Simulations of two-temperature jets in galaxy clusters: I. Effect of jet magnetization on dynamics and electron heating

Context. Non-radiating protons in the radio lobes play an essential role in shaping the jet morphology, as demonstrated in recent radio and X-ray observations. However, since protons and electrons are not always in energy equilibrium due to weak Coulomb coupling, it is difficult to estimate the energy contribution of protons for the inflation of radio lobes.Aims. The focus of this study is to examine the effect of the variable model for electron heating by turbulence and shock waves on the thermal energy distribution of electrons and protons.Methods. We performed two-temperature three-dimensional magnetohydrodynamic (3D MHD) simulations of sub-relativistic jets in the galaxy cluster, while varying the jet magnetization parameters. Because the energy partition rate between electrons and protons in shock and turbulence is determined by plasma kinetic scale physics, our global simulations include electron instantaneous heating sub-grid models for shock waves and turbulence.Results. We find that most of the bulk kinetic energy of the jet is converted into the thermal energy of protons through both shocks and turbulence. Thus, protons are energetically dominant. Meanwhile, thermal electrons stored in the lobe evolve toward energy equipartition with magnetic energy through turbulent dissipation. We further estimated the radio power and the mechanical jet power of radio lobes following the same method used for radio and X-ray observations, then we compared these powers with that of the observed radio jets. The two-temperature model quantitatively explains the radiatively inefficient radio cavities, but it cannot reproduce the radiatively efficient cavity, even for strongly magnetized jets. This implies that a significant population of pair-plasma is needed to explain radiatively efficient radio cavities.