An integral condition for corecollapse supernova explosions
Here, we derive an integral condition for corecollapse 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 delayedneutrino mechanism and derive an integral condition for spherically symmetric shock expansion, v _{s} > 0. One of the most useful onedimensional explosion conditions is the neutrino luminosity and massaccretion rate ($${L}_{\nu }\mbox{}\dot{{ \mathcal M }}$$) critical curve. Below this curve, steadystate 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 stalledshock 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 onedimensional simulations, we confirm our primary assumptions and verify that Ψ _{min} > 0 is a reliable and accurate explosion diagnostic.
 Authors:

^{[1]};
^{[2]}
 Florida State Univ., Tallahassee, FL (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 LAUR1525862
Journal ID: ISSN 15384357; TRN: US1701010
 Grant/Contract Number:
 AC5206NA25396
 Type:
 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 15384357
 Publisher:
 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
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; astronomy and astrophysics; hydrodynamics; methods: analytical; methods: numerical; shock waves; supernovae: general
 OSTI Identifier:
 1352363
Murphy, Jeremiah W., and Dolence, Joshua C.. An integral condition for corecollapse supernova explosions. United States: N. p.,
Web. doi:10.3847/15384357/834/2/183.
Murphy, Jeremiah W., & Dolence, Joshua C.. An integral condition for corecollapse supernova explosions. United States. doi:10.3847/15384357/834/2/183.
Murphy, Jeremiah W., and Dolence, Joshua C.. 2017.
"An integral condition for corecollapse supernova explosions". United States.
doi:10.3847/15384357/834/2/183. https://www.osti.gov/servlets/purl/1352363.
@article{osti_1352363,
title = {An integral condition for corecollapse supernova explosions},
author = {Murphy, Jeremiah W. and Dolence, Joshua C.},
abstractNote = {Here, we derive an integral condition for corecollapse 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 delayedneutrino mechanism and derive an integral condition for spherically symmetric shock expansion, vs > 0. One of the most useful onedimensional explosion conditions is the neutrino luminosity and massaccretion rate (${L}_{\nu }\mbox{}\dot{{ \mathcal M }}$) critical curve. Below this curve, steadystate 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 vs > 0. Assuming that these steady vs > 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 vs. Below the critical curve, Ψ may be negative, positive, and zero, which corresponds to receding, expanding, and stalledshock solutions. At the critical curve, the minimum Ψ solution is zero; above the critical curve, Ψmin > 0, and all steady solutions have vs > 0. Using onedimensional simulations, we confirm our primary assumptions and verify that Ψmin > 0 is a reliable and accurate explosion diagnostic.},
doi = {10.3847/15384357/834/2/183},
journal = {The Astrophysical Journal (Online)},
number = 2,
volume = 834,
place = {United States},
year = {2017},
month = {1}
}