Radio/X-Ray Luminosity Relation for X-Ray Bright Galactic Nuclei: Implications on Weighing Supermassive Black Hole

Abstract

Optically thin and geometrically thick accretion flows are known to be responsible for the observed radio/X-ray luminosity relation of the X-ray bright galactic nuclei. It has also been suggested that supermassive black hole masses can be estimated from measurements of the core radio luminosity and the X-ray luminosity by using the advection-dominated accretion flow (ADAF) model. In this study we increase the number of data available by compiling the radio/X-ray fluxes and the mass in published literatures, and compare the observed ratio of the luminosities with predictions from various models of optically thin accretion flows. Semi-analytically derived relations of the luminosities are presented in cases of the standard ADAF model and modified ADAF models, in which a truncation of inner parts of the flows and winds causing a reduction of the infalling matter are included. We show that the observed relation can be used indeed to estimate the supermassive black hole mass, provided that properties of such accretion flows are known. Having investigated sensitivities of the method on modifications of the 'standard' ADAF model, we find that a general trend of model predictions from the 'standard' ADAF, the truncated ADAF and the 'windy' ADAF are somewhat indistinguishable. We also find, however, that the extreme case of the windy model is inconsistent with currently available observational data, unless microphysics parameters are to be substantially changed. High resolution radio observations, however, are required to avoid the contamination of non-disk components, such as, a jet component, which, otherwise, results in the over-estimated SMBH mass.