Theoretical Derivation of $\Sigma$-$D$ Relation of Galactic SNRs

TL;DR

This paper derives the $\,\Sigma$-$D$ relation for Galactic shell-type supernova remnants during different evolutionary phases, combining theoretical formulas and statistical analysis to improve understanding of their physical properties.

Contribution

It presents a new theoretical derivation of the $\,\Sigma$-$D$ relation at different phases and compares it with statistical data, highlighting differences from previous results.

Findings

Derived flatter $\,\Sigma$-$D$ relations at early stages.

Statistical analysis of 57 Galactic shell-type remnants.

Good consistency between theoretical and statistical results.

Abstract

We derive the $\Sigma$-$D$ relation of Galactic supernova remnants of shell-type separately at adiabatic-phase and at radiative-phase through two sets of different formulas, considering the different physical processes of shell-type remnants at both stages. Also statistics on Galactic shell-type remnants about 57 was made. Then we do some comparison with other results obtained before. It shows that all the best fit lines in the $\Sigma$-$D$ relation plots newly are to some extent flatter than those derived by some authors at early time. Our theoretical and statistical outcomes are in somewhat good consistency.