Context. The shapes of dark matter halos can be used to constrain the fundamental properties of dark matter. In standard Cold Dark Matter (CDM) cosmologies, halos are typically triaxial, with a preference for prolate configurations, particularly at low masses and high redshift. Aims. We focus on the characterization of total matter 3D shape in alternative dark matter models, such as Self-Interacting Dark Matter (SIDM) and Warm Dark Matter (WDM). These scenarios predict different structural properties due to collisional effects or the suppression of small-scale power. Methods. We measure the different halo component shapes - dark matter, stars and gas - at various radii from the center in the AIDA-TNG (Alternative Interacting Dark Matter and Astrophysics - TNG), which is a suite of high-resolution cosmological simulations built upon the IllustrisTNG framework. The intent is to systematically study how different dark matter models - specifically, SIDM and WDM - affect galaxy formation and the structure of dark matter halos, when realistic baryonic physics is also included. Results. SIDM models tend to produce rounder and more isotropic halos, especially in the inner regions, as a result of momentum exchange between dark matter particles. WDM halos are also slightly more spherical than their CDM counterparts, and are typically less concentrated. In all cases, the inclusion of self-consistent baryonic physics makes the central regions of all halos rounder, while still revealing clear distinctions among the various dark matter models. Conclusions. The general framework presented in this work, based on the 3D halo shape, can be useful to interpret multi-wavelength data analyses of galaxies and clusters.
