Novel constraints on fermionic dark matter from galactic observables II: galaxy scaling relations

We have recently introduced in paper I an extension of the Ruffini-Arg\"uelles-Rueda (RAR) model for the distribution of DM in galaxies, by including for escape of particle effects. Being built upon self-gravitating fermions at finite temperatures, the RAR solutions develop a characteristic \textit{dense quantum core-diluted halo} morphology which, for fermion masses in the range $mc^2 \approx 10-345$ keV, was shown to provide good fits to the Milky Way rotation curve. We study here for the first time the applicability of the extended RAR model to other structures from dwarfs to ellipticals to galaxy clusters, pointing out the relevant case of $mc^2 = 48$ keV. By making a full coverage of the remaining free parameters of the theory, and for each galactic structure, we present a complete family of astrophysical RAR profiles which satisfy realistic halo boundary conditions inferred from observations. Each family-set of RAR solutions predicts given windows of total halo masses and central quantum-core masses, the latter opening the interesting possibility to interpret them as alternatives either to intermediate-mass BHs (for dwarf galaxies), or to supermassive BHs (SMBHs, in the case of larger galaxy types). The model is shown to be in good agreement with different observationally inferred scaling relations such as: (1) the Ferrarese relation connecting DM halos with supermassive dark central objects; and (2) the nearly constant DM surface density of galaxies. Finally, the theory provides a natural mechanism for the formation of SMBHs of few $10^8 M_\odot$ via the gravitational collapse of unstable DM quantum-cores.