Dynamical constraints on the S2 (S0-2) star possible companions
The center of the Galaxy harbors a supermassive black hole, Sgr\,A*, which is surrounded by a massive star cluster known as the S-cluster. The most extensively studied star in this cluster is the B-type main-sequence S2 star (also known as S0-2). These types of stars are commonly found in binary systems in the Galactic field, but observations do not seem to detect a companion to S2. This absence may be attributed to observational biases or to a dynamically hostile environment caused by phenomena such as tidal disruption or mergers. Using a $N$-body code with first-order post-Newtonian corrections, we investigate whether S2 can host a stellar or planetary companion. We perform $10^{5}$ simulations adopting uniform distributions for the orbital elements of the companion. Our results show that companions may exist for orbital periods shorter than 100~days, eccentricities below 0.8, and across the full range of mutual inclinations. The number of surviving companions increases with shorter orbital periods, lower eccentricities, and nearly coplanar orbits. We also find that the disruption mechanisms include mergers driven by Lidov-Kozai cycles and breakups that occur when the companion surpasses the Hill radius of its orbit. Finally, we find that the presence of a companion would alter S2's astrometric signal by no more than $ 5\,\mu{\rm as}$. Current radial-velocity detection limits constrain viable stellar binary configurations to approximately 4.4\% of the simulated cases. Including astrometric limits reduces to 4.3\%. Imposing an additional constraint that any companion must have a mass $\lesssim 2\,M_{\odot}$ (otherwise it would be visible) narrows the fraction of undetectable stellar binaries to just 3.0\%.