A classical and a relativistic law of motion for spherical supernovae

TL;DR

This paper develops differential equations modeling classical and relativistic supernova shell expansion within various circumstellar density profiles, solving them analytically and numerically to fit observations of SN 1993J over ten years.

Contribution

It introduces new differential equations for supernova expansion in different density environments and applies them to real data, improving modeling accuracy.

Findings

Better fit to SN 1993J data with Plummer profile (eta=6)

Ejected stellar mass ranges from 0.217 to 0.402 solar masses

Pre-SN envelope size varies from 0.0071 to 0.0092 parsecs

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.