Ion versus electron heating in compressively driven astrophysical gyrokinetic turbulence (2004.04922v2)

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 $Q_\rmi/Q_\rme$ as a function of the compressive-to-Alfv\'enic driving power ratio $P_\compr/P_\AW$, of the ratio of ion thermal pressure to magnetic pressure $\beta_\rmi$, and of the ratio of ion-to-electron background temperatures $T_\rmi/T_\rme$. It is shown that $Q_\rmi/Q_\rme$ is an increasing function of $P_\compr/P_\AW$. When the compressive driving is sufficiently large, $Q_\rmi/Q_\rme$ approaches $\simeq P_\compr/P_\AW$. 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 Alfv\'en waves is absent for both low and high $\beta_\rmi$, 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 $\beta_\rmi$ 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*.