Euclid preparation. LXXXV. Toward a DR1 application of higher-order weak lensing statistics

This is the second paper in the HOWLS (higher-order weak lensing statistics) series exploring the usage of non-Gaussian statistics for cosmology inference within . With respect to our first paper, we develop a full tomographic analysis based on realistic photometric redshifts that allows us to derive Fisher forecasts in the (σ_8, w_0) plane for a -like data release 1 (DR1) setup. We find that the five higher-order statistics (HOS) that satisfy the Gaussian likelihood assumption of the Fisher formalism (one-point probability distribution function, ell1-norm, peak counts, Minkowski functionals, and Betti numbers) each outperform the shear two-point correlation functions by a factor of 2.5 on the w_0 forecasts, with only marginal improvement when used in combination with two-point estimators, suggesting that every HOS is able to retrieve both the non-Gaussian and Gaussian information of the matter density field. The similar performance of the different estimators is explained by a homogeneous use of multi-scale and tomographic information, optimized to lower computational costs. These results hold for the three mass mapping techniques of the pipeline, aperture mass, Kaiser--Squires, and Kaiser--Squires plus, and they are unaffected by the application of realistic star masks. Finally, we explored the use of HOS with the Bernardeau--Nishimichi--Taruya (BNT) nulling scheme approach, finding promising results toward applying physical scale cuts to HOS.