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

TL;DR

This paper extends the energy conservation theory in the thin layer approximation to special relativity, analyzing four circumstellar medium models and applying them to supernova SN1993j with numerical and analytical results.

Contribution

It introduces a relativistic extension of the thin layer approximation and analyzes four density models for supernova environments.

Findings

Relativistic trajectories are numerically computed for supernovae.

Model parameters are fitted to SN1993j observational data.

Time dilation effects are evaluated in the supernova context.

Abstract

The theory of the conservation of energy in the thin layer approximation has been extended to special relativity. Four models for the density of the circumstellar medium are analyzed, which are represented by constant, power law, exponential and Emden (n=5) profile for density. The astrophysical results are presented in a numerical way, except for a Taylor expansion of the four trajectories in the surrounding of the origin. The free parameters of the models are particularized for SN1993j, for which the radius versus time is known. Some evaluations on the time dilation are presented.