http://arxiv.org/abs/1707.06701
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 10x the tidal heating compared to a traditional Maxwell model for a warm (1400–1600 K) Io-like satellite. Sundberg-Cooper is able to cause even larger dissipation around a critical temperature and frequency. Both advanced 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. We explore this by looking at the Laplace resonance amongst Io, Europa, and Ganymede. If Io is better modeled by the Andrade or Sundberg-Cooper models, then the Laplace resonance is no longer required, from a tidal perspective, to have occurred immediately after formation. Empirical parameters that define the Andrade anelasticity are examined in several phase spaces to provide guidance, 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 equations. Lastly, we find that realistic rheological models greatly impact the heating of heliocentric exoplanets, while the properties of tidal resilience, and fewer restrictions on resonance capture, can mean a greater number of tidally active worlds among all extrasolar systems.
J. Renaud and W. Henning
Mon, 24 Jul 17
12/42
Comments: 30 pages – 14 figures – submitted to ApJ