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It has been recently demonstrated that both, a classical Schwarzschild blackhole (BH), and a dense concentration of self-gravitating fermionic dark matter(DM) placed at the Galaxy centre, can explain the precise astrometric data(positions and radial velocities) of the S-stars orbiting SgrA*. This resultencompasses the 17 best resolved S-stars, and includes the test of generalrelativistic effects such as the gravitational redshift in the S2-star. Inaddition, the DM model features another remarkable result: the dense core offermions is the central region of a continuous density distribution of DM whosediluted halo explains the Galactic rotation curve. In this Letter, wecomplement the above findings by analyzing in both models the relativisticperiapsis precession of the S2-star orbit. While the Schwarzschild BH scenariopredicts a unique prograde precession for S2, in the DM scenario it can beeither retrograde or prograde, depending on the amount of DM mass enclosedwithin the S2 orbit, which in turn is a function of the DM fermion mass. Weshow that all the current and publicly available data of S2 can notdiscriminate between the two models, but upcoming S2 astrometry close to nextapocentre passage could potentially establish if SgrA* is governed by aclassical BH or by a quantum DM system.

What does lie at the Milky Way centre? Insights from the S2 star orbit precession