SIMBAD references

The early part of a supernova (SN) light curve is dominated by radiation escaping from the expanding shock-heated progenitor envelope. For polytropic hydrogen envelopes, the properties of the emitted radiation are described by simple analytic expressions and are nearly independent of the polytropic index, n. This analytic description holds at early time, t < few days, during which radiation escapes from shells that are initially lying near the stellar surface. We use numerical solutions to address two issues. First, we show that the analytic description holds at early time also for nonpolytropic density profiles. Second, we extend the solutions to later times, when the emission emerges from deep within the envelope and depends on the progenitor's density profile. Examining the late time behavior of the polytropic envelopes with a wide range of core to envelope mass and radius ratios, 0.1 <= M_c/M_env <= 10 and 10^–3 <= R_c/R <= 10^–1, we find that the effective temperature is well described by the analytic solution also at late time, while the luminosity, L, is suppressed by a factor, which may be approximated to be better than a 20 [30]% accuracy up to t = t_tr/a by Aexp[-(at/t_tr)^α^] with t_tr = 13 (M_env/M_☉)^3/4(M/M_env)^1/4(E/10⁵¹erg)^–1/4 days, M = M_c + M_env, A = 0.9[0.8], a = 1.7[4.6], and α = 0.8[0.7] for n = 3/2[3]. This description holds as long as the opacity is approximately that of a fully ionized gas, i.e., for T > 0.7 eV, t < 14(R/10^13.5cm)^0.55 days. The suppression of L at t_tr/a that is obtained for standard polytropic envelopes may account for the first optical peak of double-peaked SN light curves, with the first peak at a few days for M_env < 1 M_☉.