# Constraining the Dimensionality of SN Ia Spectral Variation with Twins

## TL;DR

This paper introduces a new method to estimate the number of parameters needed to describe SN Ia spectral variation, finding that only three to five parameters are sufficient, which could improve cosmological measurements.

## Contribution

The work presents a novel technique using high-dimensional space properties and twin supernovae statistics to estimate spectral variation parameters.

## Key findings

- 3 to 5 parameters explain spectral variation well
- Intrinsic parameters are approximately Gaussian-distributed
- Potential for improved SED models to reduce uncertainties

## 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.