Where Are All The Fallback Disks? Constraints on Propeller Systems

Fallback disks are expected to form around new-born neutron stars following a supernova explosion. In almost all cases, the disk will pass through a propeller stage. If the neutron star is spinning rapidly (initial period $\sim 10$ ms) and has an ordinary magnetic moment ($\sim 10^{30}$ G cm$^3$), the rotational power transferred to the disk by the magnetic field of the neutron star will exceed the Eddington limit by many orders of magnitude, and the disk will be rapidly disrupted. Fallback disks can thus survive only around slow-born neutron stars and around black holes, assuming the latter do not torque their surrounding disks as strongly as do neutron stars. This might explain the apparent rarity of fallback disks around young compact objects.