Mapping the Milky Way with LAMOST I: Method and overview
  We present a statistical method to derive the stellar density profiles of the
Milky Way from spectroscopic survey data, taking into account selection
effects. We assume that the selection function of the spectroscopic survey is
based on photometric colors and magnitudes and possibly altered during
observations and data reductions. Then the underlying selection function for a
line-of-sight can be well recovered by comparing the distribution of the
spectroscopic stars in a color-magnitude plane with that of the photometric
dataset. Subsequently, the stellar density profile along a line-of-sight can be
derived from the spectroscopically measured stellar density profile multiplied
by the selection function. The method is validated using Galaxia mock data with
two different selection functions. We demonstrate that the derived stellar
density profiles well reconstruct the true ones not only for the full targets,
but also for the sub-populations selected from the full dataset. Finally, the
method is applied to map the density profiles for the Galactic disk and halo,
respectively, using the LAMOST RGB stars. The Galactic disk extends to about
R=19 kpc, where the disk still contributes about 10% to the total stellar
surface density. Beyond this radius, the disk smoothly transitions to the halo
without any truncation, bending, or broken. Moreover, no over-density
corresponding to the Monoceros ring is found in the Galactic anti-center
direction. The disk shows moderate north-south asymmetry at radii larger than
12 kpc. On the other hand, the R-Z tomographic map directly shows that the
stellar halo is substantially oblate within a Galactocentric radius of 20 kpc
and gradually becomes nearly spherical beyond 30 kpc.
