Analytic solutions for light curves of supernovae of Type II

Abstract

By suitable transformations, primarily made to remove homologous expansion, the partial differential equations describing a Type II supernova are reduced to the time-dependent diffusion equation. The behavior of luminosity, effective temperature, B-V color, and fluid velocity is explicitly presented, with dependence on mass, energy of explosion, initial radius, and opacity shown. The solutions allow crude estimates of the mass of ejected matter (about 8 solar masses) and of Co-56 synthesized (about 0.5 solar masses in one case) to be made from observational data. From such solutions it may be possible to infer absolute luminosity from distance-independent characteristics of the event.