Investigation of mass substructure in gravitational lens system SDP.81 with ALMA long-baseline observations

The prevalence and properties of low-mass dark matter haloes serve as a crucial test for understanding the nature of dark matter, and may be constrained through the gravitational deflection of strongly lensed arcs. Previous studies found evidence for the presence of low-mass dark matter haloes in observations of the gravitationally lensed, dusty star-forming galaxy SDP.81, using the Atacama Large Millimetre/sub-millimetre Array (ALMA). In this work, we analyse these observations to assess the robustness of these reported results. While our analysis indicates that the data support additional angular structure in the lensing mass distribution beyond an elliptical power-law density profile, we do not find evidence for two previously reported sub-halo detections. However, we verify with realistic mock data that we could have found evidence in favour of a previously reported $\approx 10^{9}\,{\rm M_{\odot}}$ sub-halo with a log Bayes factor of 29, should it exist in the real data. After testing various systematics, we find that this previous sub-halo inference was most likely spurious and resulted from an inadequate smooth model, specifically, poorly fitting multipoles. While we do not find evidence in favour of any individual sub-halo, we find evidence for similarity in the lensing signatures of multipoles ($m=3,4$) and single massive sub-haloes, consistent with other recent work. We suggest that future searches for low-mass haloes in lensed arcs include lens angular structure in the form of multipoles up to 4th order and require a good-fitting smooth model as a prerequisite. Overall, our findings demonstrate the suitability of ALMA data of this quality to simultaneously constrain the abundance of low-mass haloes and lens angular structure.