The motion of S-stars around the Galactic center implies that the central gravitational potential is dominated by a compact source, Sagittarius A* (Sgr A*), which has a mass of about 4 × 106 M⊙ and is traditionally assumed to be a massive black hole (BH). The explanation of the multiyear accurate astrometric data of the S2 star around Sgr A*, including the relativistic redshift that has recently been verified, is particularly important for this hypothesis and for any alternative model. Another relevant object is G2, whose most recent observational data challenge the scenario of a massive BH: its post-pericenter radial velocity is lower than expected from a Keplerian orbit around the putative massive BH. This scenario has traditionally been reconciled by introducing a drag force on G2 by an accretion flow. As an alternative to the central BH scenario, we here demonstrate that the observed motion of both S2 and G2 is explained in terms of the dense core – diluted halo fermionic dark matter (DM) profile, obtained from the fully relativistic Ruffini-Argüelles-Rueda (RAR) model. It has previously been shown that for fermion masses 48−345 keV, the RAR-DM profile accurately fits the rotation curves of the Milky Way halo. We here show that the solely gravitational potential of such a DM profile for a fermion mass of 56 keV explains (1) all the available time-dependent data of the position (orbit) and line-of-sight radial velocity (redshift function z) of S2, (2) the combination of the special and general relativistic redshift measured for S2, (3) the currently available data on the orbit and z of G2, and (4) its post-pericenter passage deceleration without introducing a drag force. For both objects, we find that the RAR model fits the data better than the BH scenario: the mean of reduced chi-squares of the time-dependent orbit and z data are ⟨χ̄2⟩S2,RAR ≈ 3.1 and ⟨χ̄2⟩S2,BH ≈ 3.3 for S2 and ⟨χ̄2⟩G2,RAR ≈ 20 and ⟨χ̄2⟩G2,BH ≈ 41 for G2. The fit of the corresponding z data shows that while for S2 we find comparable fits, that is, χ̄2z,RAR ≈ 1.28 and χ̄2z,BH ≈ 1.04, for G2 the RAR model alone can produce an excellent fit of the data, that is, χ̄2z,RAR ≈ 1.0 and χ̄2z,BH ≈ 26. In addition, the critical mass for gravitational collapse of a degenerate 56 keV-fermion DM core into a BH is ∼ 108 M⊙. This result may provide the initial seed for the formation of the observed central supermassive BH in active galaxies, such as M 87.

The motion data of the S-stars around the Galactic center gathered in the last 28 yr imply that Sgr A* hosts a supermassive compact object of about 4 × 106M⊙, a result awarded with the Nobel Prize in Physics 2020. A non-rotating black hole (BH) nature of Sgr A* has been uncritically adopted since the S-star orbits agree with Schwarzschild geometry geodesics. The orbit of S2 has served as a test of General Relativity predictions such as the gravitational redshift and the relativistic precession. The central BH model is, however, challenged by the G2 post-peripassage motion and by the lack of observations on event-horizon-scale distances robustly pointing to its univocal presence. We have recently shown that the S2 and G2 astrometry data are better fitted by geodesics in the spacetime of a self-gravitating dark matter (DM) core – halo distribution of 56keV-fermions, “darkinos”, which also explains the outer halo Galactic rotation curves. This Letter confirms and extends this conclusion using the astrometry data of the 17 best-resolved S-stars, thereby strengthening the alternative nature of Sgr A* as a dense core of darkinos.