Core-mantle Friction Research Articles

Long-lived lunar volcanism sustained by precession-driven core-mantle friction.

Core-mantle friction induced by the precession of the Moon's spin axis is a strong heat source in the deep lunar mantle during the early phase of a satellite's evolution, but its influence on the long-term thermal evolution still remains poorly explored. Using a one-dimensional thermal evolution model, we show that core-mantle friction can sustain global-scale partial melting in the upper lunar mantle until ∼3.1 Ga, thus accounting for the intense volcanic activity on the Moon before ∼3.0 Ga. Besides, core-mantle friction tends to suppress the secular cooling of the lunar core and is unlikely to be an energy source for the long-lived lunar core dynamo. Our model also favours the transition of the Cassini state before the end of the lunar magma ocean phase (∼4.2 Ga), which implies a decreasing lunar obliquity over time after the solidification of the lunar magma ocean. Such a trend of lunar obliquity evolution may allow volcanically released water to be buried in the lunar regolith of the polar regions. As a consequence, local water ice could be more abundant than previously thought when considering only its accumulation caused by solar wind and comet spreading.

Spin evolution of Earth-sized exoplanets, including atmospheric tides and core–mantle friction

AbstractPlanets with masses between 0.1 and 10 M⊕are believed to host dense atmospheres. These atmospheres can play an important role on the planet's spin evolution, since thermal atmospheric tides, driven by the host star, may counterbalance gravitational tides. In this work, we study the long-term spin evolution of Earth-sized exoplanets. We generalize previous works by including the effect of eccentric orbits and obliquity. We show that under the effect of tides and core–mantle friction, the obliquity of the planets evolves either to 0° or 180°. The rotation of these planets is also expected to evolve into a very restricted number of equilibrium configurations. In general, none of these equilibria is synchronous with the orbital mean motion. The role of thermal atmospheric tides becomes more important for Earth-sized planets in the habitable zones of their systems; so they cannot be neglected when we search for their potential habitability.

Effect of Interplanetary Matter on the Spin Evolutions of Venus and Mercury

Differs from other planets in the Solar System, the Venus has a retrograde and long-period rotation. To ex-plain the special spin of the Venus, mechanisms such as core mantle friction inside planet[1], atmospheric tide[2-7], or twain effects together[8-11], and impact with a giant object[12,13] have been suggested. These mecha-nisms, however, need specific initial conditions with a remote probability [3,5]. The slow spin of Mercury cannot be explained very well. One viewpoint is that the unusual spins of Venus and Mercury might be naturally evolved from similar initial states by interaction with interplanetary matter during long-time evolu-tion. Based on the theory of planet formation and the orderliness of planetary distance, we discuss the possi-bility that the radial density distribution of interplanetary matter is undulated, and the wave function satisfies the formal Schrodinger equation. We calculate the evolution of planet spins under the effect of interplanetary matter during planets revolution and rotation. The results show that planets can naturally evolve to the cur-rent state (particularly the negative spin of the Venus) given the similar initial quick and positive spins.

Long-term evolution of the spin of Mercury: I. Effect of the obliquity and core–mantle friction

The present obliquity of Mercury is very low (less than 0.1°), which led previous studies to always adopt a nearly zero obliquity during the planet’s past evolution. However, the initial orientation of Mercury’s rotation axis is unknown and probably much different than today. As a consequence, we believe that the obliquity could have been significant when the rotation rate of the planet first encountered spin-orbit resonances. In order to compute the capture probabilities in resonance for any evolutionary scenario, we present in full detail the dynamical equations governing the long-term evolution of the spin, including the obliquity contribution. The secular spin evolution of Mercury results from tidal interactions with the Sun, but also from viscous friction at the core–mantle boundary. Here, this effect is also regarded with particular attention. Previous studies show that a liquid core enhances drastically the chances of capture in spin-orbit resonances. We confirm these results for null obliquity, but we find that the capture probability generally decreases as the obliquity increases. We finally show that, when core–mantle friction is combined with obliquity evolution, the spin can evolve into some unexpected configurations as the synchronous or the 1/2 spin-orbit resonance.

Mercury's capture into the 3/2 spin–orbit resonance including the effect of core–mantle friction

The rotation of Mercury is presently captured in a 3/2 spin–orbit resonance with the orbital mean motion. The capture mechanism is well understood as the result of tidal interactions with the Sun combined with planetary perturbations [Goldreich, P., Peale, S., 1966. Astron. J. 71, 425–438; Correia, A.C.M., Laskar, J., 2004. Nature 429, 848–850]. However, it is now almost certain that Mercury has a liquid core [Margot, J.L., Peale, S.J., Jurgens, R.F., Slade, M.A., Holin, I.V., 2007. Science 316, 710–714] which should induce a contribution of viscous friction at the core–mantle boundary to the spin evolution. According to Peale and Boss [Peale, S.J., Boss, A.P., 1977. J. Geophys. Res. 82, 743–749] this last effect greatly increases the chances of capture in all spin–orbit resonances, being 100% for the 2/1 resonance, and thus preventing the planet from evolving to the presently observed configuration. Here we show that for a given resonance, as the chaotic evolution of Mercury's orbit can drive its eccentricity to very low values during the planet's history, any previous capture can be destabilized whenever the eccentricity becomes lower than a critical value. In our numerical integrations of 1000 orbits of Mercury over 4 Gyr, the spin ends 99.8% of the time captured in a spin–orbit resonance, in particular in one of the following three configurations: 5/2 (22%), 2/1 (32%) and 3/2 (26%). Although the present 3/2 spin–orbit resonance is not the most probable outcome, we also show that the capture probability in this resonance can be increased up to 55% or 73%, if the eccentricity of Mercury in the past has descended below the critical values 0.025 or 0.005, respectively.

The core–mantle friction effect on the secular spin evolution of terrestrial planets

For planets having a liquid core, friction with the mantle results in an additional source of dissipating energy alternative to tides. As a consequence, the spin of the planet will slowly change: the rotation rate decreases while the equator is tilted toward the orbital plane. Here we revisit the theory of secular spin evolution due to core–mantle friction in a very general formulation. We are able to determine the core's spin vector as a function of the mantle's spin, which can be used to estimate the effective viscosity of the core as well as its ellipticity. Contrarily to previous studies, we also investigate the effect on an axially asymmetric planet ( C 22 ≠ 0), which becomes an important additional source of dissipation near spin-orbit resonances. The secular effect of core–mantle friction on the spin proves to be essential in the long-term studies of Mercury and Venus, while it can be neglected for the Earth or Mars.

Mercury's capture into the 3/2 spin-orbit resonance as a result of its chaotic dynamics.

Mercury is locked into a 3/2 spin-orbit resonance where it rotates three times on its axis for every two orbits around the sun. The stability of this equilibrium state is well established, but our understanding of how this state initially arose remains unsatisfactory. Unless one uses an unrealistic tidal model with constant torques (which cannot account for the observed damping of the libration of the planet) the computed probability of capture into 3/2 resonance is very low (about 7 per cent). This led to the proposal that core-mantle friction may have increased the capture probability, but such a process requires very specific values of the core viscosity. Here we show that the chaotic evolution of Mercury's orbit can drive its eccentricity beyond 0.325 during the planet's history, which very efficiently leads to its capture into the 3/2 resonance. In our numerical integrations of 1,000 orbits of Mercury over 4 Gyr, capture into the 3/2 spin-orbit resonant state was the most probable final outcome of the planet's evolution, occurring 55.4 per cent of the time.

Nonlinear Core-Mantle Coupling

We explore the nonlinear dynamics of a forced core-mantle system. We show that the free axisymmetric motion of a uniform-vorticity fluid core coupled to a rigid mantle (the Poincaré-Hough model) is integrable. We derive an approximate Hamiltonian for the core tilt mode that includes the leading nonlinear contribution. We then include gravitational perturbations in the analysis. We identify the principal nonlinear prograde and retrograde resonances and the characteristic excitation associated with each. We compare the nonlinear excitation with the excitation expected in the corresponding linear model. The nonlinear model indicates that for each principal commensurability there are multiple overlapping resonances, and so varying degrees of chaotic behavior are predicted. Chaotic behavior at the principal core-mantle commensurabilities is confirmed with surfaces of section. We then present the results of numerical evolutions done with a generalization of our (1994) Lie-Poisson integrator to allow for a Poincaré-Hough core, core-mantle friction, and tidal dissipation. We use our analytical and numerical models to explore the evolution of Earth through the prograde core-mantle resonances and to explore the evolution of Venus through the retrograde resonances. Heating of the core-mantle boundary during resonance passage is much greater for Venus than for Earth. We raise the question whether heating during core-mantle resonance passage could be responsible for the global resurfacing of Venus.

The four final rotation states of Venus.

Venus rotates very slowly on its axis in a retrograde direction, opposite to that of most other bodies in the Solar System. To explain this peculiar observation, it has been generally believed that in the past its rotational axis was itself rotated to 180 degrees as a result of core-mantle friction inside the planet, together with atmospheric tides. But such a change has to assume a high initial obliquity (the angle between the planet's equator and the plane of the orbital motion). Chaotic evolution, however, allows the spin axis to flip for a large set of initial conditions. Here we show that independent of uncertainties in the models, terrestrial planets with dense atmosphere like Venus can evolve into one of only four possible rotation states. Moreover, we find that most initial conditions will drive the planet towards the configuration at present seen at Venus, albeit through two very different evolutionary paths. The first is the generally accepted view whereby the spin axis flips direction. But we have also found that it is possible for Venus to begin with prograde rotation (the same direction as the other planets) yet then develop retrograde rotation while the obliquity goes towards zero: a rotation of the spin axis is not necessary in this case.

A Simple Theory on the Dynamical Effects of a Stratified Fluid Core Upon Nutational Motion of the Earth

The theory of Molodensky (1961) on dynamical effects of a stratified fluid outer core upon nutations and diurnal Earth tides is reconstructed on a new and probably much simpler ground. A theory equivalent to Molodensky's is well represented on the basis of two linear equations for angular-momentum balance of the whole Earth and the fluid outer core, which differ from the well-known equations of Poincaré (1910) only in the existence of products of inertia due to deformations of the whole Earth and fluid outer core. The products of inertia are characterized by four parameters which are easily computed for every Earth model by the usual Earth tide equations. A reciprocity relation exists between two of the parameters. The Adams-Wiliamson condition is not a necessary premise of the theory. Amplitudes of nutations and tidal gravity factors are computed for three Earth models. A dissipative core-mantle coupling is introduced into the theory qualitatively. The resulting equations are expressed in the same form as those of Sasao, Okamoto and Sakai (1977). Formulae for secular changes in the Earth-Moon system due to the core-mantle friction are derived as evidences of internal consistency of the theory.

Possible dynamical evolution of the rotation of Venus since formation

The past evolution of the rotation of Venus has been studied by a numerical integration method using the hypothesis that only solar tidal torques and core-mantle coupling have been active since formation. It is found quite conceivable that Venus had originally a rotation similar to the other planets and has evolved in 4.5×109 years from a rapid and direct rotation (12-hour spin period and nearly zero obliquity) to the present slow retrograde one. While the solid tidal torque may be quite efficient in despinning the planet, a thermally driven atmospheric tidal torque has the capability to drive the obliquity from ∼0° towards 180° and to stabilize the spin axis in the latter position. The effect of a liquid core is discussed and it is shown that core-mantle friction hastens the latter part of the evolution and makes even stronger the state of equilibrium at 180°. The model assumes a nearly stable balance between solid and atmospheric tides at the current rotation rate interpreting the present 243 day spin period as being very close to the limiting value. A large family of solutions allowing for the evolution, in a few billions years, of a rapid prograde rotation to the present state have been found. Noticeably different histories of evolution are observed when the initial conditions and the values of the physical parameters are slightly modified, but generally the principal trend is maintained. The proposed evolutionary explanation of the current rotation of Venus has led us to place constraints on the solid bodyQ and on the magnitude of the atmospheric tidal torque. While the constraints seem rather severe in the absence of core-mantle friction (aQ≃15 at the annual frequency is required, and a dominant diurnal thermal response in the atmosphere is needed), for a large range of values of the core's viscosity, the liquid core effect allows us to relax somewhat these constraints: a solid bodyQ of the order ∼40 can then be allowed. ThisQ value implies that a semi-diurnal ground pressure oscillation of ≃2 mb is needed in the atmosphere in order for a stable balance to occur between the solid and atmospheric tides at the current rotation rate. No model of atmospheric tides on Venus has been attempted in this study, however the value of 2 mb agrees well with that predicted by the model given in Dobrovolskis (1978).

On the nearly axially-symmetrical model of the hydromagnetic dynamo of the earth

A short review of the present state of the nearly axially-symmetrical dynamo model is given. A simplified theory for hydromagnetic dynamos taking into account the forces acting in the Earth's core is considered. The role of weak core-mantle friction is discussed and a form of solution is suggested which is characterized by a large geostrophic velocity in the core and by a boundary layer of a new type. The consequences of such a model (called model Z) for the Earth's dynamo are discussed.