Stellar loci IV. Red giant stars
  In the fourth paper of this series, we present the metallicity-dependent
Sloan Digital Sky Survey (SDSS) stellar color loci of red giant stars, using a
spectroscopic sample of red giants in the SDSS Stripe 82 region. The stars span
a range of 0.55 -- 1.2 mag in color g-i, -0.3 -- -2.5 in metallicity [Fe/H],
and have values of surface gravity log g smaller than 3.5 dex. As in the case
of main-sequence (MS) stars, the intrinsic widths of loci of red giants are
also found to be quite narrow, a few mmag at maximum. There are however
systematic differences between the metallicity-dependent stellar loci of red
giants and MS stars. The colors of red giants are less sensitive to metallicity
than those of MS stars. With good photometry, photometric metallicities of red
giants can be reliably determined by fitting the u-g, g-r, r-i, and i-z colors
simultaneously to an accuracy of 0.2 -- 0.25 dex, comparable to the precision
achievable with low-resolution spectroscopy for a signal-to-noise ratio of 10.
By comparing fitting results to the stellar loci of red giants and MS stars, we
propose a new technique to discriminate between red giants and MS stars based
on the SDSS photometry. The technique achieves completeness of ~ 70 per cent
and efficiency of ~ 80 per cent in selecting metal-poor red giant stars of
[Fe/H] $\le$ -1.2. It thus provides an important tool to probe the structure
and assemblage history of the Galactic halo using red giant stars.
