Using clustering redshifts to quantify the projection effects in the redMaPPer galaxy cluster catalog

Identification of galaxies as cluster members from imaging data is challenging due to photometric redshift uncertainties. The projection effect biases the estimates of a galaxy cluster's richness by misidentifying galaxies as members along its line of sight. Spectroscopic observations of cluster members can be used to calibrate the projection effects; however, current and upcoming surveys like DESI and Roman's HLSS will have sparse spectroscopic observations in cluster regions, and previous analysis approaches no longer apply to these data sets. To address this challenge, we apply the clustering redshift method to quantify projection effects in the redMaPPer galaxy cluster catalog. Using simulations, we demonstrate that we can recover the true redshift distribution of galaxy cluster members in the narrow photometric redshift bin by computing the angular cross-correlations between members and a reference sample with spectroscopic redshifts. To constrain the projection effect, we use a model that separates the distributions of actual cluster members from those of non-members. We first validate our method with the Cardinal mock redMaPPer galaxy cluster catalog. We then apply the approach to constrain the projection effects in the SDSS DR8 redMaPPer cluster catalog. The projection fractions we found are in line with earlier projection effect studies. Our future goal is to employ the clustering redshift approach to constrain the projection effect in clusters detected by LSST and the Roman Space Telescope.