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.
