ApJ: Beyond Cassini States: Analytical Framework for Non-Trivial Obliquity Steady States in Multi-Planetary Super-Earth Systems
Published in The Astrophysical Paper, 2026
| Abstract: (Current version in prep) We develop an analytical theory for tidally dissipative spin evolution in compact multi-planet superEarth systems, and identify the dynamical origin of a class of high-obliquity spin steady states beyond classical Cassini states. Previous numerical studies have revealed such “non-trivial” steady states, but their underlying mechanism remained unclear. Starting from the spin Hamiltonian in a precessing orbital frame, we treat the second outer companion as a periodic perturbation to Colombo’s Top and incorporate tides as a non-Hamiltonian dissipative term. We demonstrate that the non-trivial steady states correspond to stable dissipative limit cycles in a weakly-dissipative nearly-integrable spin system. Their locations in phase space are determined by nonlinear m : n resonances between the intrinsic libration or circulation frequency of the spin and the companion-induced driving frequency. A resonant attractor forms when perturbative driving balances tidal dissipation over one geometric recurrence cycle, while phase locking fixes the relative phase between the spin motion and the external forcing. This framework accounts for the coexistence of libration and circulation attractors, the rational relation gres = (m/n) | ∆g | , the emergence of multiple higher-order resonant branches, and the requirement that such branches survive only under suffciently weak tidal damping. The existence condition for tidal strength is compatible with realistic close-in super-Earth parameters and explains why previous simulations adopting stronger dissipation may miss these structures. Our results suggest that high obliquity can be a generic dissipative end state of multi-planet spin dynamics, rather than an outcome limited to classical Cassini-state evolution. |
Paper Link: Coming soon…