An Analytic Approximation to Radiative Blast Wave Evolution

Abstract

The evolution of the well-known Sedov-Taylor adiabatic blast waves can be derived analytically using simple physical arguments. However, radiative blast waves with energy loss concentrated at the shock front have only been studied numerically. Here we show that if the shock radius evolution can be expressed as R ~ (at)n, then using an approximation similar to that discussed by Zeldovich & Raizer for the adiabatic case, we can derive simple analytic relations for n and a as functions of the pre- and postshock adiabatic indices, the energy loss fraction e, the initial energy E0, and initial deposition size R0. These analytic results are in excellent agreement with previous numerical results. We also find that the results are much more sensitive to the postshock adiabatic index in the central cavity than the preshock adiabatic index.