Satellite and recent Earth-based observations of Io's surface reveal a specific spatial pattern of persisting hotspots and sudden high-intensity events. Io's major heat producing mechanism is tidal dissipation, which is thought to be non-uniformly distributed within Io's mantle and asthenosphere. The question arises to what extent Io's non-homogeneous heat production can cause long-wavelength variations in the interior and volcanic activity at the surface. We investigate dissipation patterns resulting from two different initially spherical symmetric visco-elastic rheological structures, which are consistent with geodetic observations. The spatial distributions of the time-averaged tidal heat production are computed by a finite element model. Whereas for the first rheological structure heat is produced only in the upper viscous layer (asthenosphere-heating model), the second rheological structure results in a more evenly distributed dissipation pattern (mixed-heating model) with tidal heating occurring in the deep mantle and the asthenosphere. To relate the heat production to the interior temperature and melt distribution, we use steady-state scaling laws of mantle convection and a simple melt migration model. The resulting long-wavelength thermal heterogeneities strongly depend on the initial tidal dissipation pattern, the thickness of the convective layer, the mantle viscosity, and the ratio between magmatic and convective heat transport. While for the asthenosphere-heating model a strong lateral temperature signal with up to 190 K peak-to-peak difference can remain, convection within a thick convective layer, as for the mixed-heating model, can reduce the lateral temperature variation to <1 K, if the mantle viscosity is sufficiently low. Models with a dominating magma heat transport preserve the long-wavelength pattern of tidal dissipation much better and are favoured, because they are better to explain Io's thick crust. The approach presented here can also be applied to investigate the effect of an arbitrary interior heating pattern on Io's volcanic activity pattern.

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In past studies, the reorientation or true polar wander (TPW) of visco-elastic bodies has been studied with approximated solutions. Two types of methods are commonly adopted: those based on the quasi-fluid approximation e.g. Ricard et al., 1993 and those based on the fluid limit approximation which only consider the final orientation (e.g. Matsuyama and Nimmo, 2007). Recently, Hu et al., (2017b) established a method which provides a dynamic solution for calculating the reorientation of tidally deformed bodies. However, they did not provide the links between the complete solution and the fluid limit solution. This paper provides a semi-analytical method for calculating the reorientation of tidally deformed bodies and shows the relation between the complete and the approximated solutions. Furthermore, we provide a criterion, the fluid limit process number F, to test for a given model and estimated TPW speed if the quasi-fluid approximation or fluid limit solution is valid. This number is a quantitative description of how close the body stays in hydrostatic equilibrium during a reorientation process. We use this number to obtain the largest allowed TPW speed of Mars as a function of viscosity, for which the approximated solutions may be used.@en

During true polar wander (TPW), the rotational axis and the axis of the maximum moment of inertia (AoM) of the body do not coincide any more. Thus, equatorial bulge readjustment happens which causes the AoM to follow the rotational axis. Strictly speaking, during TPW the body is not in hydrostatic equilibrium. However, if the speed of TPW is very slow or the viscosity of the planetary body is low enough which makes the equatorial bulge readjustment fast enough, then the body can be assumed to be in hydrostatic equilibrium. If the body is in hydrostatic equilibrium than the following approximate methods for TPW are valid: • method which assumes that the AoM and the rotational axis coincide during TPW (e.g. Nakada, 2007). • method which is based on the quasi-fluid approximation (e.g. Ricard et al, 1993). • method which is based on the fluid-limit assumption (e.g. Matsuyama & Nimmo, 2007). However, it is not clear how slow the TPW needs to be and how low the viscosity of the body needs to be to safely assume hydrostatic equilibrium. Here we present a quantitative criterion to test for a give interior model and TPW speed, if these approximations can be adopted. We define a dimensionless fluid limit process number F, which depends on the visco-elastic Love numbers, the maximum polar wander speed and a tidal deformation factor (which is 0 for negligible tidal bulges such as for Earth and Mars). @en

For large-angle long-term true polar wander (TPW) there are currently two types of nonlinear methods which give approximated solutions: those assuming that the rotational axis coincides with the axis of maximum moment of inertia (MoI), which simplifies the Liouville equation, and those based on the quasi-fluid approximation, which approximates the Love number. Recent studies show that both can have a significant bias for certain models. Therefore, we still lack an (semi)analytical method which can give exact solutions for large-angle TPW for a model based on Maxwell rheology. This paper provides a method which analytically solves the MoI equation and adopts an extended iterative procedure introduced in Hu et al. (2017) to obtain a time-dependent solution. The new method can be used to simulate the effect of a remnant bulge or models in different hydrostatic states. We show the effect of the viscosity of the lithosphere on long-term, large-angle TPW. We also simulate models without hydrostatic equilibrium and show that the choice of the initial stress-free shape for the elastic (or highly viscous) lithosphere of a given model is as important as its thickness for obtaining a correct TPW behavior. The initial shape of the lithosphere can be an alternative explanation to mantle convection for the difference between the observed and model predicted flattening. Finally, it is concluded that based on the quasi-fluid approximation, TPW speed on Earth and Mars is underestimated, while the speed of the rotational axis approaching the end position on Venus is overestimated. @en

Satellite images and recent Earth-based observations of the innermost of the Galilean moons reveal a conspicuous pattern of volcanic hotspots and paterae on its surface. This pattern is associated with the heat flux originating from tidal dissipation in Io’s mantle and asthenosphere. As shown by many analytical studies [e.g. Segatz et al. 1988], the local heat flux pattern depends on the rheology and structure of the satellite’s interior and therefore could reveal constraints on Io’s present interior. However, non-linear processes, different rheologies, and in particular lateral variations arising from the spatial heating pattern are difficult to incorporate in analytical 1D models but might be crucial. This motivates the development of a 3D finite element model of a layered body disturbed by a tidal potential. As a first step of this project we present a 3D finite element model of a spherically stratified body of linear viscoelastic rheology. For validation, we compare the resulting tidal deformation and local heating patterns with the results obtained by analytical models. Numerical errors increase with lower values of the asthenosphere viscosity. Currently, the numerical model allows realistic simulation down to viscosities of 1018 Pa s. Furthermore, we investigate an adequate way to deal with the relaxation of false modes that arise at the onset of the periodic tidal potential series in the numerical approach. Segatz, M., Spohn, T., Ross, M. N., Schubert, G. (1988). Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io. Icarus, 75(2), 187-206. @en

Existing approaches for simulating the true polar wander (TPW) of a viscoelastic body can be divided into three categories: (i) a linear dynamic approach which uses the linearized Liouville equation (e.g., Wu and Peltier (1984) and Mitrovica et al. (2005)); (ii) a nonlinear dynamic approach which is based on the quasi-fluid approximation (e.g., Sabadini and Peltier (1981), Ricard et al. (1993), and Cambiotti et al. (2011)); and (iii) a long-term limit approach which only considers the fluid limit of a reorientation (e.g., Matsuyama and Nimmo (2007)). Several limitations of these approaches have not been studied: the range for which the linear approach is accurate, the validity of the quasi-fluid approximation, and the dynamic solution for TPW of a tidally deformed rotating body. We establish a numerical procedure which is able to determine the large-angle reorientation of a viscoelastic celestial body that can be both centrifugally and tidally deformed. We show that the linear approach leads to significant errors for loadings near the poles or the equator. Second, we show that slow relaxation modes can have a significant effect on large-angle TPW of Earth or other planets. Finally, we show that reorientation of a tidally deformed body driven by a positive mass anomaly near the poles has a preference for rotating around the tidal axis instead of toward it. At a tidally deformed body which does not have a remnant bulge, positive mass anomalies are more likely to be found near the equator and the plane perpendicular to the tidal axis, while negative mass anomalies tend to be near the great circle that contains the tidal and rotational axes.

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