A Force Explosion Condition for Spherically Symmetric Core-collapse Supernovae

TL;DR

This paper derives a simple, analytic explosion condition for spherically symmetric core-collapse supernovae, linking key physical parameters to predict whether a star explodes or collapses into a black hole.

Contribution

It introduces a unified, force-based explosion criterion that encompasses previous conditions and can be applied to both simplified and complex supernova models.

Findings

The explosion condition depends on two key dimensionless parameters.

The derived condition successfully reproduces existing explosion criteria.

Numerical tests show the condition's potential as a diagnostic tool.

Abstract

Understanding which stars explode leaving behind neutron stars and which stars collapse forming black holes remains a fundamental astrophysical problem. We derive an analytic explosion condition for spherically symmetric core-collapse supernovae. The derivation starts with the exact governing equations, considers the balance of integral forces, includes the important dimensionless parameters, and includes an explicit set of self-consistent approximations. The force explosion condition is $\tilde{L}_\nu\tau_g - 0.06 \tilde{\kappa} > 0.38$, and only depends upon two dimensionless parameters. The first compares the neutrino power deposited in the gain region with the accretion power, $\tilde{L}_\nu \tau_g = L_{\nu} \tau_g R_{\rm NS}/ ( G \dot{M} M_{\rm NS})$. The second, $\tilde{\kappa} = \kappa \dot{M} / \sqrt{G M_{\rm NS} R_{\rm NS}}$, parameterizes the neutrino optical depth in the accreted matter near the neutron-star surface. Over the years, many have proposed approximate explosion conditions: the critical neutrino-luminosity, ante-sonic, and timescale conditions. We are able to derive these other conditions from the force explosion condition, which unifies them all. Using numerical, steady-state and fully hydrodynamic solutions, we test the explosion condition. The success of these tests is promising in two ways. One, the force explosion condition helps to illuminate the underlying physics of explosions. Two, this condition may be a useful explosion diagnostic for more realistic, three-dimensional radiation hydrodynamic core-collapse simulations.