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 Ni →56Co →56Fe usually directly powers the ultraviolet/optical/infrared (UVOIR) bolometric luminosity of supernovae in their quasi-steady state phase until very late times. The result for this phase is exponential/quasiexponential 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 absolute deposition is determined by specifying the initial Ni mass or fitting absolute supernova UVOIR bolometric luminosity.) The time evolution of N Ni(t) is determined by three time scales: the halflives of Ni and Co, and a fiducial time parameter t0 that governs the time-varying γ-ray optical depth behavior of a supernova. The t0 parameter can be extracted from a structural supernova model, or by fitting either the RDE deposition curve from a more detailed treatment of deposition or the observed UVOIR bolometric light curve from the quasi-steady state phase of a supernova. A t0 parameter obtained from observations can provide a constraint on the important physical parameters of the supernova. The effective use of this constraint requires having an adequate parameterized structural supernova model. The N Ni(t) function is used to analyze the preliminary UVOIR bolometric light curve of SN Ic 1998bw (the possible cause of γ-ray burst GRB980425). The SN 1998bw fiducial time t0 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 crude estimate (perhaps a factor of a few too small) of the SN 1998bw mass obtained from a parameterized core-collapse model and t0 = 134.42 days is 4.26M⊙. 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. Subject Headings: supernovae: general — supernovae: individual (SN 1992A, SN 1987A, SN 1998bw) — radiative transfer — γ-rays: theory