Constraining the Nature of Dark Matter from Tidal Radii of Cluster Galaxy Subhalos

TL;DR

This study tests whether dark matter is collisionless or self-interacting by examining the outer tidal extents of cluster subhalos through combined strong and weak lensing in eight massive clusters ($M_{200}\sim0.41$–$2.2\times10^{15}$ M$_\odot$, $z\sim0.17$–$0.54$). Using Lenstool-based multi-scale mass models, subhalos are modeled with dPIE profiles whose tidal radii are constrained by luminosity-based scaling relations, and the analysis is calibrated against Illustris-TNG cluster analogs to anchor CDM expectations. The main result is that the observed tidal radii are consistent with CDM predictions and strongly inconsistent with SIDM, ruling out significant self-interaction in cluster subhalos of $M_{\text{subhalo}}^{\text{dPIE}}\sim5\times10^{9}$–$10^{12}$ M$_\odot$; this disfavors velocity-independent or certain velocity-dependent SIDM scenarios at cluster scales. The work provides a robust, ensemble-level DM diagnostic that complements other cluster-scale tests, with future surveys and higher-resolution simulations expected to tighten these constraints, potentially probing velocity-dependent cross-sections in finer detail.

Abstract

Gravitational lensing by galaxy clusters provides a powerful probe of the spatial distribution of dark matter and its microphysical properties. Strong and weak lensing constraints on the density profiles of subhalos and their truncation radii offer key diagnostics for distinguishing between collisionless cold dark matter (CDM) and self-interacting dark matter (SIDM). Notably, in the strongly collisional SIDM regime, subhalo core collapse and enhanced mass loss from ram-pressure stripping predict steeper central density slopes and more compact truncation radii--features that are directly testable with current lensing data. We analyze subhalo truncation in eight lensing clusters (Abell 2218, 383, 963, 209, 2390, and MACS J0416.1, J1206.2, J1149.6) that span the redshift range <$z_\text{spec}$>$ \simeq 0.17$-$0.54$ with virial masses $M_{200} \simeq0.41$-$2.2\times 10^{15}$ M$_\odot$ to constrain SIDM versus CDM. Our results indicate that the outer spatial extents of subhalos are statistically consistent with CDM, corroborated by redshift- and mass-matched analogs from the Illustris-TNG simulations. We conclude that the tidal radii of cluster galaxy subhalos serve as an important and complementary diagnostic of the nature of dark matter in these violent, dense environments.

Figures (5)

• Figure 1: Comparison of density-based $r^\text{CDM}_\text{t}$ and lensing-based $r^\text{dPIE}_\text{t}$ tidal truncation radius estimates for subhalos with masses $10^{10.5\text{\textendash}12.5}$ M$_\odot$ (color-coded) in simulated Abell 2390 cluster analogs. The median $\tilde{\epsilon_i} = 0.477$ (gray line) is statistically representative across the entire sample of 2860 subhalos.
• Figure 2: Boxplot displaying the $r^\text{dPIE}_\text{t}/r^\text{CDM}_\text{t}$ distributions, which exhibit high consistency across all redshift- and mass-matched TNG-Cluster analogs of our sample (Table \ref{['tab:Cluster_Properties']}), arranged in increasing redshifts from left to right. From a final sample of 13714 subhalos in all analogs, we infer a median of $\tilde{\epsilon_i} = 0.470$ (gray line) and interquartile range of 0.391–0.553. The central 97% entries lie within 0.248–1.18.
• Figure 3: Tidal truncation radii of cluster subhalos derived from lensing-based observational inference (gray curves; gray-shading indicates conservative $5\sigma$), CDM estimates (blue circles with $\tilde{\epsilon_i} = 0.470$; arrowheads (error bars) denote the central 50% (97%) range of subhalo-to-subhalo variance inferred from TNG-Cluster in Fig. \ref{['fig:TNG_Cluster-3']}), and SIDM estimates (red; conservative upper bounds). Data points of Abell 2218 are quoted directly from Natarajan:2002cw. On a population level, CDM is consistent with, while SIDM is ruled out with high statistical significance across, the entire cluster sample. Modulo detailed cluster assembly history, the overall distribution of CDM-predicted tidal radii steadily shifts downward with decreasing redshifts (or increasing cosmic age from $t_\text{Universe} = 8.1$ Gyr to $11.4$ Gyr), indicative of continuous subhalo tidal striping. The consistent one-to-two order-of-magnitude discrepancy in SIDM predictions below the observational inference cannot be reconciled with uncertainties in either observational inference or subhalo-to-subhalo variance in $\epsilon_i$, ruling out dark matter collisionality in cluster subhalos of the mass range $M^\text{subhalo}_\text{dPIE} \simeq 5\times 10^{9\text{\textendash}12}$ M$_\odot$.
• Figure 4: Left: Projected rest-frame velocity $v_\text{rf}$ of cluster galaxy sources. We compare the galaxy membership identification from our CALSAGOS-based procedure (cyan), SIMBAD database Wenger2000AAS1439W (dark blue), or Geller2014ApJ78352G (red; for Abell 275); non-members are marked with open black circles. Gray curves denote the escape velocity curve $v_\text{esp}(R)$ inferred from the lensing-constrained NFW mass profile. Right: Line-of-sight velocity dispersion profiles of each member galaxy sample. Our independent membership identification routine yields $\sigma_\text{los}(R)$ in great agreement with published data from Geller2014ApJ78352G (red; for Abell 275), Annunziatella2016AA585A160A (yellow; for Abell 209), Biviano:2013eia (magenta; for MACS J1206).
• Figure 5: Tidal truncation radii of cluster subhalos derived from lensing-based observational inference (gray curves; gray-shading indicates conservative $5\sigma$) and CDM estimates from either $\text{\sc{Lenstool}}$-identified (blue circles, as in Fig. \ref{['fig:CDM_SIDM']}) or single best-fit NFW (cyan triangles) large-scale potentials for each cluster. We adopt $\tilde{\epsilon_i} = 0.47$; the exemplary error bar in the panel of Abell 383 shows the central 97% range of subhalo-to-subhalo variance inferred from the TNG-Cluster analogs (Fig. \ref{['fig:TNG_Cluster-3']}). We observe an overall consistency between these two estimates; points showing the largest offsets are subhalos with the smallest projected distances to the respective cluster center and expectedly sensitive to the detailed large-scale potential modeling (i.e. multi-clump vs. single NFW cusp) in the strong lensing regime. In particular, the two clusters that show the most notable offsets— MACS J0416 and J1149— have the largest projected separation between their two most massive clumps in our sample. Importantly, these two estimates are mutually compatible (within the subhalo-to-subhalo variance) and both statistically consistent with the observational inference, strengthening the robustness of our inferred SIDM constraints (Fig. \ref{['fig:CDM_SIDM']}).