Cosmic Magnification Research Articles

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

The lensing magnification effect due to large-scale structure is statistically measurable by the correlation of size fluctuations in distant galaxy images as well as by cross-correlation between foreground galaxies and background sources such as the QSO–galaxy cross-correlation. We use the halo model formulation of Takada & Jain to compute these magnification-induced correlations without employing the weak lensing approximation, μ≈ 1 + 2κ. Our predictions thus include the full contribution from non-linear magnification, δμ≳ 1, that is due to lensing haloes. We compare the model prediction with ray-tracing simulations and find excellent agreement over the range of angular scales we consider (0.5 ≲θ≲ 30 arcmin). In addition, we derive the dependence of the correlation amplitude on the maximum magnification cut-off μmax, which it is necessary to introduce in order to avoid the contributions from strong lensing events. For a general correlation function parametrized as 〈μpƒ〉 (ƒ is any cosmic field correlated with the magnification field), the amplitude remains finite for p < 1 and diverges for p≥ 1 as μmax→∞, independent of the details of the lensing mass distribution and of the separation angle. This consequence is verified by the halo model as well as by the simulations. Thus, the magnification correlation with p≤ 1 has a practical advantage in that it is insensitive to a selection effect of how strong lensing events with μ≫ 1 are observationally excluded from the sample. 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 per cent on arcmin scales for the QSO–galaxy cross-correlation, even after the 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.

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.