Weak lensing shear and aperture mass from linear to non‐linear scales

We describe the predictions for the smoothed weak lensing shear, γ s , and aperture mass, M ap , of two simple analytical models of the density field: the minimal tree model and the stellar model. Both models give identical results for the statistics of the three‐dimensional density contrast smoothed over spherical cells and only differ by the detailed angular dependence of the many‐body density correlations. We have shown in previous work that they also yield almost identical results for the probability distribution function (PDF) of the smoothed convergence, κ s . We find that the two models give rather close results for both the shear and the positive tail of the aperture mass. However, we note that at small angular scales (θ s ≲ 2 arcmin) the tail of the PDF, , for negative M ap shows a strong variation between the two models, and the stellar model actually breaks down for θ s ≲ 0.4 arcmin and M ap < 0 . This shows that the statistics of the aperture mass provides a very precise probe of the detailed structure of the density field, as it is sensitive to both the amplitude and the detailed angular behaviour of the many‐body correlations. On the other hand, the minimal tree model shows good agreement with numerical simulations over all the scales and redshifts of interest, while both models provide a good description of the PDF, , of the smoothed shear components. Therefore, the shear and the aperture mass provide robust and complementary tools to measure the cosmological parameters as well as the detailed statistical properties of the density field.