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 <$\sim 10^9{h}^{-1}{\text{M}}_{\odot }$ 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 $\sim 10$ percent and the mean of the convergence perturbation is $0.008$, corresponding to $0.017$. The contribution of magnification perturbation caused by subhaloes is $\sim 40$ percent of the total at a source redshift $z_S=0.7$ and decreases monotonically in $z_S$ to $\sim 20$ percent at $z_S=3.6$. Assuming statistical isotropy, the convergence perturbation estimated from observed 11 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 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.

13 pages, 9 figures, 2 tables, version accepted for publication in MNRAS with minor change. (First published online May 30, 2016)

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