Type Ia supernova parameter estimation: a comparison of two approaches using current datasets

TL;DR

This paper compares traditional  and likelihood methods for estimating parameters of Type Ia supernovae using SDSS data, highlighting the importance of the likelihood approach for more restrictive constraints.

Contribution

It demonstrates the differences between  and likelihood methods in supernova parameter estimation and emphasizes the advantages of the likelihood approach with current datasets.

Findings

Likelihood approach yields more restrictive parameter constraints.

Differences between methods are more significant with MLCS2k2 fitter.

Current data shows small differences in best fit values between methods.

Abstract

By using the Sloan Digital Sky Survey (SDSS) first year type Ia supernova (SN Ia) compilation, we compare two different approaches (traditional \chi^2 and complete likelihood) to determine parameter constraints when the magnitude dispersion is to be estimated as well. We consider cosmological constant + Cold Dark Matter (\Lambda CDM) and spatially flat, constant w Dark Energy + Cold Dark Matter (FwCDM) cosmological models and show that, for current data, there is a small difference in the best fit values and $\sim$ 30% difference in confidence contour areas in case the MLCS2k2 light-curve fitter is adopted. For the SALT2 light-curve fitter the differences are less significant ($\lesssim$ 13% difference in areas). In both cases the likelihood approach gives more restrictive constraints. We argue for the importance of using the complete likelihood instead of the \chi^2 approach when dealing with parameters in the expression for the variance.