Continuous image distortion by astrophysical thick lenses

TL;DR

This paper introduces a non-perturbative, continuous method for analyzing image distortion caused by astrophysical thick lenses, demonstrating high accuracy of the thin-lens approximation in realistic scenarios.

Contribution

It develops a continuous, non-perturbative approach to model gravitational lensing without relying on the thin-lens approximation, improving understanding of thick lens effects.

Findings

Thin-lens approximation is accurate within 0.01% for galaxy cluster models.

Modeling multiple clusters as a single lens plane introduces less than 0.5% error.

The method accurately predicts image shape parameters in complex lens configurations.

Abstract

Image distortion due to weak gravitational lensing is examined using a non-perturbative method of integrating the geodesic deviation and optical scalar equations along the null geodesics connecting the observer to a distant source. The method we develop continuously changes the shape of the pencil of rays from the source to the observer with no reference to lens planes in astrophysically relevant scenarios. We compare the projected area and the ratio of semi-major to semi-minor axes of the observed elliptical image shape for circular sources from the continuous, thick-lens method with the commonly assumed thin-lens approximation. We find that for truncated singular isothermal sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens approximation is accurate to better than 1 part in 10^4 in predicting the image area and axes ratios. For asymmetric thick lenses consisting of two massive clusters separated along the line of sight in redshift up to \Delta z = 0.2, we find that modeling the image distortion as two clusters in a single lens plane does not produce relative errors in image area or axes ratio more than 0.5%