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Supernova Resonance--scattering Line Profiles in the Absence of a Photosphere

In supernova spectroscopy relatively little attention has been given to the properties of optically thick spectral lines in epochs following the photosphere's recession. Most treatments and analyses of post-photospheric optical spectra of supernovae assume that forbidden-line emission comprises most if not all spectral features. However, evidence exists which suggests that some spectra exhibit line profiles formed via optically thick resonance-scattering even months or years after the supernova explosion. To explore this possibility we present a geometrical approach to supernova spectrum formation based on the "Elementary Supernova" model, wherein we investigate the characteristics of resonance-scattering in optically thick lines while replacing the photosphere with a transparent central core emitting non-blackbody continuum radiation, akin to the optical continuum provided by decaying 56Co formed during the explosion. We develop the mathematical framework necessary for solving the radiative transfer equation under these conditions, and calculate spectra for both isolated and blended lines. Our comparisons with analogous results from the Elementary Supernova code SYNOW reveal several marked differences in line formation. Most notably, resonance lines in these conditions form P Cygni-like profiles, but the emission peaks and absorption troughs shift redward and blueward, respectively, from the line's rest wavelength by a significant amount, despite the spherically symmetric distribution of the line optical depth in the ejecta. These properties and others that we find in this work could lead to misidentification of lines or misattribution of properties of line-forming material at post-photospheric times in supernova optical spectra.