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Register a new userThe Effect of Anisotropic Viscosity on Cold Fronts in Galaxy Clusters
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J. A. ZuHone
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Cold fronts -- contact discontinuities in the intracluster medium (ICM) of galaxy clusters -- should be disrupted by Kelvin-Helmholtz (K-H) instabilities due to the associated shear velocity. However, many observed cold fronts appear stable. This opens the possibility to place constraints on microphysical mechanisms that stabilize them, such as the ICM viscosity and/or magnetic fields. We performed exploratory high-resolution simulations of cold fronts arising from subsonic gas sloshing in cluster cores using the grid-based Athena MHD code, comparing the effects of isotropic Spitzer and anisotropic Braginskii viscosity (expected in a magnetized plasma). Magnetized simulations with full Braginskii viscosity or isotropic Spitzer viscosity reduced by a factor f ~ 0.1 are both in qualitative agreement with observations in terms of suppressing K-H instabilities. The RMS velocity of turbulence within the sloshing region is only modestly reduced by Braginskii viscosity. We also performed unmagnetized simulations with and without viscosity and find that magnetic fields have a substantial effect on the appearance of the cold fronts, even if the initial field is weak and the viscosity is the same. This suggests that determining the dominant suppression mechanism of a given cold front from X-ray observations (e.g. viscosity or magnetic fields) by comparison with simulations is not straightforward. Finally, we performed simulations including anisotropic thermal conduction, and find that including Braginskii viscosity in these simulations does not significant affect the evolution of cold fronts; they are rapidly smeared out by thermal conduction, as in the inviscid case.
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Cold fronts have been observed in a large number of galaxy clusters. Understanding their nature and origin is of primary importance for the investigation of the internal dynamics of clusters. To gain insight on the nature of these features, we carry out a statistical investigation of their occurrence in a sample of galaxy clusters observed with XMM-Newton and we correlate their presence with different cluster properties. We have selected a sample of 45 clusters starting from the B55 flux limited sample by Edge et al. (1990) and performed a systematic search of cold fronts. We find that a large fraction of clusters host at least one cold front. Cold fronts are easily detected in all systems that are manifestly undergoing a merger event in the plane of the sky while the presence of such features in the remaining clusters is related to the presence of a steep entropy gradient, in agreement with theoretical expectations. Assuming that cold fronts in cool core clusters are triggered by minor merger events, we estimate a minimum of 1/3 merging events per halo per Gyr.
(Abridged) Cold fronts in cluster cool cores should be erased on short timescales by thermal conduction, unless protected by magnetic fields that are draped parallel to the front surfaces, suppressing conduction perpendicular to the fronts. We present MHD simulations of cold front formation in the core of a galaxy cluster with anisotropic thermal conduction, exploring a parameter space of conduction strengths parallel and perpendicular to the field lines. Including conduction has a strong effect on the temperature of the core and the cold fronts. Though magnetic field lines are draping parallel to the front surfaces, the temperature jumps across the fronts are nevertheless reduced. The field geometry is such that the cold gas below the front surfaces can be connected to hotter regions outside via field lines along directions perpendicular to the plane of the sloshing motions and along sections of the front which are not perfectly draped. This results in the heating of this gas below the front on a timescale of a Gyr, but the sharpness of the density and temperature jumps may still be preserved. By modifying the density distribution below the front, conduction may indirectly aid in suppressing Kelvin-Helmholtz instabilities. If conduction along the field lines is unsuppressed, we find that the characteristic sharp jumps in X-ray emission seen in observations of clusters do not form. This suggests that the presence of sharp cold fronts in hot clusters could be used to place upper limits on conduction in the {it bulk} of the ICM. Finally, the combination of sloshing and anisotropic thermal conduction can result in a larger flux of heat to the core than either process in isolation. While still not sufficient to prevent a cooling catastrophe in the very central ($r sim$ 5 kpc) regions of the cool core, it reduces significantly the mass of cool gas that accumulates outside those radii.
The most massive baryonic component of galaxy clusters is the intracluster medium (ICM), a diffuse, hot, weakly magnetized plasma that is most easily observed in the X-ray band. Despite being observed for decades, the macroscopic transport properties of the ICM are still not well-constrained. A path to determine macroscopic ICM properties opened up with the discovery of cold fronts. These were observed as sharp discontinuities in surface brightness and temperature in the ICM, with the property that the brighter (and denser) side of the discontinuity is the colder one. The high spatial resolution of the Chandra X-ray Observatory revealed two puzzles about the cold fronts. First, they should be subject to Kelvin-Helmholtz instabilites, yet in many cases they appear relatively smooth and undisturbed. Second, the width of the interface between the two gas phases is typically narrower than the mean free path of the particles in the plasma, indicating negligible thermal conduction. From the time of their discovery, it was realized that these special characteristics of cold fronts may be used to probe the physical properties of the cluster plasma. In this review, we will discuss the recent simulations of cold front formation and evolution in galaxy clusters, with a focus on those which have attempted to use these features to constrain the physics of the ICM. In particular, we will focus on the effects of magnetic fields, viscosity, and thermal conductivity on the stability properties and long-term evolution of cold fronts. We conclude with a discussion on what important questions remain unanswered, and the future role of simulations and the next generation of X-ray observatories.
Sloshing cold fronts (CFs) arise from minor merger triggered gas sloshing. Their detailed structure depends on the properties of the intra-cluster medium (ICM): hydrodynamical simulations predict the CFs to be distorted by Kelvin-Helmholtz instabilities (KHIs), but aligned magnetic fields, viscosity, or thermal conduction can suppress the KHIs. Thus, observing the detailed structure of sloshing CFs can be used to constrain these ICM properties. Both smooth and distorted sloshing CFs have been observed, indicating that the KHI is suppressed in some clusters, but not in all. Consequently, we need to address at least some sloshing clusters individually before drawing general conclusions about the ICM properties. We present the first detailed attempt to constrain the ICM properties in a specific cluster from the structure of its sloshing CF. Proximity and brightness make the Virgo cluster an ideal target. We combine observations and Virgo-specific hydrodynamical sloshing simulations. Here we focus on a Spitzer-like temperature dependent viscosity as a mechanism to suppress the KHI, but discuss the alternative mechanisms in detail. We identify the CF at 90 kpc north and north-east of the Virgo center as the best location in the cluster to observe a possible KHI suppression. For viscosities $gtrsim$ 10% of the Spitzer value KHIs at this CF are suppressed. We describe in detail the observable signatures at low and high viscosities, i.e. in the presence or absence of KHIs. We find indications for a low ICM viscosity in archival XMM-Newton data and demonstrate the detectability of the predicted features in deep Chandra observations.
Table of contents (abridged): COLD FRONTS Origin and evolution of merger cold fronts Cold fronts in cluster cool cores . . . Simulations of gas sloshing. Origin of density discontinuity. . . . Effect of sloshing on cluster mass estimates and cooling flows. Zoology of cold fronts COLD FRONTS AS EXPERIMENTAL TOOL Velocities of gas flows Thermal conduction and diffusion across cold fronts Stability of cold fronts . . . Rayleigh-Taylor instability. Kelvin-Helmholtz instability. Possible future measurements using cold fronts . . . Plasma depletion layer and magnetic field. Effective viscosity of ICM. SHOCK FRONTS AS EXPERIMENTAL TOOL Cluster merger shocks Mach number determination Front width Mach cone and reverse shock? Test of electron-ion equilibrium . . . Comparison with other astrophysical plasmas Shocks and cluster cosmic ray population . . . Shock acceleration. Compression of fossil electrons. . . . Yet another method to measure intracluster magnetic field.
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