On the Origin of Flux Ratio Anomaly in Quadruple Lens Systems
Abstract
We explore the origin of flux ratio anomaly in quadruple lens systems. Using a semi-analytic method based on N-body simulations, we estimate the effect of possible magnification perturbation caused by subhaloes with a mass scale of < 109\,h-1 M in lensing galaxy haloes. Taking into account astrometric shifts, assuming that the primary lens is described by a singular isothermal ellipsoid, the expected change to the flux ratios per a multiply lensed image is just a few percent and the mean of the expected convergence perturbation at the effective Einstein radius of the lensing galaxy halo is 0.003, corresponding to the mean of the ratio of a projected dark matter mass fraction in subhaloes at the effective Einstein radius 0.006. In contrast, the expected change to the flux ratio caused by line-of-sight structures is typically 10 percent and the mean of the convergence perturbation is 0.008, corresponding to 0.017. The contribution of magnification perturbation caused by subhaloes is 40 percent of the total at a source redshift zS= 0.7 and decreases monotonically in zS to 20 percent at zS= 3.6. Assuming statistical isotropy, the convergence perturbation estimated from observed 11 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 an idea that the flux ratio anomaly is caused mainly by line-of-sight structures rather than subhaloes. We also discuss about a possible imprint of line-of-sight structures in demagnification of minimum images due to locally underdense structures in the line of sight.