We present a measurement of the free-streaming length of dark matter (DM) and subhalo abundance around 28 quadruple image strong lenses using observations from James webb space telescope mid-infrared instrument presented in Paper III of this series. We improve on previous inferences on DM properties from lensed quasars by simultaneously reconstructing extended lensed arcs with image positions and relative magnifications (flux ratios). Our forward modeling framework generates full populations of subhalos, line-of-sight halos, and globular clusters, uses an accurate model for subhalo tidal evolution, and accounts for free-streaming effects on halo abundance and concentration. Modeling lensed arcs leads to more-precise model-predicted flux ratios, breaking covariance between subhalo abundance and the free-streaming scale parametrized by the half-mode mass $m_{\mathrm{hm}}$. Assuming subhalo abundance predicted by the semianalytic model galacticus ($N$-body simulations), we infer (Bayes factor of $10:1$) $m_{\mathrm{hm}}<{10}^{7.4}{M}_{\odot }$ ($m_{\mathrm{hm}}<{10}^{7.2}{M}_{\odot }$), a 0.4 dex improvement relative to omitting lensed arcs. These bounds correspond to lower limits on thermal relic DM particle masses of 6.5 and 7.4 keV, respectively. Conversely, assuming DM is cold, we infer a projected mass in subhalos (${10}^6<m/M_{\odot }<{10}^{10.7}$) of ${1.7}_{-1.2}^{+2.6}\times {10}^7{M}_{\odot }{\mathrm{kpc}}^{-2}$ at 95% confidence. This is consistent with galacticus predictions ($0.9\times {10}^7{M}_{\odot }{\mathrm{kpc}}^{-2}$), but in mild tension with recent $N$-body simulations ($0.6\times {10}^7{M}_{\odot }{\mathrm{kpc}}^{-2}$). Our results are among the strongest bounds on warm dark matter, and the most precise measurement of subhalo abundance around strong lenses. Further improvements will follow from the large sample of lenses to be discovered by Euclid, Rubin, and Roman.

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• Dark matter
• Gravitational lenses
• Particle dark matter
• Galaxies