Star captures by quasar accretion disks:: A possible explanation of the M-σ relation

A new theory of quasars is presented in which the matter of thin accretion disks around black holes is supplied by stars that plunge through the disk. Stars in the central part of the host galaxy are randomly perturbed to highly radial orbits, and as they repeatedly cross the disk they lose orbital energy by drag, eventually merging into the disk. Requiring the rate of stellar mass capture to equal the mass accretion rate into the black hole, a relation between the black hole mass and the stellar velocity dispersion is predicted of the form M-BH proportional to sigma(*)(30/7). The normalization depends on various uncertain parameters, such as the disk viscosity, but is consistent with observation for reasonable assumptions. We show that a seed central black hole in a newly formed stellar system can grow at the Eddington rate up to this predicted mass via stellar captures by the accretion disk. Once this mass is reached, star captures are insufficient to maintain an Eddington accretion rate, and the quasar may naturally turn off as the accretion switches to a low-efficiency advection mode. The model provides a mechanism to deliver mass to the accretion disk at small radius, probably solving the problem of gravitational instability to star formation in the disk at large radius. We note that the matter from stars that is incorporated into the disk has an average specific angular momentum that is very small or opposite to that of the disk, and we discuss how a rotating disk may be maintained as it captures this matter if a small fraction of the accreted mass comes from stellar winds that form a disk extending to larger radius. We propose several observational tests and consequences of this theory.