There is surmounting observational evidence of the existence of a dark matter component in the Universe. However, there is neither theoretical consensus nor experimental proof of its exact nature. To constrain it, we must describe astrophysical data with as precise as possible theoretical models in which setting the dark matter particle candidate is only the first step. In this talk, it is discussed how the dynamics of stars in the Galactic outer halo and from the closest stars to the supermassive compact object of 4 million solar masses sitting at the Galactic center, Sgr A, constrains dark matter made of neutral fermions to have a rest mass of about 50-300 keV, an extremely tight range compared with the more than 40 orders of magnitude spanning the mass of dark matter candidates in the literature! The distribution of dark matter fermions in galaxies forms dense cores at their center. In the case of our Galaxy, a fermionic dark matter core can be an alternative to the supermassive black hole hypothesis for Sgr A, explaining the existing data from ground-based telescopes of the S-cluster stars and the Event Horizon Telescope radio data on the "black hole shadow". Far from being a disguise of black holes, the dark matter cores of tens of millions of solar masses can gravitationally collapse, providing a key channel for the formation of the supermassive black holes in the Universe, including those being observed by the James Webb Space Telescope in the farthest galaxies in the high-redshift Universe. Further future astrophysical probes for dark matter fermions are outlined.
-- postponed to 5th March 2025
