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Using a single gravitational lens system observed at ≲ 5 mas resolution with very long baseline interferometry, we place a lower bound on the mass of the fuzzy dark matter (FDM) particle, ruling out mχ ≤ 4.4 × 10−21 eV with a 20:1 posterior odds ratio relative to a smooth lens model. We generalize our result to non-scalar and multiple-field models, such as vector FDM, with mχ,vec > 1.4 × 10−21 eV. Due to the extended source structure and high angular resolution of the observation, our analysis is directly sensitive to the presence of granule structures in the main dark matter halo of the lens, which is the most generic prediction of FDM theories. A model based on well-understood physics of ultra-light dark matter fields in a gravitational potential well makes our result robust to a wide range of assumed dark matter fractions and velocity dispersions in the lens galaxy. Our result is competitive with other lower bounds on mχ from past analyses, which rely on intermediate modelling of structure formation and/or baryonic effects. Higher resolution observations taken at 10–100 GHz could improve our constraints by up to two orders of magnitude in the future.

We investigate the mass structure of a strong gravitational lens galaxy at z = 0.350, taking advantage of the milliarcsecond (mas) angular resolution of very long baseline interferometric (VLBI) observations. In the first analysis of its kind at this resolution, we jointly infer the lens model parameters and pixellated radio source surface brightness. We consider several lens models of increasing complexity, starting from an elliptical power-law density profile. We extend this model to include angular multipole structures, a separate stellar mass component, additional nearby field galaxies, and/or a generic external potential. We compare these models using their relative Bayesian log-evidence (Bayes factor). We find strong evidence for angular structure in the lens; our best model is comprised of a power-law profile plus multipole perturbations and external potential, with a Bayes factor of +14984 relative to the elliptical power-law model. It is noteworthy that the elliptical power-law mass distribution is a remarkably good fit on its own, with additional model complexity correcting the deflection angles only at the ∼5 mas level. We also consider the effects of added complexity in the lens model on time-delay cosmography and flux-ratio analyses. We find that an overly simplistic power-law ellipsoid lens model can bias the measurement of H0 by ∼3 per cent and mimic flux ratio anomalies of ∼8 per cent. Our results demonstrate the power of high-resolution VLBI observations to provide strong constraints on the inner density profiles of lens galaxies.

This paper aims to quantify how the lowest halo mass that can be detected with galaxy-galaxy strong gravitational lensing depends on the quality of the observations and the characteristics of the observed lens systems. Using simulated data, we measure the lowest detectable NFW mass at each location of the lens plane, in the form of detailed sensitivity maps. In summary, we find that: (i) the lowest detectable mass Mlow decreases linearly as the signal-to-noise ratio (SNR) increases and the sensitive area is larger when we decrease the noise; (ii) a moderate increase in angular resolution (0.07″ versus 0.09″) and pixel scale (0.01″ versus 0.04″) improves the sensitivity by on average 0.25 dex in halo mass, with more significant improvement around the most sensitive regions; (iii) the sensitivity to low-mass objects is largest for bright and complex lensed galaxies located inside the caustic curves and lensed into larger Einstein rings (i.e rE ≥ 1.0″). We find that for the sensitive mock images considered in this work, the minimum mass that we can detect at the redshift of the lens lies between 1.5 × 108 and $3\times 10^{9}\, \mathrm{M}_{\odot }$. We derive analytic relations between Mlow, the SNR and resolution and discuss the impact of the lensing configuration and source structure. Our results start to fill the gap between approximate predictions and real data and demonstrate the challenging nature of calculating precise forecasts for gravitational imaging. In light of our findings, we discuss possible strategies for designing strong lensing surveys and the prospects for HST, Keck, ALMA, Euclid and other future observations.