ELECTRON HEATING BY THE ION CYCLOTRON INSTABILITY IN COLLISIONLESS ACCRETION FLOWS. II. ELECTRON HEATING EFFICIENCY AS A FUNCTION OF FLOW CONDITIONS

In the innermost regions of low-luminosity accretion flows, including Sgr A* at the center of our Galaxy, the frequency of Coulomb collisions is so low that the plasma has two temperatures, with the ions substantially hotter than the electrons. This paradigm assumes that Coulomb collisions are the only channel for transferring the ion energy to the electrons. In this work, the second of a series, we assess the efficiency of electron heating by ion velocity-space instabilities in collisionless accretion flows. The instabilities are seeded by the pressure anisotropy induced by magnetic field amplification, coupled to the adiabatic invariance of the particle magnetic moments. Using two-dimensional particle-in-cell (PIC) simulations, we showed in Paper I that if the electron-to-ion temperature ratio is T-0e/T-0i less than or similar to 0.2, the ion cyclotron instability is the dominant mode for ion betas beta(0i) similar to 5-30 (here, beta(0i) is the ratio of ion thermal pressure to magnetic pressure), as appropriate for the midplane of low-luminosity accretion flows. In this work, we employ analytical theory and one-dimensional PIC simulations (with the box aligned with the fastest-growing wave vector of the ion cyclotron mode) to fully characterize how the electron heating efficiency during the growth of the ion cyclotron instability depends on the electron-to-proton temperature ratio, the plasma beta, the Alfven speed, the amplification rate of the mean field (in units of the ion Larmor frequency), and the proton-to-electron mass ratio. Our findings can be incorporated as a physically grounded subgrid model into global fluid simulations of low-luminosity accretion flows, thus helping to assess the validity of the two-temperature assumption.