Analytic Photometric Redshift Estimator for Type Ia Supernovae From the
  Large Synoptic Survey Telescope
  Accurate and precise photometric redshifts (photo-z's) of Type Ia supernovae
(SNe Ia) can enable the use of SNe Ia, measured only with photometry, to probe
cosmology. This dramatically increases the science return of supernova surveys
planned for the Large Synoptic Survey Telescope (LSST). In this paper we
describe a significantly improved version of the simple analytic photo-z
estimator proposed by Wang (2007) and further developed by Wang, Narayan, and
Wood-Vasey (2007). We apply it to 55,422 simulated SNe Ia generated using the
SNANA package with the LSST filters. We find that the estimated errors on the
photo-z's, \sigma_{z_{phot}}/(1+z_{phot}), can be used as filters to produce a
set of photo-z's that have high precision, accuracy, and purity. Using SN Ia
colors as well as SN Ia peak magnitude in the i band, we obtain a set of
photo-z's with 2 percent accuracy (with \sigma(z_{phot}-z_{spec})/(1+z_{spec})
= 0.02), a bias in z_{phot} (the mean of z_{phot}-z_{spec}) of -9 X 10^{-5},
and an outlier fraction (with |(z_{phot}-z_{spec})/(1+z_{spec})|>0.1) of 0.23
percent, with the requirement that \sigma_{z_{phot}}/(1+z_{phot})<0.01. Using
the SN Ia colors only, we obtain a set of photo-z's with similar quality by
requiring that \sigma_{z_{phot}}/(1+z_{phot})<0.007; this leads to a set of
photo-z's with 2 percent accuracy, a bias in z_{phot} of 5.9 X 10^{-4}, and an
outlier fraction of 0.32 percent.
