Photometric Metallicity Calibration with SDSS and SCUSS and its
  Application to distant stars in the South Galactic Cap
  Based on SDSS g, r and SCUSS (South Galactic Cap of u-band Sky Survey) $u$
photometry, we develop a photometric calibration for estimating the stellar
metallicity from $u-g$ and $g-r$ colors by using the SDSS spectra of 32,542 F-
and G-type main sequence stars, which cover almost $3700$ deg$^{2}$ in the
south Galactic cap. The rms scatter of the photometric metallicity residuals
relative to spectrum-based metallicity is $0.14$ dex when $g-r<0.4$, and $0.16$
dex when $g-r>0.4$. Due to the deeper and more accurate magnitude of SCUSS $u$
band, the estimate can be used up to the faint magnitude of $g=21$. This
application range of photometric metallicity calibration is wide enough so that
it can be used to study metallicity distribution of distant stars. In this
study, we select the Sagittarius (Sgr) stream and its neighboring field halo
stars in south Galactic cap to study their metallicity distribution. We find
that the Sgr stream at the cylindrical Galactocentric coordinate of $R\sim 19$
kpc, $\left| z\right| \sim 14$ kpc exhibits a relative rich metallicity
distribution, and the neighboring field halo stars in our studied fields can be
modeled by two-Gaussian model, with peaks respectively at [Fe/H]$=-1.9$ and
[Fe/H]$=-1.5$.
