Tidal Dissipation in Dual-Body, Highly Eccentric, and Non-synchronously Rotating Systems: Applications to Pluto-Charon and the Exoplanet TRAPPIST-1e

Abstract

Using the Andrade-derived Sundberg-Cooper rheology, we apply several improvements to the secular tidal evolution of TRAPPIST-1e and the early history of Pluto-Charon under the simplifying assumption of homogeneous bodies. By including higher-order eccentricity terms (up to and including $e^{20}$), we find divergences from the traditionally used $e^{2}$ truncation starting around $e=0.1$. Order-of-magnitude differences begin to occur for $e>0.6$. Critically, higher-order eccentricity terms activate additional spin-orbit resonances. Worlds experiencing non-synchronous rotation can fall into and out of these resonances, altering their long-term evolution. Non-zero obliquity generally does not generate significantly higher heating; however, it can considerably alter orbital and rotational evolution. Much like eccentricity, obliquity can activate new tidal modes and resonances. Tracking the dual-body dissipation within Pluto and Charon leads to faster evolution and dramatically different orbital outcomes. Based on our findings, we recommend future tidal studies on worlds with $e\geq0.3$ to take into account additional eccentricity terms beyond $e^{2}$. This threshold should be lowered to $e>0.1$ if non-synchronous rotation or non-zero obliquity is under consideration. Due to the poor convergence of the eccentricity functions, studies on worlds that may experience very high eccentricity ($e\geq0.6$) should include terms with high powers of eccentricity. We provide these equations up to $e^{10}$ for arbitrary obliquity and non-synchronous rotation. Finally, the assumption that short-period, solid-body exoplanets with $e\gtrsim0.1$ are tidally locked in their 1:1 spin-orbit resonance should be reconsidered. Higher-order spin-orbit resonances can exist even at these relatively modest eccentricities, while previous studies have found such resonances can significantly alter stellar-driven climate.