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 σ 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 -σ relation by a factor of at least ∼ 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 σ 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 -σ and σ-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 σ. 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 ∼ 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.

Dark-ages reionization and galaxy formation simulation – X. The small contribution of quasars to reionization

“…However, it has recently been suggested that the black hole sample used to derive scaling relations is likely different from the entire population, leading to a selection bias 25 (Bernardi et al 2007). For instance, using Monte Carlo simulations Shankar et al (2016) recovered the intrinsic scaling relation assuming the selection bias comes from unresolved black holes (e.g. for galaxies with a given velocity dispersion, σ * , it is more difficult to resolve smaller black holes; Batcheldor et al 2010) and showed that such a bias can lead to factors of 3 and ∼50 − 100 higher normalizations of the M bh − σ * and M bh − M * relations, respectively.…”

Selection bias in dynamically measured supermassive black hole samples: scaling relations and correlations between residuals in semi-analytic galaxy formation models

“…Indeed, the observed black-hole scaling relation involving the stellar mass was found to be much more biased than the one involving velocity dispersion (up to an order of magnitude in normalisation), and its apparent tightness could be entirely ascribed to a selection effect. Shankar et al (2016) also suggested that a selection bias more prominent in stellar mass than in velocity dispersion may explain several discrepancies often reported in the literature, i.e. the fact that the observed relation between black-hole and stellar mass predicts a local black-hole mass density two to three times higher than inferred from the relation between black-hole mass and velocity dispersion (e.g., Graham et al 2007;Tundo et al 2007;Shankar et al 2009).…”

“…We restrict to this specific SDSS subsample as velocity dispersions in late-type galaxies are not spatially resolved, though the correlation does not depend on the exact cut in p(E+S0). For consistency with the data of Savorgnan et al (2016) to which we will compare, we follow Shankar et al (2016) and correct the velocity dispersions σHL, as in Cappellari et al (2006), to a common aperture of 0.595 kpc (i.e. the one adopted by the Hyperleda data base, Paturel et al 2003).…”

“…Recently, Shankar et al (2016, see also Bernardi et al 2007, Gültekin et al 2011, Morabito & Dai 2012and van den Bosch et al 2015 showed that the local sample of galaxies with dynamical mass measurements of supermassive black holes is biased. Local galaxies hosting supermassive black holes, irrespective of their exact morphological type or the aperture within which the velocity dispersion is measured, typically present velocity dispersions that are substantially larger than those of a very large and unbiased sample from the Sloan Digital Sky Survey (SDSS) with similar stellar masses.…”

“…One of the main reasons for this bias can be traced back to the observationally imposed requirement that the black-hole gravitational sphere of influence must be resolved for the black-hole mass to be reliably estimated. Via dedicated Monte Carlo simulations and accurate analysis of the residuals around the observed black-hole scaling relations, Shankar et al (2016) found the velocity dispersion to be a more fundamental quantity than stellar mass or effective radius. Indeed, the observed black-hole scaling relation involving the stellar mass was found to be much more biased than the one involving velocity dispersion (up to an order of magnitude in normalisation), and its apparent tightness could be entirely ascribed to a selection effect.…”