Probing the Two-Temperature Paradigm: Observational Tests for the Basic Assumptions in ADAFs

We calculate the flux and spectrum of synchrotron radiation produced by high energy electrons and positrons (\epm) in an advection dominated accretion flow (ADAF) around a black hole. The \epm are from the decay of charged pions which are created through proton-proton collisions. We consider both a thermal and power-law energy distribution of protons, and show that the resulting \epm synchrotron emission produces a characteristic spectrum between radio and X-ray frequencies. While previous signatures of the hot protons were only possible at gamma-ray energies, via the production of gamma-rays through neutral pion decay, the present results provide a more observationally tractable way of probing the proton energy distribution and the two temperature structure in these accretion flows. We discuss a number of strong observational predictions from these systems, as well as the recent results of Mahadevan (1998) which appear to confirm the two temperature structure in ADAFs. We show that the results provide support for both a power-law and thermal distribution of protons, with at least a third of the viscous energy going into the power-law.