Fluid dynamics of semiradiative blast waves

We derive a self-similar solution for the propagation of an extreme relativistic (or Newtonian) radiative spherical blast wave into a surrounding cold medium. The solution is obtained under the assumption that the radiation process is fast, that it takes place only in the vicinity of the shock, and that it radiates away a fixed fraction of the energy generated by the shock. We find that the energy of the blast wave behaves as a power law of the location of the shock. The power-law index depends on the fraction of the energy emitted by the shock. We obtain an analytic solution for the interior of the blast wave. In the Newtonian regime these solutions generalize the Sedov-Taylor adiabatic solution and the pressure-driven fully radiative solution. In the extreme relativistic case, these solutions generalize the Blandford-McKee adiabatic solution. They provide a new fully radiative extreme relativistic solution that is different from the Blandford-McKee fully radiative relativistic solution. This new solution develops a hot interior that causes it to cool faster than previous estimates. These new solutions might be applicable to the study of gamma-ray burst afterglow or supernova remnants.