Selection bias in dynamically-measured super-massive black hole samples:
  its consequences and the quest for the most fundamental relation
  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 Mbh-sigma relation by a factor
of at least ~3; the bias for the Mbh-Mstar relation is even larger. Our Monte
Carlo simulations and analysis of the residuals from scaling relations both
indicate that sigma is more fundamental than Mstar or effective radius. In
particular, the Mbh-Mstar relation is mostly a consequence of the Mbh-sigma and
sigma-Mstar 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 fvir~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.
