Comparing simulated Milky Way satellite galaxies with observations using unsupervised clustering

We develop a new analysis method that allows us to compare multi-dimensional observables to a theoretical model. The method is based on unsupervised clustering algorithms which assign the observational and simulated data to clusters in high dimensionality. From the clustering result, a goodness of fit (the p-value) is determined with the Fisher-Freeman-Halton test. We first show that this approach is robust for 2D Gaussian distributions. We then apply the method to the observed MW satellites and simulated satellites from the fiducial model of our semi-analytic code A-SLOTH. We use the following 5 observables of the galaxies in the analysis: stellar mass, virial mass, heliocentric distance, mean stellar metallicity [Fe/H], and stellar metallicity dispersion {\sigma}[Fe/H]. A low p-value returned from the analysis tells us that our A-SLOTH fiducial model does not reproduce the mean stellar metallicity of the observed MW satellites well. We implement an ad-hoc improvement to the physical model and show that the number of dark matter merger trees which have p-values > 0.01 increases from 3 to 6. This method can be extended to data with higher dimensionality easily. We plan to further improve the physical model in A-SLOTH using this method to study elemental abundances of stars in the observed MW satellites.