Properties of Type-Ia Supernova Light Curves

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, $L_{\mathrm{bol}}$, 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 $L_{\mathrm{bol}}$ 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, $L_{\mathrm{bol}}(t_{15})$, must be close to the instantaneous decay luminosity at that time, $L_{\gamma }(t_{15})$. With the employed calculations and observations, the accuracy of $L_{\mathrm{bol}}=L_{\gamma }$ at $t=t_{15}$ is found to be comparable to the simple version of "Arnett's rule" ($L_{\mathrm{bol}}=L_{\gamma }$ at $t=t_{\mathrm{peak}}$). 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.

7 pages and 9 figures. Published in ApJ on 22 Mar, 2019