Black Hole Accretion in Low States: Electron Heating

Abstract

Plasmas in an accretion flow are heated by magneto-hydrodynamic turbulence generated through the magneto- rotational instability (MRI). The viscous stress driving the accretion is intimately connected to the microscopic processes of turbulence dissipation. We show that, in a few well-observed black hole accretion systems, there is compelling observational evidence of efficient electron heating by turbulence or collective plasma effects in low accretion states, when Coulomb collisions are not efficient enough to establish a thermal equilibrium between electrons and ions at small radii. We consider a Keplerian two-temperature accretion flow with a constant mass accretion rate in the pseudo- Newtonian gravitational potential and take into account the bremsstrahlung, synchrotron, and inverse Comptonization cooling processes. The balance of gravitational energy dissipation and turbulence energy cascade requires that the viscous stress be proportional to the product of the turbulence kinetic energy density and the total turbulence energy density, which may contradict the result of some shearing box simulations that the viscous stress is proportional to the magnetic field energy density. The critical mass accretion rate, below which the two-temperature solution may exist, is determined by the cooling processes and the collisional energy exchanges between electrons and ions and has very weak dependence on the collision-less heating of electrons by turbulence, which becomes more important at lower accretion rates. If the collision-less heating is dominated by the transit-time damping processes, small scale waves propagating obliquely with respect to the large scale magnetic field are prohibited, which may affect the saturate state of the MRI driven turbulence significantly. The plasma also needs to be strongly magnetized with the magnetic field and proton energy densities comparable so that electrons can share more of the dissipated gravitational energy. The heating of relativistic electrons is efficient since the heating rate is proportional to the mean momentum of the particles, and the electron heating may also be enhanced by their resonant scattering with small scale nearly parallel propagating waves.