Selection bias in dynamically measured supermassive black hole samples : its consequences and the quest for the most fundamental relation

Abstract

We compare the set of local galaxies having dynamically measured black holes with a large, unbiased sample of galaxies extracted from the Sloan Digital Sky Survey. We confirm earlier work showing that the majority of black hole hosts have significantly higher velocity dispersions sigma than local galaxies of similar stellar mass. We use Monte Carlo simulations to illustrate the effect on black hole scaling relations if this bias arises from the requirement that the black hole sphere of influence must be resolved to measure black hole masses with spatially resolved kinematics. We find that this selection effect artificially increases the normalization of the M-bh-sigma relation by a factor of at least similar to 3; the bias for the M-bh-M-star relation is even larger. Our Monte Carlo simulations and analysis of the residuals from scaling relations both indicate that sigma is more fundamental than M-star or effective radius. In particular, the M-bh-M-star relation is mostly a consequence of the M-bh-sigma and sigma-M-star relations, and is heavily biased by up to a factor of 50 at small masses. This helps resolve the discrepancy between dynamically based black hole-galaxy scaling relations versus those of active galaxies. Our simulations also disfavour broad distributions of black hole masses at fixed sigma. Correcting for this bias suggests that the calibration factor used to estimate black hole masses in active galaxies should be reduced to values of f(vir) similar to 1. Black hole mass densities should also be proportionally smaller, perhaps implying significantly higher radiative efficiencies/black hole spins. Reducing black hole masses also reduces the gravitational wave signal expected from black hole mergers.