Probing the two-temperature paradigm: observational tests for the basic assumptions in advection-dominated accretion flows

We calculate the flux and spectrum of synchrotron radiation produced by high-energy electrons and positrons (e^+/-) in an advection-dominated accretion flow (ADAF) around a black hole. The e^+/- are from the decay of charged pions which are created through proton-proton collisions. We consider both thermal and power-law energy distributions of protons, and show that the resulting e^+/- 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, which appear to confirm the two-temperature structure in ADAFs. We show that the results provide support for both power-law and thermal distributions of protons, with at least a third of the viscous energy going into the power law.