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tokens: the closure relations are determined by the Klein and Tolman conditions of thermodynamic equilibrium ( Ruffini et al. 2015 ). The solution to this system of equations leads to a continuous and novel dense core – diluted halo DM profile from the center all the way to the galactic halo (see Siutsou et al. 2015 ; Argüelles et al. 2016 ; Mavromatos et al. 2017 , for its applications). Similar core-halo profiles with applications to fermionic DM were also obtained in Bilic et al. (2002) and more recently in Chavanis et al. (2015) from a statistical approach within Newtonian gravity. The above corresponds to the original version of the RAR model, with a unique family of density profile solutions that behaves as ρ ( r )∝ r −2 at large radial distances from the center. This treatment was extended in Argüelles et al. (2018) , by introducing a cutoff in momentum space in the distribution function (DF; i.e., accounting for particle-escape effects) that allows defining the galaxy border (see Appendix A ). This extension of the RAR model was successfully applied to explain the Milky Way rotation curve, as shown in Fig. 1 , implying a more general dense core – diluted halo behavior for the DM distribution as follows: Fig. 1. Milky Way rotation curve and DM density profile from the extended RAR model with a core mass of M c = M ( r c ) = 3.5 × 10 6 M ⊙ . Top : DM (black) and baryonic (bulge + disk) contribution to the rotation curve v rot (total in red). Bottom : DM density profile. The baryonic model and the data are taken from Sofue (2013) . The parameters of the extended RAR model in this case are fermion mass m c 2 = 56 keV, temperature parameter β 0 = 1.1977 × 10 −5 , degeneracy parameter θ 0 = 37.7656, and energy cutoff parameter W 0 = 66.3407. For the RAR model fitting of the Milky Way, we follow Argüelles et al. (2018) ; see also Appendix A . – A DM core with radius r c (defined at the first maximum of the twice-peaked rotation curve), whose value is shown to be inversely proportional to the particle mass m , in which the density is nearly uniform. This central core is supported against gravity by the fermion degeneracy pressure, and general relativistic effects are appreciable. – Then, there is an intermediate region characterized by a sharply decreasing density where quantum corrections are still important, followed by an extended and diluted plateau. This region extends until the halo scale-length r h is achieved (defined at the second maximum of the rotation curve). – Finally, the DM density reaches a Boltzmann regime supported by thermal pressure with negligible general relativistic effects, and shows a behavior ρ ∝ r − n with n > 2 that is due to the phase-space distribution cutof. This leads to a DM halo bounded in radius (i.e., ρ ≈ 0 occurs when the particle escape energy approaches zero). As was explicitly shown in Argüelles et al. (2019b , a , 2018) , this type of dense core – diluted halo density profile suggests that the DM might explain