Constraining the Dimensionality of SN Ia Spectral Variation with Twins

Abstract

SNe Ia continue to play a key role in cosmological measurements. Their interpretation over a range in redshift requires a rest-frame spectral energy distribution model. For practicality, these models are parameterized with a limited number of parameters and are trained using linear or nonlinear dimensionality reduction. This work focuses on the related problem of estimating the number of parameters underlying SN Ia spectral variation (the dimensionality). I present a technique for using the properties of high-dimensional space and the counting statistics of "twin" SNe Ia to estimate this dimensionality. Applying this method to the supernova pairings from Fakhouri et al. (2015) shows that a modest number of parameters (three to five, not including extinction) explain those data well. The analysis also finds that the intrinsic parameters are approximately Gaussian-distributed. The limited number of parameters hints that improved SED models are possible that may enable substantial reductions in SN cosmological uncertainties with current and near-term datasets.

Accepted for publication in ApJ

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• A Probabilistic Autoencoder for Type Ia Supernovae Spectral Time Series
• A Spectroscopic Model of the Type Ia Supernova--Host Galaxy Mass Correlation from SALT3
• Hawai'i Supernova Flows: A Peculiar Velocity Survey Using Over a Thousand Supernovae in the Near-Infrared
• ZTF SN Ia DR2: Improved SN Ia colors through expanded dimensionality with SALT3+