HIT, other invariants, which can be important, may exist and depend on the geometric configuration. The literature investigating the intersection of MHD and chaos is sparse. The relative dispersion of charged particles is predicted to grow exponentially for intermediate times when they are initially close \cite{Misguich1982,Misguich1987}. The technique of extracting a Lyapunov-exponent spectrum from a time series \cite{Wolf1985} has been applied to experimental data from an undriven plasma system \cite{Huang1994}. Use of this technique reveals a transition from quasiperiodicity to chaos and allows the evaluation of the Lyapunov spectrum. In solar physics, a low dimensional attractor is suggested to be responsible for the data seen in pulsation events of solar radio emissions \cite{Kurths1986}. Shell models of turbulence applied to MHD with Pr $\sim 1$ have found \cite{Grappin1986} that the maximal Lyapunov exponent obeys $\lambda \sim \nu^{-1/2}$. Later results for turbulent models of Navier-Stokes found a similar scaling \cite{Yamada1987}, which is roughly the scaling found in DNS \cite{Berera2018}. MHD turbulence has a wide variety of applications, from turbulence in the solar wind \cite{Tu1995,Goldstein1995}, accretion disks \cite{Balbus1998,MacLow2004}, and the interstellar medium \cite{Goldreich1995,MacLow1999}. A lot of work in MHD turbulence has looked at magnetic reconnection at small scales, where compression enters as an important effect as well \cite{Biskamp1996,Yamada2010}. The effect of chaos on these physical systems should be understood, and could give new understanding of the dynamics. The relationship between MHD and chaos is also interesting from the viewpoint of predictability. Just as it is important to quantify the predictability of weather forecasts to understand the time horizons over which a prediction can be considered accurate, it is important to understand the predictability of forecasts where the governing equations are the MHD equations, such as in space weather \cite{Mirmomeni2009}, solar physics \cite{Karak2012}, and high latitude ground magnetic fields \cite{Weigel2003}. For instance, much effort is put into understanding solar flares, a phenomena governed by the MHD equations, because of the damage they can cause to artificial satellites and thus global communications \cite{Amari2014}. Whilst HIT is an ideal description of turbulence, it nonetheless should represent the behaviour of a turbulent system far from boundaries or at small scales. The work here may have practical use in these situations but also in tokamak reactors and fusion research where boundaries are present. More generally, establishing measures of chaos in turbulent fluids provides another probe alongside spectra for understanding the behavior of such complex systems. The paper is organized as follows: Section \ref{section3} extends the Ruelle prediction for hydrodynamic turbulence to MHD. Section \ref{sectionDNS} describes the code used and method for calculating Lyapunov exponents from the simulations. Section \ref{section5} goes over the results of the simulations and Section \ref{sectionConclusion} discusses implications of the results and application to other systems. \subsection{\label{section3}Working hypothesis for $\lambda$ in MHD} In a chaotic system, for two states which initially differ by separation $\delta_0$, % this separation will grow as $\delta(t) \sim \delta_0 \exp(\lambda t)$, where $\lambda$ is the maximal Lyapunov exponent. For fluid turbulence, this separation can either be particle positions within a Lagrangian description, or a measure of the difference between two fields within an Eulerian description. According to the theory of Ruelle \cite{Ruelle1979}, the maximal Lyapunov exponent for Navier-Stokes turbulence is given by \begin{align} \lambda \sim \frac{1}{\tau} \ , \end{align} where $\tau = \sqrt{\nu/\varepsilon_k}$ is the Kolmogorov microscale time and $\varepsilon_k$ the kinetic dissipation. The argument used by Ruelle requires the existence of an inertial range in order to justify the existence of a characteristic exponent % which is dependent only on the dissipation. Ruelle's arguments made no assumption about the frame of reference, so are equally applicable to both the Eulerian and Lagrangian descriptions. The exact relation between the Eulerian and Lagrangian descriptions for many quantities is unknown or very difficult to determine, but for application to this work of Ruelle this does not seem to be a major issue. In hydrodynamic turbulence this relation becomes \begin{align} \label{eq:alpha} \lambda \sim \frac{1}{T_0} Re^\alpha \ , \end{align} where $T_0 = L/u$ is the large eddy turnover time, Re $= uL/\nu$ is the Reynolds number, $u$ is the rms velocity, and $L$ the integral length scale, The Kolmogorov theory predicts that $\alpha = 0.5$ \cite{Crisanti1993,Kolmogorov1941a}. Intermittency corrections predict that $\alpha \lesssim 0.5$. However, DNS results have shown that, in an Eulerian description, $\alpha \gtrsim 0.5$ \cite{Berera2018,Boffetta2017,Mohan2017} whilst in a Lagrangian description $\alpha \lesssim 0.5$ \cite{Biferale2005}. These DNS results also show a corresponding behaviour for $\lambda \tau$ which either rises (for $\alpha > 0.5$) or falls (for $\alpha < 0.5$) with Re. We now look at how Ruelle's arguments can be extended to MHD. For this, observe that in the MHD evolution equations, Eq. (\ref{eq:MHD}), there is only a direct non-linearity for the velocity field itself. In contrast, the magnetic field is only indirectly non-linear via the velocity field. As such, we predict that the chaos due to the velocity field is dominant over that for the magnetic field. Thus, the Ruelle prediction, which relates the Lyapunov exponent to the smallest timescale \cite{Ruelle1979}, should only need to be modified slightly. We hypothesise that it depends on the smallest timescale that is itself dependent only on velocity field quantities. Thus we argue that the Ruelle prediction that $\lambda \sim \sqrt{\varepsilon_k / \nu}$, where $\varepsilon_k$ is the kinetic dissipation, should also hold for MHD in an Eulerian sense. This prediction that $\lambda \sim \nu^{-1/2}$ is also backed up by the findings of % shell models of turbulence mentioned previously \cite{Grappin1986,Yamada1987}. Although we expect the chaos to be dominated by the velocity field quantities, we cannot rule out that the magnetic field could strongly affect the chaos. Indeed, in Section \ref{sec:hel}, we find that an increase in magnetic helicity, a quantity which only depends on the magnetic field, decreases the level of chaos in the system. A similar effect might happen if there were a particularly strong alpha effect \cite{Brandenburg2005}. In extending findings of Eulerian chaos in hydrodynamics to MHD, there are other complications that must be tested, such as whether $\lambda \tau$ has any dependence on Re or Pr = $\nu/\eta$, the magnetic Prandtl number. Pr is known to have important effects on dissipation rates and the presence of inverse spectral transfer \cite{McKay2018}. This paper relies on this previous foundational work. Results from DNS simulations suggest that the ratio of $\varepsilon_k$ and $\varepsilon_b$ (where $\varepsilon_b$ is the magnetic dissipation) depends on the Prandtl number according to the relationship $\varepsilon_k/\varepsilon_b \sim$ Pr$^q$ \cite{Brandenburg2014,McKay2018} where $q$ depends on the presence of helicity in the system with $q > 0$ and so $\varepsilon_k$ should become totally dominant over $\varepsilon_b$. In hydrodynamics the growth rate of error is limited by $\varepsilon$ \cite{Berera2018,Boffetta2017}. This may carry over to MHD, and the specific dependence on either $\varepsilon_k$ or $\varepsilon_b$ needs to be tested. These are examined in Section \ref{section5}. | \label{sectionConclusion} The data presented here include Pr which cover three orders of magnitude. Although many of the results here are found to be independent of magnetic Prandtl number, there is direct comparison with many physical systems. Here we look at some of them in turn and see how our measurements can be useful for their further study. In toroidal plasmas, such as those found in tokamak reactors, Pr is expected to be on the order of 100 \cite{Itoh1993,Mendonca2018}. However, the turbulence is strongly confined and should be greatly affected by the boundary conditions, as such, an assumption of homogeneity and isotropy will not capture the full dynamics. There may be other practical reasons not to apply MHD as a model for the plasmas in tokamak reactors. Even so, the level of chaos in the system should be related to the generation of instabilities in the flow. These instabilities can affect the confinement of the plasma. As well, the level of instability should be affected by the level of inverse cascade, which is greater at increased Rm. Accretion disks around black holes and neutron stars are predicted to have regions where Pr is close to unity \cite{Balbus2008}. Though these should be affected by relativistic effects, if the results in this paper extend beyond the Prandtl number range of our simulations they may also apply to more typical accretion disks. By understanding the ratio of the dissipations, we can understand the relative importance of ion and electron heating in these systems which has an effect on the luminosity and thus their observational characteristics. In regions with greater chaos of the particles, those regions with lower Kolmogorov microscale time and lower magnetic helicity, the process of accretion should be reduced. If particles are, on average, moving together and not drifting apart exponentially, there should be a longer time for them to accrete. As such, in any accretion disk, we expect that the accretion rate should be increased by magnetic helicity and $\tau$. Indeed, simulations have shown already that accretion disks are associated with turbulent dynamo action, which is also associated with magnetic helicity \cite{Brandenburg2005}. Thus, an increased accretion rate should be associated with diminution of chaos, here consistent with increased magnetic helicity. Understanding the chaos seen in MHD turbulence is important for understanding the scope for prediction of turbulent conducting fluids. The findings here may also be applicable to coupled dynamical system where there is a direct non-linearity for only one of the fields and multiple relevant timescales. Our extension of the Ruelle prediction to MHD that $\lambda \sim 1/\tau$ is most consistent with our own data. We conclude that this is because the MHD equations are directly non-linear only in $\vec{u}$ and indirectly through the coupling for $\vec{b}$. We have also confirmed previous findings that show magnetic helicity results in a diminution of chaos and further predict that a fully magnetically helical system should have zero Lyapunov exponent, although these previous findings were not found in DNS \cite{Zienicke1998,Escande2000}. One of the most interesting results is the new finding that the growth of both $E_{ud}$ and $E_{bd}$ becomes linear with rates that depend on the dissipation rate of the relevant field. This may apply more generally to non-linearly coupled fields. Specifically in the case of high Pr, where $\varepsilon_k$ becomes dominant and $\varepsilon_b$ very small, then this has important implications for the long term predictability of galactic plasmas and magnetic fields. For high Re, we should expect $\lambda$ to be very large and that any small scale error should grow in size very quickly and so the the separation between the two fields will enter the linear regime very quickly. Thus, any predictability time will be dominated by $E/\varepsilon$ for the relevant field. For magnetic fields, this can become extremely large, and if there is a large amount of magnetic helicity in the system, then the predictability time of the magnetic fields can become very long. | 18 | 8 | 1808.03632 |
1808 | 1808.06151_arXiv.txt | Astronomers with experience studying quadruple lenses can reliably determine, by examination of relative positions and fluxes, whether a quartet of point sources is lensed. They have trained a neural network, located between their ears, to identify such systems. With the advent of the Gaia probe, quadruple lenses are being discovered at an astonishing rate (\cite{lemon}), and as evidenced by (\cite{delchambre}), there is a clear necessity for robust methods to model these systems. It is widely thought that the gravitational equipotentials that produce most quadruply lensed quasars can be reasonably approximated by concentric ellipses (\cite{ellipticalpotentials}). The simplest models for isothermal elliptical potentials include seven parameters, and a quartet of image positions gives eight constraints (\cite{sevenparam}). While that leaves one degree of freedom for use as a figure of merit, it can be difficult to find the best fitting model in that seven dimensional space. In what follows, we lean heavily on the work of (\cite{witt}), who finds that for elliptical potentials, the positions for all four images, the center of the lens, and the projected (but unobservable) position of the quasar all lie on an hyperbola whose asymptotes align with the potential's major and minor axes. The hyperbola gives us the position angle and restricts the positions of the lens and the source to a one dimensional locus. It reduces the dimensionality of the space to be searched from 7 to 3. We also show that for the specific case of the singular isothermal elliptical potential, there exists an ellipse mapping through all 4 image positions, whose minor axis is aligned with the major axis of the potential, has an axis ratio inverse to the axis ratio of the potential, and is centered on the source. \begin{figure*}[t!] \centering \includegraphics[width=16cm]{2M1134.pdf} \caption{Quadruple lens system 2M1134-2103, with both images at the same scale. On the left is a Sloan i filter image taken from the ATLAS survey, and the scale of this figure is 0\farcs21 per pixel. On the right is the plot our model produces for 2M1134-2103. The red dots are the image positions, the circle is the source position, and the star is the galaxy position. The parameter values are $b = 0\farcs92, q = 0.491, \theta = 133.1^{\circ}$ with $\sigma_{\ln{b}} = 0.071.$} \label{fig:2M1134} \end{figure*} We then search along Witt’s hyperbola for the source position and axis ratio that minimize the scatter in the lensing strengths determined by the positions of the four quasar images. We use this scatter as our figure of merit. In Section 2, we briefly explain gravitational lensing, and discuss the importance of quadruple lenses. In Section 3, we give background into the geometry associated with the quadruple systems, and explain our method of solving for the source position and axis ratio by minimizing the scatter in the lens strength. In Section 4, we compute our proposed figure of merit with a sample of spectroscopically confirmed quadruply lensed quasars. In Section 5, we analyze random quartets, and compare them to the known figures of merit. In Section 6, we discuss the results of the previous sections, and how they might be used to accept or reject the lensing hypothesis. | We discussed the basics of gravitational lensing, and the phenomenon of quadruple lenses. We then developed a method for modeling quadruply lensed quasars through the use of Witt's hyperbola and the complementary ellipse, as well as assigning a figure of merit to potential systems. We applied this method to 29 known quadruply lensed systems and 100 random quartets, and included their figures of merit. For future systems, this figure of merit can help astronomers determine if a newly discovered system is the product of gravitational lensing, or merely a random configuration. {\it Acknowledgements:} We thank Professor Alar Toomre for asking how we could tell quadruply lensed quasars from random quartets. We thank Professor Chuck Keeton of Rutgers for setting us straight about ellipses early in this effort and his pointing us toward Witt's work. Finally, we thank the MIT Undergraduate Research Opportunities Program for support. \printbibliography[title={References}] % \makeatletter \def\@seccntformat#1{% \expandafter\ifx\csname c@#1\endcsname\c@section\else \csname the#1\endcsname\quad \fi} \makeatother | 18 | 8 | 1808.06151 |
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1808 | 1808.07361_arXiv.txt | The analysis of distributions of some parameters of radio pulsars emitting X-ray radiation was carried out. The majority of such pulsars has short spin periods with the average value $< P >$ = 133 msec. The distribution of period derivatives reveals a bimodality, dividing millisecond ($< log \dfrac{dP}{dt}>$ = -19.69) and normal ($< log \dfrac{dP}{dt}> $ = -13.29) pulsars. Magnetic fields at the surface of the neutron star are characterized by the bimodal distribution as well. The mean values of $<log B_s>$ are $8.48$ and $12.41$ for millisecond pulsars and normal ones, respectively. The distribution of magnetic fields near the light cylinder, it does not show the noticeable bimodality. The median value of $log B_{lc}$ = 4.43 is almost three orders higher comparing with this quantity ($<log B_{lc}>$ = 1.75) for radio pulsars without registered X-ray emission. Losses of rotational energy ($<log \dfrac{dE}{dt}>$ = 35.24) are also three orders higher than corresponding values for normal pulsars. There is the strong correlation between X-ray luminosities and losses of rotational energies. The dependence of the X-ray luminosity on the magnetic field at the light cylinder has been detected. It shows that the generation of the non-thermal X-ray emission takes place at the periphery of the magnetosphere and is caused by the synchrotron mechanism. We detected the positive correlations between luminosities in radio, X-ray and gamma -ray ranges. Such correlations give the possibility to carry out a purposeful search for pulsars in one of these ranges if they radiate in other one. | One of the problems in pulsar investigations remains the understanding of the nature of their X-ray emission. There were some attempts to describe possible sources of this emission in pulsar magnetospheres (see, for example, \cite{Wang1998} and \cite{ZH2000}). However, an adequate description is absent up to now. At present there are detailed data for 61 radio pulsars from ATNF catalogue (ver. 1.58, \cite{Manchester2005}) emitting X-rays as was shown by \cite{Possenti2002, PB2015}. The X-ray observations by ROSAT (0.1-2 keV), ASCA (0.4-10 keV), XMM-Newton (0.2-12 keV) and Chandra (0.1-10 keV) have broadened significantly our understanding of origin and mechanism generation of non-thermal and thermal radiation from a neutron star, but not completely. We propose one of the ways in advancing the solution of this problem, namely the comparison of the parameters of radio pulsars, as loud and quiet X-ray sources, revealation of their essential differences and analysis of reasons causing such differences. The main aims of our work are comparing of the known pulsar parameters of two mentioned groups, search for their differences and analysis of possible reasons of such differences. The remainder of this paper is organised as follows. The used sample is presented in Section \ref{sect:sample}, also in this Section we consider some distributions of main parameters of loud and quiet pulsars. Section \ref{sect:relat} contains the analysis and the interpretation of some correlations between parameters of pulsars considered. In Section \ref{sect:conclusion} we discuss the obtained results and give the conclusions. | \label{sect:conclusion} \begin{itemize} \item The majority of radio pulsars with the registered X-ray emission has short spin periods with $<P>$ = 133 msec. \item The distribution of period derivatives shows the bimodality. One group of objects contains millisecond recycled pulsars with $<log\dfrac{dP}{dt}>$= -19.69, another one includes normal pulsars with $<log\dfrac{dP}{dt}>$ = -13.29. \item The similar bimodality is seen in the distribution of magnetic fields at the surface of the neutron star. The mean values of log B$_s$ are 8.46 and 12.43 for millisecond and normal pulsars, respectively. \item The distribution of magnetic fields at the light cylinder does not show the noticeable bimodality. Instead it can be presented by the unique gaussian. The median value of $<log B_{lc} >$ = 4.43 is almost three orders of magnitude higher than the corresponding values for radio pulsars without X-rays emission ($<log B_{lc}>$ = 1.75. \item The rate of losses of rotational energy for pulsars considered ($<log \dfrac{dE}{dt}>$ = 35.24) is also three orders higher than the corresponding values for pulsar quiet in X-rays. \item As was expected there was the strong correlation between X-ray luminosities of radio pulsars and the rates of losses of their rotational energy. The last ones are believed as the main source of energy for all processes in the pulsar magnetosphere. \item The dependence of X-ray luminosities on magnetic fields at the light cylinder is detected. This dependence shows that the generation of X-ray emission takes place at the periphery of the magnetosphere and is caused by the synchrotron mechanism. \end{itemize} The obtained results lead to the conclusion that the division of loud pulsars into 5 groups proposed by \cite{Possenti2002} is not necessary. In fact there are two populations. The first one includes pulsars with long spin periods and weak or absent X-ray radiation. They can emit thermal radiation from the surface. The second population contains objects with rather short periods. They are characterized by high magnetic fields near the light cylinder. This leads to the switching on the synchrotron mechanism and generation of non-thermal X-ray emission. The inverse Compton scattering of soft X-ray quanta on relativistic electrons can explain gamma-ray emission up to energies of hundreds GeV and may be even TeVs. The detected correlations between luminosities in different ranges give the possibility for a purposeful search for new pulsars in all diapasons if there is the registered radiation in one of these ranges. | 18 | 8 | 1808.07361 |
1808 | 1808.02544_arXiv.txt | We found that multi-periodic low-mass stars discovered by {\it Kepler} K2 in the Upper Scorpius association are close binaries with typical separations of the order of 10 au and large mass ratios. These stars were surveyed by speckle interferometry at the SOAR telescope with spatial resolution of 0\farcs04. Out of 129 observed targets, we resolved 70 pairs (including 16 previously known ones and three new triple systems). The distribution of projected separations of binaries with primary stars less massive than the Sun corresponds to a log-normal with median of 11.6 au and logarithmic dispersion of 0.60 dex, similar to M dwarfs in the field. Future orbits of newly discovered binaries will provide accurate measurements of masses to calibrate pre-main sequence evolutionary tracks; a tentative orbit of one previously known binary is determined here. | \label{sec:intro} As stars condense from gas, the excess of angular momentum is removed by a combination of mechanisms. Rotation and multiplicity of young stars reflect the result of this complex, still poorly understood process where disks play a major role. This is the context of the present work. The {\it Kepler} K2 campaigns furnished massive amounts of high-quality photometry of several young stellar clusters and associations, bringing statistical studies of stellar rotation to a new level. \citet{Rebull2018} (hereafter RSC18) found that about 20\% of low-mass stars in the Pleiades and Praesepe clusters and in the Upper Scorpius (USco) association have two or more photometric periods. They interpreted this as different rotation periods of comparable-brightness components in unresolved binaries. The location of multi-periodic stars on the color-magnitude diagrams (CMDs) supports this interpretation. However, Rebull et al. note that multiple periods can result from other phenomena such as differential rotation; they believe that low-mass multi-periodic stars are predominantly binaries, while some multi-periodic stars of higher mass are not binary. On the other hand, a binary with a large magnitude difference or an inactive component may have only one photometric period. So, not all binaries are multi-periodic and not all multi-periodic stars are binary. Identification of most low-mass multi-periodic stars with binaries still lacks a direct proof. Moreover, the separations of those hypothetical binaries remain unknown. Binary separation impacts the size and survival of the circumstellar disks which influence the rotation. \citet{Stauffer2018} determined that young low-mass multi-periodic stars rotate, on average, faster than single-stars, and related this finding to the different disk properties in single and multiple stars. We observed 129 multi-periodic stars in USco from Table~1 of RSC18 by speckle interferometry and spatially resolved 70 of them. This supports the proposed interpretation of low-mass multi-periodic stars as being mostly binaries and provides the distribution of their separations. Most resolved binaries have components of similar brightness, but we cannot tell to what extent this reflects the distribution of the mass ratios because our sample favors near-equal binaries. The observations are presented in Section~\ref{sec:obs}, their results are given in Section~\ref{sec:res} and are discussed in Section~\ref{sec:disc}. | \label{sec:disc} The large number of newly resolved binaries appears somewhat surprising, considering that USco has received considerable attention from this perspective. The pioneering work by \citet{Koehler2000} surveyed 118 stars in USco with an angular resolution of 0\farcs13 and revealed many binaries (hence the discoverer codes KOH in WDS). \citet{Kraus2007} used seeing-limited 2MASS imagery \citep[see also the follow-up work by][]{Aller2013}. \citet{Kraus2008} explored USco stars brighter than $R=14$ mag and north of $-25^\circ$ with high-contrast aperture masking, excluding known binaries, while \citet{Kraus2012} used laser adaptive optics to probe binarity of the 78 lowest-mass members of USco. \citet{Janson2013} and \citet{Laf2014} observed members of USco not covered by previous high-resolution imaging. These high-resolution studies involved modest samples and did not cover the complete USco association. As most low-mass stars are single, a sample of $\sim$100 targets yields only $\sim$20 binaries. In contrast, we start here with multi-periodic stars selected from the large parent sample. Our targets are from the outset expected to be binaries with components of comparable flux. This pre-selection ensures the large fraction of resolved binaries we found. With only a few hours of telescope time, we could substantially enlarge the number of known binaries among low-mass members of USco. Many new tight pairs have short periods and are an excellent material for future calibration of PMS stellar evolutionary models. It will be interesting to test binarity of unresolved multi-periodic targets using either a higher spatial resolution and/or a high-resolution spectroscopy. Both approaches involve large telescopes, hence pre-selection of unresolved targets from this study would be a valuable starting point allowing to save telescope time. We expect that {\it Gaia} will resolve many of these stars, will detect their accelerations, and will determine astrometric orbits of the closest and fastest pairs. Lunar occultations is another potentially interesting method of probing binarity in USco, although it is applicable only to relatively bright stars. | 18 | 8 | 1808.02544 |
1808 | 1808.02896_arXiv.txt | We examine the evolution of assembly bias using a semi-analytical model of galaxy formation implemented in the Millennium-WMAP7 N-body simulation. We consider fixed number density galaxy samples ranked by stellar mass or star formation rate. We investigate how the clustering of haloes and their galaxy content depend on halo formation time and concentration, and how these relationships evolve with redshift. At $z=0$ the dependences of halo clustering on halo concentration and formation time are similar. At higher redshift, halo assembly bias weakens for haloes selected by age, and reverses and increases for haloes selected by concentration, consistent with previous studies. The variation of the halo occupation with concentration and formation time is also similar at $z=0$ and changes at higher redshifts. Here, the occupancy variation with halo age stays mostly constant with redshift but decreases for concentration. Finally, we look at the evolution of assembly bias reflected in the galaxy distribution by examining the galaxy correlation functions relative to those of shuffled galaxy samples which remove the occupancy variation. This correlation functions ratio monotonically decreases with larger redshift and for lower number density samples, going below unity in some cases, leading to reduced galaxy clustering. While the halo occupation functions themselves vary, the assembly bias trends are similar whether selecting galaxies by stellar mass or star formation rate. Our results provide further insight into the origin and evolution of assembly bias. Our extensive occupation function measurements and fits are publicly available and can be used to create realistic mock catalogues. | \label{Sec:Intro} Cosmic structure evolves hierarchically in the cold dark matter model. Density fluctuations grow by gravitational instability and form dark matter haloes, which evolve via accretion and mergers with other haloes \citep{Press:1974}. \cite{WhiteRees:1978} formulated the basis of modern galaxy formation theory starting from this concept, postulating that galaxies form inside dark matter haloes via the cooling of gas, star formation and mergers of galaxies. This framework is the basis of semi-analytic models of galaxy formation (SAMs; see, e.g., \citealt{Baugh:2006,Benson:2010} for reviews). These models use the merger histories of dark matter haloes as the starting point to model galaxy formation. The first SAMs used merger trees constructed using Monte-Carlo approaches based on the extended Press-Schechter theory (e.g., \citealt{Lacey:1993,Cole:1994,Kauffmann:1993}), while modern SAMs use merger trees extracted from high-resolution dark matter simulations (e.g., \citealt{Kauffmann:1999,Bower:2006,DeLucia:2007,Lagos:2008,Benson:2012,Jiang:2014,Croton:2016,Lagos:2018,Stevens:2018}). This opens up the prospect of studying environmental influences on the formation histories and properties of dark matter haloes and the impact on the galaxies they host. The framework that led to SAMs also underpins the development of the halo occupation distribution (HOD) approach as an empirical description of galaxy clustering (e.g., \citealt{Peacock:2000,Berlind:2002,Cooray:2002,Zheng:2005}). The HOD formalism characterizes the relationship between galaxies and dark matter haloes in terms of the probability distribution that a halo of virial mass $M_h$ contains $N$ galaxies of a given type, together with the spatial and velocity distribution of galaxies inside haloes. An assumed cosmology and a specified shape of the HOD then allows us to predict any galaxy clustering statistic. The HOD approach is a powerful way to interpret observed galaxy clustering measurements, essentially transforming correlation function measurements to the relationship connecting galaxies with haloes (e.g., \citealt{Zehavi:2011,Coupon:2012} and references therein). It is also a useful method to characterize the predictions of galaxy formation models in a concise form that allows us to quantify the galaxy-halo relation (e.g., \citealt{Zheng:2005,C13,C17}). Another important application of the HOD approach is to facilitate the generation of realistic galaxy mock catalogues by populating dark matter haloes from an N-body simulation with galaxies that reproduce a particular target clustering measurement. This method has become increasingly popular due to the growing demand for such catalogues for planning for and interpreting the results from large galaxy surveys and due to its good performance and low computational cost (e.g., \citealt{Manera:2015,Zheng:2016}). In the standard HOD framework mass is the only halo property that plays a role. This foundation of the HOD method has its origins in the Press-Schechter formalism and the uncorrelated nature of the random walks used to describe halo assembly in excursion set theory. This leads to the prediction that the halo environment is correlated with halo mass but not with how the halo is assembled \citep{Bond:1991,Lemson:1999,White:1999}. This is, however, not the case for haloes in $N$-body simulations where halo populations of the same mass but with a different `secondary property' display different clustering, an effect that is now generally termed {\sl (halo) assembly bias}. This was convincingly demonstrated in the Millennium N-body simulation of \cite{Springel:2005} by \cite{Gao:2005} who showed the age-dependence of the clustering of haloes of the same mass (see also \citealt{Sheth:2004}); this dependence of halo clustering on secondary properties besides mass was later extended to, e.g., concentration, spin, substructure (e.g., \citealt{Wechsler:2006,Gao:2007,Jing:2007,Lacerna:2012,Xu:2017,Villarreal:2017, Mao:2018}). \cite{Croton:2007} used a SAM applied to the Millennium Simulation to show that halo assembly bias also impacts the clustering of galaxies, an effect that is now commonly referred to as {\sl galaxy assembly bias}, namely halo assembly bias as reflected in the galaxy distribution (see also \citealt{Zhu:2006,Zu:2008,Lacerna:2011,Chaves-Montero:2016}). This can potentially have important implications for interpreting galaxy clustering using the HOD framework (e.g., \citealt{Zentner:2014}). Detecting galaxy assembly bias has proven challenging and controversial. Despite some studies which claim to have uncovered the existence of assembly bias in the observable Universe (e.g., \citealt{Berlind:2006,Yang:2006,Cooper:2010,Wang:2013b, Lacerna:2014,Hearin:2015,Miyatake:2016,Saito:2016}) others argue that the impact of assembly is small \citep{Abbas:2006,Blanton:2007,Tinker:2008,Tinker:2011,Lin:2016,Zu:2016a,Dvornik:2017} or that the assembly bias signal could be a result of different systematics (e.g. \citealt{Campbell:2015b,Zu:2016b,Zu:2017,Busch:2017,Sin:2017,Tinker:2017a,Lacerna:2018}). This is the latest in a series of papers examining the spatial distribution of galaxies predicted by SAMs. \cite{C13} examined the clustering and HOD predicted by SAMS from different groups and found that the models give robust clustering predictions when the galaxies are selected by properties that scale with the halo mass (such as stellar mass). \cite{C15} studied how predicted galaxy properties (such as stellar mass, cold gas mass, star formation rate, and black hole mass) correlate with their host halo mass in different SAMs. \cite{C17} examined how the predicted HOD form evolves with redshift in SAMs. We proposed a parametric form for the evolution of the HOD fitting parameters that can be used when constructing mock galaxy catalogs or for consistently fitting clustering measurements at different epochs. Finally, in \cite{Zehavi:2017} (hereafter Z18) we use SAMs to investigate how the galaxy content of dark matter haloes is influenced by the large-scale environment and halo age at $z=0$, for galaxy samples selected by their stellar mass, finding distinct variations of the halo occupation functions. We show that haloes which form early have more massive central galaxies, and thus start hosting them at lower halo mass, and fewer satellite galaxies, compared to late-forming haloes. We also find similar results in hydrodynamical simulations \citep{Artale:2018}. These {\sl occupancy variations}, namely the dependence of the HOD on halo properties other than mass, are intimately related to assembly bias, as it is their effect combined with {\sl halo} assembly bias that gives rise to {\sl galaxy} assembly bias. Here, we build on our previous studies and investigate the evolution of assembly bias and specifically the occupancy variations in SAMs. We extend the analysis of Z18 in a number of ways: 1) we study a wide range of redshifts between $z=0$ and $z=3$; 2) we explicitly examine separately the different manifestations of assembly bias, namely halo assembly bias, occupancy variation, and galaxy assembly bias; 3) we consider galaxy samples constructed using two properties, stellar mass and star formation rate (SFR); and 4) we select haloes using two secondary parameters, halo formation time and concentration. We use the \cite{Guo:2013a} SAM which is a recent galaxy formation model from the Munich group implemented in a Millennium class N-body simulation with a WMAP-7 cosmology. \cite{Wechsler:2006} and \cite{Gao:2007} study the evolution of halo assembly bias in large $N$-body simulations using a mark-correlation statistic and the large-scale bias of the mass-halo cross-correlation, respectively. \cite{Hearin:2016} examine the redshift dependence of assembly bias in the context of an extension of the HOD framework that incorporates assembly bias (the so-called decorated HOD), finding that the impact of assembly bias on galaxy clustering weakens at higher redshift for samples with fixed stellar mass. We aim to comprehensively investigate the evolution of galaxy assembly bias using a physical galaxy formation model. We focus here on galaxy assembly bias as reflected in the halo occupation and galaxy clustering. To our knowledge this is the first work that explicitly examines the evolution of the occupancy variation, and as a consequence, of galaxy assembly bias. Our aim is to investigate the origin and evolution of assembly bias. This will enable the development of more sophisticated tests to search for assembly bias in the observable Universe. Our results will also help shape the design of new mock galaxy catalogues, which are necessary for the next generation of galaxy surveys. The outline of this paper is as follows: in Section 2 we introduce the SAM used and describe the different galaxy and halo samples employed in this work. Section 3 shows our results regarding the evolution of halo assembly bias, while Section 4 presents our main results regarding the evolution of the occupancy variation. In Section 5 we study the impact of assembly bias on galaxy clustering and the evolution of galaxy assembly bias. Finally, in Section 6 we summarise our results and present our conclusions. We describe our publicly available occupancy variation measurements and parametric fits in the appendix. Throughout the paper masses are measured in $h^{-1}\, {\rm M_{\odot}}$, the SFR is measured in $\rm M_{\odot}/yr$ and distances are measured in $h^{-1}\, {\rm Mpc}$ and are in comoving units. | We use a state-of-the-art semi-analytic model of galaxy formation, the G13 SAM model, to study the origin and evolution of assembly bias in the galaxy distribution. We identify two separate contributions to this effect: halo assembly bias, which refers to the different clustering of haloes with different `secondary property', and occupancy variation, the dependence of the number of galaxies in haloes of the same mass on a second property of the haloes. We isolate the evolution of these two effects for haloes selected by their concentration and formation redshift, two of the most common secondary properties used to measure assembly bias. The galaxy samples correspond to different number densities based on either ranked stellar mass or SFR. Our key results are shown in Figures~\ref{Fig:CF_Ev}, \ref{Fig:HOD_ratio_1} and \ref{Fig:CF_Ratio4}. We now summarise our main findings: \begin{itemize} \item At $z=0$ the concentration of dark matter haloes correlates with formation time. This correlation weakens at higher redshifts. \item Haloes at $z=0$ with high concentrations or early formation times are more clustered than those with low concentrations or late formation times. At high redshift, there are no differences in the CF measured for haloes with different formation times, but low concentration haloes are more correlated than high concentration ones. \item Haloes ranked to have an extreme concentration or formation time at a given redshift do not necessarily have the same ranking at other redshifts. We found that the main progenitors of $z=0$ haloes display clustering similar to that measured for their descendants. This means that the evolution of the halo assembly bias signal is not caused because a set of haloes (e.g., high concentration haloes) change their clustering over time, but because haloes change their ranking in terms of a secondary property. \item At $z=0$, haloes with early formation times or high concentrations are populated by galaxies starting at lower halo masses (for a fixed cut in stellar mass) but they have fewer satellite galaxies for a fixed mass compared to haloes with late formation times or low concentrations. \item For galaxies selected by SFR we generally find similar occupancy variation trends to those found for galaxies selected by stellar mass (though different shape of the HOD). Haloes with early formation times or high concentrations are first populated by galaxies at a lower mass and have fewer satellite galaxies at a given mass compared to haloes with late formation times or low concentrations. The one difference is that at higher halo masses, where the central galaxies occupation drops, there are less centrals in haloes with early formation times or high concentrations than for those with either late formation times or low concentrations. \item The occupancy variation for central galaxies in haloes with different formation times stay roughly constant as a function of redshift for a fixed galaxy number density and for galaxies selected by either stellar mass or SFR. The corresponding satellite galaxies occupancy variation decreases somewhat with increasing redshift. \item The occupancy variation for galaxies in haloes with different concentrations diminishes for the central galaxies and satellites with increasing redshift, for both stellar mass or SFR selected galaxy samples. \item The evolution of the CF of galaxy samples without occupancy variation (i.e., the shuffled samples) reflects the same trends on large scales as the evolution of halo assembly bias for haloes selected by age or concentration; the CF differences for galaxies in haloes with early and late formation times decreases with look back time, while the CF of galaxies in low-concentration haloes increases relative to the CF of galaxies in high-concentration haloes when going to higher redshifts. \item The CF of galaxies hosted by haloes with late formation times or low concentration increases relative to the CF of galaxies in haloes with early formation times or high concentrations, respectively, with increasing redshift. \item The occupancy variation tends to increase the amplitude of the CF of galaxies that live in haloes with either late formation times or low concentrations, and decrease it for galaxies that live in haloes with early formation times or high concentrations. \item Galaxy assembly bias as measured by the ratio between the CF of the model galaxies and that of the shuffled galaxies decreases with redshift, going below 1 in some cases. This CFs ratio is generally smaller for lower number densities and for SFR-selected samples. \end{itemize} The different evolution of halo assembly bias and the occupancy variation with age and concentration likely points to a different origin for the dependence on these two secondary parameters. This is further corroborated by their lack of correlation at high redshift. In general, we find similar trends in the evolution of assembly bias, for both the occupancy variation and galaxy assembly bias, for galaxies selected by SFR versus stellar mass. This is quite impressive considering that galaxy samples selected by stellar mass and by SFR exhibit quite different behaviours in the SAMs \citep{C13,C15}, and may be relevant for upcoming surveys. The results shown here will help to inform theoretical models of assembly bias and the development of observational tests to detect its existence (or absence) in the Universe. They can also be used to construct improved mock galaxy catalogues incorporating assembly bias (as standard HOD mocks do not include this effect). For these purposes we are releasing all the HODs and occupancy variation measures obtained in this work, as well as parametrised fits for them (see Appendix~A for more details). | 18 | 8 | 1808.02896 |
1808 | 1808.05222_arXiv.txt | Magnetic fields are ubiquitously observed in the interstellar medium (ISM) of present-day star-forming galaxies with dynamically relevant energy densities. Using three-dimensional magneto-hydrodynamic (MHD) simulations of the supernova (SN) driven ISM in the flux-freezing approximation (ideal MHD) we investigate the impact of the magnetic field on the chemical and dynamical evolution of the gas, fragmentation and the formation of molecular clouds. We follow the chemistry with a network of six species (H$^{+}$, H, H$_2$, C$^+$, CO, free electrons) including local shielding effects. We find that magnetic fields thicken the disc by a factor of a few to a scale height of $\sim100\,\mathrm{pc}$, delay the formation of dense (and molecular) gas by $\sim25\,\mathrm{Myr}$ and result in differently shaped gas structures. The magnetised gas fragments into fewer clumps, which are initially at subcritical mass-to-flux ratios, $M/\Phi\approx0.3(M/\Phi)_\mathrm{crit}$, and accrete gas preferentially parallel to the magnetic field lines until supercritial mass-to-flux ratios of up to order 10 are reached. The accretion rates onto molecular clouds scale with $\dot{M}\propto M^{1.5}$. The median of the inter-cloud velocity dispersion is $\sim2-5\,\mathrm{km\,s}^{-1}$ and lower than the internal velocity dispersion in the clouds ($\sim3-7\,\mathrm{km\,s}^{-1}$). However, individual cloud-cloud collisions occur at speeds of a few $10\,\mathrm{km\,s}^{-1}$. | Magnetic fields are ubiquitously observed in the interstellar medium (ISM, \citealt{Beck2009, Crutcher2012, Haverkorn2015}) and might play a vital role for the evolution of galaxies \citep[e.g.][]{NaabOstriker2017}. With mean field strengths in the spiral structures of galaxies of a few $\mu\mathrm{G}$ the magnetic energy density is typically lower than the kinetic but overall comparable to the mean thermal energy density \citep[e.g.][]{BoularesCox1990, Cox2005}. The high conductivity and the partial ionisation in the ISM result in an efficient coupling of the magnetic field with the gas and the assumption of ideal MHD is valid for a large fraction of the ISM. This allows for a dynamical impact of the magnetic field on the motions of the gas from scales of the entire galaxy \citep{Beck2001, Hanasz2009, KotarbaEtAl2009, PakmorSpringel2013, RiederTeyssier2017}, representative parts of the ISM \citep{deAvillezBreitschwerdt2005, KoyamaOstriker2009a, KoyamaOstriker2009b, HillEtAl2012, KimOstriker2015b, SILCC1, GirichidisSILCC2, PardiEtAl2017}, molecular clouds \citep{ShuAdamsLizano1987, PadoanNordlund1999, Heitsch02, MacLowKlessen2004, BanerjeeEtAl2009} down to star-forming regions \citep{HennebelleFromang2008, HennebelleTeyssier2008, HennebelleCiardi2009, PetersEtAl2011, SeifriedEtAl2010, SeifriedEtAl2011, SeifriedEtAl2012, KlassenPudritzKirk2017, KoertgenBanerjee2015}. Turbulent or turbulence-like motions, that are trans- or supersonic \citep{GoldreichKwan1974, ZuckermanEvans1974, ElmegreenScalo2004, ScaloElmegreen2004} stir the ISM. Supernovae (SNe, e.g. \citealt{GattoEtAl2015, WalchNaab2015}), stellar feedback processes like radiation \citep{WalchEtAl2013, KimKimOstriker2016, PetersEtAl2017a, HaidEtAl2018} and winds \citep{GattoEtAl2017}, gravitational instability, and differential rotation in the galactic disc form a multitude of complex dynamical interactions that are expected to shape the ISM on different scales and with different efficiencies \citep{KlessenGlover2016}. SNe and gravitational contraction are regarded as the most energetic dynamical drivers. Theoretical considerations describe the interstellar medium in present-day star-forming disc galaxies as a multi-component fluid consisting of two (cool and warm) stable \citep{Field1965,FieldGoldsmithHabing1969, WolfireEtAl1995, WolfireEtAl2003} and one hot meta-stable phases \citep{CoxSmith1974, McKeeOstriker1977, Ferriere2001}. However, due to the strong dynamics a significant fraction of the gas is in the unstable regime. In addition, there is a constant exchange between the phases. The hot gas with temperatures of the order of $10^6\,\mathrm{K}$ originates from supernovae and fills most of the volume. The warm and cold component coexist in approximate pressure equilibrium \citep[e.g.][]{Cox2005}. The hot medium is expected to be dominated by thermal and kinetic rather than magnetic energy. Contrary, the cold regions can be permeated by strong magnetic fields that can retard or theoretically completely prevent gravitational contraction and the formation of dense clouds and stars \citep{CrutcherEtAl2010,Crutcher2012,PardiEtAl2017}. The transition from magnetically sub- to supercritical regions, which is needed for gravitational forces to overcome pressure balance is still a matter of active discussion \citep[e.g.][]{KoertgenBanerjee2015, ValdiviaEtAl2016}. In the case of strong fields the contraction perpendicular to the field lines is prohibited due to the magnetic pressure. However, condensations can form along the field lines \citep{Field1965, HeitschHartmann2014, SILCC1, GirichidisSILCC2, IffrigHennebelle2017}. This paper is part of the SILCC project\footnote{\url{https://hera.ph1.uni-koeln.de/~silcc/}} (SImulating the Life Cycle of molecular Clouds) that investigates the processes in the interstellar medium using hydrodynamical simulations. The first two studies \citep{SILCC1, GirichidisSILCC2} focus on different modes of SN driving and varying SN rates. Both find that SNe partially need to explode in low-density environments to create a realistic chemical composition and launch outflows from the disc. \citet{GattoEtAl2017} uses active star clusters that self-consistently form in dense regions and accrete gas. The study also includes stellar winds in addition to SN feedback. \citet{PetersEtAl2017a} further added radiation from star clusters using the same formalism. All of these studies have a maximum grid resolution of $4\,\mathrm{pc}$, which is too coarse to study molecular clouds. The SILCC-zoom study \citep{SeifriedEtAl2017} specifically investigates the condensation of gas and the formation of clouds with a maximum resolution of $0.1\,\mathrm{pc}$ in the non-magnetised ISM and without the formation of star or star cluster particles. The high resolution accounts for a more detailed chemical evolution but restricts the study to only a few clouds. With this study we specifically aim at probing the impact of magnetic fields on the chemical evolution along with the formation of molecular clouds while keeping the dynamical connection to the large-scale ISM flows \citep[see dicussion in][]{SeifriedEtAl2017}. We increase the resolution to $1\,\mathrm{pc}$, which allows us to more accurately follow the evolution in dense regions and at the same time resolve many clouds with higher resolution to have a statistically relevant sample of molecular clouds. Following the numerics and the simulation setup (Sections~\ref{sec:methods} and \ref{sec:setup-parameters}) we first give an overview of the morphological evolution of the simulations (Section~\ref{sec:morphology-global-dynamics}), followed by an analysis of the degree of magnetisation of the gas (Section~\ref{sec:magnetisation}). We then focus on the formation of shielded and molecular gas (Section~\ref{sec:optthick}) and the fragmentation into clouds and their properties (Section~\ref{sec:clouds}). Discussions and conclusions are presented in Sections~\ref{sec:discussion} and \ref{sec:conclusions}. | \label{sec:conclusions} We perform three-dimensional simulations of the SN-driven magnetised interstellar medium with focus of the formation of molecular clouds in the presence of magnetic fields. The simulated volume covers a stratified gas distribution along $z$ with a magnetic field strength of $0$, $3$, and $6\,\mu\mathrm{G}$ in the midplane ($z=0$). The total volume covers $(500\,\mathrm{pc})^3$ with a gas surface density of $10\,\mathrm{M}_\odot\mathrm{pc}^{-2}$. We employ a chemical network including ionised, atomic and molecular hydrogen as well as CO, C$^+$ and free electrons. The effects of (self-)shielding and the attenuation of the interstellar radiation field are taken into account via the \textsc{TreeCol} algorithm. We evolve the system for a total time of $60\,\mathrm{Myr}$ with two different effective resolutions ($256^3$ and $512^3$). The results can be summarised as follows. \begin{itemize} \item In the presence of magnetic fields the morphological evolution of the ISM differs from non-magnetic environments. The magnetic pressure thickens the galactic disc leading to much larger scale heights ($\sim100-150\,\mathrm{pc}$ for the total gas, $\sim80-100\,\mathrm{pc}$ for molecular gas) compared to the non-magnetic environments, where 90\% of the total gas is confined to $30-40\,\mathrm{pc}$ and 90\% of the molecular gas is located at a height of only $20\,\mathrm{pc}$ from the disc midplane. As a result the non-magnetic simulation forms small clouds with a spherical shape close to the midplane. The thick magnetised disc allows the formation of structures at larger heights above the midplane. In addition the magnetised structures form as more massive and elongated entities. \item Both the direct support by magnetic pressure as well as the resulting lower central densities due to the extended disc structure retard the formation of dense structures and molecular clouds. In the non-magnetic simulation molecular gas starts forming after only $10\,\mathrm{Myr}$ and reaches a total mass fraction of 0.5 after $\sim20\,\mathrm{Myr}$. In contrast the simulation with an initial magnetic field strength of $6\,\mu\mathrm{G}$ needs $\sim35\,\mathrm{Myr}$ before significant amounts of H$_2$ form. Once the formation of molecular hydrogen sets in the formation rates are comparable. At the end of the simulation we do not notice a difference in total H$_2$ fraction between the non-magnetic and magnetic runs. \item Most of the gas is moving at supersonic and super-Alfv\'{e}nic velocities. The average Mach numbers in the ionised hydrogen are around $2$ with very little temporal variation and negligible difference between the magnetic and non-magnetic simulations. The Mach numbers in atomic hydrogen increase over time from $\mathcal{M}_\mathrm{s}\sim2$ to values of $4$, again with little dependence on the magnetisation. The highest Mach numbers ($\sim20-30$) are reached in the molecular gas. The final values are very similar for all simulations but due to the different formation times of molecular gas, the intermediate evolution differs with temporally lower values for the magnetic runs. The globally averaged Alfv\'{e}nic Mach numbers indicate super-Alfv\'{e}nic motions for both magnetic simulations. Over time $\mathcal{M}_\mathrm{A}$ increases to values of $\sim50-80$ for the molecular gas and $\sim20-30$ for H$^+$. The lowest Alfv\'{e}nic Mach numbers develop in atomic hydrogen with $\mathcal{M}_\mathrm{A}\sim3-8$. \item The mean magnetic field increases from the initial values of $3$ and $6\,\mu\mathrm{G}$ to $\sim10-20\,\mu\mathrm{G}$ in the dense gas. The low-density environment loses magnetic intensity to minimum values of $\sim0.1\mu\mathrm{G}$. The low-density gas with weak magnetisation shows a scaling of the field strength with density of order $B\propto\rho^\alpha$ with $\alpha\approx2/3$ as expected from dimensional arguments for a negligible magnetic field impact. At densities of order the mean ISM density ($\rho\sim10^{-24}\,\mathrm{g\,cm}^{-3}$) the field becomes stronger such that $\sim30\%$ of the mass is in regions with $\mathcal{M}_\mathrm{A}<1$ and a fraction of $\sim80\%$ with $\beta<1$. Above this density the scaling of the field becomes flatter with $\alpha\approx1/4$, which indicates that the magnetic field is able to channel the flow along the field lines suppressing the compressional effect. \item The non-magnetic simulations form significantly more molecular clouds (peak of 500 at a global molecular gas fraction of $0.4$) compared to the magnetic simulations with a maximum of $100$ clouds at approximately the same total molecular gas fraction. Over time the clouds merge and accrete material, which allows them to grow from an average mass of $10^4\,\mathrm{M}_\odot$ to $10^5\,\mathrm{M}_\odot$. The mean accretion rate scales approximately with the mass of the cloud as $\dot{M}\propto M^{1.5}$, independent of the magnetisation of the gas. The magnetised initial clouds form with a subcritical mass-to-flux ratio ($\sim0.2-0.3$ in units of the critical value), i.e. are supported by $B$ against gravitational collapse. Accretion flows that are stronger along the field lines than perpendicular to them allows the clouds to transition from sub to supercritical clouds at a time of $\sim30-40\,\mathrm{Myr}$. At the end of the simulation the clouds reach median mass-to-flux ratios of more than $10$ times the critical value. This transition is a potentially important process to delay the collapse of clouds and the formation of stars and might alter the star formation efficiency. \item The internal velocity dispersion of the clouds ranges from $\sim3-7\,\mathrm{km\,s}^{-1}$ and constantly increases over time. The inter-cloud velocity velocity dispersion is slightly lower with values from $\sim2-5\,\mathrm{km\,s}^{-1}$ and also increases. The non-magnetic run shows the largest internal and smallest inter-cloud values. For the simulation with strong magnetic fields both quantities are the same within the temporal scatter. \end{itemize} | 18 | 8 | 1808.05222 |
1808 | 1808.06401_arXiv.txt | We selected mass-transferring binary candidates from the catalog of Kepler eclipsing binary stars and investigated the dependence of the mass-transfer rate on several astrophysical quantities, including orbital period, semi-major axis, mass ratio, fill-out factor, temperature, and mass. We selected these candidates using $O-C$ diagrams and calculated their mass-transfer rates. Primary masses were obtained from the mass--temperature relation, and the temperatures of the component stars were extracted from a catalog of temperatures for Kepler eclipsing binary stars. The mass-transfer rates of overcontact systems have associations with astrophysical quantities that seem to differ from those of semi-detached or detached systems. These associations indicate that mass exchange from more- to less-massive components (from less- to more-massive components) generally becomes rapid (slow) as the mass exchange evolves. However, for mass exchange from more- to less-massive components, this tendency is not reasonable for binaries with a short period ($P<0.4$ d) and low mass ($M_1<1.2$ M$_\odot$) because the correlations of these binaries are opposite to those of binaries with long period and high mass. These different correlations likely arise from differences in correlation between subtypes of W UMa systems (i.e., W- and A-types). Alternatively, when mass exchange from more- to less-massive components reoccurs after a mass-ratio reversal, its properties may differ from those of the first mass exchange. | \label{Intro} An overcontact binary is a binary system in which both stars have exceeded their Roche lobes. The light curve of an overcontact system is continuously variable due to the tidally distorted shapes of the stars and is generally classified as belonging to the W UMa type. In such a system, mass transfer is likely to occur through Lagrange points. Mass transfer is classified into two cases: mass exchange between components and mass loss. In the case of mass exchange, all the mass lost by one component is gained by its companion and the total mass of the binary is conserved, together with the total angular momentum. Mass exchange leads to changes in the orbital period. If the rate of change of the orbital period can be obtained, the mass-exchange rate will be determined by the following equation \citep{Hilditch2001-icbs}: \begin{equation} \label{Conservative} \dot{m}_1=\frac{m_1 m_2}{3(m_1-m_2)} \frac{\dot{P}}{P}, \end{equation} where $m_1$ and $m_2$ are the masses of the two stars and $P$ and $\dot{P}$ are the orbital period and its rate of change, respectively. This equation indicates that the orbital period is shorter when mass exchange occurs from the more- to less-massive components and longer when the process occurs in the other direction. In the case of mass loss, the mass lost by one component escapes from the binary system. Mass loss is caused by phenomena such as stellar wind, outer Roche lobe overflow, or a sudden catastrophic event such as a nova or supernova. Assuming that mass is lost from only one component and the linear velocity of the component in its binary orbit remains constant, the simplest relationship between the rate of change of the period and the mass-loss rate is obtained \citep{Hilditch2001-icbs} as \begin{equation} \label{Non-Conservative} \dot{m}_1=-\frac{(m_1+m_2)}{2} \frac{\dot{P}}{P}. \end{equation} The orbital period must increase when mass loss occurs because $\dot{m}_1$ decreases. In addition to varying the shape of the Roche lobe due to mass transfer, the change of the orbital period alters the orbital separation. These changes affect the evolution of a binary star. For instance, Algol ($\beta$ Per) is a semi-detached binary in which the less-massive component appears to evolve earlier than the more-massive component. The mass-ratio reversal is explained via mass exchange between components \citep{Sarna1993-MNRAS}. Mass transfer also plays an important role in thermal relaxation oscillation (TRO) theory \citep{Flannery1976-ApJ,Lucy1976-ApJ,Robertson1977-MNRAS}. The TRO theory explains the achievement of an average thermal equilibrium in a contact system. According to this theory, a binary oscillates between contact and semi-detached phases via cyclic mass exchange and achieves thermal equilibrium on the average. As can be seen in this instance, mass transfer is associated with the evolution of a binary system. Thus, investigating the properties of mass transfer may solve problems associated with binary-system evolution. Many previous studies have focused on calculating mass-transfer rates for individual eclipsing binaries. However, several studies have presented the rates of change of period for some objects and showed correlations of period change with some astrophysical quantities \citep{Qian2002-MNRAS,Yang2009-AJ137}. Although several studies investigated the statistical properties of period change, few have focused on those of mass transfer; in other words, the statistical properties of mass transfer for binaries are not well known. This paper demonstrates the statistical properties of mass transfer for overcontact systems. Section \ref{Data} introduces the data used herein. In section \ref{Extraction}, we describe a method to select candidate mass-transferring binaries and to calculate mass-transfer rate. The dependence of this rate on astrophysical quantities is illustrated in section \ref{Dependence}, and in section \ref{Discussion}, we discuss how the mass-transfer rate changes with the evolution of binary stars. Section \ref{Conclusion} summarizes our results. | We have investigated the statistical properties of mass transfer for overcontact binaries in the KEBC, assuming that the simplest mass transfer occurs in binary systems. We have shown that the mass-transfer rate is associated with the astrophysical quantities of binary systems. Moreover, associations differ between the MEML and MELM samples, although the ML sample has dependence similar to that of the MELM sample. Most binaries with $P>0.6$ d are likely to be contaminated by semi-detached or detached systems. Furthermore, their properties differ from those of binaries with $P<0.6$ d in terms of relation to orbital period, semi-major axis, primary temperature, and primary mass. We inferred that the difference in the mass-transfer properties is due to the difference between types of binary systems. To confirm this, the properties for semi-detached and detached systems should be examined. Moreover, it should be confirmed that the properties of such systems are exactly different from those of overcontact systems. We discussed how mass-transfer rates change with the evolution of contact-binary systems and concluded the following. Mass exchange from more- to less-massive components becomes rapid as a binary evolves. By contrast, the rate of mass exchange from less- to more-massive components decreases with evolution. However, the properties of MEML binaries with short period ($P<0.4$ d) or low mass ($M<1.2$ M$_\odot$) differ from those with longer periods or higher mass. This is likely to arise from the mass-transfer properties of W-type binaries differing from those of A-type ones or because the properties of a MEML occurring after a mass-ratio reversal differed from those occurring before. We note that in practice, both processes of mass exchange between the components and mass-loss should simultaneously occur in a binary system. Furthermore, in magnetically active binaries, magnetized wind may have a long-term effect on period change. In particular, in the case of ML, angular-momentum loss via magnetized wind shortens the orbital period, which is the opposite of the period change due to ML. If this process strongly contributes to long-term period change, the estimated mass-transfer rate will deteriorate. Other probable processes that may have caused orbital-period oscillations have also been discussed because the parabolic $O-C$ curves may be confused with periodic ones. Some sample binaries for which a component has $T<6000$ K might change their orbital period by the Applegate mechanism. These binaries are likely to affect the correlation between temperature and mass-transfer rate below $T\simeq 6000$ K. Although some binaries possibly show orbital-period change by only LTTE rather than mass transfer, we have determined them to be in the minority. In addition, confusion between mass transfer and other processes possibly lead to dispersed distributions. The masses and mass ratios for sample binaries, which are necessary to calculate mass-transfer rates, are determined by photometric rather than spectroscopic data. Accordingly, these quantities and mass-transfer rates may have large uncertainties. If sample binaries with spectroscopically determined absolute parameters are used, then more reliable results would be derived. \begin{longtable}{*{10}{r}} \caption{Principal parameters for mass-transferring overcontact binaries. \label{Candidates}} \hline KIC & $P$ & $a$ & $T_1$ & $f$ & $M_1$ & $M_{\textnormal{\scriptsize acc}}/M_{\textnormal{\scriptsize d}}$ & $dP/dt$ & ME rate & ML rate \\ & days & R$_\odot$ & K & & M$_\odot$ & & $\times 10^{-7}$ d yr$^{-1}$ & $\times 10^{-7}$ M$_\odot$ yr$^{-1}$ & $\times 10^{-7}$ M$_\odot$ yr$^{-1}$ \\ \hline \endfirsthead \hline KIC & $P$ & $a$ & $T_1$ & $f$ & $M_1$ & $M_{\textnormal{\scriptsize acc}}/M_{\textnormal{\scriptsize d}}$ & $dP/dt$ & ME rate & ML rate \\ & days & R$_\odot$ & K & & M$_\odot$ & & $\times 10^{-7}$ d yr$^{-1}$ & $\times 10^{-7}$ M$_\odot$ yr$^{-1}$ & $\times 10^{-7}$ M$_\odot$ yr$^{-1}$ \\ \hline \endhead \hline \endfoot \hline \endlastfoot \hline 2159783 & $ 0.37388$ & $ 2.82$ & $ 6135$ & $ 0.902$ & $ 1.23$ & $0.736$ & $ -20.707 \pm 0.398$ & $ -63.386$ & --- \\ 2437038 & $ 0.26768$ & $ 2.11$ & $ 5715$ & $ 0.023$ & $ 1.09$ & $0.616$ & $ -8.888 \pm 0.391$ & $ -19.343$ & --- \\ 2444187 & $ 0.39016$ & $ 3.06$ & $ 6873$ & $ 0.516$ & $ 1.47$ & $1.403$ & $ 4.045 \pm 0.150$ & $ 12.572$ & $ 13.016$ \\ 2715007 & $ 0.29711$ & $ 2.38$ & $ 6173$ & $ 0.931$ & $ 1.24$ & $1.558$ & $ 56.213 \pm 0.263$ & $ 140.328$ & $ 192.843$ \\ 2854432 & $ 0.32233$ & $ 2.09$ & $ 5385$ & $ 1.090$ & $ 0.98$ & $5.225$ & $ 11.135 \pm 0.342$ & $ 2.663$ & $ 20.105$ \\ 2854752 & $ 0.47043$ & $ 3.46$ & $ 6745$ & $ 0.040$ & $ 1.43$ & $1.332$ & $ 10.737 \pm 0.406$ & $ 32.711$ & $ 28.486$ \\ 2858322 & $ 0.43640$ & $ 3.01$ & $ 5894$ & $ 0.134$ & $ 1.15$ & $1.511$ & $ 19.024 \pm 0.729$ & $ 32.714$ & $ 41.640$ \\ 3104113 & $ 0.84679$ & $ 4.31$ & $ 5799$ & $ 1.038$ & $ 1.12$ & $2.983$ & $ 7.266 \pm 0.595$ & $ 1.612$ & $ 6.403$ \\ 3127873 & $ 0.67153$ & $ 3.93$ & $ 6508$ & $ 1.100$ & $ 1.35$ & $0.332$ & $ -8.635 \pm 1.146$ & $ -2.876$ & --- \\ 3221207 & $ 0.47383$ & $ 3.64$ & $ 7201$ & $ 0.424$ & $ 1.57$ & $1.212$ & $ 11.203 \pm 0.253$ & $ 58.291$ & $ 33.831$ \\ 3745184 & $ 0.30423$ & $ 1.87$ & $ 4091$ & $ 0.116$ & $ 0.52$ & $0.815$ & $ -14.815 \pm 0.208$ & $ -37.374$ & --- \\ 3756730 & $ 0.37916$ & $ 2.67$ & $ 5876$ & $ 0.715$ & $ 1.14$ & $1.835$ & $ 3.510 \pm 0.943$ & $ 4.226$ & $ 8.176$ \\ 3848042 & $ 0.41145$ & $ 3.27$ & $ 6618$ & $ 0.864$ & $ 1.39$ & $0.988$ & $ -8.636 \pm 0.597$ & $-807.609$ & --- \\ 3936357 & $ 0.36915$ & $ 2.79$ & $ 6409$ & $ 0.732$ & $ 1.32$ & $0.617$ & $ -6.850 \pm 0.137$ & $ -13.151$ & --- \\ 4074532 & $ 0.35315$ & $ 2.63$ & $ 5657$ & $ 0.089$ & $ 1.07$ & $1.222$ & $ 27.703 \pm 0.103$ & $ 126.014$ & $ 76.302$ \\ 4464999 & $ 0.43416$ & $ 3.14$ & $ 6204$ & $ 0.315$ & $ 1.25$ & $0.759$ & $ -8.753 \pm 0.149$ & $ -26.454$ & --- \\ 4563150 & $ 0.27472$ & $ 2.01$ & $ 5225$ & $ 0.493$ & $ 0.92$ & $0.563$ & $ -4.287 \pm 0.190$ & $ -6.179$ & --- \\ 4569923 & $ 0.31358$ & $ 2.42$ & $ 5956$ & $ 0.457$ & $ 1.17$ & $1.531$ & $ 9.575 \pm 0.300$ & $ 22.412$ & $ 29.530$ \\ 4991959 & $ 0.36094$ & $ 2.71$ & $ 5735$ & $ 0.261$ & $ 1.10$ & $1.161$ & $ 2.276 \pm 0.202$ & $ 14.311$ & $ 6.433$ \\ 5015926 & $ 0.36269$ & $ 2.78$ & $ 6169$ & $ 0.081$ & $ 1.24$ & $1.331$ & $ 3.592 \pm 0.109$ & $ 12.370$ & $ 10.756$ \\ 5022573 & $ 0.44172$ & $ 3.18$ & $ 5775$ & $ 0.884$ & $ 1.11$ & $1.012$ & $ 24.207 \pm 1.490$ & $1668.919$ & $ 60.446$ \\ 5123176 & $ 0.70784$ & $ 4.65$ & $ 6648$ & $ 0.212$ & $ 1.39$ & $0.916$ & $ -1.080 \pm 0.346$ & $ -7.712$ & --- \\ 5198934 & $ 0.83474$ & $ 6.09$ & $ 9571$ & $ 0.841$ & $ 2.28$ & $1.125$ & $ 4.560 \pm 2.024$ & $ 33.303$ & $ 11.782$ \\ 5201619 & $ 0.50728$ & $ 3.83$ & $ 7248$ & $ 0.079$ & $ 1.58$ & $1.196$ & $ 3.983 \pm 0.139$ & $ 21.112$ & $ 11.406$ \\ 5296877 & $ 0.37726$ & $ 2.95$ & $ 8639$ & $ 0.994$ & $ 2.00$ & $5.114$ & $ 5.038 \pm 0.131$ & $ 2.168$ & $ 15.996$ \\ 5310387 & $ 0.44167$ & $ 2.99$ & $ 6738$ & $ 1.086$ & $ 1.42$ & $3.443$ & $ 3.696 \pm 0.179$ & $ 1.625$ & $ 7.685$ \\ 5353374 & $ 0.39332$ & $ 3.26$ & $ 7357$ & $ 0.378$ & $ 1.62$ & $1.174$ & $ 6.942 \pm 0.121$ & $ 54.642$ & $ 26.409$ \\ 5440746 & $ 0.48265$ & $ 3.36$ & $ 6670$ & $ 0.794$ & $ 1.40$ & $1.821$ & $ 8.419 \pm 0.575$ & $ 9.928$ & $ 18.940$ \\ 5450322 & $ 0.42402$ & $ 3.00$ & $ 5823$ & $ 0.905$ & $ 1.13$ & $0.786$ & $ -17.352 \pm 0.933$ & $ -56.251$ & --- \\ 5535061 & $ 0.46343$ & $ 3.33$ & $ 6687$ & $ 0.881$ & $ 1.41$ & $1.581$ & $ 1.024 \pm 0.046$ & $ 1.783$ & $ 2.537$ \\ 5703230 & $ 0.73147$ & $ 5.69$ & $ 9798$ & $ 0.849$ & $ 2.35$ & $1.047$ & $ 20.433 \pm 2.248$ & $ 464.896$ & $ 64.240$ \\ 5770431 & $ 0.39244$ & $ 2.85$ & $ 6531$ & $ 0.613$ & $ 1.36$ & $2.100$ & $ 9.336 \pm 0.199$ & $ 9.785$ & $ 23.835$ \\ 5770860 & $ 0.73756$ & $ 4.57$ & $ 6716$ & $ 0.267$ & $ 1.42$ & $1.539$ & $ 13.194 \pm 0.916$ & $ 15.669$ & $ 20.900$ \\ 5790912 & $ 0.38332$ & $ 2.94$ & $ 6014$ & $ 0.083$ & $ 1.19$ & $1.071$ & $ 11.326 \pm 0.192$ & $ 165.764$ & $ 33.981$ \\ 5820209 & $ 0.65609$ & $ 3.65$ & $ 5357$ & $-0.024$ & $ 0.97$ & $1.789$ & $ 57.680 \pm 0.933$ & $ 35.934$ & $ 66.293$ \\ 5881838 & $ 0.30033$ & $ 2.34$ & $ 5476$ & $ 0.094$ & $ 1.01$ & $0.869$ & $ -1.099 \pm 0.208$ & $ -8.156$ & --- \\ 5951553 & $ 0.43197$ & $ 2.72$ & $ 6056$ & $ 1.038$ & $ 1.20$ & $5.231$ & $ 36.899 \pm 1.347$ & $ 8.097$ & $ 61.211$ \\ 6044543 & $ 0.53209$ & $ 4.51$ & $10093$ & $ 0.118$ & $ 2.44$ & $0.765$ & $ -6.843 \pm 0.132$ & $ -34.111$ & --- \\ 6061139 & $ 0.32244$ & $ 2.35$ & $ 5258$ & $ 0.059$ & $ 0.93$ & $1.279$ & $ 6.362 \pm 0.236$ & $ 22.017$ & $ 16.406$ \\ 6118779 & $ 0.36425$ & $ 2.35$ & $ 5688$ & $ 1.092$ & $ 1.08$ & $4.917$ & $ 26.834 \pm 0.638$ & $ 6.773$ & $ 47.887$ \\ 6370361 & $ 0.45491$ & $ 3.27$ & $ 6664$ & $ 0.414$ & $ 1.40$ & $1.633$ & $ 2.867 \pm 0.104$ & $ 4.645$ & $ 7.111$ \\ 6370665 & $ 0.93232$ & $ 6.13$ & $ 9155$ & $ 1.017$ & $ 2.16$ & $1.562$ & $ 15.163 \pm 1.512$ & $ 20.820$ & $ 28.788$ \\ 6424124 & $ 0.38553$ & $ 2.55$ & $ 5906$ & $ 0.981$ & $ 1.15$ & $3.504$ & $ 10.544 \pm 0.477$ & $ 4.200$ & $ 20.275$ \\ 6467389 & $ 0.28898$ & $ 2.27$ & $ 5609$ & $ 0.064$ & $ 1.05$ & $1.276$ & $ 3.308 \pm 0.139$ & $ 14.591$ & $ 10.758$ \\ 6677225 & $ 0.52503$ & $ 4.28$ & $ 8951$ & $ 0.800$ & $ 2.10$ & $1.235$ & $ 5.636 \pm 0.223$ & $ 31.988$ & $ 20.372$ \\ 6791604 & $ 0.52881$ & $ 4.32$ & $10322$ & $ 0.127$ & $ 2.51$ & $1.871$ & $ 9.141 \pm 0.101$ & $ 16.626$ & $ 33.332$ \\ 6803335 & $ 1.11085$ & $ 5.34$ & $ 6478$ & $ 0.157$ & $ 1.34$ & $4.398$ & $ 41.130 \pm 12.125$ & $ 4.869$ & $ 30.458$ \\ 7130044 & $ 0.29767$ & $ 2.16$ & $ 4819$ & $ 0.145$ & $ 0.78$ & $1.055$ & $ 19.640 \pm 0.211$ & $ 312.512$ & $ 50.089$ \\ 7339345 & $ 0.25966$ & $ 2.06$ & $ 5236$ & $ 0.270$ & $ 0.93$ & $1.162$ & $ 13.620 \pm 0.139$ & $ 99.886$ & $ 45.161$ \\ 7458285 & $ 0.66063$ & $ 4.22$ & $ 6146$ & $ 0.153$ & $ 1.23$ & $0.861$ & $ -11.412 \pm 0.147$ & $ -43.818$ & --- \\ 7501230 & $ 0.89275$ & $ 5.67$ & $ 7450$ & $ 0.217$ & $ 1.64$ & $1.176$ & $ 10.197 \pm 0.788$ & $ 35.578$ & $ 17.379$ \\ 7506164 & $ 0.55801$ & $ 4.66$ & $ 9961$ & $ 0.912$ & $ 2.40$ & $0.802$ & $ -34.829 \pm 0.838$ & $-202.352$ & --- \\ 7518816 & $ 0.46658$ & $ 3.25$ & $ 6775$ & $ 0.090$ & $ 1.44$ & $0.465$ & $ -8.870 \pm 0.416$ & $ -7.893$ & --- \\ 7584739 & $ 0.91156$ & $ 5.90$ & $ 7687$ & $ 0.140$ & $ 1.72$ & $0.920$ & $ -23.610 \pm 0.596$ & $-170.388$ & --- \\ 7709086 & $ 0.40947$ & $ 2.98$ & $ 5938$ & $ 0.136$ & $ 1.16$ & $0.809$ & $ -14.763 \pm 0.438$ & $ -59.257$ & --- \\ 7766185 & $ 0.83546$ & $ 4.93$ & $ 6222$ & $ 0.166$ & $ 1.26$ & $1.223$ & $ 0.517 \pm 0.103$ & $ 1.164$ & $ 0.707$ \\ 7816201 & $ 0.57496$ & $ 4.41$ & $ 9526$ & $ 1.040$ & $ 2.27$ & $1.906$ & $ 9.676 \pm 0.447$ & $ 14.056$ & $ 29.125$ \\ 7871200 & $ 0.24290$ & $ 1.75$ & $ 4851$ & $ 0.653$ & $ 0.79$ & $0.534$ & $ -9.270 \pm 0.161$ & $ -11.522$ & --- \\ 7878402 & $ 0.37435$ & $ 2.72$ & $ 5613$ & $ 0.321$ & $ 1.05$ & $1.211$ & $ 9.605 \pm 0.247$ & $ 42.762$ & $ 24.710$ \\ 8039225 & $ 1.79413$ & $ 7.57$ & $ 6690$ & $ 0.578$ & $ 1.41$ & $3.591$ & $ 43.788 \pm 18.072$ & $ 4.421$ & $ 21.969$ \\ 8177958 & $ 1.23526$ & $ 6.40$ & $ 6776$ & $ 1.008$ & $ 1.44$ & $0.593$ & $-160.207 \pm 48.188$ & $ -90.454$ & --- \\ 8257903 & $ 0.51506$ & $ 3.46$ & $ 6111$ & $ 0.601$ & $ 1.22$ & $1.426$ & $ 9.988 \pm 0.265$ & $ 18.532$ & $ 20.146$ \\ 8431389 & $ 0.35109$ & $ 2.73$ & $ 6192$ & $ 0.050$ & $ 1.25$ & $0.760$ & $ -15.623 \pm 0.205$ & $ -58.611$ & --- \\ 8539720 & $ 0.74450$ & $ 4.33$ & $ 6574$ & $ 0.540$ & $ 1.37$ & $0.428$ & $ -12.018 \pm 0.682$ & $ -5.531$ & --- \\ 8545456 & $ 0.31520$ & $ 3.07$ & $ 8549$ & $ 0.391$ & $ 1.98$ & $0.970$ & $ -4.635 \pm 0.151$ & $-312.533$ & --- \\ 8685306 & $ 0.80808$ & $ 5.77$ & $ 9210$ & $ 0.892$ & $ 2.17$ & $1.236$ & $ 69.655 \pm 3.404$ & $ 264.794$ & $ 169.576$ \\ 8690104 & $ 0.40877$ & $ 2.91$ & $ 6077$ & $ 0.577$ & $ 1.21$ & $1.591$ & $ 12.093 \pm 0.252$ & $ 20.190$ & $ 29.149$ \\ 8696274 & $ 0.39149$ & $ 2.75$ & $ 6826$ & $ 1.010$ & $ 1.45$ & $0.250$ & $ -2.422 \pm 0.161$ & $ -1.000$ & --- \\ 8703528 & $ 0.39987$ & $ 2.93$ & $ 5626$ & $ 0.189$ & $ 1.06$ & $1.025$ & $ 16.079 \pm 0.172$ & $ 577.406$ & $ 42.084$ \\ 8823666 & $ 0.43245$ & $ 3.22$ & $ 6160$ & $ 0.249$ & $ 1.24$ & $1.091$ & $ 10.634 \pm 0.295$ & $ 111.450$ & $ 29.157$ \\ 8872737 & $ 0.45910$ & $ 2.93$ & $ 5410$ & $ 1.022$ & $ 0.99$ & $1.645$ & $ 12.360 \pm 0.996$ & $ 13.713$ & $ 21.333$ \\ 9020289 & $ 0.38403$ & $ 2.64$ & $ 6382$ & $ 0.995$ & $ 1.31$ & $3.765$ & $ 18.065 \pm 0.560$ & $ 7.426$ & $ 38.982$ \\ 9026766 & $ 0.27213$ & $ 2.16$ & $ 6127$ & $ 0.576$ & $ 1.23$ & $2.095$ & $ 6.614 \pm 0.104$ & $ 9.075$ & $ 22.021$ \\ 9110213 & $ 0.33705$ & $ 2.16$ & $ 4891$ & $ 0.159$ & $ 0.80$ & $0.479$ & $ -39.554 \pm 0.183$ & $ -28.990$ & --- \\ 9145707 & $ 0.32077$ & $ 2.19$ & $ 5557$ & $ 0.934$ & $ 1.04$ & $3.235$ & $ 4.035 \pm 0.090$ & $ 1.944$ & $ 8.530$ \\ 9181877 & $ 0.32101$ & $ 2.14$ & $ 4783$ & $ 0.922$ & $ 0.77$ & $1.503$ & $ 32.719 \pm 0.278$ & $ 51.788$ & $ 65.071$ \\ 9268105 & $ 0.42569$ & $ 2.82$ & $ 6105$ & $ 0.433$ & $ 1.22$ & $2.821$ & $ 4.174 \pm 0.365$ & $ 2.188$ & $ 8.096$ \\ 9283826 & $ 0.35652$ & $ 2.69$ & $ 5785$ & $ 0.282$ & $ 1.11$ & $0.830$ & $ -24.082 \pm 0.465$ & $-122.352$ & --- \\ 9453192 & $ 0.71884$ & $ 4.49$ & $ 7232$ & $ 0.674$ & $ 1.58$ & $2.084$ & $ 3.297 \pm 1.150$ & $ 2.225$ & $ 5.354$ \\ 9840412 & $ 0.87846$ & $ 5.26$ & $ 7018$ & $ 0.292$ & $ 1.51$ & $0.666$ & $-119.139 \pm 1.178$ & $-136.368$ & --- \\ 9947924 & $ 0.36281$ & $ 2.86$ & $ 6090$ & $ 0.075$ & $ 1.21$ & $0.958$ & $ -23.427 \pm 0.166$ & $-594.043$ & --- \\ 9956124 & $ 0.36273$ & $ 3.02$ & $ 7033$ & $ 0.960$ & $ 1.52$ & $1.198$ & $ 12.806 \pm 1.100$ & $ 90.099$ & $ 49.096$ \\ 9957411 & $ 0.37469$ & $ 2.64$ & $ 6262$ & $ 0.673$ & $ 1.27$ & $2.657$ & $ 11.152 \pm 0.529$ & $ 7.608$ & $ 26.026$ \\ 10007533 & $ 0.64806$ & $ 3.98$ & $ 7142$ & $ 1.054$ & $ 1.55$ & $3.390$ & $ 11.456 \pm 0.768$ & $ 3.821$ & $ 17.739$ \\ 10032935 & $ 0.32052$ & $ 2.46$ & $ 5970$ & $ 0.254$ & $ 1.17$ & $0.646$ & $ -7.417 \pm 0.156$ & $ -16.535$ & --- \\ 10084115 & $ 0.30567$ & $ 2.14$ & $ 5859$ & $ 1.070$ & $ 1.14$ & $4.239$ & $ 17.279 \pm 0.292$ & $ 6.619$ & $ 39.745$ \\ 10154189 & $ 0.41124$ & $ 3.05$ & $ 6202$ & $ 0.444$ & $ 1.25$ & $0.788$ & $ -4.032 \pm 0.274$ & $ -15.199$ & --- \\ 10229723 & $ 0.62872$ & $ 4.14$ & $ 7141$ & $ 0.590$ & $ 1.55$ & $0.542$ & $ -11.897 \pm 0.724$ & $ -11.552$ & --- \\ 10259530 & $ 0.70721$ & $ 4.92$ & $ 7721$ & $ 0.081$ & $ 1.73$ & $1.188$ & $ 5.113 \pm 0.717$ & $ 22.184$ & $ 11.502$ \\ 10267044 & $ 0.43004$ & $ 3.19$ & $ 6918$ & $ 0.684$ & $ 1.48$ & $1.709$ & $ 1.076 \pm 0.164$ & $ 1.740$ & $ 2.934$ \\ 10292413 & $ 0.55916$ & $ 3.66$ & $ 7135$ & $ 0.943$ & $ 1.55$ & $0.348$ & $ -2.313 \pm 0.210$ & $ -1.139$ & --- \\ 10322582 & $ 0.29127$ & $ 2.07$ & $ 5844$ & $ 1.094$ & $ 1.13$ & $0.225$ & $ -44.528 \pm 0.381$ & $ -16.766$ & --- \\ 10485137 & $ 0.44527$ & $ 3.18$ & $ 5998$ & $ 0.025$ & $ 1.18$ & $1.203$ & $ 15.491 \pm 0.241$ & $ 67.515$ & $ 37.711$ \\ 10796477 & $ 0.48497$ & $ 3.69$ & $ 6846$ & $ 0.197$ & $ 1.46$ & $0.963$ & $ -2.548 \pm 0.135$ & $ -67.154$ & --- \\ 11144556 & $ 0.64298$ & $ 4.16$ & $ 6629$ & $ 0.391$ & $ 1.39$ & $1.480$ & $ 7.726 \pm 0.296$ & $ 11.587$ & $ 13.980$ \\ 11151970 & $ 0.31163$ & $ 2.30$ & $ 5321$ & $ 0.806$ & $ 0.95$ & $0.750$ & $ -29.144 \pm 0.760$ & $ -89.130$ & --- \\ 11305087 & $ 0.30927$ & $ 2.49$ & $ 5732$ & $ 0.179$ & $ 1.10$ & $1.047$ & $ 16.855 \pm 0.219$ & $ 423.311$ & $ 58.347$ \\ 11404758 & $ 0.35125$ & $ 2.56$ & $ 6712$ & $ 0.686$ & $ 1.42$ & $0.289$ & $ -28.877 \pm 0.422$ & $ -15.770$ & --- \\ 11494583 & $ 0.24834$ & $ 1.64$ & $ 4713$ & $ 1.044$ & $ 0.74$ & $0.297$ & $ -11.212 \pm 0.947$ & $ -4.707$ & --- \\ 11495781 & $ 0.50793$ & $ 4.24$ & $ 9426$ & $ 1.034$ & $ 2.24$ & $1.326$ & $ 3.835 \pm 0.259$ & $ 17.292$ & $ 14.833$ \\ 11496078 & $ 0.29972$ & $ 2.54$ & $ 6188$ & $ 0.733$ & $ 1.25$ & $1.055$ & $ 11.628 \pm 0.406$ & $ 293.090$ & $ 47.099$ \\ 11509282 & $ 0.63403$ & $ 5.35$ & $11876$ & $ 0.305$ & $ 3.01$ & $1.452$ & $ 3.469 \pm 0.598$ & $ 12.148$ & $ 13.909$ \\ 11612091 & $ 0.45427$ & $ 3.05$ & $ 7084$ & $ 0.937$ & $ 1.53$ & $5.055$ & $ 7.041 \pm 0.188$ & $ 1.952$ & $ 14.220$ \\ 11703960 & $ 0.60442$ & $ 3.79$ & $ 6850$ & $ 0.539$ & $ 1.46$ & $2.751$ & $ 6.126 \pm 1.050$ & $ 2.814$ & $ 10.079$ \\ 11716688 & $ 0.30122$ & $ 2.23$ & $ 5148$ & $ 0.976$ & $ 0.89$ & $1.231$ & $ 33.435 \pm 1.095$ & $ 143.340$ & $ 90.015$ \\ 11717798 & $ 0.37471$ & $ 2.67$ & $ 5496$ & $ 0.187$ & $ 1.02$ & $1.276$ & $ 38.862 \pm 0.572$ & $ 127.371$ & $ 93.906$ \\ 11910076 & $ 0.34812$ & $ 2.44$ & $ 5601$ & $ 0.994$ & $ 1.05$ & $0.530$ & $ -65.264 \pm 1.074$ & $ -73.953$ & --- \\ 11924311 & $ 0.44512$ & $ 3.38$ & $ 6877$ & $ 0.045$ & $ 1.47$ & $1.307$ & $ 6.822 \pm 0.162$ & $ 24.401$ & $ 19.845$ \\ 12016304 & $ 1.02405$ & $ 5.33$ & $ 6884$ & $ 0.780$ & $ 1.47$ & $3.208$ & $ 17.576 \pm 3.014$ & $ 3.807$ & $ 16.540$ \\ 12055014 & $ 0.49990$ & $ 3.44$ & $ 6896$ & $ 0.840$ & $ 1.47$ & $0.473$ & $ -6.440 \pm 0.219$ & $ -5.668$ & --- \\ 12267718 & $ 0.54505$ & $ 3.61$ & $ 6983$ & $ 0.931$ & $ 1.50$ & $2.445$ & $ 2.498 \pm 0.295$ & $ 1.586$ & $ 4.844$ \\ \end{longtable} \begin{ack} Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. This paper includes data collected by the Kepler Mission. Funding for the Kepler Mission is provided by the NASA Science Mission directorate. The author is grateful to the Chukyo University Research Fund for financial assistance with this research. We are grateful to the referee, Dr Kazimierz {St{\c e}pie{\'n}}, for suggesting many valuable comments that improved this paper. \end{ack} | 18 | 8 | 1808.06401 |
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