DM halo morphological types of MW-like galaxies in the TNG50 simulation: Simple, Twisted, or Stretched

We present a comprehensive study of the shape analysis of dark matter (DM) halos in a sample of 25 Milky Way (MW) like galaxies in the TNG50 run of the IllustrisTNG project. Using an Enclosed Volume Iterative Method, we infer an oblate-triaxial shape for DM halos with a median $T\simeq 0.24$. we group DM halos in 3 different classes. Simple halos(36%) establish three principal axes whose ordering in magnitude does not change with radius and whose orientations are almost fixed throughout the entirety of the halo. Twisted halos(36%) show some levels of gradual rotations between 50 to 100 degs radially. Finally, stretched halos(28%) demonstrate a stretching in their axes lengths where the ordering of different eigenvalues change radially. And, the halo experiences a `rotation' of $\sim$90 deg at that radius. Visualizing the 3D ellipsoid of DM halos, for the first time, we report signs of a re-orienting ellipsoid in both twisted and stretched classes. We examine the impact of baryonic physics on the DM halo shape through a comparison to dark matter only (DMO) simulations. We report a triaxial-prolate DM halo with a median $T\simeq 0.64$. Therefore baryonic effects make DM halos less elongated. We analyze the impact of substructure on the DM halo shape and confirm that it is subdominant. We study the distribution of satellites with masses above $10^7 M_{\odot}$ and at the distance of less than 200 kpc. Satellites in simple halos are in general closer to the center and are more aligned with the central galaxy's angular momentum. Satellites in twisted halo class, present a bi-modal behavior in the distribution of their angles. Finally, satellites of stretched halos are farther out from the center and are more misaligned. We connect the above theoretical results to observations from the literature. Overlaying our theoretical outcome with the observational results establishes a fair agreement.