A Model-Independent Photometric Redshift Estimator for Type Ia   Supernovae
  The use of type Ia supernovae (SNe Ia) as cosmological standard candles is fundamental in modern observational cosmology. In this letter, we derive a simple empirical photometric redshift estimator for SNe Ia using a training set of SNe Ia with multiband ($griz$) light-curves and spectroscopic redshifts obtained by the Supernova Legacy Survey (SNLS). This estimator is analytical and model-independent; it does not use spectral templates. We use all the available SNe Ia from SNLS with near maximum photometry in $griz$ (a total of 40 SNe Ia) to train and test our photometric redshift estimator. The difference between the estimated redshifts $z_{phot}$ and the spectroscopic redshifts $z_{spec}$, $(z_{phot}-z_{spec})/(1+z_{spec})$, has rms dispersions of 0.031 for 20 SNe Ia used in the training set, and 0.050 for 20 SNe Ia not used in the training set. The dispersion is of the same order of magnitude as the flux uncertainties at peak brightness for the SNe Ia. There are no outlyers.   This photometric redshift estimator should significantly enhance the ability of observers to accurately target high redshift SNe Ia for spectroscopy in ongoing surveys. It will also dramatically boost the cosmological impact of very large future supernova surveys, such as those planned for Advanced Liquid-mirror Probe for Astrophysics, Cosmology and Asteroids (ALPACA), and the Large Synoptic Survey Telescope (LSST). 
Yun Wang