Energy Conservation in the thin layer approximation: IV. The light curve for supernovae

TL;DR

This paper models supernova light curves using energy conservation and various density profiles, providing analytical and relativistic trajectories, and applies the models to specific supernova and gamma-ray burst data.

Contribution

It introduces new analytical and relativistic models for supernova light curves based on different density profiles and applies them to observed data.

Findings

Successful modeling of SN 1993J light curves in multiple bands.

Application of models to gamma-ray burst light curves in keV region.

Derivation of magnetic field evolution from luminosity data.

Abstract

The light curves (LC) for Supernova (SN) can be modeled adopting the conversion of the flux of kinetic energy into radiation. This conversion requires an analytical or a numerical law of motion for the expanding radius of the SN. In the framework of conservation of energy for the thin layer approximation we present a classical trajectory based on a power law profile for the density, a relativistic trajectory based on the Navarro--Frenk--White profile for the density, and a relativistic trajectory based on a power law behaviour for the swept mass. A detailed simulation of the LC requires the evaluation of the optical depth as a function of time. We modeled the LC of SN~1993J in different astronomical bands, the LC of GRB 050814 and the LC GRB 060729 in the keV region. The time dependence of the magnetic field of equipartition is derived from the theoretical formula for the luminosity.