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

¹ European Southern Observatory (ESO), Karl-Schwarzschild Str. 2, D-85748 Garching bei München, Germany
² Max Planck Institute for Astrophysics, Karl-Schwarzschild Str. 1, D-85748 Garching bei München, Germany
³ Kapteyn Astronomical Institute, University of Groningen, Postbus 800, NL-9700 AV Groningen, The Netherlands
⁴ South African Radio Astronomy Observatory (SARAO), P.O. Box 443 Krugersdorp 1740, South Africa
⁵ Department of Physics, University of Pretoria, Lynnwood Road, Hatfield, Pretoria 0083, South Africa

^⋆ Corresponding author: hannah.stacey@eso.org

Received: 16 June 2025
Accepted: 3 September 2025

Abstract

The prevalence and properties of low-mass dark matter haloes serve as a crucial test for understanding the nature of dark matter, and these may be constrained through the gravitational deflection of strongly lensed arcs. Previous studies have 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 ≈10⁹ M_⊙ 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 of similarities 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 the fourth order and require a well-fit 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.