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Abstract:

The centre of the Galaxy harbours 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 10⁵ 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 μas. 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 ≲2 M ⊙ (otherwise it would be visible) narrows the fraction of undetectable stellar binaries to just 3.0%.

Abstract:

Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum dissipation experienced by point masses on periodic orbits within a homogeneous, fluidlike background. Our focus is on eccentric Keplerian trajectories. Although our approach is currently restricted to linear response theory, it is fully consistent within that framework. We validate our theoretical expressions for the specific case of an ideal fluid, using semi-numerical simulations of the linear response acoustic wake. We demonstrate that, for a finite-time perturbation switched on at t=0, a steady dissipation state is reached after a time bounded by twice the sound crossing time of the apocenter distance. We apply our results to model the secular evolution of compact eccentric binaries in a gaseous medium, assuming low-density conditions where the orbital elements evolve adiabatically. For unequal-mass systems with moderate initial eccentricity, the late-time eccentricity growth is significantly delayed compared to the equal-mass case, due to the binary components becoming transonic at different times along their orbital trajectory. Our approach offers a computationally efficient alternative to full simulations of the linear response wake.