East-west faults due to planetary contraction

Contraction, expansion and despinning have been common in the past evolution of Solar System bodies. These processes deform the lithosphere until it breaks along faults. Their characteristic tectonic patterns have thus been sought for on all planets and large satellites with an ancient surface. While the search for despinning tectonics has not been conclusive, there is good observational evidence on several bodies for the global faulting pattern associated with contraction or expansion, though the pattern is seldom isotropic as predicted. The cause of the non-random orientation of the faults has been attributed either to regional stresses or to the combined action of contraction/expansion with another deformation (despinning, tidal deformation, reorientation). Another cause of the mismatch may be the neglect of the lithospheric thinning at the equator or at the poles due either to latitudinal variation in solar insolation or to localized tidal dissipation. Using thin elastic shells with variable thickness, I show that the equatorial thinning of the lithosphere transforms the homogeneous and isotropic fault pattern caused by contraction/expansion into a pattern of faults striking east-west, preferably formed in the equatorial region. By contrast, lithospheric thickness variations only weakly affect the despinning faulting pattern consisting of equatorial strike-slip faults and polar normal faults. If contraction is added to despinning, the despinning pattern first shifts to thrust faults striking north-south and then to thrust faults striking east-west. If the lithosphere is thinner at the poles, the tectonic pattern caused by contraction/expansion consists of faults striking north/south. I start by predicting the main characteristics of the stress pattern with symmetry arguments. I further prove that the solutions for contraction and despinning are dual if the inverse elastic thickness is limited to harmonic degree two, making it easy to determine fault orientation for combined contraction and despinning. I give two methods for solving the equations of elasticity, one numerical and the other semi-analytical. The latter method yields explicit formulas for stresses as expansions in Legendre polynomials about the solution for constant shell thickness. Though I only discuss the cases of a lithosphere thinner at the equator or at the poles, the method is applicable for any latitudinal variation of the lithospheric thickness. On Iapetus, contraction or expansion on a lithosphere thinner at the equator explains the location and orientation of the equatorial ridge. On Mercury, the combination of contraction and despinning makes possible the existence of zonal provinces of thrust faults differing in orientation (north-south or east-west), which may be relevant to the orientation of lobate scarps.     

Coupling of thermal evolution and despinning of early Iapetus

The Cassini mission revealed two spectacular characteristics of Iapetus: (1) a geologically old and high equatorial ridge, which is unique in the Solar System and (2) a large flattening of 35 km consistent with the equilibrium figure for a hydrostatic body rotating with a period of 16 h, whereas the current spin period is 79.33 days. This study describes three-dimensional simulations of solid-state convection within an undifferentiated Iapetus. It investigates the implications for the evolution of the interior thermal structure and its spin rate and global shape using radially layered viscoelastic models. The role of the concentration in the short-lived radiogenic element [²⁶Al], just after accretion is completed, is specifically addressed. The first result is to show that whatever the [²⁶Al] value, convection occurs. As suggested by Castillo-Rogez et al. [Castillo-Rogez, J., Matson, D., Sotin, C., Johnson, T., Lunine, J., Thomas, P. [2007] Icarus, 190, 179-202], convection reduces the warming of the interior compared to the conductive evolution and therefore limits the conditions for despinning. In our calculations, two conceptual linear viscoelastic models are used. When considering a Maxwell rheology, the interior temperature (viscosity) never reaches a value high (low) enough to induce despinning. In order to promote dissipation at low temperature, a Burgers rheology, which includes an additional dissipation peak, is introduced. For favorable parameter values, this latter rheology leads to despinning. However, only models associated with large amounts of short-lived radiogenic elements lead to the observed flattening. This suggests that the accretion process needs to be completed shortly after the formation of CAIs (Calcium-Aluminum-rich Inclusions) (?4 Myr). For [²⁶Al] varying between 72 and 46 ppb, the observed flattening is obtained only for a limited range of initial spin period, between 9.5 and 10.2 h. For [²⁶Al] ranging between 30 and 15 ppb, initial spin rates smaller than 8.5 h are required. For smaller values of [²⁶Al], the body is too cold and viscous to acquire a significant flattening even if a rotation period close to the body disruption limit is considered. Even with a thin lithosphere during the early stage, our simulations show that Iapetus never reaches the equilibrium figure for a hydrostatic body due to the non-zero rigidity of the lithosphere. The 35 km value of the flattening is the result of the partial relaxation of an ancient larger flattening ranging between 45 and 80 km, depending on the evolution of the lithosphere thickness mainly controlled by the radiogenic content. A thin lithosphere is consistent with an early building of the equatorial ridge. The lithosphere thickening due to interior cooling can explain the preservation of the ridge throughout the remaining evolution of Iapetus.     

Analytical model of the long-period forced longitude librations of Mercury

The shaking of Mercury’s orbit by the planets forces librations in longitude in addition to those at harmonics of the orbital period that have been used to detect Mercury’s molten core. We extend the analytical formulation of Peale et al. (Peale, S.J., Margot, J.L., Yseboodt, M. [2009]. Icarus 199, 1-8) in order to provide a convenient means of determining the amplitudes and phases of the forced librations without resorting to numerical calculations. We derive an explicit relation between the amplitude of each forced libration and the moment of inertia parameter (B-A)/C_m. Far from resonance with the free libration period, the libration amplitudes are directly proportional to (B-A)/C_m. Librations with periods close to the free libration period of ∼12 years may have measurable (∼arcsec) amplitudes. If the free libration period is sufficiently close to Jupiter’s orbital period of 11.86 years, the amplitude of the forced libration at Jupiter’s period could exceed the 35 arcsec amplitude of the 88-day forced libration. We also show that the planetary perturbations of the mean anomaly and the longitude of pericenter of Mercury’s orbit completely determine the libration amplitudes.While these signatures do not affect spin rate at a detectable level (as currently measured by Earth-based radar), they have a much larger impact on rotational phase (affecting imaging, altimetry, and gravity sensors). Therefore, it may be important to consider planetary perturbations when interpreting future spacecraft observations of the librations.     

Behavior of planetary dynamos under the influence of external magnetic fields: Application to Mercury and Ganymede

For planets with strong intrinsic magnetic fields such as Earth and Jupiter, an external magnetic field is unlikely to affect the internal dynamo, but for bodies with weak intrinsic fields in appropriate environments, such as Mercury and Ganymede, the interaction with nearby field sources may determine the internal dynamics and overall behavior of their liquid iron cores. On the basis of simulations of such interactions using numerical models for fluid flow and dynamo generation, the parameter regimes for stable dipolar and multipolar reversing dynamo magnetic fields established for isolated systems can be substantially changed by the action of external sources. Relatively weak external background fields (as low as 2% of the averaged undisturbed field at the core-mantle boundary) may change the energy balance and alter the regime over which natural isolated dynamos operate.     

Tectonic patterns on reoriented and despun planetary bodies

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.     

The free precession and libration of Mercury

An analysis based on the direct torque equations including tidal dissipation and a viscous core-mantle coupling is used to determine the damping time scales of O(¹⁰⁵) years for free precession of the spin about the Cassini state and free libration in longitude for Mercury. The core-mantle coupling dominates the damping over the tides by one to two orders of magnitude for the plausible parameters chosen. The short damping times compared with the age of the Solar System means we must find recent or on-going excitation mechanisms if such free motions are found by the current radar experiments or the future measurement by the MESSENGER and BepiColombo spacecraft that will orbit Mercury. We also show that the average precession rate is increased by about 30% over that obtained from the traditional precession constant because of a spin-orbit resonance induced contribution by the C₂₂ term in the expansion of the gravitational field. The C₂₂ contribution also causes the path of the spin during the precession to be slightly elliptical with a variation in the precession rate that is a maximum when the obliquity is a minimum. An observable free precession will compromise the determination of obliquity of the Cassini state and hence of C/MMR² for Mercury, but a detected free libration will not compromise the determination of the forced libration amplitude and thus the verification of a liquid core.     

Despinning plus global contraction and the orientation of lobate scarps on Mercury: Predictions for MESSENGER

Observations by the Mariner 10 spacecraft suggest that the lobate scarps on Mercury, which have been interpreted to record at most 1-2 km of radial contraction of the planet after the end of the Late Heavy Bombardment, possess a global, preferred N-S orientation but lack a strong latitudinal dependence on their surface expression. Here, we reexamine the idea that a decrease in the planetary rotation rate (despinning) coupled with global contraction of at least 3-5.5 km prior to the end of Late Heavy Bombardment resulted in global N-S oriented thrust faults. The surface expression of these faults is assumed to have been erased by the end of the Late Heavy Bombardment, and the faults were subsequently reactivated by later global contraction, producing generally N-S oriented thrust faults from an isotropic stress field. We use the estimate of >3-5.5 km contraction prior to ∼4 Ga as an additional constraint to thermomechanical simulations of the evolution of Mercury, finding that a wide range of models are consistent with this observation. The fact that a wide range of states are consistent with the contraction of Mercury prior to the end of Late Heavy Bombardment but only a restricted set of states are consistent with the at most 1-2 km of subsequent contraction bolsters the idea that there may be hidden strain on Mercury, features unseen by Mariner 10 but likely visible to the MESSENGER spacecraft.     

A contraction model for the flattening and equatorial ridge of Iapetus

Others have explained the excess flattening of Iapetus by a model in which the moon formed at a high spin rate, achieved isostatic equilibrium by very rapid interior heating caused by short-lived radioactive isotopes (SLRI), and subsequently cooled, locking in the excess flattening with respect to an equilibrium shape at its present spin rate. Here we propose an alternate model that does not require an unusually high initial spin rate or the SLRI. The initial formation of Iapetus results in a slightly oblate spheroid with porosity >10%. Radioactive heating by long-lived isotopes warms the interior to about 200 K, at which point it becomes ductile and the interior compacts by 10%, while the 120 km-thick exterior shell remains strong. The shell must deform to match the reduced volume of the ductile interior, and we propose that this deformation occurs along the equator, perhaps focused by a thinner equatorial shell. The final shape of the collapsed sphere matches the observed shape of Iapetus today, described as an oblate ellipse, except along the equator where strain concentration forms a broad ridge. To maintain this non-equilibrium shape, the thickness of the shell must exceed 120 km. Testing the equatorial focusing hypothesis will require a model that includes non-linear processes to account for the finite yield strength of the thick lithosphere. Nevertheless, we show that the stress in the lithosphere generated by the contraction of the interior is about 3 times greater than the stress needed to deform the lithosphere, so some type of lithospheric deformation is expected.     

Evolution of Mercury's obliquity

Mercury has a near-zero obliquity, i.e. its spin axis is nearly perpendicular to its orbital plane. The value of the obliquity must be known precisely in order to constrain the size of the planet's core within the framework suggested by Peale [Peale, S.J., 1976. Nature 262, 765-766]. Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381-393] have suggested that Mercury's obliquity varies on thousand-year timescales due to planetary perturbations, potentially ruining the feasibility of Peale's experiment. We use a Hamiltonian approach (free of energy dissipation) to study the spin-orbit evolution of Mercury subject to secular planetary perturbations. We can reproduce an obliquity evolution similar to that of Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381-393] if we integrate the system with a set of initial conditions that differs from the Cassini state. However the thousand-year oscillations in the obliquity disappear if we use initial conditions corresponding to the equilibrium position of the Cassini state. This result indicates that planetary perturbations do not force short-period, large amplitude oscillations in the obliquity of Mercury. In the absence of excitation processes on short timescales, Mercury's obliquity will remain quasi-constant, suggesting that one of the important conditions for the success of Peale's experiment is realized. We show that interpretation of data obtained in support of this experiment will require a precise knowledge of the spin-orbit configuration, and we provide estimates for two of the critical parameters, the instantaneous Laplace plane orientation and the orbital precession rate from numerical fits to ephemeris data. Finally we provide geometrical relationships and a scheme for identifying the correct initial conditions required in numerical integrations involving a Cassini state configuration subject to planetary perturbations.     

Simulations of dense planetary rings: IV. Spinning self-gravitating particles with size distribution

Previous self-gravitating simulations of dense planetary rings are extended to include particle spins. Both identical particles as well as systems with a modest range of particle sizes are examined. For a ring of identical particles, we find that mutual impact velocity is always close to the escape velocity of the particles, even if the total rms velocity dispersion of the system is much larger, due to collective motions associated to wakes induced by near-gravitational instability or by viscous overstability. As a result, the spin velocity (i.e., the product of the particle radius and the spin frequency) maintained by mutual impacts is also of the order of the escape velocity, provided that friction is significant. For the size distribution case, smaller particles have larger impact velocities and thus larger spin velocities, particularly in optically thick rings, since small particles move rather freely between wakes. Nevertheless, the maximum ratio of spin velocities between the smallest and largest particles, as well as the ratio for translational velocities, stays below about 5 regardless of the width of the size distribution. Particle spin state is one of the important factors affecting the temperature difference between the lit and unlit face of Saturn's rings. Our results suggest that, to good accuracy, the spin frequency is inversely proportional to the particle size. Therefore, the mixing ratio of fast rotators to slow rotators on the scale of the thermal relaxation time increases with the width of the particle size distribution. This will offer means to constrain the particle size distribution with the systematic thermal infrared observations carried by the Cassini probe.     

Latitudinal librations of Mercury with a fluid core

In the framework of the space missions to Mercury, an accurate model of rotation is needed. Librations around the 3:2 spin-orbit resonance as well as latitudinal librations have to be predicted with the best possible accuracy. In this paper, we use a Hamiltonian analysis and numerical integrations to study the librations of Mercury, both in longitude and latitude. Due to the proximity of the period of the free libration in longitude to the orbital period of Jupiter, the 88-day and 11.86-year contributions dominate Mercury’s libration in longitude (with the Hermean parameters chosen). The amplitude of the libration in latitude is much smaller (under 1 arcsec) and should not be detected by the space missions. Nevertheless, we point out that this amplitude could be much larger (up to several tens of arcsec) if the free period related to the libration in latitude approaches the period of the Jupiter-Saturn Great Inequality (883 years). Given the large uncertainties on the planetary parameters, this new resonant forcing on Mercury’s libration in latitude should be borne in mind.     

The proximity of Mercury's spin to Cassini state 1 from adiabatic invariance

In determining Mercury's core structure from its rotational properties, the value of the normalized moment of inertia, C/MR², from the location of Cassini 1 is crucial. If Mercury's spin axis occupies Cassini state 1, its position defines the location of the state, where the axis is fixed in the frame precessing with the orbit. Although tidal and core-mantle dissipation drive the spin to the Cassini state with a time scale O(¹⁰⁵) years, the spin might still be displaced from the Cassini state if the variations in the orbital elements induced by planetary perturbations, which change the position of the Cassini state, cause the spin to lag behind as it attempts to follow the state. After being brought to the state by dissipative processes, the spin axis is expected to follow the Cassini state for orbit variations with time scales long compared to the 1000 year precession period of the spin about the Cassini state because the solid angle swept out by the spin axis as it precesses is an adiabatic invariant. Short period variations in the orbital elements of small amplitude should cause displacements that are commensurate with the amplitudes of the short period terms. The exception would be if there are forcing terms in the perturbations that are nearly resonant with the 1000 year precession period. The precision of the radar and eventual spacecraft measurements of the position of Mercury's spin axis warrants a check on the likely proximity of the spin axis to the Cassini state. How confident should we be that the spin axis position defines the Cassini state sufficiently well for a precise determination of C/MR²? By following simultaneously the spin position and the Cassini state position during long time scale orbital variations over past 3 million years [Quinn, T.R., Tremaine, S., Duncan, M., 1991. Astron. J. 101, 2287-2305] and short time scale variations for 20,000 years [JPL Ephemeris DE 408; Standish, E.M., private communication, 2005], we show that the spin axis will remain within one arcsec of the Cassini state after it is brought there by dissipative torques. In this process the spin is located in the orbit frame of reference, which in turn is referenced to the inertial ecliptic plane of J2000. There are no perturbations with periods resonant with the precession period that could cause large separations. We thus expect Mercury's spin to occupy Cassini state 1 well within the uncertainties for both radar and spacecraft measurements, with correspondingly tight constraints on C/MR² and the extent of Mercury's molten core. Two unlikely caveats for this conclusion are: (1) an excitation of a free spin precession by an unknown mechanism or (2) a displacement by a dissipative core mantle interaction that exceeds the measurement uncertainties.     

Reorientation of planets with lithospheres: The effect of elastic energy

It is commonly assumed that internal energy dissipation will ultimately drive planets to principal axis rotation, i.e., where the rotation vector is aligned with the maximum principle axis, since this situation corresponds to the minimum rotational energy state. This assumption simplifies long-term true polar wander (TPW) studies since the rotation pole can then be found by diagonalizing the appropriate (non-equilibrium) inertia tensor. We show that for planets with elastic lithospheres the minimum energy state does not correspond to principal axis rotation. As the planet undergoes reorientation elastic energy is stored in the deforming lithosphere, and the state of minimum total energy is achieved before principal axis rotation. We find solutions for the TPW of planets that include this effect by calculating the elastic stresses associated with deformation, and then minimizing the total (rotational and elastic) energy. These expressions indicate that the stored elastic energy acts to reduce the effective size of the driving load (relative to predictions which do not include this energy term). Our derivation also yields expressions for the TPW-induced stress field that generalizes several earlier results. As an illustration of the new theory, we consider TPW driven by the development of the Tharsis volcanic province on Mars. Once the size of the Tharsis load and the Mars model is specified, the extended theory yields a more limited range on the possible TPW.     

The interior structure of Mercury and its core sulfur content

Depth-dependent interior structure models of Mercury are calculated for several plausible chemical compositions of the core and of the mantle. For those models, we compute the associated libration amplitude, obliquity, tidal deformation, and tidal changes in the external potential. In particular we study the relation between the interior structure parameters for five different mantle mineralogies and two different temperature profiles together with two extreme crust density values. We investigate the influence of the core light element concentration, temperature, and melting law on core state and inner and outer core size. We show that a sulfur concentration above 10 wt% is unlikely if the temperature at the core-mantle boundary is above 1850 K and the silicate shell at least 240 km thick. The interior models can only have an inner core if the sulfur weight fraction is below 5 wt% for core-mantle boundary temperature in the 1850-2200 K range. Within our modeling hypotheses, we show that with the expected precision on the moment of inertia the core size can be estimated to a precision of about 50 km and the core sulfur concentration with an error of about 2 wt%. This uncertainty can only be reduced when more information on the mantle mineralogy of Mercury becomes available. However, we show that the uncertainty on the core size estimation can be greatly reduced, to about 25 km, if tidal surface displacements and tidal variations in the external potential are considered.     

On the rotation of a moonlet embedded in planetary rings

We examine the rotation of a small moonlet embedded in planetary rings caused by impacts of ring particles, using analytic calculation and numerical orbital integration for the three-body problem. Taking into account the Rayleigh distribution of particles' orbital eccentricities and inclinations, we evaluate both systematic and random components of rotation, where the former arises from an average of a large number of small impacts and the latter is contribution from large impacts. Calculations for parameter values corresponding to inner parts of Saturn's rings show that a moonlet would spin slowly in the prograde direction if most impactors are small particles whose velocity dispersion is comparable to or smaller than the moonlet's escape velocity. However, we also find that the effect of the random component can be significant, if the velocity dispersion of particles is larger and/or impacts of large particles comparable to the moonlet's size are common: in this case, both prograde and retrograde rotations can be expected. In the case of a small moonlet embedded in planetary rings of equal-sized particles, we find that the systematic component dominates the moonlet rotation when m/M?0.1 (m and M are the mass of a particle and a moonlet, respectively), while the random component is dominant when m/M?0.3. We derive the condition for the random component to dominate moonlet rotation on the basis of our results of three-body orbital integration, and confirm agreement with N-body simulation.     

Rotation rate and velocity dispersion of planetary ring particles with size distribution: I. Formulation and analytic calculation

We derive an equation for the evolution of rotational energy of Keplerian particles in a dilute disk due to mutual collisions. Three-dimensional Keplerian motion of particles is taken into account precisely, on the basis of Hill's approximation. The Rayleigh distribution of particles' orbital eccentricities and inclinations, and the Gaussian distribution of their rotation rates are also taken into account. Performing appropriate variable transformation, we show that the equation can be expressed with two terms. The first term, which we call collisional stirring term, represents energy exchange between rotation and random motion via collisions. The second term, which we call rotational friction term, tends to equalize the mean rotational energy of particles with different sizes. The equation can describe the evolution of rotational energy of Keplerian particles with an arbitrary size distribution. We analytically evaluate the rates of stirring and friction for the random kinetic energy and rotational energy due to inelastic collisions, for non-gravitating particles in a dilute disk. Using these results, we discuss equilibrium states in a disk of spinning, non-gravitating Keplerian particles.     

Models of magnetic field generation in partly stable planetary cores: Applications to Mercury and Saturn

A substantial part of Mercury's iron core may be stably stratified because the temperature gradient is subadiabatic. A dynamo would operate only in a deep sublayer. We show that such a situation arises for a wide range of values for the heat flow and the sulfur content in the core. In Saturn the upper part of the metallic hydrogen core could be stably stratified because of helium depletion. The magnetic field is unusually weak in the case of Mercury and unusually axisymmetric at Saturn. We study numerical dynamo models in rotating spherical shells with a stable outer region. The control parameters are chosen such that the magnetic Reynolds number is in the range of expected Mercury values. Because of its slow rotation, Mercury may be in a regime where the dipole contribution to the internal magnetic field is weak. Most of our models are in this regime, where the dynamo field consists mainly of rapidly varying higher multipole components. They can hardly pass the stable conducting layer because of the skin effect. The weak low-degree components vary more slowly and control the structure of the field outside the core, whose strength matches the observed field strength at Mercury. In some models the axial dipole dominates at the planet's surface and in others the axial quadrupole is dominant. Differential rotation in the stable layer, representing a thermal wind, is important for attenuating non-axisymmetric components in the exterior field. In some models that we relate to Saturn the axial dipole is intrinsically strong inside the dynamo. The surface field strength is much larger than in the other cases, but the stable layer eliminates non-axisymmetric modes. The Messenger and Bepi Colombo space missions can test our predictions that Mercury's field is large-scaled, fairly axisymmetric, and shows no secular variations on the decadal time scale.     

Rotation rate and velocity dispersion of planetary ring particles with size distribution II. Numerical simulation for gravitating particles

We examine rotation rates of gravitating particles in low optical depth rings, on the basis of the evolution equation of particle rotational energy derived by Ohtsuki [Ohtsuki, K., 2006. Rotation rate and velocity dispersion of planetary ring particles with size distribution. I. Formulation and analytic calculation. Icarus 183, 373-383]. We obtain the rates of evolution of particle rotation rate and velocity dispersion, using three-body orbital integration that takes into account distribution of random velocities and rotation rates. The obtained stirring and friction rates are used to calculate the evolution of velocity dispersion and rotation rate for particles in one- and two-size component rings as well as those with a narrow size distribution, and agreement with N-body simulation is confirmed. Then, we perform calculations to examine equilibrium rotation rates and velocity dispersion of gravitating ring particles with a broad size distribution, from 1 cm up to 10 m. We find that small particles spin rapidly with 〈ω²〉^1/2/Ω?¹⁰²-¹⁰³, where ω and Ω are the particle rotation rate and its orbital angular frequency, respectively, while the largest particles spin slowly, with 〈ω²〉^1/2/Ω?1. The vertical scale height of rapidly rotating small particles is much larger than that of slowly rotating large particles. Thus, rotational states of ring particles have vertical heterogeneity, which should be taken into account in modeling thermal infrared emission from Saturn's rings.     

Revisiting the thermal inertia of Iapetus: Clues to the thickness of the dark material

The energy balance at the surface of an airless planetary body is strongly influenced by the bolometric Bond albedo and the surface thermal inertia. Both of these values may be calculated through the application of a thermal model to measured surface temperatures. The accuracy of either, though, increases if the value of the other is better constrained. In this study, we used the improved global bolometric Bond albedo map of Iapetus derived from Cassini VIMS and ISS and Voyager ISS data in conjunction with Cassini CIRS temperature data to reevaluate surface thermal inertia across Iapetus. Results showed the thermal inertia of the dark terrain varies between 11 and 14.8 J m⁻² K⁻¹ s^−1/2 while the light material varies between 15 and 25 J m⁻² K⁻¹ s^−1/2. Using an approximation to the thermal properties of the dark overburden derived from our thermal inertia results, we can implement our thermal model to provide estimates on the dark material thickness, which was found to lie between 7 cm and 16 cm. In order to develop an accurate global thermal model, a weighted function that approximates the surface thermal inertia across Iapetus was developed and verified via our measurements. The global bolometric Bond albedo map, surface thermal inertia map, and the thermal model are then used to synthesize global temperature maps that may be used to study the stability of volatiles.     

Highly reducing conditions during core formation on Mercury: Implications for internal structure and the origin of a magnetic field

The high average density and low surface FeO content of the planet Mercury are shown to be consistent with very low oxygen fugacity during core segregation, in the range 3-6 log units below the iron-wüstite buffer. These low oxygen fugacities, and associated high metal content, are characteristic of high-iron enstatite (EH) and Bencubbinite (CB) chondrites, raising the possibility that such materials may have been important building blocks for this planet. With this idea in mind we have explored the internal structure of a Mercury sized planet of EH or CB bulk composition. Phase equilibria in the silicate mantle have been modeled using the thermodynamic calculator p-MELTS, and these simulations suggest that orthopyroxene will be the dominant mantle phase for both EH and CB compositions, with crystalline SiO₂ being an important minor phase at all pressures. Simulations for both compositions predict a plagioclase-bearing “crust” at low pressure, significant clinopyroxene also being calculated for the CB bulk composition. Concerning the core, comparison with recent high pressure and high temperature experiments relevant to the formation of enstatite meteorites, suggest that the core of Mercury may contain several wt.% silicon, in addition to sulfur. In light of the pressure of the core-mantle boundary on Mercury (∼7 GPa) and the pressure at which the immiscibility gap in the system Fe-S-Si closes (∼15 GPa) we suggest that Mercury’s core may have a complex shell structure comprising: (i) an outer layer of Fe-S liquid, poor in Si; (ii) a middle layer of Fe-Si liquid, poor in S; and (iii) an inner core of solid metal. The distribution of heat-producing elements between mantle and core, and within a layered core have been quantified. Available data for Th and K suggest that these elements will not enter the core in significant amounts. On the other hand, for the case of U both recently published metal/silicate partitioning data, as well as observations of U distribution in enstatite chondrites, suggest that this element behaves as a chalcophile element at low oxygen fugacity. Using these new data we predict that U will be concentrated in the outer layer of the mercurian core. Heat from the decay of U could thus act to maintain this part of Mercury’s core molten, potentially contributing to the origin of Mercury’s magnetic field. This result contrasts with the Earth where the radioactive decay of U represents a negligible contribution to core heating.