Improving the accuracy of cosmic magnification statistics

The systematic magnification of background sources by the weak gravitational-lensing effects of foreground matter, also called cosmic magnification, is becoming an efficient tool both for measuring cosmological parameters and for exploring the distribution of galaxies relative to the dark matter. We extend here the formalism of magnification statistics by estimating the contribution of second-order terms in the Taylor expansion of the magnification and show that the effect of these terms was previously underestimated. We test our analytical predictions against numerical simulations and demonstrate that including second-order terms allows the accuracy of magnification-related statistics to be substantially improved. We also show, however, that both numerical and analytical estimates can provide only lower bounds to real correlation functions, even in the weak lensing regime. We propose to use count-in-cells estimators rather than correlation functions for measuring cosmic magnification since they can more easily be related to correlations measured in numerical simulations.