A Study of the Tidal and Thermal Evolution of Rocky & Icy Worlds Utilizing Advanced Rheological Models

Abstract

In this thesis, we explore the thermal and orbital evolution of rocky and icy worlds that are under the influence of strong tidal forcing. Tides are an important mechanism that extracts energy from the orbit and spin of a planet or moon and deposits it, via frictional heating, into its interior. The efficiency of tidal dissipation is restricted by a planet's ability to flex under stress and strain. Recent laboratory work has shown that the atomic and microphysical processes that ultimately govern this efficiency are not well modeled by the rheological laws traditionally used in tidal studies. We utilize the more accurate rheologies of Andrade (1910) and Sundberg & Cooper (2010) to describe the dissipation efficiency via the complex Love number (Love 1892). These are used in an interior model that allows the heat generated by tides to warm a planet's interior, potentially to the point of partial melting. Heat extraction is modeled by one dimensional, parameterized thermal convection in either the silicate mantle or, as is the case for Chapters 4 and 5, in an icy shell. Depending upon the rheology, the magnitude of dissipation can vary significantly with the internal temperature---creating a feedback where tides create heat which may increase or decrease the strength of the tides. We have found that the Andrade and Sundberg-Cooper rheologies can produce 10—100x greater dissipation compared to traditionally used models at cooler temperatures and higher tidal frequencies. This increased dissipation allows for a greater number of thermal equilibria between heat production and extraction. This may cause one world to experience more rapid orbit and spin changes while another sees stable, moderate dissipation over long time periods. We present the mathematical tools so that others may use these rheologies in future studies. To emphasize the impact of these models, we also explored three specific types of systems: the Laplace resonance between the innermost Galilean moons of Jupiter, tides in collisionally-formed binary Trans-Neptunian Objects, and tides in heliocentric Earth and super-Earth sized exoplanets. Increased dissipation at lower temperatures leads to greater tidal stability in Laplace-like resonances. This increased tidal resilience allows for more orbital and thermal perturbations without knocking one or more of the resonant planets or moons into an unrecoverable cooling phase. For the Galilean moons, this suggests that Io has been, and will remain, the dominant dissipator. This is contrary to the results of traditional rheologies, which suggest that Europa may become very hot in the next 500 million years. Andrade-like rheologies also lessen restrictions on the initial conditions of the resonance, whereas traditional models would require the resonance to begin very shortly after planet formation, or for it to have produced more extreme orbital forcing. It is thought that binary TNOs (such as Pluto-Charon and Eris-Dysnomia) are formed by a grazing impact or near miss capture event that leaves them with high, non-synchronous spins and large eccentricities. These small bodies were thought to be geologically uninteresting until observations revealed young active surfaces, such as that seen on Pluto by the New Horizons spacecraft. We show that there exists a Goldilocks zone of moderate heating that can result in sub-surface liquid water oceans for millions of years after a formation event. The large number of binary TNOs suggests that this might have been the largest reservoir of liquid water in our Solar System's history, albeit for a short time. Lastly, moving beyond our Solar System, the same resilience that is seen in the Galilean moons will be applicable for exoplanets in compact, multi-planet systems. Meaning that more systems will be stable, from a tidal perspective, for long-time periods. For exoplanets orbiting cooler, M-dwarf stars, the amount of tidal heating impacts the traditional habitable zone, especially for Andrade-like rheologies. For planets orbiting sun-like stars, heliocentric tides will likely not be important from a habitability perspective. However, we can still learn much about planetary interiors by studying these hot, non-habitable planets. We present one such pathway where a tidally-locked, Earth-sized exoplanet experiencing extreme dayside-to-nightside temperature differences will have a significantly altered interior. These worlds will experience large-scale hemispheric flows of mantle material from dayside-to-nightside and a large interior density gradient which may be unstable from a spin perspective. Any change to spin-axis orientation or a potential break of the tidal-lock could offer an observational clue to exoplanet interiors.