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ABSTRACT Expanding from previous work, we present weak-lensing (WL) measurements for a total sample of 30 distant (zmedian = 0.93) massive galaxy clusters from the South Pole Telescope Sunyaev–Zel’dovich (SPT-SZ) Survey, measuring galaxy shapes in Hubble Space Telescope (HST) Advanced Camera for Surveys images. We remove cluster members and preferentially select z ≳ 1.4 background galaxies via V − I colour, employing deep photometry from VLT/FORS2 and Gemini-South/GMOS. We apply revised calibrations for the WL shape measurements and the source redshift distribution to estimate the cluster masses. In combination with earlier Magellan/Megacam results for lower-redshifts clusters, we infer refined constraints on the scaling relation between the SZ detection significance and the cluster mass, in particular regarding its redshift evolution. The mass scale inferred from the WL data is lower by a factor $0.76^{+0.10}_{-0.14}$ (at our pivot redshift z = 0.6) compared to what would be needed to reconcile a flat Planck νΛCDM cosmology (in which the sum of the neutrino masses is a free parameter) with the observed SPT-SZ cluster counts. In order to sensitively test the level of (dis-)agreement between SPT clusters and Planck, further expanded WL follow-up samples are needed. 

Abstract We provide the first combined cosmological analysis of the South Pole Telescope (SPT) and Planck cluster catalogs. The aim is to provide an independent calibration for Planck scaling relations, exploiting the cosmological constraining power of the SPT-SZ cluster catalog and its dedicated weak lensing (WL) and X-ray follow-up observations. We build a new version of the Planck cluster likelihood. In the ν Λ CDM scenario, focusing on the mass slope and mass bias of Planck scaling relations, we find α SZ = 1.49 − 0.10 + 0.07 and 1 − b SZ = 0.69 − 0.14 + 0.07 , respectively. The results for the mass slope show a ∼4 σ departure from the self-similar evolution, α SZ ∼ 1.8. This shift is mainly driven by the matter density value preferred by SPT data, Ω m = 0.30 ± 0.03, lower than the one obtained by Planck data alone, Ω m = 0.37 − 0.06 + 0.02 . The mass bias constraints are consistent both with outcomes of hydrodynamical simulations and external WL calibrations, (1 − b ) ∼ 0.8, and with results required by the Planck cosmic microwave background cosmology, (1 − b ) ∼ 0.6. From this analysis, we obtain a new catalog of Planck cluster masses M 500 . We estimate the ratio between the published Planck M SZ masses and our derived masses M 500 , as a “measured mass bias,” 1 − b M . We analyze the mass, redshift, and detection noise dependence of 1 − b M , finding an increasing trend toward high redshift and low mass. These results mimic the effect of departure from self-similarity in cluster evolution, showing different dependencies for the low-mass, high-mass, low- z , and high- z regimes.