Constraints on the Process that Regulates the Growth of Supermassive Black Holes Based on the Intrinsic Scatter in theMbh‐σsphRelation

We show that the observed scatter in the relations between the mass ofsupermassive black holes (SMBHs), M_bh, and the velocity dispersion sigma ormass M_sph of their host spheroid, place interesting constraints on the processthat regulates SMBH growth in galaxies. When combined with the observedproperties of early-type SDSS galaxies, the observed intrinsic scatters implythat SMBH growth is regulated by the spheroid velocity dispersion rather thanits mass. The M_bh-M_sph relation is therefore a by-product of a morefundamental M_bh-sigma relation. We construct a theoretical model for thescatter among baryon modified dark matter halo profiles, out of which wegenerate a population of spheroid hosts and show that these naturally lead to arelation between effective radius and velocity dispersion of the form R_sph ~sigma^1.5 with a scatter of ~0.2dex, in agreement with the correspondingprojection of the fundamental plane for early type galaxies in SDSS. At theredshift of formation, our model predicts the minimum scatter that SMBHs canhave at fixed velocity dispersion or spheroid mass under different formationscenarios. We also estimate the additional scatter that is introduced intothese relations through collisionless mergers of purely stellar spheroids atz<1. We find that the observed scatter in the M_bh-sigma and M_bh-M_sphrelations preclude the properties of dark matter halos from being the governingfactor in SMBH growth. Finally, we show that SMBH growth governed by theproperties of the host spheroid can lead to the observed values of scatter inthe M_bh-sigma and M_bh-M_sph relations, only if the SMBH growth is limited bymomentum or energy feedback over the dynamical time of the host spheroid.Comment: 11 pages, 8 figures. Submitted to Ap