Sunyaev-Zel'dovich Effect and X-ray Scaling Relations from Weak-Lensing Mass Calibration of 32 SPT Selected Galaxy Clusters

Uncertainty in the mass-observable scaling relations is currently the limiting factor for galaxy cluster based cosmology. Weak gravitational lensing can provide a direct mass calibration and reduce the mass uncertainty. We present new ground-based weak lensing observations of 19 South Pole Telescope (SPT) selected clusters at redshifts $0.29 \leq z \leq 0.61$ and combine them with previously reported space-based observations of 13 galaxy clusters at redshifts $0.576 \leq z \leq 1.132$ to constrain the cluster mass scaling relations with the Sunyaev-Zel'dovich effect (SZE), the cluster gas mass \mgas, and \yx, the product of \mgas\ and X-ray temperature. We extend a previously used framework for the analysis of scaling relations and cosmological constraints obtained from SPT-selected clusters to make use of weak lensing information. We introduce a new approach to estimate the effective average redshift distribution of background galaxies and quantify a number of systematic errors affecting the weak lensing modelling. These errors include a calibration of the bias incurred by fitting a Navarro-Frenk-White profile to the reduced shear using $N$-body simulations. We blind the analysis to avoid confirmation bias. We are able to limit the systematic uncertainties to 5.6% in cluster mass (68% confidence). Our constraints on the mass--X-ray observable scaling relations parameters are consistent with those obtained by earlier studies, and our constraints for the mass--SZE scaling relation are consistent with the simulation-based prior used in the most recent SPT-SZ cosmology analysis. We can now replace the external mass calibration priors used in previous SPT-SZ cosmology studies with a direct, internal calibration obtained on the same clusters.