Mass and Mean Velocity Dispersion Relations for Supermassive Black Holes in Galactic Bulges

Abstract

Growing evidence indicate supermassive black holes (SMBHs) in the mass range of $M_{\mathrm{BH}}$$\sim 10^6-10^{10}{M}_{\odot }$ lurking in central bulges of many galaxies. Extensive observations reveal fairly tight power laws of $M_{\mathrm{BH}}$ versus the mean stellar velocity dispersion $\sigma$ 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 $M_{\mathrm{BH}}-\sigma$ 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 $M_{\mathrm{BH}}-\sigma$ relation and a scenario for the evolution of SMBHs in different host bulges.

arXiv comment8 pages, 2 figures, accepted for publication in the Proceedings of Science for VII Microquasar Workshop: Microquasars and Beyond

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