A metric space for Type Ia supernova 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 5972Å/Si ii 6355Å and the line velocity of S ii 5640Å/Si ii 6355Å) 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 colors and SALT2 parameters c and x 1 . 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.

SUGAR: An improved empirical model of Type Ia supernovae based on spectral features

“…In this new basis, the variables are uncorrelated, and an approximation of the input data is found by neglecting the dimensions corresponding to the smallest eigenvalues. This method has been employed in the case of SNe Ia by Guy et al (2007), Kim et al (2013), andSasdelli et al (2015). However, in the case considered here, some directions are dominated by noise, so their eigenvectors would align along the direction of measurement errors rather than the intrinsic sample variance.…”

Optimal Classification and Outlier Detection for Stripped-envelope Core-collapse Supernovae

“…PCA is a dimensionality reduction algorithm that linearly transforms data in order to capture as much information as possible in the smallest number of transformed features, called principal components (PC's). PCA has been previously applied to attempt to understand the diversity of SNe Ia subtypes (Cormier & Davis 2011;Sasdelli et al 2014) and nebular phase superluminous supernovae (Nicholl et al 2019), but this is the first application of PCA to SESNe in the photospheric phase. After applying a PCA decomposition to our SESNe spectral dataset, we use a multi-class linear SVM, a supervised learning method, to classify our SNe.…”

Photometric supernovae redshift systematics requirements

“…However, even with current samples systematics contribute at least equally to statistical uncertainty in the cosmological use of SN Ia. These systematics can be addressed through careful characterization of the supernova properties, through enhanced wavelength coverage into the infrared [10,11] and ultraviolet [12,13], and in particular spectroscopic data [14][15][16]. Spectroscopy not only confirms the source to be a true SN Ia but also give subtyping, e.g.…”