Cosmological cluster-scale strong gravitational lensing probes the mass distribution of the dense cores of massive dark matter halos and the structures along the line of sight from background sources to the observer. It is frequently assumed that the primary lens mass dominates the lensing, with the contribution of secondary masses along the line of sight being neglected. Secondary mass structures may, however, affect both the detectability of strong lensing in a given survey and modify the properties of the lensing that is detected. In this paper, we utilize a large cosmological N-body simulation and a multiple lens plane (and many source planes) ray-tracing technique to quantify the influence of line of sight halos on the detectability of cluster-scale strong lensing in a cluster sample with a mass limit that encompasses current cluster catalogs from the South Pole Telescope. We extract both primary and secondary halos from the Outer Rim simulation and consider two strong lensing realizations: one with only the primary halos included, and the other contains all secondary halos down to a mass limit. In both cases, we use the same source information extracted from the Hubble Ultra Deep Field, and create realistic lensed images consistent with moderately deep ground-based imaging. The results demonstrate that down to the mass limit considered the total number of lenses is boosted by about 13-21% when considering the complete multi-halo lightcone. The increment in strong lens counts peaks at lens redshifts of 0.6 approximately with no significant effect at z<0.3. The strongest trends are observed relative to the primary halo mass, with no significant impact in the most massive quintile of the halo sample, but increasingly boosting the observed lens counts toward small primary halo masses, with an enhancement greater than 50% in the least massive quintile of the halo masses considered.
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