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We investigate whether the oblate, spheroidal morphology of common dwarfspheroidal galaxies (dSph) may result from the slow relaxation of stellarorbits within a halo of Wave Dark Matter ($\psi$DM) when starting from aninitial disk of stars. Stellar orbits randomly walk over a Hubble time,perturbed by the pervasive "granular" interference pattern of $\psi$DM, thatfully modulates the dark matter density on the de Broglie scale. Oursimulations quantify the level of stellar disk thickening over the Hubble time,showing that distribution of stars is predicted to become an oblate spheroid ofincreasing radius, that plausibly accounts for the morphology of dSph galaxies.We predict a low level of residual rotation remains after a Hubble time at the1-3 km/s level, depending on orientation, that compares with recent claims ofrotation for some well studied local dSph galaxies. This steady internaldynamical evolution may be witnessed directly with JWST for well resolved dwarfgalaxies, appearing more oblate with look back time and tending to small disksof young stars at high redshift.

Explaining the oblate morphology of dwarf spheroidals with Wave Dark Matter perturbations