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Detailed comparison of Milky Way models based on stellar population synthesis and SDSS star counts at the north Galactic pole

We test the ability of the TRILEGAL and Besancon models to reproduce the CMD of SDSS data at the north Galactic pole (NGP). We show that a Hess diagram analysis of colour-magnitude diagrams is much more powerful than luminosity functions (LFs) in determining the Milky Way structure. We derive a best-fitting TRILEGAL model to simulate the NGP field in the (g-r, g) CMD of SDSS filters via Hess diagrams. For the Besancon model, we simulate the LFs and Hess diagrams in all SDSS filters. We use a chi2 analysis and determine the median of the relative deviations in the Hess diagrams to quantify the quality of the fits by the TRILEGAL models and the Besancon model in comparison and compare this with the Just-Jahreiss model. The input isochrones in the colour-absolute magnitude diagrams of the thick disc and halo are tested via the observed fiducial isochrones of globular clusters (GCs). We find that the default parameter set lacking a thick disc component gives the best representation of the LF in TRILEGAL. The Hess diagram reveals that a metal-poor thick disc is needed. In the Hess diagram, the median relative deviation of the TRILEGAL model and the SDSS data amounts to 25 percent, whereas for the Just-Jahreiss model the deviation is only 5.6 percent. The isochrone analysis shows that the representation of the MS of (at least metal-poor) stellar populations in the SDSS system is reliable. In contrast, the RGBs fail to match the observed fiducial sequences of GCs. The Besancon model shows a similar median relative deviation of 26 percent in (g-r, g). In the u band, the deviations are larger. There are significant offsets between the isochrone set used in the Besancon model and the observed fiducial isochrones. In contrast to Hess diagrams, LFs are insensitive to the detailed structure of the Milky Way components due to the extended spatial distribution along the line of sight.