Dynamics of Binary Planets within Star Clusters

Abstract: 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 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 Jupiter-Mass Binary Objects (JuMBOs) by the James Webb Space Telescope (JWST), our simulations suggest that to match the observed $\sim$9% wide binary fraction, an initial semimajor axis of $a_0 \sim$ 10-20 au and a density-weighted residence time of $\chi \gtrsim 10^4$ Myr pc$^{-3}$ are favored. These results imply that the JWST JuMBOs probably formed as tight binaries near the cluster core.