Magnetic probing of planetary interiors

The following general question is addressed: what can be learned about a planetary interior from measurements of the global planetary magnetic field at (or near) its surface? The discussion is placed in the context of Earth, for clarity, but the considerations apply to terrestrial planets in general (so long as the observed magnetism is either predominantly of internal origin, or else external source effects can be successfully filtered out of the observations). Attention is given to the idealized but typical situation of a rotating but spherically symmetric planet containing a highly conducting uniform fluid core surrounded by a nearly insulating rigid mantle, whose conductivity, a function of at most radius only, falls monotonically from its largest value at the base of the planetary mantle to zero at the planetary surface; the largest value of mantle conductivity as well as the mean value for the whole mantle and the mantle conductance are assumed small compared to the corresponding values of the core. Exterior to the planet is vacuum in the sense of an electrically uncharged insulator. The core fluid is inviscid, Boussinesq and gravitationally driven.Complete and perfect observations of either the instantaneous internal vector magnetic field together with its secular variation at a single epoch, or more realistically, the instantaneous internal vector magnetic field alone at two separated epochs are presumed available; the time separation between measurement epochs is long compared the Ohmic diffusion time of the planetary mantle, but small compared to that of the liquid core.Under such circumstances we describe how information about each of the following planetary properties can, in principle (though not without practical difficulty) be retrieved from the observations: (1) depth of the core-mantle boundary (a result of Hide); (2) depth to the current and motion sources responsible for the planetary dynamo; (3) presence or absence of small-scale turbulence in the upper reaches of the core; (4) large-scale horizontal fluid motion at the top of the core; (5) strength of horizontal currents, zonal magnetic fields, Coriolis and Lorentz forces at the top of the core; and (6) current system in the mantle and strength of electromagnetic core-mantle coupling.     

General considerations of the physics of planetary interiors

A deeper understanding of the constituents of the Solar System has been obtained over the last decade due primarily to the success of a variety of space missions which have provided a wealth of data to augment that obtained from Earth based observatories. Although the measurements refer directly to both the surface and atmospheric conditions, inferences can be made about conditions within the main bodies of the planets. This has been achieved through the closest collaboration between physicists, chemists and geologists in the study of these problems.In the present review we explore in a general way some of the types of problem involved with the physics of the interiors of planetary bodies. Concern will be with elucidating the structure of these bodies on the basis of the properties observed now. The arguments will be made in general terms and will not be concerned with any one planet in close detail.     

The significance of ferroelectric phase transitions for the Earth and planetary interiors

With the compelling evidence for orthorhombic perovskite ABO₃ structures in a major part of the earth's mantle, the question of whether any of these are ferroelectric (FE) or antiferroelectric should be of supreme importance. To answer this question the authors have conducted dielectric property studies at pressures up to 5.5 GPa on single crystals and polycrystalline aggregates of BaTiO₃ as well as other FE materials representing FE polarization mechanisms. The results indicate that: (1) h.p.-induced FE phases are indeed likely to play an important part in the earth's mantle; and (2) existing FE state, occuring as elastic and dielectric inhomogeneities, can persist to much higher pressures than expected on the basis of the pressure dependence of isolated and unclamped FE crystals. It is suggested that the presence of FE states in the earth's mantle may be responsible for some of its anomalous elastic and dielectric features, especially its attenuating properties. It is conjectured that effects of FE states on properties of the Jovian planets might even be more prominant, especially those involving dielectric constant and polarization.     

High-pressure studies of ferroelectric phases related to the earth and planetary interiors

To determine the effects of high-pressure constraints on the overall behaviour of ferroelectrics (FE) of both the perovskite “soft-mode” and hydrogen-bonded types, the authors have conducted dielectric property measurements to 5.5 GPa on single crystals and polycrystalline aggregates of several ferroelectrics (BaTiO₃, Pb(Zr,Ti)O₃, triglycine sulphate, Rochelle salt). The results of the experiments indicate: (1) dielectric hysteresis is possible in ferroelectrics which are under high-pressure conditions of deviatoric stresses and strains in which the FE phase forms part of a composite system; that is, under the conditions it would encounter if it formed part of a planetary interior; (2) the continued stability of these FE phases is not restricted to a particular polarization mechanism; (3) existing FE states, occurring as elastic and dielectric inhomogeneities, can persist to much higher pressures than expected on the basis of the pressure dependence of isolated and unconstrained FE crystals.     

Global magnetohydrostatic fields in stellar atmosphere

Abstract

The equilibrium properties of the magnetic field of an axisymmetric star are studied. A family of analytical solutions to the magnetohydrostatic equations is found, which are used to model the slow evolution of the field through a series of equilibria.

Firstly, a model is set up for a force-free dipole-like field, which has a toroidal field component; it is found that, as such a field is twisted up, a critical point is reached, at which the field topology changes. If the twist is increased beyond this point, there is no physically reasonable equilibrium. Next, an untwisted magnetostatic dipole-like field is studied, with an increasing pressure differential between pole and equator. A critical point again occurs when the pressure differential becomes too large. Finally a force-free quadrupole-like field is modelled, which is being twisted up, for example by differential rotation; this has similar properties to the dipole-like field. In each case, it is suggested that, when the critical point is reached, the field will no longer evolve smoothly, but will change catastrophically to a new stable, releasing energy. Such an event could represent the onset of a stellar flare or some other dynamic stellar process.     

Are anharmonicity corrections needed for temperature-profile calculations of interiors of terrestrial planets?

It is shown that there is linearity between the thermal pressure P_TH and T between the Debye temperature θ and some high temperature $\text{T}{}^1$. $\text{T}{}^1$ has been measured at 1 atm and is reported for several minerals including, for example, MgO (1300 K) and forsterite (1200 K). The change in thermal pressure from room temperature for five solids, so far measured, indicate striking linearity with T at high temperatures.It is further shown that the value of $\text{T}{}^1$ increases greatly as the pressure increases. It is therefore concluded that P_TH is probably linear with T for mantle minerals under mantle conditions. The proportionality constant is derived from the measurements of thermal expansivity and bulk modulus at high temperature and zero pressure.The argument is then reversed. Assuming that the thermal pressure is in fact linear with T for the various shells in a planet, the resulting density and temperature profile of the planet is derived. The resulting density profile of the Earth compares favorably with corresponding values of recent seismic profiles.     

New light on post-main sequence stellar evolution

The 8 m class telescopes now coming on stream, the availability of new instruments on 4 m telescopes and mm/radio telescopes, are beginning to throw new light on post-main sequence stellar evolution. The February RAS discussion meeting, organized by Nye Bevan, described the impact of these facilities on our understanding of this phase. Myfanwy Bryce reports.     

Hydrocarbon generation in the interiors of Kamchatka and its relationship to volcanism and hydrothermal activity

This paper considers oil-and-gas provinces and the epochs of hydrocarbon generation in Kamchatka. We distinguish the following epochs of hydrocarbon generation: the Early Mesozoic, the Early Cretaceous, the Late Cretaceous, the Early Paleogene, the Late Paleogene, the Miocene, and the Pliocene-Quaternary. We emphasize the fact that all gas generation epochs were related to deep processes, including volcanism and hydrothermal activity.     

Nonlinear dynamics of a stellar dynamo in a spherical shell

Abstract

A simple mean-field model of a nonlinear stellar dynamo is considered, in which dynamo action is supposed to occur in a spherical shell, and where the only nonlinearity retained is the influence of the Lorentz forces on the zonal flow field. The equations are simplified by truncating in the radial direction, while full latitudinal dependence is retained. The resulting nonlinear p.d.e.'s in latitude and time are solved numerically, and it is found that while regular dynamo wave type solutions are stable when the dynamo number D is sufficiently close to its critical value, there is a wide variety of stable solutions at larger values of D. Furthermore, two different types of dynamo can coexist at the same parameter values. Implications for fields in late-type stars are discussed.     

A Numerical Algorithm for Time Integration of the Problems of Ideal Magnetohydrodynamics Based on Analyticity of Their Solutions

Izvestiya, Physics of the Solid Earth - Abstract—We show that a solution of the system of three-dimensional equations of ideal magnetohydrodynamics is analytic in the spatial and temporal...     

High-frequency waves in hot magnetized solar and stellar coronal plasmas

The characteristics of low-damping high-frequency waves in hot magnetized solar and stellar coronal plasmas under the conditions when the electron gyrofrequency ω_He is equal to or higher than the electron plasma frequency ω_pe have been analyzed using the numerical solution of the dispersion equation. It is shown that the wave branches corresponding to the Z mode and ordinary waves approach each other when the magnetic field increases and become almost indistinguishable in a wide frequency range at all angles between the wave vector and magnetic field. A branch with anomalous dispersion appears at angles close to 90°. A new interpretation of broadband pulsations and spikes is suggested on the basis of the results.     

Planetary, stellar and galactic evolution from a rocky perspective

Monica M Grady reviews the treasure trove of astronomical data that comes to Earth in the form of meteorites.     

Magnetohydrodynamics (MHD) numerical simulations on the interaction of the solar wind with the magnetosphere: A review

The magnetosphere is the outermost layer of the geospace, and the interaction of the solar wind with the magnetosphere is the key element of the space weather cause-and-effect chain process from the Sun to Earth, which is one of the most challenging scientific problems in the geospace weather study. The nonlinearity, multiple component, and time-dependent nature of the geospace make it very difficult to describe the physical process in geospace using traditional analytic analysis approach. Numerical simulations, a new research tool developed in recent decades, have a deep impact on the theory and application of the geospace. MHD simulations started at the end of the 1970s, and the initial study was limited to two-dimensional (2D) cases. Due to the intrinsic three-dimensional (3D) characteristics of the geospace, 3D MHD simulations emerged in the 1980s, in an attempt to model the large-scale structures and fundamental physical processes in the magnetosphere. They started to combine with the space exploration missions in the 1990s and make comparisons with observations. Physics-based space weather forecast models started to be developed in the 21st century. Currently only a few space-power countries such as USA and Japan have developed 3D magnetospheric MHD models. With the rapid advance of space science in China, we have developed a new global MHD model, namely PPMLR-MHD, which has high order spatial accuracy and low numerical dissipation. In this review, we will briefly introduce the global 3D MHD modeling, especially the PPMLR-MHD code, and summarize our recent work based on the PPMLR-MHD model, with an emphasis on the interaction of interplanetary shocks with the magnetosphere, large-scale current systems, reconnection voltage and transpolar potential drop, and Kelvin-Helmholtz (K-H) instability at the magnetopause.     

Penetrative convection in rotating fluids: A model for the base of stellar convection zones

Abstract

To model penetrative convection at the base of a stellar convection zone we consider two plane parallel, co-rotating Boussinesq layers coupled at their fluid interface. The system is such that the upper layer is unstable to convection while the lower is stable. Following the method of Kondo and Unno (1982, 1983) we calculate critical Rayleigh numbers R_c for a wide class of parameters. Here, R_c is typically much less than in the case of a single layer, although the scaling R_c～T^2/3 as T → ∞ still holds, where T is the usual Taylor number. With parameters relevant to the Sun the helicity profile is discontinuous at the interface, and dominated by a large peak in a thin boundary layer beneath the convecting region. In reality the distribution is continuous, but the sharp transition associated with a rapid decline in the effective viscosity in the overshoot region is approximated by a discontinuity here. This source of helicity and its relation to an alpha effect in a mean-field dynamo is especially relevant since it is a generally held view that the overshoot region is the location of magnetic field generation in the Sun.     

Density,stress, and gravity anomalies in the interiors of the earth and mars and the probable geodynamical implications: Comparative analysis

The formulas that allow, within the quadratic approximation, for the contribution of the anomalous masses, distributed along the height relative to the reference ellipsoid, in the Stokes parameters are derived. It is shown that the contribution of the quadratic terms is largest and commensurate, by the order of magnitude, with the linear contribution if the anomalous masses have a dipole distribution along the height. The quadratic contribution is particularly significant for Mars, where the span of relative variations in the surface topography is by an order of magnitude larger than in the Earth. The problem is solved and the method is developed for finding the depths of compensation for the topographical harmonics of different order and degree. The most probable levels of compensation for topographic irregularities are determined by the analysis of the distribution histograms for the depths of compensation. The maps of lateral distributions of the compensating masses at the selected levels are calculated. It is shown that the observed anomalous structures generate the anomalies in the internal gravity field, which may serve as a cause for the convective motion in the mantle and core of the planet. Besides, the probable nonisostatic vertical stresses in the crust and mantle of the Earth and Mars are calculated.     

Meridional circulation from differential rotation in an adiabatically stratified solar/stellar convection zone

Meridional circulation in stellar convection zones is not generally well observed, but may be critical for the workings of MHD dynamos operating in these domains. Coriolis forces from differential rotation play a large role in determining what the meridional circulation is. Here, we consider the question of whether a stellar differential rotation that is constant on cylinders concentric with the rotation axis can drive a meridional circulation. Conventional wisdom says that it can not. Using two related forms of the governing equations that respectively estimate the longitudinal components of the curl of the meridional mass flux and the vorticity, we show that such differential rotation will drive a meridional flow. This is because to satisfy anelastic mass conservation, non-spherically symmetric pressure contours must be present for all differential rotations, not just ones that depart from constancy on cylinders concentric with the rotation axis. Therefore, the fluid is always baroclinic if differential rotation is present. This is because, in anelastic systems, the perturbation pressure must satisfy a Poisson type equation, as well as an equation of state and a thermodynamic equation. We support our qualitative reasoning with numerical examples, and show that meridional circulation is sensitive to the magnitude and form of departures from rotation constant on cylinders. The effect should be present in 3D global anelastic convection simulations, particularly those for which the differential rotation driven by global convection is nearly cylindrical in profile. For solar-like differential rotation, Coriolis forces generally drive a two-celled circulation in each hemisphere, with a second, reversed flow at high latitudes. For solar like turbulent viscosities, the meridional circulation produced by Coriolis forces is much larger than observed on the Sun. Therefore, there must be at least one additional force, probably a buoyancy force, which opposes the meridional flow to bring its amplitude down to observed values.