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Simplified analytic methods are frequently used to model the light curves ofsupernovae and other energetic transients and to extract physical quantities,such as the ejecta mass and amount of radioactive heating. The applicabilityand quantitative accuracy of these models, however, have not been clearlydelineated. Here we carry out a systematic study comparing certain analyticmodels to numerical radiation transport calculations. We show that the neglectof time-dependent diffusion limits the accuracy of common Arnett-like analyticmodels, and that the widely-applied Arnett's rule for inferring radioactivemass does not hold in general, with an error that increases for models withlonger diffusion times or more centralized heating. We present new analyticrelations that accurately relate the peak time and luminosity of an observedlight curve to the physical ejecta and heating parameters. We further show thatrecombination and the spatial distribution of heating modify the peak of thelight curve and that these effects can be accounted for by varying a singledimensionless parameter in the new relations. The results presented should beuseful for estimating the physical properties of a wide variety of transientphenomena.

Physics of Luminous Transient Light Curves: A New Relation Between Peak Time and Luminosity