A Monte-Carlo Method for Estimating Stellar Photometric Metallicity
  Distributions
  Based on the Sloan Digital Sky Survey (SDSS), we develop a new monte-carlo
based method to estimate the photometric metallicity distribution function
(MDF) for stars in the Milky Way. Compared with other photometric calibration
methods, this method enables a more reliable determination of the MDF, in
particular at the metal-poor and metal-rich ends. We present a comparison of
our new method with a previous polynomial-based approach, and demonstrate its
superiority. As an example, we apply this method to main-sequence stars with
$0.2<g-r<0.6$, $6$ kpc$<R<9$ kpc, and in different intervals in height above
the plane, $|Z|$. The MDFs for the selected stars within two relatively local
intervals ($0.8$ kpc$<|Z|<1.2$ kpc, $1.5$ kpc$<|Z|<2.5$ kpc) can be well-fit by
two Gaussians, with peaks at [Fe/H] $\approx-0.6$ and $-1.2$ respectively, one
associated with the disk system, the other with the halo. The MDFs for the
selected stars within two more distant intervals ($3$ kpc$<|Z|<5$ kpc, $6$
kpc$<|Z|<9$ kpc) can be decomposed into three Gaussians, with peaks at [Fe/H]
$\approx-0.6$, $-1.4$ and $-1.9$ respectively, where the two lower peaks may
provide evidence for a two-component model of the halo: the inner halo and the
outer halo. The number ratio between the disk component and halo component(s)
decreases with vertical distance from the Galactic plane, consistent with the
previous literature.
