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Title: An integral condition for core-collapse supernova explosions

Abstract

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.

Authors:
 [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:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
National Science Foundation (NSF); USDOE
OSTI Identifier:
1352363
Report Number(s):
LA-UR-15-25862
Journal ID: ISSN 1538-4357; TRN: US1701010
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: 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
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; astronomy and astrophysics; hydrodynamics; methods: analytical; methods: numerical; shock waves; supernovae: general

Citation Formats

Murphy, Jeremiah W., and Dolence, Joshua C. An integral condition for core-collapse supernova explosions. United States: N. p., 2017. Web. doi:10.3847/1538-4357/834/2/183.
Murphy, Jeremiah W., & Dolence, Joshua C. An integral condition for core-collapse supernova explosions. United States. doi:10.3847/1538-4357/834/2/183.
Murphy, Jeremiah W., and Dolence, Joshua C. Tue . "An integral condition for core-collapse supernova explosions". United States. doi:10.3847/1538-4357/834/2/183. https://www.osti.gov/servlets/purl/1352363.
@article{osti_1352363,
title = {An integral condition for core-collapse supernova explosions},
author = {Murphy, Jeremiah W. and Dolence, Joshua C.},
abstractNote = {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, vs > 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 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 stalled-shock 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 one-dimensional simulations, we confirm our primary assumptions and verify that Ψmin > 0 is a reliable and accurate explosion diagnostic.},
doi = {10.3847/1538-4357/834/2/183},
journal = {The Astrophysical Journal (Online)},
number = 2,
volume = 834,
place = {United States},
year = {Tue Jan 10 00:00:00 EST 2017},
month = {Tue Jan 10 00:00:00 EST 2017}
}

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  • We explore the dependence on spatial dimension of the viability of the neutrino heating mechanism of core-collapse supernova explosions. We find that the tendency to explode is a monotonically increasing function of dimension, with three dimensions (3D) requiring {approx}40%-50% lower driving neutrino luminosity than one dimension and {approx}15%-25% lower driving neutrino luminosity than two dimensions (2D). Moreover, we find that the delay to explosion for a given neutrino luminosity is always shorter in 3D than 2D, sometimes by many hundreds of milliseconds. The magnitude of this dimensional effect is much larger than the purported magnitude of a variety of othermore » effects, such as nuclear burning, inelastic scattering, or general relativity, which are sometimes invoked to bridge the gap between the current ambiguous and uncertain theoretical situation and the fact of robust supernova explosions. Since real supernovae occur in three dimensions, our finding may be an important step toward unraveling one of the most problematic puzzles in stellar astrophysics. In addition, even though in 3D, we do see pre-explosion instabilities and blast asymmetries, unlike the situation in 2D, we do not see an obvious axially symmetric dipolar shock oscillation. Rather, the free energy available to power instabilities seems to be shared by more and more degrees of freedom as the dimension increases. Hence, the strong dipolar axisymmetry seen in 2D and previously identified as a fundamental characteristic of the shock hydrodynamics may not survive in 3D as a prominent feature.« less
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