Relativistic scaling laws for the light curve in supernovae

TL;DR

This paper develops relativistic and classical models for supernova light curves, incorporating optical depth corrections, and applies these models to various supernovae and gamma-ray burst data, enhancing understanding of their luminosity evolution.

Contribution

It introduces a unified framework with relativistic and classical formulas for supernova light curves, including optical depth corrections and applications to multiple supernovae and GRB data.

Findings

Successful fitting of light curves for SN 2005cf and SN 2004A.

Derived relativistic flux formula using Taylor expansion.

Corrected Arnett's luminosity formula for optical depth effects.

Abstract

In order to explain light curve (LC) for Supernova (SN) we derive a classical formula for the conversion of the flux of kinetic energy into radiation. We then introduce a correction for the absorption adopting an optical depth as function of the time. The developed framework allows to fit the LC of type Ia SN 2005cf ( B and V ) and type IIp SN 2004A (B,V,I and R ). A relativistic formula for the flux of kinetic energy is also derived in terms of a Taylor expansion and the application is done to the LC of GRB 050814. The decay of the radioactive isotopes as a driver the LC for SNs is also reviewed and a new formulation is introduced. The Arnett's formula for bolometric luminosity is corrected for the optical depth and applied to SN 2001ay.