Shock cooling emission from explosions of red super-giants: II. An analytic model of deviations from blackbody emission

Light emission in the first hours and days following core-collapse supernovae (SNe) is dominated by the escape of photons from the expanding shock heated envelope. In a preceding paper, Paper I, we provided a simple analytic description of the time dependent luminosity, $L$, and color temperature, $T_{\rm col}$, valid up to H recombination ($T\approx0.7$ eV), for explosions of red supergiants with convective polytropic envelopes without significant circum-stellar medium (CSM). The analytic description was calibrated against "gray" (frequency-independent) photon diffusion numeric calculations. Here we present the results of a large set of 1D multi-group (frequency-dependent) calculations, for a wide range of progenitor parameters (mass, radius, core/envelope mass ratios, metalicity) and explosion energies, using opacity tables that we constructed (and made publicly available), including the contributions of bound-bound and bound-free transitions. We provide an analytic description of the small, $\simeq10\%$ deviations of the spectrum from blackbody at low frequencies, $hν< 3T_{\rm col}$, and an improved (over Paper I) description of `line dampening' for $hν> 3T_{\rm col}$. We show that the effects of deviations from initial polytropic density distribution are small, and so are the effects of `expansion opacity' and deviations from LTE ionization and excitation (within our model assumptions). A recent study of a large set of type II SN observations finds that our model accounts well for the early multi-band data of more than 50\% of observed SNe (the others are likely affected by thick CSM), enabling the inference of progenitor properties, explosion velocity, and relative extinction.