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

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 aim to present the first attempt at modelling line-of-sight (LOS) 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 have focussed 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 simulated a mock cluster that resembles MACS J0416.1-2403 in order to explore the effects of LOS 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 LOS 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 factor 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. In addition, LOS galaxies cannot explain the apparent discrepancy in the properties of massive sub-halos between MACS J0416.1-2403 and N-body simulated clusters. Since our model of MACS J0416.1-2403 with LOS galaxies only reduced modestly the rms offset in the image positions, we conclude that additional complexities would be needed in future models of MACS J0416.1-2403.