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ABSTRACT Strong gravitational lensing provides a purely gravitational means to infer properties of dark matter haloes and thereby constrain the particle nature of dark matter. Strong lenses sometimes appear as four lensed images of a background quasar accompanied by spatially resolved emission from the quasar host galaxy encircling the main deflector (lensed arcs). We present methodology to simultaneously reconstruct lensed arcs and relative image magnifications (flux ratios) in the presence of full populations of subhaloes and line-of-sight haloes. To this end, we develop a new approach for multiplane ray tracing that accelerates lens mass and source light reconstruction by factors of $$\sim\!\! 100\!\!-\!\!1000$$. Using simulated data, we show that simultaneous reconstruction of lensed arcs and flux ratios isolates small-scale perturbations to flux ratios by dark matter substructure from uncertainties associated with the main deflector mass profile on larger angular scales. Relative to analyses that use only image positions and flux ratios to constrain the lens model, incorporating arcs strengthens likelihood ratios penalizing warm dark matter with a suppression scale $$m_{\rm {hm}} / {\rm M}_{\odot }$$ in the ranges of $$\left[10^7 \!\!-\!\! 10^{7.5}\right]$$, $$\left[10^{7.5} \!\!-\!\! 10^{8}\right]$$, $$\left[10^8 \!\!-\!\! 10^{8.5}\right]$$, and $$\left[10^{8.5} \!\!-\!\! 10^{9}\right]$$ by factors of 1.3, 2.5, 5.6, and 13.1, respectively, for a cold dark matter ground truth. The 95 per cent exclusion limit improves by 0.5 dex in $$\log _{10} m_{\rm {hm}}$$. The enhanced sensitivity to low-mass haloes enabled by these methods pushes the observational frontier of substructure lensing to the threshold of galaxy formation, enabling stringent tests of any theory that alters the properties of dark matter haloes. 

ABSTRACT This is the second in a series of papers in which we use JWST Mid Infrared Instrument multiband imaging to measure the warm dust emission in a sample of 31 multiply imaged quasars, to be used as a probe of the particle nature of dark matter. We present measurements of the relative magnifications of the strongly lensed warm dust emission in a sample of nine systems. The warm dust region is compact and sensitive to perturbations by populations of haloes down to masses $$\sim 10^6$$ M$$_{\odot }$$. Using these warm dust flux-ratio measurements in combination with five previous narrow-line flux-ratio measurements, we constrain the halo mass function. In our model, we allow for complex deflector macromodels with flexible third- and fourth-order multipole deviations from ellipticity, and we introduce an improved model of the tidal evolution of subhaloes. We constrain a WDM model and find an upper limit on the half-mode mass of $$10^{7.6}\, {\rm M}_\odot$$ at posterior odds of 10:1. This corresponds to a lower limit on a thermally produced dark matter particle mass of 6.1 keV. This is the strongest gravitational lensing constraint to date, and comparable to those from independent probes such as the Ly $$\alpha$$ forest and Milky Way satellite galaxies.