Theoretical Analysis of Random Scattering Induced by Microlensing

TL;DR

This paper provides a refined theoretical analysis of the probability density function of light deflection angles caused by microlenses, improving existing models and offering practical fitting formulas for cosmological microlensing studies.

Contribution

It introduces a revised coefficient for the deflection PDF, develops an accurate fitting formula, and proposes a better Gaussian approximation for theoretical applications.

Findings

Updated coefficient from 3.05 to 1.454 improves PDF fit

Developed an accurate, replaceable fitting formula for the PDF

Identified a more suitable Gaussian approximation for the deflection PDF

Abstract

Theoretical investigations into the deflection angle caused by microlenses offer a direct path to uncovering principles of the cosmological microlensing effect. This work specifically concentrates on the the probability density function (PDF) of the light deflection angle induced by microlenses. We have made several significant improvements to the widely used formula from Katz et al. First, we update the coefficient from 3.05 to 1.454, resulting in a better fit between the theoretical PDF and our simulation results. Second, we developed an elegant fitting formula for the PDF that can replace its integral representation within a certain accuracy, which is numerically divergent unless arbitrary upper limits are chosen. Third, to facilitate further theoretical work in this area, we have identified a more suitable Gaussian approximation for the fitting formula.