Recent studies have shown that the number counts of convergence peaks $N(\kappa )$ in weak lensing (WL) maps, expected from large forthcoming surveys, can be a useful probe of cosmology. We follow up on this finding, and use a suite of WL convergence maps, obtained from ray-tracing N-body simulations, to study (i) the physical origin of WL peaks with different heights, and (ii) whether the peaks contain information beyond the convergence power spectrum $P_{\ell }$. In agreement with earlier work, we find that high peaks (with amplitudes $\gtrsim 3.5\sigma$, where $\sigma$ is the r.m.s. of the convergence $\kappa$) are typically dominated by a single massive halo. In contrast, medium-height peaks ($\approx 0.5–1.5\sigma$) cannot be attributed to a single collapsed dark matter halo, and are instead created by the projection of multiple (typically, 4–8) halos along the line of sight, and by random galaxy shape noise. Nevertheless, these peaks dominate the sensitivity to the cosmological parameters $w$, ${\sigma }_8$, and ${\Omega }_m$. We find that the peak-height distribution and its dependence on cosmology differ significantly from predictions in a Gaussian random field. We directly compute the marginalized errors on $w$, ${\sigma }_8$, and ${\Omega }_m$ from the $N(\kappa )+P_{\ell }$ combination, including redshift tomography with source galaxies at $z_s=1$ and $z_s=2$. We find that the $N(\kappa )+P_{\ell }$ combination has approximately twice the cosmological sensitivity compared to $P_{\ell }$ alone. These results demonstrate that $N(\kappa )$ contains non-Gaussian information complementary to the power spectrum.

• Received 25 March 2011

DOI:https://doi.org/10.1103/PhysRevD.84.043529