Probability Distribution Functions of Cosmological Lensing: Convergence, Shear, and Magnification

TL;DR

This paper uses high-resolution ray-tracing simulations to analyze the probability distribution functions of cosmological lensing effects like convergence, shear, and magnification, revealing new insights into their behaviors and implications for distant sources.

Contribution

It introduces analytical formulas for lensing PDFs and explores the relation between convergence and magnification, accounting for shot noise effects in simulations.

Findings

Convergence and magnification PDFs are closely related via an approximate relation.

Mean convergence in the source plane is systematically negative.

Analytical formulas reproduce simulated PDFs across various redshifts and smoothing sizes.

Abstract

We perform high resolution ray-tracing simulations to investigate probability distribution functions (PDFs) of lensing convergence, shear, and magnification on distant sources up to the redshift of $z_s=20$. We pay particular attention to the shot noise effect in $N$-body simulations by explicitly showing how it affects the variance of the convergence. We show that the convergence and magnification PDFs are closely related with each other via the approximate relation $\mu=(1-\kappa)^{-2}$, which can reproduce the behavior of PDFs surprisingly well up to the high magnification tail. The mean convergence measured in the source plane is found to be systematically negative, rather than zero as often assumed, and is correlated with the convergence variance. We provide simple analytical formulae for the PDFs, which reproduce simulated PDFs reasonably well for a wide range of redshifts and smoothing sizes. As explicit applications of our ray-tracing simulations, we examine the strong lensing probability and the magnification effects on the luminosity functions of distant galaxies and quasars.