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Strong gravitational lensing can be used to find otherwise invisible darkmatter subhaloes. In such an analysis, the lens galaxy mass model is asignificant source of systematic uncertainty. In this paper we analyse theeffect of angular complexity in the lens model. We use multipole perturbationswhich introduce low-order deviations from pure ellipticity in the isodensitycontours, keeping the radial density profile fixed. We find that, in HST-likedata, multipole perturbations consistent with those seen in galaxy isophotesare very effective at causing false positive substructure detections. We showthat the effectiveness of this degeneracy depends on the deviation from a pureellipse and the lensing configuration. We find that, when multipoles of one percent are allowed in the lens model, the area in the observation where a subhalocould be detected drops by a factor of three. Sensitivity away from the lensedimages is mostly lost. However, the mass limit of detectable objects on orclose to the lensed images does not change. We do not expect the addition ofmultipole perturbations to lens models to have a significant effect on theability of strong lensing to constrain the underlying dark matter model.However, given the high rate of false positive detections, angular complexitybeyond the elliptical power-law should be included for such studies to bereliable. We discuss implications for previous detections and future work.

Angular complexity in strong lens substructure detection