Out of sight, out of mind? The impact of correlated clustering in
  substructure lensing
  A promising route for revealing the existence of dark matter structures on
mass scales smaller than the faintest galaxies is through their effect on
strong gravitational lenses. We examine the role of local, lens-proximate
clustering in boosting the lensing probability relative to contributions from
substructure and unclustered line-of-sight (LOS) halos. Using two cosmological
simulations that can resolve halo masses of $M_{\rm halo} \simeq 10^{9}\
M_{\odot}$ (in a simulation box of length $L_{\rm box}{\sim}100\,{\rm Mpc}$)
and $10^{7}\ M_{\odot}$ ($L_{\rm box}\sim20\,{\rm Mpc}$), we demonstrate that
clustering in the vicinity of the lens host produces a clear enhancement
relative to an assumption of unclustered halos that persists to $> 20\,R_{\rm
vir}$. This enhancement exceeds estimates that use a two-halo term to account
for clustering, particularly within $2-5\,R_{\rm vir}$. We provide an analytic
expression for this excess, clustered contribution. We find that local
clustering boosts the expected count of $10^9 \ M_\odot$ perturbing halos by
${\sim}35\%$ compared to substructure alone, a result that will significantly
enhance expected signals for low-redshift ($z_l \simeq 0.2$) lenses, where
substructure contributes substantially compared to LOS halos. We also find that
the orientation of the lens with respect to the line of sight (e.g., whether
the line of sight passes through the major axis of the lens) can also have a
significant effect on the lensing signal, boosting counts by an additional
$\sim 50\%$ compared to a random orientations. This could be important if
discovered lenses are biased to be oriented along their principal axis.
