The light echo systems of historical supernovae in the Milky Way and local group galaxies provide an unprecedented opportunity to reveal the effects of asymmetry on observables, particularly optical spectra. Scattering dust at different locations on the light echo ellipsoid witnesses the supernova from different perspectives and the light consequently scattered towards Earth preserves the shape of line profile variations introduced by asymmetries in the supernova photosphere. However, the interpretation of supernova light echo spectra to date has not involved a detailed consideration of the effects of outburst duration and geometrical scattering modifications due to finite scattering dust filament dimension, inclination, and image point-spread function and spectrograph slit width. In this paper, we explore the implications of these factors and present a framework for future resolved supernova light echo spectra interpretation, and test it against Cas A and SN 1987A light echo spectra. We conclude that the full modeling of the dimensions and orientation of the scattering dust using the observed light echoes at two or more epochs is critical for the correct interpretation of light echo spectra. Indeed, without doing so one might falsely conclude that differences exist when none are actually present.
Download