2025ApJ...984..101M

In Milgrom's MOdified Newtonian Dynamics (MOND) framework, the dynamical mass of a galaxy is fully determined by its baryonic matter distribution. Using this framework, we fit the distribution of cold and hot gas halos-focusing on the hot gas-around Sloan Digital Sky Survey central galaxies, utilizing weak lensing signals from the DECaLS survey. The central galaxies are classified into the total sample and the star-forming sample. Hot gas halo densities nearly follow Plummer's profile for both samples across all mass bins out to extended radii. We then demonstrate the rotation curves of the galaxy samples. Furthermore, the stellar fraction, M_*/(M_* + M_g), is between 0.3 and 0.8 in all mass bins of the star-forming sample, which is higher than in the total sample. Additionally, we use the satellite kinematics method in MOND to verify our findings from the weak lensing method. We find good agreement between the two methods, indicating that weak lensing signals reliably measure the dynamical mass of central galaxies and can constrain the distribution of missing baryons in galaxy clusters. Combining both methods, we discover a baryonic mass to line-of-sight velocity dispersion of satellites (M_b-σ_s) relation. More sophisticated models, such as Osipkov-Merritt anisotropy profiles, were found unnecessary, as simple isotropic or mildly radially anisotropic MOND models align well with the observed M_b-σ_s relation. Moreover, the isotropic model remains consistent with this relation even when considering external fields from large-scale structures.