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

TL;DR

This study reanalyzes ALMA long-baseline observations of the lensed dusty galaxy SDP.81 to test claims of low-mass sub-halo detections and to assess the role of lens angular structure. Using a Bayesian pixellated lens model that includes a smooth elliptical power-law plus external shear, angular multipoles up to order $m=4$, and a pseudo-Jaffe sub-halo, the authors compare against previous results and perform extensive tests with mock data and different source grids. They find evidence for angular structure in the lens potential but no robust evidence for any individual sub-halo, and show that degeneracies between multipoles and sub-halo signatures can mimic each other; a hypothetical $\sim 10^{9}\,M_\odot$ sub-halo would have been detectable if real, suggesting prior detections were spurious due to smooth-model inadequacy. The work demonstrates that ALMA data of this quality can constrain both sub-halo abundances and lens angular structure, highlighting the need to model higher-order angular components to avoid false positives in sub-halo searches.

Abstract

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.

Figures (7)

• Figure 1: ALMA images of SDP 81 with natural weighting of the visibilities created via forward-modelling. The synthesised beam FWHM with natural weighting is $26\times33$ mas and $33\times42$ mas for bands 7 (left) and 6 (right), respectively.
• Figure 2: Maximum a posteriori lens models for the band 7 data. First column: lens model; crosses show lens and sub-halo positions; critical curves in black. Second column: difference in convergence relative to the PL model; contours of the sky model in grey. Third column: difference in magnification relative to the PL model; contours of the sky model in black. Fourth column: image of the residuals (data$-$model) normalised by the RMS noise ($\sigma$), with the mask shown by the dashed outline. Last column: reconstructed source with Gouraud interpolation and caustics in black. The locations of I16 and H16 purported sub-haloes are shown with a diamond and a circle, respectively.
• Figure 3: Heat map showing the log Bayes factors of the models tested on the real band 7 data (y-axis model relative to x-axis model).
• Figure 4: Heat map showing the log Bayes factors of the models tested on mock band 7 data (y-axis relative to x-axis).
• Figure 5: Heat map showing the log Bayes factors of the models tested on the real band 7 data (y-axis model relative to x-axis model), using a regular source grid of 10 mas.