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

Gas-rich ultra-diffuse galaxies (UDGs) are an unusually sharp test for 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 Pi\~na et al. with the current outer-radius prescription of hyperconical modified gravity (HMG), using the published baryonic masses and circular velocities at the outer radii. 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 observed values, the fixed asymptotic branch gives $\chi^2\simeq18.1$ for six objects, whereas Newtonian baryons alone give $\chi^2\simeq9.7$, but MOND interpolation is much worse ($\chi^2\simeq 615.7$). Using combined uncertainties, the per-galaxy HMG tension ranges from $0.2\sigma$ to $2.1\sigma$, very similar to the $0.1\sigma$ to $1.7\sigma$ found for Newtonian baryons, and much smaller than the $3.7\sigma$ to $5.9\sigma$ obtained for MOND. 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 UDG sample. Gas-rich UDGs therefore provide a useful discriminant between MOND and HMG.