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[21.02] A Theoretical Model for M_bh - sigma Relation for Supermassive Black Holes

D. Richstone (Dept. of Astronomy, U. Michigan), D. Graff (Dept. of Astronomy, U. Michigan), F. C. Adams (Dept. of Physics & Dept. of Astronomy, U. Michigan)

We consider an overdense region of the universe at the point of maximum expansion. This region is idealized as a cold, slowly-rotating, quasi-isothermal sphere (mass proportional to radius). A small black hole is assumed to exist or form quickly at the center.

Under these assumptions, both the ballistic orbits of dark matter or stellar particles, and the flow of baryonic gas, carry a significant fraction of the gas and dark matter into the central black hole, which grows until the periapse of the typical infalling particle exceeds a few Schwarzschild Radii.

Using the fundamental plane to set the angular momentum of the perturbation sets the zero point of the relation. This yields M_bh = 10⁸ Msun (\sigma/200 km s^-1)⁴. The model predicts a ratio of black hole mass to host mass of .004 (\sigma/200 km s^-1). These relationships are consistent with those reported by Gebhardt et.al. and Ferrarese & Merritt.

We gratefully acknowledge support of STScI and of NASA.

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