Spectroscopic Quantification of Projection Effects in the SDSS redMaPPer Galaxy Cluster Catalogue

TL;DR

This study quantifies how projection effects influence the SDSS redMaPPer galaxy cluster catalogue, revealing significant contamination that varies with richness and impacts mass estimates, using spectroscopic data for validation.

Contribution

It provides the first empirical model of projection effects in the SDSS redMaPPer catalogue based on spectroscopic redshifts, improving understanding of cluster richness and mass relations.

Findings

Projection effects account for ~16% of richness in low-richness clusters.

Projection effects decrease with increasing cluster richness.

The velocity dispersion–richness relation is approximately linear after correction.

Abstract

Projection effects, whereby galaxies along the line-of-sight to a galaxy cluster are mistakenly associated with the cluster halo, present a significant challenge for optical cluster cosmology. We use statistically representative spectral coverage of luminous galaxies to investigate how projection effects impact the low-redshift limit of the Sloan Digital Sky Survey (SDSS) redMaPPer galaxy cluster catalogue. Spectroscopic redshifts enable us to differentiate true cluster members from false positives and determine the fraction of candidate cluster members viewed in projection. Our main results can be summarized as follows: first, we show that a simple double-Gaussian model can be used to describe the distribution of line-of-sight velocities in the redMaPPer sample; second, the incidence of projection effects is substantial, accounting for $\sim 16$ per cent of the weighted richness for the lowest richness objects; third, projection effects are a strong function of richness, with the contribution in the highest richness bin being several times smaller than for low-richness objects; fourth, our measurement has a similar amplitude to state-of-the-art models, but finds a steeper dependence of projection effects on richness than these models; and fifth, the slope of the observed velocity dispersion--richness relation, corrected for projection effects, implies an approximately linear relationship between the true, three-dimensional halo mass and three-dimensional richness. Our results provide a robust, empirical description of the impact of projection effects on the SDSS redMaPPer cluster sample and exemplify the synergies between optical imaging and spectroscopic data for studies of galaxy cluster astrophysics and cosmology.