A log-quadratic relation between the nuclear black hole masses and velocity dispersions of galaxies

Abstract

We demonstrate that a log-linear relation does not provide an adequate description of the correlation between the masses of super massive black holes (SMBHs, Mbh) and the velocity dispersions of their host spheroid (σ). An unknown relation between and log σ may be expanded to second order to obtain a log-quadratic relation of the form. We perform a Bayesian analysis using the local sample described in Tremaine et al., and solve for and α, in addition to the intrinsic scatter (δ). We find unbiased parameter estimates of and. At the 90 per cent level the relation does not follow a uniform power law. Indeed, over the velocity range the logarithmic slope of the best-fitting relation varies betwe..