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

The unusually large "dwarf" galaxy Crater II, with its small velocity dispersion, (cid:39) 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 (cid:39) 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, (cid:39) 0 . 25 kpc and higher velocity dispersions, (cid:39) 9km/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 (cid:39) 20 kpc established by Gaia, implying significant tidal stripping of Crater II by the Milky Way is expected.