On Proton Energization in Accretion Flows

Two-temperature advection dominated accretion flow (ADAF) or hot ion tori (HIT) models help explain low luminosity stellar and galactic accreting sources and may complement observational support for black holes in nature. But low radiative efficiencies demand that ions receive a fraction $\eta \gsim 99%$ of energy dissipated in the turbulent accretion. The $\eta$ depends on the ratio of particle to magnetic pressure. If compressive modes of dissipation, like magnetic mirroring, dominate incompressible modes, then even when the pressure ratio is O(1), the required large $\eta$ can be attained. However the relative importance of compressive vs. incompressible modes is hard to estimate. The larger up in the turbulent cascade, the more compressible the turbulence. The relevant length scale for particle energization can be determined by equating the dominant eddy turnover time to the time for which an energy equal to that in the turbulence can be drained. Based on the large scales resulting from this estimate, it is suggested that compressive mirroring may be important. Also, regardless of the precise $\eta$ or dissipation mechanism, non-thermal protons seem natural in two- temperature discs because all dissipation mechanisms, and the use of an isotopic pressure, require wave-particle resonances that operate only on a subset of the particles. Finally, it is briefly mentioned how mirroring may help to generate an ADAF or HIT in the first place.