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Exploiting the powerful tool of strong gravitational lensing by galaxyclusters to study the highest-redshift Universe and cluster mass distributionsrelies on precise lens mass modelling. In this work, we present the firstattempt at modelling line-of-sight mass distribution in addition to that of thecluster, extending previous modelling techniques that assume mass distributionsto be on a single lens plane. We focus on the Hubble Frontier Field clusterMACS J0416.1-2403, and our multi-plane model reproduces the observed imagepositions 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 explorethe effects of line-of-sight structures on cluster mass modelling. Bysystematically analysing the mock cluster under different model assumptions, wefind that neglecting the lensing environment has a significant impact on thereconstruction of image positions (rms ~0.3"); accounting for line-of-sightgalaxies as if they were at the cluster redshift can partially reduce thisoffset. Moreover, foreground galaxies are more important to include into themodel than the background ones. While the magnification factors of the lensedmultiple images are recovered within ~10% for ~95% of them, those ~5% that lienear critical curves can be significantly affected by the exclusion of thelensing environment in the models (up to a factor of ~200). In addition,line-of-sight galaxies cannot explain the apparent discrepancy in theproperties of massive subhalos between MACS J0416.1-2403 and N-body simulatedclusters. Since our model of MACS J0416.1-2403 with line-of-sight galaxies onlyreduced modestly the rms offset in the image positions, we conclude thatadditional complexities, such as more flexible halo shapes, would be needed infuture models of MACS J0416.1-2403.

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