Critical Conditions for Core-Collapse Supernovae

TL;DR

This paper analytically determines the critical neutrino luminosity needed for core-collapse supernova explosions, linking it to proto-neutron star properties and confirming results with numerical data.

Contribution

It provides an analytical derivation of the critical conditions for supernova explosions, connecting neutrino luminosity, PNS mass, and temperature.

Findings

Critical neutrino luminosity scales with PNS mass and temperature.

Neutrinosphere pressure exceeds hydrostatic limit at critical luminosity.

Near-critical flow approximates a ballistic shell on an isothermal layer.

Abstract

The explosion of a core-collapse supernova can be approximated by the breakdown of steady-state solutions for accretion onto a proto-neutron star (PNS). We analytically show that as the neutrino luminosity exceeds a critical value L_c, the neutrinosphere pressure exceeds the hydrostatic limit even for an optimal shock radius R. This yields L_c \propto M^2 T^2 (with logarithmic corrections) and R \propto M/T, in agreement with numerical results, where M, T are the PNS mass, neutrino temperature. The near-critical flow can be approximated as a ballistic shell on top of an isothermal layer.