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

We describe a method formeasuring the integrated Comptonization ( YSZ) 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 beta- model source profile and integrate YSZ 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 beta- model parameters for inputted clusters. We measure YSZ for simulated semi- analytic clusters and find that YSZ is most accurately determined in an angular aperture comparable to the SPT beam size. We demonstrate the utility of this method to measure YSZ and to constrain mass scaling relations using X- ray mass estimates for a sample of 18 galaxy clusters from the SPT- SZ survey. Measuring YSZ within a 0. 75 radius aperture, we find an intrinsic log- normal scatter of 21% 11% in YSZ at a fixed mass. Measuring YSZ 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 YSZ measured within an aperture comparable to the SPT beam size is equivalent, in terms of scatter with cluster mass, to SPT cluster detection significance.