A core-collapse supernova is generated by the passage of a shock wave through the envelope of a massive star, where the shock wave is initially launched from the ‘bounce’ of the neutron star formed during the collapse of the stellar core. Instead of successfully exploding the star, however, numerical investigations of core-collapse supernovae find that this shock tends to ‘stall’ at small radii (≲10 neutron star radii), with stellar material accreting on to the central object through the standing shock. Here, we present time-steady, adiabatic solutions for the density, pressure, and velocity of the shocked fluid that accretes on to the compact object through the stalled shock, and we include the effects of general relativity in the Schwarzschild metric. Similar to previous works that were carried out in the Newtonian limit, we find that the gas ‘settles’ interior to the stalled shock; in the relativistic regime analysed here, the velocity asymptotically approaches zero near the Schwarzschild radius. These solutions can represent accretion on to a material surface if the radius of the compact object is outside of its event horizon, such as a neutron star; we also discuss the possibility that these solutions can approximately represent the accretion of gas on to a newly formed black hole following a core-collapse event. Our findings and solutions are particularly relevant in weak and failed supernovae, where the shock is pushed to small radii and relativistic effects are large.
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
- NSF-PAR ID:
- 10465052
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 955
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 110
- Size(s):
- ["Article No. 110"]
- Sponsoring Org:
- National Science Foundation
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