The first-year shear catalog of the Subaru Hyper Suprime-Cam SSP Survey
  We present and characterize the catalog of galaxy shape measurements that
will be used for cosmological weak lensing measurements in the Wide layer of
the first year of the Hyper Suprime-Cam (HSC) survey. The catalog covers an
area of 136.9 deg$^2$ split into six fields, with a mean $i$-band seeing of
$0.58$ arcsec and $5\sigma$ point-source depth of $i\sim 26$. Given
conservative galaxy selection criteria for first year science, the depth and
excellent image quality results in unweighted and weighted source number
densities of 24.6 and 21.8 arcmin$^{-2}$, respectively. We define the
requirements for cosmological weak lensing science with this catalog, then
focus on characterizing potential systematics in the catalog using a series of
internal null tests for problems with point-spread function (PSF) modeling,
shear estimation, and other aspects of the image processing. We find that the
PSF models narrowly meet requirements for weak lensing science with this
catalog, with fractional PSF model size residuals of approximately $0.003$
(requirement: 0.004) and the PSF model shape correlation function
$\rho_1<3\times 10^{-7}$ (requirement: $4\times 10^{-7}$) at 0.5$^\circ$
scales. A variety of galaxy shape-related null tests are statistically
consistent with zero, but star-galaxy shape correlations reveal additive
systematics on $>1^\circ$ scales that are sufficiently large as to require
mitigation in cosmic shear measurements. Finally, we discuss the dominant
systematics and the planned algorithmic changes to reduce them in future data
reductions.
