Morphology of dark matter haloes beyond triaxiality

The morphology of haloes inform about both cosmological and galaxy formation models. We use the Minkowski Functionals (MFs) to characterize actual haloes, only partially captured by smooth density profile, going beyond spherical or ellipsoidal symmetry. employ semi-analytical with NFW $\alpha\beta\gamma$-profile shape obtain a clear interpretation MFs as function inner outer slope, concentration sphericity parameters. same models mimic profile $N$-body showing that their clearly differ sensitive internal substructures. This highlights benefit at halo scales promising statistics improve spatial modeling dark matter, crucial for future lensing, Sunyaev-Zel'dovich, X-ray mass maps well matter detection based on high-accuracy data.