Dark Energy Survey Year 1 Results: Redshift distributions of the weak
  lensing source galaxies
  We describe the derivation and validation of redshift distribution estimates
and their uncertainties for the galaxies used as weak lensing sources in the
Dark Energy Survey (DES) Year 1 cosmological analyses. The Bayesian Photometric
Redshift (BPZ) code is used to assign galaxies to four redshift bins between
z=0.2 and 1.3, and to produce initial estimates of the lensing-weighted
redshift distributions $n^i_{PZ}(z)$ for bin i. Accurate determination of
cosmological parameters depends critically on knowledge of $n^i$ but is
insensitive to bin assignments or redshift errors for individual galaxies. The
cosmological analyses allow for shifts $n^i(z)=n^i_{PZ}(z-\Delta z^i)$ to
correct the mean redshift of $n^i(z)$ for biases in $n^i_{\rm PZ}$. The $\Delta
z^i$ are constrained by comparison of independently estimated 30-band
photometric redshifts of galaxies in the COSMOS field to BPZ estimates made
from the DES griz fluxes, for a sample matched in fluxes, pre-seeing size, and
lensing weight to the DES weak-lensing sources. In companion papers, the
$\Delta z^i$ are further constrained by the angular clustering of the source
galaxies around red galaxies with secure photometric redshifts at 0.15<z<0.9.
This paper details the BPZ and COSMOS procedures, and demonstrates that the
cosmological inference is insensitive to details of the $n^i(z)$ beyond the
choice of $\Delta z^i$. The clustering and COSMOS validation methods produce
consistent estimates of $\Delta z^i$, with combined uncertainties of
$\sigma_{\Delta z^i}=$0.015, 0.013, 0.011, and 0.022 in the four bins. We
marginalize over these in all analyses to follow, which does not diminish the
constraining power significantly. Repeating the photo-z procedure using the
Directional Neighborhood Fitting (DNF) algorithm instead of BPZ, or using the
$n^i(z)$ directly estimated from COSMOS, yields no discernible difference in
cosmological inferences.
