We present the characteristics of a mode of axial oscillation between Earth's mantle, fluid core and solid inner core that has not been previously reported. The mode involves a quasi-rigid rotation of the fluid core outside the tangent cylinder (TC) exchanging its angular momentum with the mantle via a three step process. First, by a magnetic torque with the fluid inside the TC; second by a magnetic torque between the latter and the inner core; and finally by a gravitational torque between the inner core and mantle. Although the gravitational torque is purely between the mantle and inner core, the mode involves an oscillation of the whole of the core, and we refer to it as the core-mantle gravitational (CMG) mode. This form of gravitational oscillation occurs when the magnetic field within the core is sufficiently strong that the propagation time of Alfvén waves is shorter than the mode period, which is the case for Earth. We show how the period, quality factor $Q$ and structure of the CMG mode depends on the strength of the gravitational torque and viscous relaxation time $\tau_i$ of the inner core. For Earth, the CGM mode period should be in the range of 40 to 100 years, but viscous relaxation of the inner core likely implies a small $Q$, below 1 if $\tau_i<10$ years. Our results suggest that the CMG mode may act to amplify resonantly, though only modestly, multi-decadal changes in the length of day driven by zonal accelerations in the fluid core.

Lava planets likely did not form in their current orbits, instead migrating inward via orbital decay, which influenced the evolution of their magma oceans. We introduce a coupled thermal-orbital evolution model to explore how rocky planets migrate from the inner edge of the protoplanetary disk, with periods of 1-10 days, to orbital periods of less than 1 day. In our model, mantle melting is controlled by tidal heating and stellar flux, while orbits evolve via tidal migration. The mantle's tidal quality factor varies with its temperature and structure, creating a feedback loop between thermal evolution and orbital decay. We use our numerical model to simulate the migration of seven known lava planets: K2-141b, K2-360b, TOI-141b, TOI-431b, TOI-2431b, HD 3167b, and GJ 367b. Migration occurs in two stages: an initial high-eccentricity stage reducing the semimajor axis by a factor of similar to 2, followed by a low-eccentricity stage reducing it by a factor of similar to 5. A successful migration from similar to 0.1 au to a present-day orbit requires starting eccentricities >= 0.9 and sustained eccentricity forcing with emin >= 10-2 . The rate of migration depends on the state of the mantle: slow when mostly molten, fast when mostly solid. This pathway works for most lava planets, but not for TOI-431b or GJ 367b, suggesting that multiple migration pathways are possible for lava planets.

Abstract Mercury's unique interior structure and magnetic field generation remain to be fully understood. We construct models to further constrain Mercury's interior and test the hypothesis that iron snow within the liquid core drives the dynamo. We build upon previous models by incorporating an updated iron‐sulfur‐silicon (Fe‐S‐Si) core alloy composition and use a Monte Carlo approach to explore the parameter space consistent with geodetic and geophysical constraints. A high normalized moment of inertia (MoI) of , in combination with thermal and geochemical constraints, favors models with an Earth‐like mantle density of kg/, an inner core km in radius, and a core silicon content of at least 6 wt%. In contrast, a lower value of MoI favors models with lower mantle densities of kg/, an inner core radius in the range of 850–1,450 km, and a core silicon content less than 8 wt%. We also show that the formation of iron snow requires a sulfur concentration greater than wt%. However, the expected geochemistry of the core restricts the sulfur content to less than 2 wt%. This inconsistency suggests the absence of snow layers in Mercury's present‐day core and that its dynamo is not driven by sulfur‐induced iron crystallization.

A number of recent studies have made use of statistics derived from geodynamo simulations to constrain the flow at the top of the Earth's core. Here we adapt these methods to infer possible core surface flow solutions over the past 9000 years, using a low degree geomagnetic field model, based on archaeomagnetic and sedimentary archives. Despite the low spatial resolution of the field model, we find that the largest scale aspects of the recovered flow agree well with those derived from historical field models. In particular we see the growth of an eccentric planetary gyre over the past 400 years and find that a similar feature appears on bimillennial timescales, concurrent with pulses in the zonal flow. In the flow model vigorous gyre structures are not persistent but appear as transient features with durations of a few hundred years. The zonal flow is westward over the entire period with a mean value of 0.09 degrees /yr. Finally, we consider the variations in length-of-day that are implied by the flow model under the assumption of geostrophy, and compare the total clock error with that inferred from records of historical solar eclipses. Good agreement is found between the two series of mantle rotation for at least the past 1200 years, with anomalously slow mantle rotation coupled with reduced westward zonal flow. Further back in time a rigorous assessment is hard to make, owing to uncertainty surrounding the exact locations of eclipses.

The mantle-inner core gravitational (MICG) mode is the free mode axial oscillation between the mantle and inner core sustained by the gravitational torque between their degree 2 order 2 density structures. Here, we investigate how the MICG mode is affected by oscillations of cylindrical surfaces in the fluid outer core in the form of Alfvén waves. The latter are triggered by oscillations of the tangent cylinder (TC) moving jointly with the inner core and propagate away from the rotation axis. We show that the MICG mode remains a distinct normal mode of oscillation of the core-mantle system only when the triggered Alfvén waves are attenuated before they traverse the width of the fluid core. For an internal magnetic field strength of a few mT, as we expect in Earth's core, Alfvén waves can readily traverse the width of the core, and the MICG mode is absorbed into the spectrum of torsional oscillation (TO) modes. The MICG period retains a dynamical influence, acting as a point of resonance for TO modes, and marking the transition from a TO mode in which the motion of the TC (including the inner core) is weakly impacted by gravitational coupling to one in which the oscillating motion of the TC is strongly restricted. Our results imply that the observed 6-year periodic signal in the length of day cannot be interpreted as the signature of the MICG mode and must instead be caused by TO modes, or more generally, by the propagation of Alfvén waves.

Magneto-Coriolis (MC) modes in Earth's fluid core involve oscillations sustained by the combined effect of the Lorentz and Coriolis forces. Here, we investigate the properties of MC modes that involve purely axisymmetric flow, which we term axiMC modes. We provide a basic description of the wave dynamics of these modes, and simple predictions for the expected scalings of their frequency omega, decay rate lambda and quality factor Q based on a uniform ambient magnetic field. In particular, Q scales with the Elsasser number Lambda, which depends on the square of the r.m.s. strength of the azimuthally averaged meridional field. When Lambda>1, Q>1 and axiMC modes may be excited; when Lambda << 1, Q << 1 and axiMC modes revert to quasi-free magnetic decay modes. We present computations of axiMC modes in an inviscid, electrically conducting sphere for two idealized ambient magnetic field configurations, a uniform axial field and an axial poloidal field. We show that a flow gradient in the axial direction is a key property of axiMC modes. For the uniform axial field, omega, lambda and Q follow the scalings expected for a uniform field. For the axial poloidal field, the structure of the modes changes substantially when Lambda greater than or similar to 1, becoming more concentrated in regions of lower field strength. The combination of this structural change and advection of field lines by flow significantly increases lambda, resulting in a Q that remains close to 1 even at high Lambda. For a magnetic field strength inside the Earth's core of a few mT, the gravest axiMC modes are expected to have periods in the range of one thousand to a few thousand years and a Q not substantially above 1. AxiMC modes may be connected to a part of the observed millennial changes in Earth's magnetic field, may exchange axial angular momentum with the mantle, and hence may also explain a part of the observed millennial changes in length of day.

We investigate viscous dissipation in linear flows driven by small-amplitude longitudinal librations in rotating fluid spheres focusing on the rapid rotation regime applicable to planets. Viscous coupling can resonate with inertial modes in the bulk of the fluid when the frequency of the forcing is within the range $(0,2\Omega _0)$ , where $\Omega _0$ is the mean angular velocity of the sphere. We solve the linearised equations of motion with a semi-spectral numerical method and with an asymptotic expansion exploiting the small Ekman number, $E$ , which quantifies the strength of viscous forces relative to the Coriolis force. Our results confirm that the dominant contribution to the dissipation occurs in the Ekman boundary layer with leading-order scaling $E^{1/2}$ . When the forcing frequency coincides with that of an inertial mode, dissipation is reduced by as much as 9 % compared with boundary layer theory alone. The percentage-wise reduction is independent of $E$ and the frequency width of the reduction envelope scales as $E^{1/2}$ . At non-resonant frequencies conic shear layers develop in the bulk interior and, together with the Ekman layer bulge at critical latitude, slightly enhance dissipation. We confirm critical latitude bulge and shear layer contributions to the overall dissipation scale as $E^{4/5}$ and $E^{6/5}$ respectively, becoming negligible compared with dissipation in the main boundary layer as $E\rightarrow 0$ . The frequencies at which the dissipation enhancement from critical latitude effects is maximised are displaced from the inviscid limit periodic orbit frequencies by a factor that scales with $E^{0.23}$ .

Earth’s spin axis slowly moves relative to the crust over time. A 120-year-long record of this polar motion from astronomical and more modern geodetic measurements displays interannual and multidecadal fluctuations of 20 to 40 milliarcseconds superimposed on a secular trend of about 3 milliarcseconds per year. Earth’s polar motion is thought to be driven by various surface and interior processes, but how these processes operate and interact to produce the observed signal remains enigmatic. Here we show that predictions made by an ensemble of physics-informed neural networks trained on measurements to capture geophysical processes can explain the main features of the observed polar motion. We find that glacial isostatic adjustment and mantle convection primarily account for the secular trend. Mass redistribution on the Earth’s surface—for example, ice melting and global changes in water storage—yields a relatively weak trend but explains about 90% of the interannual and multidecadal variations. We also find that core processes contribute to both the secular trend and fluctuations in polar motion, either due to variations in torque at the core–mantle boundary or dynamical feedback of the core in response to surface mass changes. Our findings provide constraints on core–mantle interactions for which observations are rare and global ice mass balance over the past century and suggest feedback operating between climate-related surface processes and core dynamics.

The melting of ice sheets and global glaciers results in sea-level rise, a pole-to-equator mass transport increasing Earth’s oblateness and resulting in an increase in the length of day (LOD). Here, we use observations and reconstructions of mass variations at the Earth’s surface since 1900 to show that the climate-induced LOD trend hovered between 0.3 and 1.0 ms/cy in the 20th century, but has accelerated to 1.33 ± 0.03 ms/cy since 2000. We further show that surface mass transport fully explains the accelerating trend in the Earth oblateness observed in the past three decades. We derive an independent measure of the decreasing LOD trend induced by Glacial Isostatic Adjustment (GIA) of − 0.80 ± 0.10 ms/cy, which provides a constraint for the mantle viscosity. The sum of this GIA rate and lunar tidal friction fully explains the secular LOD trend that is inferred from the eclipse record in the past three millennia prior to the onset of contemporary climate change. Projections of future climate warming under high emission scenarios suggest that the climate-induced LOD rate may reach 2.62 ± 0.79 ms/cy by 2100, overtaking lunar tidal friction as the single most important contributor to the long-term LOD variations.

The Earth's spin axis is inclined by SMALL ELEMENT OF = 23.4 degrees with respect to the ecliptic normal and precesses in space with a period of 26 kyr. The fluid core and solid inner core precess at slightly different angles. Here, we compute their differential precession angles on the basis of an elastically deforming Earth and dissipative torques inferred from nutation observations. We show that the precession angle of the fluid core is larger than that of the mantle by 1.714 arcsec and lags behind it by 0.0124 arcsec. The precession angle of the spin (and figure) axis of the inner core is smaller than that of the mantle by 1.861 arcsec and trails behind it by 3.660 arcsec. These correspond to differential velocities (Delta v) at the core mantle boundary (CMB) and inner core boundary (ICB) of 2.11 and 2.21 mm/s, to associated boundary layer Reynolds (Re) numbers of 247 and 258, and to dissipations Dof 4.6 and 14.5 GW. At such Re values the flow in the core should feature wavelike instabilities but should not be in a fully developed turbulent regime. Delta v and Re at the CMB have remained approximately constant in the past 4 Gyr, and D has been steadily decreasing from a maximum of approximately double its present-day value. At the ICB, Delta v, Re and Dhave all increased since inner core formation. Future projections indicate that Re and Dat the ICB may reach 500 and 100 GW, respectively, in a few Gyr. Our results suggest that, for the whole of Earth's history, dissipation from the misaligned precession of the fluid and solid cores has contributed only a small fraction of the total heat flux out of the core and has not provided an important power source for maintaining the geodynamo.

The seven planets orbiting TRAPPIST-1 have sizes and masses similar to Earth and mean densities that suggest that their interior structures are comprised of a fluid iron core and rocky mantle. Here we use idealized analytical models to compute estimates of the viscous dissipation in the fluid cores of the TRAPPIST-1 planets induced by mantle libration and precession. The dissipation induced by the libration at orbital periods is largest for TRAPPIST-1b, of the order of 600 MW, and decreases with orbital distance, to values of 5–500 W for TRAPPIST-1h, depending on its triaxial shape. Extrapolating these results to the larger libration amplitudes expected at longer periods, dissipation may perhaps be as high as 1 TW in TRAPPIST-1b. Orbital precession induces a misalignment between the spin axes of the fluid core and mantle of a planet, the amplitude of which depends on the resonant amplification of its free precession and free core nutation. Assuming Cassini states, we show that the dissipation from this misalignment can reach a few TW for planets e and f. Our dissipation estimates are lower bounds, as we neglect ohmic dissipation, which may dominate if the fluid cores of the TRAPPIST-1 planets sustain magnetic fields. Our results suggest that dissipation induced by precession can be of the same order as tidal dissipation for the outermost planets, may perhaps be sufficient to supply the power to a generate a magnetic field in their liquid cores, and likely played an important role in the evolution of the TRAPPIST-1 system.

Abstract The differential axial rotation of the solid inner core (IC) is suggested by seismic observations and expected from core dynamics models. A rotation of the IC by an angle α takes its degree 2, order 2 topography (peak‐to‐peak amplitude δh) out of its gravitational alignment with the mantle. This creates a gravity variation of degree 2, order 2 proportional to δh and to α. Here, we use gravity observations from Satellite Laser Ranging, the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On to reconstruct the time‐variable S2,2 Stokes coefficient. We show that for δh = 90 m, S2,2 provides upper bounds on α of 0.09°, 0.3°, and 0.4° at periods of ∼4, ∼6, and ∼12 years, respectively. These are overestimates, as our reconstructed S2,2 signal likely remains polluted by hydrology, although viscous relaxation of the IC can permit larger amplitudes.

Earth and Space Science Open Archive This work has been accepted for publication in Journal of Geophysical Research - Planets. Version of RecordESSOAr is a venue for early communication or feedback before peer review. Data may be preliminary. Learn more about preprints. preprintOpen AccessYou are viewing the latest version by default [v3]Deviation of Mercury's spin axis from an exact Cassini state induced by dissipationAuthorsIanMacPhersoniDMathieuDumberryiDSee all authors Ian MacPhersoniDUniversity of AlbertaiDhttps://orcid.org/0000-0002-8401-5458view email addressThe email was not providedcopy email addressMathieu DumberryiDCorresponding Author• Submitting AuthorUniversity of AlbertaiDhttps://orcid.org/0000-0001-5677-1582view email addressThe email was not providedcopy email address

Abstract In a reference frame rotating with Mercury's mantle and crust, the inner core and fluid core precess in a retrograde sense with a period of 58.646 days. The precession of a triaxial inner core with a different density than the fluid core induces a periodic gravity variation of degree 2, order 1. Elastic deformations from the pressure that the precessing fluid core exerts on the core‐mantle boundary also contribute to this gravity signal. We show that the periodic change in Stokes coefficients ΔC21 and ΔS21 for this signal of internal origin is of the order of 10−10, similar in magnitude to the signal from solar tides. The relative contribution from the inner core increases with inner core radius and with the amplitude of its tilt angle with respect to the mantle. The latter depends on the strength of electromagnetic coupling at the inner core boundary which in turn depends on the radial magnetic field Br; a larger Br generates a larger tilt. The inner core signal features a contrast between ΔC21 and ΔS21 due to its triaxial shape, discernible for an inner core radius >500 km if Br > 0.1 mT, or for an inner core radius >1100 km if Br < 0.01 mT. A detection of this contrast would confirm the presence of an inner core and place constraints on its size and the strength of the internal magnetic field. These would provide key constraints for the thermal evolution of Mercury and for its dynamo mechanism.

We compute predictions of the deviation of Mercury's spin axis from an exact Cassini state caused by tidal dissipation, and viscous and electromagnetic (EM) friction at the core-mantle boundary (CMB) and inner core boundary (ICB). Viscous friction at the CMB generates a phase lead, viscous and EM friction at the ICB produce a phase lag; the magnitude of the deviation depends on the inner core size, kinematic viscosity and magnetic field strength, but cannot exceed an upper bound. For a small inner core, viscous friction at the CMB results in a maximum phase lead of 0.027 arcsec. For a large inner core (radius >1000 km), EM friction at the ICB generates the largest phase lag, but it does not exceed 0.1 arcsec. Elastic deformations induced by the misaligned fluid and solid cores play a first order role in the phase lead/lag caused by viscous and EM coupling, and contribute to a perturbation in mantle obliquity on par with that caused by tidal deformations. Tidal dissipation results in a phase lag and its magnitude (in units of arcsec) is given by the empirical relation (80/Q), where Q is the quality factor; Q=80 results in a phase lag of 1 arcsec. A large inner core with a low viscosity of the order of 10^17 Pa s or lower can significantly affect Q and thus the resulting phase lag. The limited mantle phase lag suggested by observations (<10 arcsec) implies a lower limit on the bulk mantle viscosity of approximately 10^17 Pa s.

Summary Geodetic observations from space continuously record surface deformation and global mass redistribution with an increasing accuracy. In parallel, surficial processes (oceanic, atmospheric, and hydrological loading) are more and more precisely modeled.We propose a confrontation of the geodetic Global Positioning System (GPS) and gravity-field satellite laser ranging (SLR) observations at decadal and interannual time scales, in terms of resolution, correlation and comparison with surficial loading models. We focus on the largest global scale signals of degree 2. At interannual periods, surface deformations retrieved from GPS time-series do not exceed 0.8 mm. Our analysis does not reveal the presence of a dominant signal at a specific period, except perhaps for a signal of approximately 3 yr likely connected to the loading response to El Nio / Southern Oscillations. Contrary to the results of previous studies, we do not find in GPS time-series a clear 6-yr oscillation associated with a degree-2 order-2 pattern. Interannual variations in the degree-2 Stokes coefficients of the gravity field do not exceed 2 × 10−11. We do not detect a dominant gravity signal at one specific period but instead a broad spectrum of frequencies. The comparison between the degree 2 deformations built from GPS time-series with a prediction from SLR derived gravity variations reveals some correlations, though their differences remain important. This highlights the present day limitations of these techniques in their ability to characterize global scale interannual variations. Hydrological loading models show some correlations with both GPS and SLR signals, but we cannot firmly establish that continental hydrology is dominantly responsible for the observed variations. Given the current limits in the resolution of both gravity and surface deformation and in the modelling of surface processes, we conclude that it will be a challenge to retrieve a geodetic signal of sub-decadal period originating in the Earth’s core.

We present a model of the Cassini state of Mercury that comprises an inner core, a fluid core, and a mantle. Our model includes inertial and gravitational torques between interior regions, and viscous and electromagnetic (EM) coupling at the boundaries of the fluid core. We show that the coupling between Mercury's interior regions is sufficiently strong that the obliquity of the mantle spin axis deviates from that of a rigid planet by no more than 0.01 arcmin. The mantle obliquity decreases with increasing inner core size, but the change between a large and no inner core is limited to 0.015 arcmin. EM coupling is stronger than viscous coupling at the inner core boundary and, if the core magnetic field strength is above 0.3 mT, locks the fluid and solid cores into a common precession motion. Because of the strong gravitational coupling between the mantle and inner core, the larger the inner core is, the more this coprecessing core is brought into an alignment with the mantle, and the more the obliquity of the polar moment of inertia approaches that expected for a rigid planet. The misalignment between the polar moment of inertia and mantle spin axis increases with inner core size, but is limited to 0.007 arcmin. Our results imply that the measured obliquities of the mantle spin axis and polar moment of inertia should coincide at the present-day level of measurement errors, and cannot be distinguished from the obliquity of a rigid planet.

We present calculations of interior models of Mercury that are constrained to match Mercury's mean density, normalized moment of inertia factor (MoI), and 88 days libration amplitude. We show that models matching a MoI = 0.333 ± 0.005, based on a recent obliquity measurement require a new perspective on Mercury's interior. Specifically, we confirm the mandatory presence of a large inner core > 600 km in radius which, however, leads to lower mantle densities in comparison to previous models and implies a mantle with > 5wt.% C, > 10wt.% magnesium sulfide (MgS), or is partially convecting. Furthermore, we also show that the core radius is lower than previous estimates, making it inconsistent with current estimates from magnetic induction measurements. In addition, the requirement of low viscosities in the lower mantle to match recent estimates of k 2 imply a significantly weaker mantle than previously believed, potentially including partial melting.

Changes in the Earth's rotation are deeply connected to fluid dynamical processes in the outer core. This connection can be explored by studying the associated Earth eigenmodes with periods ranging from nearly diurnal to multi-decadal. It is essential to understand how the rotational and fluid core eigenmodes mutually interact, as well as their dependence on a host of diverse factors, such as magnetic effects, density stratification, fluid instabilities or turbulence. It is feasible to build detailed models including many of these features, and doing so will in turn allow us to extract more (indirect) information about the Earth's interior. In this article, we present a review of some of the current models, the numerical techniques, their advantages and limitations and the challenges on the road ahead.

The spin axes of the mantle, fluid core and solid inner core of the Moon precess at frequency $\Omega_p=2\pi/18.6$ yr$^{-1}$ though with different orientations, leading to viscous friction at the core-mantle boundary (CMB) and inner core boundary (ICB). Here, we use a rotational model of the Moon with a range of inner core and outer core radii to investigate the relative importance of viscous dissipation at the CMB and ICB, and to show how this dissipation is connected to the phase lead angle ($\phi_p$) of the mantle ahead of its Cassini state. We show that when the inner core radius is $>80$ km and the free inner core nutation frequency $\Omega_{ficn}$ approaches $\Omega_p$, viscous dissipation at the ICB can be comparable to that at the CMB, and in the most extreme cases exceed it by as much as a factor 10. If so, the viscous dissipation in the lunar core projected back in time depends on how $\Omega_{ficn}$ has evolved relative to $\Omega_p$. We further show that constraints on the CMB and ICB radii of the lunar core can in principle be extracted by matching the observed phase lead of $\phi_p=0.27$ arcsec; this requires an improved estimate of tidal dissipation and an accurate model of the turbulent viscous torque. Lastly, when our rotational model is constrained to match $\phi_p=0.27$ arcsec, our results suggest that the viscous dissipation at the ICB is likely insufficient to have ever been above the threshold to power a thermally driven dynamo.