Cosmological information in weak lensing peaks

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Recent studies have shown that the number counts of convergence peaks $N(\ensuremath{\kappa})$ 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 ${P}_{\ensuremath{\ell}}$. In agreement with earlier work, we find that high peaks (with amplitudes $\ensuremath{\gtrsim}3.5\ensuremath{\sigma}$, where $\ensuremath{\sigma}$ is the r.m.s. of the convergence $\ensuremath{\kappa}$) are typically dominated by a single massive halo. In contrast, medium-height peaks ($\ensuremath{\approx}0.5--1.5\ensuremath{\sigma}$) 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 $w$, ${\ensuremath{\sigma}}_{8}$, and ${\ensuremath{\Omega}}_{m}$. 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 $w$, ${\ensuremath{\sigma}}_{8}$, and ${\ensuremath{\Omega}}_{m}$ from the $N(\ensuremath{\kappa})+{P}_{\ensuremath{\ell}}$ combination, including redshift tomography with source galaxies at ${z}_{s}=1$ and ${z}_{s}=2$. We find that the $N(\ensuremath{\kappa})+{P}_{\ensuremath{\ell}}$ combination has approximately twice the cosmological sensitivity compared to ${P}_{\ensuremath{\ell}}$ alone. These results demonstrate that $N(\ensuremath{\kappa})$ contains non-Gaussian information complementary to the power spectrum.