Tidally Heated Terrestrial Exoplanets

Abstract

This work models the surface and internal temperatures for hypothetical terrestrial planets in situations involving extreme tidal heating. The feasibility of such planets is evaluated in terms of the orbital perturbations that may give rise to them, their required proximity to a host star, and the potential for the input tidal heating to cause significant partial melting of the mantle. Trapping terrestrial planets into 2:1 resonances with migrating Hot Jupiters is considered as a reasonable way for Earth-like worlds to both maintain high eccentricities and to move to short enough orbital periods (1–20 days) for extreme tidal heating to occur. Secular resonance and secular orbital perturbations may support moderate tidal heating at a low equilibrium eccentricity.

At orbital periods below 10–30 days, with eccentricities from 0.01 to 0.1, tidal heat may greatly exceed radiogenic heat production. It is unlikely to exceed insolation, except when orbiting very low luminosity hosts, and thus will have limited surface temperature expression. Observations of such bodies many not be able to detect tidal surface enhancements given a few percent uncertainty in albedo, except on the nightside of spin synchronous airless objects. Otherwise detection may occur via spectral detection of hotspots or high volcanic gas concentrations including sulfur dioxide and hydrogen sulfide. The most extreme cases may be able to produce magma oceans, or magma slush mantles with up to 40–60% melt fractions. Tides may alter the habitable zones for smaller red dwarf stars, but are generally detrimental.

Multiple viscoelastic models, including the Maxwell, Voigt-Kelvin, Standard Anelastic Solid, and Burgers rheologies are explored and applied to objects such as Io and the super-Earth planet GJ 876d. The complex valued Love number for the Burgers rheology is derived and found to be a useful improvement when modeling the low temperature behavior of tidal bodies, particularly during low eccentricity excursions. Viscoelastic solutions for GJ 876d are typical of extreme short period high eccentricity objects with tidal-convective equilibrium heat rates between ∼10,000 to 500,000 terawatts.