Weak shock propagation with accretion. I. Self-similar solutions and application to failed supernovae

Understand

We present solutions for the self-similar propagation of a shock wave in a hydrostatic, adiabatic medium with a point mass gravitational field.

• In contrast to the well-known, Sedov-Taylor blastwave, these solutions apply to the case when the shock Mach number is of order a few, and the energy of the shocked fluid is not conserved but self-consistently modified by the binding energy of the ambient medium that is swept up by the passage of the shock.
• Furthermore, we show that there is one solution (for a given ambient density profile) that smoothly passes through a sonic point in the post-shock flow and results in accretion onto the central object; in analogy with the Bondi problem, we propose that these solutions are the ones that are most relevant in astrophysical environments.
• We apply these accreting models to failed supernovae, in which neutron star formation does not unbind the envelope, but a weak shock is still generated in the outer layers of the star from neutrino-induced mass loss.