The cosmological information of shear peaks: beyond the abundance

We study the cosmological information of weak lensing (WL) peaks, focusing on two other statistics besides their abundance: the stacked tangential-shear profiles and the peak-peak correlation function. We use a large ensemble of simulated WL maps with survey specifications relevant to future missions like Euclid and lsst, to measure and examine the three peak probes. We find that the auto-correlation function of peaks with high signal-to-noise (S{N ) ratio measured from fields of size 144 deg has a maximum of „ 0.3 at an angular scale θ „ 10 arcmin. For peaks with smaller S{N , the amplitude of the correlation function decreases, and its maximum occurs on smaller angular scales. The stacked tangential-shear profiles of the peaks also increase with their S{N . We compare the peak observables measured with and without shape noise and find that for S{N „ 3 only „ 5% of the peaks are due to large-scale structures, the rest being generated by shape noise. The correlation function of these small peaks is therefore very weak compared to that of small peaks measured from noise-free maps, and also their mean tangential-shear profile is a factor of a few smaller than the noise-free one. The covariance matrix of the probes is examined: the correlation function is only weakly covariant on scales θ ă 30 arcmin, and slightly more on larger scales; the shear profiles are very correlated for θ ą 2 arcmin, with a correlation coefficient as high as 0.7. The cross-covariance of the three probes is relatively weak: the peak abundance and profiles have the largest correlation coefficient „ 0.3. Using the Fisher-matrix formalism, we compute the cosmological constraints for tΩm, σ8, w, nsu considering each probe separately, as well as in combination. We find that the peakpeak correlation and shear profiles yield marginalized errors which are larger by a factor of 2 ́4 for tΩm, σ8u than the errors yielded by the peak abundance alone, while the errors for tw, nsu are similar. By combining the three probes, the marginalized constraints are tightened by a factor of „ 2 compared to the peak abundance alone, the least contributor to the error reduction being the correlation function. This work therefore recommends that future WL surveys use shear peaks beyond their abundance in order to constrain the cosmological model.