The observational and theoretical analysis on different scales, ranging from galactic to cosmological, strongly indicates the necessity of dark matter in the Universe. Modern astrophysics therefore aims to reveal its nature, rather than its existence. Preferentially, it consist of particles beyond the standard model of particle physics. In order to explain galactic structures without focusing on a particular particle candidate, a self-gravitating system, composed of massive fermions in spherical symmetry, is considered here. The finite mass distribution of such a component is obtained after solving the Einstein equation for a thermal and semi-degenerate fermionic gas, described by a perfect fluid in hydrostatic equilibrium and exposed to cutoff effects (e.g. evaporation). Within this more general approach a new family of density profiles arises which explains dark matter halo constraints of the Galaxy and provides at the same time an alternative to the central black hole scenario in SgrA*. This analysis narrows the allowed particle mass to mc² = 48 - 345 keV. It is bolstered by the successful application (for mc² ~ 50 keV) to different galaxy types from dwarfs to ellipticals, including disk galaxies from the SPARC data base. The key result is that there is a continuous underlying dark matter distribution, covering the whole galactic extent. It governs the dynamics of the galactic center (e.g. nuclei) as well as the galactic halo. Based on the model predictions, it is clear that fermionic dark matter with particle masses in the keV regime is able to explain the relation between dark and baryonic components as well as dark components only. The radial acceleration correlation is reproduced here and represents the former group. Equally important is the natural outcome of the observationally confirmed link between a central dark object and its harboring dark matter halo. Interestingly, the very same dark matter distributions provide a satisfactory explanation for the constancy of the central dark matter surface density, valid for various galaxy types.
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