# MACS J0416.1-2403: Impact of line-of-sight structures on strong gravitational lensing modelling of galaxy clusters

## TL;DR

This study models the impact of line-of-sight structures on strong gravitational lensing by galaxy clusters, revealing significant effects on image position accuracy and magnification estimates, and emphasizing the importance of including environmental factors.

## Contribution

First to incorporate line-of-sight mass distributions into multi-plane lens models of galaxy clusters, improving understanding of environmental effects on lensing accuracy.

## Key findings

- Neglecting line-of-sight structures significantly affects image position reconstructions.
- Including line-of-sight galaxies reduces positional offsets and improves magnification estimates.
- Foreground galaxies are more influential than background ones in lens modeling.

## Abstract

Exploiting the powerful tool of strong gravitational lensing by galaxy clusters to study the highest-redshift Universe and cluster mass distributions relies on precise lens mass modelling. In this work, we present the first attempt at modelling line-of-sight mass distribution in addition to that of the cluster, extending previous modelling techniques that assume mass distributions to be on a single lens plane. We focus on the Hubble Frontier Field cluster MACS J0416.1-2403, and our multi-plane model reproduces the observed image positions with a rms offset of ~0.53". Starting from this best-fitting model, we simulate a mock cluster that resembles MACS J0416.1-2403 in order to explore the effects of line-of-sight structures on cluster mass modelling. By systematically analysing the mock cluster under different model assumptions, we find that neglecting the lensing environment has a significant impact on the reconstruction of image positions (rms ~0.3"); accounting for line-of-sight galaxies as if they were at the cluster redshift can partially reduce this offset. Moreover, foreground galaxies are more important to include into the model than the background ones. While the magnification factors of the lensed multiple images are recovered within ~10% for ~95% of them, those ~5% that lie near critical curves can be significantly affected by the exclusion of the lensing environment in the models (up to a factor of ~200). In addition, line-of-sight galaxies cannot explain the apparent discrepancy in the properties of massive subhalos between MACS J0416.1-2403 and N-body simulated clusters. Since our model of MACS J0416.1-2403 with line-of-sight galaxies only reduced modestly the rms offset in the image positions, we conclude that additional complexities, such as more flexible halo shapes, would be needed in future models of MACS J0416.1-2403.