A numerical study of Galactic Centre stars

We present a simulation of the orbits of Galactic Centre stars, also known as 'S-stars', with the purpose of describing the motion of those bodies for which complete orbits are known with greater accuracy. The aim is to have a better understanding of the inner parts of the Galactic potential. The simulation assumes that the spacetime around the central black hole of the Galaxy may be modelled by the Schwarzschild metric, while stellar interactions are approximated classically. We model the central object as a black hole with mass 4.31 × 106 M⊙, fix the Galactic Centre distance at R = 8.33 kpc and include 37 orbiting stars, all of which have masses of 10 M⊙, except for S2, which has a mass of 20 M⊙. Our method allows us to predict the semimajor axis, a; eccentricity, ϵ; and period, T for these stars and predict their periastron shift, δΘ. In particular for S2, the most scrutinized star, we find δΘ = 11.9342 arcmin, in strong agreement with the observed value.