Flux Ratios as a Probe of Dark Substructures in Quadruple-Image Gravitational Lenses

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