2024ApJ...970..119P

Light echoes give us a unique perspective on the nature of supernovae and nonterminal stellar explosions. Spectroscopy of light echoes can reveal details on the kinematics of the ejecta, probe asymmetry, and reveal details of ejecta interaction with circumstellar matter, thus expanding our understanding of these transient events. However, the spectral features arise from a complex interplay between the source photons, the reflecting dust geometry, and the instrumental setup and observing conditions. In this work, we present an improved method for modeling these effects in light echo spectra, one that relaxes the simplifying assumption of a light-curve-weighted sum, and instead estimates the true relative contribution of each phase of a transient event to the observed spectrum. We discuss our logic, the gains we obtain over light echo analysis methods used in the past, and prospects for further improvements. Lastly, we show how the new method improves our analysis of echoes from Tycho's supernova (SN 1572) as an example.