Gas-rich ultra-diffuse galaxies: alleviating the MOND tension with hyperconical modified gravity

Abstract Gas-rich ultra-diffuse galaxies (UDGs) provide an unusually sharp test of gravity models tied to the baryonic Tully–Fisher relation because several systems appear to rotate too slowly for their baryonic masses. This study revisits the six isolated gas-rich UDGs analysed by Mancera PiÃña et al. with the current outer-radius prescription of hyperconical modified gravity (HMG), using the published baryonic masses, outer circular velocities, and Newtonian disc-based comparison velocities. The scan over the neighbourhood-scale parameter drives the model towards the asymptotic branch of HMG. For that limit, the HMG velocities are still systematically high for four of the six galaxies. Relative to the published central values and asymmetric 1σ velocity errors, the fixed asymptotic branch gives χ2 ≃ 17.1 for six objects, whereas the published Newtonian outer-radius disc estimates give χ2 ≃ 9.3 and a standard MOND interpolation is much worse (χ2 ≃ 615.7). Using combined observational and model uncertainties, the per-galaxy HMG tension ranges from 0.2σ to 2.0σ, very similar to the 0.1σ to 1.7σ found for the Newtonian disc-based values, and much smaller than the 3.7σ to 5.9σ obtained for MOND. The likelihood scan showed that the preferred solutions lie on the asymptotic weak-coupling branch. We conclude that the present outer-radius HMG implementation alleviates the difficulties of MOND, but is still not sufficient to account for the published central values of the gas-rich UDG sample. Gas-rich UDGs therefore provide a useful discriminant between MOND and HMG.