Abstract
Growing evidence indicate supermassive black holes (SMBHs) in the mass range of MBH∼ 106− 10M lurking in central bulges of many galaxies [1, 2]. Extensive observations reveal fairly tight power laws of MBH 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 MBH−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 MBH−σ relation and a scenario for the evolution of SMBHs in different host bulges.
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