Supermassive black holes in galactic bulges

Growing evidence indicate supermassive black holes (SMBHs) in a mass range of MBH ∼ 106 − 1010M ¯ lurking in central stellar bulges of galaxies. Extensive observa-tions reveal fairly tight power laws of MBH versus the mean stellar velocity dispersion σ of the host stellar bulge. Together with evidence for correlations between MBH and other properties of host bulges, the dynamic evolution of a bulge and the formation of a central SMBH should be linked. In this Letter, we reproduce the empirical MBH−σ power laws based on our recent theoretical analyses (Lou & Wang; Wang & Lou; Lou, Jiang & Jin) for a self-similar general polytropic quasi-static dynamic evolution of bulges with self-gravity and spherical symmetry and present a sensible criterion of forming a central SMBH. The key result is MBH = L σ1/(1−n) where 2/3 < n < 1 and L is a proportional coefficient characteristic of different classes of host bulges. By fitting and comparing several empiricalMBH−σ power laws, we conclude that SMBHs and galactic bulges grow and evolve in a coeval manner and most likely there exist sev-eral classes of galactic bulge systems in quasi-static self-similar evolution and that to mix them together can lead to an unrealistic fitting. Based on our bulge-SMBH model, we provide explanations for intrinsic scatter in the relation and a unified scenario for the formation and evolution of SMBHs in different classes of host bulges