On the origin of the flux ratio anomaly in quadruple lens systems

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 ≲109 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 〈δκsub〉 = 0.003, corresponding to the mean of the ratio of a projected dark matter mass fraction in subhaloes at the effective Einstein radius 〈fsub〉 = 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 〈|δκlos|〉 = 0.008, corresponding to 〈flos〉 = 0.017. The contribution of the magnification perturbation caused by subhaloes is ∼40 per cent of the total at a source redshift zS = 0.7 and decreases monotonically in zS to ∼20 per cent at zS = 3.6. Assuming statistical isotropy, the convergence perturbation estimated from 11 observed quadruple lens systems has a positive correlation with the source redshift zS, which is much stronger than that with the lens redshift zL. 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.