Early spectrum and bolometric corrections for SN 1987A

In order to relate the visual magnitudes observed at early times for SN 1987A with the theoretical luminosities obtained from supernova models, it is necessary to know the bolometric corrections for the just-exploded star. In this paper we develop an analytic model to derive the continuum spectrum and thence the absolute bolometric magnitudes and the bolometric corrections of SN 1987A in the first 2 days after the explosion, i.e., up until the time that the full spectrum was measured. We integrate the equation of radiative transfer over realistic envelope profiles given by computer outputs by deriving an analytical relation between optical depth, density, and temperature and by extending the Milne-Schwarzschild type of solution to the case of spherical geometry; in order to account for the strong dominance of scattering over absorption in the early atmosphere due to the high degree of ionization of hydrogen and helium, we calculate self-consistently the nonthermal source function with an interative procedure. We can in this way describe both the extended nature of the envelope and the non-LTE state of the radiation field, which both cause a dilution of the emerging flux and thence yield an effective temperature lower than the color temperature. The explicit results we obtain for Woosley's model 10H at t = 0.5 days show indeed a significant deviation from the simple "blackbody approximation" used so far: the calculated spectrum has a net excess of higher frequency emission when compared with blackbody, and the total luminosity is much lower than in the thermal case. The precise values for the magnitudes derived from this depend on the absorptive processes, here represented by the Doppler-enhanced line opacity due to the metals in the rapidly expanding atmosphere. With a physically reasonable estimate of these effects, we get for the visual brightness a value which is about half a magnitude fainter than the one calculated so far using a sharp photosphere, blackbody sources, and "static" line opacities and which, unlike the previous one, fits the observations quite well. Yet we point out that this alone is not enough to single out Woosley's model 10H as the right model for SN 1987A.