What Do the Hitomi Observations Tell Us About the Turbulent Velocities in the Perseus Cluster? Probing the Velocity Field with Mock Observations
aa r X i v : . [ a s t r o - ph . H E ] J a n Draft version January 26, 2018
Preprint typeset using L A TEX style emulateapj v. 12/16/11
WHAT DO THE
HITOMI
OBSERVATIONS TELL US ABOUT THE TURBULENT VELOCITIES IN THEPERSEUS CLUSTER? PROBING THE VELOCITY FIELD WITH MOCK OBSERVATIONS
J. A. ZuHone , E. D. Miller , E. Bulbul , I. Zhuravleva Draft version January 26, 2018
ABSTRACT
Hitomi made the first direct measurements of galaxy cluster gas motions in the Perseus cluster, which implied thatits core is fairly “quiescent”, with velocities less than ∼
200 km s − , despite the presence of an active galactic nucleusand sloshing cold fronts. Building on previous work, we use synthetic Hitomi /SXS observations of the hot plasmaof a simulated cluster with sloshing gas motions and varying viscosity to analyze its velocity structure in a similarfashion. We find that sloshing motions can produce line shifts and widths similar to those measured by
Hitomi . Wefind these measurements are unaffected by the value of the gas viscosity, since its effects are only manifested clearlyon angular scales smaller than the SXS ∼
1’ PSF. The PSF biases the line shift of regions near the core as much as ∼ −
50 km s − , so it is crucial to model this effect carefully. We also infer that if sloshing motions dominate theobserved velocity gradient, Perseus must be observed from a line of sight which is somewhat inclined from the planeof these motions, but one that still allows the spiral pattern to be visible. Finally, we find that assuming isotropy ofmotions can underestimate the total velocity and kinetic energy of the core in our simulation by as much as ∼ Hitomi observations.
Subject headings: galaxies: clusters: intracluster medium — techniques: spectroscopic — X-rays:galaxies: clusters — methods: numerical INTRODUCTIONThe dominant baryonic component of galaxy clus-ters, the intracluster medium (ICM), emits prodi-giously in X-rays. Coupled with significant theoreti-cal progress in understanding the underlying emissionmechanisms, the past and current generation of X-ray telescopes, especially
Chandra , XMM-Newton , and
Suzaku , have revealed a wealth of knowledge about theproperties of the ICM, including its density, temper-ature, and chemical composition (Reiprich et al. 2009;Eckert et al. 2013; Mernier et al. 2015; McDonald et al.2016; Bartalucci et al. 2017; Ezer et al. 2017)Since clusters of galaxies are dynamic objects, form-ing as the result of the bottom-up process of cosmo-logical structure formation, the kinematical propertiesof the ICM are also important. Theoretical studiesof galaxy clusters have shown that determining theproperties of the ICM velocity field is important fora number of reasons. Kinetic energy in the form ofbulk motions and turbulence provides a form of pres-sure support against gravity supplemental to thermalpressure, biasing mass estimates based on the assump-tion of hydrostatic equilibrium, as predicted by simula-tions (Evrard et al. 1996; Rasia et al. 2006; Nagai et al.2007; Piffaretti & Valdarnini 2008; Takizawa et al. 2010;Suto et al. 2013; Nelson et al. 2014). Dissipation of tur-bulent kinetic energy into heat, in addition to turbu- Harvard-Smithsonian Center for Astrophysics, 60 GardenSt., Cambridge, MA 02138, USA Kavli Institute for Astrophysics and Space Research, Mas-sachusetts Institute of Technology, 77 Massachusetts Avenue,Cambridge, MA 02139, USA Kavli Institute for Particle Astrophysics and Cosmology,Stanford University, 452 Lomita Mall, Stanford, California94305-4085, USA Department of Physics, Stanford University, 382 Via PuebloMall, Stanford, California 94305-4060, USA lent transport and mixing of hot gas, may partiallyoffset gas cooling in cluster cool cores (Fujita et al.2004; Dennis & Chandran 2005; ZuHone et al. 2010;Banerjee & Sharma 2014; Zhuravleva et al. 2014). Thevelocity structure on small length scales places con-straints on the microphysics of the ICM, in particu-lar its viscosity (Fabian et al. 2003; Roediger et al. 2013;ZuHone et al. 2015). Finally, ICM turbulence is likelya key ingredient for the origin of non-thermal phenom-ena such as radio halos and radio mini-halos (Ohno et al.2002; Brunetti & Lazarian 2007; Donnert et al. 2013;ZuHone et al. 2013; Fujita et al. 2015).However, up until recently the kinematical proper-ties of the cluster plasma were largely elusive, due tothe fact that no X-ray instrument had the spectral res-olution required to resolve shifting and broadening ofspectral lines due to the Doppler effect. Nearly allprevious indications of motions in the ICM, thoughlargely indisputable, had been indirect. The RGSgrating on
XMM-Newton can provide weak upper lim-its on Doppler broadening of spectral lines in cool-core clusters (Sanders et al. 2011; Bulbul et al. 2012;Sanders & Fabian 2013; Pinto et al. 2015, and referencestherein). Upper limits on line shifts in the ICM werealso determined with the X-ray Imaging Spectrome-ter (XIS) on
Suzaku (Ota et al. 2007; Sugawara et al.2009; Tamura et al. 2014). In one cluster, A2256, thebulk motion was fast enough ( ∼ − ) to pro-duce a line shift measurable by XIS (Tamura et al.2011). Indirect estimates of the ICM turbulent velocitycan be obtained from measurements of resonant scat-tering (e.g., Churazov et al. 2004; Werner et al. 2009;de Plaa et al. 2012; Zhuravleva et al. 2013), pressurefluctuations (Schuecker et al. 2004; Khatri & Gaspari2016), or surface brightness fluctuations (Churazov et al.2012; Zhuravleva et al. 2015). Also, the existence of r (kpc)10 −3 −2 −1 n e ( c m − ) Perse sSim lation, t=0 Gyr 10 r (kpc)2345678 k T ( k e V ) Fig. 1.—
Density and temperature profiles of our cluster model compared to those from the Perseus cluster, using the analytical fittingformulas from Churazov et al. (2003). features such as shock fronts and cold fronts are clearindications of gas motions driven by cluster mergers(Markevitch & Vikhlinin 2007) and active galactic nu-cleus (AGN) activity (Randall et al. 2015).The general possibility of measuring gas motions ingalaxy clusters directly was first achieved recently bythe
Hitomi
X-ray Observatory (Takahashi et al. 2014).
Hitomi possessed a Soft X-ray Spectrometer (SXS) mi-crocalorimeter with an energy resolution of ∆ E ∼ . E ∼ . − . ×
3’ field. At the energy of the Fe-K α line, E ≈ . − . Sadly, in lateMarch of 2016 Hitomi lost contact with the ground, andit was unable to be recovered.
Hitomi observed the core of the Perseus cluster (Abell426) in early 2016 with the SXS. The analysis of twoobservations with a total of 230 ks of exposure timewere reported in Hitomi Collaboration et al. (2016, here-after H16) The analysis of two additional observations,for a combined total of 320 ks of exposure time, werereported in Hitomi Collaboration et al. (2017a, here-after H17). The Perseus cluster is an ideal candi-date to study gas motions in clusters. First, it isnearby ( z = 0.0179), large, and bright. The centralgalaxy, NGC 1275, possesses a powerful AGN that isblowing bubbles into the Perseus ICM, driving shocks,turbulence, and sound waves (Boehringer et al. 1993;Churazov et al. 2000; Fabian et al. 2000, 2002, 2003,2006; Zhuravleva et al. 2016). Additionally, the spiral-shaped cold fronts beginning in the core region andextending out to larger radii indicate the presence ofsloshing gas motions (see the left panel of Figure 3 ofH16), presumably initiated by a previous encounter witha subcluster (Churazov et al. 2003; Fabian et al. 2011;Simionescu et al. 2012; Walker et al. 2017).Both H16 and H17 reported the measurement of line shifts and broadening in Perseus, at a significance whichclearly indicates the presence of gas motions. However,H16 reported the gas motions in the core were some-what modest, with a line-of-sight velocity dispersion of164 ±
10 km s − , and a gradient in the line-of-sight ve-locity of 150 ±
70 km s − . The implied pressure sup-port from the velocity dispersion is ∼ ∼
200 km s − , whereas elsewhere the velocity disper-sion is lower at ∼
100 km s − . They also reported a bulkvelocity gradient across the core region of ∼
100 km s − .In a separate paper, Hitomi Collaboration et al. (2017b)presented evidence for resonant scattering in the core ofPerseus based on the Hitomi measurements, obtainingestimates on turbulent velocities consistent with thosemeasured from line-of-sight Doppler shifts. Given that
Chandra and
XMM-Newton observations of Perseus indi-cate the presence of “cluster weather” due to AGN activ-ity and gas sloshing, the apparently “quiescent” natureof the cluster core indicated by the
Hitomi observationscomes as somewhat of a surprise. The authors of H16noted that “a low level of turbulent pressure measuredfor the core region of a cluster, which is continuouslystirred by a central AGN and gas sloshing, is surpris-ing and may imply that turbulence in the intraclustermedium is difficult to generate and/or easy to damp”(page 119, H16).For the reasons listed above, the discovery of such alow level of gas motion has important implications. Ifgas motions are difficult to generate or easy to damp, itmay imply that a) the sources of cluster weather are notas strong as previously thought or b) that the viscosity ofthe cluster gas may be significant, potentially providingconstraints on the plasma physics of the ICM and im-pacting turbulent reacceleration models for radio halosand radio mini-halos. For this reason, it is important todetermine what implications the
Hitomi observations ofPerseus may have for these questions.In this work, we use hydrodynamical simulations ofgas sloshing in a galaxy cluster core similar to that ofPerseus to investigate these questions. In particular, weseek to determine whether or not it is true that conclu-sions about the damping properties of the plasma, or itsviscosity, can be drawn from the
Hitomi observations. Todo this, we examine the effect of viscosity on the mea-surements of gas motions in such a cluster by simulatingtwo extreme cases: a cluster plasma which is inviscid andone which is very viscous, more than expected from theo-retical arguments. We examine projected line shifts andwidths directly from the simulation and compare themto those estimated from mock
Hitomi /SXS observations,taking into account the spatial and spectral resolutionof the instrument. An analysis of the velocity field ofthese simulations, including mock
Hitomi observations,was previously presented in ZuHone et al. (2016, here-after Z16), but in this work we seek to be informed by the
Hitomi observations of Perseus by applying a very similaranalysis and attempting to use them to place constraintson the light of sight along which Perseus is viewed fromEarth.Of course, the core of Perseus hosts a powerful AGN,which will drive gas motions, and other sources of bulkand turbulent motion may exist within the core in ad-dition to the sloshing motions evidenced by the spiralcold fronts. These possibilities have already been investi-gated by Lau et al. (2017), Bourne & Sijacki (2017), andHillel & Soker (2017). We will briefly comment on theseresults in Section 4. However, given the prominence ofthe spiral feature in Perseus, it is likely that its associ-ated gas motions make a significant contribution to theobserved line shifts and broadening seen in the
Hitomi observations, and so it is worthwhile to examine it inisolation.The structure of this paper is as follows: in Section 2we briefly outline the setup of the galaxy cluster simula-tions and the procedure for creating mock X-ray observa-tions. In Section 3 we present the results of our analysis,and in Section 4 we summarize these results and presentour conclusions. All calculations assume a flat ΛCDMcosmology with h = 0.71, Ω m = 0.27, and Ω Λ = 0.73. METHODS2.1.
N-body/Hydrodynamic Simulations
The two cluster merger simulations examined in thiswork were originally presented in ZuHone et al. (2010),and model an off-center collision between a large, cool-core cluster and a smaller subcluster. This configura-tion produces sloshing cold fronts and gas motions in thelarge cluster’s core. These simulations were performedwith the parallel N-body/hydrodynamics adaptive meshrefinement (AMR) astrophysical simulation code
FLASH (Dubey et al. 2009). The full details of the setup of thesimulations and algorithms employed can be found inZuHone et al. (2010) and Z16, but we provide a shortsummary here.The simulations used
FLASH ’s standard hydrodynam-ics module employing the Piecewise-Parabolic Method of Colella & Woodward (1984) for treatment of the clusterplasma, under the assumption of an ideal gas equationof state with γ = 5 /
3, and a mean molecular weight of µ = 0 . X = 0 .
75. The dark mattercomponent of the clusters is modeled by a collection ofmassive particles, using an N -body module which usesthe particle-mesh method to map accelerations from theAMR grid to the particle positions. The gravitationalpotential of the self-gravitating gas and dark matter iscomputed using a multigrid solver (Ricker 2008). Thephysics of the two simulations are identical with the im-portant exception that one is inviscid, and the other isviscous, with isotropic Spitzer viscosity (Spitzer 1962;Sarazin 1988): µ = 0 . n i k B Tν ii (1) ≈ . × − T / ln Λ i g cm − s − , where n i is the ion number density, ν ii is the ion-ion col-lision frequency, the temperature T is in Kelvin, and theion Coulomb logarithm ln Λ i ≈
40, appropriate for condi-tions in the ICM. Such a high viscosity for the ICM is un-likely, due to the anisotropic nature of the ion viscosity ina high- β magnetized plasma (Braginskii 1965), and alsobecause microscale plasma instabilities may set an upperlimit on the viscosity that is much lower than expectedfor a collisional plasma (Kunz et al. 2014). However, thissimulation still serves as a useful test case, since it allowsus to examine the effects of the gas motions on the spec-tral lines in the limit that turbulence and instabilities arecompletely suppressed.This work uses the simulations “R5b500” and“R5b500v” from ZuHone et al. (2010), the only differ-ence between these two simulations being the addition ofviscosity to the latter. Both simulations are set up withthe initial condition of a large, ∼ M ⊙ cool-core clus-ter, and a smaller, dark matter-only subcluster 5 timesless massive, separated at a distance of 3 Mpc, with animpact parameter along the y -axis of the simulation of b = 500 kpc, on a bound orbit in the x - y plane of the sim-ulation domain. The initial velocities of the clusters arein the x -direction and are set using Equations 4 and 5 ofZuHone et al. (2010). Figure 1 shows the initial densityand temperature profiles of our model cluster comparedto analytical profiles fitted to the data of the Perseuscluster from Churazov et al. (2003). Though there aredifferences between our model and Perseus, the densityand temperature profiles are very similar in terms of theirshape and overall normalization, so our simulation is agood candidate for studying the dynamics of gas motionsin a Perseus-like system.2.1.1. Geometry of the Problem
Due to the aforementioned symmetry of the simula-tion, the resulting gas motions are predominantly in thevelocity components along the x and y axes, and thespiral pattern is seen most prominently in projectionswith lines of sight near the z -axis. For projected quanti-ties and synthetic observations, we choose lines of sightwhich result in an appearance of the simulated clusterwhich closely resembles the position and orientation of θ = 0 ∘ θ = 22.5 ∘ θ = 45 ∘ θ = 67.5 ∘ θ = 90 ∘ Fig. 2.—
Maps of the projected X-ray surface brightness in the 0.6-9 keV band of the inviscid simulation, projected along 5 differentlines of sight, each given in terms of the angle between the z and the x -axis of the simulation. The cross indicates the position of thegravitational potential minimum of the cluster, and the square indicates the location of the simulated SXS pointing. the Perseus cold fronts. For all maps presented in thiswork, the “up” direction ˆ n corresponds to the - y -axisof the simulation, and the line-of-sight vector ˆ ℓ is deter-mined by an angle θ , which is the angle away from the z -axis of the simulation in the x − z plane towards the x -axis. Therefore, an angle of θ = 0 ◦ is aligned with the z -axis, and an angle of θ = 90 ◦ is aligned with the x -axis.As in Z16, we choose the epoch t = 3.0 Gyr of bothsimulations, finding this to be a moment in time wherethe shape and orientation of the cold fronts is a goodmatch to those in Perseus. However, our simulated clus-ter is not an exact match. In particular, the sizes of thecold fronts at this moment of the simulation are some-what larger than those in Perseus, by a factor of roughly ∼
2. For this reason, when making projections and syn-thetic observations we choose the redshift of the clusterto be z = 0 .
043 instead of the redshift z = 0 . Hitomi observations of Perseus. For the calculationsin this work, we will work in the rest frame of the maincluster. 2.2.
Synthetic X-ray Observations
The most important results from this work are derivedfrom synthetic
Hitomi /SXS observations of our simulatedclusters. These observations are produced from our sim-ulation outputs using the two software packages. Weuse the pyXSIM (ZuHone et al. 2014) package to cre-ate samples of X-ray photons from our hydrodynamicsimulations, and we use the SOXS package to convolvethese X-ray photons with the Hitomi /SXS instrumentalresponses. pyXSIM takes a 3D hydrodynamic simulation and pro-duces a distribution of synthetic X-ray photons from thesimulation variables of density, temperature, and veloc-ity assuming that the X-ray emission arises from a ther-mal plasma, using the PHOX algorithm originally de-scribed in Biffi et al. (2012, 2013). We assume the X-ray emission can be described by an
APEC model andAtomDB version 3.0.8 (Smith et al. 2001; Foster et al.2012). Since the simulation does not include metallic-ity, we assume a spatially constant metallicity of Z =0.7 Z ⊙ , appropriate for the Perseus core (Matsushita2011). We assume Asplund et al. (2009) abundances.Photons are generated from each cell in the simulationto produce a large initial sample of candidate eventsfrom which to produce mock observations. This sam- θ = 0 ∘ θ = 22.5 ∘ θ = 45 ∘ θ = 67.5 ∘ θ = 90 ∘ −200−1000100200300 μ ℓ μ k m / s ℓ Fig. 3.—
Maps of the emission-weighted velocity line shift in km s − of the inviscid simulation, projected along 5 different lines of sight,each given in terms of the angle between the z and the x -axis of the simulation. The cross indicates the position of the gravitationalpotential minimum of the cluster, and the square indicates the location of the simulated SXS pointing. ple is projected along several lines of sight ˆ ℓ to a 2Dplane as described above. The energies of the photonsare then Doppler shifted by the velocity v ℓ = ˆ ℓ · v oftheir originating gas cells along the line of sight andcosmologically redshifted. Lastly, a number of photonsare absorbed by foreground Galactic neutral hydrogen,assuming the Tuebingen-Boulder ISM absorption model( TBabs , Wilms et al. 2000), assuming a Galactic columndensity of N H = 4 × cm − . We do not explicitlyinclude the effect of systematic errors due to the gainuncertainty of the SXS, which amounts to an error ofapproximately 50 km s − on line shift measurements.Therefore, the only source of error associated with ourmock observation measurements is statistical. All errorbars in figures are 1- σ , and errors on line shift, line width,and derived quantities have been computed via standarderror propagation.These photon samples then serve as inputs to the “in-strument simulator” module of SOXS . We have imple-mented a simple model for the
Hitomi /SXS instrumentin
SOXS , assuming a square field of view 3’ on a side,with 0.5’ pixels and a Gaussian spatial PSF of ∼ SOXS simulates the detec-tion of the events, smears the position on the chip usingthe model for the PSF, and convolves the photon en-ergies with an ARF and RMF that were created usingthe publicly available HEASOFT v6.20 FTOOLS, alongwith Hitomi CALDB v5 (release date 2016-12-23). Weignore the effects of instrumental and astrophysical back- ground since their contribution to the X-ray emission isexpected to be much smaller than that of the cluster corein the reference band under consideration of 6.0-8.0 keVsurrounding the Fe-K lines which will strongly constrainthe Doppler shifting and broadening. RESULTS3.1.
Projected Velocity Fields
We first examine maps of X-ray surface brightness (inthe 0.6-9.0 keV band), line shift, and line width at thefull resolution of our simulations, along different lines ofsight, presented in Figures 2-7. The line shift and linewidth have been computed by integrating the emission-weighted velocity field along the line of sight: µ ℓ ( χ ) = Z v ℓ ( r ) w ǫ ( r )ˆ ℓ · d r (2) σ ℓ ( χ ) = Z v ℓ ( r ) w ǫ ( r )ˆ ℓ · d r − µ ℓ ( χ ) , (3)where w ǫ ( r ) = ǫ ( r ) Z ǫ ( r )ˆ ℓ · d r , (4) ǫ is the X-ray emissivity, χ is the 2D coordinate in theplane of the sky, and r is the 3D coordinate in the sim-ulation domain. In each of these figures, the projectedposition of the cluster potential minimum is marked with θ = 0 ∘ θ = 22.5 ∘ θ = 45 ∘ θ = 67.5 ∘ θ = 90 ∘ σ ℓ ℓ k m / s ) Fig. 4.—
Maps of the emission-weighted velocity line width in km s − of the inviscid simulation, projected along 5 different lines of sight,each given in terms of the angle between the z and the x -axis of the simulation. The black cross indicates the position of the gravitationalpotential minimum of the cluster, and the square indicates the location of the simulated SXS pointing. a cross symbol, and the simulated Hitomi /SXS pointingis indicated by a square. The surface brightness mapsin Figures 2 and 5 are shown to faciliate easy identifica-tion of features in the velocity maps with respect to thelocation of the cold fronts.The line shift maps are shown in Figures 3 and 6. Thegas regions underneath the cold fronts (where “under”and “over” refer to the directions closer and further awayfrom the cluster core, respectively) surrounding the clus-ter center are regions which can be observed with a sig-nificant line shift, provided that the line of sight is notperpendicular to the merger plane, i.e. along the z -axis.When viewed along the z -axis ( θ = 0 ◦ ), the line shift hasa random pattern across the core and is very modest,with values | µ ℓ | ∼ <
60 km s − in the inviscid simulation,and even less in the viscous simulation. This is easilyunderstood: this axis is perpendicular to the plane ofthe gas motions induced by the merger, and so althoughthere are gas motions in this direction also, they are sym-metric across the x - y plane of the simulation domain andhence cancel each other out. Whatever smaller-scale tur-bulence may be driven in this direction has an averagevelocity of nearly zero also.As the line of sight is rotated from the z -axis to the x -axis, the magnitude of the line shift underneath the coldfronts increases, in keeping with the fact that our line ofsight now includes components of the velocity field withinthe cluster merger plane. Underneath the southern coldfront, with its edge roughly 100 kpc to the south of thecore, µ ℓ increases to µ ℓ ∼
300 km s − when viewed along the x -axis ( θ = 90 ◦ ). The velocity of the gas underneathnorthern cold front, roughly 200 kpc to the north of thecore, has a line shift of µ ℓ ∼ −
250 km s − . Within theregion of the simulated SXS pointing, there is a velocitygradient across the core (on opposite sides of the clus-ter potential minimum) of several hundred km s − . Allof these features, which are on length scales comparableto the size of the cold fronts themselves, are commonto both the inviscid and the viscous simulations. Un-surprisingly, the inviscid simulation is more disturbed byinstabilities and turbulence on smaller length scales thanthe viscous simulation.The line width maps are shown in Figures 4 and 7.Both the core region and the northern cold front are re-gions with significant line broadening. This is true forboth the inviscid and viscous simulations, though theline widths are somewhat larger in the inviscid case, withlargest values of σ ∼ −
250 km s − in that simulationversus σ ∼ −
200 km s − in the viscous simulation.As in the case of the line shift, the major difference inthe maps of line width between the two simulations isthat the inviscid simulation shows more evidence of tur-bulence and instabilities than the viscous simulation, butthe large-scale features are very similar.The Chandra observations of the Perseus cluster haveshown clear indications of sloshing gas motions, as evi-dence by spiral-shaped cold fronts. When viewing coldfronts along a line of sight nearly aligned with the planeof the gas motions, the associated surface brightness andtemperature jumps are still visible but the spiral pattern θ = 0 ∘ θ = 22.5 ∘ θ = 45 ∘ θ = 67.5 ∘ θ = 90 ∘ Fig. 5.—
Maps of the projected X-ray surface brightness in the 0.6-9 keV band of the viscous simulation, projected along 5 differentlines of sight, each given in terms of the angle between the z and the x -axis of the simulation. The cross indicates the position of thegravitational potential minimum of the cluster, and the square indicates the location of the simulated SXS pointing. is far less obvious (see the last panels of Figures 2 and 5).The Hitomi observations of the Perseus cluster reveal avelocity gradient across the cluster core, but such gradi-ents would only be viewable in a sloshing cluster core ifthe line of sight is not perpendicular to the plane of thosemotions defined by the orbital plane of the main clusterand its perturber. To satisfy the twin conditions of view-ing both spiral-shaped cold fronts and a gradient in theline shift from the same sloshing motions, we thereforesuggest that the system must be viewed at an intermedi-ate angle between the extremes of perpendicular to andparallel with this plane. For the rest of this work, weadopt the line of sight defined by θ = 45 ◦ as a “fiducial”orientation which provides a match to these features ofboth the Chandra and
Hitomi data.3.2.
Mock Hitomi/SXS Observations
We make mock observations of our simulated clustersusing the procedure described in Section 2.2. In Figures2-7, we previously noted the position of our simulatedSXS pointing. This pointing was chosen to provide aqualitative match to location of the existing observationof the Perseus cluster and to capture the dynamics ofthe core region bounded by the innermost cold fronts.For all of our mock observations, our exposure time is300 ks. For our simulated cluster, this exposure timegives counting statistics which are similar to those fromthe
Hitomi observations of Perseus as detailed in H16 and H17. For each mock observation, we obtain the spectrumwithin each of 9 1 ′ × ′ regions which tile the SXS fieldof view, in order to at least somewhat mitigate the ef-fects of the PSF. We also obtain the spectrum withintwo larger regions, an “Inner” region and an “Outer”region (shown in Figure 8), the former close to the clus-ter potential minimum and the latter somewhat furtheraway, to measure the velocity difference between theseregions. These regions are similar to the regions chosenin H16 (see their Figure 3). We fit each spectrum withinthe 6.0-8.0 keV band, in the region of the Fe-K lines,to a tbabs*bapec model with XSPEC , again assumingAsplund et al. (2009) abundances. For each fit, we holdthe Galactic hydrogen column and the metallicity pa-rameters fixed at the input values noted above. All otherparameters are free to vary. For the exposure time wesimulated, the typical statistical 1 σ error on the line shiftfor the 1 ′ × ′ regions is ∼ ±
10 km s − , and the typicalstatistical 1 σ error on the line width is ∼ ±
10 km s − .3.2.1. Line Shift and Width Maps
Figure 8 shows maps of the line shift for both simula-tions, with the inviscid simulation in the left panels andthe viscous simulation in the right panels, for our fiducialline of sight of θ = 45 ◦ . The full-resolution maps of X-ray surface brightness and line shift are also included in http://heasarc.gsfc.nasa.gov/xanadu/xspec/ θ = 0 ∘ θ = 22.5 ∘ θ = 45 ∘ θ = 67.5 ∘ θ = 90 ∘ −200−1000100200300 μ ℓ μ k m / s ℓ Fig. 6.—
Maps of the emission-weighted velocity line shift in km s − of the viscous simulation, projected along 5 different lines of sight,each given in terms of the angle between the z and the x -axis of the simulation. The cross indicates the position of the gravitationalpotential minimum of the cluster, and the square indicates the location of the simulated SXS pointing. these panels to facilitate easy comparison. The “Inner”and “Outer” regions used to compute the velocity gra-dient across the core are marked, as well as the clusterpotential minimum with a cross. Two maps of the lineshift based on the mock SXS observations are shown: onewith the ∼
1’ spatial PSF, and another with no PSF, butwith the same spatial binning of the events into the 9regions.The first thing to note about the plots is that the large-scale features of the line shift (on scales ∼
1’ and above)are accurately captured by the mock observations andthe spectral fitting. In the northeast region of the SXSpointing, nearest the core region, the line shift is nega-tive, while in the regions further away from the core, theline shift is positive. This is in accordance with the be-havior of the line shift in the full-resolution maps. Theextreme values of the line shift seen in the full-resolutionmaps are not present in the SXS-based maps, since theregions moving at these velocities make up a small por-tion of the gas emission, and at the lower resolution ofSXS the line shift is dominated by gas motions withsomewhat smaller values of the velocity magnitude. Be-cause most of the differences in the line shift between theinviscid and viscous simulations occur at scales smallerthan the SXS PSF, the line shift maps between the twodifferent simulations at this resolution look very similar.From these maps it can also be seen that the PSF hasan effect on the estimated line shift. Photons emittedfrom the core region will be scattered into nearby regions,biasing the line shift in these regions in the direction ofthe line shift of the core. Depending on the brightness in a given 1’ region, as many as ∼ Hitomi observations of galaxy clusters in H16, H17, Z16, andKitayama et al. (2014). The magnitude of this shift canbe as much as ∼ −
50 km s − for 1 ′ × ′ regions nearthe core, larger than the statistical error for the sameregions and comparable to the systematic error.Figure 9 shows similar maps of the line width for bothsimulations, with the inviscid simulation in the left pan-els and the viscous simulation in the right panels, for ourfiducial line of sight of θ = 45 ◦ , along with the corre-sponding full-resolution maps. Two of the main featuresfrom the line shift maps also manifest themselves in theline width maps: the large-scale features of the line shift(on scales ∼
1’ and above) are accurately captured by themock observations and the spectral fitting, and the ex-treme values of the line shift seen in the full-resolutionmaps are not present in the SXS-based maps. The valueof the line width in the different pixels is not biased tothe same degree by the effect of the PSF as the line shift:the bias on the line width is typically ∼ −
25 km s − ,comparable to the 1 σ statistical error on the line width.Differences between the inviscid and viscous simulationsare more apparent in the maps of the line width thanthey are of the line shift.3.2.2. Properties of the Velocity Field in the Inner andOuter Regions of the Core
We can use the “Inner” and “Outer” regions shown inFigure 8 to calculate line shifts in regions close to and far θ = 0 ∘ θ = 22.5 ∘ θ = 45 ∘ θ = 67.5 ∘ θ = 90 ∘ σ ℓ ℓ k m / s ) Fig. 7.—
Maps of the emission-weighted velocity line width in km s − of the viscous simulation, projected along 5 different lines ofsight, each given in terms of the angle between the z and the x -axis of the simulation. The cross indicates the position of the gravitationalpotential minimum of the cluster, and the square indicates the location of the simulated SXS pointing. away from the cluster center and determine the velocitydifference between these two regions, in a similar mannerto what was done for Perseus in H16. The values of theline shift in these regions as a function of viewing angleare shown in Figure 10. For each of the two regions, theline shift in these regions begins near zero at θ = 0 ◦ ,and its absolute value increases as θ approaches 90 ◦ , inline with the expectations from Section 3.1. Assumingthe SXS PSF, the maximum difference in the line shiftbetween the two models for viscosity is ∼ −
60 km s − in both regions (the blue and orange solid curves in bothpanels). With no PSF applied, the difference in the lineshift between the two cases is slightly smaller, being ∼ −
40 km s − in both regions (the green and red solidcurves in both panels). The green and red dashed curvesin both panels show the line shift computed for the sameregions by taking an average of the line shift from thefull-resolution maps weighted by the surface brightness.These curves agree very well with the fitted values ofthe line shift from the mock observations without thePSF. This indicates that the difference in the line shiftinduced by the PSF from the “true” value is roughly ∼ −
40 km s − , larger than the statistical errors onthe line shift but smaller than or comparable to the erroron the line shift from the gain uncertainty.Figure 11 shows the velocity difference ∆ µ ℓ betweenthese two regions as a function of viewing angle. Thevelocity difference between the two different simulationsis roughly the same (regardless of whether or not thePSF is applied), indicating that viscosity has essentially no affect on this quantity. This is likely due to thefact that the velocity difference arises from gas motionsthat exist at length scales far above those which evena strong viscosity is able to damp. However, the differ-ence between the mock observations with and withoutthe application of the PSF is more dramatic–if the PSFis applied it decreases the velocity difference by nearly ∼ −
60 km s − for θ > ◦ . At our fiducial valueof θ = 45 ◦ , ∆ µ ℓ ∼ −
130 km s − if the SXS PSF isapplied, and ∆ µ ℓ ∼ −
180 km s − if it is not. The ve-locity gradient estimated directly from the full-resolutionmaps is given by the dashed lines, and is in agreementwith the measurements with no PSF applied. This effectis easily understood to be due to the fact that the two re-gions are on opposite sides of the bright cluster core, andscattering of photons emitted from this region into thetwo different regions biases the line shift of each regionslightly towards that of the core, reducing the differencebetween the two.3.2.3. Velocity Dispersion
We also determined the velocity dispersion in the coreregion. Figure 12 shows the average velocity dispersionin the core region as a function of viewing angle θ , de-termined by fitting for the velocity dispersion in eachof the 9 1 ′ × ′ regions described above and averagingthem. This was also done for the full resolution maps bytaking the emission-weighted average within each of the9 regions and averaging those, which are shown in Fig-ure 12 by the dashed lines. The PSF has little effect onthe measurement of the velocity dispersion, which is ex-0 InnerOuter
Inviscid
X-ray Surface Brightness Line ShiftLine Shift, SXS 100 kpcLine Shift, SXS w/out PSF −200−1000100200300 V e l o c i t y ( k m / s ) InnerOuter
Viscous
X-ray Su face B ightness Line ShiftLine Shift, SXS Line Shift, SXS w/out PSF100 kpc −200−1000100200300 V e l o c i t y ( k m / s ) Fig. 8.—
Comparisons of line shifts obtained from the simulation itself and estimated from spectral fitting to mock X-ray observations,for both simulations. In both sets of panels, the plotted quantities from the top-left going counterclockwise are: X-ray surface brightnessfrom the simulation, line shift from the simulation, line shift measured by SXS, and line shift measured by SXS in the absence of spatialPSF effects. The black or white square in each sub-panel shows the SXS field of view. The “Inner” and “Outer” regions where the lineshift is measured for Figures 10 and 11 are also marked. The cross indicates the position of the of the gravitational potential minimum ofthe cluster.
X-ray Surface Brightness
Inviscid
Velocity DispersionVelocity Dispersion, SXS 100 kpcVelocity Dispersion,SXS w/out PSF V e l o c i t y ( k m / s ) X-ray Surface Brightness
Viscous
Velocity DispersionVelocity Dispersion, SXS Velocity Dispersion,SXS w/out PSF 100 kpc V e l o c i t y ( k m / s ) Fig. 9.—
Comparisons of line widths obtained from the simulation itself and estimated from spectral fitting to mock X-ray observations,for both simulations. In both sets of panels, the plotted quantities from the top-left going counterclockwise are: X-ray surface brightnessfrom the simulation, line width from the simulation, line width measured by SXS, and line width measured by SXS in the absence ofspatial PSF effects. The black or white square in each sub-panel shows the SXS field of view. The cross indicates the position of the of thegravitational potential minimum of the cluster. pected, since effect was measured to be small in Section3.2.1, and whatever differences exist are averaged out bytaking the mean value over the entire core region. Theviscous simulation has a velocity dispersion that mea-sures roughly 20-30 km s − less than the inviscid simu-lation, regardless of viewing angle, a ∼ σ effect. Thisvelocity dispersion is comparable to that measured forthe Perseus cluster by Hitomi . 3.2.4.
Determining the Kinematic Properties of the Core
A primary goal of the
Hitomi observations of Perseus(and of all similar future observations of clusters withmicrocalorimeters) is to determine the kinetic energy as-sociated with gas motions. This requires summing thetotal contribution to the velocity field as measured fromboth the line shift and line width. However, knowing thevelocity in the components perpendicular to our sightline is also required, which of course is unmeasurable.1 μ ℓ ( k m s − ) InnerμRegion
InviscidVisco sInviscidℓμSXSVisco sℓμSXSInviscidℓμSXSμw/o tμPSFVisco sℓμSXSμw/o tμPSF
O terμRegion
Fig. 10.—
Line shifts estimated from spectral fitting and obtained from the simulation. Left panel: The line shift from from the “Inner”region of the cluster as a function of viewing angle from both simulations, with and without the SXS PSF applied. Right panel: The lineshift from the “Outer” region of the cluster as a function of viewing angle from both simulations, with and without the SXS PSF applied.The dashed vertical line in both panels indicates our fiducial orientation of θ = 45 ◦ . Δ μ ℓ ( k m s − ) InviscidViscousInviscidμΔSXSViscousμΔSXSInviscidμΔSXSΔ ℓoutΔPSFViscousμΔSXSΔ ℓoutΔPSF
Fig. 11.—
Velocity gradient across the cluster core estimatedfrom spectral fitting and obtained from the simulation, for bothsimulations and both PSF models, as a function of viewing angle.The dashed vertical line indicates our fiducial orientation of θ =45 ◦ . We may estimate the average velocity in the core alongour line of sight via the root-mean-squared velocity: v ℓ, rms = q h v ℓ i = q h σ ℓ + µ ℓ i (5) σ ( ( k m s − ) Inviscid, Emission-WeightedViscous, Emission-WeightedInviscid, SXSViscous, SXSInviscid, SXS w/out PSFViscous, SXS w/out PSF
Fig. 12.—
Velocity dispersion in the core region as a function ofviewing angle, where an average is taken over the 9 1 ′ × ′ regionswhich tile the SXS field of view. The dashed vertical line indicatesour fiducial orientation of θ = 45 ◦ . where the average is emission-weighted and is takenover the entire SXS field of view. Figure 13 shows theroot-mean square velocity averaged over the entire coreregion, as a function of the line-of-sight angle θ . Likethe velocity dispersion, the SXS PSF has little effect onthis measurement, but the inviscid and viscous cases are2 v r m s , ℓ ( k m s ( ) Inviscid, Emission-WeightedViscous, Emission-WeightedInvsicid, Mass-WeightedViscous, Mass-WeightedInviscid, SXSViscous, SXSInviscid, SXS w/out PSFViscous, SXS w/out PSF
Fig. 13.—
Estimation of the total average velocity within the coreas computed using Equation 6 from the mock
Hitomi observations,compared to data obtained from the simulation, as a function ofviewing angle. The large “ × ”’s indicate the mass-weighted aver-aged velocity magnitude within the core region obtained from thesimulation. The dashed vertical line indicates our fiducial orienta-tion of θ = 45 ◦ . v ℓ ℓ r m s / v t o t ℓ r m s InvsicidViscous
Fig. 14.—
The ratio of the estimated root-mean-squared veloc-ity in the core, assuming isotropy, to the true root-mean-squaredvelocity, as a function of viewing angle θ . The dashed vertical lineindicates our fiducial orientation of θ = 45 ◦ . separated by approximately 40-50 km s − , a roughly 2-3 σ difference. The total velocity estimated in the sameway from the full-resolution maps (the dashed lines) isin good agreement with the simulated Hitomi measure-ments. For this plot, we also show the mass-weighted velocity component along the sight line averaged withina sphere of 100 kpc centered on the cluster potential min-imum, given by the “ × ” symbols in the figure, which alsoagrees well with the other measurements. This region isroughly the size covered by our simulated SXS pointing.In order to use this measurement to make an estimateof the velocity in the core averaged over all components,the simplest assumption to make is that the velocity fieldis isotropic. This implies: v tot , rms ∼ √ v ℓ, rms (6)How accurate is the assumption of isotropy? Assumingthe velocity field in the cluster core is at least somewhatanisotropic, the answer depends on the line of sight. Theresult is shown in Figure 14, which shows the ratio of theestimate of the “total” root-mean-squared velocity in thecore assuming isotropy and the true root-mean-squaredvelocity summed over all components as a function of ourline of sight θ . For our simulated cluster, if the cluster isbeing viewed along a sight line near the plane of the gasmotions ( θ = 90 ◦ ), then assuming isotropy will providean underestimate of the kinetic energy in the core by only ∼ θ = 0 ◦ ) will underestimate the kineticenergy of the core by ∼ θ = 45 ◦ ), the kinetic energy is underestimatedby ∼ x − y plane of both simulations at our chosen epoch,with velocity vectors overlaid. A white circle marks theregion within which the mass-weighted velocities werecomputed for Figure 13. One can see that there is asubstantial flow of velocity in the x − y plane, and in factthe fastest flow in this region is mainly in the y -direction,up to 800-900 km s − , which is not covered by any ofthe lines of sight we simulated. If we measure from thesimulation what the relative contributions to the kineticenergy are from the three principal components of thevelocity within the central spherical region of 100 kpc,we find: h v x i / h v i ≈ . , (7) h v y i / h v i ≈ . , (8) h v z i / h v i ≈ . , (9)showing that the contribution from the y -componentof the velocity, not visible from any of our sight lines,makes up nearly ∼
60% of the kinetic energy within thisregion.This flow also is in gas that is less dense than the dens-est parts of the core by a factor of several, so its surfacebrightness would be less by over an order of magnitude,and thus not contribute as much to the emission-weighted3 −200 −100 0 100 200Image x (kpc)−200−1000100200 I m ag e y ( k p c ) Inviscid 10 -27 -26 ρ g ( g c m − ) −200 −100 0 100 200Image x (kpc)−200−1000100200 I m ag e y ( k p c ) Inviscid 0100200300400500600700800900 | v | ( k m s − ) −200 −100 0 100 200Image x (kpc)−200−1000100200 I m ag e y ( k p c ) Viscous 10 -27 -26 ρ g ( g c m − ) −200 −100 0 100 200Image x (kpc)−200−1000100200 I m ag e y ( k p c ) Viscous 0100200300400500600700800900 | v | ( k m s − ) Fig. 15.—
Slices in the x − y plane of density (left panels) and velocity magnitude (right panels) through the center of our cluster, forboth the inviscid (top panels) and the viscous (bottom panels) simulations. Vectors indicate the direction of velocity within the plane. Thewhite circle marks the region within which 3D velocity information is measured in Section 3.2.4. Each panel is 500 kpc on a side. velocity even if it were within our sight line. This indi-cates that there may be even faster flows in Perseus thatare simply not seen because they are in fainter regions.Despite this, we find that the total kinetic energy in thecore is still a small fraction of the thermal energy: ≈ ≈ SUMMARYIn this work, we have examined the velocity field ofthe ICM of a simulated galaxy cluster similar in char-acter to the Perseus cluster, in the sense that our clus-ter also possesses subsonic sloshing gas motions as evi-denced by spiral-shaped cold fronts. We produced syn-thetic
Hitomi /SXS observations of this velocity field and performed similar analyses to those performed on thePerseus data. We have reached the following conclusions: • We find that sloshing motions can produce lineshifts and widths comparable to that found by
Hit-omi in the Perseus cluster. Assuming our fiducialline of sight, we measure a velocity gradient be-tween the inner and outer regions of the cluster coreof roughly ∆ µ ℓ ∼ −
130 km s − if the SXS PSFis modeled, and roughly ∆ µ ℓ ∼ −
180 km s − if the PSF is assumed to be a delta function. Themagnitude of the velocity gradient is not stronglyaffected by viscosity. Along the same sight line,we measure an average velocity dispersion of σ ∼
150 km s − within the core region for the inviscidsimulation, and σ ∼
110 km s − for the viscoussimulation. • We find that the ∼
1’ PSF of the SXS has a non-4 negligible effect on the measurement of the lineshift on opposite sides of the cluster core, due tothe fact that the line shift in these regions is bi-ased by the presence of photons scattering intothem from the core region. We find that this ef-fect of PSF scattering induces a bias of roughly ∼ −
40 km s − on the line shift in the directionof the line shift of the bright cluster core for theregions nearer to and farther away from the clus-ter core. The bias on the line shift for individualresolution elements may be even larger. The ef-fect of this bias is to decrease the velocity gradient∆ µ ℓ from its true value by ∼ −
60 km s − . Wefind a less significant effect of the PSF on velocitybroadening, provided that the velocity broadeningis measured on spatial scales at and below the scaleof the PSF. When the PSF is not applied, we findthat the velocities estimated from spectral fittingare in agreement with those directly measured fromthe simulation. • If both the spiral-shaped cold fronts and the ob-served velocity gradient in the Perseus cluster coreare due largely to the bulk motions induced bygas sloshing, this indicates that the system maybe viewed along a line of sight that is somewhatinclined with respect to the midplane of the coldfronts. We find that an angle of ∼ ◦ provides anorientation which shows both spiral cold fronts anda significant line shift difference between the innerand outer parts of the core. • We show that overall the line shifts and widthsmeasured within the core region at the spatial res-olution of the SXS are very similar between an in-viscid simulation and a highly viscous simulation.Line widths are more affected by viscosity thanvelocity gradients across the core, but the differ-ence in line width between the two simulations isnot drastic. This indicates that the observed ev-idence of gas motions in the Perseus cluster aremore than likely to originate from velocity struc-tures with characteristic scales larger than thosethat even a strong viscosity is expected to damp.These scales are also near or larger than the SXSspatial resolution. This is expected and is in linewith previous results (Inogamov & Sunyaev 2003,Z16). This is also not inconsistent with the inter-pretation given by H17 that the Gaussianity of theline shapes implies that the driving scale of tur-bulence is just below ∼
100 kpc, since this wouldbe roughly the scale of the sloshing motions them-selves, and likely still larger than the dissipationscale of the turbulent motions. We also note thatZ16 reported that bulk motions such as sloshingcan also produce line shapes that are remarkablyconsistent with Gaussianity, even in the absence ofa developed turbulent cascade. These considera-tions imply that drawing strong conclusions aboutthe microphysics of the cluster plasma (in particu-lar its viscosity) from the
Hitomi results should beavoided, since they simply do not have the spatialresolution required to probe the scales where sucheffects would be manifest in the observations. For this, the resolution of
Athena or Lynx is likelyto be required. The fact that the viscosity of theICM is likely to be at least an order of magni-tude less than the Spitzer value (based on plasmaphysics considerations, see Section 2.1) strengthensthis conclusion. • For these simulations, we find that an estimate ofthe average velocity within the core made from themock
Hitomi observations agrees well with the av-erage velocity in the core obtained directly from thesimulation. Yet, this does not rule out the possibil-ity of gas motions which are much faster in portionsof the core which are either less dense/bright or notwithin the line of sight. In our simulation, a sub-stantial portion of the kinetic energy ( ∼ • The kinetic energy in the core region measuredfrom our simulation is still less than 10% of thethermal energy, in agreement with the estimatesmade from the
Hitomi observations of Perseus.This is true irrespective whether or not the ICM isviscous, indicating the reason for the “quiescent”nature of the plasma is the lack of strong driversof gas motions in the core (such as a recent ma-jor merger) and not viscosity. Though the core ofthe Perseus cluster is likely quiescent in this sense,given the possibility that a significant velocity com-ponent may not be within our line of sight, thisclaim should be made with caution.Other recent comparisons have been made betweensimulations and the
Hitomi observations. Lau et al.(2017) performed an analysis of mock
Hitomi observa-tions of clusters from cosmological simulations and iso-lated clusters with AGN feedback. They concluded thatcosmic accretion and mergers could produce line-of-sightvelocity dispersions and line shifts compatible with the
Hitomi observations of Perseus, while AGN feedback isable to produce velocity dispersion measurements whichare compatible with the
Hitomi observations, but not thecore-scale velocity gradient, since the turbulence drivenby AGN feedback is too stochastic. They argued fromthese results that cosmic accretion/mergers and AGNfeedback are complementary drivers of the velocity fieldin cluster cores, and their combination likely explains thelevel of shear and velocity dispersion seen in the Perseuscluster.A similar conclusion was reached by Bourne & Sijacki(2017), who simulated AGN-driven jets and mock
Hitomi observations in isolated galaxy cluster models, and mod-els which included realistic cosmic substructure. Theirisolated-cluster simulations show that though the AGNfeedback drives turbulence, it is mostly confined to thejet lobe regions, and no significant line shift gradientsare produced. By contrast, their simulations which in-clude gas motions driven by substructure produce line Hitomi obser-vations. We also note that Hillel & Soker (2017) usedsimulations of jet-driven AGN feedback to show that ve-locity dispersions comparable to that observed by
Hitomi could be produced.By contrast, we conclude that sloshing motions drivenby the “cosmic accretion” of a smaller subcluster aloneare sufficient to produce both the signatures of core-scalevelocity gradients and velocity dispersion. This is trueeven if the viscosity is unrealistically high, since the dom-inant contribution to the line width arises from gas mo-tions with characteristic scales greater than the dissipa-tion scale. Needless to say, our simulations do not in-clude the effects of cooling or AGN feedback, which areessential for a more complete model of the dynamics ofthe core of Perseus. In particular, if our simulations hadthe effects of AGN feedback they would likely show astronger velocity dispersion near the AGN, as reportedby H17. It should also be noted in this context thatsince the AGN plays an outsized role in the dynamicsof the cluster core in Perseus, that the sloshing motionsthemselves may be the product not of cosmic accretionbut of the AGN feedback. Fabian et al. (2011) arguedthat ICM structures seen in Perseus within the central ∼
100 kpc of the cluster center are due to AGN activity,whereas structures outside of this region are due to cos-mic accretion and mergers. Given that cool-core clusterssuch as Perseus have steep entropy profiles, their atmo-spheres are highly stratified and spiral structures in thevelocity field can develop naturally by any process that produces an offset between gas and dark matter in thecore, provided there is enough angular momentum im-parted to the gas. Investigating all of these possibilitiesis left for future work.We thank the anonymous referee whose comments im-proved this paper. This work required the use and inte-gration of a number of software packages for astronomy:1. yt (Turk et al. 2011)
2. pyXSIM (ZuHone et al. 2014)3. SOXS4. AstroPy (Astropy Collaboration et al. 2013)
5. APLpy
6. AstroPy Regions
7. XSPEC8. CIAO We are thankful to the developers of these packages. Theauthors thank Mark Bautz for useful discussions. JAZacknowledges support through Chandra Award NumberG04-15088X issued by the Chandra X-ray Center, whichis operated by the Smithsonian Astrophysical Observa-tory for and on behalf of NASA under contract NAS8-03060. EDM and EB acknowledge support from NASAgrant NNX15AC76G. Calculations were performed usingthe computational resources of the Advanced Supercom-puting Division at NASA/Ames Research Center.
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