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

Abstract 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 χ2 value of over 10 000 for a modest number of degrees of freedom, O(200), indicates a 100σ 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 quick particle mesh and MultiDark(MD)-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 per cent would remove the remaining tension.