Estimation of Galactic model parameters with the SDSS and metallicity distribution in two fields in the anti-centre direction of the Galaxy

We estimated the Galactic model parameters from the SDSS data reduced for two fields in the anti-centre direction of the Galaxy, $l= 180^{o}$, and symmetric relative to the Galactic plane, $b=+45^{o}$ and $b=-45^{o}$. The large size of each field, 60 deg$^{2}$, and the faint limiting apparent magnitude, g=22, give us the chance to determine reliable parameters for three components, thin and thick discs and halo, in the north and south hemispheres of the Galaxy, except the scalelengths for two discs which are adopted from Juri\'c et al. (2005). Metallicities were evaluated by a recent calibration for SDSS, and absolute magnitudes of stars with $4<M(g)\leq8$ were derived as a function of (g-r) colour and metallicity. Conspicuous differences could not be detected between the corresponding Galactic model parameters for the thin disc of north and south fields, and our results are consistent with the ones in the literature. The same case is valid for the halo, especially the axis ratios for two fields are exactly equal, $\kappa=0.45$. The metallicity distribution for unevolved G type stars with $5<M(g)\leq6$ shows three substructures relative to the distance from the Galactic plane: for $z^{*}<3$ kpc, the metallicity gradient for two fields is $d[M/H]/dz \sim -0.20(\pm0.02)$ dex kpc$^{-1}$, consistent with the formation scenario of the thin disc. For $5<z^{*}<10$ kpc, $d[M/H]/dz \sim -0.03(\pm0.001)$ dex kpc$^{-1}$ for two fields, confirming that the metallicity gradient for the halo component is close to zero. When we combine these substructures, however, we find a smooth metallicity gradient for two fields, $-0.30(\pm0.04)$ dex kpc$^{-1}$.