SNEMO: Improved Empirical Models for Type Ia Supernovae.

Type Ia supernova cosmology depends on the ability to fit and standardize observations of supernova magnitudes with an empirical model. We present here a series of new models of Type Ia Supernova spectral time series that capture a greater amount of supernova diversity than possible with the models that are currently customary. These are entitled SuperNova Empirical MOdels (\textsc{SNEMO}\footnote{https://snfactory.lbl.gov/snemo}). The models are constructed using spectrophotometric time series from $172$ individual supernovae from the Nearby Supernova Factory, comprising more than $2000$ spectra. Using the available observations, Gaussian Processes are used to predict a full spectral time series for each supernova. A matrix is constructed from the spectral time series of all the supernovae, and Expectation Maximization Factor Analysis is used to calculate the principal components of the data. K-fold cross-validation then determines the selection of model parameters and accounts for color variation in the data. Based on this process, the final models are trained on supernovae that have been dereddened using the Fitzpatrick and Massa extinction relation. Three final models are presented here: \textsc{SNEMO2}, a two-component model for comparison with current Type~Ia models; \textsc{SNEMO7}, a seven component model chosen for standardizing supernova magnitudes which results in a total dispersion of $0.100$~mag for a validation set of supernovae, of which $0.087$~mag is unexplained (a total dispersion of $0.113$~mag with unexplained dispersion of $0.097$~mag is found for the total set of training and validation supernovae); and \textsc{SNEMO15}, a comprehensive $15$ component model that maximizes the amount of spectral time series behavior captured.