REVISITING THE SCALING RELATIONS OF BLACK HOLE MASSES AND HOST GALAXY PROPERTIES

Abstract

New kinematic data and modeling efforts in the past few years have substantially expanded and revised dynamical measurements of black hole masses ( M • ) at the centers of nearby galaxies. Here we compile an updated sample of 72 black holes and their host galaxies, and present revised scaling relations between M • and stellar velocity dispersion (σ), V -band luminosity ( L ), and bulge stellar mass ( M bulge ), for different galaxy subsamples. Our best-fitting power-law relations for the full galaxy sample are log 10 ( M • ) = 8.32 + 5.64log 10 (σ/200 km s −1 ), log 10 ( M • ) = 9.23 + 1.11log 10 ( L /10 11 L ☉ ), and log 10 ( M • ) = 8.46 + 1.05log 10 ( M bulge /10 11 M ☉ ). A log-quadratic fit to the M • –σ relation with an additional term of β 2 [log 10 (σ/200 km s −1 )] 2 gives β 2 = 1.68 ± 1.82 and does not decrease the intrinsic scatter in M • . Including 92 additional upper limits on M • does not change the slope of the M • –σ relation. When the early- and late-type galaxies are fit separately, we obtain similar slopes of 5.20 and 5.06 for the M • –σ relation but significantly different intercepts— M • in early-type galaxies are about two times higher than in late types at a given sigma. Within early-type galaxies, our fits to M • (σ) give M • that is about two times higher in galaxies with central core profiles than those with central power-law profiles. Our M • – L and M • – M bulge relations for early-type galaxies are similar to those from earlier compilations, and core and power-law galaxies yield similar L - and M bulge -based predictions for M • . When the conventional quadrature method is used to determine the intrinsic scatter in M • , our data set shows weak evidence for increased scatter at M bulge < 10 11 M ☉ or L V < 10 10.3 L ☉ , while the scatter stays constant for 10 11 < M bulge < 10 12.3 M ☉ and 10 10.3 < L V < 10 11.5 L ☉ . A Bayesian analysis indicates that a larger sample of M • measurements would be needed to detect any statistically significant trend in the scatter with galaxy properties.