Cosmological Mestel Disks and The Rossby Vortex Instability: The Origin of Supermassive Black Holes

A scenario is put forth for the formation of supermassive black holes at the centers of galaxies. It depends upon the formation of a Mestel disk with a flat rotation curve, M<r ∝ r and Σ ∝ 1/r. Such disks could form from the collapse of uniformly rotating, isolated, gaseous clouds, either proto-galactic, galaxy-mass damped Lyα clouds or the gas that survives galaxy mergers. We propose that in either case the disk will be unstable to the Rossby vortex instability (RVI). This instability grows from any large, steep pressure gradient in an optically thick disk. Such pressure gradients either occur adjacent to compact objects or could be triggered by heating from individual supernovae in and around the disk. Upon excitation, the RVI transports angular momentum outward, accreting nearly all mass within the initiation radius. We have calculated that in very thin disks, the non-linear vortices initiated by the RVI can transport angular momentum far more efficiently than turbulence. Compared to a viscosity-based Shakura-Sunyaev disk, the RVI transports angular momentum out to a much larger radius, so more mass is accreted into the central black hole. A typical galaxy rotational velocity is vrot = 200 km s −1, and the critical column density, necessary to initiate the RVI is ΣCCD ' 100 g cm−2. For M<r = 2πr Σ, we have rCCD = v 2 rot/(2πΣCCDG), and the mass accreted becomes MBH = v 4 rot/(2πΣCCDG ) = 3 × 10M . Both the black hole mass MBH and its v rot dependence are in good agreement with recent observations, because vrot = √ 3 σc, where σc is the velocity dispersion of the bulge at the radius of mutual contact. Subject headings: accretion disks — black hole physics — galaxies:formation galaxies:kinematics and dynamics — hydrodynamics — instabilities MS 227, Los Alamos National Laboratory, P.O. Box 1663, MS B227, Los Alamos, NM 87545; [email protected]. Princeton University Observatory, Princeton University, Peyton Hall, Ivy Lane, Princeton, NJ 08544; [email protected].