A Statistical Strategy for the Sunyaev-Zel’dovich Effects Cluster Data

We present a statistical strategy for the efficient determination of the cluster luminosity function from the Sunyaev-Zel’dovich (SZ) effects survey. The strategy is set up to match in particular the upcoming AMiBA (Array for Microwave Background Anisotropy) experiment. To determine the cluster luminosity function from the noise contaminated SZ map, we first define the zeroth-order cluster luminosity function as a discrepancy between the measured peak number density of the SZ map and the mean number density of noise. Then we demonstrate that the noise contamination effects can be removed by the stabilized deconvolution of the zeroth-order cluster luminosity function with the one-dimensional Gaussian distribution. We test this analysis technique against Monte-Carlo simulations, and find that it works quite well especially in the medium amplitude range where the conventional cluster identification method based on the threshold cut-off usually fails. Subject headings: galaxy clusters:luminosity function — methods:data analysis