The flux-ratio anomalies observed in multiply-lensed quasar images are most plausibly explained as the result of perturbing structures superposed on the underlying smooth matter distribution of the primary lens. The cold dark matter cosmological mode
l predicts that a large number of substructures should survive inside larger halos but, surprisingly, this population alone has been shown to be insufficient to explain the observed distribution of the flux ratios of quasars multiple images. Other halos (and their own subhalos) projected along the line of sight to the primary lens have been considered as additional source of perturbation. In this work, we use ray tracing through the Millennium II simulation to investigate the importance of projection effects due to halos and subhalos of mass m>1E8 Msun/h and extend our analysis to lower masses, m>1E6 Msun/h, using Monte-Carlo halo distributions. We find that the magnitude of the violation depends strongly on the density profile and concentration of the intervening halos, but clustering plays only a minor role. For a typical lensing geometry (lens at redshift 0.6 and source at redshift 2), background haloes (behind the main lens) are more likely to cause a violation than foreground halos. We conclude that line-of-sight structures can be as important as intrinsic substructures in causing flux-ratio anomalies. The combined effect of perturbing structures within the lens and along the line of sight in the LCDM universe results in a cusp-violation probability of 20-30%. This alleviates the discrepancy between models and current data, but a larger observational sample is required for a stronger test of the theory.
We use high-resolution Aquarius simulations of Milky Way-sized haloes in the LCDM cosmology to study the effects of dark matter substructures on gravitational lensing. Each halo is resolved with ~ 10^8 particles (at a mass resolution ~ 10^3-4 M_sun/h
) within its virial radius. Subhaloes with masses larger than 10^5 M_sun/h 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 M_sun/h 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 about 0.001. 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.
