The importance of secondary halos for strong lensing in massive galaxy
  clusters across redshift
  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.
