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.