Searching for light echoes due to circumstellar matter in SNe Ia spectra

We present an analytical model for light echoes (LEs) coming from circumstellar material (CSM) around Type Ia Supernovae (SNe Ia). Using this model we find two spectral signatures at 4100 Å and 6200 Å that are useful to identify LEs during the Lira law phase (between 35 and 80 days after maximum light) coming from nearby CSM at distances of 0.01–0.25 pc. We analyze a sample of 89 SNe Ia divided into two groups according to their $B-V$ decline rate during the Lira law phase, and search for LEs from CSM interaction in the group of SNe with steeper slopes by comparing their spectra with our LE model. We find that a model with LEs + pure extinction from interstellar material (ISM) fits the observed spectra better than a pure ISM extinction model that is constant in time, but we find that a decreasing extinction alone explains the observations better without the need of LEs, possibly implying dust sublimation due to the radiation from the SN.