Dynamics of Binary Planets within Star Clusters

TL;DR

This study combines analytical models and simulations to explore how binary planets evolve and remain stable within star clusters, highlighting the importance of stellar encounters and initial conditions.

Contribution

The paper introduces an improved critical flyby criterion for binary stability and applies it to explain the formation of JWST's JuMBOs.

Findings

Orbital stability depends mainly on orbital period.

Critical flybys can produce a wide range of binary parameters.

Formation of JuMBOs likely occurred near cluster cores.

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.