  Wide field surveys will soon be discovering Type Ia supernovae (SNe) at rates
of several thousand per year. Spectroscopic follow-up can only scratch the
surface for such enormous samples, so these extensive data sets will only be
useful to the extent that they can be characterized by the survey photometry
alone. In a companion paper (Rodney and Tonry, 2009) we introduced the SOFT
method for analyzing SNe using direct comparison to template light curves, and
demonstrated its application for photometric SN classification. In this work we
extend the SOFT method to derive estimates of redshift and luminosity distance
for Type Ia SNe, using light curves from the SDSS and SNLS surveys as a
validation set. Redshifts determined by SOFT using light curves alone are
consistent with spectroscopic redshifts, showing a root-mean-square scatter in
the residuals of RMS_z=0.051. SOFT can also derive simultaneous redshift and
distance estimates, yielding results that are consistent with the currently
favored Lambda-CDM cosmological model. When SOFT is given spectroscopic
information for SN classification and redshift priors, the RMS scatter in
Hubble diagram residuals is 0.18 mags for the SDSS data and 0.28 mags for the
SNLS objects. Without access to any spectroscopic information, and even without
any redshift priors from host galaxy photometry, SOFT can still measure
reliable redshifts and distances, with an increase in the Hubble residuals to
0.37 mags for the combined SDSS and SNLS data set. Using Monte Carlo
simulations we predict that SOFT will be able to improve constraints on
time-variable dark energy models by a factor of 2-3 with each new generation of
large-scale SN surveys.
