2025MNRAS.540..247E

The nature of dark matter is poorly constrained on subgalactic scales. Alternative models to cold dark matter, such as warm dark matter or self-interacting dark matter, could produce very different dark haloes on these scales. One of the few known dark haloes smaller than a galaxy was discovered in the triple source plane strong lens system J0946 + 1006. Previous studies have found that this structure is much more concentrated than expected in Lambda cold dark matter ($\Lambda$CDM), but have assumed the dark halo is at the same redshift as the main deflector ($z_{\rm main}=0.222$). In this paper, we fit for the redshift of this dark halo. We reconstruct the first two sources in the system using a forward modelling approach, allowing for additional complexity from multipole perturbations. We find that the perturber redshift is $z_{\rm halo} = {0.207}^{+0.019}_{-0.019}$, and lower bounds on the evidence strongly prefer a subhalo over a line-of-sight structure. Whilst modelling both background sources does not improve constraints on the redshift of the subhalo, it breaks important degeneracies affecting the reconstruction of multipole perturbations. We find that the subhalo is a more than $5\sigma$ outlier from the $\Lambda$CDM $v_{\rm max}$-$r_{\rm max}$ relation and has a steep profile with an average slope of $\gamma _{\rm 2D} = {-1.81}^{+0.15}_{-0.11}$ for radii between $0.75 \,{\rm and}\, 1.25$ kpc. This steep slope might indicate dark matter self-interactions causing the subhalo to undergo gravothermal collapse; such collapsed haloes are expected to have $\gamma _{\rm 2D} \approx -2$.