2003ApJ...590..944W

We show empirically that fits to the color-magnitude relation of Type Ia supernovae (SNe Ia) after optical maximum can provide accurate relative extragalactic distances. We report the discovery of an empirical color relation for SN Ia light curves: during much of the first month past maximum, the magnitudes of SNe Ia defined at a given value of color index have a very small magnitude dispersion; moreover, during this period the relation between B magnitude and B-V color (or B-R or B-I color) is strikingly linear, to the accuracy of existing well-measured data. These linear relations can provide robust distance estimates, in particular, by using the magnitudes when the SN reaches a given color. After correction for light-curve stretch factor or decline rate, the dispersion of the magnitudes taken at the intercept of the linear color-magnitude relation is found to be around 0.08 mag for the subsample of SNe with (B_max-V_max)≤0.05 mag and around 0.11 mag for the subsample with (B_max-V_max)≤0.2 mag. This small dispersion is consistent with being mostly due to observational errors. The method presented here and the conventional light-curve fitting methods can be combined to further improve statistical dispersions of distance estimates. It can be combined with the magnitude at maximum to deduce dust extinction. The slopes of the color-magnitude relation may also be used to identify intrinsically different SN Ia systems. The method provides a tool that is fundamental to using SNe Ia to estimate cosmological parameters such as the Hubble constant and the mass and dark energy content of the universe.