Measurement of Galaxy Cluster Integrated Comptonization and Mass Scaling Relations with the South Pole Telescope

We describe a method for measuring the integrated Comptonization (Y _SZ) of clusters of galaxies from measurements of the Sunyaev-Zel'dovich (SZ) effect in multiple frequency bands and use this method to characterize a sample of galaxy clusters detected in the South Pole Telescope (SPT) data. We use a Markov Chain Monte Carlo method to fit a β-model source profile and integrate Y _SZ within an angular aperture on the sky. In simulated observations of an SPT-like survey that include cosmic microwave background anisotropy, point sources, and atmospheric and instrumental noise at typical SPT-SZ survey levels, we show that we can accurately recover β-model parameters for inputted clusters. We measure Y _SZ for simulated semi-analytic clusters and find that Y _SZ is most accurately determined in an angular aperture comparable to the SPT beam size. We demonstrate the utility of this method to measure Y _SZ and to constrain mass scaling relations using X-ray mass estimates for a sample of 18 galaxy clusters from the SPT-SZ survey. Measuring Y _SZ within a 0.'75 radius aperture, we find an intrinsic log-normal scatter of 21% ± 11% in Y _SZ at a fixed mass. Measuring Y _SZ within a 0.3 Mpc projected radius (equivalent to 0.'75 at the survey median redshift z = 0.6), we find a scatter of 26% ± 9%. Prior to this study, the SPT observable found to have the lowest scatter with mass was cluster detection significance. We demonstrate, from both simulations and SPT observed clusters that Y _SZ measured within an aperture comparable to the SPT beam size is equivalent, in terms of scatter with cluster mass, to SPT cluster detection significance.