Flux-ratio anomalies in cusp quasars reveal dark matter beyond CDM

Abstract

Strongly lensed quasars in cusp configurations provide a uniquely sensitive probe of small-scale dark matter structure. Using the largest microlensing-free flux ratios for 17 quadruply imaged cusps, we combine these with extensive Monte Carlo simulations of mock lens realizations under cold dark matter (CDM), self-interacting dark matter (SIDM), and fuzzy dark matter (FDM) scenarios. Building on this, we propose a region (minor-axis and narrow major-axis cusp lenses) where flux-ratio anomalies persist even under globally parameterized models ("macromodels") with multipole freedom (capturing disk, asymmetric, or merger-driven structures). Within this region, J1042+1641 is $>3σ$ incompatible with both CDM and SIDM. Our results yield a Bayes factor exceeding $100$, providing very strong evidence for FDM over even the most optimistic CDM and SIDM scenarios. As only 11 cusp lenses lie within this region, extending to larger samples will be essential for assessing its statistical generality and for decisively confirming these findings with future microlensing-free flux ratio data.

Figures (12)

• Figure 1: Top panels: Effective convergence perturbations ($\kappa_{\mathrm{eff,sub}}$; see Eq. (\ref{['eq:kappa_eff_sub']})) induced by substructure in a representative lens with significant $m=3/4$ multipoles, characterized by a major-axis angle $\phi = 70.63^\circ$ (see Extended Data Table. \ref{['tab:mock_all_sim_185_key']} for macromodel parameters). The black ellipse denotes the critical curve, and the insets show the distinct perturbation patterns associated with different dark matter scenarios at each cusp image position (A, B and C). The colours encode the angular misfit $\chi^{2}$ (see Eq. (\ref{['Eq:kasquare']})), constructed from $\phi$ and $\phi_{1}$. Middle panels: Source-plane caustics, with background colour indicating $\log|\mu|$. Insets illustrate the corresponding source positions for the points in the top panels, with colours also encoding $\chi^{2}$. They highlight substructure-induced distortions and local variations in the caustic shape across different dark matter scenarios. Bottom panels: Scatter distributions of $R_{\mathrm{cusp}}$ obtained while traversing $\phi$ near the cusp angle. As the source approaches the narrow cusp, the differences among CDM, SIDM, and FDM increase substantially. In particular, interference-driven density fluctuations in FDM produce a larger fraction of high-$R_{\mathrm{cusp}}$ points.
• Figure 1: Workflow used in this study. (a) Observational data provide the image positions, flux ratios, and the geometric opening angle $\phi$. (b) From these quantities, we compute the observed $R_{\rm cusp}$, which defines the constraints used to evaluate different dark matter scenarios. (c) We construct mock macrolens models. (d) We then add small-scale structure corresponding to CDM, SIDM, and FDM scenarios onto the smooth lens potentials. (e) Using our JAX-accelerated GPU implementation of the multi-plane lensing framework, we generate the lensing realizations. (f) A two-stage MCMC procedure samples source-plane configurations consistent with the target geometry, yielding weighted realizations of $R_{\rm cusp}$. (g) For each dark matter scenario, we accumulate more than $10^{7}$ realizations to construct statistical predictions in the $(R_{\rm cusp},\phi)$ plane. (h) Comparison with the observational measurements through Bayesian marginalisation then yields the relative support for competing dark matter microphysics.
• Figure 2: Normalized $R_{\mathrm{cusp}}$ distributions predicted under different dark matter scenarios for cusp-configured mock lens systems generated using a SIE model with external shear (see Extended Data Fig. \ref{['tab:Bey_smooth']} for smooth-lens predictions). The lens populations are separated into major-axis and minor-axis cusp configurations (see Extended Data Fig. \ref{['fig:Major_Minor']}). The distributions are constructed by samples $\phi$ from $30^\circ$ to $150^\circ$ and applying a normalized KDE within each $\phi$ bin. The $n\sigma$ contours correspond to highest-probability-density regions enclosing 68.3%, 95%, and 99.7% of the total KDE probability mass, respectively. The left, middle, and right columns correspond to mock lenses populated with CDM, SIDM, and FDM substructures, respectively. Each dark matter system contains $\sim10^7$ data points. The background colour map represents the KDE-normalized density computed from these data points in each $\phi$ bin. Systems marked with red labels denote $2\sigma$ outliers (see Extended Data Table. \ref{['tab:individual_norms']} for the per-system density values).
• Figure 2: Background-subtracted gravitational lensing images of the selected cusp lenses. The JWST systems are taken from the GO-2046 program Nierenberg:2023tviKeeley:2024brxKeeley:2025oigGilman:2025fhy, while the HST images use archival near-infrared data (see Extended Data Table. \ref{['tab:cusp_sample_obs']} for details). In both cases, the wavebands adopted for the photometric measurements probe emission regions that are effectively microlensing-free, although the images shown here are for illustration only. Lenses are grouped into major-axis (upper two rows) and minor-axis (lower two rows) cusps, ordered by increasing opening angle $\phi$. Systems such as B2045 and J1042 exhibit pronounced flux-ratio anomalies and are of particular interest in this work.
• Figure 3: Same as Fig. \ref{['fig:NomonizedKDE']}, but for mock lens systems generated with the SIE with external and multipole.