Planetary Dynamos Research Articles

Magnetic Taylor-Proudman Constraint Explains Flows into the Tangent Cylinder.

Tangent cylinders (TCs) have shaped our understanding of planetary dynamos and liquid cores. The Taylor-Proudman constraint creates these imaginary surfaces because of planetary rotation, separating polar and equatorial regions, but cannot explain the flows meandering through them. Here, we establish and verify experimentally that magnetic fields aligned with rotation drive flows into TCs, linked to the flows along TCs by a magnetic Taylor-Proudman constraint. This constraint explains and quantifies how magnetic fields reshape rotating flows in planetary interiors and magnetorotating flows in general.

Magnetic Field of Gas Giant Exoplanets and Its Influence on the Retention of Their Exomoons

We study the magnetic and tidal interactions of a gas-giant exoplanet with its host star and with its exomoons, and focus on their retention. We briefly revisit the scaling law for planetary dynamo in terms of its mass, radius, and luminosity. Based on the virial theorem, we construct an evolution law for planetary magnetic field and find that its initial entropy is important for the field evolution of a high-mass planet. We estimate the magnetic torques on orbit arising from the star–planet and planet–moon magnetic interactions, and find that it can compensate tidal torques and bypass frequency valleys where dynamical-tide response is ineffective. For exomoon’s retention, we consider two situations. In the presence of a circumplanetary disk (CPD), by comparison between CPD’s inner and outer radii, we find that planets with too strong magnetic fields or too small distance from its host star tend not to host exomoons. During the subsequent CPD-free evolution, we find, by comparison between a planet’s spin-down and a moon’s migration timescales, that hot Jupiters with periods of several days are unlikely to retain large exomoons, albeit they could be surrounded by rings from the debris of tidally disrupted moons. In contrast, moons, if formed around warm or cold Jupiters, can be preserved. Finally, we estimate the radio power and flux density due to the star–planet and planet–moon magnetic interactions and give the upper limit of detection distance by FAST.

Solenoidal force balances in numerical dynamos

Numerical simulations of the geodynamo (and other planetary dynamos) have made significant progress in recent years. As computing power has advanced, some new models claim to be ever more appropriate for understanding Earth's core dynamics. One measure of the success of such models is the ability to replicate the expected balance between forces operating within the core; Coriolis and Lorentz forces are predicted to be most important. The picture is complicated for an incompressible flow by the existence of the pressure gradient force which renders the gradient parts of all other forces dynamically unimportant. This can confuse the situation, especially when the scale dependence of forces is considered. In this work we investigate force balances through the alternative approach of eliminating gradient parts of each force to form ‘solenoidal force balances’. We perform a length-scale-dependent analysis for several spherical simulations and find that removal of gradient parts offers an alternative picture of the force balance compared with looking at traditional forces alone. Solenoidal force balances provide some agreement with the results of previous studies but also significant differences. They offer a cleaner overall picture of the dynamics and introduce differences at smaller scales. This has implications for geodynamo models purporting to have reached Earth-like regimes: in order to achieve a meaningful comparison of forces, only the solenoidal part of forces should be considered.

Paleomagnetic evidence for a long-lived, potentially reversing martian dynamo at ~3.9 Ga.

The 4.1-billion-year-old meteorite Allan Hills 84001 (ALH 84001) may preserve a magnetic record of the extinct martian dynamo. However, previous paleomagnetic studies have reported heterogeneous, nonunidirectional magnetization in the meteorite at submillimeter scales, calling into question whether it records a dynamo field. We use the quantum diamond microscope to analyze igneous Fe-sulfides in ALH 84001 that may carry remanence as old as 4.1 billion years (Ga). We find that individual, 100-μm-scale ferromagnetic mineral assemblages are strongly magnetized in two nearly antipodal directions. This suggests that the meteorite recorded strong fields following impact heating at 4.1 to 3.95 Ga, after which at least one further impact heterogeneously remagnetized the meteorite in a nearly antipodal local field. These observations are most simply explained by a reversing martian dynamo that was active until 3.9 Ga, thereby implying a late cessation for the martian dynamo and potentially documenting reversing behavior in a nonterrestrial planetary dynamo.

Nonlinear Parametric Resonance in the Simplest Model of a Solar Dynamo

The properties of nonlinear parametric resonance are investigated using the example of the low-mode Parker dynamo model. This model is a system of four ordinary differential equations and in the simplest approximation describes the processes of generation and oscillation of large-scale magnetic fields in stellar systems. In the absence of nonlinear effects, the problem under consideration, by analogy with a system of harmonic oscillations, admits an asymptotic division of multiple resonant frequencies. However, despite the fact that at first glance at these frequencies it is reasonable to expect an amplification of the amplitude in the nonlinear case, it is demonstrated that in the presence of nonlinear terms, the behavior of the system is significantly more complex. In particular, generation suppression can be observed at resonant or low frequencies, while amplification occurs in the immediate vicinity of the resonance or at sufficiently high frequencies. The reasons are discussed for this behavior, as well as the possibility of the influence of parametric resonance on the establishment of planetary dynamo cycles.

Hand Magnets and the Destruction of Ancient Meteorite Magnetism

AbstractMeteorites provide invaluable records of planetary formation and evolution. Studies of their paleomagnetism have constrained accretion in the protoplanetary disk, the thermal evolution and differentiation of planetesimals, and the history of planetary dynamos. Yet, the potential of these magnetic records in advancing the field of planetary science is severely hindered by a widely used technique: application of hand magnets to assist in meteorite classification. Touching a meteorite with a magnet results in near‐instantaneous destruction of its magnetic record. Here, we showcase the destructive effects of exposing meteorites to magnets through numerical modeling, a controlled remagnetization experiment on a terrestrial basalt, and a paleomagnetic study of the oldest known Martian meteorite, the Northwest Africa (NWA) 7034 pairing group. NWA 7034 is a polymict regolith breccia containing zircon crystals with crystallization ages older than 4.4 billion years. As such it contains materials that are sufficiently old to have formed during the time Mars is most likely to have had a core dynamo. Unfortunately, we found that all nine paired stones of NWA 7034 that we investigated were remagnetized by hand magnets, as has been observed for many other hot desert meteorites. We recommend that magnets not be applied to meteorites during collection and curation. Instead, a low‐field susceptibility meter is a far more sensitive and completely nondestructive tool for meteorite classification.

The role of slow magnetostrophic waves in the formation of the axial dipole in planetary dynamos

The preference for the axial dipole in planetary dynamos is investigated through the analysis of wave motions in spherical dynamo models. Our study focuses on the role of slow magnetostrophic waves, which are generated from localized balances between the Lorentz, Coriolis and buoyancy (MAC) forces. Since the slow waves are known to intensify with increasing field strength, simulations in which the field grows from a small seed towards saturation are useful in understanding the role of these waves in dynamo action. Axial group velocity measurements in the energy-containing scales show that fast inertial waves slightly modified by the magnetic field and buoyancy are dominant under weak fields. However, the dominance of the slow waves is evident for strong fields satisfying ∣ωM/ωC∣∼ 0.1, where ωM and ωC are the frequencies of the Alfvén and inertial waves respectively. A MAC wave window of azimuthal wavenumbers is identified in which helicity generation by the slow waves strongly correlates with dipole generation. Analysis of the magnetic induction equation suggests a poloidal–poloidal field conversion in the formation of the dipole. Finally, the attenuation of slow waves may result in polarity reversals in a strongly driven Earth's core.

Maximum Energies of Trapped Particles Around Magnetized Planets and Small Bodies

AbstractEnergetic charged particles trapped in planetary radiation belts are hazardous to spacecraft. Planned missions to iron‐rich asteroids with possible strong remanent magnetic fields require an assessment of trapped particles energies. Using laboratory measurements of iron meteorites, we estimate the largest possible asteroid magnetic moment. Although weak compared to moments of planetary dynamos, the small body size may yield strong surface fields. We use hybrid simulations to confirm the formation of a magnetosphere with an extended quasi‐dipolar region. However, the short length scale of the field implies that energetic particle motion would be nonadiabatic, making existing radiation belt theories not applicable. Our idealized particle simulations demonstrate that chaotic motions lead to particle loss at lower energies than those predicted by adiabatic theory, which may explain the energies of transiently trapped particles observed at Mercury, Ganymede, and Earth. However, even the most magnetized asteroids are unlikely to stably trap hazardous particles.

Tidal dynamo in solar-like close binary stars

Abstract Thermal convection is commonly believed to be the energy source of stellar or planetary dynamo. In this short paper we provide another possibility, namely large-scale tidal flow. In close binary stars, say, solar-like stars with orbital period at 2 or 3 days, large-scale tidal flow is comparable to or even stronger than convective flow, and it can induce magnetic dynamo action. Based on dynamo equation and tidal theory we estimate the magnetic energy induced by large-scale tidal flow, which is proportional to the cube of orbital frequency. Our estimation can be tested by the future spectropolarimetric observations and numerical simulations for close binary stars.

A Dynamo Simulation Generating Saturn‐Like Small Magnetic Dipole Tilts

AbstractAmong planetary dynamos, the magnetic field of Saturn stands out in its exceptional level of axisymmetry. One of its peculiar features is that the magnetic dipole mode is tilted with respect to the planetary rotation axis by only ≈0.007° or less. Numerical dynamo simulations performed in this context have had great difficulty in producing such small dipole tilt angles without introducing ad hoc ingredients such as a latitudinally varying heat flux pattern in the outer layers or stably stratified layers (SSLs). Here we present a numerical dynamo simulation that generates a highly axisymmetric dynamo with a dipole tilt of about ≈0.0008° on average. The model consists of a deep dynamo layer and an overlying low‐conductivity layer but without any SSLs. We highlight a novel mechanism where strong differential rotation generated in the atmospheric layer penetrates into the dynamo region, helping to maintain a very small magnetic dipole tilt.

A New Model of Jupiter's Magnetic Field at the Completion of Juno's Prime Mission

AbstractA spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during 32 of its first 33 polar orbits. These Prime Mission orbits sample Jupiter's magnetic field nearly uniformly in longitude (∼11° separation) as measured at equator crossing. The planetary magnetic field is represented with a degree 30 spherical harmonic and the external field is approximated near the origin with a simple external spherical harmonic of degree 1. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model (“JRM33”) of the planetary magnetic field with spherical harmonic coefficients reasonably well determined through degree and order 13. Useful information regarding the field extends through degree 18, well fit by a Lowes' spectrum with a dynamo core radius of 0.81 Rj, presumably the outer radius of the convective metallic hydrogen region. This new model provides a most detailed view of a planetary dynamo and evidence of advection of the magnetic field by deep zonal winds in the vicinity of the Great Blue Spot (GBS), an isolated and intense patch of flux near Jupiter's equator. Comparison of the JRM33 and JRM09 models suggests secular variation of the field in the vicinity of the GBS during Juno's nearly 5 years of operation in orbit about Jupiter. The observed secular variation is consistent with the penetration of zonal winds to a depth of ∼3,500 km where a flow velocity of ∼0.04 ms−1 is required to match the observations.

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 (Sex) scaling law for strongly coupled liquids, with normalized diffusivity D⋆ = 0.621 exp(0.842Sex) and viscosity η⋆ = 0.171 exp(-0.843Sex). 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 Modular Model of Jupiter's Magnetospheric Magnetic Field Based on Juno Data

AbstractAccurate modeling of Jupiter's magnetospheric magnetic field is important for not only scientific research but also mission planning. We develop a new empirical global model of Jupiter's magnetic field in the Juno era, including components from the planetary dynamo, Chapman‐Ferraro currents, and equatorial current sheet. The internal field is based on the JRM09 model. The shielding field is obtained by minimizing the component normal to Jupiter's magnetopause and varies due to the change of solar wind dynamic pressure. Combined with the curved magnetodisk, the high‐resolution TS07 method is used for modeling Jupiter's magnetodisc and tail currents. The best‐fitting results show an asymmetric magnetodisc current system in azimuthal direction with a tilted angle to Jupiter's magnetic equator. The sweep‐back effects of Jupiter's magnetic fields are also reproduced by the radial current system. This new model is validated by comparing with Juno's magnetometer data in the range from 5 Rj to 60 Rj, where Rj = 71,492 km is the radius of Jupiter.

The Linkage between the Core Mass and the Magnetic Field of an Extrasolar Giant Planet from Future Radio Observations

Abstract Close-in gas giants are expected to have a strong magnetic field of ∼10–100 G. Magnetic fields in extrasolar giant planets are detectable by future radio observations in ≳10 MHz and the spectropolarimetry of atomic lines. In contrast, the elusive interiors of exoplanets remain largely unknown. Here we consider the possibility of inferring the existence of the innermost cores of extrasolar giant planets through the detection of planetary magnetic fields. We simulated the long-term thermal evolution of close-in giant planets with masses of 0.2–10 M Jup to estimate their magnetic field strengths. A young, massive gas giant tends to have a strong magnetic field. The magnetic field strength of a hot Jupiter is insensitive to its core mass, whereas the core strongly affects the emergence of a planetary dynamo in a hot Saturn. No dynamo-driven magnetic field is generated in a hot Saturn with no core or a small one until ∼10–100 Myr if metallization of hydrogen occurs at ≳1–1.5 Mbar. The magnetic field strength of an evolved gas giant after ∼100 Myr is almost independent of the stellar incident flux. Detecting the magnetic field of a young, hot Saturn as a good indicator of its core may be challenging because of the weakness of radio signals and the shielding effect of plasma in Earth’s ionosphere. Hot Jupiters with ≳0.4 M Jup can be promising candidates for future ground-based radio observations.

The underexplored frontier of ice giant dynamos.

The Voyager 2 flybys of Uranus and Neptune revealed the first multipolar planetary magnetic fields and highlighted how much we have yet to learn about ice giant planets. In this review, we summarize observations of Uranus' and Neptune's magnetic fields and place them in the context of other planetary dynamos. The ingredients for dynamo action in general, and for the ice giants in particular, are discussed, as are the factors thought to control magnetic field strength and morphology. These ideas are then applied to Uranus and Neptune, where we show that no models are yet able to fully explain their observed magnetic fields. We then propose future directions for missions, modelling, experiments and theory necessary to answer outstanding questions about the dynamos of ice giant planets, both within our solar system and beyond. This article is part of a discussion meeting issue 'Future exploration of ice giant systems'.

On the helicity characteristics and induced emf of magnetic-Coriolis wave packets

SUMMARY In a rapidly rotating Boussinesq fluid, buoyant anomalies radiate low-frequency inertial wave packets that disperse along the rotation axis. The wave packets lead to axially elongated vortices, which propagate negative (positive) kinetic helicity upwards (downwards) with respect to the rotation vector. The kinetic helicity carried by the inertial wave packets is near-maximal relative to the velocity and vorticity fields. In classical mean-field theory, kinetic helicity is often associated with the α-effect, which is thought to be an important ingredient for planetary dynamos. The modification of inertial wave packets in the presence of a transverse uniform magnetic field is investigated here, motivated by small-scale dynamics in planetary cores, where a large-scale magnetic field affects fluid motions. We study numerically the dispersion of wave packets from an isolated buoyant source and from a random layer of buoyant anomalies, while varying the Lehnert number Le—the ratio of the frequencies of Alfvén and inertial waves. We find that for Le < 0.1, the vortices are columnar and continue to segregate kinetic helicity so that it is negative (positive) above (below) the buoyant source. Importantly, the wave packets induce an α-effect, which remains strong and coherent for Earth-like values of the Lehnert number (Le < 0.1). The interaction of wave packets emitted by multiple neighbouring buoyant sources results in an α-effect that is stronger than the α-effect induced by wave packets launched from an isolated buoyant source, and we provide an analytical explanation for this. The coherence of the α-effect induced by the wave packets, for Earth-like values of the Lehnert number, lends support to the α2 dynamo model driven by helical waves.

Lagrangian Statistics of Heat Transfer in Homogeneous Turbulence Driven by Boussinesq Convection

The movement of heat in a convecting system is typically described by the nondimensional Nusselt number, which involves an average over both space and time. In direct numerical simulations of turbulent flows, there is considerable variation in the contributions to the Nusselt number, both because of local spatial variations due to plumes and because of intermittency in time. We develop a statistical approach to more completely describe the structure of heat transfer, using an exit-distance extracted from Lagrangian tracer particles, which we call the Lagrangian heat structure. In a comparison between simulations of homogeneous turbulence driven by Boussinesq convection, the Lagrangian heat structure reveals significant non-Gaussian character, as well as a clear trend with Prandtl number and Rayleigh number. This has encouraging implications for simulations performed with the goal of understanding turbulent convection in natural settings such as Earth’s atmosphere and oceans, as well as planetary and stellar dynamos.

Stability of H3O at extreme conditions and implications for the magnetic fields of Uranus and Neptune

The anomalous nondipolar and nonaxisymmetric magnetic fields of Uranus and Neptune have long challenged conventional views of planetary dynamos. A thin-shell dynamo conjecture captures the observed phenomena but leaves unexplained the fundamental material basis and underlying mechanism. Here we report extensive quantum-mechanical calculations of polymorphism in the hydrogen-oxygen system at the pressures and temperatures of the deep interiors of these ice giant planets (to >600 GPa and 7,000 K). The results reveal the surprising stability of solid and fluid trihydrogen oxide (H3O) at these extreme conditions. Fluid H3O is metallic and calculated to be stable near the cores of Uranus and Neptune. As a convecting fluid, the material could give rise to the magnetic field consistent with the thin-shell dynamo model proposed for these planets. H3O could also be a major component in both solid and superionic forms in other (e.g., nonconvecting) layers. The results thus provide a materials basis for understanding the enigmatic magnetic-field anomalies and other aspects of the interiors of Uranus and Neptune. These findings have direct implications for the internal structure, composition, and dynamos of related exoplanets.

On magnetostrophic dynamos in annular cores

ABSTRACTMagnetostrophic dynamos are studied in an annular core, adapting the seminal work of Taylor [The magnetohydrodynamics of a rotating fluid and the Earth's dynamo problem. Proc. R. Soc. London A. 1963, 274, 274] for a fluid-filled core. The model consists of an inviscid fluid core and a concentric solid inner core. The fluid is supposed to obey the Boussinesq equations of motion and is driven into motion by a flow-forcing function consisting of the buoyancy force of an adverse radial temperature gradient, opposed by the Lorentz force of the self-sustained magnetic field. Coriolis forces act but inertial and viscous forces are ignored. Taylor (1963) showed how such a “magnetostrophic dynamo” can be found when there is no solid inner core, but his ideas have to be non-trivially generalised when an inner core is present. That is undertaken in this paper. In the 1993, CUP book, “Theory of Solar and Planetary Dynamos”, Hollerbach and Proctor gave examples in which the zonal flow created by a specified flow-forcing function may be singular on the “tangent cylinder”, an imaginary cylinder tangential to the inner core and parallel to the polar axis. It is shown here how this singularity is related to the flow-forcing function, and how discontinuities of other components of the fluid velocity on the tangent cylinder are determined by that function. In appendix A, an identity is established between the leading terms in the Fourier expansion of two of the cylindrical components of an arbitrary vector field. In appendix B, eight examples are given relevant to annular dynamos. In appendix C, equatorial symmetry is considered.

A physical conjecture for the dipolar–multipolar dynamo transition

In numerical simulations of planetary dynamos there is an abrupt transition in the dynamics of both the velocity and magnetic fields at a ‘local’ Rossby number of 0.1. For smaller Rossby numbers there are helical columnar structures aligned with the rotation axis, which efficiently maintain a dipolar field. However, when the thermal forcing is increased, these columns break down and the field becomes multi-polar. Similarly, in rotating turbulence experiments and simulations there is a sharp transition at a Rossby number of ${\sim}0.4$. Again, helical axial columnar structures are found for lower Rossby numbers, and there is strong evidence that these columns are created by inertial waves, at least on short time scales. We perform direct numerical simulations of the flow induced by a layer of buoyant anomalies subject to strong rotation, inspired by the equatorially biased heat flux in convective planetary dynamos. We assess the role of inertial waves in generating columnar structures. At high rotation rates (or weak forcing) we find columnar flow structures that segregate helicity either side of the buoyant layer, whose axial length scale increases linearly, as predicted by the theory of low-frequency inertial waves. As the rotation rate is weakened and the magnitude of the buoyant perturbations is increased, we identify a portion of the flow which is more strongly three-dimensional. We show that the flow in this region is turbulent, and has a Rossby number above a critical value $Ro^{crit}\sim 0.4$, consistent with previous findings in rotating turbulence. We suggest that the discrepancy between the transition value found here (and in rotating turbulence experiments), and that seen in the numerical dynamos ($Ro^{crit}\sim 0.1$), is a result of a different choice of the length scale used to define the local $Ro$. We show that when a proxy for the flow length scale perpendicular to the rotation axis is used in this definition, the numerical dynamo transition lies at $Ro^{crit}\sim 0.5$. Based on this we hypothesise that inertial waves, continually launched by buoyant anomalies, sustain the columnar structures in dynamo simulations, and that the transition documented in these simulations is due to the inability of inertial waves to propagate for $Ro>Ro^{crit}$.