Large Longitude Libration of Mercury Reveals a Molten Core

Fluid Dynamics Experiments for Planetary Interiors

Understanding fluid flows in planetary cores and subsurface oceans, as well as their signatures in available observational data (gravity, magnetism, rotation, etc.), is a tremendous interdisciplinary challenge. In particular, it requires understanding the fundamental fluid dynamics involving turbulence and rotation at typical scales well beyond our day-to-day experience. To do so, laboratory experiments are fully complementary to numerical simulations, especially in systematically exploring extreme flow regimes for long duration. In this review article, we present some illustrative examples where experimental approaches, complemented by theoretical and numerical studies, have been key for a better understanding of planetary interior flows driven by some type of mechanical forcing. We successively address the dynamics of flows driven by precession, by libration, by differential rotation, and by boundary topography.

Atomic transport properties of liquid iron at conditions of planetary cores

Atomic transport properties of liquid iron are important for understanding the core dynamics and magnetic field generation of terrestrial planets. Depending on the sizes of planets and their thermal histories, planetary cores may be subject to quite different pressures (P) and temperatures (T). However, previous studies on the topic mainly focus on the P-T range associated with the Earth's outer core; a systematic study covering conditions from small planets to massive exoplanets is lacking. Here, we calculate the self-diffusion coefficient D and viscosity η of liquid iron via ab initio molecular dynamics from 7.0 to 25 g/cm³ and 1800 to 25 000 K. We find that D and η are intimately related and can be fitted together using a generalized free volume model. The resulting expressions are simpler than those from previous studies where D and η were treated separately. Moreover, the new expressions are in accordance with the quasi-universal atomic excess entropy (S_ex) scaling law for strongly coupled liquids, with normalized diffusivity D^⋆ = 0.621 exp(0.842S_ex) and viscosity η^⋆ = 0.171 exp(-0.843S_ex). We determine D and η along two thermal profiles of great geophysical importance: the iron melting curve and the isentropic line anchored at the ambient melting point. The variations of D and η along these thermal profiles can be explained by the atomic excess entropy scaling law, demonstrating the dynamic invariance of the system under uniform time and space rescaling. Accordingly, scale invariance may serve as an underlying mechanism to unify planetary dynamos of different sizes.

A new quantum model of the magnetic field of the Hot Earth, Moon and terrestrial planets

Distribution of Pand Swaves velocities in the Earth’s inner core suggests that its matter has been quantum entangled since the origin of the Earth and the Solar system. This assumption we made allows us to develop the quantum model of the geomagnetic field evolution from its start to its disappearance. Unlike the generally accepted dynamo our model provides an obvious source of energy which is a phase transition and the thermal, mechanical and electrical energy released during it. The latter generates a double electric layer which rotation gives rise to the initial dipole field. Changing its direction the phase transition causes a reversal of the magnetic field. Magnetic and paleomagnetic data on the Earth, Moon, Mercury and Mars analyzed in the frameworks the Hot Earth model and features of their gravitation recorded at NASA project offered as conditions for the planets formation and evolution and so predictions for the further evolution of the Earth and its magnetic field.

Fe Melting Transition: Electrical Resistivity, Thermal Conductivity, and Heat Flow at the Inner Core Boundaries of Mercury and Ganymede

The electrical resistivity and thermal conductivity behavior of Fe at core conditions are important for understanding planetary interior thermal evolution as well as characterizing the generation and sustainability of planetary dynamos. We discuss the electrical resistivity and thermal conductivity of Fe, Co, and Ni at the solid–liquid melting transition using experimental data from previous studies at 1 atm and at high pressures. With increasing pressure, the increasing difference in the change in resistivity of these metals on melting is interpreted as due to decreasing paramagnon-induced electronic scattering contribution to the total electronic scattering. At the melting transition of Fe, we show that the difference in the value of the thermal conductivity on the solid and liquid sides increases with increasing pressure. At a pure Fe inner core boundary of Mercury and Ganymede at ~5 GPa and ~9 GPa, respectively, our analyses suggest that the thermal conductivity of the solid inner core of small terrestrial planetary bodies should be higher than that of the liquid outer core. We found that the thermal conductivity difference on the solid and liquid sides of Mercury’s inner core boundary is ~2 W(mK)−1. This translates into an excess of total adiabatic heat flow of ~0.01–0.02 TW on the inner core side, depending on the relative size of inner and outer core. For a pure Fe Ganymede inner core, the difference in thermal conductivity is ~7 W(mK)−1, corresponding to an excess of total adiabatic heat flow of ~0.02 TW on the inner core side of the boundary. The mismatch in conducted heat across the solid and liquid sides of the inner core boundary in both planetary bodies appears to be insignificant in terms of generating thermal convection in their outer cores to power an internal dynamo suggesting that chemical composition is important.

Geodetic evidence that Mercury has a solid inner core

Geodetic analysis of radio tracking measurements of the MESSENGER spacecraft while in orbit about Mercury has yielded new estimates for the planet's gravity field, tidal Love number, and pole coordinates. The derived right ascension (α = 281.0082° ± 0.0009°; all uncertainties are 3 standard deviations) and declination (δ =61.4164° ± 0.0003°) of the spin pole place Mercury in the Cassini state. Confirmation of the equilibrium state with an estimated mean (whole-planet) obliquity ϵ of 1.968 ± 0.027 arcmin enables the confident determination of the planet's normalized polar moment of inertia (0.333 ± 0.005), which indicates a high degree of internal differentiation. Internal structure models generated by a Markov-Chain Monte Carlo process and consistent with the geodetic constraints possess a solid inner core with a radius (r _ic ) between 0.3 and 0.7 that of the outer core (r _oc ).

Oscillation-induced sand dunes in a liquid-filled rotating cylinder

The dynamics of granular medium in a liquid-filled horizontal cylinder with a time-varying rotation rate is experimentally studied. When the cylinder is purely rotated, the granular medium develops an annular layer near the cylindrical wall. The interface between fluid and sand is smooth and axisymmetric. The time variation of the rotation rate initiates the azimuthal oscillation of the liquid in the cylinder's frame of reference and provokes the onset of quasisteady relief in the form of regular dunes. The stability of the axisymmetric sand surface and dynamics of regular dunes are examined. It is found that the ripple formation is provoked by the quasisteady instability of the Stokes boundary layer. In the range of high Reynolds numbers, the ripple formation occurs at a constant critical Shields number θ_{c}≃0.05. The spatial period of the relief is not sensitive to the fluid viscosity and granule diameter; it is determined by the amplitude of oscillation and ratio between the oscillation frequency and mean rotation rate. Long-term experiments show that there are forward and backward azimuthal drifts of dunes. An initial analysis of the issues related to the dune migration is provided.

Flow patterns in a rotating horizontal cylinder partially filled with liquid

The dynamics of an annular layer of low-viscosity liquid inside a rapidly rotating horizontal cylinder is experimentally studied. Under gravity, the liquid performs forced azimuthal oscillations in the cavity frame. We examined the stability of the two-dimensional azimuthal flow and discovered two novel types of axisymmetric liquid flows. First, a large-scale axially symmetric flow is excited near the end walls. The inertial modes generated in the corner regions are proven to be responsible for such a flow. Second, a small-scale flow in the form of the Taylor-Gortler vortices appears due to the centrifugal instability of the oscillatory liquid flow. The spatial period of the vortices is in qualitative agreement with the data obtained in the experimental and numerical studies of cellular flow in librating containers.

Ancient planetary dynamos, take two

Magnetic studies of Earth and Mercury constrain their ancient core dynamics [Also see Report by Tarduno et al. ]

Modular model for Mercury's magnetospheric magnetic field confined within the average observed magnetopause

Accurate knowledge of Mercury's magnetospheric magnetic field is required to understand the sources of the planet's internal field. We present the first model of Mercury's magnetospheric magnetic field confined within a magnetopause shape derived from Magnetometer observations by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft. The field of internal origin is approximated by a dipole of magnitude 190 nT R_M³, where R_M is Mercury's radius, offset northward by 479 km along the spin axis. External field sources include currents flowing on the magnetopause boundary and in the cross-tail current sheet. The cross-tail current is described by a disk-shaped current near the planet and a sheet current at larger (≳ 5 R_M ) antisunward distances. The tail currents are constrained by minimizing the root-mean-square (RMS) residual between the model and the magnetic field observed within the magnetosphere. The magnetopause current contributions are derived by shielding the field of each module external to the magnetopause by minimizing the RMS normal component of the magnetic field at the magnetopause. The new model yields improvements over the previously developed paraboloid model in regions that are close to the magnetopause and the nightside magnetic equatorial plane. Magnetic field residuals remain that are distributed systematically over large areas and vary monotonically with magnetic activity. Further advances in empirical descriptions of Mercury's magnetospheric external field will need to account for the dependence of the tail and magnetopause currents on magnetic activity and additional sources within the magnetosphere associated with Birkeland currents and plasma distributions near the dayside magnetopause.

Constraints on Mimas' interior from Cassini ISS libration measurements

Like our Moon, the majority of the solar system's satellites are locked in a 1:1 spin-orbit resonance; on average, these satellites show the same face toward the planet at a constant rotation rate equal to the satellite's orbital rate. In addition to the uniform rotational motion, physical librations (oscillations about an equilibrium) also occur. The librations may contain signatures of the satellite's internal properties. Using stereophotogrammetry on Cassini Image Science Subsystem (ISS) images, we measured longitudinal physical forced librations of Saturn's moon Mimas. Our measurements confirm all the libration amplitudes calculated from the orbital dynamics, with one exception. This amplitude depends mainly on Mimas' internal structure and has an observed value of twice the predicted one, assuming hydrostatic equilibrium. After considering various possible interior models of Mimas, we argue that the satellite has either a large nonhydrostatic interior, or a hydrostatic one with an internal ocean beneath a thick icy shell.

Simulation of the planetary interior differentiation processes in the laboratory

A planetary interior is under high-pressure and high-temperature conditions and it has a layered structure. There are two important processes that led to that layered structure, (1) percolation of liquid metal in a solid silicate matrix by planet differentiation, and (2) inner core crystallization by subsequent planet cooling. We conduct high-pressure and high-temperature experiments to simulate both processes in the laboratory. Formation of percolative planetary core depends on the efficiency of melt percolation, which is controlled by the dihedral (wetting) angle. The percolation simulation includes heating the sample at high pressure to a target temperature at which iron-sulfur alloy is molten while the silicate remains solid, and then determining the true dihedral angle to evaluate the style of liquid migration in a crystalline matrix by 3D visualization. The 3D volume rendering is achieved by slicing the recovered sample with a focused ion beam (FIB) and taking SEM image of each slice with a FIB/SEM crossbeam instrument. The second set of experiments is designed to understand the inner core crystallization and element distribution between the liquid outer core and solid inner core by determining the melting temperature and element partitioning at high pressure. The melting experiments are conducted in the multi-anvil apparatus up to 27 GPa and extended to higher pressure in the diamond-anvil cell with laser-heating. We have developed techniques to recover small heated samples by precision FIB milling and obtain high-resolution images of the laser-heated spot that show melting texture at high pressure. By analyzing the chemical compositions of the coexisting liquid and solid phases, we precisely determine the liquidus curve, providing necessary data to understand the inner core crystallization process.

Planetary science. The strangest terrestrial planet

NASA's MESSENGER mission previously revealed that Mercury has a volcanic crust; now it finds evidence for an inner “anticrust.”