Dark matter as a Bose-Einstein condensate , such as the axionic scalar field particles of String Theory , can explain the coldness of dark matter on large scales .
Pioneering simulations in this context predict a rich wave-like structure , with a ground state soliton core in every galaxy surrounded by a halo of excited states that interfere on the de Broglie scale .
This de Broglie scale is largest for low mass galaxies as momentum is lower , providing a simple explanation for the wide cores of dwarf spheroidal galaxies .
Here we extend these ‘ ‘ wave dark matter '' ( \psi DM ) predictions to the newly discovered class of ‘ ‘ Ultra Diffuse Galaxies '' ( UDG ) that resemble dwarf spheroidal galaxies but with more extended stellar profiles .
Currently the best studied example , DF44 , has a uniform velocity dispersion of \simeq 33 km/s , extending to a least 3 kpc , that we show is reproduced by our \psi DM simulations with a soliton radius of \simeq 0.5 kpc .
In the \psi DM context , we show the relatively flat dispersion profile of DF44 lies between massive galaxies with compact dense solitons , as may be present in the Milky Way on a scale of 100pc and lower mass galaxies where the velocity dispersion declines centrally within a wide , low density soliton , like Antlia II , of radius 3Kpc .
In contrast , standard CDM requires excessive tangential stellar motions predominate to counter the inherent central cusp which would otherwise enhance the central velocity dispersion .