Increased Tidal Dissipation Using Advanced Rheological Models: Implications for Io and Tidally Active Exoplanets

TL;DR

This paper compares advanced rheological models to traditional ones, showing they significantly increase tidal heating estimates for rocky bodies, which impacts understanding of planetary evolution and habitability.

Contribution

It introduces and evaluates Andrade and Sundberg-Cooper rheologies, demonstrating their effects on tidal dissipation and planetary resilience, expanding scenarios for tidally active worlds.

Findings

Andrade and Sundberg-Cooper models produce at least 10× more tidal heating than Maxwell.

These models enable cooler planets to remain tidally active, termed 'tidal resilience.'

Implications for the evolution and long-term states of tidally active planets.

Abstract

The advanced rheological models of Andrade (1910) and Sundberg & Cooper (2010) are compared to the traditional Maxwell model to understand how each affects the tidal dissipation of heat within rocky bodies. We find both the Andrade and Sundberg-Cooper rheologies can produce at least 10$\times$ the tidal heating compared to a traditional Maxwell model for a warm (1400-1600 K) Io-like satellite. Sundberg-Cooper can cause even larger dissipation around a critical temperature and frequency. These models allow cooler planets to stay tidally active in the face of orbital perturbations-a condition we term 'tidal resilience.' This has implications for the time evolution of tidally active worlds, and the long-term equilibria they fall into. For instance, if Io's interior is better modeled by the Andrade or Sundberg-Cooper rheologies, the number of possible resonance-forming scenarios that still produce a hot, modern Io is expanded, and these scenarios do not require an early formation of the Laplace resonance. The two primary empirical parameters that define the Andrade anelasticity are examined in several phase spaces to provide guidance on how their uncertainties impact tidal outcomes, as laboratory studies continue to constrain their real values. We provide detailed reference tables on the fully general equations required for others to insert the Andrade and Sundberg-Cooper models into standard tidal formulae. Lastly, we show that advanced rheologies greatly impact the heating of short-period exoplanets and exomoons, while the properties of tidal resilience can mean a greater number of tidally active worlds among all extrasolar systems.