tokens: thick disc was assumed to span from 9 to 11 Gyr. We also checked with an age span of 10–12 Gyr for the thick disc and found that it gives the same best-fitting parameters. The slight decrease in the mean metallicity of the thick disc compared to the estimate based on simply measuring the metallicity of stars within 5 R /kpc 11 and 1 | z |/kpc 2, is due to the inclusion of stars lying between 2 | z |/kpc 3 in the fitting process. This suggests that there is a small vertical gradient in the metallicity of the thick disc as found by others previously (Kordopatis et al. 2011 ; Duong et al. 2018 ). Note, stars in 2 | z |/kpc 3 were not included in the former scheme as they could be contaminated with stars from the metal-poor stellar halo and could suffer from volume incompleteness. However, they are included in the later scheme because it takes both these effects into account. In Fig. 12 we show the mean metallicity as function of Galactocentric radius R for different slices in height | z | for all stars with positive rotation about the Galaxy, which should eliminate star belonging to the halo. Results from APOGEE-DR14 and GALAH DR2c are shown separately. We also plot Galaxia predictions from the MP and MR models. The MP model clearly has a thick disc that is too metal poor to fit the observed data for | z | > 1 kpc. The new MR model reproduces the GALAH data very well. It also reproduces the APOGEE data very well, except for the slice closest to the mid-plane and the slice furthest from the mid-plane. Compared to GALAH, stars in APOGEE that are close to the mid-plane are metal rich, but the stars progressively become metal poor with increasing height above the mid-plane. These differences could be due to systematics in abundances between the two surveys, but could also be due to the different selection function of the surveys. The effect of selection function is clearly visible in Fig. 12(f) corresponding to the top most slice (2 | z |/kpc 3). Here, the MR model has a thick disc with a mean metallicity of −0.16. However, the mean metallicity of stars in this slice is −0.2. This is due to two reasons. First, because the metal poor stars are more luminous and are visible furthest in a magnitude-limited survey, we find that this effect decreases the metallicity of thick disc stars in this slice by 0.02 dex. Secondly, the top most slice has a larger contribution from the (metal poor) halo compared to other slices and this contamination decreases the metallicity of stars in this slice by −0.015 dex. Fig. 12 shows that close to the mid-plane there is a strong radial metallicity gradient. As we move away from the mid-plane the gradient diminishes progressively to zero. Close to the plane, a radial gradient of −0.07 (dashed line), as used in the Besançon (MP) and MR models, is roughly consistent with the observed data. Figure 12. Mean metallicity as function of Galactocentric radius R for different slices in height | z | for all stars with positive
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