Constraints on $R^n$ gravity from precession of orbits of S2-like stars: a case of a bulk distribution of mass

Abstract

Here we investigate possible applications of observed stellar orbits around Galactic Center for constraining the R${}^n$ gravity at Galactic scales. For that purpose, we simulated orbits of S2-like stars around the massive black hole at Galactic Center, and study the constraints on the R${}^n$ gravity which could be obtained by the present and next generations of large telescopes. Our results show that R${}^n$ gravity affects the simulated orbits in the qualitatively similar way as a bulk distribution of matter (including a stellar cluster and dark matter distributions) in Newton's gravity. In the cases where the density of extended mass is higher, the maximum allowed value of parameter ${\hat{I}}^2$ in R${}^n$ gravity is noticeably smaller, due to the fact that the both extended mass and $R^n$ gravity cause the retrograde orbital precession.

10 pages, 4 figures, accepted for publication in Advances in Space Research