Self-gravitating Equilibria of Non-minimally Coupled Dark Matter Halos

We investigate self-gravitating equilibria of halos constituted by dark matter (DM) non-minimally coupled to gravity. In particular, we consider a theoretically motivated non-minimal coupling that may arise when the averaging/coherence length L associated with the fluid description of the DM collective behavior is comparable to the local curvature scale. In the Newtonian limit, such a non-minimal coupling amounts to a modification of the Poisson equation by a term L-2 backward difference (2)rho proportional to the Laplacian of the DM density rho itself. We further adopt a general power-law equation of state p proportional to rho(Gamma)r(alpha) relating the DM dynamical pressure p to density rho and radius r, as expected for phase-space density stratification during the gravitational assembly of halos in a cosmological context. We confirm previous findings that, in the absence of non-minimal coupling, the resulting density rho(r) features a steep central cusp and an overall shape mirroring the outcomes of N-body simulations in the standard ?CDM cosmology, as described by the classic Navarro-Frenk-White or Einasto profiles. Most importantly, we find that the non-minimal coupling causes the density distribution to develop an inner core and a shape that closely follows the Burkert profile out to several core scale radii. In fact, we highlight that the resulting mass distributions can fit, with an accuracy comparable to Burkert's one, the coadded rotation curves of dwarf, DM-dominated galaxies. Finally, we show that non-minimally coupled DM halos are consistent with the observed scaling relation between the core radius r(0) and core density rho(0), in terms of a universal core surface density rho(0) x r(0) among different galaxies.