RedMaPPer - IV. Photometric membership identification of red cluster galaxies with 1 per cent precision

In order to study the galaxy population of galaxy clusters with photometric data, one must be able to accurately discriminate between cluster members and non-members. The redMaPPer cluster finding algorithm treats this problem probabilistically, focusing exclusively on the red galaxy population. Here, we utilize Sloan Digital Sky Survey (SDSS) and Galaxy And Mass Assembly spectroscopic membership rates to validate the redMaPPer membership probability estimates for clusters with z ε [0.1, 0.3]. We find small - but correctable - biases, sourced by three different systematics. The first two were expected a priori, namely blue cluster galaxies and correlated structure along the line of sight. The third systematic is new: the redMaPPer template fitting exhibits a non-trivial dependence on photometric noise, which biases the original redMaPPer probabilities when utilizing noisy data. After correcting for these effects, we find exquisite agreement (≈1 per cent) between the photometric probability estimates and the spectroscopic membership rates, demonstrating that we can robustly recover cluster membership estimates from photometric data alone. As a byproduct of our analysis we find that on average unavoidable projection effects from correlated structure contribute ≈6 per cent of the richness of a redMaPPer galaxy cluster. This work also marks the second public release of the SDSS redMaPPer cluster catalogue.