Stars in the Local Galactic Thick Disk and Halo in Gaia EDR3: A
  catalogue of Half a Million Local Main-sequence Stars with Photometric
  Metallicities
  We present a catalogue of 551,214 main-sequence stars in the local ($d < 2$
kpc) Galactic thick disk and halo, based on a search of stars with large proper
motions ($\mu_{\mathrm{tot}} > 40.0$ mas/yr) in the Gaia Early Data Release 3.
We derive photometric metallicity calibrated from the
colour-luminosity-metallicity distribution of 20,047 stars with spectroscopic
metallicities, collected from various spectroscopic surveys, including SDSS
SEGUE/APOGEE, GALAH DR3, and LAMOST DR6. We combine these results to construct
an empirical colour-magnitude-metallicity grid, which can be used to estimate
photometric metallicities for low-mass metal-poor stars of K and M subtypes
from their absolute $G$ magnitude and colour values. We find that low-mass,
high-velocity stars in our catalogue share similar kinematics as reported in
recent studies of more luminous Galactic halo stars. The pseudo-kinematic
analysis of our sample recovers the main local halo structures, including the
Gaia-Enceladus Stream and the Helmi stream; aside from these the local halo
stars appear to show a remarkably smooth distribution in velocity space. Since
the future Gaia data release will provide radial velocity measurements for only
a small number of our sample, our catalogue provides targets of high interest
for the future spectroscopic observation programs like SDSS-V, DESI MW survey,
WEAVE, and/or 4MOST.
