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*.
Highlights
Most astrophysical systems, e.g., the solar wind, lowluminosity accretion disks, supernova remnants, and the intracluster medium, are in a collisionless turbulent state
Recent two-temperature generalrelativistic magnetohydrodynamic (GRMHD) simulations of Sgr A* show that the electron temperature there is at most kBTe=mec2 ∼ 10 [9], so the increase in the electron inertia is not large enough to break the scale separation between ρi and ρe, which is the main physical characteristic of our plasma that sets its behavior in what concerns energy partition
When βi 1⁄4 0.1, Qi=Qe 1⁄4 Pcompr=PAW holds for all Pcompr=PAW, meaning that all of the compressive power is converted into ion heating, and all Alfvenic power is converted into electron heating. This i i i i i i i result was theoretically predicted in Ref. [31] and is easy to understand physically: When βi ≪ 1, ions are too slow to resonate with AWs, and so the Alfvenic cascade goes from the reduced MHD (RMHD) to electron RMHD (ERMHD) regime without losing power and gets dissipated on electrons
Summary
E.g., the solar wind, lowluminosity accretion disks, supernova remnants, and the intracluster medium, are in a collisionless turbulent state. Heat is generally deposited into ions and electrons unequally, resulting in a two-temperature state, e.g., in the solar wind [1], accretion disks around black holes [2,3], and the intracluster medium [4]. For the last few years, turbulent heating has been studied by means of particle-in-cell [11,12,13,14,15,16,17,18] and gyrokinetic (GK) [19,20,21,22] simulations In these kinetic simulations, turbulence is excited by injection of artificially configured box-scale fluctuations. We investigate the properties of the phase-space spectra to understand the heating mechanisms related to the compressive cascade
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