A metric space for Type Ia supernova spectra: a new method to assess explosion scenarios

Over the past years, Type Ia supernovae (SNe Ia) have become a major tool to determine the expansion history of the Universe, and considerable attention has been given to, both, observations and models of these events. However, until now, their progenitors are not known. The observed diversity of light curves and spectra seems to point at different progenitor channels and explosion mechanisms. Here, we present a new way to compare model predictions with observations in a systematic way. Our method is based on the construction of a metric space for SN Ia spectra by means of linear principal component analysis, taking care of missing and/or noisy data, and making use of partial least-squares regression to find correlations between spectral properties and photometric data. We investigate realizations of the three major classes of explosion models that are presently discussed: delayed-detonation Chandrasekhar-mass explosions, sub-Chandrasekhar-mass detonations and double-degenerate mergers, and compare them with data. We show that in the principal component space, all scenarios have observed counterparts, supporting the idea that different progenitors are likely. However, all classes of models face problems in reproducing the observed correlations between spectral properties and light curves and colours. Possible reasons are briefly discussed.