Abstract
Io's spectacular volcanic activity involves strong tidal dissipation in its interior. Magnetic induction measurements and surface observations of the volcanic activity indicate the presence of significant melt in the interior, but the melt distribution remains unconstrained.
Tidal deformation of a planetary body is strongly related to the rheological properties of the interior, and thus, to a larger extent, to the melt content. The amplitude of tidal deformation may be monitored by future missions from spacecraft tracking, altimetry and high-resolution imaging, giving access to the potential and displacement Love numbers k(2), h(2) and l(2).
To anticipate such measurements, we compute the tidal response described by both shear and bulk viscoelastic rheology for various rheological properties and distributions of melt within Io's interior. We show that the distribution of tidal heating between the mantle and the asthenosphere is very sensitive to the assumed melt fraction in the asthenosphere.
For melt fraction smaller that a critical value called rheological critical melt fraction (phi(c)), corresponding to a transition from solid-dominated behavior to liquid-dominated one, the dissipation is mostly occurring in the mantle. For this mantle-dominated regime, a viscosity of the solid rock matrix smaller than 10(17)-10(18) Pa s is required to reproduce the estimated heat output (ranging between 65 and 125 TW).
For melt fraction slightly above phi(c) dissipation mostly occurs in the asthenosphere, resulting in a radical change of dissipation pattern characterized by a reduction of polar contribution. Despite this clear transition, changes in terms of Love numbers k(2), h(2) and l(2) are subtle and would require high precision measurements. k(2) is only slightly sensitive to the melt distribution and is mainly sensitive to the density of the metallic core, with a Love number potentially as high as 0.1 for a low density core and below 0.06 for a high density core. h(2) and especially l(2) are more sensitive to the melt distribution, with a clear distinction between mantle-dominated and asthenosphere-dominated regimes, difference that is amplified by the contribution of bulk viscoelastic response.
The combined detection of high h(2) (> 0.2) and l(2) (> 0.07) values and a low k(2) ( phi(c)) of the partially molten asthenosphere. Accurate determination of Love numbers, combined with libration and magnetic induction measurement may provide crucial constraints on the melt profile in Io's interior.