Tidal Dissipation in Dual-body, Highly Eccentric, and Nonsynchronously Rotating Systems: Applications to Pluto–Charon and the Exoplanet TRAPPIST-1e

Joe P Renaud,Avi Mandell,Terry Hurford,Marc Neveu,Amirhossein Bagheri,Prabal Saxena,Wade G Henning

doi:10.3847/psj/abc0f3

Abstract

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.

Highlights

New observations of extrasolar planets and Solar System objects are motivating a resurgence in improved modeling of tidal dissipation
We have found that using traditional tidal evolution formulae, which truncate eccentricity functions to e2, on planets and moons in highly eccentric orbits (e ≥ 0.1) can lead to significant changes to spin rate evolution and modest errors in heating rates
These errors can increase by orders of magnitude for very high eccentricity (e ≥ 0.6)

Summary

Introduction

New observations of extrasolar planets and Solar System objects are motivating a resurgence in improved modeling of tidal dissipation. For many real systems, both worlds may dissipate strongly enough to affect the system’s evolution, as is the case for Io and Jupiter (Hussmann & Spohn 2004) In such cases, a dual-body dissipation model is required. Binary systems, where two co-orbiting bodies have very similar mass, naturally lack one clear dominant source of dissipation In cases such as Pluto and Charon (Farinella et al 1979; Dobrovolskis et al 1997; Cheng et al 2014; Barr & Collins 2015), or the early Earth and Moon (Touma & Wisdom 1998; Canup & Asphaug 2001; Cuk & Stewart 2012; Zahnle et al 2015; Rufu & Canup 2020), the threshold for when a dual-dissipation model is required is not always clear. The development and testing of the best theoretical set of governing equations available is a critical starting point

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Conclusion