Convergence Peak Counts: A Non-Gaussian Shear Statistic and Its Amplitude Sensitivity

Peaks in a reconstructed convergence map carry information about the nonlinear matter distribution that two-point statistics discard. This paper computes the smoothed convergence dispersion for a representative source sample, obtaining a dispersion of 0.0044 at a smoothing scale of 2 arcminutes, and estimates the surface density of peaks above three times that dispersion as 0.84 per square degree, or about 845 peaks over a thousand-square-degree survey. A five-percent reduction in the clustering amplitude changes the high-peak abundance by -15.1 percent in the scaling adopted, several times the amplitude change itself, which is the attraction of the statistic: its sensitivity is amplified. The same amplification applies to noise and systematics, which is the corresponding cost. All quantities are computed from stated assumptions, not measured.