Selecting M-giants with infra-red photometry: Distances, metallicities
  and the Sagittarius stream
  Using a spectroscopically confirmed sample of M-giants, M-dwarfs and quasars
from the LAMOST survey, we assess how well WISE $\&$ 2MASS color-cuts can be
used to select M-giant stars. The WISE bands are very efficient at separating
M-giants from M-dwarfs and we present a simple classification that can produce
a clean and relatively complete sample of M-giants. We derive a new photometric
relation to estimate the metallicity for M-giants, calibrated using data from
the APOGEE survey. We find a strong correlation between the $(W1-W2)$ color and
$\rm [M/H]$, where almost all of the scatter is due to photometric
uncertainties. We show that previous photometric distance relations, which are
mostly based on stellar models, may be biased and devise a new empirical
distance relation, investigating trends with metallicity and star formation
history. Given these relations, we investigate the properties of M-giants in
the Sagittarius stream. The offset in the orbital plane between the leading and
trailing tails is reproduced and, by identifying distant M-giants in the
direction of the Galactic anti-center, we confirm that the previously detected
debris in the outer halo is the apocenter of the trailing tail. We also find
tentative evidence supporting an existing overdensity near the leading tail in
the Northern Galactic hemisphere, possibly an extension to the trailing tail
(so-called Branch C). We have measured the metallicity distribution along the
stream, finding a clear metallicity offset between the leading and trailing
tails, in agreement with models for the stream formation. We include an online
table of M-giants to facilitate further studies.
