Constraints on dissipation in the deep interiors of Ganymede and Europa from tidal phase-lags

Abstract

Jupiter’s satellites are subject to strong tidal forces which result in variations of the gravitational potential and deformations of the satellites’ surfaces on the diurnal tidal cycle. Such variations are described by the Love numbers $k_2$ and $h_2$ for the tide-induced potential variation due to internal mass redistribution and the radial surface displacement, respectively. The phase-lags $\phi _{k_2}$ and $\phi _{h_2}$ of these complex numbers contain information about the rheological and dissipative states of the satellites. Starting from interior structure models and assuming a Maxwell rheology to compute the tidal deformation, we calculate the phase-lags in application to Ganymede and Europa. For both satellites we assume a decoupling of the outer ice-shell from the deep interior by a liquid subsurface water ocean. We show that, in this case, the phase-lag difference $\varDelta \phi = \phi _{k_2}- \phi _{h_2}$ can provide information on the rheological and thermal state of the deep interiors if the viscosities of the deeper layers are small. In case of Ganymede, phase-lag differences can reach values of a few degrees for high-pressure ice viscosities ${<}10^{14}$ Pa s and would indicate a highly dissipative state of the deep interior. In this case $\varDelta \phi$ is dominated by dissipation in the high-pressure ice layer rather than dissipation within the ice-I shell. These phase lags would be detectable from spacecraft in orbit around the satellite. For Europa $\varDelta \phi$ could reach values exceeding $20^\circ$ and phase-lag measurements could help distinguish between (1) a hot dissipative silicate mantle which would in thermal equilibrium correspond to a very thin outer ice-I shell and (2) a cold deep interior implying that dissipation would mainly occur in a thick (several tens of km) outer ice-I shell. These measurements are highly relevant for ESA’s Jupiter Icy Moons Explorer (JUICE) and NASA’s Europa Multiple Flyby Mission, both targeted for the Jupiter system.