Adiabatic and Non‐Adiabatic Electron Heating at Quasi‐Perpendicular Collisionless Shocks

The relative contribution of adiabatic and non‐adiabatic processes to electron heating across collisionless shocks remains an open question. We analyze the evolution of suprathermal electrons across 310 quasi‐perpendicular shocks with Alfvénic Mach numbers in the normal‐incidence frame M A − N I F $\left({M}_{A-NIF}\right)$ ranging from 1.7 to 48, using in situ measurements of Earth's bow shock by the Magnetospheric Multiscale (MMS) spacecraft. We introduce a novel non‐adiabaticity measure derived from the electron distribution function and based on Liouville's theorem. Our results reveal, for the first time, that the electron heating mechanism is governed by the Alfvénic Mach number in the de Hoffman‐Teller frame M A − H T $\left({M}_{A-HT}\right)$ , with a transition from predominantly adiabatic to non‐adiabatic heating occurring at M A − H T ≳ 30 ${M}_{A-HT}\gtrsim 30$ . Furthermore, by examining the spectral index of the suprathermal electron distribution, we find that for shocks exhibiting dominant non‐adiabatic electron dynamics, the observed electron heating is consistent with the predictions of the stochastic shock drift acceleration (SSDA) mechanism.