ARE PARTICLES IN ADVECTION-DOMINATED ACCRETION FLOWS THERMAL

We investigate the form of the momentum distribution function for prot ons and electrons in an advection-dominated accretion flow (ADAF). We show that for all accretion rates, Coulomb collisions are too ineffici ent to thermalize the protons. The proton distribution function is the refore determined by the viscous heating mechanism, which is unknown. The electrons, however, can exchange energy quite efficiently through Coulomb collisions and the emission and absorption of synchrotron phot ons. We find that for accretion rates greater than similar to 10(-3) o f the Eddington accretion rate, the electrons have a thermal distribut ion throughout the accretion flow. For lower accretion rates, the elec tron distribution function is determined by the electron's source of h eating, which is primarily adiabatic compression. Using the principle of adiabatic invariance, we show that an adiabatically compressed, col lisionless gas maintains a thermal distribution until the particle ene rgies become relativistic. We derive a new, nonthermal distribution fu nction for relativistic energies and provide analytic formulae for the synchrotron radiation from this distribution. Finally, we discuss its implications for the emission spectra from ADAFs.