Radio/X‐Ray Luminosity Relation for Advection‐dominated Accretion: Implications for Emission‐Line Galaxies and the X‐Ray Background

Recent studies of the cosmic X-ray background (XRB) have suggested the possible existence of a population of relatively faint sources with hard X-ray spectra; however, the emission mechanism remains unclear. If the hard X-ray emission is from the radiatively inefficient, advection-dominated accretion flows (ADAFs) around massive black holes in galactic nuclei, X-ray luminosity and radio luminosity satisfy the approximate relation LR ~ 7 ? 1035(?/15 GHz)7/5(M/107 M?)(LX/1040 ergs s-1)1/10 ergs s-1, where LR = ?L? is the radio luminosity at frequency ?, M is the mass of the accreting black hole, and 1040 LX 1042 ergs s-1 is the 2-10 keV X-ray luminosity. These sources are characterized by inverted radio spectra I? ?2/5. For example, an ADAF X-ray source with luminosity LX ~ 1041 ergs s-1 has a nuclear radio luminosity of ~4 ? 1036(M/3 ? 107 M?) ergs s-1 at ~20 GHz, and if it is at a distance of ~10(M/3 ? 107 M?)1/2 Mpc, it would be detected as a ~1 mJy point radio source. High-frequency (~20 GHz), high angular resolution radio observations provide an important test of the ADAF emission mechanism. Since LR depends strongly on black hole mass and only weakly on X-ray luminosity, the successful measurement of nuclear radio emission could provide an estimate of black hole mass. Because the X-ray spectra produced by ADAFs are relatively hard, sources of this emission are natural candidates for contributing to the hard (>2 keV) background.