A more general model for the intrinsic scatter in type Ia supernova distance moduli

We describe a new formalism to fit the parameters {alpha} and {beta} that are used in the SALT2 model to determine the standard magnitudes of Type Ia supernovae (SNe Ia). The new formalism describes the intrinsic scatter in SNe Ia by a covariance matrix in place of the single parameter normally used. We have applied this formalism to the Sloan Digital Sky Survey Supernova Survey (SDSS-II) data and conclude that the data are best described by {alpha} = 0.135{sup +.033} - .017 and {beta} = 3.19{sup +0.14} - 0.24, where the error is dominated by the uncertainty in the form of the intrinsic scatter matrix. Our result depends on the introduction of a more general form for the intrinsic scatter of the distance moduli of SNe Ia than is conventional, resulting in a larger value of {beta} and a larger uncertainty than the conventional approach. Although this analysis results in a larger value of {beta} and a larger error, the SDSS data differ (at a 98% confidence level) from {beta} = 4.1, the value expected for extinction by the type of dust found in the Milky Way. We have modeled the distribution of SNe Ia in terms of their colormore » and conclude that there is strong evidence that variation in color is a significant contributor to the scatter of SNe Ia around their standard candle magnitude.« less