NOISY WEAK-LENSING CONVERGENCE PEAK STATISTICS NEAR CLUSTERS OF GALAXIES AND BEYOND

Taking into account noise from intrinsic ellipticities of source galaxies, in this paper, we study the peak statistics in weak-lensing convergence maps around clusters of galaxies and beyond. We emphasize how the noise peak statistics is affected by the density distribution of nearby clusters, and also how cluster-peak signals are changed by the existence of noise. These are the important aspects to be thoroughly understood in weak-lensing analyses for individual clusters as well as in cosmological applications of weak-lensing cluster statistics. We adopt Gaussian smoothing with the smoothing scale theta(G) = 0.5 arcmin in our analyses. It is found that the noise peak distribution near a cluster of galaxies sensitively depends on the density profile of the cluster. For a cored isothermal cluster with the core radius R-c, the inner region with R <= R-c appears noisy containing on average similar to 2.4 peaks with nu >= 5 for R-c = 1.7 arcmin and the true peak height of the cluster nu = 5.6, where nu denotes the convergence signal-to-noise ratio. For a Navarro-Frenk-White (NFW) cluster of the same mass and the same central nu, the average number of peaks with nu >= 5 within R <= R-c is similar to 1.6. Thus a high peak corresponding to the main cluster can be identified more cleanly in the NFW case. In the outer region with R-c < R <= 5R(c), the number of high noise peaks is considerably enhanced in comparison with that of the pure noise case without the nearby cluster. For nu >= 4, depending on the treatment of the mass-sheet degeneracy in weak-lensing analyses, the enhancement factor f is in the range of similar to 5 to similar to 55 for both clusters as their outer density profiles are similar. The properties of the main-cluster-peak identified in convergence maps are also significantly affected by the presence of noise. Scatters as well as a systematic shift for the peak height are present. The height distribution is peaked at nu similar to 6.6, rather than at nu = 5.6, corresponding to a shift of Delta nu similar to 1, for the isothermal cluster. For the NFW cluster, Delta nu similar to 0.8. The existence of noise also causes a location offset for the weak-lensing identified main-cluster-peak with respect to the true center of the cluster. The offset distribution is very broad and extends to R similar to R-c for the isothermal case. For the NFW cluster, it is relatively narrow and peaked at R similar to 0.2R(c). We also analyze NFW clusters of different concentrations. It is found that the more centrally concentrated the mass distribution of a cluster is, the less its weak-lensing signal is affected by noise. Incorporating these important effects and the mass function of NFW dark matter halos, we further present a model calculating the statistical abundances of total convergence peaks, true and false ones, over a large field beyond individual clusters. The results are in good agreement with those from numerical simulations. The model then allows us to probe cosmologies with the convergence peaks directly without the need of expensive follow-up observations to differentiate true and false peaks.