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

In this paper we describe the predictions for the smoothed weak lensing shear and aperture-mass 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 3-d 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 pdf of the smoothed convergence, ${\kappa }_s$. We find that both 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 (${\theta }_s\text{la}{2}^{\mathrm{\prime }}$) the tail of the pdf $\text{cP}(\text{Map})$ for negative $\text{Map}$ shows a strong variation between the two models and the stellar model actually breaks down for ${\theta }_s\text{la}{0.4}^{\mathrm{\prime }}$ and $\text{Map}<0$. 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 scales and redshifts of interest, while both models provide a good description of the pdf $\text{cP}({\gamma }_{is})$ of the smoothed shear components. Therefore, the shear and the aperture-mass provide robust and complimentary tools to measure the cosmological parameters as well as the detailed statistical properties of the density field.