Going deep with Minkowski functionals of convergence maps

Stage IV lensing surveys promise to make available an unprecedented amount of excellent data which will represent a huge leap in terms of both quantity and quality. This will open the way to the use of novel tools, which go beyond the standard second order statistics probing the high order properties of the convergence field. We discuss the use of Minkowski Functionals (MFs) as complementary probes to increase the lensing Figure of Merit (FoM), for a survey made out of a wide total area $A_{\rm{tot}}$ imaged at a limiting magnitude $\rm{mag_{W}}$ containing a subset of area $A_{\rm{deep}}$ where observations are pushed to a deeper limiting magnitude $\rm{mag_{D}}$. We present an updated procedure to match the theoretically predicted MFs to the measured ones, taking into account the impact of map reconstruction from noisy shear data. We validate this renewed method against simulated data sets with different source redshift distributions and total number density, setting these quantities in accordance with the depth of the survey. We can then rely on a Fisher matrix analysis to forecast the improvement in the FoM due to the joint use of shear tomography and MFs under different assumptions on $(A_{\rm{tot}},\,A_{\rm{deep}},\,\rm{mag_{D}})$, and the prior on the MFs nuisance parameters. It turns out that MFs can provide a valuable help in increasing the FoM of the lensing survey, provided the nuisance parameters are known with a non negligible precision. What is actually more interesting is the possibility to compensate for the loss of FoM due to a cut in the multipole range probed by shear tomography, which makes the results more robust against uncertainties in the modeling of nonlinearities. This makes MFs a promising tool to both increase the FoM and make the constraints on the cosmological parameters less affected by theoretical systematic effects.