Critical Conditions for Core-Collapse Supernovae

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) [proportionally] M(2)T(2) (with logarithmic corrections) and R [proportionally] M/T, in agreement with numerical results, where M and T are the PNS mass and neutrino temperature, respectively. The near-critical flow can be approximated as a ballistic shell on top of an isothermal layer.