Ionization, Magneto-rotational, and Gravitational Instabilities in Thin Accretion Disks Around Supermassive Black Holes

We consider the combined role of the thermal ionization, magneto-rotational and gravitational instabilities in thin accretion disks around supermassive black holes. We find that in the portions of the disk unstable to the ionization instability, the gas remains well coupled to the magnetic field even on the cold, neutral branch of the thermal limit cycle. This suggests that the ionization instability is not a significant source of large amplitude time-dependent accretion in AGN. We also argue that, for accretion rates greater than 10^{-2} solar masses per year, the gravitationally unstable and magneto-rotationally unstable regions of the accretion disk overlap; for lower accretion rates they may not. Some low-luminosity AGN, e.g. NGC 4258, may thus be in a transient phase in which mass is building up in a non-accreting gravitationally and magneto-rotationally stable ``dead zone.'' We comment on possible implications of these findings.