Halo model prediction of the cosmic magnification statistics: the full non-linear contribution

The lensing magnification effect due to large-scale structure is statistically measurable by correlation of size fluctuations in distant galaxy images as well as by the QSO-galaxy cross-correlation. We use the halo model formulation of Takada & Jain (2003) to compute these magnification-induced correlations without employing the weak lensing approximation, mu=1+2kappa. Our predictions thus include the full contribution from non-linear magnification that is due to lensing halos. We compare the model prediction with ray-tracing simulations and find excellent agreement over a range of angular scales (0.'5<theta<30'). The non-linear magnification contribution enhances the amplitude of the magnification correlation relative to the weak lensing approximation, and the non-linear correction is more significant on smaller angular scales and for sources at higher redshifts. The enhancement amounts to 10-25% on arcminite scales for the QSO-galaxy cross-correlation, even after inclusion of a realistic model of galaxy clustering within the host halo. Therefore, it is necessary to account for the non-linear contribution in theoretical models in order to make an unbiased, cosmological interpretation of the precise measurements expected from forthcoming massive surveys.