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Journal Articles Monthly Notices of the Royal Astronomical Society Year : 2003

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 <μpf> (f 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.

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hal-04111165 , version 1 (09-06-2023)



Masahiro Takada, Takashi Hamana. Halo model predictions of the cosmic magnification statistics: the full non-linear contribution. Monthly Notices of the Royal Astronomical Society, 2003, 346, pp.949-962. ⟨10.1111/j.1365-2966.2003.07145.x⟩. ⟨hal-04111165⟩
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