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Abstract We present a comprehensive analysis of the shape of dark matter (DM) halos in a sample of 25 Milky Way-like galaxies in TNG50 simulation. Using an enclosed volume iterative method, we infer an oblate-to-triaxial shape for the DM halo with median T ≃ 0.24. We group DM halos into three different categories. Simple halos (32% of the population) establish principal axes whose ordering in magnitude does not change with radius and whose orientations are almost fixed throughout the halo. Twisted halos (32%) experience levels of gradual rotations throughout their radial profiles. Finally, stretched halos (36%) demonstrate a stretching in the lengths of their principal axes where the ordering of different eigenvalues changes with radius. Subsequently, the halo experiences a “rotation” of ∼90° where the stretching occurs. Visualizing the 3D ellipsoid of each halo, for the first time, we report signs of a reorienting ellipsoid in twisted and stretched halos. We examine the impact of baryonic physics on DM halo shape through a comparison to dark matter only (DMO) simulations. This suggests a triaxial (prolate) halo. We analyze the impacts of substructure on DM halo shape in both hydrodynamical and DMO simulations and confirm that they are subdominant. We study the distribution of satellites in our sample. In simple and twisted halos, the angle between satellites’ angular momentum and the galaxy’s angular momentum grows with radius. However, stretched halos show a flat distribution of angles. Overlaying our theoretical outcome on the observational results presented in the literature establishes a fair agreement.

We study the chaotic-like behavior of cosmological simulations by quantifying how minute perturbations grow over time and manifest as macroscopic differences in galaxy properties. When we run pairs of "shadow" simulations that are identical except for random minute initial displacements to particle positions (e.g., of order 10 -7 pc), the results diverge from each other at the individual galaxy level (while the statistical properties of the ensemble of galaxies are unchanged). After cosmological times, the global properties of pairs of "shadow" galaxies that are matched between the simulations differ from each other, generally at a level of ∼2-25%, depending on the considered physical quantity. We perform these experiments using cosmological volumes of (25-50 Mpc h)3 evolved either purely with dark matter, or with baryons and star formation but no feedback, or else using the full feedback model of the IllustrisTNG project. The runs cover four resolution levels spanning a factor of 512 in mass. We find that, without feedback, the differences between shadow galaxies generally become smaller as the resolution increases-but with the IllustrisTNG model, the results mostly converge toward a "floor. " This hints at the role of feedback in setting the chaotic properties of galaxy formation. Importantly, we compare the macroscopic differences between shadow galaxies to the overall scatter in various galaxy scaling relations, and conclude that, for the star formation-mass and the Tully-Fisher relations, the butterfly effect in our simulations contributes significantly to the overall scatter. We find that our results are robust to whether random numbers are used in the subgrid models or not. We discuss the implications for galaxy formation theory in general and for cosmological simulations in particular.