ELECTRON HEATING BY THE ION CYCLOTRON INSTABILITY IN COLLISIONLESS ACCRETION FLOWS. I. COMPRESSION-DRIVEN INSTABILITIES AND THE ELECTRON HEATING MECHANISM

In systems accreting well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the plasma in the innermost regions of the disk is believed to be collisionless and have two temperatures, with the ions substantially hotter than the electrons. However, whether a collisionless faster-than-Coulomb energy transfer mechanism exists in two-temperature accretion flows is still an open question. We study the physics of electron heating during the growth of ion velocity-space instabilities by means of multidimensional, fully kinetic, particle-in-cell (PIC) simulations. A background large-scale compression-embedded in a novel form of the PIC equations-continuously amplifies the field. This constantly drives a pressure anisotropy P-perpendicular to > P-parallel to because of the adiabatic invariance of the particle magnetic moments. We find that, for ion plasma beta values beta(0i) similar to 5-30 appropriate for the midplane of low-luminosity accretion flows (here, beta(0i) is the ratio of ion thermal pressure to magnetic pressure), mirror modes dominate if the electron-to-proton temperature ratio is T-0e/T-0i greater than or similar to 0.2, whereas for T-0e/T-0i less than or similar to 0.2 the ion cyclotron instability triggers the growth of strong Alfven-like waves, which pitch-angle scatter the ions to maintain marginal stability. We develop an analytical model of electron heating during the growth of the ion cyclotron instability, which we validate with PIC simulations. We find that for cold electrons (beta(0e) less than or similar to 2m(e)/m(i), where beta(0e) is the ratio of electron thermal pressure to magnetic pressure), the electron energy gain is controlled by the magnitude of the E-cross-B velocity induced by the ion cyclotron waves. This term is independent of the initial electron temperature, so it provides a solid energy floor even for electrons starting with extremely low temperatures. On the other hand, the electron energy gain for beta(0e) less than or similar to 2m(e)/m(i)-governed by the conservation of the particle magnetic moment in the growing fields of the instability-is proportional to the initial electron temperature, and it scales with the magnetic energy of ion cyclotron waves. Our results have implications for two-temperature accretion flows as well as for solar wind and intracluster plasmas.