Semianalytic continuum spectra of Type 2 supernovae
We extend the approximate radiative transfer analysis of Hershkowitz, Linder, & Wagoner (1986) to a more general class of supernova model atmospheres, using a simple fit to the effective continuum opacity produced by lines (Wagoner, Perez, & Vasu 1991). At the low densities considered, the populations of the excited states of hydrogen are governed mainly by photoionization and recombination, and scattering dominates absorptive opacity. We match the asymptotic expressions for the spectral energy density J(sub nu) at the photosphere, whose location at each frequency is determined by a first-order calculation of the deviation of J(sub nu) from the Planck function B(sub nu). The emergent spectral luminosity then assumes the form L(sub nu) = 4 pi(squared)r(squared)(sub *) zeta(squared)B(sub nu)(T(sub p)), where T(sub p)(nu) is the photospheric temperature zeta is the dilution factor, and r(sub *) is a fiducial radius (ultimately taken to be the photospheric radius r(sub p)(nu)). The atmosphere is characterized by an effective temperature T(sub e) (varies as L(sup 1/4)r(sup -1/2)(sub *)) and hydrogen density n(sub H) = dependence of zeta on frequency nu and the parameters T(sub p), r(sub p), and alpha. The resulting understanding of the dependence of the spectral luminosity on observable parameters which characterize the relevant physical conditions will be of particular use in assessing the reliability of the expanding photosphere method of distance determination. This is particularly important at cosmological distances, where no information about the progenitor star will be available. This technique can also be applied to other low-density photosphere.