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 apowerful means of probing the small scale structure of Dark Matter (DM) halos.A family of smooth lens models can precisely predict certain combinations offlux ratios using only the positions of the images and lens as inputs. Using 5observed lens systems we show that real galaxies {\it cannot} be described bysmooth singular isothermal ellipsoids, nor by the more general ellipticalpower-law potentials. Large scale distortions from the elliptical models cannot yet be ruled out. Nevertheless we find, by comparing with simulations, thatthe data can be accounted for by a significant ($\sim 5-10%$) amount of darksubstructures within a projected distance of several kpc from the center oflenses. This interpretation favors the Cold Dark Matter (CDM) model other thewarm or self-interacting DM models.Comment: 6 pages with 2 PS figs, resubmitted to ApJ Letter, added a figure to show the amount of substruture needed and tables of model parameter