2026ApJ...998...22F

We study the problem of steady-state spherical accretion onto a black hole, in which the internal energy of the flow is governed by radiation and photon diffusion dominates the energy flux at large radii. In the freefall limit, the fluid equations can admit two types of solutions for a given accretion rate: (1) accretion flows that become isothermal at large radii, and (2) solutions in which the temperature at infinity vanishes as a power law of the radius. Using boundary-layer theory, we obtain analytic solutions for the two cases and apply our results to fallback accretion onto a black hole following a failed supernova (SN) explosion. We give predictions for the observational signature of fallback accretion using realistic progenitor properties from MESA, both for a fully ionized inflow and for the more realistic case in which recombination/ionization take place due to low photospheric temperatures. The observed fading sources coincident with the failed-SNe candidates in NGC 6946 and M31 are too luminous to be powered by spherical accretion onto newly formed black holes; the observed sources are instead likely due to accretion of the turbulent, convective envelope of the supergiant progenitor.