Dents in the Mirror: A Novel Probe of Dark Matter Substructure in Galaxy Clusters from the Astrometric Asymmetry of Lensed Arcs

TL;DR

This work introduces a forward-modeling, likelihood-free ABC approach to constrain the CDM subhalo mass fraction $f_{\rm sub}$ in galaxy clusters by exploiting astrometric perturbations in lensed arcs near critical curves. The method combines a semi-analytic tidal-evolution model for subhalos with a smooth cluster macrolens, quantifies arc asymmetry through the metric $\xi = \log(1 - |\rho_{\rm mid}|)$, and infers $f_{\rm sub}$ from mock and real arc data. Validation on mock arcs shows the technique recovers the true $f_{\rm sub}$ within the 68% CI in about 73% of cases, and the constraints sharpen with multiple arcs or higher astrometric precision. Applied to AS1063 System 1 and the Warhol Arc, the joint analysis yields $\log f_{\rm sub} = -2.68^{+0.58}_{-0.74}$, with AS1063 providing a measurable constraint and Warhol offering an upper limit, both broadly consistent with CDM predictions. The framework paves the way for robust cluster-scale constraints on dark matter substructure as larger samples of high-resolution arcs become available from JWST and future surveys.

Abstract

Astrometric perturbations of lensed arcs behind galaxy clusters have been recently suggested as promising probes of small-scale ($\lesssim10^9 M_{\odot}$) dark matter substructure. Populations of cold dark matter (CDM) subhalos, predicted in hierarchical structure formation theory, can break the symmetry of arcs near the critical curve, leading to positional shifts in the observed images. We present a novel statistical method to constrain the average subhalo mass fraction ($f_{\rm sub}$) in clusters that takes advantage of this induced positional asymmetry. Focusing on CDM, we extend a recent semi-analytic model of subhalo tidal evolution to accurately simulate realistic subhalos within a cluster-scale host. We simulate the asymmetry of lensed arcs from these subhalo populations using Approximate Bayesian Computation. Using mock data, we demonstrate that our method can reliably recover the simulated $f_{\rm sub}$ to within 68\% CI in 73\% of cases, regardless of the lens model, astrometric precision, and image morphology. We show that the constraining power of our method is optimized for larger samples of well observed arcs, ideal for recent JWST observations of cluster lenses. As a preliminary test, we apply our method to the MACSJ0416 Warhol arc and AS1063 System 1. For Warhol we constrain the upper limit on $\log f_{\rm sub} < -3.40^{+1.06}_{-0.97}$, while for AS1063 System 1 we constrain $\log f_{\rm sub} = -2.36^{+0.56}_{-0.89}$ (both at 68\% CI), consistent with CDM predictions. We elaborate on our method's limitations and its future potential to place stringent constraints on dark matter properties in cluster environments.

Figures (14)

• Figure 1: Example realizations of dark matter subhalo populations sampled with the same $f_{\rm sub}$. This illustrates the scatter of the asymmetry from realizations sampled with the same $f_{\rm sub}$. The circular window is the 2" aperture that the SHMF is sampled within surrounding the perpendicular arc in Figure \ref{['fig:perpendiculararc']}. The initial unperturbed image positions and midpoints are shown as closed green diamonds and closed yellow triangles respectively. The perturbed image positions and midpoints from the dark matter subhalo population are shown as open green diamonds and open yellow triangles respectively. The unperturbed and perturbed critical curve are shown as dashed light red and dashed bright red lines. Concentrations of matter represent evolved dark matter subhalos. Purple contours trace the density profile, with subhalos easily visible. Top: The presented realization is an example arc with low asymmetry, as can be seen by the low displacement of the perturbed midpoints. Bottom: The presented realization is an example arc with high asymmetry, as can be seen by the large displacement of the perturbed midpoints. Both realizations are made with $\log \Sigma_{\rm sub} = -1.5$ and $\log f_{\rm bound} = -1.0$, thus having $\log f_{\rm sub} = -2.6$ (see Section \ref{['txt:methodology']}). The measured asymmetry metric (see Section \ref{['txt:asymmetry']}) is $\xi = -2.43$ and $\xi = -0.17$ for the top and bottom panels, respectively.
• Figure 2: The cluster lens surface mass density distribution used as the large scale macrolens for this work. The lens is made of 3 NSIEs whose properties are listed in Table \ref{['tab:macrolens']}. The morphology is designed to imitate a merging cluster. The lens is placed at a redshift $z_d = 0.25$. 3 sources (blue diamonds) are placed near to the caustic (cyan lines) folds at a redshift $z_s = 1$, forming 3 images (green diamonds) per source. 2 images per source form very close to the critical curve (light red dashed lines). The pairs of images that form near the critical curve simulate knots belonging to the same source galaxy, which imitates the common description of a lensed arc in lens modelling. The black box denotes the window in which we simulate subhalo populations.
• Figure 3: View of the Arc region highlighted by the black box in Figure \ref{['fig:mainlens']}. The 3 knots (green diamonds) are highlighted here, representing the knots in the same source galaxy that has been lensed across the critical curve (light red dashed line). As expected in lensing theory, the midpoints of each image pair (yellow triangles) form along the critical curve. Since the source is located on a caustic fold, the critical curve can be approximated as a straight line, and thus the midpoints form in a straight line. The window shown here is the region that we simulate subhalo populations. The top panel shows a perpendicular arc while the bottom panel shows a parallel arc. Since subhalo populations will affect these arcs differently, we treat them as independent cases.
• Figure 4: The infall (dashed) and bound (solid) subhalo mass functions that we sample from at each realization for our simulation. For illustrative purposes, darker shades of blue correspond to increasing $\Sigma_{\rm sub}$. The infall SHMF is restricted to subhalos in the mass range $6 < \log (m/M_{\odot}) < 10$. The bound SHMF is calculated from the tidal stripping model presented in du25. Shaded regions indicate the $1\sigma$ scatter in sampling the SHMF.
• Figure 5: Summary plots of the tidal stripping process and how it manifests in the subhalo density profiles. For this example, the subhalo population is simulated to have a Gaussian bound mass fraction distribution: $\log f_{\rm bound} \sim \mathcal{N}\left(-1.0,0.5\right)$. We note that this mean bound mass fraction is the center of the log-uniform prior we set for $\bar{f}_{\rm bound}$. From this distribution, the tidal evolution tracks from du25 are used to calculate the each subhalo's corresponding truncation radius $r_t$, and normalization $f_t$, with some scatter. These tidal tracks can be visualized as a tight relation between $f_{\rm bound}$ and $r_t$ ( Top) and $f_{\rm bound}$ and $f_t$ ( Bottom). In both panels, blue contours are logarithmically spaced 2D density distributions for the parameters, red dots are an example subhalo population (for illustrative purposes $\log \Sigma_{\rm sub} = -1.0$ is shown, although the tidal tracks are the same for any value of $\Sigma_{\rm sub}$), and dashed lines are the means of the parameter distributions (top and right histograms).