Binary stars in the Milky Way nuclear stellar cluster

Intermediate mass galaxies, including the Milky Way, typically host both a supermassive black hole (SMBH) and a nuclear stellar cluster (NSC). Binary systems residing in an NSC evolve dynamically via frequent close encounters with surrounding stars and secular processes related to the SMBH. Although the evolution of very soft and very hard binaries can be predicted semi-analytically, the situation is more complex for binaries that lie near the hard-soft boundary. We aim to follow the evolution of such binaries throughout the age of the NSC (∼ 10 Gyr ) and determine their evolutionary outcomes and the effects on a binary population in the NSC. By employing numerical simulations of three-body encounters between binary systems and a tertiary star, while also considering the secular evolution in the form of von Zeipel-Lidov-Kozai oscillations and tidal dissipation, we followed the evolution of moderately soft and hard binaries ($0.03-2.5 au $) with initial masses of łesssim 2 M _⊙ at galactocentric radii of 0.1 and 0.3,pc. We find that inward migration caused by three-body encounters leads to the destruction of binaries through mergers and evaporation, while outward migration is a pathway to retaining intact binaries for ≳ 10 Gyr . All binaries that remain intact are hard and circular, but the outcomes for binaries initially at the hard-soft boundary are highly stochastic. From the destroyed binaries, we find that i) ∼0.3% of evaporated binaries fall into the SMBH's loss cone ii) ≳1% of the mergers occur late enough to be observed as blue straggler stars (BSSs) on the main-sequence or as recently evolved red giants iii) ∼1% of the mergers originating at $0.1 pc $ merge at orbits completely confined to the inner arcsec of the NSC, and iv) łesssim 80% of collisions between a field star in the NSC and one of the binary stars leads to a subsequent merger with the other binary star, a three-body pile-up (3BPU). These 3BPUs are relatively common within the first 1-2 Gyr but stagnate afterwards and could serve as a way to form more massive BSSs. We predict that a small but possibly substantial fraction of binaries in the NSC originated closer to the SMBH compared to their present-day orbits. Conversely, we expect evaporated binary stars and merger products in the form of BSSs close to the SMBH originated further out in the NSC. The orbits of the binaries and the merger products confined to the inner arcsec of the NSC have ended up there after ≳ 300 Myr and have circular orbits. They are therefore unlikely to be related to the formation of the S-stars or G-objects and instead suggest that the inner arcsec is contaminated with BSSs from earlier star formation events.