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 3-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. 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 chi2 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 the bias on the dark energy equation of state parameter $w$ is negligible. However, incorrect model uncertainties can lead to a significant bias on the distance moduli, with up to ~0.05 mag redshift-dependent variation. 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. However, this uncertainty depends on the samples used, and thus this small $w$-uncertainty is not guaranteed in future cosmology results.