Going deep with Minkowski functionals of convergence maps

Aims. Stage IV lensing surveys promise to make an unprecedented amount of excellent data available. This will represent a huge leap in terms of quantity and quality and will open the way for the use of novel tools that surpass the standard second-order statistics for probing the high-order properties of the convergence field. Motivated by these considerations, some of us have started a long-term project aiming at using Minkowski functionals (MFs) as complementary and supplementary probes to increase the lensing figure of merit (FoM).Methods. As a second step on this path, we discuss the use of MFs for a survey consisting of a wide total area Atot that is imaged at a limiting magnitude magW and contains a subset of area Adeep, where observations are pushed to a deeper limiting magnitude magD. We present an updated procedure to match the theoretically predicted MFs to the measured MFs, and take the effect of map reconstruction from noisy shear data into account. We validate this renewed method against simulated datasets 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 that is due to the joint use of shear tomography and MFs under different assumptions on (Atot,  Adeep, and magD), and the prior on the MFs nuisance parameters.Results. We find that MFs can provide valuable help in increasing the FoM of the lensing survey when the nuisance parameters are known with non-negligible precision. The possibility of compensating for the loss of FoM through a cut in the multipole range that is probed by shear tomography is even more interesting. This makes the results more robust against uncertainties in the modeling of nonlinearities. This makes MFs a promising tool for increasing the FoM and also protects the constraints on the cosmological parameters mainly from theoretical systematic effects.Key words: gravitational lensing: weak / cosmology: theory / methods: statistical