The physics of Type Ia supernova light curves. I. Analytic results and time dependence

We develop an analytic solution of the radiation transport problem for Type Ia supernovae (SNe Ia) and show that it reproduces bolometric light curves produced by more detailed calculations under the assumption of a constant-extinction coefficient. This model is used to derive the thermal conditions in the interior of SNe Ia and to study the sensitivity of light curves to various properties of the underlying supernova explosions. Although the model is limited by simplifying assumptions, it is adequate for demonstrating that the relationship between SNe Ia maximum-light luminosity and rate of decline is most easily explained if SNe Ia span a range in mass. The analytic model is also used to examine the size of various terms in the transport equation under conditions appropriate to maximum light. For instance, the Eulerian and advective time derivatives are each shown to be of the same order of magnitude as other order v/c terms in the transport equation. We conclude that a fully time-dependent solution to the transport problem is needed in order to compute SNe Ia light curves and spectra accurate enough to distinguish subtle differences of various explosion models.