We present thermal Sunyaev-Zel'dovich effect (SZE) measurements for 42 galaxy clusters observed at 150 GHz with the APEX-SZ experiment. For each cluster, we model the pressure profile and calculate the integrated Comptonization Y to estimate the total thermal energy of the intracluster medium (ICM). We compare the measured Y values to X-ray observables of the ICM from the literature (cluster gas mass M gas , temperature T X , and Y X = M gas T X ) that relate to total cluster mass. We measure power law scaling relations, including an intrinsic scatter, between the SZE and X-ray observables for three subsamples within the set of 42 clusters that have uniform X-ray analysis in the literature. We observe that differences between these X-ray analyses introduce significant variability into the measured scaling relations, particularly affecting the normalization. For all three subsamples, we find results consistent with a self-similar model of cluster evolution dominated by gravitational effects. Comparing to predictions from numerical simulations, these scaling relations prefer models that include cooling and feedback in the ICM. Lastly, we measure an intrinsic scatter of ∼ 28 per cent in the Y − Y X scaling relation for all three subsamples.

The use of galaxy clusters as precision cosmological probes relies on an accurate determination of their masses. However, inferring the relationship between cluster mass and observables from direct observations is difficult and prone to sample selection biases. In this work, we use weak lensing as the best possible proxy for cluster mass to calibrate the Sunyaev-Zel'dovich (SZ) effect measurements from the APEX-SZ experiment. For a well-defined (ROSAT) X-ray complete cluster sample, we calibrate the integrated Comptonization parameter, Y SZ , to the weak-lensing derived total cluster mass, M 500 . We employ a novel Bayesian approach to account for the selection effects by jointly fitting both the SZ Comptonization, Y SZ -M 500 , and the X-ray luminosity, L x -M 500 , scaling relations. We also account for a possible correlation between the intrinsic (log-normal) scatter of L x and Y SZ at fixed mass. We find the corresponding correlation coefficient to be r = 0.47 +0.24 −0.35 , and at the current precision level our constraints on the scaling relations are consistent with previous works. For our APEX-SZ sample, we find that ignoring the covariance between the SZ and X-ray observables biases the normalization of the Y SZ -M 500 scaling high by 1-2σ and the slope low by ∼ 1σ, even when the SZ effect plays no role in the sample selection. We conclude that for higher-precision data and larger cluster samples, as anticipated from on-going and near-future cluster cosmology experiments, similar biases (due to intrinsic covariances of cluster observables) in the scaling relations will dominate the cosmological error budget if not accounted for correctly.

We present a weak lensing analysis for galaxy clusters from the APEX-SZ survey. For 39 massive galaxy clusters that were observed via the Sunyaev-Zel'dovich effect (SZE) with the APEX telescope, we analyse deep optical imaging data from WFI(@2.2mMPG/ESO) and Suprime-Cam(@SUBARU) in three bands. The masses obtained in this study, including an X-ray selected subsample of 27 clusters, are optimised for and used in studies constraining the mass to observable scaling relations at fixed cosmology. A novel focus of our weak lensing analysis is the multi-colour background selection to suppress effects of cosmic variance on the redshift distribution of source galaxies. We investigate the effects of cluster member contamination through galaxy density, shear profile, and recovered concentrations. We quantify the impact of variance in source redshift distribution on the mass estimate by studying nine subfields of the COSMOS survey for different cluster redshift and manitude limits. We measure a standard deviation of ∼ 6% on the mean angular diameter distance ratio for a cluster at z = 0.45 and shallow imaging data of R ≈ 23 mag. It falls to ∼ 1% for deep, R = 26 mag, observations. This corresponds to 8.4% and 1.4% scatter in M 200 . Our background selection reduces this scatter by 20 − 40%, depending on cluster redshift and imaging depth. We derived cluster masses with and without using a mass concentration relation and find consistent results, and concentrations consistent with the used mass-concentration relation.