The effects of the spin and quadrupole moment of SgrA* on the orbits of S stars

TL;DR

This paper analytically and numerically investigates how the spin and quadrupole moment of SgrA* influence the orbits of nearby stars, aiming to aid future tests of relativistic effects and the no-hair theorem at the Galactic Center.

Contribution

It provides second post-Newtonian analytical expressions for orbital precession rates and introduces observer-independent quantities to study spin effects on stellar orbits around SgrA*.

Findings

Derived 2PN analytical expressions for orbital precession rates.

Simulated star orbits closer to SgrA* to compare with analytical predictions.

Identified orbital precession rates related to the black hole's spin and quadrupole moment.

Abstract

Measuring the astrometric and spectroscopic data of stars orbiting the central black hole in our galaxy (Sgr A*) offers a promising way to measure relativistic effects. In principle, the "no-hair" theorem can be tested at the Galactic Center by monitoring the orbital precession of S-stars due to the angular momentum (spin) and quadrupole moment of Sgr A*. Closer-in stars, more strongly affected by the black hole's rotation, may be required. GRAVITY+ could detect such stars that are currently too faint for GRAVITY. We aim to analytically and numerically characterize orbital reorientations induced by spin-related effects of Sgr A* up to the second post-Newtonian (2PN) order. We use the two-timescale method to derive the 2PN analytical expressions of the secular evolution of the orbital parameters that are related to the observer. To study the interaction between the orbital and spin orientations, we introduce observer-independent quantities that offer insight into the Kerr geometry. We also use the post-Newtonian code OOGRE to simulate hypothetical stars orbiting closer to Sgr A*, where spin and quadrupole effects are stronger. This enables comparison with our analytical predictions. We exhibit three orbital-timescale precession rates that encode the in-plane pericenter shift and the out-of-plane redirection of the osculating ellipse. We provide the 2PN expressions of these precession rates and express the orbit-integrated associated angular shifts of the pericenter and of the ellipse axes. We relate these orbital-timescale precession rates to the secular-timescale precession of the orbital angular momentum around the black hole spin axis. We consider that the theoretical insight we provide in this article will be useful in constraining the spin effect of Sgr A* with GRAVITY+ observations.