Precise Clustering and Density Evolution of redMaPPer Galaxy Clusters versus MXXL Simulation

Abstract

We construct a large, redshift complete sample of distant galaxy clusters by correlating Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12) redshifts with clusters identified with the red-sequence Matched-filter Probabilistic Percolation (redMaPPer) algorithm. Our spectroscopic completeness is 97% for ~ 7,000 clusters within the redMaPPer selection limit, $z⩽$ 0.325, so that our cluster correlation functions are much more precise than earlier work and not suppressed by photometric redshifts. We derive an accurate power-law mass-richness relation from the observed abundance with respect to the mass function from Millennium XXL (MXXL) simulation, adjusted to the Planck weighted cosmology. The number density of clusters is found to decline by 20% over the range 0.1 $<z<$ 0.3, in good agreement with the evolution predicted by MXXL. Our projected three-dimensional correlation function scales with richness, $\lambda$, rising from $r_0=$ 14 h${}^{-1}$ Mpc at $\lambda \simeq$ 25, to $r_0=$ 22 h${}^{-1}$ Mpc at $\lambda \simeq$ 60, with a gradient that matches MXXL when applying our mass-richness relation, whereas the observed amplitude of the correlation function at $⟨z⟩=$ 0.24 exceeds the MXXL prediction by 20% at the $\simeq$ 2.5$\sigma$ level. This tension cannot be blamed on spurious, randomly located clusters as this would reduce the correlation amplitude. Full consistency between the correlation function and the abundances is achievable for the pre-Planck values of ${\sigma }_8=$ 0.9, ${\Omega }_m=$ 0.25, and h = 0.73, matching the improved distance ladder estimate of the Hubble constant.

19 pages, 18 figures

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