Io exhibits widespread volcanism powered by tides raised by Jupiter. The distribution of volcanoes offers a window into the interior of the moon. The distribution shows more volcanism at the equator as well as peak volcanic output which is shifted by roughly 30-60 degrees to the east of the subjovian point [1]. Models of tidal dissipation that assume a spherically symmetric, solid Io cannot reproduce this shift [2]. More recently, it has been proposed that tidal dissipation in a magma ocean [3] or in a non-spherically symmetric, solid Io [4] can induce this lag. In this study, we explore the second option and show that solid-body dissipation can induce an eastward shift of the tidal dissipation pattern.@en

Thousands of exoplanets have been discovered; however, the detection of exomoons remains elusive. Tidally heated exomoons have been proposed as candidate targets for observation; vigorous tidal dissipation can raise the moon's surface temperature, making direct imaging possible, and cause widespread volcanism that can have a signature in transits. We assess whether the required amounts of tidal dissipation can be attained and how long it can be sustained. In a first step, we look at the thermal state of a super-Io for different orbital configurations. We show that close-in exomoons with moderate (e ≈ eIo) to high (e ≈ 0.1) orbital eccentricities can feature surface heat fluxes 1-3 orders of magnitude higher than that of Io if heat transfer is dominated by heat piping or the moon has a magma ocean. In a second step, we investigate the longevity of a super-Io. The free eccentricity of an isolated close-in exomoon is quickly dampened due to tides; high orbital eccentricities can be maintained if the moon is in a mean-motion resonance with another moon and the planet is highly dissipative. However, this scenario leads to fast orbital migration. For a Mars-sized exomoon, we find that tides alone can raise the surface temperatures to more than 400 K for 10 million yr, and surface heat fluxes higher than that of Io can be maintained for billions of years. Such tidally active bodies are expected to feature more vigorous volcanic activity than Io. The material outgassed via volcanism might be detected in transits.

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Io's spectacular and unique appearance is characterised by its yellowish surface, colourful lava deposits, and black calderas. The reason for this appearance is extensive tidal heating in the moon's interior. Caught in the Laplace resonance with the Galilean moons Ganymede and Europa, Io is the most tidally heated and volcanically active world in the Solar System. It is therefore the best place to study fundamental processes important for the early evolution of terrestrial planets, and the habitability of icy satellites and terrestrial exoplanets subject to tidal heating. The physical state of Io’s interior, the driving tidal dissipation and heat transport mechanisms are unknown, however, form a strongly interconnected system: 1) Io’s internal temperature and melt distribution are controlled by tidal dissipation and heat loss processes; 2) The total amount and pattern of tidal dissipation depend on the rheological properties of Io's interior; 3) These rheological properties, in turn, depend on the internal temperature and melt distribution. Due to the strong dependence on melt, Io's volcanic activity hints at the dynamics beneath the surface and can therefore be used to improve our understanding of the underlying mechanisms. Aim of this thesis is to improve our understanding of these interconnections (1-3) and to constrain Io's current interior dynamics based on the moon's volcanic activity derived from satellite and Earth-based observations over the last 20 years. @en

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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Tidal dissipation makes Jupiter's moon Io the most volcanically active body in the solar system. Most of the heat generated in the interior is lost through volcanic activity. In this study, we aim to answer the questions: Can convection and melt migration in the mantle explain the spatial characteristics of Io's observed volcanic pattern? And, if so, what constraints does this place on the viscosity and thickness of the convective layer? We examine three different spatial characteristics of Io's volcanic activity: (i) The presence of global volcanism, (ii) the presence of large-scale variations in Io's volcanic activity, and (iii) the number of Io's volcanic systems. Our study relies on the assumptions that melt in the mantle controls Io's global volcanism, that the large-scale variations of Io's volcanic activity are caused by nonuniform tidal heating, and that the spatial density of volcanoes correlates with the spatial density of convective anomalies in the mantle. The results show that the observed small and large-scale characteristics of Io's volcanic pattern can be explained by sublithospheric anomalies influenced and caused by convective flow. Solutions that allow for active volcanism and Io's specific large-scale variations in volcanic activity range from a thick mantle of a high viscosity ((Formula presented.) Pa s) to a thin asthenosphere of a low viscosity ((Formula presented.) Pa s). Provided that Io's volcanoes are induced by convective anomalies in the mantle, we find that more than 80% of Io's internal heat is transported by magmatic processes and that Io's upper mantle needs to be thicker than 50 km.

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Undergoing extreme tidal dissipation, Io serves as an archetype of tidally heated rocky exoplanets and exomoons. Therefore, understanding Io’s dissipative processes and their interactions with Io's interior provides insights into the evolution of these tidally heated bodies. Tidal dissipation depends on Io’s rheological structure and is thought to be radially and laterally non-uniformly distributed within Io’s interior. We explore whether the heterogeneous nature of tidal heating causes regional variations of Io's temperature-dependent melt fraction and rheology. Furthermore, we investigate to which extent these regional variations in turn change Io’s tidal dissipation pattern. To study the spatial effect of the heterogeneous heat production on Io's interior structure we developed a model that couples Io's non-uniform heating pattern with Io's main heat transport mechanisms [1]. The initial tidal heating pattern is calculated from a 1-dimensional rheological structure. From the resulting temperature and melt distribution we derive the regionally varying viscosity and rigidity structure. In a second step, we use a finite-element model to re-calculate Io’s tidal dissipation pattern using the updated tidally induced three-dimensional viscosity and rigidity distribution. Our results reveal that for models with a magma-dominating heat transport peak-to-peak variations in the global temperature field of up to 190 K arise. However, for models with a convection-dominating heat transport and low reference viscosities of the convective layer, variations are fully damped. In particular for models with strong tidally-induced lateral variations, the newly obtained dissipation patterns strongly differ from the initial dissipation patterns resulting from 1-dimensional structures. The updated patterns show asymmetric contributions towards the 0°/180°W/E plane and contain additional spherical components with degrees > 4. Our results show that three-dimensional structures are inevitable for bodies with strong tidal dissipation, and 3D modelling approaches for the computation of thermal heat transport and tidal dissipation are necessary. [1] Steinke, T., et al.,2019, Icarus, Tidally induced lateral variations of Io's interior. @en

Jupiter’s moon Ganymede might be in possession of a subsurface ocean located between two ice layers. However, from Galileo data it is not possible to unambiguously infer the thickness and densities of the individual layers. The upcoming icy satellite mission JUICE (JUpiter ICy moons Explorer) will have the possibility to perform more detailed investigations of Ganymede’s interior structure with the radio science experiment 3GM and the GAnymede Laser Altimeter (GALA). Here we investigate the possibility to derive the rotational state of the outer ice shell by using topography measured by laser altimetry. We discuss two different methods to invert synthetic laser altimetry data. Method 1 is based on a spherical harmonics expansion and Method 2 solves for B-splines on a rectangular grid. While Method 1 has significant limitations due to the omission of high degrees of the global expansion, Method 2 leads to stable results allowing for an estimate of the in-orbit measurement accuracy. We estimate that GALA can measure the amplitude of Ganymede’s librations with an accuracy of 2.5–6.6 µrad (6.6–17.4 m at the equator). This allows for determining the thickness of an elastic ice shell, if decoupled from the deeper interior by a subsurface ocean, to about an accuracy of 24–65 km.

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Recent Earth-based observations of Io reveal a specific distribution of persistent hotspots and sudden highintensity events. The volcanic pattern is commonly associated with the heat flux originating from Io’s tidally heated mantle and asthenosphere. Io’s interior state is a complex system of heat production, heat transport, melt, and temperature-dependent rheology. The spatial pattern of dissipated heat, for example, depends on the interior rheology but at the same time the heating influences the rheology, in particular due to the temperature-dependence of the mantle viscosity. We present an iterative procedure to investigate the strength and characteristics of this specific feedback. The tidal dissipation is calculated by a viscoelastic model of a spherical body disturbed by a tidal force. The model is based on finite elements so it can deal with lateral variations of the viscosity. We use simple scaling laws to relate the temperature-dependent viscosity distribution to the spatial heat production and heat transport by mantle convection. In an iterative procedure, the viscosity distribution is updated and a new heat dissipation pattern is calculated until convergence is found. The results show that the heat in Io’s interior and consequently the heat flux at the surface are strongly smoothed. The comparison of the converged models and the initial models of different Rayleigh numbers and types of mantle rheology reveals a diverge characteristics of the feedback. This possibly changes the way the observed distribution of volcanos on Io’s surface is related to Io’s interior properties. @en

We computed interior structure models of Mercury and analyzed their viscoelastic tidal response. The models are consistent with MErcury Surface, Space Environment, GEochemistry, and Ranging mission inferences of mean density, mean moment of inertia, moment of inertia of mantle and crust, and tidal Love number k₂. Based on these constraints we predict the tidal Love number h₂ to be in the range from 0.77 to 0.93. Using an Andrade rheology for the mantle the tidal phase-lag is predicted to be 4° at maximum. The corresponding tidal dissipation in Mercury's silicate mantle induces a surface heat flux smaller than 0.16 mW/m². We show that, independent of the adopted mantle rheological model, the ratio of the tidal Love numbers h₂ and k₂ provides a better constraint on the maximum inner core size with respect to other geodetic parameters (e.g., libration amplitude or a single Love number), provided it responds elastically to the solar tide. For inner cores larger than 700 km, and with the expected determination of h₂ from the upcoming BepiColombo mission, it may be possible to constrain the size of the inner core. The measurement of the tidal phase-lag with an accuracy better than ≈0.5° would further allow constraining the temperature at the core-mantle boundary for a given grain size and therefore improve our understanding of the physical structure of Mercury's core.

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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