An analytical model for the plateau stage of Type II supernovae

Abstract

This paper presents an analytical model for hydrogen envelope cooling in Type II supernovae during the plateau phase. Observable features of SN IIp light curves, such as the duration of the plateau, t(p), and its V magnitude, are expressed through such basic parameters as the energy of explosion, the mass, and the initial radius of the envelope. The relationships derived are in excellent agreement with similar ones obtained from fits to a grid of hydrodynamical calculations. The duration of the plateau turns out to be most sensitive to the envelope mass and much less to the explosion energy and the initial radius. This conclusion provides support for the results of the previous analytical models of SN IIp's. We present relationships, allowing observers to estimate the basic SN parameters from observational data. For the 'average' Type IIp supernova our estimate gives results close to those obtained with the fitting of hydrodynamical models.