The Fundamental Plane of Black Hole Accretion and Its Use as a Black Hole-Mass Estimator

We present an analysis of the fundamental plane of black hole accretion, an empirical correlation of the mass of a black hole (M), its 5 GHz radio continuum luminosity (νLν), and its 2–10 keV X-ray power-law continuum luminosity (LX). We compile a sample of black holes with primary,
direct black hole-mass measurements that also have sensitive, high-spatial-resolution radio and X-ray data. Taking into account a number of systematic sources of uncertainty and their correlations with the measurements, we use Markov chain Monte Carlo methods to fit a masspredictor function of the form = + m x e m
log 10 ( ) M M R 8 0 - log 10 erg s ( ) LR 38 1 + xm - log 10 erg s (L ) X X 40 1 . Our best-fit results are μ0 = 0.55 ± 0.22, ξμR = 1.09 ± 0.10, and xm = - - + 0.59 X 0.15 0.16 with the natural logarithm of the Gaussian intrinsic scatter
in the log-mass direction òm = - - + ln 0.04 0.13 0.14. This result is a significant improvement over our
earlier mass scaling result because of the increase in active galactic nuclei sample size (from 18 to 30), improvement in our X-ray binary sample selection, better identification of Seyferts, and improvements in our analysis that takes into
account systematic uncertainties and correlated uncertainties. Because of these significant improvements, we are able to consider potential influences on our sample by including all sources with compact radio and X-ray emission but ultimately conclude that the fundamental plane can empirically describe all such sources. We end with advice for how to use this as a tool for estimating black hole masses.