A More General Model for the Intrinsic Scatter in Type Ia Supernova Distance Moduli

Understand

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.

• The new formalism describes the intrinsic scatter in Type Ia supernovae 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 $\alpha=0.135_{-.017}^{+.033}$ and $\beta=3.19_{-0.24}^{+0.14}$, 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 Type Ia supernovae than is conventional, resulting in a larger value of $\beta$ and a larger uncertainty than the conventional approach.