Modelling the Milky Way. I -- Method and first results fitting the thick disk and halo with DES-Y3 data

We present MWFitting, a method to fit the stellar components of the Galaxy by comparing Hess Diagrams (HDs) from TRILEGAL models to real data. We apply MWFitting to photometric data from the first three years of the Dark Energy Survey (DES). After removing regions containing known resolved stellar systems such as globular clusters, dwarf galaxies, nearby galaxies, the Large Magellanic Cloud and the Sagittarius Stream, our main sample spans a total area of $\sim$2,300 deg$^2$ distributed across the DES footprint. We further explore a smaller subset ($\sim$ 1,300 deg$^2$) that excludes all regions with known stellar streams and stellar overdensities. Validation tests on synthetic data possessing similar properties to the DES data show that the method is able to recover input parameters with a precision better than 3\%. Based on the best-fit models, we create simulated stellar catalogues covering the whole DES footprint down to $g = 24$ magnitude. Comparisons of data and simulations provide evidence for a break in the power law index describing the stellar density of the Milky Way (MW) halo. Several previously discovered stellar over-densities are recovered in the residual stellar density map, showing the reliability of MWFitting in determining the Galactic components. Simulations made with the best-fitting parameters are a promising way to predict MW star counts for surveys such as LSST and Euclid.