An Integral Condition for Core-Collapse Supernova Explosions

Abstract

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 ($L_{\nu }-\dot{\mathcal{M}}$) 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, $\Psi >0$. $\Psi$ roughly describes the balance between pressure and gravity, and we show that this parameter is equivalent to the $\tau$ condition used to infer the $L_{\nu }-\dot{\mathcal{M}}$ critical curve. The illuminating difference is that there is a direct relationship between $\Psi$ and $v_s$. Below the critical curve, $\Psi$ may be negative, positive, and zero, which corresponds to receding, expanding, and stalled-shock solutions. At the critical curve, the minimum $\Psi$ solution is zero; above the critical curve, ${\Psi }_{\min }>0$, and all steady solutions have $v_s>0$. Using one-dimensional simulations, we confirm our primary assumptions and verify that ${\Psi }_{\min }>0$ is a reliable and accurate explosion diagnostic.

18 pages and 12 figures; published in ApJ. Figures 8 & 9 and equation 21 show the main results

References in corpus (8)

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Cited by in corpus (25)

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• Revival of the Fittest: Exploding Core-Collapse Supernovae from 12 to 25 M${}_{\odot }$
• Turbulence in Core-Collapse Supernovae
• The Essential Character of the Neutrino Mechanism of Core-Collapse Supernova Explosions
• How Turbulence Enables Core-Collapse Supernova Explosions
• Confronting Models of Massive Star Evolution and Explosions with Remnant Mass Measurements
• Binary-Stripped Stars as Core-Collapse Supernovae Progenitors
• The physics of Core-Collapse Supernovae: explosion mechanism and explosive nucleosynthesis
• It's written in the massive stars: The role of stellar physics in the formation of black holes
• Mass ejection in failed supernovae: equation of state and neutrino loss dependence
• Convection-Aided Explosions in One-Dimensional Core-Collapse Supernova Simulations I: Technique and Validation
• The Progenitor Age and Mass of the Black-Hole-Formation Candidate N6946-BH1
• Explodability criteria for the neutrino-driven supernova mechanism
• Effects of rotation and magnetic field on the revival of a stalled shock in supernova explosions
• Progenitor Mass Distribution for 22 Historic Core-Collapse Supernovae
• The non-linear onset of neutrino-driven convection in two and three-dimensional core-collapse supernovae
• The Antesonic Condition for the Explosion of Core-Collapse Supernovae I: Spherically Symmetric Polytropic Models: Stability & Wind Emergence
• A Force Explosion Condition for Spherically Symmetric Core-collapse Supernovae
• The Force Explosion Condition is Consistent with Spherically Symmetric CCSN Explosions
• The Antesonic Condition for the Explosion of Core-Collapse Supernovae II: Rotation and Turbulence
• Explosion Energies for Core-collapse Supernovae I: Analytic, Spherically Symmetric Solutions
• A Parametric Study of the Acoustic Mechanism for Core-Collapse Supernovae
• Self Similar Adiabatic Strong Explosion in a Medium Gravitationally Free Falling to a Point Mass
• Imagination and Understanding through Astrophysical Imagery