EDGE: the shape of dark matter haloes in the faintest galaxies

Collisionless dark matter only (DMO) structure formation simulations predict that dark matter (DM) haloes are prolate in their centres and triaxial towards their outskirts. The addition of gas condensation transforms the central DM shape to be rounder and more oblate. It is not clear, however, whether such shape transformations occur in 'ultra-faint' dwarfs, which have extremely low baryon fractions. We present the first study of the shape and velocity anisotropy of ultra-faint dwarf galaxies that have gas mass fractions of f_gas(r < R_half) < 0.06. These dwarfs are drawn from the Engineering Dwarfs at Galaxy formation's Edge (EDGE) project, using high-resolution simulations that allow us to resolve DM halo shapes within the half-light radius (~100 pc). We show that gas-poor ultra-faints (M_200c ≤ 1.5 × 10⁹ M_⊙; f_gas < 10^-5) retain their pristine prolate DM halo shape even when gas, star formation, and feedback are included. This could provide a new and robust test of DM models. By contrast, gas-rich ultra-faints (M_200c > 3 × 10⁹ M_⊙; f_gas > 10^-4) become rounder and more oblate within ~10 half-light radii. Finally, we find that most of our simulated dwarfs have significant radial velocity anisotropy that rises to $\tilde{\beta } \gt 0.5$ at R ≳ 3R_half. The one exception is a dwarf that forms a rotating gas/stellar disc because of a planar, major merger. Such strong anisotropy should be taken into account when building mass models of gas-poor ultra-faints....