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Mass and Mean Velocity Dispersion Relations for Supermassive Black Holes in Galactic Bulges
Growing evidence indicate supermassive black holes (SMBHs) in the mass range
of lurking in central bulges of many
galaxies. Extensive observations reveal fairly tight power laws of
versus the mean stellar velocity dispersion of the host bulge. 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 power laws based on a self-similar
general polytropic quasi-static bulge evolution and a sensible criterion of
forming a SMBH surrounding the central density singularity of a general
singular polytropic sphere (SPS) \cite{loujiang2008}. Other properties of host
bulges and central SMBHs are also examined. Based on our model, we discuss the
intrinsic scatter of the relation and a scenario for the
evolution of SMBHs in different host bulges.Comment: 8 pages, 2 figures, accepted for publication in the Proceedings of
Science for VII Microquasar Workshop: Microquasars and Beyon
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