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,μ{\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%.

💡 Research Summary

This paper investigates the dynamical feasibility of the S2 star (S0-2) hosting a stellar or planetary companion. S2 is a B-type main-sequence star orbiting the supermassive black hole Sagittarius A* at the Galactic Center. While such stars are commonly found in binary systems elsewhere in the Galaxy, no companion to S2 has been detected observationally. This absence could be due to observational biases or the dynamically hostile environment near the black hole, which can disrupt binaries via tidal forces and mergers.

To address this, the authors performed a large set of numerical simulations using the N-body code TIDYMESS, which includes first-order post-Newtonian corrections. They modeled the hierarchical three-body system consisting of Sgr A*, S2, and a potential companion. A total of 10^5 simulations were run, with the companion’s initial orbital elements (orbital period, eccentricity, mutual inclination, mass ratio, etc.) sampled from uniform distributions within physically plausible ranges, excluding orbits within the Roche limit. Each system was evolved for 1 million years, and a binary was considered disrupted if it experienced a merger (stars within Roche limit) or a gravitational breakup (positive orbital energy).

The key findings are:

1. Survival Constraints: Companions can only survive in orbits with periods shorter than 100 days and eccentricities below 0.8. The survival rate increases with shorter periods, lower eccentricities, and orbits that are nearly coplanar with S2’s orbit around Sgr A*.
2. Disruption Mechanisms: The primary disruption mechanisms are mergers driven by extreme eccentricity excitations from Lidov-Kozai cycles, and breakups where the companion exceeds the Hill radius of its orbit around S2 due to perturbations from the black hole.
3. Role of General Relativity: For very short-period binaries (P < ~2.5 days), general relativistic precession can suppress the full Lidov-Kozai cycles, allowing some survival even at the critical mutual inclinations (60°–120°) where the effect is typically strongest.
4. Observational Constraints: When current detection limits are applied—specifically, a radial velocity semi-amplitude below 25 km/s (from Chu et al. 2018) and a companion mass less than ~2 solar masses (to remain undetected in direct imaging)—the fraction of simulated binary configurations that are both dynamically stable and observationally undetectable is reduced to just 3.0% of the initial sample.
5. Astrometric Impact: The presence of such a companion would perturb S2’s astrometric position by no more than 5 microarcseconds, a negligible amount for current and near-future tests of gravity using S2’s orbit.

In conclusion, the study demonstrates that while it is dynamically possible for S2 to host a companion, the parameter space for such a companion to remain both bound and hidden from current observations is extremely narrow (approximately 3% of a broad initial parameter distribution). This result strongly suggests that S2 is most likely a single star, but does not completely rule out a low-mass, short-period companion. The minimal astrometric bias also indicates that any undetected companion would not significantly compromise high-precision tests of general relativity conducted with S2.