Radio/X-ray luminosity relation for X-ray-bright galactic nuclei: Implications for weighing supermassive black holes

Optically thin and geometrically thick accretion flows are known to be responsible for the observed radio/X-ray luminosity relation of 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 amount 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. Semianalytically 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 indeed be used 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 nondisk components such as a jet component, which otherwise results in an overestimation of SMBH mass.