A metric space for Type Ia supernova spectra

Abstract

We develop a new framework for use in exploring Type Ia supernovae (SNe Ia) spectra. Combining principal component analysis (PCA) and partial least square (PLS) analysis we are able to establish correlations between the principal components (PCs) and spectroscopic/photometric SNe Ia features. The technique was applied to ∼120 SN and ∼800 spectra from the Nearby Supernova Factory. The ability of PCA to group together SNe Ia with similar spectral features, already explored in previous studies, is greatly enhanced by two important modifications: (1) the initial data matrix is built using derivatives of spectra over the wavelength, which increases the weight of weak lines and discards extinction, and (2) we extract time evolution information through the use of entire spectral sequences concatenated in each line of the input data matrix. These allow us to define a stable PC parameter space which can be used to characterize synthetic SN Ia spectra by means of real SN features. Using PLS, we demonstrate that the information from important previously known spectral indicators (namely the pseudo-equivalent width of Si ii 5972 Å/Si ii 6355 Å and the line velocity of S ii 5640 Å/Si ii 6355 Å) at a given epoch is contained within the PC space and can be determined through a linear combination of the most important PCs. We also show that the PC space encompasses photometric features like B/V magnitudes, B − V colours and salt2 parameters c and x1. The observed colours and magnitudes, which are heavily affected by extinction, cannot be reconstructed using this technique alone. All the above-mentioned applications allowed us to construct a metric space for comparing synthetic SN Ia spectra with observations.