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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.
(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 presen
(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, ra
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
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 rece
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.