Enceladus's crust as a non-uniform thin shell: II tidal dissipation

Variations in shell thickness over the surface of the egg have been studied in a number of normal and abnormally thin shells. There is far less variation around the latitudes of the egg than there is longitudinally. Different birds give, for normal shells, different patterns of thickness from pole to pole, but for any one bird the pattern is usually fairly constant. The most frequent general pattern is one in which the broad and narrow caps each have a thickness greater than most intermediate latitudes, but the minimum value may fall in different positions in different eggs.Abnormally thin shells seem to deviate from the normal pattern for the same bird, but it will be necessary to carry out more work on this before reliable conclusions can be drawn.With a collection of eggs, the thickness of one latitude is highly correlated with the thickness of another latitude and it is possible to calculate from assumed values for one latitude the pattern for the rest of the shell.Various methods for obtaining an accurate value for mean shell thickness by using a sample of measurements have been compared.

Ocean tidal heating in icy satellites with solid shells

<p>In close exoplanetary systems, tidal interactions are known to shape the orbital architecture of the system, modify star and planet spins, and have an impact on the internal structure of the bodies through tidal heating. Most stars around which planets have been discovered are low-mass stars and thus feature a magnetised convective envelope, as is also expected in giant gaseous planets like Hot-Jupiter. Tidal flows, and more specifically inertial waves (restored by the Coriolis acceleration, and recently discovered in the Sun) tidally-excited, are the main direct manifestation of tidal interactions in the convective envelopes of these bodies. Furthermore, inertial waves are small-scale waves that are sensitive to nonlinearities, especially in close Hot-Jupiter systems with strong tidal forcing. The nonlinear self-interaction of inertial waves is known to trigger differential rotation in convective shells, as shown in numerical and experimental hydrodynamical studies. Since inertial waves are a key contribution to the tidal dissipation in close star-planet systems, it is essential to have the finest understanding of tidal inertial wave propagation and dissipation in such a complex nonlinear, magnetised, and differentially rotating environment.<br />In this context, we investigate how nonlinearities affect the tidal flow properties, thanks to new 3D hydrodynamic and magneto-hydrodynamic nonlinear simulations of tides, in an adiabatic and incompressible convective shell. First, we show to what extent the emergence of differential rotation is modifying the tidal dissipation rates, prior to linear predictions. In this newly generated zonal flows, nonlinear self-interactions of tidal inertial waves can also trigger different kind of instabilities and resonances between the waves and the background sheared flow, when the tidal forcing is strong enough or the viscosity low enough. These different processes disrupt the energetic exchanges between tidal waves and the background flow, and also further modifies the tidal dissipation rates. Secondly, we present the first non-linear numerical analysis of tidal flows in a magnetised convective shell. One main effect of the magnetic field in our model is to mitigate zonal flows triggered by the nonlinear interaction of inertial waves. The consequences for tidal flows are important, since the installation of zonal flows in nonlinear hydrodynamical simulations is the main cause of significant changes in tidal dissipation and angular momentum exchanges, compared to linear predictions for a uniformly rotating body. </p>

In this paper, we present the consistent evolution of short-period exoplanets coupling the tidal and gravothermal evolution of the planet. Contrarily to previous similar studies, our calculations are based on the complete tidal evolution equations of the Hut model, valid at any order in eccentricity, obliquity and spin. We demonstrate, both analytically and numerically, that, except if the system was formed with a nearly circular orbit (e<0.2), solving consistently the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal models truncated at second order in eccentricity, as done in all previous studies, lead to erroneous tidal evolutions. As a consequence, tidal energy dissipation rates are severely underestimated in all these calculations and the characteristic timescales for the various orbital parameters evolutions can be wrong by up to three orders in magnitude. Based on these complete, consistent calculations, we revisit the viability of the tidal heating hypothesis to explain the anomalously large radius of transiting giant planets. We show that, even though tidal dissipation does provide a substantial contribution to the planet's heat budget and can explain some of the moderately bloated hot-Jupiters, this mechanism can not explain alone the properties of the most inflated objects, including HD 209458b. Indeed, solving the complete tidal equations shows that enhanced tidal dissipation and thus orbit circularization occur too early during the planet's evolution to provide enough extra energy at the present epoch. In that case another mechanisms, such as stellar irradiation induced surface winds dissipating in the planet's tidal bulges, or inefficient convection in the planet's interior must be invoked, together with tidal dissipation, to provide all the pieces of the abnormally large exoplanet puzzle.

Tidal heating in icy satellite oceans

Volcanic activity at Europa&amp;#8217;s seafloor is one of the key questions regarding the habitability of its subsurface ocean. The suitable conditions for hydrothermalism on Europa&amp;#8217;s seafloor are conditioned by the heat released from the underlying silicate mantle, supplied by both radiogenic and tidal heating. The orbital resonance between Io, Europa, and Ganymede forces their orbit and maintains non-zero eccentricities. Tidal heating due to eccentricity tides on Io is so extreme that it&amp;#160; produces intense volcanism.&amp;#160; Even though tidal heating&amp;#160; in Europa&amp;#8217;s silicate mantle is expected to be much weaker than on Io due to its greater distance to Jupiter,&amp;#160;&amp;#160; B&amp;#283;hounkov&amp;#225; et al. [1] showed that it may still be sufficient to maintain Europa&amp;#8217;s mantle in a partially molten state&amp;#160; for several tens to hundred millions of years, particularly during periods of increased eccentricity. Due to inefficient melt transport through the thick lithosphere of Europa [2], melt produced during periods of enhanced eccentricity may accumulate and in turn affect the tidal heating, as it is the case for Io, implying a possible runaway melt process in the silicate interior of Europa.&amp;#160;In this context, the goal of this study is to evaluate the effect of melt accumulation on the tidal heat production of Europa&amp;#8217;s silicate mantle. For that purpose, we follow the approach developed to model the solid tides in Io&amp;#8217;s partially molten interior [3], taking into account the effect of melt on the viscoelastic properties of the mantle. We adapt it to the context of Europa, corresponding to a deeper and thinner asthenosphere than on Io. We show that, whatever the partially molten layer thickness, melt accumulation increases tidal heat production and tidal dissipation even exceeds radiogenic heating. For equivalent volume of accumulated melt, the thinner the layer, the more pronounced this effect is. Our results show that the accumulation of melt, over timescales consistent with the 3D model prediction of B&amp;#283;hounkov&amp;#225; et al. [1], may significantly affect the tidal dissipation amplitude and its pattern. The potential presence of such melt accumulations may be tested by future measurements by Europa Clipper and JUICE from the combined analysis of gravimetric, altimetric and magnetic data, which might reveal long-wavelength anomalies which could be confronted to our model prediction.&amp;#160;[1] B&amp;#283;hounkov&amp;#225; et al., GRL, 48(3), e2020GL090077 (2021),&amp;#160; [2] Bland and Elder, GRL, 49(5), e2021GL096939 (2022). [3] Kervazo et al., A&amp;amp;A, 650, A72 (2021)&amp;#160;

Constraining the thickness of Europa’s water–ice shell: Insights from tidal dissipation and conductive cooling

This study explores the influence of shell thickness on photocurrent density in polymer-based solar cells incorporating gold-silver (Au-Ag) and silver-gold (Ag-Au) metal-metal core-shell nanoparticles. Efficient light trapping and absorption in polymer solar cells remain a key challenge, necessitating innovative approaches to improve performance. Addressing this gap, the research investigates how variations in shell thickness impact the plasmonic enhancement of photocurrent density. Simulations reveal that increasing shell thickness initially boosts photocurrent density due to enhanced plasmonic effects but stabilizes or declines slightly beyond an optimal thickness. For example, at a cell thickness of 80 nm, photocurrent densities of 13.74 mA/cm², 16.62 mA/cm², and 19.3 mA/cm² were achieved for the reference cell (without nanoparticles), a cell with Ag nanoparticles, and a cell with Au-Ag nanoparticles, respectively. These results underscore the critical role of shell thickness and material composition in optimizing core-shell nanoparticles for maximizing solar cell efficiency, offering insights for advancing polymer-based photovoltaic technologies. Keywords: Core-shell nanoparticles; organic solar cell; photocurrent; plasmonic nanoparticles; polymer solar cell.

We use the super Earth 55 Cnc e as a case study to address an observable effect of tidal heating. We investigate whether planet-planet interactions can force the eccentricity of this planet to a level affecting the eclipse depth observed with Spitzer. Using the constant time lag tidal model, we first calculate the observed planet flux as a function of albedo and eccentricity, for different tidal dissipation constants and for two extreme cases: a planet with no heat redistribution and a planet with full heat redistribution. We derive the values of albedo and eccentricity that match the observed transit depth. We then perform N-body simulations of the planetary system including tides and General Relativity to follow the evolution of the eccentricity of planet e. We compare the range of eccentricities given by the simulations with the eccentricities required to alter the eclipse depth. We find that the eccentricity of planet e can be large enough to contribute at a measurable level to the thermal emission measured with Spitzer. This affects the constraints on the albedo of the planet, which can be as high as 0.9 (instead of 0.55 when ignoring tidal heating). We also derive a maximum value for the eccentricity of planet e directly from the eclipse depth: e<0.015 assuming Earth's dissipation constant. Transiting exoplanets in multiple planet systems are exceptional targets for testing tidal models because their tidal luminosity may be observable. Future multi-wavelengths observations of eclipse depth and phase curves (for instance with EChO and JWST) should allow us to better resolve the temperature map of these planets and break the degeneracy between albedo and tidal heating that remains for single band observations. In addition, an accurate determination of the eccentricity will make it possible to constrain the dissipation rate of the planet and to probe its internal structure.

We study the susceptibility of extrasolar Earth-like planets to tidal dissipation by varying orbital, rheological, and heat transfer parameters. We employ a three-dimensional numerical method solving the coupled problem of mantle convection and tidal dissipation. A reference model mimicking a plate tectonic regime and reproducing Earth's present-day heat output is considered. Four other models representing less efficient heat transfer regimes are also investigated. For these five initial models, we determine the orbital configurations under which a positive feedback between tidal dissipation and temperature evolution leads to a thermal runaway. In order to describe the occurrence of thermal runaways, we develop a scaling that relates the global dissipated power to a characteristic temperature and to the orbital parameters. For all numerical experiments sharing the same initial temperature conditions, we show that the reciprocal value of the runaway timescale depends linearly on the global dissipated power at the beginning of the simulation. In the plate tectonic-like regime, Earth-like planets in the habitable zone (HZ) of 0.1 M☉ stars experience thermal runaways for 1:1 spin–orbit resonance if the eccentricity is sufficiently high (e>0.02 at a 4 day period, e>0.2 at a 10 day period). For less efficient convective regimes, runaways are obtained for eccentricities as low as ∼0.004 at the inner limit of the HZ. In the case of 3:2 spin–orbit resonance, the occurrence of thermal runaways is independent of eccentricity and is predicted for orbital periods lower than 12 days. For less efficient convective regimes, runaways may occur at larger orbital periods potentially affecting the HZ of stars with a mass up to 0.4 M☉. Whatever the convective regime and spin–orbit resonance, tidal heating within Earth-like planets orbiting in the HZ of stars more massive than 0.5 M☉ is not significant.

Saturn's moon Enceladus has a global subsurface ocean and a porous rocky core in which water‐rock reactions likely occur; it is thus regarded as a potentially habitable environment. For icy moons like Enceladus, tidal heating is considered to be the main heating mechanism, which has generally been modeled using viscoelastic solid rheologies in existing studies. Here we provide a new framework for calculating tidal heating based on a poroviscoelastic model in which the porous solid and interstitial fluid deformation are coupled. We show that the total heating rate predicted for a poroviscoelastic core is significantly larger than that predicted using a classical viscoelastic model for intermediate to large ( &gt; 10 14 Pa · s) rock viscosities. The periodic deformation of the porous rock matrix is accompanied by interstitial pore fluid flow, and the combined effects through viscous dissipation result in high heat fluxes particularly at the poles. The heat generated in the rock matrix is also enhanced due to the high compressibility of the porous matrix structure. For a sufficiently compressible core and high permeability, the total heat production can exceed 10 GW—a large fraction of the moon's total heat budget—without requiring unrealistically low solid viscosities. The partitioning of heating between rock and fluid constituents depends most sensitively on the viscosity of the rock matrix. As the core of Enceladus warms and weakens over time, pore fluid motion likely shifts from pressure‐driven local oscillations to buoyancy‐driven global hydrothermal convection, and the core transitions from fluid‐dominated to rock‐dominated heating.

This study systematically investigated the impact of tetraethyl orthosilicate (TEOS) content on the composition and microstructure of SiO2‐coated KxNa1‐xNbO3 core‐shell structured fillers (KNN@SiO2). Subsequently, these fillers were incorporated into Polyvinylidene fluoride (PVDF) to fabricate KNN@SiO2/PVDF composites, and the impact of SiO2 shell thickness on the dielectric properties was thoroughly explored, revealing the underlying mechanisms. It was found that variations in the SiO2 shell thickness significantly affected the dielectric characteristics of the composites, with the dielectric constant showing a non‐monotonic dependence. The dielectric constant of the composites first went up and then went down with the rise in shell thickness, with a maximum value of approximately 27 for 6‐KNN@SiO2/PVDF. The dielectric loss also exhibited a non‐monotonic trend, with the lowest loss observed for 6‐KNN@SiO2/PVDF. This study proposed the Shell Exchange Affects Dielectric Cluster Region Mechanism (SE‐DCRM) to explain the abnormal changes in relaxation time and permittivity of the composites caused by the coating thickness of KNN@SiO2 fillers. The results provide a deeper understanding of the polarization mechanisms and optimization strategies of core‐shell structured fillers within ceramic/polymer composites.Highlights Prepared KNN@SiO2/PVDF composites with varying shell thicknesses. Observed non‐monotonic dependence of dielectric constant on shell thickness. Optimized polarization characteristics of composites by adjusting SiO2 thickness. Proposed Shell Exchange Affects Dielectric Cluster Region Mechanism (SE‐DCRM). SE‐DCRM effectively explains abnormal dielectric property changes in composites.

Context. Binary stars cannot be fully understood without assessing the interaction effects between the two components and the impact of these effects on observational diagnostics. Periastron brightening events, also known as the heartbeat phenomenon, are a clear manifestation of this type of interaction. Aims. We aim to explore the role of tidal shear energy dissipation in stars undergoing periastron brightening events. Methods. We performed a computation from first principles that uses a quasi-hydrodynamic Lagrangian scheme to simultaneously solve the orbital motion and the equations of motion of a 3D grid of volume elements covering the inner, rigidly rotating “core” of a tidally perturbed star. The equations of motion include the gravitational acceleration of both stars, the centrifugal, Coriolis, gas pressure accelerations, and viscous coupling between volume elements. The method is illustrated for a grid of model binary systems with a 10 M⊙ primary that is perturbed by a 6.97 M⊙ companion in eccentric orbits (e = 0 − 0.7). The model is then applied to the heartbeat star MACHO 80.7443.1718. Results. We find an increase by factors ∼10−6–10−3 in tidal shear energy dissipation at periastron, consistent with the majority of observed heartbeat stars. The magnitude of the periastron effect correlates with the degree of departure from synchronicity: stars rotating much faster or much slower than the synchronous rate at periastron present the strongest effect. We confirm that for eccentricities ≤0.3, pseudo-synchronization occurs for 0.8 &lt; ω/Ωave &lt; 1, where Ωave is the average orbital angular velocity. The minimum energy rotation rate (pseudo-synchronism) for e = 0.5 and 0.7 occurs for 1.0 &lt; ω/Ωave &lt; 1.15. The tidal shear energy dissipation model reproduces from first principles the ∼23% maximum brightness enhancement at periastron of MACHO 80.7443.1718. Conclusions. Our results suggest that the magnitude and shape of the heartbeat signal may serve as diagnostics for the internal stellar rotation and turbulent viscosity values.

Context. Tidal dissipation in planets and in stars is one of the key physical\nmechanisms that drive the evolution of planetary systems.\n Aims. Tidal dissipation properties are intrisically linked to the internal\nstructure and the rheology of studied celestial bodies. The resulting\ndependence of the dissipation upon the tidal frequency is strongly different in\nthe cases of solids and fluids.\n Methods. We compute the tidal evolution of a two-body coplanar system, using\nthe tidal quality factor's frequency-dependencies appropriate to rocks and to\nconvective fluids.\n Results. The ensuing orbital dynamics comes out smooth or strongly erratic,\ndependent on how the tidal dissipation depends upon frequency.\n Conclusions. We demonstrate the strong impact of the internal structure and\nof the rheology of the central body on the orbital evolution of the tidal\nperturber. A smooth frequency-dependence of the tidal dissipation renders a\nsmooth orbital evolution while a peaked dissipation can furnish erratic orbital\nbehaviour.\n

Roger, L. M., Richardson, A. J., McKinnon, A. D., Knott, B., Matear, R., and Scadding, C. 2012. Comparison of the shell structure of two tropical Thecosomata (Creseis acicula and Diacavolinia longirostris) from 1963 to 2009: potential implications of declining aragonite saturation. – ICES Journal of Marine Science, 69: 465–474. Thecosomata (shelled pteropod molluscs) are calcifiers that play an important role in the ocean carbonate cycle. Ocean acidification as a result of the uptake of CO2 affects pteropods by increasing dissolution rates of their aragonite skeletons. Two species of pteropod found in Australian tropical waters were studied, Creseis acicula and Diacavolinia longirostris. To assess the changes in their aragonite shells, shell morphology, growth patterns, structure, size, and porosity are described for both species, from material collected at seven sites between the 1960s and the 2000s. Shell characteristics were used to explore variations over time potentially related to ocean acidification. The aragonite saturation level (Ωarag) of surface waters was hindcast and a decline equivalent to −10% (average of the seven sites) was found. Simultaneously, variations in shell thickness were recorded (C. acicula by −4.43 µm, D. longirostris by −5.37 µm) over the study period along with a significant increase in shell porosity (C. acicula: +1.43%, D. longirostris: +8.69%). The work, although not conclusive, does suggest that pteropods off Northern Australia may have been influenced by the decline in Ωarag over the past few decades. Such adverse effects could ultimately affect thecosome survival and that of their predators.