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

Date Published:

May 1, 2017


We probe the higher order clustering of the galaxies in the final datarelease (DR12) of the Sloan Digital Sky Survey Baryon OscillationSpectroscopic Survey (BOSS), using the method of germ-grain Minkowskifunctionals (MFs). Our sample consists of 410 615 BOSS galaxies from thenorthern Galactic cap in the redshift range 0.450-0.595. We show the MFsto be sensitive to contributions up to the six-point correlationfunction for this data set. We ensure with a custom angular mask thatthe results are more independent of boundary effects than in previousanalyses of this type. We extract the higher order part of the MFs andquantify the difference to the case without higher order correlations.The resulting χ2 value of over 10 000 for a modest numberof degrees of freedom, O(200), indicates a 100σ deviation anddemonstrates that we have a highly significant signal of thenon-Gaussian contributions to the galaxy distribution. This statisticalpower can be useful in testing models with differing higher ordercorrelations. Comparing the galaxy data to the quick particle mesh andMultiDark(MD)-Patchy mocks, we find that the latter better describes theobserved structure. From an order-by-order decomposition, we expectthat, for example, already a reduction of the amplitude of the MD-Patchymock power spectrum by 5 per cent would remove the remaining tension.