Stability and Evolution of Supernova Fallback Disks

We show that thin accretion disks made of carbon or oxygen are subject to the same thermal ionization instability as hydrogen and helium disks. We argue that the instability applies to disks of any metal content. The relevance of the instability to supernova fallback disks probably means that their power-law evolution breaks down when they first become neutral. We construct simple analytical models for the viscous evolution of fallback disks to show that it is possible for these disks to become neutral when they are still young (ages of a few 10³ to 10⁴ yr), compact in size (a few 10⁹ to 10¹¹ cm) and generally accreting at sub-Eddington rates (M~a few 10¹⁴-10¹⁸ g s^-1). Based on recent results on the nature of viscosity in the disks of close binaries, we argue that this time may also correspond to the end of the disk activity period. Indeed, in the absence of a significant source of viscosity in the neutral phase, the entire disk will likely turn to dust and become passive. We discuss various applications of the evolutionary model, including anomalous X-ray pulsars and young radio pulsars. Our analysis indicates that metal-rich fallback disks around newly born neutron stars and black holes become neutral generally inside the tidal truncation radius (Roche limit) for planets at ~10¹¹ cm. Consequently, the efficiency of the planetary formation process in this context will mostly depend on the ability of the resulting disk of rocks to spread via collisions beyond the Roche limit. It appears easier for the merger product of a doubly degenerate binary, whether it is a massive white dwarf or a neutron star, to harbor planets because its remnant disk has a rather large initial angular momentum, which allows it to spread beyond the Roche limit before becoming neutral. The early super-Eddington phase of accretion is a source of uncertainty for the disk evolution models presented here.