We aim to verify whether refracted gravity (RG) is capable of describing the dynamics of disk galaxies without resorting to the presence of dark matter. RG is a classical theory of gravity in which the standard Poisson equation is modified with the introduction of the gravitational permittivity, which is a universal monotonic function of the local mass density. We used the rotation curves and the radial profiles of the stellar velocity dispersion perpendicular to the galactic disks of 30 disk galaxies from the DiskMass Survey (DMS) to determine the gravitational permittivity. RG describes the rotation curves and the vertical velocity dispersions by requiring galaxy mass-to-light ratios that are in agreement with stellar population synthesis models, and disk thicknesses that are in agreement with observations, once observational biases are taken into account. Our results rely on setting the three free parameters of the gravitational permittivity for each individual galaxy. However, we show that the differences of these parameters from galaxy to galaxy can, in principle, be ascribed to statistical fluctuations. We adopted an approximate procedure to estimate a single set of parameters that may properly describe the kinematics of the entire sample and suggest that the gravitational permittivity is indeed a universal function. Finally, we showed that the RG models of the individual rotation curves can only partly describe the radial acceleration relation (RAR) between the observed centripetal acceleration derived from the rotation curve and the Newtonian gravitational acceleration originating from the baryonic mass distribution. Evidently, the RG models underestimate the observed accelerations by 0.1 to 0.3 dex at low Newtonian accelerations. An additional problem that ought to be considered is the strong correlation, at much more than 5σ, between the residuals of the RAR models and three radially-dependent properties of the galaxies, whereas the DMS data show a considerably less significant correlation, at more than 4σ, for only two of these quantities. These correlations might be the source of the non-null intrinsic scatter of the RG models: this non-null scatter is at odds with the observed intrinsic scatter of other galaxy samples different from DMS, which is consistent with zero. Further investigations are required to assess whether these discrepancies in the RAR originate from the DMS sample, which might not be ideal for deriving the RAR, or whether they are genuine failures of RG.
The Intrinsic Scatter of the Radial Acceleration Relation