Calibrating optical galaxy cluster projection effects with sparse spectroscopic samples: A clustering redshift approach

Wide-field optical imaging surveys are efficient at identifying galaxy clusters, but optically identified clusters suffer from projection effects--physically unassociated galaxies along the line of sight can be misidentified as cluster members due to distance uncertainties. Previous studies have used spectroscopic follow-up observations of cluster members to quantify projection effects; however, such follow-up efforts cannot keep pace with the rapidly growing cluster samples. On the other hand, spectroscopic surveys designed for large-scale structure studies collect tens of millions of spectra but tend to have sparse spectra in cluster regions. To bridge this gap, we develop a clustering redshift approach that cross-correlates cluster members with sparse, non-cluster-targeted spectroscopic galaxy samples. We validate this approach using the Cardinal simulation, recovering the correct spectroscopic distribution and projection effect parameters of redMaPPer cluster members. Our approach is insensitive to the selection of the spectroscopic sample and paves the way for calibrating the upcoming LSST clusters using DESI and Roman spectroscopic samples.