Testing Models of Intrinsic Brightness Variations in Type Ia Supernovae, and their Impact on Measuring Cosmological Parameters

For spectroscopically confirmed Type Ia supernovae we evaluate models of intrinsic brightness variations with detailed data/Monte Carlo comparisons of the dispersion in the following quantities: Hubble-diagram scatter, color difference (B – V – c) between the true B – V color and the fitted color (c) from the SALT-II light curve model, and photometric redshift residual. The data sample includes 251 ugriz light curves from the three-season Sloan Digital Sky Survey-II and 191 griz light curves from the Supernova Legacy Survey 3 year data release. We find that the simplest model of a wavelength-independent (coherent) scatter is not adequate, and that to describe the data the intrinsic-scatter model must have wavelength-dependent variations resulting in a ~0.02 mag scatter in B – V – c. Relatively weak constraints are obtained on the nature of intrinsic scatter because a variety of different models can reasonably describe this photometric data sample. We use Monte Carlo simulations to examine the standard approach of adding a coherent-scatter term in quadrature to the distance-modulus uncertainty in order to bring the reduced χ2 to unity when fitting a Hubble diagram. If the light curve fits include model uncertainties with the correct wavelength dependence of the scatter, we find that this approach is valid and that the bias on the dark energy equation-of-state parameter w is much smaller (~0.001) than current systematic uncertainties. However, incorrect model uncertainties can lead to a significant bias on the distance moduli, with up to ~0.05 mag redshift-dependent variation. This bias is roughly reduced in half after applying a Malmquist bias correction. For the recent SNLS3 cosmology results, we estimate that this effect introduces an additional systematic uncertainty on w of ~0.02, well below the total uncertainty. This uncertainty depends on the choice of viable scatter models and the choice of supernova (SN) samples, and thus this small w-uncertainty is not guaranteed in future cosmology results. For example, the w-uncertainty for SDSS+SNLS (dropping the nearby SNe) increases to ~0.04.