Tidal Dissipation in Dual-body, Highly Eccentric, and Nonsynchronously 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 nonsynchronous rotation can fall into and out of these resonances, altering their long-term evolution. Nonzero 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 ≥ 0.3 to take into account additional eccentricity terms beyond e 2. This threshold should be lowered to e > 0.1 if nonsynchronous rotation or nonzero obliquity is under consideration. Due to the poor convergence of the eccentricity functions, studies on worlds that may experience very high eccentricity (e ≥ 0.6) should include terms with high powers of eccentricity. We provide these equations up to e 10 for arbitrary obliquity and nonsynchronous rotation. Finally, the assumption that short-period, solid-body exoplanets with e ≳ 0.1 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.

The Tidal-Thermal Evolution of the Pluto-Charon System

“…Figure 2c shows that the eccentricity of the orbit increases for a very short time in the beginning before Charon's fall into the 3:2 spin-orbit resonance, at which point, the eccentricity starts to dampen smoothly to 0, dictating the fall of Charon into the tidallylocked stated. A qualitatively similar behaviour in the orbital evolution was observed by Renaud et al (2021), but because of a different initial ̇ ∕ and differences in planetary structure (physical properties and attenuation), the exact timing of the 3:2 and 1:1 resonance captures vary slightly in comparison to our results.…”

“…As for the timing of the formation of the Pluto system, we assume 1) that the accretion process has been completed after the CAIs have formed, and therefore disregard the contribution from short-lived radionuclides, and 2) that Charon formed 200 Myr after the formation of Pluto (e.g., Canup et al, 2021). In connection with the initial thermal state of Pluto and Charon, we assume an initially homogeneous interior temperature, and consider both a cold-and a hot-start case (e.g., Bierson et al, 2020;Renaud et al, 2021). Cold-start (180 K) corresponds to an absent or very thin ocean layer (15 km thickness), whereas a hot-start commences right at the point where the ocean layer (280 km thickness) starts to crystallize, corresponding to ∼270 K for pure water and ∼250 K in the case contaminants are present.…”

“…During the deceleration of the spin of the planetary objects, heat is produced by friction, which, in addition to radiogenic heating, changes the thermal structure of the planet. As the planetary objects thermally evolve, their interior properties change, which in turn, influences their tidal response (e.g., Robuchon and Nimmo, 2011;Saxena et al, 2018;Samuel et al, 2019;Bagheri et al, 2021;Renaud et al, 2021). Hence, the tidal and thermal evolution co-modulate, necessitating their joint consideration in evaluating the evolution of planetary systems.…”

“…Saxena et al (2018), for example, observed that subsurface oceans containing a small amount of impurities and tidal heating due to initially high spin rates may enable liquid water and cryovolcanism to persist until the present (Moore et al, 2016;Neveu et al, 2015;Beyer et al, 2019). Yet, these studies generally did not consider dissipation in both bodies and relied on tidal evolution models that are inadequate for the case of a highly eccentric and nonsynchronously rotating system (Bagheri et al, 2021;Renaud et al, 2021). Specifically, tidal models that truncate eccentricity functions to 2 (where is eccentricity) on eccentric orbits (>0.1) impart changes in spin rate evolution, spin-orbit resonances, and errors in heating rates that typically increase significantly for very high eccentricity (>0.5), which is not observed when higher-order terms are included.…”

On the Origin of the Pluto System

“…The innermost distance at which Charon could have formed would be near the Roche limit, which is at ≈2.5 R P for Pluto and Charon's densities. During tidal expansion of the mutual orbit, tides raised on Pluto and Charon by one another could have either increased or decreased the orbital eccentricity depending on the relative strength of tidal dissipation associated with combinations of spin and orbital frequencies at any given time (Renaud et al, 2021). The pace of orbital expansion, eccentricity change, and spin synchronization could have quickened or stalled in the vicinity of spin-orbit resonances.…”