  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.
