The propagation of strong shocks into planetary and stellar atmospheres with graded density profiles
Previous works developed an analytic model for the propagation of shock waves into atmospheres with a uniform density. In this work, we generalized this formalism to account for 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. We also demonstrate how these results can be applied to a wide range of problems in astrophysics.