Electron heating at quasi-perpendicular collisionless shocks: adiabatic vs non-adiabatic

The mechanism of electron heating across collisionless shocks remains an open question. The mechanisms suggested to address this problem revolve around the adiabatic or the non-adiabatic\stochastic dynamics of electrons across the shock. In this letter, we analyze the evolution of the electron velocity distribution function observed across 313 shocks with 1.7<M_A<48. We use a Liouville mapping technique to show that the electron heating mechanism shifts from predominantly adiabatic to predominantly non-adiabatic as the Alfvenic Mach number in the de Hoffmann-Teller frame increases. We also show that for shocks with non-adiabatic heating of electrons, the heating mechanism is consistent with the stochastic shock drift acceleration (SSDA) mechanism.