UV/Optical emission from the expanding envelopes of type II supernovae

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 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 non-polytropic 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 polytropic envelopes with a wide range of core to envelope mass and radius ratios, $0.1\le M_{\rm c}/M_{\rm env}\le10$ and $10^{-3}\le R_{\rm c}/R\le10^{-1}$, 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 better than $20[30]\%$ accuracy up to $t=t_{\rm tr}/a$ by $A\exp[-(at/t_{\rm tr})^\alpha]$ with $t_{\rm tr} = 15 (M_{\rm env}/M_\odot)^{3/4}(E/10^{51}{\rm erg})^{-1/4}~\rm d$, $A=0.9[0.8]$, $a=1.7[4.6]$ and $\alpha=0.8[0.7]$ for $n=3/2[3]$. This description holds as long as the opacity is approximately that of a fully ionized gas, i.e. for $T>0.7~\rm eV$, $t<14(R/10^{13.5}{\rm cm})^{0.55}~\rm d$. The suppression of $L$ at $t_{\rm tr}/a$ obtained for standard polytropic envelopes may account for the first optical peak of double-peaked SN light curves, with first peak at a few days for $M_{\rm env}<1M_\odot$.