The Propagation of Strong Shocks into Planetary and Stellar Atmospheres

TL;DR

This paper develops a mathematical model using self-similar solutions to describe how shock waves propagate through varying density profiles in astrophysical environments, validated by numerical simulations.

Contribution

It introduces a new analytical framework for modeling shock wave propagation in graded density media applicable to diverse astrophysical phenomena.

Findings

Model accurately predicts shock evolution in different density profiles

Results agree with numerical simulations across various scenarios

Applicable to planetary, stellar atmospheres, and supernovae

Abstract

In this work we present a mathematical model for the propagation of the shock waves that occur in graded density profiles. These waves can occur in a wide range of astrophysical events, such as collisions in planetary and stellar atmospheres, common envelope explosions and peculiar type Ia supernovae. The behaviour of the shock wave and its evolution can be modelled using type II self similar solutions. In such solutions the evolution of the shock wave is determined by boundary conditions at the shock front and a singular point in the shocked region. We show how the evolution can be determined for different equations of state and density profiles, and compare these results to numerical simulations. These findings are also applied to a variety of astrophysical phenomena to further test their validity.