The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: higher-order correlations revealed by germ-grain Minkowski Functionals

We probe the higher-order clustering of the galaxies in the final data release (DR12) of the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (BOSS) using the method of germ-grain Minkowski Functionals (MFs). Our sample consists of 410,615 BOSS galaxies from the northern Galactic cap in the redshift range 0.450--0.595. We show the MFs to be sensitive to contributions up to the six-point correlation function for this data set. We ensure with a custom angular mask that the results are more independent of boundary effects than in previous analyses of this type. We extract the higher-order part of the MFs and quantify the difference to the case without higher-order correlations. The resulting $\chi^{2}$ value of over 10,000 for a modest number of degrees of freedom, O(200), indicates a 100-sigma deviation and demonstrates that we have a highly significant signal of the non-Gaussian contributions to the galaxy distribution. This statistical power can be useful in testing models with differing higher-order correlations. Comparing the galaxy data to the QPM and MultiDark-Patchy mocks, we find that the latter better describes the observed structure. From an order-by-order decomposition we expect that, for example, already a reduction of the amplitude of the MD-Patchy mock power spectrum by 5% would remove the remaining tension.