Dwarfs in the Milky Way halo outer rim: first infall or backsplash satellites?

Leo T is a gas-rich dwarf located at $414\, {\rm kpc}$ (1.4R_vir) distance from the Milky Way (MW) and it is currently assumed to be on its first approach. Here, we present an analysis of orbits calculated backwards in time for the dwarf with our new code DELOREAN, exploring a range of systematic uncertainties, e.g. MW virial mass and accretion, M31 potential, and cosmic expansion. We discover that orbits with tangential velocities in the Galactic standard-of-rest frame lower than $| \vec{u}_{\rm t}^{\rm GSR}| \le 63^{+47}_{-39}\, {\rm km}\, {\rm s}^{\rm -1}$ result in backsplash solutions, i.e. orbits that entered and left the MW dark matter halo in the past, and that velocities above $| \vec{u}_{\rm t}^{\rm GSR}| \ge 21^{+33}_{-21}\, {\rm km}\, {\rm s}^{\rm -1}$ result in wide-orbit backsplash solutions with a minimum pericentre range of $D_{\rm min} \ge 38^{+26}_{-16}\, {\rm kpc}$ , which would allow this satellite to survive gas stripping and tidal disruption. Moreover, new proper motion estimates overlap with our orbital solution regions. We applied our method to other distant MW satellites, finding a range of gas stripped backsplash solutions for the gasless Cetus and Eridanus II, providing a possible explanation for their lack of cold gas, while only first infall solutions are found for the H I-rich Phoenix I. We also find that the cosmic expansion can delay their first pericentre passage when compared to the non-expanding scenario. This study explores the provenance of these distant dwarfs and provides constraints on the environmental and internal processes that shaped their evolution and current properties.