Study of errors in strong gravitational lensing

TL;DR

This study evaluates the accuracy of strong gravitational lensing mass estimates of galaxy clusters, showing that the thin lens approximation introduces minimal error, but truncation methods can significantly affect results, informing future precision cosmology.

Contribution

It provides a detailed comparison of relativistic null geodesic calculations with conventional lensing approximations, highlighting the impact of truncation methods on mass estimation accuracy.

Findings

Thin lens approximation causes less than 0.3% error in isothermal sphere models.

Truncation methods can introduce errors up to an order of magnitude.

Future lensing studies can rely on thin lens approximation with careful truncation handling.

Abstract

We examine the accuracy of strong gravitational lensing determinations of the mass of galaxy clusters by comparing the conventional approach with the numerical integration of the fully relativistic null geodesic equations in the case of weak gravitational perturbations on Robertson-Walker metrics. In particular, we study spherically-symmetric, three-dimensional singular isothermal sphere models and the three-dimensional matter distribution of Navarro et al. (1997), which are both commonly used in gravitational lensing studies. In both cases we study two different methods for mass-density truncation along the line of sight: hard truncation and conventional (no truncation). We find that the relative error introduced in the total mass by the thin lens approximation alone is less than 0.3% in the singular isothermal sphere model, and less than 2% in the model of Navarro et al. (1997). The removal of hard truncation introduces an additional error of the same order of magnitude in the best case, and up to an order of magnitude larger in the worst case studied. Our results ensure that the future generation of precision cosmology experiments based on lensing studies will not require the removal of the thin-lens assumption, but they may require a careful handling of truncation.