2024ApJ...975L..38H

We develop analytical tools and perform three-body simulations to investigate the orbital evolution and dynamical stability of binary planets within star clusters. Our analytical results show that the orbital stability of a planetary-mass binary against passing stars is mainly related to its orbital period. Critical flybys, defined as stellar encounters with energy kicks comparable to the binary binding energy, can efficiently produce a wide range of semimajor axes (a) and eccentricities (e) from a dominant population of primordially tight Jupiter-mass binary objects (JuMBOs). The critical flyby criterion we derived offers an improvement over the commonly used tidal radius criterion, particularly in high-speed stellar encounters. Applying our results to the recently discovered JuMBOs by the James Webb Space Telescope (JWST), our simulations suggest that to match the observed ∼9% wide binary fraction, an initial semimajor axis of a₀ ∼ 10-20 au and a density-weighted residence time of χ ≳ 10⁴ Myr pc^–3 are favored. These results imply that the JWST JuMBOs probably formed as tight binaries near the cluster core.