The study of the dynamical mass of the Local Group requires a detailed knowledge of the velocity of its elements, in particular of the Milky Way (MW) and the Andromeda galaxy (M31). Nevertheless, a discrepancy between the proper motion of the disk of M31 and the global motion of its satellites has been identified. Moreover, recent results showing the influence of the Magellanic complex on the displacement of the MW disk suggest a possible decoupling between the different components of spiral galaxies, notably the dark and baryonic parts. To explore this possibility, we study the position and kinematic deviations that may arise between the disk of a MW (or M31)-like galaxy and its halo, from constrained high resolution cosmological simulations of the Local Group in realistic environment, namely HESTIA simulations. We focus on the 3-dimensional analysis of the centers of mass (COM). We present two parts. We first consider individual particles to track down the very nature and amplitude of the physical deviations of the COM with respect to the distance from the disk center. Dark matter is dominating the behavior of the COM of all particles at all distances. But the total COM is also very close to the COM of stars. In the absence of a significant merger, the velocity offsets are marginal (10 km/s) but the positional shifts can be important compared to the disk characteristics (> 10 kpc). In the event of a major merger, discrepancies are found to be of the same order as the recent finding for the MW under the Magellanic Clouds influence. In a second part, we put the accent on the study of various populations of subhaloes and satellites. We show that while satellites properly represent the entire subhalo population, there exists strong mismatch in phase space between their COM and the host disk. Moreover, the results are highly inhomogeneous between the simulations, and thus between the accretion histories. It is highlighted that these shifts are mainly due to the three or four most massive objects. We will finally compare these results in the light of our observational knowledge.
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