The Division between Weak and Strong Explosions from Failed Supernovae

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 an 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 nonterminal stellar eruptions and the response of a gaseous disk to gravitational-wave induced mass loss from a binary black hole merger.