The fate of fallback matter around newly born compact objects

The presence of fallback disks around young neutron stars (NSs) has been invoked over the years to explain a large variety of phenomena. Here we perform a numerical investigation of the formation of such disks during a supernova (SN) explosion, considering both NS and black hole (BH) remnants. Using the public code MESA, we compute the angular momentum distribution of the pre-SN material, for stars with initial masses M in the range 13-40 M _·, initial surface rotational velocities v surf between 25% and 75% of the critical velocity, and for metallicities Z of 1%, 10%, and 100% of the solar value. These pre-SN models are exploded with energies E varying between 10 ⁵⁰-3 × 10⁵² erg, and the amount of fallback material is computed. We find that, if magnetic torques play an important role in angular momentum transport, then fallback disks around NSs, even for low-metallicity main-sequence stars, are not an outcome of SN explosions. Formation of such disks around young NSs can only happen under the condition of negligible magnetic torques and a fine-tuned explosion energy. For those stars that leave behind BH remnants, disk formation is ubiquitous if magnetic fields do not play a strong role; however, unlike the NS case, even with strong magnetic coupling in the interior, a disk can form in a large region of the Z, M, v _surf, E parameter space. Together with the compact, hyperaccreting fallback disks widely discussed in the literature, we identify regions in the above parameter space that lead to extended, long-lived disks around BHs. We find that the physical conditions in these disks may be conducive to planet formation, hence leading to the possible existence of planets orbiting BHs.