The Slope of the Black Hole Mass versus Velocity Dispersion Correlation

Observations of nearby galaxies reveal a strong correlation between the massof the central dark object M and the velocity dispersion sigma of the hostgalaxy, of the form log(M/M_sun) = a + b*log(sigma/sigma_0); however, publishedestimates of the slope b span a wide range (3.75 to 5.3). Merritt & Ferraresehave argued that low slopes (<4) arise because of neglect of random measurementerrors in the dispersions and an incorrect choice for the dispersion of theMilky Way Galaxy. We show that these explanations account for at most a smallpart of the slope range. Instead, the range of slopes arises mostly because ofsystematic differences in the velocity dispersions used by different groups forthe same galaxies. The origin of these differences remains unclear, but wesuggest that one significant component of the difference results from Ferrarese& Merritt's extrapolation of central velocity dispersions to r_e/8 (r_e is theeffective radius) using an empirical formula. Another component may arise fromdispersion-dependent systematic errors in the measurements. A new determinationof the slope using 31 galaxies yields b=4.02 +/- 0.32, a=8.13 +/- 0.06, forsigma_0=200 km/s. The M-sigma relation has an intrinsic dispersion in log Mthat is no larger than 0.3 dex. In an Appendix, we present a simple model forthe velocity-dispersion profile of the Galactic bulge.Comment: 37 pages, 9 figure