Angular complexity in strong lens substructure detection

Strong gravitational lensing can be used to find otherwise invisible dark matter subhaloes. In such an analysis, the lens galaxy mass model is a significant source of systematic uncertainty. In this paper we analyse the effect of angular complexity in the lens model. We use multipole perturbations which introduce low-order deviations from pure ellipticity in the isodensity contours, keeping the radial density profile fixed. We find that, in HST-like data, multipole perturbations consistent with those seen in galaxy isophotes are very effective at causing false positive substructure detections. We show that the effectiveness of this degeneracy depends on the deviation from a pure ellipse and the lensing configuration. We find that, when multipoles of one per cent are allowed in the lens model, the area in the observation where a subhalo could be detected drops by a factor of three. Sensitivity away from the lensed images is mostly lost. However, the mass limit of detectable objects on or close to the lensed images does not change. We do not expect the addition of multipole perturbations to lens models to have a significant effect on the ability of strong lensing to constrain the underlying dark matter model. However, given the high rate of false positive detections, angular complexity beyond the elliptical power-law should be included for such studies to be reliable. We discuss implications for previous detections and future work.