Long-term classical and general relativistic effects on the radial velocities of the stars orbiting Sgr A*

TL;DR

This paper analytically examines how general relativistic effects, the black hole's quadrupole moment, and dark matter influence the long-term radial velocities of stars orbiting Sgr A*, with a focus on the S2 star.

Contribution

It provides a detailed analytical calculation of the cumulative effects of relativistic and dark matter influences on stellar radial velocities near Sgr A*.

Findings

Secular radial accelerations depend on orbit eccentricity.

Relativistic and quadrupole effects cause measurable velocity variations.

Dark matter distribution also contributes to the radial velocity changes.

Abstract

We analytically work out the cumulative, i.e. averaged over one orbital revolution, time variations of the radial velocity v_r of a typical S star orbiting the Supermassive Black Hole (SBH) hosted by the Galactic Center (GC) in Sgr A* caused by several dynamical effects. They are the general relativistic gravitoelectromagnetic (GEM) fields of the SBH, its quadrupole mass moment Q2, and a diffuse dark matter distribution around the SBH. All of them induce non-zero secular radial accelerations proportional to the eccentricity e of the orbit. By taking the S2 star, orbiting the SBH along a highly eccentric (e = 0.8831) ellipse with a period Pb = 15.9 yr, we numerically compute the magnitudes of its radial accelerations (Abridged).