The presence of fallback disks around young neutron stars 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 explosion , considering both neutron star ( NS ) and black hole ( BH ) remnants .
Using the public code MESA , we compute the angular momentum distribution of the pre-supernova material , for stars with initial masses M in the range 13 - 40 ~ { } M _ { \odot } , initial surface rotational velocities { \varv _ { \mathrm { 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 \times 10 ^ { 52 } ergs , 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 which 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, { \varv _ { \mathrm { surf } } } ,E parameter space .
Together with the compact , hyperaccreting fallback disks widely discussed in the literature , we identify regions in the above parameter space which 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 black holes .