#### Abstract

Motivated by the observed correlation between black hole masses $\mbh$ and the velocity dispersion $\sigma$ of host galaxies, we develop a theoretical model of black hole formation in galactic bulges (this paper generalizes an earlier ApJ Letter). The model assumes an initial state specified by a a uniform rotation rate $\Omega$ and a density distribution of the form $\rho = \aeff^2 / 2 \pi G r^2$ (so that $\aeff$ is an effective transport speed). The black hole mass is determined when the centrifugal radius of the collapse flow exceeds the capture radius of the central black hole (for Schwarzschild geometry). This model reproduces the observed correlation between the estimated black hole masses and the velocity dispersions of galactic bulges, i.e., $\mbh \approx 10^8 M_\odot (\sigma/200 {\rm km s^{-1}})^4$, where $\sigma = \sqrt{2} \aeff$. To obtain this normalization, the rotation rate $\Omega \approx 2 \times 10^{15}$ rad/s. The model also defines a bulge mass scale $M_B$. If we identify the scale $M_B$ with the bulge mass, the model determines the ratio $\mrat$ of black hole mass to the host mass: $\mrat$ $\approx$ 0.0024 $(\sigma/200 {\rm km s^{-1}})$, again in reasonable agreement with observed values. In this scenario, supermassive black holes form quickly (in $\sim10^5$ yr) and are born rapidly rotating (with $a/M \sim 0.9$). This paper also shows how these results depend on the assumed initial conditions; the most important quantity is the initial distribution of specific angular momentum in the pre-collapse state. (Refer to PDF file for exact formulas.)

#### Publication Date

7-1-2003

#### Document Type

Article

#### Department, Program, or Center

School of Physics and Astronomy (COS)

#### Recommended Citation

The Astrophysical Journal 591 (2003) 125-137

#### Campus

RIT – Main Campus

## Comments

Also archived at: arXiv:astro-ph/0304004 v1 31 Mar 2003 / The date stated on this paper is incorrect. This work was supported by NASA through the Long Term Space Astrophysics program and the Space Telescope Science Institute, and by the University of Michigan through the Michigan Center for Theoretical Physics.ISSN:1538-4365 Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.