Pad\'e approximant for the equation of motion of a supernova remnant

TL;DR

This paper develops Padé approximant-based equations of motion for supernova remnants within the thin layer approximation, considering different circumstellar density profiles, and applies them to real SNR data, achieving less than 10% error.

Contribution

It introduces a novel application of Padé approximants to model SNR dynamics with various density profiles, improving solution accuracy over traditional methods.

Findings

Percentage error of solutions is always below 10%.

The model predicts velocity decrease over ten years for SNRs.

Applied equations fit well to observed SNR data.

Abstract

In this paper we derive three equations of motion for a supernova remnant (SNR) in the framework of the thin layer approximation using the Pad\'e approximant. The circumstellar medium is assumed to follow a density profile of either an exponential type, a Gaussian type, or a Lane--Emden ($n=5$) type. The three equations of motion are applied to four SNRs: Tycho, Cas A, Cygnus loop, and SN~1006. The percentage error of the Pad\'e approximated solution is always less than $10\%$. The theoretical decrease of the velocity over ten years for SNRs is evaluated.