Measuring type Ia supernova distances and redshifts from their multi-band light curves

The distance and redshift of a type Ia supernova can be determined simultaneously through its multi-band light curves. This fact may be used for imaging surveys that discover and obtain photometry for large numbers of supernovae; so many that it would be difficult to obtain a spectroscopic redshift for each. Using available supernova-analysis tools we find that there are several conditions in which a viable distance–redshift can be determined. Uncertainties in the effective distance at z∼0.3z∼0.3 are dominated by redshift uncertainties coupled with the steepness of the Hubble law. By z∼0.5z∼0.5 the Hubble law flattens out and distance modulus uncertainties dominate. Observations that give S/N=50 at peak brightness and a four-day observer cadence in each of griz  -bands are necessary to match the intrinsic supernova magnitude dispersion out to z=1.0z=1.0. Lower S/NS/N can be tolerated with the addition of redshift priors (e.g. from a host-galaxy photometric redshift), observations in an additional redder band, or by focusing on supernova redshifts that have particular leverage for this measurement. More stringent S/NS/N requirements are anticipated as improved systematics control over intrinsic color, metallicity, and dust is attempted to be drawn from light curves.