The impact of the dynamical state of gas-rich satellite galaxies at the early moments of their infall into their host systems and the relation to their quenching process are not completely understood at the low-mass regime. Two such nearby systems are the infalling Milky Way (MW) dwarfs Leo T and Phoenix located near the MW virial radius at $414 both of which present intriguing offsets between their gaseous and stellar distributions. Here we present hydrodynamic simulations with ramses to reproduce the observed dynamics of Leo T: its $80 stellar- offset and the 35 offset between its older ($ $) and younger ($ stellar population. We considered internal and environmental properties such as stellar winds, two components, cored and cuspy dark matter profiles, and different satellite orbits considering the MW circumgalactic medium. We find that the models that best match the observed morphology of the gas and stars include mild stellar winds that interact with the generating the observed offset, and dark matter profiles with extended cores. The latter allow long oscillations of the off-centred younger stellar component, due to long mixing timescales ($ and the slow precession of near-closed orbits in the cored potentials; instead, cuspy and compact cored dark matter models result in the rapid mixing of the material ($ These models predict that non-equilibrium substructures, such as spatial and kinematic offsets, are likely to persist in cored low-mass dwarfs and to remain detectable on long timescales in systems with recent star formation.
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