2016MNRAS.461..164I

We explore the origin of the flux ratio anomaly in quadruple lens systems. Using a semi-analytic method based on N-body simulations, we estimate the effect of a possible magnification perturbation caused by subhaloes with a mass scale of <=10^9 h^-1 M_☉ in lensing galaxy haloes. Taking into account astrometric shifts and assuming that the primary lens is described by a singular isothermal ellipsoid, the expected change to the flux ratios for a multiply lensed image is just a few per cent and the mean of the expected convergence perturbation at the effective Einstein radius of the lensing galaxy halo is <δκ_sub> =0.003, corresponding to the mean of the ratio of a projected dark matter mass fraction in subhaloes at the effective Einstein radius <f_sub> =0.006. In contrast, the expected change to the flux ratio caused by line-of-sight structures is typically ∼10 per cent and the mean of the convergence perturbation is <|δκ_los|> =0.008, corresponding to <f_los> =0.017. The contribution of the magnification perturbation caused by subhaloes is ∼40 per cent of the total at a source redshift z_S=0.7 and decreases monotonically in z_S to ∼20 per cent at z_S=3.6. Assuming statistical isotropy, the convergence perturbation estimated from 11 observed quadruple lens systems has a positive correlation with the source redshift z_S, which is much stronger than that with the lens redshift z_L. This feature also supports that the flux ratio anomaly is caused mainly by line-of-sight structures rather than subhaloes. We also discuss a possible imprint of line-of-sight structures in the demagnification of minimum images due to locally underdense structures in the line of sight.