We estimated the Galactic model parameters from the Sloan Digital Sky Survey ( 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 } ( north field ) and b = -45 ^ { o } ( south field ) .
The large size of each field , 60 deg ^ { 2 } , and the faint limiting apparent magnitude , g _ { 0 } = 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 Jurić et al .
( [ 2005 ] ) .
Metallicities were evaluated by a recent calibration for SDSS , and absolute magnitudes of stars with 4 < M ( g ) \leq 8 were derived as a function of ( g - r ) _ { 0 } colour and metallicity .
A \chi ^ { 2 } method was employed to fit the analytical density laws to the observational-based space densities with the addition constraint of producing local densities consistent with those derived from Hipparcos .
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 , and close to the one of Jurić et al .
( 2005 ) .
However , we revealed differences between the scaleheights and local space densities for the thick disc of the north and south fields .
The metallicity distribution for unevolved G type stars with 5 < M ( g ) \leq 6 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 ( \pm 0.02 ) dex kpc ^ { -1 } , consistent with the formation scenario of the thin disc .
For 5 < z ^ { * } < 10 kpc , d [ M / H ] / dz \sim - 0.03 ( \pm 0.001 ) dex kpc ^ { -1 } for two fields , confirming that the metallicity gradient for the halo component is close to zero .
However , the tendency of the metallicity for stars with 3 < z ^ { * } < 5 kpc , corresponding to the transition region from thick disc to halo is different .
For the north field d [ M / H ] / dz = -0.36 ( \pm 0.12 ) dex kpc ^ { -1 } , whereas it is half of this value for the south field , d [ M / H ] / dz = -0.18 ( \pm 0.01 ) dex kpc ^ { -1 } .
The origin of this conflict is probably due to the different structure of the thick disc in opposite latitudes of the Galaxy .
When we combine these substructures , however , we find a smooth metallicity gradient for two fields , -0.30 ( \pm 0.04 ) dex kpc ^ { -1 } .