Constraints on the Richness-Mass Relation and the Optical-SZE Positional Offset Distribution for SZE-Selected Clusters

Abstract

We cross-match galaxy cluster candidates selected via their Sunyaev-Zel'dovich effect (SZE) signatures in 129.1 deg${}^2$ of the South Pole Telescope 2500d SPT-SZ survey with optically identified clusters selected from the Dark Energy Survey (DES) science verification data. We identify 25 clusters between $0.1\lesssim z\lesssim 0.8$ in the union of the SPT-SZ and redMaPPer (RM) samples. RM is an optical cluster finding algorithm that also returns a richness estimate for each cluster. We model the richness $\hat{I}»$-mass relation with the following function $⟨\ln \hat{I}»|M_{500}⟩\propto B_{\hat{I}}»\ln M_{500}+C_{\hat{I}}»\ln E(z)$ and use SPT-SZ cluster masses and RM richnesses $\hat{I}»$ to constrain the parameters. We find $B_{\hat{I}}»=1.14_{-0.18}^{+0.21}$ and $C_{\hat{I}}»=0.73_{-0.75}^{+0.77}$. The associated scatter in mass at fixed richness is $\ddot{I}{ƒ}_{\ln M|\hat{I}»}=0.18_{-0.05}^{+0.08}$ at a characteristic richness $\hat{I}»=70$. We demonstrate that our model provides an adequate description of the matched sample, showing that the fraction of SPT-SZ selected clusters with RM counterparts is consistent with expectations and that the fraction of RM selected clusters with SPT-SZ counterparts is in mild tension with expectation. We model the optical-SZE cluster positional offset distribution with the sum of two Gaussians, showing that it is consistent with a dominant, centrally peaked population and a sub-dominant population characterized by larger offsets. We also cross-match the RM catalog with SPT-SZ candidates below the official catalog threshold significance $\hat{I}¾=4.5$, using the RM catalog to provide optical confirmation and redshifts for additional low-$\hat{I}¾$ SPT-SZ candidates.In this way, we identify 15 additional clusters with $\hat{I}¾\in [4,4.5]$ over the redshift regime explored by RM in the overlapping region between DES science verification data and the SPT-SZ survey.

15 pages, 8 Figures, submitted to MNRAS