MBH-σ relation for a complete sample of soft X-ray-selected active galactic nuclei

We present the black hole mass-bulge velocity dispersion relation for a complete sample of 75 soft X-ray selected active galactic nuclei (AGNs): 43 broad-line Seyfert 1 galaxies (BLS1s) and 32 narrow-line Seyfert 1 galaxies (NLS1s). We use luminosity and FWHM(Hbeta) as surrogates for black hole mass and FWHM([O III]) as a surrogate for the bulge velocity dispersion. We find that NLS1s lie below the M-BH-sigma relation of BLS1s, confirming the Mathur et al. result. The statistical result is robust and not due to any systematic measurement error. This has important consequences toward our understanding of black hole formation and growth: black holes grow by accretion in well-formed bulges, possibly after a major merger. As they grow, they get closer to the M-BH-sigma relation for normal galaxies. The accretion is highest in the beginning and dwindles as the time goes by. Our result does not support theories of M-BH-sigma relation in which the black hole mass is a constant fraction of the bulge mass/ velocity dispersion at all times or those in which bulge growth is controlled by AGN feedback.