Weak Lensing by Line-of-sight Halos as the Origin of Flux-ratio
  Anomalies in Quadruply Lensed QSOs
  We explore the weak lensing effect by line-of-sight halos and sub-halos with
a mass of M < 10^7 solar mass in QSO-galaxy strong lens systems with quadruple
images in a concordant LCDM universe. Using a polynomially fitted non-linear
power spectrum P(k) obtained from N-body simulations that can resolve halos
with a mass of M ~ 10^5 solar mass, or structures with a comoving wavenumber of
k ~ 3*10^2 h/Mpc, we find that the ratio of magnification perturbation due to
intervening halos to that of a primary lens is typically ~10 per cent and the
predicted values agree well with the estimated values for 6 observed QSO-galaxy
lens systems with quadruple images in the mid-infrared band without considering
the effects of substructures inside a primary lens. We also find that the
estimated amplitudes of convergence perturbation for the 6 lenses increase with
the source redshift as predicted by theoretical models. Using an extrapolated
matter power spectrum, we demonstrate that small halos or sub-halos in the
line-of-sight with a mass of M=10^3-10^7 solar mass, or structures with a
comoving wavenumber of k=3*10^2-10^4 h/Mpc can significantly affect the
magnification ratios of the lensed images. Flux ratio anomalies in QSO-galaxy
strong lens systems offer us a unique probe into clustering property of
mini-halos with a mass of M < 10^6 solar mass.
