Constraining Ultralight Scalar Dark Matter in the Galactic Center with the S2 Orbit

Abstract: The dense environment of our Galactic Center (GC) offers a unique laboratory for probing ultralight dark matter (ULDM). We explore the prospect of detecting a scalar ULDM field through its effects on the orbital dynamics of S-stars around the supermassive black hole in the GC, Sgr A$^*$. We consider both linear and quadratic couplings between the real scalar field $φ$ and Standard Model particles, and analyze two representative ULDM structures: the scalar gravitational atom and the spherical soliton. We find that quadratic coupling induces a non-oscillatory perturbation, leading to a long-term secular orbital evolution. We use the observed periastron precession rate of S2 star to put stringent constraints on the total ULDM mass in the GC and the quadratic coupling constant. For the gravitational atom $|211\rangle$ state, we constrain the mass ratio of ULDM to Sgr A$^*$ to $β\lesssim 10^{-3}$ at $m \sim 10^{-18}$ eV, and for the spherical soliton which extends to $\sim 0.2\,$pc, the mass ratio is limited to $β\lesssim 1$ at $m \sim 3\times10^{-20}$ eV. Notably, the resulting limits on the quadratic coupling constant surpass current bounds in the mass range $10^{-20} \,\text{eV} \lesssim m \lesssim 10^{-18}$ eV.