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 model 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.
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