Energy Conservation in the thin layer approximation: V. The surface brightness in supernova remnants

TL;DR

This paper derives new equations of motion for supernova remnants within the thin-layer approximation, linking energy conservation to surface brightness evolution and applying these models to galactic and extragalactic data.

Contribution

It introduces two novel equations of motion for SNRs based on different density and mass dependence assumptions, and derives scaling laws for surface brightness evolution.

Findings

New equations of motion for SNRs are formulated.

Scaling laws for surface brightness over time are derived.

Models are validated with galactic and extragalactic data.

Abstract

Two new equations of motion for a supernova remnant (SNR) are derived in the framework of energy conservation for the thin-layer approximation. The first one is based on an inverse square law for the surrounding density and the second one on a non-cubic dependence of the swept mass. Under the assumption that the observed radio-flux scales as the flux of kinetic energy, two scaling laws are derived for the temporal evolution of the surface brightness of SNRs. The astrophysical applications cover two galactic samples of surface brightness and an extragalactic one.