Modelling the line-of-sight contribution in substructure lensing

TL;DR

This paper analyzes how line-of-sight dark matter haloes influence gravitational lensing features like Einstein rings, providing a mass-redshift relation to distinguish between substructures and line-of-sight effects, aiding dark matter model testing.

Contribution

It introduces a method to rescale detection thresholds from substructures to line-of-sight haloes and assesses their relative contributions and degeneracies in lensing observations.

Findings

Line-of-sight haloes dominate substructures in lensing signals, especially at high redshifts.

Substructures account for about 30% of perturbers at low redshift, less than 10% at high redshift.

High-quality data can recover line-of-sight halo redshifts with 0.15 accuracy at 68% confidence.

Abstract

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.