Based on Sloan Digital Sky Survey ( SDSS ) photometric data , Gu developed a new Monte-Carlo-based method for estimating the stellar metallicity distribution functions ( MDFs ) .
This method enables a more reliable determination of MDFs compared with the conventional polynomial-based methods .
In this work , MDF determined from the method are well fit by three-Gaussian model , with peaks at { [ Fe / H ] } = -0.68 , -1.38 , and -1.90 , associated with the thick disk , inner halo , and outer halo , respectively .
The vertical metallicity gradient within 1 < Z < 5 { kpc } is { d } \langle { [ Fe / H ] } \rangle / { d } Z \approx - 0.19 { dex } \cdot { kpc } % ^ { -1 } around R = 8.25 { kpc } .
But the mean radial gradient is almost negligible .
The density profile of the thick disk is fitted with modified double exponential law decaying to a constant at far distance .
The scale height and scale length thus estimated are H \approx 1.13 { kpc } and L \approx 3.63 { kpc } , which are in consistent with the results determined from star-counts method in previous studies .
The halos are described with two-axial power-law ellipsoid and the axis ratios of both inner halo and outer halo , inferred from stellar number density in R - Z plane , are q _ { ih } \approx 0.49 and q _ { oh } \approx 0.61 , respectively .
It also manifests that the outer halo is a more spherical than inner halo .
Moreover , the halo power-law indices estimated are n _ { ih } \approx 3.4 and n _ { oh } \approx 3.1 , indicating that the stellar number density of inner halo changes more steeper than that of outer halo .