Title:	Self-regulated black hole accretion, the M-σ relation and the growth of bulges in galaxies
Authors:	Begelman, M.C. Nath, Biman B.
Issue Date:	Aug-2005
Publisher:	Blackwell Publishing for the Royal Astronomical Society
Citation:	Monthly Notices of the Royal Astronomical Society, 2005, Vol.361, Issue 4, p1387-1392.
Abstract:	We argue that the velocity dispersions and masses of galactic bulges and spheroids are byproducts of the feedback that regulates rapid black hole growth in protogalaxies. We suggest that the feedback energy liberated by accretion must pass through the accreting material, in an energy-conserving flux near the black hole and a momentum-conserving flux farther away from the black hole. If the inflowing gas dominates the gravitational potential outside the Bondi radius, feedback from Eddington-limited accretion drives the density profile of the gas to that of a singular isothermal sphere. We find that the velocity dispersion associated with the isothermal potential, σ, increases with time as the black hole mass M grows, in such a way that M~σ4. The coefficient of this proportionality depends on the radius at which the flow switches from energy conserving to momentum conserving, and gives the observed M-σ relation if the transition occurs at ~100 Schwarzschild radii. We associate this transition with radiative cooling and show that bremsstrahlung, strongly boosted by inverse Compton scattering in a two-temperature (Tp〉〉Te) plasma, leads to a transition at the desired radius. According to this picture, bulge masses Mb are insensitive to the virial masses of their dark matter haloes, but correlate linearly with black hole mass. Our analytic model also explains the Mb-σ (Faber-Jackson) relation as a relic of black hole accretion. The model naturally explains why the M-σ relation has less scatter than either the M-Mb (Magorrian) or the Faber-Jackson relation. It suggests that the M-σ relation could extend down to very low velocity dispersions, and predicts that the relation should not evolve with redshift.
Description:	Restricted Access. An open access version is available at arXiv.org.(one of the alternative locations)
URI:	http://hdl.handle.net/2289/2220
ISSN:	0035-8711
Alternative Location:	http://arxiv.org/abs/astro-ph/0504400 http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=2005MNRAS.361.1387B http://dx.doi.org/10.1111/j.1365-2966.2005.09249.x
Copyright:	(2005) Blackwell Publishing for the Royal Astronomical Society
Appears in Collections:	Research Papers (A&A)

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