Are Particles in Advection‐dominated Accretion Flows Thermal?

Abstract

We investigate the form of the momentum distribution function for protons and\nelectrons in an advection-dominated accretion flow (ADAF). We show that for all\naccretion rates, Coulomb collisions are too inefficient to thermalize the\nprotons. The proton distribution function is therefore determined by the\nviscous heating mechanism, which is unknown. The electrons, however, can\nexchange energy quite efficiently through Coulomb collisions and the emission\nand absorption of synchrotron photons. We find that for accretion rates greater\nthan \\sim 10^{-3} of the Eddington accretion rate, the electrons have a thermal\ndistribution throughout the accretion flow. For lower accretion rates, the\nelectron distribution function is determined by the electron's source of\nheating, which is primarily adiabatic compression. Using the principle of\nadiabatic invariance, we show that an adiabatically compressed collisionless\ngas maintains a thermal distribution until the particle energies become\nrelativistic. We derive a new, non-thermal, distribution function which arises\nfor relativistic energies and provide analytic formulae for the synchrotron\nradiation from this distribution. Finally, we discuss its implications for the\nemission spectra from ADAFs.\n