Propagation of weak shocks in cool-core galaxy clusters in two-temperature magnetohydrodynamics with anisotropic thermal conduction

We investigate how different magnetohydrodynamic models of propagation of a weak (Mach number similar to 1.2) shock in the core of a galaxy cluster affect its observational appearance, using the Perseus cluster as our fiducial model. In particular, we study how thermal conduction, both isotropic and anisotropic, and ion-electron temperature equilibration modify a weak shock. Strong thermal conduction is expected to produce an electron temperature precursor. Less prominent pressure and density precursors are formed as well. A longer equilibration time largely reduces the density precursor but does not change the electron temperature precursor much. When thermal conduction becomes anisotropic, the intracluster magnetic field imprints its characteristic spatial scale on the distortions of the shock induced by heat fluxes.