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Understanding the "Feeble Giant" Crater II with tidally stretched Wave Dark Matter

The unusually large "dwarf" galaxy Crater II, with its small velocity dispersion, $\simeq 3$ km/s, defies expectations that low mass galaxies should be small and dense. We combine the latest stellar and velocity dispersion profiles finding Crater II has a prominent dark core of radius $\simeq 0.71^{+0.09}_{-0.08}$ kpc, surrounded by a low density halo, with a transition visible between the core and the halo. We show that this profile matches the distinctive core-halo profile predicted by "Wave Dark Matter" as a Bose-Einstein condensate, $ψ$DM, where the ground state soliton core is surrounded by a tenuous halo of interfering waves, with a marked density transition predicted between the core and halo. Similar core-halo structure is seen in most dwarf spheroidal galaxies (dSph), but with smaller cores, $\simeq 0.25$ kpc and higher velocity dispersions, $\simeq 9$km/s, and we argue here that Crater II may have been a typical dSph that has lost most of its halo mass to tidal stripping, so its velocity dispersion is lower by a factor of 3 and the soliton is wider by a factor of 3, following the inverse scaling required by the Uncertainty Principle. This tidal solution for Crater II in the context of $ψ$DM, is supported by its small pericenter of $\simeq 20$ kpc established by Gaia, implying significant tidal stripping of Crater II by the Milky Way is expected.