[Paper Review] Gravitational imaging through a triple source plane lens: revisiting the $Λ$CDM-defying dark subhalo in SDSSJ0946+1006

Daniel Ballard, Wolfgang Enzi+3 more|arXiv (Cornell University)|Sep 8, 2023

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy89 references3 citations

TL;DR

This study reanalyzes the triple-source-plane lens SDSSJ0946+1006 using multi-band HST and VLT-MUSE data to reassess a previously reported dark subhalo that appeared inconsistent with ΛCDM predictions. It finds a 5.9σ substructure with mass log₁₀(M/M☉) = 9.2⁺⁰.⁴₋₀.¹ and concentration log₁₀c = 2.4⁺⁰.⁵₋₀.³, now consistent with CDM simulations, while highlighting that detection significance is highly sensitive to source regularization schemes.

ABSTRACT

The $Λ$CDM paradigm successfully explains the large-scale structure of the Universe, but is less well constrained on sub-galactic scales. Gravitational lens modelling has been used to measure the imprints of dark substructures on lensed arcs, testing the small-scale predictions of $Λ$CDM. However, the methods required for these tests are subject to degeneracies among the lens mass model and the source light profile. We present a case study of the unique compound gravitational lens SDSSJ0946+1006, wherein a dark, massive substructure has been detected, whose reported high concentration would be unlikely in a $Λ$CDM universe. For the first time, we model the first two background sources in both I- and U-band HST imaging, as well as VLT-MUSE emission line data for the most distant source. We recover a lensing perturber at a $5.9σ$ confidence level with mass $\log_{10}(M_\mathrm{sub}/M_{\odot})=9.2^{+0.4}_{-0.1}$ and concentration $\log_{10}c=2.4^{+0.5}_{-0.3}$. The concentration is more consistent with CDM subhalos than previously reported, and the mass is compatible with that of a dwarf satellite galaxy whose flux is undetectable in the data at the location of the perturber. A wandering black hole with mass $\log_{10}(M_\mathrm{BH}/M_{\odot})=8.9^{+0.2}_{-0.1}$ is a viable alternative model. We systematically investigate alternative assumptions about the complexity of the mass distribution and source reconstruction; in all cases the subhalo is detected at around the $\geq5σ$ level. However, the detection significance can be altered substantially (up to $11.3σ$) by alternative choices for the source regularisation scheme.

Motivation & Objective

• To reassess the existence and properties of a previously reported dark subhalo in the triple-source-plane lens SDSSJ0946+1006, which was claimed to defy ΛCDM predictions.
• To investigate whether the subhalo's high concentration and mass are consistent with cold dark matter (CDM) simulations, given new multi-wavelength data.
• To evaluate the robustness of the subhalo detection against systematic uncertainties in lens modeling, particularly source reconstruction and regularization schemes.
• To determine whether alternative mass models—such as a wandering black hole—can explain the lensing anomalies without invoking a dark subhalo.
• To assess the impact of source regularization (gradient vs. curvature) on substructure detection significance and Bayesian evidence in strong lensing modeling.

Proposed method

• Performs joint lens modeling of I- and U-band HST imaging for the two closer sources (s1 and s2) and VLT-MUSE emission-line data for the distant source (s3).
• Employs a parametric macro-model for the main deflector and a non-parametric substructure model to detect dark perturbers.
• Uses Bayesian evidence and significance testing (via χ² and posterior sampling) to evaluate substructure detection across multiple model variants.
• Systematically varies source regularization schemes: gradient-based (fiducial) vs. curvature-based, to assess their impact on detection significance.
• Tests model robustness by including higher-order multipoles (3rd and 4th order) in the main deflector and allowing ellipticity for s1.
• Compares alternative mass models, including a wandering black hole, to determine if they can reproduce the lensing anomalies without a dark subhalo.

Figure 1: HST imaging of J0946 in the I–band (left) and U–band (middle), and continuum–subtracted VLT–MUSE narrow–band imaging (width 5 Å centred at $8475$ Å) showing the Ly– $\alpha$ emission at $z=5.975$ (right). The cyan cross represents the best fit location of the substructure in as reported in

Experimental results

Research questions

• RQ1 Is the previously reported dark subhalo in SDSSJ0946+1006 still inconsistent with ΛCDM predictions when reanalyzed with multi-band and multi-instrument data?
• RQ2 How does the choice of source regularization (gradient vs. curvature) affect the significance of substructure detection in strong lensing models?
• RQ3 Can a wandering black hole with mass ~10⁸.⁹M☉ explain the lensing anomalies as well as a dark subhalo?
• RQ4 How robust is the substructure detection when the complexity of the macro-model (e.g., multipoles, ellipticity) is varied?
• RQ5 To what extent do the subhalo’s mass and concentration now align with predictions from ΛCDM simulations compared to earlier claims?

Key findings

• A dark substructure is detected at 5.9σ significance with mass log₁₀(M/M☉) = 9.2⁺⁰.⁴₋₀.¹ and concentration log₁₀c = 2.4⁺⁰.⁵₋₀.³, now consistent with CDM simulations at 2.0σc.
• The substructure’s mass is compatible with that of a dwarf satellite galaxy whose light is undetectable in the data at its location.
• Detection significance can vary dramatically—up to 11.3σ—depending on whether curvature or gradient regularization is used for source reconstruction.
• Despite higher significance under curvature regularization, Bayesian evidence strongly prefers the fiducial gradient regularization scheme.
• The inclusion of higher-order multipoles and variable ellipticity in the macro-model does not significantly alter the substructure detection, which remains ≥6σ in the best-fit model.
• A wandering black hole with mass log₁₀(M/M☉) = 8.9⁺⁰.²₋₀.¹ is a viable alternative to the dark subhalo model, though not preferred by evidence.

Figure 3: Mock data for our sensitivity test, where panels (left to right) show the initial model image, a zoomed inset around the location of the reported substructure, the effect of blurring by the HST I–band PSF, and the addition of background noise akin to the original HST I–band data. The top r