A classical and a relativistic law of motion for spherical supernovae

Abstract

In this paper we derive some first order differential equations which model the classical and the relativistic thin layer approximations. The circumstellar medium is assumed to follow a density profile of Plummer type, or of Lane--Emden ($n=5$) type, or a power law. The first order differential equations are solved analytically, or numerically, or by a series expansion, or by recursion. The initial conditions are chosen in order to model the temporal evolution of SN 1993J over ten years and a smaller chi-squared is obtained for the Plummer case with eta=6. The stellar mass ejected by the SN progenitor prior to the explosion, expressed in solar mass, is identified with the total mass associated with the selected density profile and varies from $0.217$ to $0.402$ when the central number density is $10^7$ particles per cubic centimeter. The Full width at half maximum of the three density profiles, which can be identified with the size of the Pre-SN 1993J envelope, varies from 0.0071 pc to 0.0092 pc.

15 figures and 34 pages

References in corpus (3)

• A new method of determining the initial size and Lorentz factor of gamma-ray burst fireballs using a thermal emission component
• The host galaxy of the super-luminous SN 2010gx and limits on explosive nickel-56 production
• SN 1993J VLBI (IV): A Geometric Determination of the Distance to M81 with the Expanding Shock Front Method

Cited by in corpus (2)

• Energy Conservation in the thin layer approximation: III. The spherical relativistic case for supernovae
• Energy Conservation in the thin layer approximation: IV. The light curve for supernovae