Ionization, magnetorotational, and gravitational instabilities in thin accretion disks around supermassive black holes

We consider the combined role of the thermal ionization, magnetorotational, 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 active galactic nuclei (AGNs). We also argue that, for (M) over dot greater than or similar to 10(-2) M. yr(-1), the gravitationally unstable and magnetorotationally 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 nonaccreting gravitationally and magnetorotationally stable dead zone. We comment on possible implications of these findings.