A test of the fermionic dark matter nature of the supermassive compact object at the center of our galaxy

The extensive and continuous monitoring of the closest stars to the Galactic center has been producing over decades a large amount of high-quality data of their positions and velocities. The explanation of these data, especially the S2 star motion, reveals the presence of a compact source, Sagittarius A* (Sgr A*), whose mass must be about 4 x 10(6) M-circle dot. This result has been protagonist of the awarded Nobel Prize in Physics 2020 to Reinhard Genzel and Andrea Ghez "for the discovery of a supermassive compact object at the centre of our galaxy." Traditionally, the nature of Sgr A* has been attributed to a supermassive black hole (SMBH), even though a proof of its existence is absent. Further, recent data on the motion of the G2 cloud show that its post-peripassage velocity is lower than the expected one from a Keplerian orbit around the hypothesized SMBH. An attempt to overcome this difficulty has used a friction force, produced (arguably) by an accretion flow whose presence is also observationally unconfirmed. We advance an alternative scenario that identifies the nature of the supermassive compact object in a highly concentrated core of dark matter (DM) made of fermions, that is, inos, which we here refer to as darkinos. This DM concentration is predicted by the core-halo profile obtained from the Ruffini-Arguelles-Rueda fermionic DM model, which also fits the Galactic-halo rotation curves. We show that the sole DM core, for 56 keV darkinos, explains the orbits of S2 and G2. No drag force or other external agents are needed, that is, their motion is purely geodesic. A core made of these darkinos becomes unstable against gravitational collapse into a BH for a mass of similar to 10(8)M(circle dot); hence, they can provide the BH seeds from which grow the observed central SMBHs in active galaxies, for example, M87.