Constraints on the richness-mass relation and the optical-SZE positional offset distribution for SZE-selected clusters

We cross-match galaxy cluster candidates selected via their Sunyaev-Zel'dovich effect (SZE) signatures in 129.1 deg² of the South Pole Telescope 2500d SPT-SZ survey with optically identified clusters selected from the Dark Energy Survey science verification data. We identify 25 clusters between 0.1 ≲ z ≲ 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 λ-mass relation with the following function 〈lnλ|M₅₀₀〉 ∝ BλlnM₅₀₀ + Cλln E(z) and use SPT-SZ cluster masses and RM richnesses λ to constrain the parameters. We find Bλ = 1.14_-0.18^+0.21 and Cλ = 0.73_-0.75^+0.77. The associated scatter in mass at fixed richness is σlnM|λ = 0.18_-0.05^+0.08 at a characteristic richness λ=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 RMselected 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 subdominant population characterized by larger offsets. We also cross-match the RMcatalogue with SPT-SZ candidates below the official catalogue threshold significance ξ = 4.5, using the RM catalogue to provide optical confirmation and redshifts for 15 additional clusters with ξ ∈ [4, 4.5].