Title: Mass and Velocity Dispersion Relations for Supermassive Black Holes in Galactic Bulges
Abstract: Growing evidence indicate supermassive black holes (SMBHs) in the mass range of M BH ∼ 10 6 -10 10 M lurking in central bulges of many galaxies [1,2].Extensive observations reveal fairly tight power laws of M BH versus the mean stellar velocity dispersion σ of the host bulge [3,4,5].The dynamic evolution of a bulge and the formation of a central SMBH should be physically linked by various observational clues.In this contribution, we reproduce the empirical M BH -σ power laws based on a self-similar general polytropic quasi-static bulge evolution [6, 7] and a sensible criterion of forming a SMBH surrounding the central density singularity of a general singular polytropic sphere (SPS) [8].Other properties of host bulges and central SMBHs are also examined.Based on our model, we discuss the intrinsic scatter of the M BH -σ relation and a scenario for the evolution of SMBHs in different host bulges.