Flux ratios as a probe of dark substructures in quadruple-image gravitational lenses

We demonstrate that the flux ratios of 4-image lensed quasars provide a powerful means of probing the small scale structure of Dark Matter (DM) halos. A family of smooth lens models can precisely predict certain combinations of flux ratios using only the positions of the images and lens as inputs. Using 5 observed lens systems we show that real galaxies {\it cannot} be described by smooth singular isothermal ellipsoids, nor by the more general elliptical power-law potentials. Large scale distortions from the elliptical models can not yet be ruled out. Nevertheless we find, by comparing with simulations, that the data can be accounted for by a significant ($\sim 5-10%$) amount of dark substructures within a projected distance of several kpc from the center of lenses. This interpretation favors the Cold Dark Matter (CDM) model other the warm or self-interacting DM models.