A deconstruction of methods to derive one-point lensing statistics

TL;DR

This paper compares approximate methods for deriving lensing statistics, finding they work well for mild lensing but lose accuracy in strong lensing regimes, informing future gravitational lensing studies.

Contribution

It evaluates the effectiveness of PINOCCHIO and turboGL methods for lensing PDFs across regimes, highlighting their limitations and accuracy in weak lensing scenarios.

Findings

Effective for mild lensing applications

Break down in strong lensing regimes due to nonlinear effects

PINOCCHIO's moments are 6-10% smaller than N-body simulations

Abstract

Gravitational lensing is a crucial tool for exploring cosmic phenomena, providing insights into galaxy clustering, dark matter, and dark energy. Given the substantial computational demands of $N$-body simulations, approximate methods like $\texttt{PINOCCHIO}$ and $\texttt{turboGL}$ have been proposed as viable alternatives for simulating lensing probability density functions (PDFs). This paper evaluates these methods and their effectiveness across both weak and strong lensing regimes, with a focus in the context where baryonic effects are negligible. Our comparative analysis reveals that these methods are effective for applications where lensing is mild, such as the majority of sources of electromagnetic and gravitational waves. However, both $\texttt{PINOCCHIO}$ and $\texttt{turboGL}$ break down for large values of convergence and magnification due to their loss of accuracy in capturing small-scale nonlinear matter fields, owing to oversimplified assumptions about internal halo structures and reliance on perturbation theory. $\texttt{PINOCCHIO}$ yields second-to-fourth moments of the lensing PDFs, which are 6-10% smaller than those resulting from $N$-body simulations in regimes where baryonic effects are minimal. These findings aim to inform future studies on gravitational lensing of point sources, which are increasingly relevant with upcoming supernova and gravitational wave datasets.