Dissipation in rocky planets for strong tidal forcing

Abstract

Aims. We plan to reproduce a previously published calculation for the tidal dissipation in Io and extend the employed model to investigate the heat transport mechanism in Io and the thickness of Io's asthenosphere. Additionally, we apply this model to an exoplanet and obtain insights into the dependencies of the modified tidal quality factor (Q′) on the size of the planet and its orbital eccentricity. Methods. Tidal dissipation depends on the heat transport mechanism. For strong tidal forcing an equilibrium between heat transport by convection and heat production by tidal dissipation can be obtained that determines the tidal dissipation. By this means, we checked whether convection is the dominant heat transport mechanism in Io. The tidal dissipation also depends on the interior model of Io. We considered various asthenosphere thicknesses and determined which of these gives results compatible with observations. We determined the modified tidal quality factors (Q′) for Corot 7 b for various orbital parameters, but in a way that tidal forcing is strong. We used convection and melt migration as possible heat transport mechanism. We repeated this for a hypothetical planet with the size and density of Io on the orbit of Corot 7 b. Results. We find that a heat transport dominated by convection in Io is possible, but the grain sizes need to be smaller than 2.2 mm. For larger grain sizes melt migration is the dominant heat transport mechanism. Moreover, Io's asthenosphere needs to be thicker than 100 km. The computation of the modified tidal quality factors (Q′) for Corot 7 b and a planet with the size and density of Io on the orbit of Corot 7 b show that Q′ is scattered over several orders of magnitude, but a value of 100 for Q′ is an acceptable estimate for a rocky planet under strong tidal forcing.