Novel constraints on fermionic dark matter from galactic observables I: The Milky Way

We have recently introduced a new model for the distribution of dark matter (DM) in galaxies based on a self-gravitating system of massive fermions at finite temperatures, the Ruffini-Arg\"uelles-Rueda (RAR) model. We show that this model, for fermion masses in the keV range, explains the DM halo of the Galaxy and predicts the existence of a denser quantum core at the center. We demonstrate here that the introduction of a cutoff in the fermion phase-space distribution, necessary to account for the finite Galaxy size, defines a new solution with a central core which represents an alternative to the black hole (BH) scenario for SgrA*. For a fermion mass in the range $mc^2 = 48$ -- $345$~keV, the DM halo distribution is in agreement with the Milky Way rotation curve data, while harbors a dense quantum core of about $4\times10^6 M_\odot$ within the S2-star pericenter.