The division between weak and strong explosions from failed supernovae

TL;DR

This paper investigates the conditions under which failed supernovae produce weak or strong explosions, revealing that the outcome depends on the neutrino mass loss and stellar properties, with implications for stellar evolution and gravitational wave events.

Contribution

It introduces self-similar solutions describing shock propagation in failed supernovae and identifies a critical neutrino mass loss threshold determining explosion strength.

Findings

Weak shocks are unstable and lead to minimal mass ejection.

Above a critical neutrino mass loss, only strong explosions occur.

A second self-similar solution describes gas settling near the black hole.

Abstract

Some massive stars likely fail to produce core-collapse supernovae, but these failed supernovae (FSNe) can generate an electromagnetic outburst prior to the disappearance of the star, as the mass lost to neutrinos during the stellar core-collapse results in the formation and breakout of a second shock. We show that when the mass lost to neutrinos is sufficiently small, there are two self-similar solutions that describe the propagation of a weak shock into a hydrodynamically expanding envelope that simultaneously yield accretion onto the black hole. The larger-Mach number solution is unstable and yields the minimum Mach number that a shock must have to strengthen into the energy-conserving regime. Above a critical mass loss there are no weak-shock solutions, implying that there are only strong explosions if the neutrino mass loss is above a critical value, and this value is a few percent of the mass of the star (and is physically achievable) for typical parameters. Our results imply that the fate of the explosion from a FSN -- weak with little to no mass ejection or strong with the expulsion of the majority of the envelope -- is a sensitive function of the stellar properties and the neutrino mass loss. We also show that there is a second type of self-similar solution for the shock that results in the ``settling'' of the gas near the compact object, which may be applicable to non-terminal stellar eruptions and the response of a gaseous disc to gravitational-wave induced mass loss from a binary black hole merger.