Electron Heating in the Transrelativistic Perpendicular Shocks of Tilted Accretion Flows

Abstract

General relativistic magnetohydrodynamic (GRMHD) simulations of black hole tilted disks—where the angular momentum of the accretion flow at large distances is misaligned with respect to the black hole spin—commonly display standing shocks within a few to tens of gravitational radii from the black hole. In GRMHD simulations of geometrically thick, optically thin accretion flows, applicable to low-luminosity sources like Sgr A* and M87*, the shocks have transrelativistic speed, moderate plasma beta (the ratio of ion thermal pressure to magnetic pressure is β pi1 ∼ 1–8), and low sonic Mach number (the ratio of shock speed to sound speed is M s ∼ 1–6). We study such shocks with 2D particle-in-cell simulations, and we quantify the efficiency and mechanisms of electron heating for the special case of preshock magnetic fields perpendicular to the shock direction of propagation. We find that the postshock electron temperature T e2 exceeds the adiabatic expectation T e2,ad by an amount T e 2 / T e 2 , ad − 1 ≃ 0.0016 M s 3.6 , nearly independent of the plasma beta and of the preshock electron-to-ion temperature ratio T e1/T i1, which we vary from 0.1 to unity. We investigate the heating physics for M s ∼ 5–6 and find that electron superadiabatic heating is governed by magnetic pumping at T e1/T i1 = 1, whereas heating by B-parallel electric fields (i.e., parallel to the local magnetic field) dominates at T e1/T i1 = 0.1. Our results provide physically motivated subgrid prescriptions for electron heating at the collisionless shocks seen in GRMHD simulations of black hole accretion flows.