Love numbers for Io with a magma ocean

Abstract

The volcanic activity of Jupiter’s moon Io is driven by the heat generated by tidal deformation induced by its orbital resonance with Europa and Ganymede. The question of whether tidal dissipation primarily occurs in a partially molten solid layer (“magmatic sponge”) or in a hypothetical liquid magma ocean has long been a subject of debate. The data collected by the Juno spacecraft during two recent flybys of Io has allowed, for the first time, to quantify Io’s tidal deformation. The analysis of the data by Park et al. (2024) reveals that the Love number $k_2$ is about 0.125 and the tidal dissipation parameter $Q$ is about 11.4. These values are compatible with a solid mantle but they do not exclude the possibility that a global magma ocean exists in the deep ($>$320 km) interior. Using a model based on the solution of the Navier–Stokes equation, we investigate the dependence of the Love number on the position of the ocean and examine how much it is affected by the Coriolis force, an effect that was not included in the study of Park et al. (2024). Varying the viscosity of the magma, the depth and the thickness of the ocean in the range of $10^2$–$10^7$ Pa s, 50–400 km and 0.1–20 km, respectively, and considering only the models with a dissipation power of about 100 TW, we show that a magma ocean located at a depth of $\lesssim 200$ km predicts either too large $k_2$ or too long time lag, implying that the existence of a shallow magma ocean in Io is unlikely. A thin ($<$10 km) magma ocean located at a depth of $\gtrsim 250$ km is compatible with the observation and could, in principle, be detected by accurate measurement of degree 2 zonal and sectorial Love numbers. Our results are in general agreement with those of Park et al. (2024), indicating that Io’s enormous volcanic activity is unlikely to be driven by a global fluid magma ocean located at a shallow depth. This conclusion is conditioned by the reliability of the method used to interpret the Juno data. As the tidal response of Io with a magma ocean is affected by the Coriolis force, the Love number depends on the harmonic order, which can complicate the analysis of the information collected during the flybys. The effect of fluid tides was not considered in the data processing, and therefore, the conclusions of Park et al. (2024) cannot be definitely confirmed.