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

Abstract

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.

Figures (4)

• Figure 1: Validation of our clustering-$z$ method (cross-correlating cluster members and LRGs) using the Cardinal simulation. The four panels correspond to four cluster redshift ($z_{\rm cl}$) bins. In each panel, the blue histogram shows the spectroscopic redshift ($z_{\rm spec}$) distribution of member galaxies, while the black points with error bars show our clustering-$z$ measurements for the same galaxies. The agreements show that the clustering-$z$ method is viable for calibrating the projection effects of galaxy cluster members. In each panel, we fit a double Gaussian model to $\hat{\phi}_{\rm u}$ to describe physically associated members (orange dashed curves) and projected members (gray dotted curves).
• Figure 2: Similar to Fig. \ref{['fig:cardinal_LRG']}, but using ELGs as the reference sample. The ELG sample has a wider redshift coverage but a lower number density, resulting in noisier clustering-$z$ measurements.
• Figure 3: Projection effect parameters derived from the clustering-$z$ measurements using LRGs (orange) and ELGs (blue), compared with those derived from spectroscopic redshifts (black). Both reference samples recover the spectroscopic results, indicating that our method is insensitive to reference sample selection.
• Figure 4: Individual redMaPPer members' line-of-sight velocities vs. the richness of their host clusters. We use a maximum likelihood approach to estimate velocity dispersions vs. richness. The lines indicate the boundary between physically associated and projected members.