Theory and Modeling of Planetary Dynamos

Numerical dynamo models are increasingly successful in modeling many features of the geomagnetic field. Moreover, they have proven to be a useful tool for understanding how the observations connect to the dynamo mechanism. More recently, dynamo simulations have also ventured to explain the surprising diversity of planetary fields found in our solar system. Here, we describe the underlying model equations, concentrating on the Boussinesq approximations, briefly discuss the numerical methods, and give an overview of existing model variations. We explain how the solutions depend on the model parameters and introduce the primary dynamo regimes. Of particular interest is the dependence on the Ekman number which is many orders of magnitude too large in the models for numerical reasons. We show that a minor change in the solution seems to happen at $\mbox {E}=3\mbox {$\times 10^{-6}$}$ whose significance, however, needs to be explored in the future. We also review three topics that have been a focus of recent research: field reversal mechanisms, torsional oscillations, and the influence of Earth’s thermal mantle structure on the dynamo. Finally we discuss the possibility of tidally or precession driven planetary dynamos.     

Dynamo Models for Planets Other Than Earth

Observations from planetary spacecraft missions have demonstrated a spectrum of dynamo behaviour in planets. From currently active dynamos, to remanent crustal fields from past dynamo action, to no observed magnetization, the planets and moons in our solar system offer magnetic clues to their interior structure and evolution. Here we review numerical dynamo simulations for planets other than Earth. For the terrestrial planets and satellites, we discuss specific magnetic field oddities that dynamo models attempt to explain. For the giant planets, we discuss both non-magnetic and magnetic convection models and their ability to reproduce observations of surface zonal flows and magnetic field morphology. Future improvements to numerical models and new missions to collect planetary magnetic data will continue to improve our understanding of the magnetic field generation process inside planets.     

Planetary Magnetic Fields: Achievements and Prospects

The past decade has seen a wealth of new data, mainly from the Galilean satellites and Mars, but also new information on Mercury, the Moon and asteroids (meteorites). In parallel, there have been advances in our understanding of dynamo theory, new ideas on the scaling laws for field amplitudes, and a deeper appreciation on the diversity and complexity of planetary interior properties and evolutions. Most planetary magnetic fields arise from dynamos, past or present, and planetary dynamos generally arise from thermal or compositional convection in fluid regions of large radial extent. The relevant electrical conductivities range from metallic values to values that may be only about one percent or less that of a typical metal, appropriate to ionic fluids and semiconductors. In all planetary liquid cores, the Coriolis force is dynamically important. The maintenance and persistence of convection appears to be easy in gas giants and ice-rich giants, but is not assured in terrestrial planets because the quite high electrical conductivity of an iron-rich core guarantees a high thermal conductivity (through the Wiedemann-Franz law), which allows for a large core heat flow by conduction alone. This has led to an emphasis on the possible role of ongoing differentiation (growth of an inner core or “snow”). Although planetary dynamos mostly appear to operate with an internal field that is not very different from (2ρΩ/σ)^1/2 in SI units where ρ is the fluid density, Ω is the planetary rotation rate and σ is the conductivity, theoretical arguments and stellar observations suggest that there may be better justification for a scaling law that emphasizes the buoyancy flux. Earth, Ganymede, Jupiter, Saturn, Uranus, Neptune, and probably Mercury have dynamos, Mars has large remanent magnetism from an ancient dynamo, and the Moon might also require an ancient dynamo. Venus is devoid of a detectable global field but may have had a dynamo in the past. Even small, differentiated planetesimals (asteroids) may have been capable of dynamo action early in the solar system history. Induced fields observed in Europa and Callisto indicate the strong likelihood of water oceans in these bodies. The presence or absence of a dynamo in a terrestrial body (including Ganymede) appears to depend mainly on the thermal histories and energy sources of these bodies, especially the convective state of the silicate mantle and the existence and history of a growing inner solid core. As a consequence, the understanding of planetary magnetic fields depends as much on our understanding of the history and material properties of planets as it does on our understanding of the dynamo process. Future developments can be expected in our understanding of the criterion for a dynamo and on planetary properties, through a combination of theoretical work, numerical simulations, planetary missions (MESSENGER, Juno, etc.) and laboratory experiments.     

Flux-Transport Solar Dynamos

Large-scale solar dynamo models were first built by Parker (1955). Over the past half a century these models have evolved significantly. We discuss here the development of a class of large-scale dynamo models which include, along with the α-effect and Ω-effect, an important third process, flux transport by meridional circulation. We present the properties of this ‘flux-transport’ dynamo, including the crucial role meridional circulation plays in giving this dynamo predictive power.     

Mars Crustal Magnetism

Mars lacks a detectable magnetic field of global scale, but boasts a rich spectrum of magnetic fields at smaller spatial scales attributed to the spatial variation of remanent magnetism in the crust. On average the Mars crust is 10 times more intensely magnetized than that of the Earth. It appears likely that the Mars crust acquired its remanence in the first few hundred million years of evolution when an active dynamo sustained an intense global field. An early dynamo era, ending in the Noachian, or earliest period of Mars chronology, would likely be driven by thermal convection in an early, hot, fluid core. If crustal remanence was acquired later in Mars history, a dynamo driven by chemical convection associated with the solidification of an inner core is likely. Thermal evolution models cannot yet distinguish between these two possibilities. The magnetic record contains a wealth of information on the thermal evolution of Mars and the Mars dynamo, but we have just begun to decipher its message.     

High X-ray luminosity from dynamo stars

In the present work we intend to show that a stellar dynamo mechanism can produce high X-ray luminosities and also give account for modulation periods of the order thousand seconds or larger.We outline here that the model we propose does not require the presence of a very compact object in a binary system; indeed, we intend to show that faint late main sequence stars sufficiently fast rotating, can give rise by dynamo action to sufficiently high magnetic fields to give account for the strong X-ray emission of some galactic X-ray sources.We examine the possibility that also a fraction of those X-ray sources usually depicted as accreting binary systems may be interpreted as active stars supplied by the - dynamo mechanism.     

Solar Cycle Forecasting

Predicting the behavior of a solar cycle after it is well underway (2–3 years after minimum) can be done with a fair degree of skill using auto-regression and curve fitting techniques that don’t require any knowledge of the physics involved. Predicting the amplitude of a solar cycle near, or before, the time of solar cycle minimum can be done using precursors such as geomagnetic activity and polar fields that do have some connection to the physics but the connections are uncertain and the precursors provide less reliable forecasts. Predictions for the amplitude of cycle 24 using these precursor techniques give drastically different values. Recently, dynamo models have been used directly with assimilated data to predict the amplitude of sunspot cycle 24 but have also given significantly different predictions. While others have questioned both the predictability of the solar cycle and the ability of current dynamo models to provide predictions, it is clear that cycle 24 will help to discriminate between some opposing dynamo models.     

Daily variations of the geomagnetic field

The atmospheric dynamo theory of the daily magnetic variations (S) has received substantial support from recent observational and theoretical work. In particular, several features of the variations, such as their remarkable enhancement close to the dip equator and other effects indicating a strong control by the main geomagnetic field, are well explained by the dynamo theory. Also the detection of ionospheric currents by instrumental rockets has confirmed an essential part of the theory.Considerable impetus was given to their study by the acquirement of much new data on magnetic variations during the IGY-IQSY period. Additional observations in the Pacific area were obtained during the IQSY by the establishment of four island stations equipped with newly developed magnetometers. A major advance at other stations was the development of automatic standard observatories using nuclear magnetometers.Several methods for the world-wide analysis of the S-field have been developed. A possibility now being studied is the completely automatic evaluation and construction by computers of ionospheric current charts for any day and any epoch UT.Some theoretical and statistical papers are briefly reviewed. These include discussions of the day-to-day variability of S, seasonal changes of the S-field, the nature of the equatorial electrojet, the possibility of solar wind effects contributing to the daily variations, and the modification of the dynamo theory to take account of the possible flow of electric current from the ionosphere along magnetic lines of force in the magnetosphere.Finally, an attempt to extend the dynamo theory of S by treating the ionosphere as a three-dimensional medium, instead of regarding it as a thin shell, has revealed that, although the relations between the horizontal components of electric field and current density in the dynamo layer are given with reasonable accuracy by the well-known layer equations, the assumption, implicit in the thin shell treatment, that the horizontal currents are non-divergent is not in fact true. Hence a revision of some earlier theoretical work on S appears necessary.     

Physical Causes of Solar Activity

The magnetic fields that dominate the structure of the Sun's atmosphere are controlled by processes in the solar interior, which cannot be directly observed. Magnetic activity is found in all stars with deep convective envelopes: young and rapidly rotating stars are very active but cyclic activity only appears in slow rotators. The Sun's 11-year activity cycle corresponds to a 22-year magnetic cycle, since the sunspot fields (which are antisymmetric about the equator) reverse at each minimum. The record of magnetic activity is aperiodic and is interrupted by episodes of reduced activity, such as the Maunder Minimum in the seventeenth century, when sunspots almost completely disappeared. The proxy record from cosmogenic isotopes shows that similar grand minima recur at intervals of around 200 yr. The Sun's large-scale field is generated by dynamo action rather than by an oscillator. Systematic magnetic cycles are apparently produced by a dynamo located in a region of weak convective overshoot at the base of the convection zone, where there are strong radial gradients in the angular velocity . The crucial parameter (the dynamo number) increases with increasing and kinematic (linear) theory shows that dynamo action can set in at an oscillatory (Hopf) bifurcation that is probably subcritical. Although it has been demonstrated that the whole process works in a self-consistent model, most calculations have relied on mean-field dynamo theory. This approach is physically plausible but can only be justified under conditions that do not apply in the Sun. Still, mean-field dynamos do reproduce the butterfly diagram and other key features of the solar cycle. An alternative approach is to study generic behaviour in low-order models, which exhibit two forms of modulation, associated with symmetry-breaking and with reduced activity. Comparison with observed behaviour suggests that modulation of the solar cycle is indeed chaotic, i.e. deterministically rather than stochastically driven.     

Large-scale electric fields and currents and related geomagnetic variations in the quiet plasmasphere

At the end of the sixties it became obvious that two-dimensional dynamo models can explain nearly all facts, which had been found morphologically for mean annual Sq-fields. During the recent decade new or improved methods to measure electric fields (e.g. incoherent scatter facilities) and to investigate great data files have been developed. New informations received with these methods about the existence of regular variations of the Sq-field in dependence on season and universal time and about the electric field have been summarized in Section 2. All attempts to describe also these variations with a two-dimensional dynamo model did not lead to any success, but showed a strong theoretical over-estimation of the asymmetries. Therefore, it must be concluded that three-dimensional plasmaspheric current systems, taking into consideration the coupling between both hemispheres along the high-conducting magnetic field lines, are needed in order to explain the regular variations of the Sq -field. The basic equations for two- and three-dimensional dynamo models, different methods for the solution of these equations and the resulting models from different authors are compiled and discussed (Section 3).Based on all morphological and theoretical results a plasmaspheric-ionospheric current system has been constructed and some properties of the plasmaspheric field-aligned current distribution, have been derived.     

Planetary Dynamos from a Solar Perspective

Direct numerical simulations of the geodynamo and other planetary dynamos have been successful in reproducing the observed magnetic fields. We first give an overview on the fundamental properties of planetary magnetism. We review the concepts and main results of planetary dynamo modeling, contrasting them with the solar dynamo. In planetary dynamos the density stratification plays no major role and the magnetic Reynolds number is low enough to allow a direct simulation of the magnetic induction process using microscopic values of the magnetic diffusivity. The small-scale turbulence of the flow cannot be resolved and is suppressed by assuming a viscosity far in excess of the microscopic value. Systematic parameter studies lead to scaling laws for the magnetic field strength or the flow velocity that are independent of viscosity, indicating that the models are in the same dynamical regime as the flow in planetary cores. Helical flow in convection columns that are aligned with the rotation axis play an important role for magnetic field generation and forms the basis for a macroscopic α-effect. Depending on the importance of inertial forces relative to rotational forces, either dynamos with a dominant axial dipole or with a small-scale multipolar magnetic field are found. Earth is predicted to lie close to the transition point between both classes, which may explain why the dipole undergoes reversals. Some models fit the properties of the geomagnetic field in terms of spatial power spectra, magnetic field morphology and details of the reversal behavior remarkably well. Magnetic field strength in the dipolar dynamo regime is controlled by the available power and found to be independent of rotation rate. Predictions for the dipole moment agree well with the observed field strength of Earth and Jupiter and moderately well for other planets. Dedicated dynamo models for Mercury, Saturn, Uranus and Neptune, which assume stably stratified layers above or below the dynamo region, can explain some of the unusual field properties of these planets.     

Magnetic Fields in Massive Stars, Their Winds, and Their Nebulae

Massive stars are crucial building blocks of galaxies and the universe, as production sites of heavy elements and as stirring agents and energy providers through stellar winds and supernovae. The field of magnetic massive stars has seen tremendous progress in recent years. Different perspectives—ranging from direct field measurements over dynamo theory and stellar evolution to colliding winds and the stellar environment—fruitfully combine into a most interesting and still evolving overall picture, which we attempt to review here. Zeeman signatures leave no doubt that at least some O- and early B-type stars have a surface magnetic field. Indirect evidence, especially non-thermal radio emission from colliding winds, suggests many more. The emerging picture for massive stars shows similarities with results from intermediate mass stars, for which much more data are available. Observations are often compatible with a dipole or low order multi-pole field of about 1 kG (O-stars) or 300 G to 30?kG (Ap/Bp stars). Weak and unordered fields have been detected in the O-star ζ Ori A and in Vega, the first normal A-type star with a magnetic field. Theory offers essentially two explanations for the origin of the observed surface fields: fossil fields, particularly for strong and ordered fields, or different dynamo mechanisms, preferentially for less ordered fields. Numerical simulations yield the first concrete stable (fossil) field configuration, but give contradictory results as to whether dynamo action in the radiative envelope of massive main sequence stars is possible. Internal magnetic fields, which may not even show up at the stellar surface, affect stellar evolution as they lead to a more uniform rotation, with more slowly rotating cores and faster surface rotation. Surface metallicities may become enhanced, thus affecting the mass-loss rates.     

Polarity Reversals from Paleomagnetic Observations and Numerical Dynamo Simulations

Recent advances in the study of geomagnetic field reversals are reviewed. These include studies of the transitional field during the last geomagnetic reversal and the last geomagnetic excursion based on paleomagnetic observations, and analysis of reversals in self-consistent 3D numerical dynamo simulations. Field models inferred from observations estimate reversal duration in the range of 1–10 kyr (depending on site location). The transitional fields during both the Matuyama/Brunhes reversal and the Laschamp excursion are characterized by low-latitude reversed flux formation and subsequent poleward migration. During both events the dipole as well as the non-dipole field energies decrease. However, while the non-dipole energy dominates the dipole energy for a period of 2 kyr in the reversal, the non-dipole energy merely exceeds the dipole energy for a very brief period during the excursion. Numerical dynamo simulations show that stronger convection, slower rotation, and lower electrical conductivity provide more favorable conditions for reversals. A non-dimensional number that depends on the typical length scale of the flow and represents the relative importance of inertial effects, termed the local Rossby number, seems to determine whether a dynamo will reverse or not. Stable polarity periods in numerical dynamos may last about 1 Myr, whereas reversals may last about 10 kyr. Numerical dynamo reversals often involve prolonged dipole collapse followed by shorter directional instability of the dipole axis, with advective processes governing the field variation. Magnetic upwellings from the equatorial inner-core boundary that produce reversed flux patches at low-latitudes of the core-mantle boundary could be significant in triggering reversals. Inferences from the observational and modeling sides are compared. We summarize with an outlook on some open questions and future prospects.     

Solar Magnetism: The State of Our Knowledge and Ignorance

We review some longstanding scientific mysteries related to solar magnetism, with final attention to the mystery of the “turbulent diffusion” essential for the theoretical α ω-dynamo that is believed to be the source of the magnetic fields of the Sun. Fundamental difficulties with the concept of turbulent diffusion of magnetic fields suggest that the solar dynamo problem needs to be reformulated. An alternative dynamo model is proposed, but it remains to be shown that the model can provide the quantitative aspects of the cyclic magnetic fields of the Sun.     

Origin of Sunspots

Sunspots, seen as cool regions on the surface of the Sun, are a thermal phenomenon. Sunspots are always associated with bipolar magnetic loops that break through the solar surface. Thus to explain the origin of sunspots we have to understand how the magnetic field originates inside the Sun and emerges at its surface. The field predicted by mean-field dynamo theories is too weak by itself to emerge at the surface of the Sun. However, because of the turbulent character of solar convection the fields generated by dynamo are intermittent – i.e., concentrated into ropes or sheets with large spaces in between. The intermittent fields are sufficiently strong to be able to emerge at the solar surface, in spite of the fact that their mean (average) value is weak. It is suggested here that magnetic fields emerge at the solar surface at those random times and places when the total magnetic field (mean field plus fluctuations) exceeds the threshold for buoyancy. The clustering of coherently emerged loops results in the formation of a sunspot. A non-axisymmetric enhancement of the underlying magnetic field causes in the clustering of sunspots forming sunspot groups, clusters of activity and active longitudes. The mean field, which is not directly observable, is also important, being responsible for the ensemble regularities of sunspots, such as Hale's law of sunspot polarities and the 11-year periodicity.     

Energy Supply Processes for Solar Flares and Magnetospheric Substorms

It is shown that solar flares and magnetospheric substorms must primarily be caused by a dynamo process, rather than magnetic reconnection – a spontaneous, explosive annihilation of magnetic energy stored prior to the onset. Magnetic energy in the vicinity of solar flares and in the magnetotail shows often an increase at their onset, not a decrease. It is unfortunate that many observed features of solar flares and substorms have tacitly been ascribed to unproven (3-D) characteristics of the neutral line for a long time. In the future, it is necessary to study carefully their driving process and examine how the driven magnetic field system evolves, leading to solar flares and substorms.     

Lunar Magnetic Field Observation and Initial Global Mapping of Lunar Magnetic Anomalies by MAP-LMAG Onboard SELENE (Kaguya)

The magnetic field around the Moon has been successfully observed at a nominal altitude of ～100 km by the lunar magnetometer (LMAG) on the SELENE (Kaguya) spacecraft in a polar orbit since October 29, 2007. The LMAG mission has three main objectives: (1) mapping the magnetic anomaly of the Moon, (2) measuring the electromagnetic and plasma environment around the Moon and (3) estimating the electrical conductivity structure of the Moon. Here we review the instrumentation and calibration of LMAG and report the initial global mapping of the lunar magnetic anomaly at the nominal altitude. We have applied a new de-trending technique of the Bayesian procedure to multiple-orbit datasets observed in the tail lobe and in the lunar wake. Based on the nominal observation of 14 months, global maps of lunar magnetic anomalies are obtained with 95% coverage of the lunar surface. After altitude normalization and interpolation of the magnetic anomaly field by an inverse boundary value problem, we obtained full-coverage maps of the vector magnetic field at 100 km altitude and the radial component distribution on the surface. Relatively strong anomalies are identified in several basin-antipode regions and several near-basin and near-crater regions, while the youngest basin on the Moon, the Orientale basin, has no magnetic anomaly. These features well agree with characteristics of previous maps based on the Lunar Prospector observation. Relatively weak anomalies are distributed over most of the lunar surface. The surface radial-component distribution estimated from the inverse boundary value problem in the present study shows a good correlation with the radial component distribution at 30 km altitude by Lunar Prospector. Thus these weak anomalies over the lunar surface are not artifacts but likely to be originated from the lunar crustal magnetism, suggesting possible existence of an ancient global magnetic field such as a dynamo field of the early Moon. The possibility of the early lunar dynamo and the mechanism of magnetization acquisition will be investigated by a further study using the low-altitude data of the magnetic field by Kaguya.     

航空直流发电机用轴承的受力分析

对航空直流发电机所选用的轴承进行了受力分析、寿命计算和强度审核。此方法同样适合于航空直流起动发电机和交流发电机轴承的受力分析。