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A new theory of quasars is presented in which the matter of thin accretiondisks 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 highlyradial orbits, and as they repeatedly cross the disk they lose orbital energyby drag, eventually merging into the disk. Requiring the rate of stellar masscapture to equal the mass accretion rate into the black hole, a relationbetween the black hole mass and the stellar velocity dispersion is predicted ofthe form M_{BH} \propto sigma_*^{30/7}. The normalization depends on variousuncertain parameters such as the disk viscosity, but is consistent withobservation for reasonable assumptions. We show that a seed central black holein a newly formed stellar system can grow at the Eddington rate up to thispredicted mass via stellar captures by the accretion disk. Once this mass isreached, star captures are insufficient to maintain an Eddington accretionrate, and the quasar may naturally turn off as the accretion switches to alow-efficiency advection mode. The model provides a mechanism to deliver massto the accretion disk at small radius, probably solving the problem ofgravitational instability to star formation in the disk at large radius. Wenote that the matter from stars that is incorporated to the disk has an averagespecific angular momentum that is very small or opposite to that of the disk,and discuss how a rotating disk may be maintained as it captures this matter ifa small fraction of the accreted mass comes from stellar winds that form a diskextending to larger radius. We propose several observational tests andconsequences of this theory.Comment: submitted to Ap

Star Captures by Quasar Accretion Disks: A Possible Explanation of theM‐σ Relation