skip to main content


Title: An integral condition for core-collapse supernova explosions

Here, we derive an integral condition for core-collapse supernova (CCSN) explosions and use it to construct a new diagnostic of explodability. The fundamental challenge in CCSN theory is to explain how a stalled accretion shock revives to explode a star. In this manuscript, we assume that the shock revival is initiated by the delayed-neutrino mechanism and derive an integral condition for spherically symmetric shock expansion, v s > 0. One of the most useful one-dimensional explosion conditions is the neutrino luminosity and mass-accretion rate ($${L}_{\nu }\mbox{--}\dot{{ \mathcal M }}$$) critical curve. Below this curve, steady-state stalled solutions exist, but above this curve, there are no stalled solutions. Burrows & Goshy suggested that the solutions above this curve are dynamic and explosive. In this manuscript, we take one step closer to proving this supposition; we show that all steady solutions above this curve have v s > 0. Assuming that these steady v s > 0 solutions correspond to explosion, we present a new dimensionless integral condition for explosion, Ψ > 0. Ψ roughly describes the balance between pressure and gravity, and we show that this parameter is equivalent to the τ condition used to infer the $${L}_{\nu }\mbox{--}\dot{{ \mathcal M }}$$ critical curve. The illuminating difference is that there is a direct relationship between Ψ and v s. Below the critical curve, Ψ may be negative, positive, and zero, which corresponds to receding, expanding, and stalled-shock solutions. At the critical curve, the minimum Ψ solution is zero; above the critical curve, Ψ min > 0, and all steady solutions have v s > 0. Using one-dimensional simulations, we confirm our primary assumptions and verify that Ψ min > 0 is a reliable and accurate explosion diagnostic.
 [1] ; ORCiD logo [2]
  1. Florida State Univ., Tallahassee, FL (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 1538-4357; TRN: US1701010
Grant/Contract Number:
Accepted Manuscript
Journal Name:
The Astrophysical Journal (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal (Online); Journal Volume: 834; Journal Issue: 2; Journal ID: ISSN 1538-4357
Institute of Physics (IOP)
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
National Science Foundation (NSF); USDOE
Country of Publication:
United States
79 ASTRONOMY AND ASTROPHYSICS; astronomy and astrophysics; hydrodynamics; methods: analytical; methods: numerical; shock waves; supernovae: general
OSTI Identifier: