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The presence of large dark matter cores in dwarf galaxies has long beenpuzzling and many are now known to be surrounded by an extensive halo of stars.Distinctive core-halo structure is characteristic of dark matter as a BoseEinstein condensate, $\psi$DM, with a dense, soliton core predicted in everygalaxy, representing the ground state, surrounded by a large, tenuous halo ofexcited density waves. A marked density transition is predicted between thecore and the halo set by the de Broglie wavelength, as the soliton core is aprominent standing wave that is denser by over an order of magnitude than thesurrounding halo. Here we identify this predicted behavior in the stellarprofiles of the well known "isolated" dwarfs that lie outside the Milky Way,each with a clear density transition at $\simeq 1.0~{\rm kpc}$, implying a verylight boson, $m_{\psi} \simeq 10^{-22}$eV. The classical dwarf galaxiesorbiting within the Milky Way also show this predicted core-halo structure butwith larger density transitions of over two orders of magnitude, that we showimplies tidal stripping of dwarf galaxies by the Milky way, as the tenuous halois more easily stripped than the stable soliton core. We conclude that darkmatter as a light boson explains the observed family of classical dwarfprofiles with tidal stripping included, in contrast to the standard heavyparticle interpretation where low mass galaxies should be concentrated andcore-less, quite unlike the core-halo structure observed.

Detection of a universal core-halo transition in dwarf galaxies as predicted by Bose-Einstein dark matter