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

TL;DR

This study explores how R^n gravity influences stellar orbits near the Galactic Center, comparing effects to those of extended mass distributions, and assesses constraints using current and future telescopic observations.

Contribution

It demonstrates that R^n gravity's effects on stellar orbits are similar to those of extended mass distributions, providing a method to constrain R^n gravity parameters through orbital precession observations.

Findings

R^n gravity causes retrograde orbital precession similar to extended mass effects.

Higher density of extended mass results in smaller allowed R^n gravity parameter β.

Simulations suggest potential constraints on R^n gravity with upcoming telescopic data.

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 $\beta$ 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.