Novel constraints on fermionic dark matter from galactic observables.

We have recently introduced a new model for the distribution of dark matter (DM) in galaxies, the Ruffini-Arg\"uelles-Rueda (RAR) model, based on a self-gravitating system of massive fermions at finite temperatures. The RAR model, for fermion masses above keV, successfully describes the DM halos in galaxies, and predicts the existence of a denser quantum core towards the centre of each configuration. We demonstrate here, for the first time, 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 compact quantum core which represents an alternative to the central black hole (BH) scenario for SgrA*. For a fermion mass in the range $48\,{\rm keV} \lesssim m c^2\lesssim 345\,{\rm keV}$, the DM halo distribution fulfills the most recent data of the Milky Way rotation curves, while harbors a dense quantum core of $4\times10^6 M_\odot$ within the S2 star pericentre. In particular, for a fermion mass of $mc^2 \sim 50\,{\rm keV}$ the model is able to explain the DM halos from typical dwarf spheroidal to normal elliptical galaxies, while harboring dark and massive compact objects from $\sim 10^3 M_\odot$ up to $\sim 10^8 M_\odot$ at their respective centres. The model is shown to be in good agreement with different observationally inferred universal relations, such as the ones connecting DM halos with supermassive dark central objects, while it provides a natural mechanism for the formation of supermassive BHs as heavy as $M_{BH}\sim$ few $10^8 M_\odot$.