Energy partition between ions and electrons in high Mach number nonrelativistic collisionless shocks

Astrophysical environments such as supernova remnants and galaxy clusters host nonrelativistic collisionless shocks which can accelerate and heat protons and electrons. These shocks are capable of equilibrating the temperature between the particle species. We use two-dimensional particle-in-cell simulations in order to investigate the structure of magnetized nonrelativistic shocks and to study the downstream electron-to-ion temperature ratio, T_e/T_i, over a wide range of sonic, M_s, and Alfvénic Mach numbers, M_A. We find that for M_s < 2, the electron-to-ion temperature ratio shows weak dependence on M_A, and the two species are close to energy equipartition. At higher M_s, the temperature ratio is predominately determined by M_A, experiencing a minimum value of T_e/T_i ~ 0.1 at M_A ~ 10 and reaching an asymptotic value of T_e/T_i ~ 0.3 at higher Mach numbers, 60 < M_A < 140. In general, the downstream electron temperature is of order of 10% of the upstream ion kinetic energy. This is considerably larger than the adiabatic prediction of the 1/1836 electron-ion temperature ratio in an electron-ion collisionless shock. High M_A shocks are susceptible to the Weibel instability, which creates filamentary structures at the shock foot and ramp. The presence of filaments in density and magnetic field at the high M_A shock precursor is responsible for the super-adiabatic heating of electrons, through energization from parallel electric field oscillations associated with the screening of the cross-shock potential electric field. We focus on the details of this heating mechanism and its dependence on shock parameters.