On the Origin of Flux Ratio Anomaly in Quadruple Lens Systems
  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
<$\sim 10^9\,h^{-1} \textrm{M}_\odot$ 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.
