The Slope of the Black Hole Mass versus Velocity Dispersion Correlation

Abstract

Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object M BH and the velocity dispersion of the host galaxy, of the form logðM BH =M Þ ¼ þ logð = 0 Þ; however, published estimates of the slope span a wide range (3.75-5.3). Merritt & Ferrarese have argued that low slopes (d4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations and several others account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of systematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritt's extrapolation of central velocity dispersions to r e =8 (r e is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the measurements. A new determination of the slope using 31 galaxies yields ¼ 4:02 AE 0:32, ¼ 8:13 AE 0:06 for 0 ¼ 200 km s À1 . The M BH -relation has an intrinsic dispersion in log M BH that is no larger than 0.25-0.3 dex and may be smaller if observational errors have been underestimated. In an appendix, we present a simple kinematic model for the velocity-dispersion profile of the Galactic bulge.

Black hole masses in active galaxies

“…From FWHM(Hβ) and the AGN's optical continuum luminosity, the black hole mass was estimated to be ∼ 1.6 × 10 5 M , while the stellar velocity dispersion is 36 ± 5 km s −1 . With this black hole mass estimate, POX 52 falls almost exactly on an extrapolation of the local M − σ relation of Tremaine et al (2002).…”

M-σ relation in radio-loud AGNs and NLS1s

“…1, it is found that radio-quiet AGNs follow the M bh -σ relation defined by Tremaine et al (2002) but with a larger scatter. However, the radio-loud AGNs and NLS1s seemed not to follow this relation.…”

“…For nearby inactive galaxies, there exists a tight correlation (hereafter M bh − σ relation) M bh = 10 8.13 (σ/(200kms −1 )) 4.02 M (Tremaine et al 2002). Whether all kinds of AGNs follow this relation or not is still a matter to debate.…”

Elliptical Galaxies with Emission Lines from the Sloan Digital Sky Survey

“…It will be easy to understand Seyfert and LINER activities in elliptical galaxies, such as the host galaxies of the most powerful AGNs (quasars) are usually the massive elliptical galaxies (Floyd et al 2004), that is because the recent discovery of a tight relation between bulge velocity dispersion and black hole mass, which strongly suggests that massive black holes are ubiquitous and scale with the bulge masses (Ho & Kormendy 2000;Tremaine et al 2002). While the pure star-forming activities in elliptical galaxies are especially rare, the nature and triggering mechanism are still open questions.…”