Empirical Evidence of Non-Minimally Coupled Dark Matter in the Dynamics of Local Spiral Galaxies?

We look for empirical evidence of a non-minimal coupling (NMC) between dark matter (DM) and gravity in the dynamics of local spiral galaxies. In particular, we consider a theoretically motivated NMC that may arise dynamically from the collective behavior of the coarse-grained DM field (e.g., via Bose-Einstein condensation) with averaging/coherence length $L$. In the Newtonian limit, this NMC amounts to modify the Poisson equation by a term $L^{2} \nabla^{2} \rho$ proportional to the Laplacian of the DM density itself. We show that such a term, when acting as a perturbation over the standard Navarro-Frenk-White (NFW) profile of cold DM particles, can substantially alter the dynamical properties of galaxies, in terms of their total radial acceleration within the disk and rotation velocity. Specifically, we find that this NMC model can properly fit the stacked rotation curves of local spiral galaxies with different velocities at the optical radius, including dwarfs and low-surface brightness systems, at a level of precision comparable to, and in some instances even better than, the phenomenological Burkert profile. Finally we show that, extrapolating down to smaller masses the scaling of $L$ vs. halo mass found from the above rotation curve analysis, the NMC model can adequately reproduce the radial acceleration relation (or RAR) in shape and normalization down to the dwarf spheroidal galaxy range, a task which constitutes a serious challenge for alternative DM models even inclusive of baryonic effects.