Constraints on a Fifth Force from the Stellar Orbits Around the Central Supermassive Black Hole of the Milky Way

Here we investigate a possible presence of a fifth force at the Galactic Center (GC), and its potential influence on the stellar orbits around the central supermassive black hole (SMBH) of our Galaxy. For this purpose we simulated the stellar orbits in a Yukawa gravity model that predicts the emergence of a fifth force, and fitted them into the observed orbit of S2 star around Sgr A* at the GC. The fitting was performed using Markov chain Monte Carlo (MCMC) method which enabled us to constrain the parameters of Yukawa interaction describing the strength δ and the range λ of a fifth force. We studied the following cases for a fifth force range λ: (i) when it is about a few hundred AU (i.e., deep inside the orbit of S2 star), (ii) when it is about a thousand AU (i.e., approximately the size of S2 star orbit), and (iii) when it is several thousand AU (i.e., much larger than the size of S2 star orbit). The obtained results showed that as the range λ of a fifth force increases, its strength δ also increases and relative error Δδ/δ decreases. The resulting fifth-force strengths in all three cases are respectively: δ∼0.005, 0.02 and 0.15. These results are consistent with the corresponding results of both our previous studies and those of other authors, regardless of the different Yukawa-like potentials used to model a fifth force. In addition, assuming that the orbital precession of S2 star is close to the prediction of General Relativity (GR) for its Schwarzschild precession, we studied whether the possible small discrepancies from this prediction could be also caused by a fifth force. For this purpose we used the fSP parameter that was recently measured in the case of S2 star by GRAVITY Collaboration in 2020, and that describes the extent to which some gravitational model is relativistic. We found that the obtained estimates in all three cases are compatible, within the error intervals, with the measured value of fSP=1.10±0.19.