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On the Efficiency of Thermal Conduction in Galaxy Clusters

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 Added by Fulai Guo
 Publication date 2018
  fields Physics
and research's language is English




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Galaxy clusters host a large reservoir of diffuse plasma with radially-varying temperature profiles. The efficiency of thermal conduction in the intracluster medium (ICM) is complicated by the existence of turbulence and magnetic fields, and has received a lot of attention in the literature. Previous studies suggest that the magnetothermal instability developed in outer regions of galaxy clusters would drive magnetic field lines preferentially radial, resulting in efficient conduction along the radial direction. Using a series of spherically-symmetric simulations, here we investigate the impact of thermal conduction on the observed temperature distributions in outer regions of three massive clusters, and find that thermal conduction substantially modifies the ICM temperature profile. Within 3 Gyr, the gas temperature at a representative radius of $0.3r_{500}$ typically decreases by ~10 - 20% and the average temperature slope between $0.3r_{500}$ and $r_{500}$ drops by ~ 30 - 40%, indicating that the observed ICM would not stay in a long-term equilibrium state in the presence of thermal conduction. However, X-ray observations show that the outer regions of massive clusters have remarkably similar radially-declining temperature profiles, suggesting that they should be quite stable. Our study thus suggests that the effective conductivity along the radial direction must be suppressed below the Spitzer value by a factor of 10 or more, unless additional heating sources offset conductive cooling and maintain the observed temperature distributions. Our study provides a smoking-gun evidence for the suppression of parallel conduction along magnetic field lines in low-collisionality plasmas by kinetic mirror or whistler instabilities.



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We present an implementation of thermal conduction including the anisotropic effects of magnetic fields for SPH. The anisotropic thermal conduction is mainly proceeding parallel to magnetic fields and suppressed perpendicular to the fields. We derive the SPH formalism for the anisotropic heat transport and solve the corresponding equation with an implicit conjugate gradient scheme. We discuss several issues of unphysical heat transport in the cases of extreme ansiotropies or unmagnetized regions and present possible numerical workarounds. We implement our algorithm into the GADGET code and study its behaviour in several test cases. In general, we reproduce the analytical solutions of our idealised test problems, and obtain good results in cosmological simulations of galaxy cluster formations. Within galaxy clusters, the anisotropic conduction produces a net heat transport similar to an isotropic Spitzer conduction model with an efficiency of one per cent. In contrast to isotropic conduction our new formalism allows small-scale structure in the temperature distribution to remain stable, because of their decoupling caused by magnetic field lines. Compared to observations, isotropic conduction with more than 10 per cent of the Spitzer value leads to an oversmoothed temperature distribution within clusters, while the results obtained with anisotropic thermal conduction reproduce the observed temperature fluctuations well. A proper treatment of heat transport is crucial especially in the outskirts of clusters and also in high density regions. Its connection to the local dynamical state of the cluster also might contribute to the observed bimodal distribution of cool core and non cool core clusters. Our new scheme significantly advances the modelling of thermal conduction in numerical simulations and overall gives better results compared to observations.
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Active galactic nucleus (AGN) jets are believed to be important in solving the cooling flow problem in the intracluster medium (ICM), while the detailed mechanism is still in debate. Here we present a systematic study on the energy coupling efficiency $eta_{rm cp}$, the fraction of AGN jet energy transferred to the ICM. We first estimate the values of $eta_{rm cp}$ analytically in two extreme cases, which are further confirmed and extended with a parameter study of spherical outbursts in a uniform medium using hydrodynamic simulations. We find that $eta_{rm cp}$ increases from $sim 0.4$ for a weak isobaric injection to $gtrsim 0.8$ for a powerful point injection. For any given outburst energy, we find two characteristic outburst powers that separate these two extreme cases. We then investigate the energy coupling efficiency of AGN jet outbursts in a realistic ICM with hydrodynamic simulations, finding that jet outbursts are intrinsically different from spherical outbursts. For both powerful and weak jet outbursts, $eta_{rm cp}$ is typically around $0.7-0.9$, partly due to the non-spherical nature of jet outbursts, which produce backflows emanating from the hotspots, significantly enhancing the ejecta-ICM interaction. While for powerful outbursts a dominant fraction of the energy transferred from the jet to the ICM is dissipated by shocks, shock dissipation only accounts for $lesssim 30%$ of the injected jet energy for weak outbursts. While both powerful and weak outbursts could efficiently heat cooling flows, powerful thermal-energy-dominated jets are most effective in delaying the onset of the central cooling catastrophe.
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(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 large temperature difference between cold gas clouds around galaxies and the hot halos that they are moving through suggests that thermal conduction could play an important role in the circumgalactic medium. However, thermal conduction in the presence of a magnetic field is highly anisotropic, being strongly suppressed in the direction perpendicular to the magnetic field lines. This is commonly modelled by using a simple prescription that assumes that thermal conduction is isotropic at a certain efficiency $f<1$, but its precise value is largely unconstrained. We investigate the efficiency of thermal conduction by comparing the evolution of 3D hydrodynamical (HD) simulations of cold clouds moving through a hot medium, using artificially suppressed isotropic thermal conduction (with $f$), against 3D magnetohydrodynamical (MHD) simulations with (true) anisotropic thermal conduction. Our main diagnostic is the time evolution of the amount of cold gas in conditions representative of the lower (close to the disc) circumgalactic medium of a Milky Way-like galaxy. We find that in almost every HD and MHD run, the amount of cold gas increases with time, indicating that hot gas condensation is an important phenomenon that can contribute to gas accretion onto galaxies. For the most realistic orientations of the magnetic field with respect to the cloud motion we find that $f$ is in the range 0.03 -- 0.15. Thermal conduction is thus always highly suppressed, but its effect on the cloud evolution is generally not negligible.
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