A metric space for type Ia supernova spectra

TL;DR

This paper introduces a new PCA-PLS based framework for analyzing Type Ia supernova spectra, enabling better correlation with spectral and photometric features and creating a metric space for comparing synthetic and observed spectra.

Contribution

The study develops a novel PCA-PLS approach that incorporates spectral derivatives and temporal sequences, enhancing spectral grouping and feature correlation in SN Ia analysis.

Findings

PCA effectively groups similar SN Ia spectral features.

PC space contains key spectral indicators like pEW and line velocities.

The method constructs a metric space for comparing synthetic and real spectra.

Abstract

We develop a new framework for use in exploring Type Ia Supernova (SN Ia) spectra. Combining Principal Component Analysis (PCA) and Partial Least Square analysis (PLS) we are able to establish correlations between the Principal Components (PCs) and spectroscopic/photometric SNe Ia features. The technique was applied to ~120 supernova 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 (pEW) of Si II 5972 / Si II 6355 and the line velocity of S II 5640 / Si II 6355) 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 or V magnitudes, B-V color and SALT2 parameters c and x1. The observed colors and magnitudes, that 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.