2010ApJ...719.1408F

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 θ_G= 0.5arcmin 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 ∼2.4 peaks with ν ≥ 5 for R_c= 1.7arcmin and the true peak height of the cluster ν = 5.6, where ν denotes the convergence signal-to-noise ratio. For a Navarro-Frenk-White (NFW) cluster of the same mass and the same central ν, the average number of peaks with ν ≥ 5 within R ≤ R_c is ∼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 ν ≥ 4, depending on the treatment of the mass-sheet degeneracy in weak-lensing analyses, the enhancement factor f is in the range of ∼5 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 ν ∼ 6.6, rather than at ν = 5.6, corresponding to a shift of Δν ∼ 1, for the isothermal cluster. For the NFW cluster, Δν ∼ 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 ∼ R_c for the isothermal case. For the NFW cluster, it is relatively narrow and peaked at R ∼ 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.