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.
