Modelling the line-of-sight contribution in substructure lensing
  We investigate how Einstein rings and magnified arcs are affected by
small-mass dark-matter haloes placed along the line-of-sight to gravitational
lens systems. By comparing the gravitational signature of line-of-sight haloes
with that of substructures within the lensing galaxy, we derive a mass-redshift
relation that allows us to rescale the detection threshold (i.e. lowest
detectable mass) for substructures to a detection threshold for line-of-sight
haloes at any redshift. We then quantify the line-of-sight contribution to the
total number density of low-mass objects that can be detected through strong
gravitational lensing. Finally, we assess the degeneracy between substructures
and line-of-sight haloes of different mass and redshift to provide a
statistical interpretation of current and future detections, with the aim of
distinguishing between CDM and WDM. We find that line-of-sight haloes
statistically dominate with respect to substructures, by an amount that
strongly depends on the source and lens redshifts, and on the chosen dark
matter model. Substructures represent about 30 percent of the total number of
perturbers for low lens and source redshifts (as for the SLACS lenses), but
less than 10 per cent for high redshift systems. We also find that for data
with high enough signal-to-noise ratio and angular resolution, the non-linear
effects arising from a double-lens-plane configuration are such that one is
able to observationally recover the line-of-sight halo redshift with an
absolute error precision of 0.15 at the 68 per cent confidence level.
