Ion versus electron heating in compressively driven astrophysical gyrokinetic turbulence

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*.