KiDS-450: cosmological constraints from weak-lensing peak statistics – II: Inference from shear peaks using N-body simulations

We study the statistics of peaks in a weak-lensing reconstructed mass map of the first 450 deg2 of the Kilo Degree Survey (KiDS-450). The map is computed with aperture masses directly applied to the shear field with an NFW-like compensated filter. We compare the peak statistics in the observations with that of simulations for various cosmologies to constrain the cosmological parameter S₈ = σ ₈ √Ω ₘ/0. 3, which probes the (Ωm, σ8) plane perpendicularly to its main degeneracy. We estimate S8 = 0. 750 ± 0. 059, using peaks in the signal-to-noise range 0 ≤ S/N ≤ 4, and accounting for various systematics, such as multiplicative shear bias, mean redshift bias, baryon feedback, intrinsic alignment, and shear-position coupling. These constraints are ∼ 25 per cent tighter than the constraints from the high significance peaks alone (3 ≤ S/N ≤ 4) which typically trace single-massive haloes. This demonstrates the gain of information from low-S/N peaks. However, we find that including S/N 8 compared to the shear two-point correlation functions alone, highlighting the great potential of peaks as a cosmological probe.