Projection effects of large-scale structures on weak-lensing peak abundances

High peaks in weak lensing (WL) maps originate dominantly from the lensing effects of single massive halos. Their abundance is therefore closely related to the halo mass function and thus a powerful cosmological probe. On the other hand, however, besides individual massive halos, large-scale structures (LSS) along lines of sight also contribute to the peak signals. In this paper, with ray tracing simulations, we investigate the LSS projection effects. We show that for current surveys with a large shape noise, the stochastic LSS effects are subdominant. For future WL surveys with source galaxies having a median redshift $z_{\mathrm{med}}\sim1$ or higher, however, they are significant. For the cosmological constraints derived from observed WL high peak counts, severe biases can occur if the LSS effects are not taken into account properly. We extend the model of \citet{Fan2010} by incorporating the LSS projection effects into the theoretical considerations. By comparing with simulation results, we demonstrate the good performance of the improved model and its applicability in cosmological studies.