Modelling the line-of-sight contribution in substructure lensing

We investigate how Einstein rings and magnified arcs are affected by -mass dark-matter haloes placed along the line-of-sight to gravitational systems. By comparing the gravitational signature of line-of-sight haloes that of substructures within the lensing galaxy, we derive a mass-redshift that allows us to rescale the detection threshold (i. e. lowest mass) for substructures to a detection threshold for line-of-sight at any redshift. We then quantify the line-of-sight contribution to the number density of low-mass objects that can be detected through strong lensing. Finally, we assess the degeneracy between substructures line-of-sight haloes of different mass and redshift to provide a interpretation of current and future detections, with the aim of between CDM and WDM. We find that line-of-sight haloes dominate with respect to substructures, by an amount that depends on the source and lens redshifts, and on the chosen dark model. Substructures represent about 30 percent of the total number of for low lens and source redshifts (as for the SLACS lenses), but than 10 per cent for high redshift systems. We also find that for data high enough signal-to-noise ratio and angular resolution, the non-linear arising from a double-lens-plane configuration are such that one is to observationally recover the line-of-sight halo redshift with an error precision of 0. 15 at the 68 per cent confidence level.