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~0.3 are dominated by redshift
uncertainties coupled with the steepness of the Hubble law. By z~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=1.0. Lower S/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/N requirements are anticipated
as improved systematics control over intrinsic color, metallicity, and dust is
attempted to be drawn from light curves.Comment: 16 pages, 4 figures, Astroparticle Physics, accepte
