Weak Lensing by Line-of-sight Halos as the Origin of Flux-ratio Anomalies in Quadruply Lensed QSOs

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We explore the weak lensing effect by line-of-sight halos and sub-halos with a mass of M < 10⁷ 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 10⁵ solar mass, or structures with a comoving wavenumber of k 3*10² 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=10³-10⁷ solar mass, or structures with a comoving wavenumber of k=3*10²-10⁴ 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 < 10⁶ solar mass.