Polar ring galaxies in wave dark matter: from isotropic collapse to polar accretion

We present a numerical study of polar ring galaxy formation in the wave-dominated (ultralight scalar field) dark matter paradigm. Using full 3D simulations of the Schrödinger–Poisson system in an expanding Universe, we show that isotropic collapse of a scalar field produces a nearly spherical halo, with only a mild flattening in the inner core. Gas accreted from a preferred polar direction forms a stable, long-lived polar ring, reproducing the observed morphology of polar ring galaxies like NGC 4650A. Our results indicate that polar ring galaxies require anisotropic accretion geometry, while the wave dark matter potential provides a stable environment for such structures.