Weak lensing peak statistics -- steepness versus height

In weak-lensing cosmological studies, peak statistics is sensitive to nonlinear structures and thus complementary to cosmic shear two-point correlations. In this paper, we explore a new approach, namely, the peak steepness statistics, with the overall goal to understand the cosmological information embedded there in comparison with the commonly used peak height statistics. We perform the analyses with ray-tracing simulations considering different sets of cosmological parameters $\Omega_{\rm m}$ and $\sigma_8$. A theoretical model to calculate the abundance of high peaks based on steepness is also presented, which can well describe the main trend of the peak distribution from simulations. We employ $\Delta\chi^2$ and Fisher analyses to study the cosmological dependence of the two peak statistics using our limited sets of simulations as well as our theoretical model. Within our considerations without including potential systematic effects, the results show that the steepness statistics tends to have higher sensitivities to the cosmological parameters than the peak height statistics and this advantage is diluted with the increase of the shape noise. Using the theoretical model, we investigate the physical reasons accounting for the different cosmological information embedded in the two statistics. Our analyses indicate that the projection effect from large-scale structures plays an important role to enhance the gain from the steepness statistics. The redshift and cosmology dependence of dark matter halo density profiles also contributes to the differences between the two statistics.