Effects of dark matter substructures on gravitational lensing: results from the Aquarius simulations

We use the high-resolution Aquarius simulations of the formation of Milky Way-sized haloes in the Lambda cold dark matter cosmology to study the effects of dark matter substructures on gravitational lensing. Each halo is resolved with similar to 10(8) particles (at a mass resolution m(p) similar to 10(3) to 10(4) h(-1) M-circle dot) within its virial radius. Subhaloes with masses m(sub) greater than or similar to 10(5) h(-1) M-circle dot are well resolved, an improvement of at least two orders of magnitude over previous lensing studies. We incorporate a baryonic component modelled as a Hernquist profile and account for the response of the dark matter via adiabatic contraction. We focus on the 'anomalous' flux ratio problem, in particular on the violation of the cusp-caustic relation due to substructures. We find that subhaloes with masses less than similar to 10(8) h(-1)M(circle dot) play an important role in causing flux anomalies; such low-mass subhaloes have been unresolved in previous studies. There is large scatter in the predicted flux ratios between different haloes and between different projections of the same halo. In some cases, the frequency of predicted anomalous flux ratios is comparable to that observed for the radio lenses, although in most cases it is not. The probability for the simulations to reproduce the observed violations of the cusp lenses is approximate to 10(-3). We therefore conclude that the amount of substructure in the central regions of the Aquarius haloes is insufficient to explain the observed frequency of violations of the cusp-caustic relation. These conclusions are based purely on our dark matter simulations which ignore the effect of baryons on subhalo survivability.