Self similar Shocks in Atmospheric Mass Loss due to Planetary Collisions

Abstract

We present a mathematical model for the propagation of the shock waves that occur during planetary collisions. Such collisions are thought to occur during the formation of terrestrial planets, and they have the potential to erode the planet's atmosphere. We show that under certain assumptions, this evolution of the shock wave can be determined using the method of self similar solutions. This self similar solution is of type II, which means that it only applies to a finite region behind the shock front. This region is bounded by the shock front and the sonic point. Energy and matter continuously flow through the sonic point, so that energy in the self similar region is not conserved, as is the case for type I solutions. Instead, the evolution of the shock wave is determined by boundary conditions at the shock front and at the sonic point. We show how the evolution can be determined for different equations of state, allowing these results to be readily used to calculate the atmospheric mass loss from planetary cores made of different materials.