The mass-concentration relation of dark matter halos reflects the assembly history of objects in hierarchical structure formation scenarios , and depends on fundamental quantities in cosmology such as the slope of the primordial matter power-spectrum .
This relation is unconstrained by observations on sub-galactic scales .
We derive the first measurement of the mass-concentration relation using the image positions and flux ratios from eleven quadruple-image strong gravitational lenses ( quads ) in the mass range 10 ^ { 6 } -10 ^ { 10 } { M _ { \odot } } , assuming cold dark matter .
Our analysis framework includes both subhalos and line of sight halos , marginalizes over nuisance parameters describing the lens macromodel , accounts for finite source effects on lensing observables , and simultaneously constrains the normalization and logarithmic slope of the mass-concentration relation , and the normalization of the subhalo mass 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 .
For a 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 the theoretical predictions from mass-concentration relations in the literature , and establish strong lensing by galaxies as a powerful probe of halo concentrations on sub-galactic scales across cosmological distance .