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The mass-concentration relation of dark matter halos reflects the assemblyhistory of objects in hierarchical structure formation scenarios, and dependson fundamental quantities in cosmology such as the slope of the primordialmatter power-spectrum. This relation is unconstrained by observations onsub-galactic scales. We derive the first measurement of the mass-concentrationrelation using the image positions and flux ratios from eleven quadruple-imagestrong gravitational lenses (quads) in the mass range $10^{6} - 10^{10}M_{\odot}$, assuming cold dark matter. Our analysis framework includes bothsubhalos and line of sight halos, marginalizes over nuisance parametersdescribing the lens macromodel, accounts for finite source effects on lensingobservables, and simultaneously constrains the normalization and logarithmicslope of the mass-concentration relation, and the normalization of the subhalomass function. At $z=0$, we constrain the concentration of $10^{8} M_{\odot}$halos $c=12_{-5}^{+6}$ at $68 \%$ CI, and $c=12_{-9}^{+15}$ at $95 \%$ CI. Fora $10^{7} M_{\odot}$ halo, we obtain $68 \%$ ($95 \%$) constraints$c=15_{-8}^{+9}$ ($c=15_{-11}^{+18}$), while for $10^{9} M_{\odot}$ halos$c=10_{-4}^{+7}$ ($c=10_{-7}^{+14}$). These results are consistent with thetheoretical predictions from mass-concentration relations in the literature,and establish strong lensing by galaxies as a powerful probe of haloconcentrations on sub-galactic scales across cosmological distance.

Constraints on the mass-concentration relation of cold dark matter halos with 11 strong gravitational lenses