Possibilities and difficulties of applying the theory of magnetic field generation by convection flows in rotating spherical fluid shells to the Giant Planets are outlined. Recent progress in the understanding of the distribution of electrical conductivity in the Giant Planets suggests that the dynamo process occurs predominantly in regions of semiconductivity. In contrast to the geodynamo the magnetic field generation in the Giant Planets is thus characterized by strong radial conductivity variations. The importance of the constraint on the Ohmic dissipation provided by the planetary luminosity is emphasized. Planetary dynamos are likely to be of an oscillatory type, although these oscillations may not be evident from the exterior of the planets.
This Special Topic focuses on magnetohydrodynamic (MHD) processes in deep interiors of planets, in which their fluid dynamos are in operation. The dynamo-generated, global, magnetic fields provide a background for our solar-terrestrial environment. Probing the processes within the dynamos is a significant theoretical and computational challenge and any window into interior dynamics greatly increases our understanding. Such a window is provided by exploring rapid dynamics, particularly MHD waves about the dynamo-defined basic state. This field is the subject of current attention as geophysical …
We present a dynamo mechanism arising from the presence of barotropically unstable zonal jet currents in a rotating spherical shell. The shear instability of the zonal flow develops in the form of a global Rossby mode, whose azimuthal wavenumber depends on the width of the zonal jets. We obtain self-sustained magnetic fields at magnetic Reynolds numbers greater than 1000. We show that the propagation of the Rossby waves is crucial for dynamo action. The amplitude of the axisymmetric poloidal magnetic field depends on the wavenumber of the Rossby mode, and hence on the width of the zonal jets. …
Dynamos operating in the interiors of rapidly rotating planets and low-mass stars might belong to a similar category where rotation plays a vital role. We quantify this similarity using scaling laws. We analyse direct numerical simulations of Boussinesq and anelastic spherical shell dynamos. These dynamos represent simplified models which span from Earth-like planets to rapidly rotating low-mass stars. We find that magnetic field and velocity in these dynamos are related to the available buoyancy power via a simple power law which holds over wide variety of control parameters.
The numerical simulations of planetary dynamos still operate in a regime very far from the planets. For example, it seems unlikely that viscous forces are at all significant in planetary interiors, yet some of the simulations display a significant dependence on viscosity, and indeed in some of the simulations the dynamo mechanism is itself viscously driven, taking the form of helical Ekman pumping within columnar convection rolls. Given the similarity of the external magnetic fields observed in the terrestrial planets and gas giants, and the extremely small value of the Ekman number in all suc…
Recent discoveries of water-rich, sub-Neptunian to Neptunian-massed exoplanets with short-period orbits present a new parameter space for the study of exoplanetary dynamos. We explore the geometry of the dynamo source region within this parameter space using 1-D interior structure models. We model planets with 4 chemically distinct layers that consist of (1) an iron core, (2) a silicate layer, (3) an H2O layer, and (4) an H/He envelope. By varying the total planetary mass in the range of 1 - 19 Earth masses, the mass fraction of the H/He envelope between 0.1 - 5.1%, and the equilibrium tempera…
Planetary and stellar magnetic fields are thought to be sustained by helical motions ($α$-effect) and, if present, differential rotation ($Ω$-effect). In the Sun, the strong differential rotation in the tachocline is responsible for an efficient $Ω$-effect creating a strong axisymmetric azimuthal magnetic field. This is a prerequisite for Parker dynamo waves that may be responsible for the solar cycle. In the liquid iron cores of terrestrial planets, the Coriolis force organizes convection into columns with a strong helical flow component. These likely dominate magnetic field generation while …
In this paper, we find the internal stratification for terrestrial planets with given mass-radius pairs, and use the core size and density to estimate their maximum dipolar magnetic moment. We also comment on the temporal evolution, although more information (e.g., core composition, mantle rheology and history) is crucial in determining the state of the dynamo with planetary age.
We propose new scaling laws for the properties of planetary dynamos. In particular, the Rossby number, the magnetic Reynolds number, the ratio of magnetic to kinetic energy, the Ohmic dissipation timescale and the characteristic aspect ratio of the columnar convection cells are all predicted to be power-law functions of two observable quantities: the magnetic dipole moment and the planetary rotation rate. The resulting scaling laws constitute a somewhat modified version of the scalings proposed in Christensen & Aubert (2006) and Christensen (2010). The main difference is that, in view of the s…
Hot Jupiters have proven themselves to be a rich class of exoplanets which test our theories of planetary evolution and atmospheric dynamics under extreme conditions. Here, we present three-dimensional magnetohydrodynamic simulations and analytic results which demonstrate that a dynamo can be maintained in the thin, stably-stratified atmosphere of a hot Jupiter, independent of the presumed deep-seated dynamo. This dynamo is maintained by conductivity variations arising from strong asymmetric heating from the planets' host star. The presence of a dynamo significantly increases the surface magne…
The geo and solar magnetic fields have long been thought to be very different objects both in terms of spatial structure and temporal behavior. The recently discovered field structure of a fully convective star is more reminiscent of planetary magnetic fields than the Sun's magnetic field (Donati J.-F. et al., Science, 311 (2006) 633), despite the fact that the physical and chemical properties of these objects clearly differ. This observation suggests that a simple controlling parameter could be responsible for these different behaviors. We report here the results of three-dimensional simulati…
We review some of the recent progress on modeling planetary and stellar dynamos. Particular attention is given to the dynamo mechanisms and the resulting properties of the field. We present direct numerical simulations using a simple Boussinesq model. These simulations are interpreted using the classical mean-field formalism. We investigate the transition from steady dipolar to multipolar dynamo waves solutions varying different control parameters, and discuss the relevance to stellar magnetic fields. We show that owing to the role of the strong zonal flow, this transition is hysteretic. In th…
The magnetization of solar and extrasolar gas giants is critically dependent on electronic and mass transport coefficients of their convective fluid interiors. We analyze recent laboratory experimental results on metallic hydrogen to derive a new conductivity profile for the Jovian-like planets. We combine this revised conductivity with a polytropic-based thermodynamic equation of state to study the dynamo action in 100 extrasolar giant planets varying from synchronous hot jupiters to fast rotators, with masses ranging from 0.3MJ to 15MJ. We find conducting cores larger than previous estimates…
The thermal evolution of rocky planets on geological timescales (Gyr) depends on the heat input from the long-lived radiogenic elements potassium, thorium, and uranium. Concentrations of the latter two in rocky planet mantles are likely to vary by up to an order of magnitude between different planetary systems because Th and U, like other heavy r-process elements, are produced by rare stellar processes. Here we discuss the effects of these variations on the thermal evolution of an Earth-size planet, using a 1D parameterized convection model. Assuming Th and U abundances consistent with geochem…
The Juno mission is delivering spectacular data of Jupiter's magnetic field, while the gravity measurements finally allow constraining the depth of the winds observed at cloud level. However, to which degree the zonal winds contribute to the planet's dynamo action remains an open question. Here we explore numerical dynamo simulations that include an Jupiter-like electrical conductivity profile and successfully model the planet's large scale field. We concentrate on analyzing the dynamo action in the Steeply Decaying Conductivity Region (SDCR) where the high conductivity in the metallic Hydroge…
Glorified dimensional analysis is used to derive scaling rules for internal and external magnetic field strengths and various time scales. Naive dimensional analysis is inconclusive because of multiple time scales, but physical arguments serve to weed out irrelevant parameters. Time scales can be derived from linearized instability analysis instead of ill-founded assumptions of Magnetic-Archimedean-Coriolis (MAC) balance. Further relationships can be derived from high-level models of coupled main field components and differential rotation. The ratios of the external dipole field to internal ma…
To ascertain whether magnetic dynamos operate in rocky exoplanets more massive or hotter than the Earth, we developed a parametric model of a differentiated rocky planet and its thermal evolution. Our model reproduces the established properties of Earth's interior and magnetic field at the present time. When applied to Venus, assuming that planet lacks plate tectonics and has a dehydrated mantle with an elevated viscosity, the model shows that the dynamo shuts down or never operated. Our model predicts that at a fixed planet mass, dynamo history is sensitive to core size, but not to the initia…
Among 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 $\approx 0.007^{\circ}$ 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 (SSL). Here we present a numerical dynamo simulation that generates a highly…
Long-lived thermal dynamo generation on differentiated, impact-disrupted planetesimals
organization= Centre for Planetary Habitability , addressline= Department of Geosciences, University of Oslo , city= Oslo , country= Norway；organization= Department of Earth Sciences , addressline= University of Oxford, South Parks Road , city= Oxford , postcode= OX1 3AN , country= UK
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…
We present a thermal evolution model coupled with a Henyey solver to study the circumstances under which a rocky planet could potentially host a dynamo in its liquid iron core and/or magma ocean. We calculate the evolution of planet thermal profiles by solving the energy balance equations for both the mantle and the core. We use a modified mixing length theory to model the convective heat flow in both the magma ocean and solid mantle. In addition, by including the Henyey solver, we self-consistently account for adjustments in the interior structure and heating (cooling) due to planet contracti…
Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo proble…
The paper considers dynamo generated by a shallow fluid layer in a celestial body (planet or star). This dynamo is based on the extra invariant for interacting magnetic Rossby waves. The magnetohydrodynamics (MHD) is linearized on the background of strong toroidal magnetic field. The extra invariant is used to show that the background field is maintained.
On the weak synchronization of a nonlinear solar dynamo oscillator by coherent planetary timing
Académie des Sciences, Institut de France（法兰西科学院，法兰西学院）；Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences（俄罗斯科学院地震预测理论与数学地球物理研究所）；Accademia Nazionale delle Scienze detta dei XL（XL国家科学学院）；DeepField Sensing；Muséum National d’Histoire Naturelle, CNRS, UMR 7196, INSERM U1154（法国国家自然历史博物馆，CNRS，UMR 7196，INSERM U1154）；Sorbonne Université, CNRS, METIS, UMR 7619（索邦大学，CNRS，METIS，UMR 7619）
The observed surface dynamics of Jupiter and Saturn is dominated by a banded system of zonal winds. Their depth remains unclear but they are thought to be confined to the very outer envelopes where hydrogen remains molecular and the electrical conductivity is small. The dynamo maintaining the dipole-dominated magnetic fields of both gas giants likely operates in the deeper interior where hydrogen assumes a metallic state. Here, we present numerical simulations that attempt to model both the zonal winds and the interior dynamo action in an integrated approach. Using the anelastic version of the…
Planetary magnetic fields could impact the evolution of planetary atmospheres and have a role in the determination of the required conditions for the emergence and evolution of life (planetary habitability). We study here the role of rotation in the evolution of dynamo-generated magnetic fields in massive earth-like planets, Super Earths (1-10 $M_\oplus$). Using the most recent thermal evolution models of Super Earths (Gaidos et al. 2010; Tachinami et al. 2011) and updated scaling laws for convection-driven dynamos, we predict the evolution of the local Rossby number. This quantity is one of t…
We report on our continued efforts to understand and delineate the magnetic dynamo-induced behavior/variability of red dwarf (K5 V - M6 V) stars over their long lifetimes. These properties include: rotation, light variations (from star spots), coronal-chromospheric XUV activity and flares. This study is being carried out as part of the NSF-sponsored Living with a Red Dwarf program. The Living with a Red Dwarf program's database of dM stars with photometrically determined rotation rates (from starspot modulations) continues to expand, as does the inventory of archival XUV observations. When all…
The Juno mission will measure Jupiter's magnetic field with unprecedented precision and provide a wealth of additional data that will allow to constrain the planet's interior structure and dynamics. Here we analyse 66 numerical simulations in order to explore the sensitivity of the dynamo-generated magnetic field to the planets interior properties. The degree l=4 field model VIP4 and up-to-date interior models based on ab initio simulations serve as benchmarks. Our results suggest that VIP4-like magnetic fields can be found for a number of different models. We find that whether we assume an id…
We used a thermal model of an iron core to calculate magnetodynamo evolution in Earth-mass rocky planets to determine the sensitivity of dynamo lifetime and intensity to planets with different mantle tectonic regimes, surface temperatures, and core properties. The heat flow at the core-mantle boundary (CMB) is derived from numerical models of mantle convection with a viscous/pseudo-plastic rheology that captures the phenomenology of plate-like tectonics. Our thermal evolution models predict a long-lived (~8 Gyr) field for Earth and similar dynamo evolution for Earth-mass exoplanets with plate …
Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significan…
We show that hemispherical dynamos can result from weak equatorial symmetry breaking of the flow in the interior of planets and stars. Using a model of spherical dynamo, we observe that the interaction between a dipolar and a quadrupolar mode can localize the magnetic field in only one hemisphere when the equatorial symmetry is broken. This process is shown to be related to the one that is responsible for reversals of the magnetic field. These seemingly very different behaviors are thus understood in a unified framework.
The migration of the giant planets due to the scattering of planetesimals causes powerful resonances to move through the asteroid belt and the terrestrial planet region. Exactly when and how the giant planets migrated is not well known. In this paper we present results of an investigation of the formation of the terrestrial planets during and after the migration of the giant planets. The latter is assumed to have occurred immediately after the dissipation of the nebular disk -- i.e. "early" with respect to the timing of the Late Heavy Bombardment (LHB). The presumed cause of our modeled early …
Exoplanetary systems host giant planets on substantially non-circular, close-in orbits. We propose that these eccentricities arise in a phase of giant impacts, analogous to the final stage of Solar System assembly that formed Earth's Moon. In this scenario, the planets scatter each other and collide, with corresponding mass growth as they merge. We numerically integrate an ensemble of systems with varying total planet mass, allowing for collisional growth, to show that (1) the high-eccentricity giants observed today may have formed preferentially in systems of higher initial total planet mass,…
The detection of many extrasolar gas giants with high eccentricities indicates that dynamical instabilities in planetary systems are common. These instabilities can alter the orbits of gas giants as well as the orbits of terrestrial planets and therefore eject or move a habitable planet out of the habitable zone. In this work 423 simulations with 153 different hypothetical planetary systems with gas giants and terrestrial planets have been modelled to explore the orbital stability of habitable planets. The initial parameter variations include the number, distances and masses of the giant plane…
In this chapter we summarize current knowledge of the internal structure of giant planets. We concentrate on the importance of heavy elements and their role in determining the planetary composition and internal structure, in planet formation, and during the planetary long-term evolution. We briefly discuss how internal structure models are derived, present the possible structures of the outer planets in the Solar System, and summarise giant planet formation and evolution. Finally, we introduce giant exoplanets and discuss how they can be used to better understand giant planets as a class of pl…
The orbital distributions of currently observed extrasolar giant planets allow marginally stable orbits for hypothetical, terrestrial planets. In this paper, we propose that many of these systems may not have additional planets on these "stable" orbits, since past dynamical instability among giant planets could have removed them. We numerically investigate the effects of early evolution of multiple giant planets on the orbital stability of the inner, sub-Neptune-like planets which are modeled as test particles, and determine their dynamically unstable region. Previous studies have shown that t…
Evidence of mutually inclined planetary orbits has been reported for giant planets these last years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and investigate whether it can possibly lead to the existence of inclined terrestrial planets. We have performed 126 simulations of the late-stage planetary accretion in eccentric and inclined giant planet systems. The physical and orbital parameters of the giant planet systems result from n-body simulations of three giant planets in the late stage of the gas disc, under …
Giant planet migration is an important phenomenon in the evolution of planetary systems. Recent works have shown that giant planet growth and migration can shape the asteroid belt, but these works have not considered interactions between planetesimals. We have calculated the evolution of planetesimal disks, including planetesimal-planetesimal collisions, during gas giant growth and migration. The numbers, locations, and impact velocities of these collisions depend on the specific growth and migration path. We find that giant planet growth alone has little effect on impact velocities, and most …
The giant planets of the solar system likely played a large role in shaping the architecture of the terrestrial planets. Using an updated collision model, we conduct a suite of high resolution N-body integrations to probe the relationship between giant planet mass, and terrestrial planet formation and system architecture. We vary the mass of the planets that reside at Jupiter's and Saturn's orbit and examine the effects on the interior terrestrial system. We find a correlation between the mass of the exterior giant planets and the collision history of the resulting planets, which holds implica…
Eating planets makes you younger: The magnetic dynamo rejuvenation of GJ 504 by planetary engulfment
Leiden University（莱顿大学）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）；Université de Liège（列日大学）；Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Roma（意大利国家天体物理研究所罗马天文台）；University of Oslo（奥斯陆大学）；Eberhard-Karls Universität Tübingen（蒂宾根大学）
The generation of magnetic field in an electrically conducting fluid generally involves the complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process is of great importance in geophysics, planetary science and astrophysics, since magnetic fields are known to play a key role in the dynamics of these systems. This paper gives an introduction to dynamo theory for the fluid dynamicist. It proceeds by laying the groundwork, introducing the equations and techniques that are at the heart of dynamo theory, before presenting some simple dynamo solutions. The problems…
The presence of giant planets influences potentially habitable worlds in numerous ways. Massive celestial neighbors can facilitate the formation of planetary cores and modify the influx of asteroids and comets towards Earth-analogs later on. Furthermore, giant planets can indirectly change the climate of terrestrial worlds by gravitationally altering their orbits. Investigating 147 well characterized exoplanetary systems known to date that host a main sequence star and a giant planet we show that the presence of 'giant neighbors' can reduce a terrestrial planet's chances to remain habitable, e…
A large fraction of known Jupiter like exoplanets are inflated as compared to Jupiter. These "hot" Jupiters orbit close to their parent star and are bombarded with intense starlight. Many theories have been proposed to explain their radius inflation and several suggest that a small fraction of the incident starlight is injected in to the planetary interior which helps to puff up the planet. How will such energy injection affect the planetary dynamo? In this Letter, we estimate the surface magnetic field strength of hot Jupiters using scaling arguments that relate energy available in planetary …
