Probing dark matter with strong gravitational lensing through an effective density slope

Many dark matter (DM) models that are consistent with current cosmological data show differences in the predicted (sub)halo mass function, especially at sub-galactic scales, where observations are challenging due to the inefficiency of star formation. Strong gravitational lensing has been shown to be a useful tool for detecting dark low-mass (sub)haloes through perturbations in lensing arcs, therefore allowing the testing of different DM scenarios. However, measuring the total mass of a perturber from strong lensing data is challenging. Overestimating or underestimating perturber masses can lead to incorrect inferences about the nature of DM. In this paper, we argue that inferring an effective slope of the DM density profile, which is the power-law slope of perturbers at intermediate radii, where we expect the perturber to have the largest observable effect, is a promising way to circumvent these challenges. Using N-body simulations, we show that (sub)halo populations under different DM scenarios differ in their effective density slope distributions. Using realistic mocks of Hubble Space Telescope observations of strong lensing images, we show that the effective density slope of perturbers can be robustly measured with high enough accuracy to discern between different models. We also present our measurement of the effective density slope $\gamma =1.96\substack{+0.12 \\ -0.12}$ for the perturber in JVAS B1938+666, which is a 2σ outlier of the cold DM scenario. More measurements of this kind are needed to draw robust conclusions about the nature of DM.