A Reader Friendly Formalism for Circumstellar Material-Supernova Ejecta Interaction Model

TL;DR

This paper simplifies and corrects the semi-analytic model for supernova ejecta interacting with circumstellar material, making it more accessible for order-of-magnitude estimates and parameter analysis.

Contribution

It provides a re-derivation of the model's formulae, making them more reader-friendly and correcting previous minor errors.

Findings

Simplified formula expressions for CSM-ejecta interaction.

Corrected minor errors in the previous model.

Enhanced usability for parameter estimation.

Abstract

The interaction of a SN ejecta with a pre-existing circumstellar material (CSM) is one of the most promising energy sources for a variety of optical transients. Recently, a semi-analytic method developed by Chatzopoulos et al. (2012, hereafter CWV12) has been commonly used to describe the optical light curve behaviors under such a scenario. We find that the expressions for many key results in CWV12 are too complicated for readers to make order of magnitude estimation or parameter dependency judgement. Based on the same physical picture, here we independently re-derive all the formulae and re-establish a set of reader friendly formula expressions. Nevertheless, we point out and correct some minor errors or typos existing in CWV12.