The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Evolution of higher-order correlations demonstrated with Minkowski Functionals

We probe the higher-order galaxy clustering in the final data release (DR12) of the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (BOSS) using germ-grain Minkowski Functionals (MFs). Our data selection contains $979,430$ BOSS galaxies from both the northern and southern galactic caps over the redshift range $z=0.2-0.6$. We extract the higher-order part of the MFs, detecting the deviation from the purely Gaussian case with $\chi^2 \sim $\mathcal{O}$(10^3)$ on 24 degrees of freedom across the entire data selection. We measure significant redshift evolution in the higher-order functionals for the first time. We find $15-35\mathrm{\%}$ growth, depending on functional and scale, between our redshift bins centered at $z=0.325$ and $z=0.525$. We show that the structure in higher order correlations grow faster than that in the two-point correlations, especially on small scales where the excess approaches a factor of $2$. We demonstrate how this trend is generalizable by finding good agreement of the data with a hierarchical model in which the higher orders grow faster than the lower order correlations. We find that the non-Gaussianity of the underlying dark matter field grows even faster than the one of the galaxies due to decreasing clustering bias. Our method can be adapted to study the redshift evolution of the three-point and higher functions individually.