Search

The goal of this work is to investigate under which circumstances the tidal response of a stratified body can be approximated by that of a homogeneous body. We show that any multilayered planet model can be approximated by a homogeneous body, with the same dissipation of tidal energy as a function of the excitation frequency, as long as the rheology of the homogeneous model is sufficiently complex. Moreover we provide two straightforward methods for finding the parameters of the homogeneous rheology that would exhibit the same tidal response as the layered body. These results highlight the fact that the two models cannot be distinguished from each other only by the measurement of the second degree tidal Love number and quality factor, and that we do not need the complexity of the multilayer planet model in order to estimate its tidal dissipation. The methodology promises a great simplification of the treatment of multilayered bodies in numerical simulations because the treatment of a homogeneous body -- even with a complex rheological model -- can be computationally better handled than that of a multilayered planet., 10 pages, 11 figures, accepted for publication in MNRAS

1. Introduction Tethys is unusual among icy moons for its low bulk mean density of 0.985 g/cm3, suggesting a low rock mass fraction and/or high porosity. Like other mid-sized icy satellites Tethys has an intense fracture history [1], including Ithaca Chasma as well as several hundred arcuate andlinear troughs, grooves, and cracks. Unique to Tethys, however, are dark reddish linear features visible to Cassini under high solar illumination conditions (a lower albedo and flatter spectral signature in the green–IR range; Figs. 1, 2). Our CDAP-funded research is focused on mapping these features and testing hypotheses for their formation and implications for Tethys’ evolution Figure 1: Color view of Tethys showing IR lineations (reddish arcs). Cassini IR3, green, UV3 image composite. Figure 2: Preliminary spectral plot showing IR lineaments (red) and adjacent cratered plains (green) from ISS images. Figure 3: Global map of fractures, ridges, and lineations on Tethys. IR lineations are shown in red. Odysseus is large circle at upper center. 1.1 IR-Lineations There are at least three prominent sets in the northern anti-Saturn hemisphere, centered on the anti-Saturn meridian (Fig. 3). Each setconsists of ~5–10 parallel lineations a few kilometers across and 50–250 km long. The lineations are remarkably curvilinear (i.e., non-sinuous), do not follow great circles, and are not deflected by major impact structures: they cross the floor of the 400-km-diameter, 9-km-deep Odysseus impact basin as if it were not there. Although more poorly observed, sub-Saturn hemispheric color imaging at low-phase angle clearly shows a similar set of arcuate, reddishlineations on that hemisphere, despite deposition of E-ring dust particles from Enceladus [2] indicating that these features are being renewed on some time-scale. The red lineaments centered near ~25° N, 175°E were imaged at high resolution. Mapping at ~90–125 m/pixel (Fig. 4) (together with stereo andlower resolution color imaging) shows no discrete scarp, ridge, or other tectonic manifestation along the ~100 km portion of the feature soimaged. Only a faint discoloration of the surface has been identified (Fig. 5). Further, >20 dark spots 200–800 m in diameter lie along this setof lineaments. These spots are characterized by very low albedos, sharp boundaries, and no evidence of raised rims consistent with an impactorigin. Of these, >60% are situated at the bottom of impact craters. Figure 4: High-resolution, 90 m/pixel mosaic of IR lineaments, merged with IR3–Gr–UV3 color mosaic. Figure 5: Enlargement of high-resolution view in Figure 4 showing reddish lineament (red arrows) and small dark spots (blue arrows). Red streaks centered at 45° N, 333°E were targeted for high resolution ISS and VIMS observations in late 2015 (although the VIMS cubes were partially corrupted). As at the above site no discrete faults, scarps or grooves was resolved here despite pixel scales as good as ~60 m. 2. Origin of IR-Lineaments The spatial pattern of IR lineaments on Tethys shows a strong symmetry (Fig. 3), centered on the current tidal axis with Saturn. A lack ofcorrelation with local geology might suggest an exogenic origin. Conversely, there are no rayed craters at the radial centers of these features.Further, the locations of the patterns on both the sub- and anti-Saturn hemispheres, and the lineaments’ parallel orientations, argue against adisrupted comet origin (à la SL9). The lineaments have no systematic orientation relative to Odysseus, indicating that stresses arising fromthe relaxation of that basin [3] are not responsible for these features. Global stresses might have produced the pattern we observe. The IR lineaments may match patterns of strain predicted to result from a non-synchronous rotation stress state, although this is unlikely for a cold, triaxial body like Tethys. The best-fit patterns correspond to a combination of global expansion with true polar wander or tidal axis reorientation (Fig. 6a, b). The misfit for global expansion combined recession is significantly larger (Fig. 6c). The dramatic lack of such features in the southern hemisphere (Fig. 3), where only a few short isolated red streaks are evident, is not explained by any currently considered stress regime. Figure 6: (a-c) Observed (red) and predicted (green) tectonic patterns due to combination of global expansion with (a) true polar wander, (b) tidal axis reorientation, (c) orbit recession. Solid and open circles indicate location of initial rotation and tidal axes. (d) Relative frequency distribution of misfit between observed and predicted fault segment azimuths for processes in panels a-c. Labels show mean misfit for each model. The lack of obvious tectonic deformation despite the strong color signature is unusual (although features may exist below the currentresolution limit). The lineaments could be reactivated ancient fractures, producing a temporal discoloration. At present there is no topographic or morphologic signature to support this. If tectonic, the lineaments might be still forming, with deformation only on a scale below that which we can resolve. The dark and reddish coloration could be due to a particulate contaminant in the ice grains that is more spectrally visible if the grain sizes are larger along the streaks. Alternatively, a dark reddish contaminant has been deposited on the surface along the streaks. Such a contaminant could be due to precipitation of a distinct material along unresolved surface or near-surface fractures, with subsequent mixing of contaminant into the local regolith. VIMS spectral cubes are being reprocessed to verify whether organic rich materials may be involved. Low-volume but persistentoutgassing and emplacement of volatiles from the interior (possibly due to clathrate decomposition associated with fracture formation) thecolors of which are distinct from the evolved surface and/or result from alteration due to exposure to the space environment, may be responsible. The coloration of Tethys unique red streaks, and collocated dark spots, are consistent with active alteration of the surface, given that E-ringaccumulation is expected to remove intrinsic color signatures in a geologically short time period. Differences in particle sizes of the outgassed material may add to this spectral distinctiveness.

Various theories have been proposed to explain the Moon's current inclined orbit. We test the viability of these theories by reconstructing the thermal-orbital history of the Moon. We build on past thermal-orbital models and incorporate the evolution of the lunar figure including a fossil figure component. Obliquity tidal heating in the lunar magma ocean would have produced rapid inclination damping, making it difficult for an early inclination to survive to the present-day. An early inclination is preserved only if the solid-body of the early Moon were less dissipative than at present. If instabilities at the Laplace plane transition were the source of the inclination, then the Moon had to recede slowly, which is consistent with previous findings of a weakly dissipative early Earth. If collisionless encounters with planetesimals up to 140 Myr after Moon formation excited the inclination, then the Moon had to migrate quickly to pass through the Cassini state transition at 33 Earth radii and reach a period of limited inclination damping. The fossil figure was likely established before 16 Earth radii to match the present-day degree-2 gravity field observations., 18 pages, 6 figures

Summary Ocean worlds like Enceladus and Europa experience tides that deform their solid shells and induce ocean currents. These worlds can be labelled thin-shell worlds; their outermost layers (ocean and ice shell) are thin compared to the radius. We present a new model to study the tidal response of thin-shell worlds. Compared to previous work, our model can accommodate radial density stratification of the ocean and lateral variations of layer properties such as thickness. We examine how these factors affect the tidal response. Ocean thickness variations change the characteristic eigenfrequencies of thin-shell worlds and alter the eigenmodes excited by the tidal force. Zonal thickness variations hinder Rossby waves excited by the obliquity tide and we argue this has important implications for the thermal and orbital evolution of Triton and the Moon. Internal gravity modes are excited in stratified subsurface oceans. Energy dissipation due to resonant internal gravity waves can contribute to the thermal budget of some moons, especially small icy worlds like Enceladus where energy dissipation due to internal tides is compatible with the observed endogenic activity. 1. Introduction Tides play an essential role in the thermal and orbital evolution of planets and moons. A clear example are icy moons with subsurface oceans. Tides deform and might crack their ice shells, drive ocean currents, and result in energy dissipation that can dominate the body's internal heat budget. Many icy moons can be described as thin-shell words. Their outermost layers consist of a liquid shell covered by a solid shell, both of which have a small thickness compared to the radius. Bodies with shallow magma oceans also fall within this category. The dynamics of these bodies can be described by vertically averaging the mass and momentum conservation equations, leading to the Laplace Tidal Equations for the ocean (Laplace, 1798) and the viscoelastic thin-shell equations for the solid shell (e.g., Beuthe, 2018). Thin-shell dynamics have been used to describe the tidal dynamics of subsurface oceans and ice shells of icy moons (e.g., Tyler, 2008; Matsuyama et al., 2018; Beuthe,2016, 2018). Previous work has often relied on the assumptions of (1) no density stratification and (2) no lateral properties variations (e.g., ocean thickness). However, both (1) and (2) can be relevant in thin-shell worlds. Geographical variations in tidal heating can cause lateral variations in shell thickness (Ojakangas & Stevenson, 1989). Gravity and altimetry data indicates that Enceladus' ocean and ice shell vary in thickness (Beuthe et al., 2016; Hemingway & Mittal, 2019; Câdek et al., 2016); and recent work shows that different processes can produce and maintain stratified density profiles. We develop a spectral method based on spherical harmonics that allows to efficiently compute the tidal dynamics of thin-shell worlds and apply it to several cases where assumptions (1) and (2) are not justified. 2. Unstratified Shells of Constant Thickness The tidal response of unstratified oceans of constant thickness covered by constant thickness shells has been widely studied (e.g., Beuthe et al., 2016; Matsuyama et al., 2018). The ocean response to the eccentricity and obliquity tide is given by a combination of surface gravity and Rossby modes whose eigenfrequencies depend on the Lamb parameter (Ω2R2/gHocean) and the effective rigidity (EHlid/gρR2). These modes can resonate with the tidal force and result in strong ocean currents and subsequent energy dissipation. Surface gravity modes are resonant for ocean thicknesses much smaller than those characteristic of the moons of the outer Solar System. The obliquity tide can excite Rossby waves of high amplitude, which can become an important contributor to the thermal budget in moons with high orbital obliquity like Triton. 3. Unstratified Shells of Variable Thickness Ocean thickness variations alter the eigenfrequencies of the system and can introduce new resonant modes. Equatorially asymmetric thickness variations allows the excitation of asymmetric modes by the symmetric eccentricity tide and symmetric modes by the asymmetric obliquity tide. While oceans of uniform thickness always respond with a longitudinal wave length equal to that of the tidal forcing, the tides of oceans with sectorial and tesseral thickness variations contains different longitudinal wave lengths. Energy dissipation due to Rossby waves excited by the obliquity tide is severely reduced when zonal ocean thickness variations are considered. We show that even a small deviation from uniform thickness can lead to a decrease of energy dissipation of orders of magnitude. We argue that this allows to reconcile a primordial origin of the Moon's obliquity with the presence of a long-lived magma ocean early during its evolution. 4. Stratified Shells of Constant Thickness Ocean stratification makes it possible for the tidal force to excite internal gravity modes that propagate at the interface between layers of different density. We consider a simple two-layer ocean to study internal gravity waves and show that internal modes can be specially relevant in moons with high effective rigidity. This is the case of Enceladus for which we find that resonant internal waves in stratified oceans with Δρ/ρ>10-3 can lead to tenths of GW of energy dissipation. Internal modes are characterised by a strong shear at the density interface that can lead to Kelvin-Helmholtz instabilities, ocean mixing and hence feedback to the ocean stratification structure. Figure 1: Energy dissipation due to obliquity tides in a surface unstratified ocean with degree two ocean thickness variations. Figure 2: Energy dissipation due to internal waves excited by the eccentricity tide in a stratified subsurface ocean with Lamb parameter 5·10-3 and effective rigidity 10 (similar to Enceladus). References Beuthe, M. 2016, Icarus, 280, 278 , doi: 10.1016/j.icarus.2016.08.009 —. 2018, Icarus, 302, 145, doi: 10.1016/j.icarus.2017.11.009 Beuthe, M., Rivoldini, A., & Trinh, A. 2016, Geophys. Res. Lett., 43,10,088, doi: 10.1002/2016GL070650 Câdek, O., Tobie, G., Van Hoolst, T., et al. 2016, Geophys. Res. Lett., 43, 5653, doi: 10.1002/2016GL068634 Hemingway, D. J., & Mittal, T. 2019, Icarus, 332, 111 , doi: 10.1016/j.icarus.2019.03.011 Laplace, P.-S. 1798, Traité de mécanique céleste, Tome II, Livre IV, Des oscillations de la mer et de l’atmosphère Matsuyama, I., Beuthe, M., Hay, H. C., Nimmo, F., & Kamata, S. 2018, Icarus, 312, 208 , doi: 10.1016/j.icarus.2018.04.013 Ojakangas, G. W., & Stevenson, D. J. 1989, Icarus, 81, 220 , doi: 10.1016/0019-1035(89)90052-3 Tyler, R. H. 2008, Nature, 456, 770, doi: 10.1038/nature07571

We develop a simple scaling argument for frictional dissipation in rubble-pile asteroids, parameterized as an effective dissipation factor Q. This scaling is combined with a prediction (Goldreich, P., Sari, R., 2009. Tidal evolution of rubble piles. Astrophys. J. 691, 54–60) for the tidal response amplitude, parameterized by the Love number k2. We compare the combined scaling with k2/Q values inferred from asteroid binaries in which the semi-major axis is determined by a balance between tidal dissipation and the binary YORP (or BYORP) effect (Jacobson, S.A., Scheeres, D.J., 2011. Long-term stable equilibria for synchronous binary asteroids. Astrophys. J. Lett. 736, L19). The k2/Q scaling matches the inferred values if dissipation is confined to a regolith layer of thickness ∼ 30 m, similar to the available asteroid regolith thickness estimates. The scaling suggests a regolith thickness that is independent of (or decreases slightly with) increasing asteroid radius; this result is consistent with at least one model of regolith generation via impacts.

Subsurface ocean tides act as a mechanism to dissipate tidal energy in icy satellite interiors. We numerically model the effect of an ice shell on ocean tides using non-linear bottom drag for the first time. We demonstrate that subsurface oceans experience tidal pressurization due to the confining nature of the ice shell, and find that Enceladus’ eccentricity forcing can generate up to 2.2 kPa of pressure excess at the ocean surface. Existing free-surface oceanic energy dissipation scaling laws are extended to subsurface oceans, and are benchmarked against our numerical results to within 10 %. We show that for the large bodies Ganymede, Europa and Titan, an ice shell increases eccentricity tidal heating due to self-gravity, whereas the shell’s suppressive mechanical forcing reduces eccentricity tide dissipation on Enceladus and Dione by several orders of magnitude due to their high effective rigidities. In contrast, the ice shell enhances obliquity-forced dissipation in all satellites investigated, except Triton, because the largely divergence-free ocean response is unaffected by the shell’s rigidity but is still enhanced by self-gravity. We conclude that the fundamental difference in ocean response to obliquity and eccentricity forcing, combined with self-gravity, results in increased obliquity heating and suppressed eccentricity heating in small satellites. For large satellites with low effective rigidities, the type of ocean response is less important because the shell’s mechanical forcing has little impact on the flow, whereas self-gravity will enhance the response, and consequently dissipation, regardless of the forcing. Overall, obliquity tides are likely to dominate the tidal heating budget of icy satellite oceans, remaining the most prominent source of fluid dissipation in subsurface barotropic ocean tides.

There is compelling evidence for subsurface water oceans among the three outer Galilean satellites, and evidence for an internal magma ocean in the innermost moon, Io. Tidal forces from Jupiter periodically deform these bodies, causing heating and deformation that, if measured, can probe their interior structures. In addition to Jupiter-raised tides, each moon also raises tides on the others. We investigate moon-moon tides for the first time in the Galilean moons, and show that they can cause significant heating through the excitation of high-frequency resonant tidal waves in their subsurface oceans. The heating occurs both in the crust and ocean, and can exceed that of other tidal sources and radiogenic decay if the ocean is inviscid enough. The resulting tidal deformation can be used to constrain subsurface ocean thickness. Our understanding of the thermal-orbital evolution and habitability of the Jovian system may be fundamentally altered as a result.

We assess the gravity constraints on the interior structure of Europa in anticipation of the Europa Clipper mission.Moore and Schubert (2000) illustrated that the diurnal tide amplitude, quantified by the diurnal (tidal) Love numbers, k2d and h2d, can be used to determine the presence of a subsurface liquid ocean due to the significant increase in tidal amplitudes associated with the mechanical decoupling of the shell with a subsurface ocean. However, they considered a limited range of possible interior parameters except the ice shell rigidity, which was assumed to be in the range of 1-10 GPa. We consider a wider range of possible interior structure parameters and a more realistic ice shell rigidity range of 1-4 GPa. Inferring the presence of a subsurface ocean is slightly easier than previously thought (Verma & Margot 2018), with required absolute precisions of 0.08 for k2d , and 0.44 for h2d .Previous work have considered diurnal (tidal) gravity constraints alone or static gravity constraints alone using a forward modeling approach (e.g. Anderson et al., 1998; Moore and Schubert, 2000; Wahr et al., 2006). We evaluate constraints on interior structure parameters using Bayesian inversion with the mass, static gravity, and diurnal gravity as constraints, allowing a probabilistic view of Europa's interior structure. Given the same relative uncertainties, the static Love numbers provide stronger constraints on the interior structure relative to those from the mean moment of inertia (MOI). Additionally, the static Love numbers can be inferred directly from the static gravity field whereas inferring the MOI requires the Radau-Darwin approximation.Jointly considered with the static shape, the static gravity field can constrain the average and long-wavelength thickness of the shell. For an isostatically compensated shell, it is usual to conceptualize the crust as a series of independently floating columns of equal cross-sectional area which, by application of Archimedes' principle, should have equal mass above the depth of compensation. However, this approach is unphysical in the presence of curvature and self-gravitation. We consider alternative prescriptions of Airy isostasy: the equal-pressure prescription (Hemingway and Matsuyama, 2017), and the minimum-stress prescription (Dahlen 1982; Beuthe et al., 2016; Trinh et al., 2019). The gravitational coefficients are more sensitive to shell thickness than would be expected from the classical (equal-mass) approach, illustrating that the equal-mass prescription can lead to large errors in the inferred average shell thickness and its lateral variations.Diurnal gravity data alone can only constrain the product of the shell rigidity and thickness (Moore and Schubert, 2000; Wahr et al., 2006). An additional observational constraint that is sensitive to these parameters is the libration amplitude, which can be obtained from direct imaging or from altimeter data. We show that a joint gravity and libration analysis is able to separately constrain the shell thickness and rigidity.

International audience; The global-scale crustal structure of Mars is shaped by impact basins, volcanic provinces, and a hemispheric dichotomy with a thin crust beneath the northern lowlands and a thick crust beneath the southern highlands. The southern highlands are commonly treated as a coherent terrain of ancient crust with a common origin and shared geologic history, plausibly originating from a giant impact(s) or a hemispheric-scale mantle upwelling. Previous studies have quantified the contribution of volcanism to this crustal structure; however, the influence of large impacts remains unclear. Here we present reconstructions of the past crustal thickness of Mars (about 4.2 Gyr ago) where the four largest impact basins (Hellas, Argyre, Isidis and Utopia) are removed, assuming mass conservation, as well as the main volcanic provinces of Tharsis and Elysium. Our reconstruction shows more subdued crustal thickness variations than at present, although the crustal dichotomy persists. However, our reconstruction reveals a region of discontinuous patches of thick crust in the southern highlands associated with magnetic and geochemical anomalies. This region, corresponding to Terra Cimmeria–Sirenum, is interpreted as a discrete crustal block. Our findings suggest that the southern highlands are composed of several crustal blocks with different geological histories. Such a complex architecture of the southern highlands is not explained by existing scenarios for crustal formation and evolution. A discrete block of thick ancient crust revealed by a crustal reconstruction suggests a complex geologic history for the southern highlands of Mars.

Callisto is thought to possess a subsurface ocean, which will dissipate energy due to obliquity tides. This dissipation should have damped any primordial inclination within 1 Gyr - and yet Callisto retains a present-day inclination. We argue that Callisto's inclination and eccentricity were both excited in the relatively recent past (~0.3 Gyr). This excitation occurred as Callisto migrated outwards according to the "resonance-locking" model and passed through a 2:1 mean-motion resonance with Ganymede. Ganymede's orbital elements were likewise excited by the same event. To explain the present-day orbital elements we deduce a solid-body tidal k2/Q~0.05 for Callisto and a significantly lower value for Ganymede., Comment: 12 pages, 9 figures, accepted in MNRAS

International audience; The Virgil Fossae region on Pluto exhibits three spatially coincident properties that are suggestive of recent cryovolcanic activity over an area approximately 300 by 200 km. Situated in the fossae troughs or channels and in the surrounding terrain are exposures of H2O ice in which there is entrained opaque red-colored matter of unknown composition. The H2O ice is also seen to carry spectral signatures at 1.65 and 2.2 μm of NH3 in some form, possibly as a hydrate, an ammoniated salt, or some other compound. Model calculations of NH3 destruction in H2O ice by galactic cosmic rays suggest that the maximum lifetime of NH3 in the uppermost meter of the exposed surface is ~109 years, while considerations of Lyman-α ultraviolet and solar wind charged particles suggest shorter timescales by a factor of 10 or 10000. Thus, 109 y is taken as an upper limit to the age of the emplacement event, and it could be substantially younger. The red colorant in the ammoniated H2O in Virgil Fossae and surroundings may be a macromolecular organic material (tholin) thought to give color to much of Pluto's surface, but probably different in composition and age. Owing to the limited spectral range of the New Horizons imaging spectrometer and the signal precision of the data, apart from the H2O and NH3 signatures there are no direct spectroscopic clues to the chemistry of the strongly colored deposit on Pluto. We suggest that the colored material was a component of the fluid reservoir from which the material now on the surface in this region was erupted. Although other compositions are possible, if it is indeed a complex organic material it may incorporate organics inherited from the solar nebula, further processed in a warm aqueous environment inside Pluto. A planet-scale stress pattern in Pluto's lithosphere induced by true polar wander, freezing of a putative interior ocean, and surface loading has caused fracturing in a broad arc west of Sputnik Planitia, consistent with the structure of Virgil Fossae and similar extensional features. This faulting may have facilitated the ascent of fluid in subsurface reservoirs to reach the surface as flows and as fountains of cryoclastic materials, consistent with the appearance of colored, ammoniated H2O ice deposits in and around Virgil Fossae. Models of a cryoflow emerging from sources in Virgil Fossae indicate that the lateral extent of the flow can be several km (Umurhan et al., 2019). The deposit over the full length (> 200 km) of the main trough in the Virgil Fossae complex and extending through the north rim of Elliot crater and varying in elevation over a range of ~2.5 km, suggests that it debouched from multiple sources, probably along the length of the strike direction of the normal faults defining the graben. The source or sources of the ammoniated H2O are one or more subsurface reservoirs that may or may not connect to the global ocean postulated for Pluto's interior. Alternatives to cryovolcanism in producing the observed characteristics of the region around Virgil Fossae are explored in the discussion section of the paper.

Planetary tectonics provide a record of the myriad of processes that shape planetary surfaces and interiors. While there is a long history of mapping and modeling planetary tectonics, stresses from disparate processes are not generally captured by a single model. We present a comprehensive and general stress and tectonics model that can consider multiple stress-generating mechanisms simultaneously. The model is applicable to mass loading with arbitrary geometry, rotational and orbital perturbations, and arbitrary elastic lithosphere thicknesses. This wholistic approach to tectonic modeling has important implications for understanding both lunar evolution and tectonics across the solar system. We apply this model to the Moon, which exhibits a global pattern of thrust faults. The ubiquitous presence of young thrust faults suggests that isotropic contraction plays a dominant role. However, their non-random orientation requires additional stress-generating mechanisms that are not isotropic. Best-fit solutions correspond to models combining isotropic contraction with orbit recession, despinning, and South Pole-Aitken ejecta loading and the corresponding true polar wander. Contraction and despinning assuming an elastic shell with a thinner equatorial region can lead to misfits that are smaller than those assuming a constant thickness elastic shell. The young age of the faults favors recent contraction and recession; however, unrelaxed stresses from older processes combined with recent contractional stresses can also generate young faults. This possibility is supported by the Moon's ability to preserve a fossil figure.

Icy satellites that contain subsurface oceans require sufficient thermal energy to prevent the liquid portion of their interiors from freezing. We develop a numerical finite difference model to solve the Laplace Tidal Equations on a sphere in order to simulate tidal flow and thermal energy dissipation in these oceans, neglecting the presence of an icy lid. The model is applied to Titan and Enceladus, where we explore how Rayleigh (linear) and bottom (quadratic) drag terms affect dissipation. The latter drag regime can only be applied numerically. We find excellent agreement between our results and recent analytical work. Obliquity tide Rossby-wave resonant features become independent of ocean thickness under the bottom drag regime for thick oceans. We show that for Titan, dissipation from this Rossby-wave resonance can act to dampen the rate of outward orbital migration by up to 40% for Earth-like values of bottom drag coefficient. Gravity-wave resonances can act to cause inward migration, although this is unlikely due to the thin oceans required to form such resonances. The same is true of all eccentricity tide resonances on Enceladus, such that dissipation becomes negligible for thick oceans under the bottom drag regime.

The location of Sputnik Planitia on Pluto is shown to result from volatiles sequestered within the basin forcing the reorientation of the dwarf planet, as supported by the planet-wide fault network. James Keane et al. report that the location of Sputnik Planitia, the approximately 1,000-kilometre-diameter topographic basin that dominates the surface of Pluto, is a natural consequence of the infill of volatile ices within the basin and the resulting reorientation (true polar wander) of the dwarf planet. As Sputnik Planitia slowly loaded with volatiles, the pull of tidal torques from Charon would have resulted in the eventual alignment of the basin with the Pluto–Charon tidal axis. Sputnik Planitia probably formed northwest of its present location, and was loaded with volatiles over million-year timescales as a result of volatile transport cycles. This is one of four papers on the geology of Sputnik Planitia in this issue of Nature. In News & Views, Amy Barr puts these latest contributions into context. Pluto is an astoundingly diverse, geologically dynamic world. The dominant feature is Sputnik Planitia—a tear-drop-shaped topographic depression approximately 1,000 kilometres in diameter possibly representing an ancient impact basin1,2. The interior of Sputnik Planitia is characterized by a smooth, craterless plain three to four kilometres beneath the surrounding rugged uplands, and represents the surface of a massive unit of actively convecting volatile ices (N2, CH4 and CO) several kilometres thick1,2,3,4,5. This large feature is very near the Pluto–Charon tidal axis. Here we report that the location of Sputnik Planitia is the natural consequence of the sequestration of volatile ices within the basin and the resulting reorientation (true polar wander) of Pluto. Loading of volatile ices within a basin the size of Sputnik Planitia can substantially alter Pluto’s inertia tensor, resulting in a reorientation of the dwarf planet of around 60 degrees with respect to the rotational and tidal axes. The combination of this reorientation, loading and global expansion due to the freezing of a possible subsurface ocean generates stresses within the planet’s lithosphere, resulting in a global network of extensional faults that closely replicate the observed fault networks on Pluto. Sputnik Planitia probably formed northwest of its present location, and was loaded with volatiles over million-year timescales as a result of volatile transport cycles on Pluto6,7. Pluto’s past, present and future orientation is controlled by feedbacks between volatile sublimation and condensation, changing insolation conditions and Pluto’s interior structure.

The TRAPPIST-1 system is sufficiently closely packed that tides raised by one planet on another are significant. We investigate whether this source of tidal heating is comparable to eccentricity tides raised by the star. Assuming a homogeneous body with a Maxwell rheology, we find that energy dissipation from stellar tides always dominates over that from planet-planet tides across a range of viscosities. TRAPPIST-1 g may experience the greatest proportion of planet-planet tidal heating, where it can account for between 2% and 20% of the total amount of tidal heating, for high ($10^{21}$ Pa s) and low viscosity ($10^{14}$ Pa s) regimes, respectively. If planet-planet tidal heating is to exceed that from stellar eccentricity tides, orbital eccentricities must be no more than e=$10^{-3}$ to $10^{-4}$ for most of the TRAPPIST-1 planets., Comment: 14 pages - 7 figures - accepted to ApJ

Tidal dissipation is a major heat source for the icy satellites of the giant planets. Several icy satellites likely possess a subsurface ocean underneath an ice shell. Previous studies of tidal dissipation on icy satellites, however, have either assumed a static ocean or ignored the effect of the ice lid on subsurface ocean dynamics. In this study, we examine inertial effects on tidal deformation of satellites with a dynamic ocean overlain by an ice lid based on viscoelasto-gravitational theory. Although ocean dynamics is treated in a simplified fashion, we find a resonant configuration when the phase velocity of ocean gravity waves is similar to that of the tidal bulge. This condition is achieved when a subsurface ocean is thin (

We investigate on narrow bandgap CIGSe solar cells for tandem application in a spectral splitting devices. Numerical simulations using SCAPS are performed to optimize the Ga content throughout the absorber layer, depending on the illumination condition (AM 1.5 and tandem conditions using two different splitting filters; 620 nm and 880 nm). The simulations show a strong dependence of the efficiency on the minimum bandgap of the absorber, but not on the depth of the narrow bandgap region. Narrow bandgap CIGSe solar cells are experimentally realized and electrically characterized. A similar trend as what was deduced from the simulation is observed on the experiments when the solar cells are characterized in the tandem conditions. For the 880 nm splitting filter, an efficiency of 5.5% is experimentally obtained with a minimum bandgap of 1.05 eV. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

As a long-term energy source, tidal heating in subsurface oceans of icy satellites can influence their thermal, rotational, and orbital evolution, and the sustainability of oceans. We present a new theoretical treatment for tidal heating in thin subsurface oceans with overlying incompressible elastic shells of arbitrary thickness. The stabilizing effect of an overlying shell damps ocean tides, reducing tidal heating. This effect is more pronounced on Enceladus than on Europa because the effective rigidity on a small body like Enceladus is larger. For the range of likely shell and ocean thicknesses of Enceladus and Europa, the thin shell approximation of Beuthe (2016) is generally accurate to less than about 4%.The time-averaged surface distribution of ocean tidal heating is distinct from that due to dissipation in the solid shell, with higher dissipation near the equator and poles for eccentricity and obliquity forcing respectively. This can lead to unique horizontal shell thickness variations if the shell is conductive. The surface displacement driven by eccentricity and obliquity forcing can have a phase lag relative to the forcing tidal potential due to the delayed ocean response. For Europa and Enceladus, eccentricity forcing generally produces greater tidal amplitudes due to the large eccentricity values relative to the obliquity values. Despite the small obliquity values, obliquity forcing generally produces larger phase lags due to the generation of Rossby-Haurwitz waves. If Europa's shell and ocean are respectively 10 and 100 km thick, the tide amplitude and phase lag are 26.5 m and $, Icarus, accepted for publication

Dissipation of tidal energy is an important mechanism for the evolution of outer Solar System satellites, several of which are likely to contain subsurface oceans. We extend previous theoretical treatments for ocean tidal dissipation by taking into account the effects of ocean loading, self-attraction, and deformation of the solid regions. These effects modify both the forcing potential and the ocean thicknesses for which energy dissipation is resonantly enhanced, potentially resulting in orders of magnitude changes in the dissipated energy flux. Assuming a Cassini state obliquity, Enceladus’ dissipated energy flux due to the obliquity tide is smaller than the observed value by many orders of magnitude. On the other hand, the dissipated energy flux due to the resonant response to the eccentricity tide can be large enough to explain Enceladus’ observed heat flow.

As first noted 200 years ago by Laplace, the Moon's rotational and tidal bulges are significantly larger than expected, given the Moon's present orbital and rotational state. This excess deformation has been ascribed to a fossil figure, frozen in when the Moon was closer to the Earth. However, the observed figure is only consistent with an eccentric and non-synchronous orbit, contrary to our understanding of the Moon's formation and evolution. Here, we show that lunar mascons and impact basins have a significant contribution to the observed lunar figure. Removing their contribution reveals a misaligned fossil figure consistent with an early epoch of true polar wander (driven by the formation of the South Pole-Aitken Basin) and an early low-eccentricity, synchronous lunar orbit. This new self-consistent model solves a long-standing problem in planetary science and will inform future studies of the Moon's dynamical evolution and early dynamo.

The Gravity Recovery and Interior Laboratory (GRAIL) mission has sampled lunar gravity with unprecedented accuracy and resolution. The lunar GM, the product of the gravitational constant G and the mass M, is very well determined. However, uncertainties in the mass and mean density, 3345.56 ± 0.40 kg/m3, are limited by the accuracy of G. Values of the spherical harmonic degree-2 gravity coefficients J2 and C22, as well as the Love number k2 describing lunar degree-2 elastic response to tidal forces, come from two independent analyses of the 3 month GRAIL Primary Mission data at the Jet Propulsion Laboratory and the Goddard Space Flight Center. The two k2 determinations, with uncertainties of ~1%, differ by 1%; the average value is 0.02416 ± 0.00022 at a 1 month period with reference radius R = 1738 km. Lunar laser ranging (LLR) data analysis determines (C − A)/B and (B − A)/C, where A

Planetary bodies can undergo reorientation due to mass redistribution associated with internal or external processes such as convection or impacts. Mass redistribution produces perturbations to the inertia tensor, and the planet must reorient to adjust to the new orientation of the maximum principal axis. The amount of reorientation depends on the competing sizes of the applied load and the remnant bulge. For tidally deformed satellites in synchronous rotation, the slow rotation and correspondingly small remnant bulge makes them prone to reorientation. Reorientation can generate gravity and topography perturbations and large tectonic stresses. Observational constraints based on gravity, tectonic, and paleomagnetic data suggest that many Solar System bodies appear to have undergone significant reorientation.

The unusual shape of the Moon given its present rotational and orbital state has been explained as due to a fossil figure preserving a record of remnant rotational and tidal deformation (Jeffreys, H. [1915]. Mem. R. Astron. Soc. 60, 187–217; Lambeck, K., Pullan, S. [1980]. Phys. Earth Planet. Interiors 22, 29–35; Garrick-Bethell, I., Wisdom, J., Zuber, M.T. [2006]. Science 313, 652–655). However, previous studies assume infinite rigidity and ignore deformation due to changes in the rotational and orbital potentials as the Moon evolves to the present state. We interpret the global lunar figure with a physical model that takes into account this deformation. Although the Moon deforms in response to rotational and orbital changes, a fossil figure capable of explaining the observed figure can be preserved by an elastic lithosphere.

The Orientale basin is the youngest and best-preserved major impact structure on the Moon. We used the Gravity Recovery and Interior Laboratory (GRAIL) spacecraft to investigate the gravitational field of Orientale at 3- to 5-kilometer (km) horizontal resolution. A volume of at least (3.4 ± 0.2) × 106 km3 of crustal material was removed and redistributed during basin formation. There is no preserved evidence of the transient crater that would reveal the basin’s maximum volume, but its diameter may now be inferred to be between 320 and 460 km. The gravity field resolves distinctive structures of Orientale’s three rings and suggests the presence of faults associated with the outer two that penetrate to the mantle. The crustal structure of Orientale provides constraints on the formation of multiring basins.

SUMMARY We outline a linearized rotational stability theory for predicting the time dependence of true polar wander (TPW) on a Maxwell viscoelastic body in response to mantle convective loading. The new theory is based on recent advances in ice age rotation theory. A comparison between predictions based on the new theory and analytic expressions for equilibrium (infinite-time) TPW on planetary models with elastic lithospheres demonstrates that the linearized theory can, in the case of loading at mid-latitudes, predict TPW of over 20° to better than 5 per cent accuracy. We present predictions of TPW for loading with periodic and net ramp-up time histories. Moreover, we compare the time dependence of TPW under assumptions consistent with the canonical equilibrium stability theory adopted in most previous analyses of convection-induced TPW, and a stability theory that includes two effects that have not been considered in previous geophysical analyses: (1) the so-called ‘remnant rotational bulge’ associated with the imperfect reorientation of the rotational bulge due to the presence of an elastic lithosphere; and (2) a stable (over the timescale of the forcing) excess ellipticity. As a first application of the new theory, we consider recent inferences of rapid (order 1 Myr) TPW motion of amplitude 10°–20° during the Late Cretaceous. We conclude that excursions of this amplitude and timescale are physically implausible.

SUMMARY Palaeomagnetic records spanning the last 100 Myr indicate that the reorientation of the Earth’s rotation axis relative to the surface geography (or true polar wander, TPW) has been confined to a range less than 6 ◦ from its present location. This limited TPW is unexpected given that a canonical theory for the rotational stability of the Earth generally predicts that mantle convection should drive larger displacements of the pole. We argue, following earlier work, thatthemutedTPWisaconsequenceofthestable,excessflatteningoftheEarth’sfiguredriven by plate subduction and deep mantle superplumes rising beneath Africa and the Pacific. In particular, we show that the TPW record is consistent with convection-induced perturbations to the Earth’s inertia tensor of order 20 per cent or less of the excess flattening over the last 100 Myr; this upper bound will be higher if the Earth’s lithosphere retains any significant elastic strength over such long timescales. This inferred stability of the Earth’s figure has important implications for our understanding of deep mantle structure and the long-term, global-scale evolution of the Earth.

We extend previous work on the global tectonic patterns generated by despinning with a self-consistent treatment of the isotropic despinning contraction that has been ignored. We provide simple analytic approximations that quantify the effect of the isotropic despinning contraction on the global shape and tectonic pattern. The isotropic despinning contraction of Mercury is ∼93 m (T/1 day)−2, where T is the initial rotation period. If we take into account both the isotropic contraction and the degree-2 deformations associated with despinning, the preponderance of compressional tectonic features on Mercury’s surface requires an additional isotropic contraction ≳1 km (T/1 day)−2, presumably due to cooling of the interior and growth of the solid inner core. The isotropic despinning contraction of Iapetus is ∼9 m (T/16 h)−2, and it is not sensitive to the presence of a core or the thickness of the elastic lithosphere. The tectonic pattern expected for despinning, including the isotropic contraction, does not explain Iapetus’ ridge. Furthermore, the ridge remains unexplained with the addition of any isotropic compressional stresses, including those generating by cooling.

We present a model for the dispersal of protoplanetary disks by winds from either the central star or the inner disk. These winds obliquely strike the flaring disk surface and strip away disk material by entraining it in an outward radial-moving flow at the disk-wind interface. This interface lies several disk scale heights above the mid plane. The disk dispersal time depends on the velocity at which disk material flows into the mixing layer. If this velocity is ~10% of the sound speed, the disk dispersal time at ~1–10 AU is ~5 Myr for a 0.01 M ๏ disk around a solar mass star, with a spherical wind launched from the inner disk or central star with a typical mass loss rate of 10 -8 M ๏ yr -1 and terminal velocity of v w = 100 kms -1 . We conclude that wind stripping is not a dominant disk dispersal mechanism compared with viscous accretion and photoevaporation. Nevertheless, wind stripping may affect the evolution of the intermediate disk regions.

The areal centroids of the youngest polar deposits on Mars are offset from those of adjacent paleopolar deposits by 5-10 degrees. We test the hypothesis that the offset is the result of true polar wander (TPW), the motion of the solid surface with respect to the spin axis, caused by a mass redistribution within or on the surface of Mars. In particular, we consider TPW driven by late-stage volcanism during the late Hesperian to Amazonian. There is observational and qualitative support for this hypothesis: in both North and South, observed offsets lie close to a great circle 90 degrees from Tharsis, as expected for polar wander after Tharsis formed. We calculate the magnitude and direction of TPW produced by mapped late-stage lavas for a range of lithospheric thicknesses, lava thicknesses, eruption histories, and prior polar wander events. If Tharsis formed close to the equator, the stabilizing effect of a fossil rotational bulge located close to the equator leads to predicted TPW of, Accepted by Earth and Planetary Science Letters. 3 tables, 8 figures

Several processes may produce global tectonic patterns on the surface of a planetary body. The stresses associated with distortions of biaxial figures due to despinning or reorientation were first calculated by Vening Meinesz [Vening Meinesz, F.A., 1947. Trans. Am. Geophys. Union 28 (1), 1–23]. We adopt a mathematically equivalent, but physically more meaningful treatment for distortions associated with rotation. The new approach allows us to find analytic solutions for the general case of stresses associated with distortions of biaxial or triaxial planetary figures. Distortions of biaxial figures may be driven by variations in rotation rate, rotation axis orientation, or the combination of both. Distortions of triaxial figures may be driven by the same mechanisms and/or variations in tidal axis orientation for tidally deformed satellites. While the magnitude of the resulting stresses depends on the adopted elastic and physical parameters, the expected tectonic pattern is independent of these parameters for these mechanisms. Reorientation of the rotation/tidal axis alone is expected to produce normal/thrust faulting provinces enclosing the initial rotation/tidal poles, and thrust/normal faulting provinces enclosing the final rotation/tidal poles. Reorientation of both the rotation and tidal axis results in a wide variety of tectonic patterns for different reorientation geometries. On Europa, the tidal axis reorientation which generally accompanies rotation axis reorientations may provide an alternative explanation for tectonic features that have been interpreted as evidence for non-synchronous rotation. The observed tectonic pattern on Enceladus is more easily explained by a large reorientation (∼90°) of the rotation axis, than by rotation rate variations.

Studies extending over three decades have concluded that the current orientation of the martian rotation pole is unstable. Specifically, the gravitational figure of the planet, after correction for a hydrostatic form, has been interpreted to indicate that the rotation pole should move easily between the present position and a site on the current equator, 90 ◦ from the location of the massive Tharsis volcanic province. We demonstrate, using general physical arguments supported by a fluid Love number analysis, that the so-called non-hydrostatic theory is an inaccurate framework for analyzing the rotational stability of planets, such as Mars, that are characterized by long-term elastic strength within the lithosphere. In this case, the appropriate correction to the gravitational figure is the equilibrium rotating form achieved when the elastic lithospheric shell (of some thickness LT) is accounted for. Moreover, the current rotation vector of Mars is shown to be stable when the correct non-equilibrium theory is adopted using values consistent with recent, independent estimates of LT. Finally, we compare observational constraints on the figure of Mars with non-equilibrium predictions based on a large suite of possible Tharsis-driven true polar wander (TPW) scenarios. We conclude, in contrast to recent comparisons of this type based on a non-hydrostatic theory, that the reorientation of the pole associated with the development of Tharsis was likely less than 15 ◦ and that the thickness of the elastic lithosphere at the time of Tharsis formation was at least ∼50 km. Larger Tharsis-driven TPW is possible if the present-day gravitational form of the planet at degree 2 has significant contributions from non-Tharsis loads; in this case, the most plausible source would be internal heterogeneities linked to convection.

International audience; The Tharsis region is the largest volcanic complex on Mars and in the Solar System. Young lava flows cover its surface (from the Amazonian period, less than 3 billion years ago) but its growth started during the Noachian era (more than 3.7 billion years ago). Its position has induced a reorientation of the planet with respect to its spin axis (true polar wander, TPW), which is responsible for the present equatorial position of the volcanic province. It has been suggested that the Tharsis load on the lithosphere influenced the orientation of the Noachian/Early Hesperian (more than 3.5 billion years ago) valley networks1 and therefore that most of the topography of Tharsis was completed before fluvial incision. Here we calculate the rotational figure of Mars (that is, its equilibrium shape) and its surface topography before Tharsis formed, when the spin axis of the planet was controlled by the difference in elevation between the northern and southern hemispheres (hemispheric dichotomy). We show that the observed directions of valley networks are also consistent with topographic gradients in this configuration and thus do not require the presence of the Tharsis load. Furthermore, the distribution of the valleys along a small circle tilted with respect to the equator is found to correspond to a southern-hemisphere latitudinal band in the pre-TPW geographical frame. Preferential accumulation of ice or water in a south tropical band is predicted by climate model simulations of early Mars applied to the pre-TPW topography. A late growth of Tharsis, contemporaneous with valley incision, has several implications for the early geological history of Mars, including the existence of glacial environments near the locations of the pre-TPW poles of rotation, and a possible link between volcanic outgassing from Tharsis and the stability of liquid water at the surface of Mars.

The question of whether there were oceans on Mars is a compelling topic. All seemed clear when a set of surface features that ring the martian plains for thousands of kilometres were interpreted as relics of former shorelines. But topographic profiles along the putative shorelines revealed long-wavelength trends in elevation, with amplitudes of up to several kilometres. This argued against the shoreline hypothesis. Now, though, the ocean is back with a bang. Perron et al. show that polar wander — a change in the orientation of the planet's surface with respect to its pole of rotation — can explain the shoreline deformation. Moreover, the track of polar wander that would have caused the observed deformation seems consistent with the planet's rotational dynamics. The surface of Mars has a set of features that ring the plains for thousands of kilometres, which have been interpreted as a series of former shorelines. But topographic profiles along the putative shorelines contain long-wavelength trends in elevation that have been taken as an argument against the shoreline (and ocean) hypothesis. This paper demonstrates that true polar wander could bring the elevations of the proposed shorelines into line, reviving the ocean hypothesis. A suite of observations suggests that the northern plains of Mars, which cover nearly one third of the planet's surface, may once have contained an ocean1,2,3,4,5,6,7. Perhaps the most provocative evidence for an ancient ocean is a set of surface features that ring the plains for thousands of kilometres and that have been interpreted as a series of palaeoshorelines of different age1,7. It has been shown, however, that topographic profiles along the putative shorelines contain long-wavelength trends with amplitudes of up to several kilometres4,5,8, and these trends have been taken as an argument against the martian shoreline (and ocean) hypothesis8. Here we show that the long-wavelength topography of the shorelines is consistent with deformation caused by true polar wander—a change in the orientation of a planet with respect to its rotation pole—and that the inferred pole path has the geometry expected for a true polar wander event that postdates the formation of the massive Tharsis volcanic rise.

The earliest dynamic and thermal history of the Moon is not well understood. The hydrogen content of deposits near the lunar poles may yield insight into this history, because these deposits (which are probably composed of water ice) survive only if they remain in permanent shadow. If the orientation of the Moon has changed, then the locations of the shadowed regions will also have changed. The polar hydrogen deposits have been mapped by orbiting neutron spectrometers, and their observed spatial distribution does not match the expected distribution of water ice inferred from present-day lunar temperatures. This finding is in contrast to the distribution of volatiles observed in similar thermal environments at Mercury's poles. Here we show that polar hydrogen preserves evidence that the spin axis of the Moon has shifted: the hydrogen deposits are antipodal and displaced equally from each pole along opposite longitudes. From the direction and magnitude of the inferred reorientation, and from analysis of the moments of inertia of the Moon, we hypothesize that this change in the spin axis, known as true polar wander, was caused by a low-density thermal anomaly beneath the Procellarum region. Radiogenic heating within this region resulted in the bulk of lunar mare volcanism and altered the density structure of the Moon, changing its moments of inertia. This resulted in true polar wander consistent with the observed remnant polar hydrogen. This thermal anomaly still exists and, in part, controls the current orientation of the Moon. The Procellarum region was most geologically active early in lunar history, which implies that polar wander initiated billions of years ago and that a large portion of the measured polar hydrogen is ancient, recording early delivery of water to the inner Solar System. Our hypothesis provides an explanation for the antipodal distribution of lunar polar hydrogen, and connects polar volatiles to the geologic and geophysical evolution of the Moon and the bombardment history of the early Solar System.

Predictions of the Earth's response to the ice age appear to simultaneously reconcile a set of astronomical, geodetic and ancient eclipse observations related to changes in rotation, thus ruling out ice melting as a major contributor to 20th century sea-level rise. We demonstrate that the reconciliation disappears when an improved theory of rotational stability is applied. Furthermore, our reanalysis of longer satellite records renders previous estimates of the secular change in rotation rate suspect. The updated ice-age predictions and observations permit an anomalous 20th century ice flux of ∼1 mm/yr equivalent sea-level rise. Thus, the full suite of Earth rotation observations are consistent with a connection between climatic warming and recent melting of ice reservoirs.

SUMMARY Predictions of glaciation-induced changes in the Earth’s rotation vector exhibit sensitivities to Earth structure that are unique within the suite of long-wavelength observables associated with glacial isostatic adjustment (henceforth GIA), and, despite nearly a quarter of a century of research, these sensitivities remain enigmatic. Previous predictions of present-day true polar wander (TPW) speed driven by GIA have indicated, for example, a strong sensitivity to variations in the thickness of the elastic lithosphere and the treatment (phase or chemical?) of the density discontinuity at 670-km depth. Nakada recently presented results that suggest that the predictions are also sensitive to the adopted rheology of the lithosphere; however, his results have introduced an intriguing paradox. In particular, predictions generated using a model with an extremely high-viscosity lithospheric lid do not converge to results for a purely elastic lithosphere of the same thickness. Mitrovica (as cited by Nakada) has suggested that the paradox originates from an inaccuracy in the traditional rotation theory (e.g. Wu & Peltier) associated with the treatment of the background equilibrium rotating form upon which any load- and rotation-induced perturbations are superimposed. We revisit these issues using a new treatment of the linearized Euler equations governing load-induced rotation perturbations on viscoelastic earth models. We demonstrate that our revised theory, in which the background form of the planet combines a hydrostatic component and an observationally inferred excess ellipticity, resolves the apparent paradox. Calculations using the revised theory indicate that earlier predictions based on earth models with purely elastic lithospheric lids are subject to large errors; indeed, previously noted sensitivities of TPW speed predictions to the thickness and rheology (elastic versus viscous) of the lithosphere largely disappear in the application of the new theory. Significant errors are also incurred by neglecting the stabilizing influence of the Earth’s excess ellipticity. Finally, we demonstrate that the contribution from rotational feedback on predictions of present-day rates of change of the geoid (sea surface) and crustal velocities are overestimated by the traditional rotation theory, and this has implications for analyses of ongoing satellite (e.g. GRACE) missions and geodetic GPS surveys.

True polar wander (TPW), a reorientation of the rotation axis relative to the solid body, is driven by mass redistribution on the surface or within the planet and is stabilized by two aspects of the planet's viscoelastic response: the delayed viscous readjustment of the rotational bulge and the elastic stresses in the lithosphere. The latter, following Willemann (1984), is known as remnant bulge stabilization. In the absence of a remnant bulge, the rotation of a terrestrial planet is said to be inherently unstable. Theoretical treatments have been developed to treat the final (equilibrium) state in this case and the time-dependent TPW toward this state, including nonlinear approaches that assume slow changes in the inertia tensor. Moreover, remnant bulge stabilization has been incorporated into both equilibrium and linearized, time-dependent treatments of rotational stability. We extend the work of Ricard et al. (1993) to derive a nonlinear, time-dependent theory of TPW that incorporates stabilization by both the remnant bulge and viscous readjustment of the rotational bulge. We illustrate the theory using idealized surface loading scenarios applied to models of both Earth and Mars. We demonstrate that the inclusion of remnant bulge stabilization reduces both the amplitude and timescale of TPW relative to calculations in which this stabilization is omitted. Furthermore, given current estimates of mantle viscosity for both planets, our calculations indicate that departures from the equilibrium orientation of the rotation axis in response to forcings with timescale of 1 Myr or greater are significant for Earth but negligible for Mars.