Properties of Type-Ia Supernova Light Curves

TL;DR

This paper establishes a relationship between diffusion and gamma-ray escape timescales in Type-Ia supernovae, linking bolometric luminosity and radioactive decay, which enhances understanding of supernova light curves.

Contribution

It introduces an analytical relation connecting key timescales and luminosities in SN Ia, supported by calculations and observations, refining the interpretation of their light curves.

Findings

The intersection of $L_{bol}$ and $L_eta$ occurs at about 1.7 times the diffusion timescale.

Gamma-ray escape timescale is approximately 2.7 times the diffusion timescale.

$L_{bol}$ at 15 days post-peak closely matches $L_eta$ at that time.

Abstract

I show that the characteristic diffusion timescale and the gamma-ray escape timescale, of SN Ia supernova ejecta, are related with each other through the time when the bolometric luminosity, $L_{\rm bol}$, intersects with instantaneous radioactive decay luminosity, $L_\gamma$, for the second time after the light-curve peak. Analytical arguments, numerical radiation-transport calculations, and observational tests show that $L_{\rm bol}$ generally intersects $L_\gamma$ at roughly $1.7$ times the characteristic diffusion timescale of the ejecta. This relation implies that the gamma-ray escape timescale is typically 2.7 times the diffusion timescale, and also implies that the bolometric luminosity 15 days after the peak, $L_{\rm bol}(t_{15})$, must be close to the instantaneous decay luminosity at that time, $L_\gamma (t_{15})$. With the employed calculations and observations, the accuracy of $L_{\rm bol}=L_\gamma$ at $t=t_{15}$ is found to be comparable to the simple version of "Arnett's rule" ($L_{\rm bol}=L_\gamma$ at $t=t_{\rm peak}$). This relation aids the interpretation of SN Ia supernova light curves and may also be applicable to general hydrogen-free explosion scenarios powered by other central engines.