Early expansion and luminosity evolution of supernovae

The initial planar expansion of a supernova can be described by a self-similar solution if the progenitor star is sufficiently compact that radiative transfer effects do not play an important role during this phase. The later free expansion of the gas leads to radial power laws for the density and pressure profiles, although the effects of spherical geometry give some inaccuracy in this result. If the initial expansion does set up power laws for the density and pressure, effects of radiative diffusion can be described by a self-similar diffusion wave that moves back into the gas. The self-similar solution shows that there is a sharp transition between adiabatic flow and flow with constant comoving luminosity. The model is applied to SN 1987A and shown to approximately reproduce the declining luminosity observed during the first few days after the explosion.