Dynamical Signatures of Formation and Evolution: Free Eccentricity Analysis of Pluto's Small Satellites

Pluto's small satellites—Styx, Nix, Kerberos, and Hydra—occupy nearly circular orbits that are nearly coplanar with that of Pluto-Charon. While several formation scenarios have been proposed, none has yet provided a fully self-consistent explanation for how these satellites arrived at their present orbits. Early in-situ formation near their current locations—following the Charon-forming impact—is one of the most promising explanations (Woo & Lee 2018), though its dynamical viability depends critically on the free eccentricities of the small satellites.

We adopt the theoretical framework of Lee & Peale (2006) and Woo & Lee (2020), which provides a proper non-Keplerian description of circumbinary orbits and defines free eccentricity as an appropriate generalization of eccentricity for such orbits. Based on this framework, we conduct orbital simulations using the latest ephemerides by Porter & Canup (2023) and Brozović & Jacobson (2024) and apply the fast Fourier transform (FFT) to extract the free eccentricity component of each satellite. To assess the robustness of our results, we also estimate uncertainties in the extracted free eccentricities by repeating the analysis with the uncertainties in the ephemerides reported by Porter & Canup (2023).

We find that the free eccentricities of Nix, Kerberos, and Hydra are consistent with previous values but the free eccentricity of Styx is significantly different. The consistency of the extracted free eccentricities across two independent sets of initial conditions supports the robustness of our results. Based on these dynamical constraints, we then carry out tidal evolution simulations under the in-situ formation scenario to test whether the observed free eccentricities and orbital structure can be reproduced by the early in-situ formation scenario through long-term interactions with the tidally evolving Pluto–Charon binary.

Our results demonstrate that free eccentricity analysis offers a robust way to constrain the formation of Pluto's small satellites. This approach provides a dynamic link between the current orbital structure and the formation and evolution of the system, and may also offer insights into the formation of circumbinary planets in extrasolar systems.

This work is supported in part by Hong Kong RGC grant 17309323.

Figure 1. Free eccentricities of Pluto’s small satellites versus their orbital distances normalized by Pluto’s radius. Black circles with error bars are from Porter & Canup (2023); red triangles are from Brozović & Jacobson (2024). Vertical dashed lines mark the current 3:1 to 6:1 mean-motion commensurabilities with Charon.