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Register a new userAnisotropic thermal conduction in galaxy clusters with MHD in Gadget
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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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(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.
(abridged) The ICM has been suggested to be buoyantly unstable in the presence of magnetic field and anisotropic thermal conduction. We perform first cosmological simulations of galaxy cluster formation that simultaneously include magnetic fields, radiative cooling and anisotropic thermal conduction. In isolated and idealized cluster models, the magnetothermal instability (MTI) tends to reorient the magnetic fields radially. Using cosmological simulations of the Santa Barbara cluster we detect radial bias in the velocity and magnetic fields. Such radial bias is consistent with either the inhomogeneous radial gas flows due to substructures or residual MTI-driven field rearangements that are expected even in the presence of turbulence. Although disentangling the two scenarios is challenging, we do not detect excess bias in the runs that include anisotropic thermal conduction. The anisotropy effect is potentially detectable via radio polarization measurements with LOFAR and SKA and future X-ray spectroscopic studies with the IXO. We demonstrate that radiative cooling boosts the amplification of the magnetic field by about two orders of magnitude beyond what is expected in the non-radiative cases. At z=0 the field is amplified by a factor of about 10^6 compared to the uniform magnetic field evolved due to the universal expansion alone. Interestingly, the runs that include both radiative cooling and anisotropic thermal conduction exhibit stronger magnetic field amplification than purely radiative runs at the off-center locations. In these runs, shallow temperature gradients away from the cluster center make the ICM neutrally buoyant. The ICM is more easily mixed in these regions and the winding up of the frozen-in magnetic field is more efficient resulting in stronger magnetic field amplification.
Transport equations for electron thermal energy in the high $beta_e$ intracluster medium (ICM) are developed that include scattering from both classical collisions and self-generated whistler waves. The calculation employs an expansion of the kinetic electron equation along the ambient magnetic field in the limit of strong scattering and assumes whistler waves with low phase speeds $V_wsim{v}_{te}/beta_ell{v}_{te}$ dominate the turbulent spectrum, with $v_{te}$ the electron thermal speed and $beta_egg1$ the ratio of electron thermal to magnetic pressure. We find: (1) temperature-gradient-driven whistlers dominate classical scattering when $L_c>L/beta_e$, with $L_c$ the classical electron mean-free-path and $L$ the electron temperature scale length, and (2) in the whistler dominated regime the electron thermal flux is controlled by both advection at $V_w$ and a comparable diffusive term. The findings suggest whistlers limit electron heat flux over large regions of the ICM, including locations unstable to isobaric condensation. Consequences include: (1) the Field length decreases, extending the domain of thermal instability to smaller length-scales, (2) the heat flux temperature dependence changes from $T_e^{7/2}/L$ to $V_wnT_esim{T}_e^{1/2}$, (3) the magneto-thermal and heat-flux driven buoyancy instabilities are impaired or completely inhibited, and (4) sound waves in the ICM propagate greater distances, as inferred from observations. This description of thermal transport can be used in macroscale ICM models.
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.
The relevance of non-thermal cluster studies and the importance of combining observations of future radio surveys with WFXT data are discussed in this paper.
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