Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution

We estimate the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S-stars, specifically of S2, S38 and S55 stars. We also take into account case of bulk mass distribution near Galactic Center. We assume that the Schwarzschild orbital precession of mentioned S-stars is the same like in General Relativity (GR) in all studied cases. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center and showed that it is close to the GR prediction. The astronomical data analysis of S38 and S55 orbits showed that also in these cases orbital precession is close to the GR prediction. Based on this observational fact, we evaluated parameters of the Hybrid Palatini Gravity model with the Schwarzschild precession of the S2, S38 and S55 stars and we estimated the range of parameters of Hybrid Palatini gravity model for which the orbital precession is like in GR for all tree stars. We also evaluated parameters of the Hybrid Palatini Gravity model in case of different values of bulk mass density distribution of extended matter. We believe that proposed method is a useful tool to evaluate parameters of the gravitational potential at the Galactic Center.