Detection of spatial clustering in the 1000 richest SDSS DR8 redMaPPer clusters with Nearest Neighbor distributions

Understand

Distances to the $k$-nearest-neighbor ($k$NN) data points from volume-filling query points are a sensitive probe of spatial clustering.

• Here we present the first application of $k$NN summary statistics to observational clustering measurement, using the 1000 richest redMaPPer clusters ($0.1\leqslant z\leqslant 0.3$) from the SDSS DR8 catalog.
• A clustering signal is defined as a difference in the cumulative distribution functions (CDFs) of $k$NN distances from fixed query points to the observed clusters versus a set of unclustered random points.
• We find that the $k=1,2$-NN CDFs of redMaPPer deviate significantly from the randoms' across scales of 35 to 155 Mpc, which is a robust signature of clustering.