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Scott Randall

Publications and source records attributed to Scott Randall.

At least 19 recordsLinked to original sources

Advancing Fundamental Physics and Cosmology with high-resolution X-ray imaging

Black Holes are the key to solving many unanswered questions in fundamental physics: in particular, the very extreme properties shown by supermassive black holes at the centers of galaxies make them obvious candidates for testing gravity theories in the strong-field regime. Since X-rays are generated by matter under extreme physical conditions, ultra-high resolution X-ray imaging (uXRI) will directly image the region near the event horizon of black holes in X-rays, similar to the Event Horizon Telescope in the radio band, enabling unprecedented tests of General Relativity and alternative theories of gravity near supermassive black holes. On the other hand, clusters of galaxies hold the potential of unveiling many unknowns in cosmology. uXRI will unlock this potential by probing small-scale plasma properties in the intracluster medium, providing the missing link required to establish galaxy clusters as reliable tools for high-precision cosmology. Moreover, uXRI will enable mapping of Dark Matter from galaxy cluster dynamics via proper motion measurements. Finally, uXRI will open a new field of precision X-ray astrometry, allowing for measuring pulsar parallaxes to support nanoHertz gravitational wave searches.

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A Deep Chandra View of Abell 2597: Bubbles, Shocks, Cold Fueling, and a Plasma Depletion Layer

To examine how AGN feedback shapes the intracluster medium (ICM) and fuels black hole accretion in the cool-core galaxy cluster Abell 2597, we present deep ($\sim$600 ks) Chandra X-ray observations complemented by archival GMRT radio and SINFONI near-infrared data. Radio-mode AGN activity has inflated seven X-ray cavities and driven one to three potential weak shocks ($M \sim 1.05-1.14$) extending to $\sim 150$ kpc, suggesting recurrent outbursts occurring on $\sim 10^7$ year timescales. We also detect a narrow, $\sim$57 kpc X-ray surface brightness deficit-a potential plasma depletion layer-likely shaped by residual sloshing motions that amplified magnetic fields and/or displaced gas within the cluster core. Although the AGN injects $\sim 10^{44}$ erg s$^{-1}$ of energy, comparable to the cluster's cooling luminosity, radiative cooling persists at $\sim$15 M$_{\odot} $yr$^{-1}$, replenishing the billion solar mass cold gas reservoir at the heart of the brightest cluster galaxy. Sustaining this level of activity requires a continuous fuel supply, yet the estimated Bondi accretion power ($\sim 2 \times 10^{43}$ erg s$^{-1}$) falls an order of magnitude short of the observed cavity power, suggesting that "hot" gas fueling is insufficient. Instead, archival ALMA observations continue to support a chaotic cold accretion scenario, where turbulence-driven condensation fuels the AGN at rates exceeding Bondi accretion, sustaining a self-regulated feedback cycle that repeatedly shapes the core of Abell 2597.

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SDSS-C4 3028: The Nearest Blue Galaxy Cluster Devoid of an Intracluster Medium

SDSS-C4 3028 is a galaxy cluster at $z=0.061$, notable for its unusually high fraction of star-forming galaxies with 19 star-forming and 11 quiescent spectroscopically-confirmed member galaxies. From Subaru/HSC imaging, we derived a weak lensing mass of $M_{200} = (1.3 \pm 0.9) \times 10^{14} \rm M_\odot$, indicating a low-mass cluster. This is in excellent agreement with its dynamical mass of $M_{200} = (1.0\pm0.4)\times10^{14} \rm M_\odot$, derived from SDSS spectroscopic data. XMM-Newton observations reveal that its X-ray emission is uniform and fully consistent with the astrophysical X-ray background, with no evidence for an intracluster medium (ICM). The 3$\sigma$ upper limit of $L_{\rm X}(0.1-2.4\rm keV)=7.7\times10^{42}$ erg s$^{-1}$ on the cluster's X-ray luminosity falls below the value expected from the $L_{\rm X}-M_{\rm halo}$ scaling relation of nearby galaxy clusters. We derived star-formation histories for its member galaxies using the photometric spectral energy distribution from SDSS, 2MASS, and WISE data. Most of its quiescent galaxies reside within the central 300 kpc, while star-forming ones dominate the outer region (300 kpc - 1 Mpc). The core region has formed the bulk of its stellar mass approximately 1.5 Gyr earlier than the outskirts. We infer a long quenching time of $>3$ Gyr for its quiescent galaxies, consistent with slow quenching mechanisms such as galaxy-galaxy interaction or strangulation. These findings suggest that SDSS-C4 3028 may have undergone an "inside-out" formation and quenching process. Its ICM may have been expelled by intense AGN feedback after core formation but before full cluster assembly. The high fraction ($\sim$0.63) of star-forming members likely results from the absence of ram pressure stripping in this blue cluster, supporting the important role of ram pressure stripping in quenching galaxies in clusters.

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Constraints on Non-Thermal Pressure at galaxy cluster outskirts from a Joint SPT and XMM-Newton Analysis

We present joint South Pole Telescope (SPT) and XMM-Newton observations of 8 massive galaxy clusters (0.8--1.7$\times$10$^{15}$ M$_{\odot}$) spanning a redshift range of 0.16 to 0.35. Employing a novel SZ+X-ray fitting technique, we effectively constrain the thermodynamic properties of these clusters out to the virial radius. The resulting best-fit electron density, deprojected temperature, and deprojected pressure profiles are in good agreement with previous observations of massive clusters. For the majority of the cluster sample (5 out of 8 clusters), the entropy profiles exhibit a self-similar behavior near the virial radius. We further derive hydrostatic mass, gas mass, and gas fraction profiles for all clusters up to the virial radius. Comparing the enclosed gas fraction profiles with the universal gas fraction profile, we obtain non-thermal pressure fraction profiles for our cluster sample at $>$$R_{500}$, demonstrating a steeper increase between $R_{500}$ and $R_{200}$ that is consistent with the hydrodynamical simulations. Our analysis yields non-thermal pressure fraction ranges of 8--28% (median: 15 $\pm$ 11%) at $R_{500}$ and 21--35% (median: 27 $\pm$ 12%) at $R_{200}$. Notably, weak-lensing mass measurements are available for only four clusters in our sample, and our recovered total cluster masses, after accounting for non-thermal pressure, are consistent with these measurements.

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PSZ2 G181.06+48.47 II: radio analysis of a low-mass cluster with exceptionally-distant radio relics

We report upgraded Giant Metrewave Radio Telescope and Karl J. Jansky Very Large Array radio observations of a low-mass merging galaxy cluster PSZ2 G181.06+48.47. This exceptional galaxy cluster hosts two megaparsec-scale diffuse sources, symmetrically located with respect to the cluster center and separated by about 2.6 Mpc in projection. We detect these low surface brightness sources in our new high-frequency observations (0.3-2 GHz) and classify them as radio relics associated with merger-driven shock fronts. The southwest relic exhibits an inverted morphology and shows evidence of spectral steepening in the post-shock region, potentially tracing a high Mach number shock ($\sim 4$) under the framework of diffusive shock acceleration. The northeast relic is found to be highly polarized with a 22% average polarization fraction at 1.5 GHz and aligned magnetic field vectors. Its spectral and polarization properties, along with the presence of a nearby tailed galaxy, support re-acceleration scenarios. The merger axis defined by the two relics is tilted by $\sim 45$ degree with respect to the plane of the sky, which implies an unprecedented physical separation of $\sim 3.5$ Mpc. We also detect a possible faint radio halo, suggesting weak turbulence in the central cluster region. We conclude that the faint double relics can be best explained by two outward moving shock waves in which particles are (re-)accelerated and that the cluster is in an evolved merger state. PSZ2 G181.06+48.47 presents a unique opportunity to investigate particle acceleration in low mass systems characterized by large relic separations.

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PSZ2 G181.06+48.47 I: X-ray exploration of a low-mass cluster with exceptionally-distant radio relics

Relics are diffuse, highly-polarized radio sources that trace merger-driven shocks at the periphery of merging galaxy clusters. The LOFAR survey recently discovered a rare example of double relics in the low-mass cluster PSZ2 G181.06+48.47. Through a detailed exploration of new Chandra and XMM-Newton observations, we reveal that PSZ2 G181.06+48.47 has a lower mass ($M_{500,X}=2.32^{+0.29}_{-0.25}\times10^{14}$ M$_{\odot}$) than previously thought. Despite its cool global temperature of $kT_{500}=3.62^{+0.15}_{-0.07}$ keV, PSZ2 G181.06+48.47 is one of the most disturbed clusters in the Planck sample, with a complex morphological and thermodynamic structure. We discover a set of three discontinuities within <500 kpc of the cluster center, and, from a surface brightness analysis, place $5\sigma$ upper limits of $M_{NE}<1.43$ and $M_{SW}<1.57$ for any shock associated with the relic locations. We also revise established scaling relations for double radio-relics by adding 12 new systems not included in previous work. The PSZ2 G181.06+48.47 relics have the widest separation (scaled for $r_{500}$) of all known double-relic systems. The exceptional distance from the cluster center ($>r_{200}$), indicates the relics may be associated with shocks in the ``run-away" phase. We propose that this late-stage, post-apocenter merger is captured as the two subclusters with a mass ratio of 1.2-1.4 fall back into each other. The outer relic shocks were likely produced at the first core passage, while the inner discontinuities are associated with the second infall.

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Multi-frequency Radio Observations of the Dissociative Cluster Merger CIZA J0107.7+5408

We present new radio observations of the galaxy cluster merger CIZA J0107.7+5408 (CIZA0107), a large, roughly equal mass, post-core passage, dissociative binary system at z = 0.1066. CIZA0107 is an elongated, disturbed system, hosting two subclusters with optical galaxy number density peaks offset from their associated X-ray density peaks and double-peaked diffuse radio structure. We present new 240-470 MHz and 2.0-4.0 GHz Very Large Array observations of CIZA0107. We image the diffuse emission at high resolution, constrain its integrated spectrum, and map the spectral index distribution. We confirm the presence of steep-spectrum ($\alpha$ $\sim$ -1.3) emission on a scale of about 0.5 Mpc in both subclusters. We identify two smaller ultra-steep spectrum ($\alpha$ $<$ -2) regions, superimposed on larger-scale radio emission associated with the southwestern subcluster. At 340 MHz, we detect a radio edge bounding the emission to the south and show that it is coincident with a weak (M $\sim$ 1.2) shock identified in the Chandra image. At 3 GHz, the emission does not show any corresponding edge-like feature, and in fact it extends beyond the shock. We investigate the nature of the emission in CIZA0107 and find that, while the system may host a double halo structure, we cannot rule out a scenario in which the emission arises from two relics projected on the central cluster regions.

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On the Particle Acceleration Mechanisms in a Double Radio Relic Galaxy Cluster, Abell 1240

We present a 368 ks deep Chandra observation of Abell~1240, a binary merging galaxy cluster at a redshift of 0.195 with two Brightest Cluster Galaxies (BCGs) may have passed each other 0.3 Gyr ago. Building upon previous investigations involving GMRT, VLA, and LOFAR data, our study focuses on two prominent extended radio relics at the north-west (NW) and south-east (SE) of the cluster core. By leveraging the high-resolution Chandra imaging, we have identified two distinct surface brightness edges at $\sim$ 1 Mpc and 1.2 Mpc NW and SE of the cluster center, respectively, coinciding with the outer edges of both relics. Our temperature measurements hint the edges to be shock front edges. The Mach numbers, derived from the gas density jumps, yield $\cal{M}_{\rm SE}$ = 1.49$^{+0.22}_{-0.24}$ for the South Eastern shock and $\cal{M}_{\rm NW}$ = 1.41$^{+0.17}_{-0.19}$ for the North Western shock. Our estimated Mach numbers are remarkably smaller compared to those derived from radio observations ($\cal{M}_{\rm SE}$ = 2.3 and $\cal{M}_{\rm NW}$ = 2.4), highlighting the prevalence of a re-acceleration scenario over direct acceleration of electrons from the thermal pool. Furthermore, we compare the observed temperature profiles across both shocks with that of predictions from collisional vs. collisionless models. Both shocks favor the Coulomb collisional model, but we could not rule out a purely collisionless model due to pre-shock temperature uncertainties.

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Mapping the imprints of stellar and AGN feedback in the circumgalactic medium with X-ray microcalorimeters

The Astro2020 Decadal Survey has identified the mapping of the circumgalactic medium (CGM, gaseous plasma around galaxies) as a key objective. We explore the prospects for characterizing the CGM in and around nearby galaxy halos with a future, large grasp X-ray microcalorimeter. We create realistic mock observations from hydrodynamical simulations (EAGLE, IllustrisTNG, and Simba) that demonstrate a wide range of potential measurements, which will address the open questions in galaxy formation and evolution. By including all background and foreground components in our mock observations, we show why it is impossible to perform these measurements with current instruments, such as X-ray CCDs, and only microcalorimeters will allow us to distinguish the faint CGM emission from the bright Milky Way (MW) foreground emission lines. We find that individual halos of MW mass can, on average and depending on star formation rate, be traced out to large radii, around R500, and for larger galaxies even out to R200, using prominent emission lines, such as OVII, or OVIII. Furthermore, we show that emission line ratios for individual halos can reveal the radial temperature structure. Substructure measurements show that it will be possible to relate azimuthal variations to the feedback mode of the galaxy. We demonstrate the ability to construct temperature, velocity, and abundance ratio maps from spectral fitting for individual galaxy halos, which reveal rotation features, AGN outbursts, and enrichment.

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Line Emission Mapper (LEM): Probing the physics of cosmic ecosystems

The Line Emission Mapper (LEM) is an X-ray Probe for the 2030s that will answer the outstanding questions of the Universe's structure formation. It will also provide transformative new observing capabilities for every area of astrophysics, and to heliophysics and planetary physics as well. LEM's main goal is a comprehensive look at the physics of galaxy formation, including stellar and black-hole feedback and flows of baryonic matter into and out of galaxies. These processes are best studied in X-rays, and emission-line mapping is the pressing need in this area. LEM will use a large microcalorimeter array/IFU, covering a 30x30' field with 10" angular resolution, to map the soft X-ray line emission from objects that constitute galactic ecosystems. These include supernova remnants, star-forming regions, superbubbles, galactic outflows (such as the Fermi/eROSITA bubbles in the Milky Way and their analogs in other galaxies), the Circumgalactic Medium in the Milky Way and other galaxies, and the Intergalactic Medium at the outskirts and beyond the confines of galaxies and clusters. LEM's 1-2 eV spectral resolution in the 0.2-2 keV band will make it possible to disentangle the faintest emission lines in those objects from the bright Milky Way foreground, providing groundbreaking measurements of the physics of these plasmas, from temperatures, densities, chemical composition to gas dynamics. While LEM's main focus is on galaxy formation, it will provide transformative capability for all classes of astrophysical objects, from the Earth's magnetosphere, planets and comets to the interstellar medium and X-ray binaries in nearby galaxies, AGN, and cooling gas in galaxy clusters. In addition to pointed observations, LEM will perform a shallow all-sky survey that will dramatically expand the discovery space.

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Gas sloshing and cold fronts in pre-merging galaxy cluster Abell 98

We present deep Chandra observations of the pre-merger galaxy cluster Abell 98. Abell 98 is a complex merging system. While the northern (A98N) and central subclusters (A98S) are merging along the north-south direction, A98S is undergoing a separate late-stage merger, with two distinct X-ray cores. We report detection of gas sloshing spirals in A98N and in the eastern core of A98S. We detect two cold front edges in A98N. We find two more surface brightness edges along the east direction of the eastern core and west direction of the western core of A98S. We measure the temperatures and gas densities across those edges, and find that the eastern edge appears to be a cold front while the western edge is a shock front with a Mach number of $\cal{M}$ $\approx$ 1.5. We detect a "tail" of X-ray emission associated with the eastern core of A98S. Our measurement indicates that the tail is cooler than the surrounding gas at a 4.2-$\sigma$ level, suggesting the tail is part of a cool core remnant that has been ram-pressure stripped.

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Chemical abundances in the outskirts of nearby galaxy groups measured with joint Suzaku and Chandra observations

We report results from deep Suzaku and mostly snapshot Chandra observations of four nearby galaxy groups: MKW4, Antlia, RXJ1159+5531, and ESO3060170. Their peak temperatures vary over 2-3 keV, making them the smallest systems with gas properties constrained to their viral radii. The average Fe abundance in the outskirts (R $>$ 0.25R$_{200}$) of their intragroup medium (IGrM) is $Z_{\rm Fe}=0.309\pm0.018$ $Z_\odot$ with $\chi^2$ = 14 for 12 degrees of freedom, which is remarkably uniform and strikingly similar to that of massive galaxy clusters, and is fully consistent with the numerical predictions from the IllustrisTNG cosmological simulation. Our results support an early-enrichment scenario among galactic systems over an order of magnitude in mass, even before their formation. When integrated out to R$_{200}$, we start to see a tension between the measured Fe content in ICM and what is expected from supernovae yields. We further constrain their O, Mg, Si, S, and Ni abundances. The abundance ratios of those elements relative to Fe are consistent with the predictions (if available) from IllustrisTNG. Their Type Ia supernovae fraction varies between 14%-21%. A pure core collapsed supernovae enrichment at group outskirts can be ruled out. Their cumulative iron-mass-to-light ratios within R$_{200}$ are half that of the Perseus cluster, which may imply that galaxy groups do not retain all of their enriched gas due to their shallower gravitational potential wells, or that groups and clusters may have different star formation histories.

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Discovery of a pre-merger shock in an intercluster filament in Abell 98

We report the first unambiguous detection of an axial merger shock in the early-stage merging cluster Abell 98 using deep (227 ks) Chandra observations. The shock is about 420 kpc south from the northern subcluster of Abell 98, in between the northern and central subclusters, with a Mach number of M $\approx$ 2.3 $\pm$ 0.3. Our discovery of the axial merger shock front unveils a critical epoch in the formation of a massive galaxy cluster, when two subclusters are caught in the early phase of the merging process. We find that the electron temperature in the post-shock region favors the instant collisionless model, where electrons are strongly heated at the shock front, by interactions with the magnetic field. We also report on the detection of an intercluster gas filament, with a temperature of kT = 1.07 $\pm$ 0.29 keV, along the merger axis of Abell 98. The measured properties of the gas in the filament are consistent with previous observations and numerical simulations of the hottest, densest parts of the warm-hot intergalactic medium (WHIM), where WHIM filaments interface with the virialization regions of galaxy clusters.

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The deepest $Chandra$ view of RBS 797: evidence for two pairs of equidistant X-ray cavities

We present the first results of a deep $Chandra$ observation of the galaxy cluster RBS 797, whose previous X-ray studies revealed two pronounced X-ray cavities in the east-west (E-W) direction. Follow-up VLA radio observations of the central active galactic nucleus (AGN) uncovered different jet and lobe orientations, with radio lobes filling the E-W cavities and perpendicular jets showing emission in the north-south (N-S) direction over the same scale ($\approx$30 kpc). With the new $\sim$427 ks total exposure, we report the detection of two additional, symmetric X-ray cavities in the N-S direction at nearly the same radial distance as the E-W ones. The newly discovered N-S cavities are associated with the radio emission detected at 1.4 GHz and 4.8 GHz in archival VLA data, making RBS 797 the first galaxy cluster found to have four equidistant, centrally-symmetric, radio-filled cavities. We derive the dynamical and radiative ages of the four cavities from X-ray and radio data, respectively, finding that the two outbursts are approximately coeval, with an age difference of $\lessapprox$10 Myr between the E-W and N-S cavities. We discuss two scenarios for the origin of the two perpendicular, equidistant cavity systems: either the presence of a binary AGN which is excavating coeval pairs of cavities in perpendicular directions, or a fast ($<$10 Myr) jet reorientation event which produced subsequent, misaligned outbursts.

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Joint Suzaku and Chandra observations of the MKW4 galaxy group out to the virial radius

We present joint Suzaku and Chandra observations of MKW4. With a global temperature of 1.6 keV, MKW4 is one of the smallest galaxy groups that have been mapped in X-rays out to the virial radius. We measure its gas properties from its center to the virial radius in the north, east, and northeast directions. Its entropy profile follows a power-law of $\propto r^{1.1}$ between R$_{500}$ and R$_{200}$ in all directions, as expected from the purely gravitational structure formation model. The well-behaved entropy profiles at the outskirts of MKW4 disfavor the presence of gas clumping or thermal non-equilibrium between ions and electrons in this system. We measure an enclosed baryon fraction of 11% at R$_{200}$, remarkably smaller than the cosmic baryon fraction of 15%. We note that the enclosed gas fractions at R$_{200}$ are systematically smaller for groups than for clusters from existing studies in the literature. The low baryon fraction of galaxy groups, such as MKW4, suggests that their shallower gravitational potential well may make them more vulnerable to baryon losses due to AGN feedback or galactic winds. We find that the azimuthal scatter of various gas properties at the outskirts of MKW4 is significantly lower than in other systems, suggesting that MKW4 is a spherically symmetric and highly relaxed system.

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X-ray scaling relations for a representative sample of Planck selected clusters observed with XMM-Newton

We report the scaling relations derived by fitting the X-ray parameters determined from analyzing the XMM-Newton observations of 120 galaxy clusters in the Planck Early Sunyaev-Zel'dovich sample spanning the redshift range of 0.059$<$$z$$<$0.546. We find that the slopes of all the investigated scaling relations significantly deviate from the self-similar predictions, if self-similar redshift evolution is assumed. When the redshift evolution is left free to vary, the derived slopes are more in agreement with the self-similar predictions. Relaxed clusters have on average $\sim$30$\%$ higher X-ray luminosity than disturbed clusters at a given mass, a difference that, depending on the relative fraction of relaxed and disturbed clusters in the samples (e.g. SZ vs X-ray selected), have a strong impact in the normalization obtained in different studies. Using the core-excised cluster luminosities reduces the scatter and brings into better agreement the $L$-$M_{tot}$ and $L$-$T$ relations determined for different samples. $M_{tot}$-$T$, $M_{tot}$-$Y_X$, and $M_{tot}$-$M_{gas}$ relations show little dependence on the dynamical state of the clusters, but the normalizations of these relations may depend on the mass range investigated. Although most of the clusters investigated in this work reside at relatively low redshift, the fits prefer values of $\gamma$, the parameter accounting for the redshift evolution, different from the self-similar predictions. This suggests an evolution ($<$2$\sigma$ level, with the exception of the $M_{tot}$-$T$ relation) of the scaling relations. For the first time, we find significant evolution ($>$3$\sigma$) of the $M_{tot}$-$T$ relation, pointing to an increase of the kinetic-to-thermal energy ratio with redshift. This is consistent with a scenario in which higher redshift clusters are on average more disturbed than their lower redshift counterparts.

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Probing Macro-Scale Gas Motions and Turbulence in Diffuse Cosmic Plasmas

Clusters of galaxies, the largest collapsed structures in the Universe, are located at the intersection of extended filaments of baryons and dark matter. Cosmological accretion onto clusters through large scale filaments adds material at cluster outskirts. Kinetic energy in the form of bulk motions and turbulence due to this accretion provides a form of pressure support against gravity, supplemental to thermal pressure. Significant amount of non-thermal pressure support could bias cluster masses derived assuming hydrostatic equilibrium, the primary proxy for cluster cosmology studies. Sensitive measurements of Doppler broadening and shift of astrophysical lines, and the relative fluctuations in thermodynamical quantities (e.g., density, pressure, and entropy) are primary diagnostic tools. Forthcoming planned and proposed X-ray (with large etendue, throughput, and high spectral resolution) and SZ observatories will provide crucial information on the assembly and virialisation processes of clusters, involving turbulent eddies cascading at various spatial scales and larger gas bulk motions in their external regions to the depth or their potential wells.

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Stripped elliptical galaxies as probes of ICM physics: III. Deep Chandra Observation of NGC 4552 - Measuring the Viscosity of the Intracluster Medium

We present results from a deep (200 ks) Chandra observation of the early-type galaxy NGC 4552 (M89) which is falling into the Virgo cluster. Previous shallower X-ray observations of this galaxy showed a remnant gas core, a tail to the South of the galaxy, and twin `horns' attached to the northern edge of the gas core [machacek05a]. In our deeper data, we detect a diffuse, low surface brightness extension to the previously known tail, and measure the temperature structure within the tail. We combine the deep Chandra data with archival XMM-Newton observations to put a strong upper limit on the diffuse emission of the tail out to a large distance (10$\times$the radius of the remnant core) from the galaxy center. In our two previous papers [roediger15a,roediger15b], we presented the results of hydrodynamical simulations of ram pressure stripping specifically for M89 falling into the Virgo cluster and investigated the effect of ICM viscosity. In this paper, we compare our deep data with our specifically tailored simulations and conclude that the observed morphology of the stripped tail in NGC 4552 is most similar to the inviscid models. We conclude that, to the extent the transport processes can be simply modeled as a hydrodynamic viscosity, the ICM viscosity is negligible. More generally, any micro-scale description of the transport processes in the high-$\beta$ plasma of the cluster ICM must be consistent with the efficient mixing observed in the stripped tail on macroscopic scales.

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