Self Similar Adiabatic Strong Explosion in a Medium Gravitationally Free Falling to a Point Mass

TL;DR

This paper generalizes the classical explosion model to include a medium falling into a point mass, analyzing shock behavior and critical energy thresholds relevant to supernova explosions.

Contribution

It introduces a new model for adiabatic explosions in a gravitationally free-falling medium and verifies it with numerical simulations, highlighting the impact of energy and material distribution.

Findings

Existence of a critical energy threshold for shock propagation

Critical energy decreases with higher adiabatic index

Application to core collapse supernova shock bounce

Abstract

We develop a generalisation to the classical Sedov Taylor explosion where the medium free falls to a point mass at the centre of the explosion. To verify our analytic results, we compare them to a suite of numerical simulations. We find that there exists a critical energy below which, instead of propagating outward the shock stalls and collapses under gravity. Furthermore, we find that the value of the critical energy threshold decreases when the adiabatic index increases and material is more evenly distributed within the shocked region. We apply this model to the problem of a shock bounce in core collapse supernova, in which the proto neutron star serves as the point mass. The relation between the threshold energy and the distribution of mass in the shock might help explain how turbulence prevents shock stalling and recession in a core collapse supernova explosion.