Ion versus Electron Heating in Compressively Driven Astrophysical Gyrokinetic Turbulence

Abstract

The partition of irreversible heating between ions and electrons in compressively driven (but subsonic) collisionless turbulence is investigated by means of nonlinear hybrid gyrokinetic simulations. We derive a prescription for the ion-to-electron heating ratio Q_{i}/Q_{e} as a function of the compressive-to-Alfvénic driving power ratio P_{compr}/P_{AW}, of the ratio of ion thermal pressure to magnetic pressure β_{i}, and of the ratio of ion-to-electron background temperatures T_{i}/T_{e}. It is shown that Q_{i}/Q_{e} is an increasing function of P_{compr}/P_{AW}. When the compressive driving is sufficiently large, Q_{i}/Q_{e} approaches ≃P_{compr}/P_{AW}. This indicates that, in turbulence with large compressive fluctuations, the partition of heating is decided at the injection scales, rather than at kinetic scales. Analysis of phase-space spectra shows that the energy transfer from inertial-range compressive fluctuations to sub-Larmor-scale kinetic Alfvén waves is absent for both low and high β_{i}, meaning that the compressive driving is directly connected to the ion-entropy fluctuations, which are converted into ion thermal energy. This result suggests that preferential electron heating is a very special case requiring low β_{i} and no, or weak, compressive driving. Our heating prescription has wide-ranging applications, including to the solar wind and to hot accretion disks such as M87 and Sgr A*.