Properties of Type-Ia Supernova Light Curves

I show that the characteristic diffusion timescale and the gamma-ray escape timescale, of SN Ia ejecta, are related with each other through the time when the bolometric luminosity, L-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-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-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-bol = L gamma at t = t(15) is found to be comparable to the simple version of Arnett's rule (L-bol = L-gamma at t = t(peak)). This relation aids the interpretation of SN Ia light curves and may also be applicable to general hydrogen-free explosion scenarios powered by other central engines.