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We use high-resolution Aquarius simulations of the formation of Milky Way-sized haloes in the ΛCDM cosmology to study the effects of dark matter substructures on gravitational lensing. Each halo is resolved with ∼ 10 8 particles (at a mass resolution mp ∼ 10 3 to 10 4 h −1 M⊙) within its virial radius. Subhaloes with masses msub ∼ 105 h −1 M ⊙ 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 ∼ 10 8 h −1 M ⊙ 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, although in most cases it is not. The probability
Xu et al. (Thu,) studied this question.