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 $\lambda$-mass relation with the following function $⟨\ln \lambda |M_{500}⟩\propto B_{\lambda }\ln M_{500}+C_{\lambda }\ln E(z)$ and use SPT-SZ cluster masses and RM richnesses $\lambda$ to constrain the parameters. We find $B_{\lambda }=1.14_{-0.18}^{+0.21}$ and $C_{\lambda }=0.73_{-0.75}^{+0.77}$. The associated scatter in mass at fixed richness is ${\sigma }_{\ln M|\lambda }=0.18_{-0.05}^{+0.08}$ at a characteristic richness $\lambda =70$. 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 $\xi =4.5$, using the RM catalog to provide optical confirmation and redshifts for additional low-$\xi$ SPT-SZ candidates.In this way, we identify 15 additional clusters with $\xi \in [4,4.5]$ 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

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