Solid tides in Io’s partially molten interior

Abstract

Context. Io’s spectacular activity is driven by tidal dissipation within its interior, which may undergo a large amount of melting. While tidal dissipation models of planetary interiors classically assume that anelastic dissipation is associated only with shear deformation, seismological observation of the Earth has revealed that bulk dissipation might be important in the case of partial melting. Aims. Although tidal dissipation in a partially molten layer within Io’s mantle has been widely studied in order to explain its abnormally high heat flux, bulk dissipation has never been included. The aim of this study is to investigate the role of melt presence on both shear and bulk dissipation, and the consequences for the heat budget and spatial pattern of Io’s tidal heating. Methods. The solid tides of Io are computed using a viscoelastic compressible framework. The constitutive equation including bulk dissipation is derived and a synthetic rheological law for the dependence of the viscous and elastic parameters on the melt fraction is used to account for the softening of a partially molten silicate layer. Results. Bulk dissipation is found to be negligible for melt fraction below a critical value called rheological critical melt fraction. This corresponds to a sharp transition from the solid behavior to the liquid behavior, which typically occurs for melt fractions ranging between 25 and 40%. Above rheological critical melt fraction, bulk dissipation is found to enhance tidal heating up to a factor of ten. The thinner the partially molten layer, the greater the effect. The addition of bulk dissipation also drastically modifies the spatial pattern of tidal dissipation for partially molten layers. Conclusions. Bulk dissipation can significantly affect the heat budget of Io, possibly contributing from 50 to 90% of the global tidal heat power. More generally, bulk dissipation may play a key role in the tidally induced activity of extrasolar lava worlds.