Hydrodynamics of Core-Collapse Supernovae at the Transition to Explosion. I. Spherical Symmetry

TL;DR

This paper investigates the hydrodynamic mechanisms behind the transition from stalled to exploding supernova shocks in spherical symmetry, identifying key instability conditions and thresholds for runaway expansion.

Contribution

It provides high-resolution simulations revealing the role of radial instability and specific energy in shock revival, with new criteria for instability and explosion thresholds.

Findings

Radial instability can trigger runaway if parameters are constant.

Transition occurs when fluid in the gain region gains positive energy.

Instability thresholds differ from steady-state limits.

Abstract

We study the transition to runaway expansion of an initially stalled core-collapse supernova shock. The neutrino luminosity, mass accretion rate, and neutrinospheric radius are all treated as free parameters. In spherical symmetry, this transition is mediated by a global non-adiabatic instability that develops on the advection time and reaches non-linear amplitude. Here we perform high-resolution, time-dependent hydrodynamic simulations of stalled supernova shocks with realistic microphysics to analyze this transition. We find that radial instability is a sufficient condition for runaway expansion if the neutrinospheric parameters do not vary with time and if heating by the accretion luminosity is neglected. For a given unstable mode, transition to runaway occurs when fluid in the gain region reaches positive specific energy. We find approximate instability criteria that accurately describe the behavior of the system over a wide region of parameter space. The threshold neutrino luminosities are in general different than the limiting value for a steady-state solution. We hypothesize that multidimensional explosions arise from the excitation of unstable large-scale modes of the turbulent background flow, at threshold luminosities that are lower than in the laminar case.