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

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.

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