Radioactive Decay Energy Deposition in Supernovae and the Exponential/Quasi-Exponential Behavior of Late-Time Supernova Light Curves

The radioactive decay energy (RDE) deposition in supernovae from the decay chain Ni56-Co56-Fe56 usually directly powers the UV/optical/IR (UVOIR) bolometric luminosity of supernovae in their quasi-steady state phase until very late times. The result for this phase is exponential/quasi-exponential UVOIR bolometric light curves and often exponential/quasi-exponential broad band light curves. A presentation is given of a simple, approximate, analytic treatment of RDE deposition that provides a straightforward understanding of the exponential/quasi-exponential behavior of the UVOIR bolometric luminosity and a partial understanding of the exponential/quasi-exponential behavior of the broad band light curves. The treatment reduces to using a normalized deposition function N_{Ni}^{*}(t) as an analysis tool. The one free parameter of N_{Ni}^{*}(t) is a fiducial time t_{0} which governs time-varying gamma-ray optical depth behavior of a supernova. The N_{Ni}^{*}(t) function is used to analyze the preliminary UVOIR bolometric light curve of SN Ic 1998bw (the possible cause of gamma-ray burst GRB980425). The SN 1998bw t_{0} is found to be 134.42 days and a prediction is made for the evolution of the SN 1998bw RDE deposition curve and quasi-steady state UVOIR bolometric light curve out to day 1000 after the explosion. A very crude estimate of the SN 1998bw mass obtained from the light curve analysis is 4.26 M_{Sun}. As further examples of the simple analytic treatment, the RDE deposition and luminosity evolution of SN Ia 1992A and SN II 1987A have also been examined. The simple analytic treatment of RDE deposition has actually existed for 20 years at least without, apparently, being discussed at length. The main value of this paper is the explicit, detailed, general presentation of this analytic treatment.