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

TL;DR

This paper explores how non-minimal coupling of dark matter to gravity can produce halo density profiles with cores, aligning well with observed galaxy rotation curves and scaling relations, unlike standard cuspy models.

Contribution

It demonstrates that non-minimal coupling modifies dark matter halo profiles from cuspy to cored, fitting galaxy rotation curves and scaling relations better than traditional models.

Findings

Non-minimal coupling induces core-like density profiles in dark matter halos.

The resulting profiles fit dwarf galaxy rotation curves as well as Burkert profiles.

Halo scaling relations are consistent with observed core surface densities.

Abstract

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 which may arise when the averaging/coherence length $L$ associated to 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 $L^2\,\nabla^2\rho$ proportional to the Laplacian of the DM density $\rho$ itself. We further adopt a general power-law equation of state $p\propto \rho^{\Gamma}\, r^\alpha$ relating the DM dynamical pressure $p$ to density $\rho$ and radius $r$, as expected by phase-space density stratification during the gravitational assembly of halos in a cosmological context. We confirm previous findings that, in absence of the 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 $\Lambda$CDM cosmology, as described by the classic NFW or Einasto profiles. Most importantly, we find that the non-minimal coupling causes the density distribution to develop an inner core and a shape closely following, out to several core scale radii, the Burkert profile. In fact, we highlight that the resulting mass distributions can fit, with an accuracy comparable to the Burkert's one, the co-added 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 an universal core surface density $\rho_0\times r_0$ among different galaxies.