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We probe the higher-order clustering of the galaxies in the final datarelease (DR12) of the Sloan Digital Sky Survey Baryon Oscillation SpectroscopicSurvey (BOSS) using the method of germ-grain Minkowski Functionals (MFs). Oursample consists of 410,615 BOSS galaxies from the northern Galactic cap in theredshift range 0.450--0.595. We show the MFs to be sensitive to contributionsup to the six-point correlation function for this data set. We ensure with acustom angular mask that the results are more independent of boundary effectsthan in previous analyses of this type. We extract the higher-order part of theMFs 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 offreedom, O(200), indicates a 100-sigma deviation and demonstrates that we havea highly significant signal of the non-Gaussian contributions to the galaxydistribution. This statistical power can be useful in testing models withdiffering higher-order correlations. Comparing the galaxy data to the QPM andMultiDark-Patchy mocks, we find that the latter better describes the observedstructure. 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.

monthly notices of the royal astronomical society

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