Classical and relativistic laws of motion for spherical supernovas

TL;DR

This paper develops differential equations modeling the motion of supernova remnants under classical and relativistic assumptions, applying various approximation methods to fit observational data of specific supernovae and remnants.

Contribution

It introduces a unified approach to derive and solve motion equations for supernova remnants using multiple approximation techniques, including Padé, for diverse density profiles.

Findings

Analytical and numerical solutions for supernova remnant evolution.

Application of models to observed supernovae over ten years.

Effective approximation methods for complex astrophysical dynamics.

Abstract

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 which can be exponential, Gaussian, Plummer-like, self-gravitating of Lane--Emden ($n=5$) type, or power law. The first order differential equations are solved analytically, or numerically, or by a series expansion, or by recursion, or by Pad\'e approximation. The initial conditions are chosen in order to model the temporal evolution of SN 1993J over ten years. The Pad\'e approximated equations of motion are applied to four SNRs: Tycho, Cas A, Cygnus loop, and SN~1006.