The energy flux number and three types of planetary dynamo

It is proposed that the existence and nature of a planetary dynamo can be characterized by a dimensionless number Φ ≡ F_eR/ϱλ²ω, called the energy flux number, where F_e is the energy flux available for dynamo generation, R is the core radius (or thickness of the dynamo generating region), ϱ is the fluid density, λ is the magnetic diffusivity and ω is the angular velocity. For Φ ≲ 1, there is no dynamo. For 1 ≲ Φ ≲ 10^2.5 there is an “energy-limited dynamo”, in which F_e is insufficient to enable the dynamo to reach the dynamically desirable state A ≡ B²/8πϱλω ∼ 1, where B is a typical field amplitude (in Gauss). For 10^2.5 ≲ Φ ≲ 10⁵, there is a dynamically determined dynamo (Λ ∼ 1) in which the magnetic Reynolds number of turbulent eddies is small. For Φ ≳ 10⁵, there is a turbulent dynamo. Probable planetary examples of these three dynamo states are Mercury (Φ ∼ 10²-10³), Earth (Φ ∼ 10⁴) and Jupiter (Φ ∼ 10¹¹), respectively.     

Recent advances in planetary magnetism

During the past decade, significant advances in thein situ measurements of planetary magnetic fields have been made. The U.S.A. and U.S.S.R. have conducted spacecraft investigations of all the planets, from innermost Mercury out to Jupiter. Unexpectedly, Mercury was found to possess a global magnetic field but neither the Moon nor Venus do. The results at Mars are incomplete butif a global field exists, it is clearly quite weak. The main magnetic field of Jupiter has been measured directly for the first time and confirms, as well as augments appreciably, the past 2 decades of groundbased radio astronomical studies which provided indirect evidence of the field. Progress in developing analytically complete models of the dynamo process suggests a possible common origin for Mercury, Earth and Jupiter.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Dynamo action in an ambient field

The origin of global magnetic fields in celestial bodies is generally ascribed to dynamo action by fluid motions in their electrically conducting interiors. Some objects – e.g. close‐in extra‐solar planets or the moons of some giant planets – are embedded in ambient magnetic fields which modify the generation of the internal field in these bodies. Recently, the feedback of the magnetospheric field by Chapman‐Ferraro currents in the magnetopause onto the interior dynamo has been proposed to explain the observed weakness of the intrinsic magnetic field of planet Mercury. We study a simplified mean‐field dynamo model which allows us to analytically address various issues like positive and negative feedback situations, stationary versus time‐dependent solutions, and the stability of weak and strong field branches. We discuss the influence of the response function on the solutions when the external field depends on the strength of the intrinsic field like in the situation of the feedback dynamo of Mercury. We find that the feedback mechanism works only for a narrow range of dynamo numbers in the case of Mercury which makes him unique in our solar system. We conclude with some implications for extra‐solar planets (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulent dynamo in asymptotic giant branch stars

Using recent results on the operation of turbulent dynamos, we show that a turbulent dynamo may amplify a large-scale magnetic field in the envelopes of asymptotic giant branch (AGB) stars. We propose that a slow rotation of the AGB envelope can fix the symmetry axis, leading to the formation of an axisymmetric magnetic field structure. Unlike solar-type αω dynamos, the rotation has only a small role in amplifying the toroidal component of the magnetic field; instead of an αω dynamo we propose an α ² ω . The magnetic field may reach a value of     , where B _e is the equipartition (between the turbulent and magnetic energy densities) magnetic field. The large-scale magnetic field is strong enough for the formation of magnetic cool spots on the AGB stellar surface. The spots may regulate dust formation, and hence the mass-loss rate, leading to axisymmetric mass loss and the formation of elliptical planetary nebulae (PNe). Despite its role in forming cool spots, the large-scale magnetic field is too weak to play a dynamic role and directly influence the wind from the AGB star, as required by some models. We discuss other possible problems in models where the magnetic field plays a dynamic role in shaping the AGB winds, and argue that they cannot explain the formation of non-spherical PNe.     

Investigations of spherical kinematic mean-field dynamo models

The paper supplements an earlier one on the mean-field approach to spherical kinematic dynamo models (Rädler 1980a) by results of numerical investigations. A number of dynamo models working on the basis of the α²-mechanism are considered. Cases of pure α²-mechanism are studied, which includes only the simplest form of α-effect and no other induction effect, as well as cases with several additional effects due to fluctuating or mean motions. By the pure α²-mechanism axisymmetric and non-axisymmetric fields, can be excited and maintained with nearly equal ease. Part of the additional induction effects, however, clearly favour axisymmetric fields, and others non-axisymmetric fields. The non-axisymmetric fields are waves which travel in azimuthal direction, eastward or westward, depending on the models. For special dynamo models the transition from α² to αω-mechanism and properties of the latter are investigated. The results support the presumption that the αω-mechanism is able to maintain only axisymmetric but never non-axisymmetric fields. Conditions for the occurrence of non-oscillatory or oscillatory fields are discussed, and again the influence of additional induction effects is studied. There are further presented a model with βω-mechanism maintaining an axisymmetric non-oscillatory field, and models with two kinds of δω-mechanisms allowing axisymmetric non-oscillatory and oscillatory fields. Some ideas concerning dynamo models for the Earth, the Sun and magnetic stars are discussed. It seems possible to construct dynamo models for the Earth, on the basis of the α²-mechanism which explain not only the presence of a magnetic field with a strong dipole part but also the inclination of the dipole axis against the axis of rotation, the occurrence of higher multipoles and the westward drift of the non-axisymmetric parts. Models with αω, βω or δω-mechanism, which have to be considered in the case of a strong differential rotation inside the core, provide an explanation at first only of the axisymmetric parts of the field, and the non-axisymmetric parts have then to be interpreted, for example, as MAC-waves. As far as dynamo models for the Sun are concerned, in addition to the possibility of an αω-mechanism also that of a βω or δω-mechanism is discussed, which, however, does not look not very promising. In the models developed so far, which work with the αω-mechanism, only a few of the induction effects of fluctuating motions have been included; it seems necessary to investigate also influences of other effects. The sectorial structure of the solar magnetic field can hardly be understood in terms of the traditional mean-field concept. The magnetic stars possess fields which strongly deviate from symmetry with respect to the axis of rotation. The occurrence of such fields seems understandable only if there is no noticeable differential rotation. They can be maintained by an α²-mechanism but hardly by αω, βω or δω-mechanisms.     

Observations of suprathermal electrons in Mercury's magnetosphere during the three MESSENGER flybys

In 2008 the MESSENGER spacecraft made the first direct observation of Mercury's magnetosphere in the more than 30 years since the Mariner 10 encounters. During MESSENGER's first flyby on 14 January 2008, the interplanetary magnetic field (IMF) was northward immediately prior to and following MESSENGER's equatorial passage through this small magnetosphere. The Energetic Particle Spectrometer (EPS), one of two sensors on the Energetic Particle and Plasma Spectrometer instrument that responds to electrons from ∼35 keV to 1 MeV and ions from ∼35 keV to 2.75 MeV, saw no increases in particle intensity above instrumental background (∼5 particles/cm²/sr/s/keV at 45 keV) at any time during the probe's magnetospheric passage. During MESSENGER's second flyby on 6 October 2008, there was a steady southward IMF, and intense reconnection was observed between the planet's magnetic field and the IMF. However, once again EPS did not observe bursts of energetic particles similar to those reported by Mariner 10 from its March 1974 encounter. On 29 September 2009, MESSENGER flew by Mercury for the third and final time before orbit insertion in March 2011. Although a spacecraft safe-hold event stopped science measurements prior to the outbound portion of the flyby, all instruments recorded full observations until a few minutes before the closest approach. In particular, the MESSENGER Magnetometer documented several substorm-like signatures of extreme loading of Mercury's magnetotail, but again EPS measured no energetic ions or electrons above instrument background during the inbound portion of the flyby. MESSENGER's X-Ray Spectrometer (XRS) nonetheless observed photons resulting from low-energy (∼10 keV) electrons impinging on its detectors during each of the three flybys. We infer that suprathermal plasma electrons below the EPS energy threshold caused the bremsstrahlung seen by XRS. In this paper, we summarize the energetic particle observations made by EPS and XRS during MESSENGER's three Mercury flybys, and we revisit the observations reported by Mariner 10 in the context of these new results.     

Optimal dynamos in the cores of terrestrial exoplanets: Magnetic field generation and detectability

A potentially promising way to gain knowledge about the internal dynamics of extrasolar planets is by remote measurement of an intrinsic magnetic field. Strong planetary magnetic fields, maintained by internal dynamo action in an electrically conducting fluid layer, are helpful for shielding the upper atmosphere from stellar wind induced mass loss and retaining water over long (Gyr) time scales. Here we present a whole planet dynamo model that consists of three main components: an internal structure model with composition and layers similar to the Earth, an optimal mantle convection model that is designed to maximize the heat flow available to drive convective dynamo action in the core, and a scaling law to estimate the magnetic field intensity at the surface of a terrestrial exoplanet. We find that the magnetic field intensity at the core surface can be up to twice the present-day geomagnetic field intensity, while the magnetic moment varies by a factor of 20 over the models considered. Assuming electron cyclotron emission is produced from the interaction between the stellar wind and the exoplanet magnetic field we estimate the cyclotron frequencies around the ionospheric cutoff at 10 MHz with emission fluxes in the range 10⁻⁴-10⁻⁷ Jy, below the current detection threshold of radio telescopes. However, we propose that anomalous boosts and modulations to the magnetic field intensity and cyclotron emission may allow for their detection in the future.     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

Speculations on the origin of the magnetic field of Mercury

The intrinsic magnetic field of Mercury may be generated by a dynamo process in a liquid core, despite the planet's slow rotation rate. It is argued that, provided the core of Mercury is partially liquid, it will be dynamically very similar to that of the Earth.     

Dynamics of electrons and heavy ions in Mercury's magnetosphere

Several basic magnetospheric processes at Mercury have been investigated with simple models. These include the adiabatic acceleration and convection of equatorially mirroring charged particles, the current sheet acceleration effect, and the acceleration of Na⁺ and other exospheric ions by the magnetospheric electric and magnetic fields near the planetary surface. The current steady-state treatment of the magnetospheric drift and convection processes suggests that the region of the inner magnetosphere as explored by the Mariner 10 spacecraft during its encounter with Mercury should be largely devoid of energetic (>100 keV) electrons in equatorial mirroring motion. As for ion motion, the large gyroradii of the heavy ions permit surface reimpact as well as loss via intercepting the magnetopause. Because of the kinetic energy gained in the gyromotion, the first effect could lead to sputtering processes and hence generation of secondary ions and neutrals. The second effect could account for the loss of about 50% of Mercury's exospheric ions.     

Planetary dynamos: effects of electrically conducting flows overlying turbulent regions of magnetic field generation

A fully three-dimensional, nonlinear, time-dependent, multi-layered spherical kinematic dynamo model is used to study the effect on the observable external magnetic field of flow in an electrically conducting layer above a spherical turbulent dynamo region in which the α effect generates the magnetic field. It is shown that the amplitude and structure of an observable planetary magnetic field are largely determined by the magnitude and structure of the flow in the overlying layer. It is also shown that a strong-field planetary dynamo can be readily produced by the effect of an electrically conducting flow layer at the top of a convective core. The overlying layer and the underlying convective region constitute a magnetically strongly coupled system. Such overlying layers might exist at the top of the Earth's core due to chemical or thermal causes, in the cores of other terrestrial planets for similar reasons, and in Saturn due to the differentiation of helium from hydrogen. An electrically conducting and differentially rotating layer could exist above the metallic hydrogen region in Jupiter and affect the jovian magnetic field similar to the overlying layers in other planets. Lateral temperature gradients resulting in thermal winds drive the flow in the overlying layers. All planetary magnetic fields could be maintained by similar turbulent convective dynamos in the field-generation regions of planets with the differences among observable magnetic fields due to different circulations in the overlying electrically conducting layers.     

Electron transport and precipitation at Mercury during the MESSENGER flybys: Implications for electron-stimulated desorption

To examine electron transport, energization, and precipitation in Mercury's magnetosphere, a hybrid simulation study has been carried out that follows electron trajectories within the global magnetospheric electric and magnetic field configuration of Mercury. We report analysis for two solar-wind parameter conditions corresponding to the first two MESSENGER Mercury flybys on January 14, 2008, and October 6, 2008, which occurred for similar solar wind speed and density but contrasting interplanetary magnetic field (IMF) directions. During the first flyby the IMF had a northward component, while during the second flyby the IMF was southward. Electron trajectories are traced in the fields of global hybrid simulations for the two flybys. Some solar wind electrons follow complex trajectories at or near where dayside reconnection occurs and enter the magnetosphere at these locations. The entry locations depend on the IMF orientation (north or south). As the electrons move through the entry regions they can be energized as they execute non-adiabatic (demagnetized) motion. Some electrons become magnetically trapped and drift around the planet with energies on the order of 1–10 keV. The highest energy of electrons anywhere in the magnetosphere is about 25 keV, consistent with the absence of high-energy (>35 keV) electrons observed during either MESSENGER flyby. Once within the magnetosphere, a fraction of the electrons precipitates at the planetary surface with fluxes on the order of 10⁹ cm⁻² s⁻¹ and with energies of hundreds of eV. This finding has important implications for the viability of electron-stimulated desorption (ESD) as a mechanism for contributing to the formation of the exosphere and heavy ion cloud around Mercury. From laboratory estimates of ESD ion yields, a calculated ion production rate due to ESD at Mercury is found to be on par with ion sputtering yields.     

Nonhelical mean‐field dynamos in a sheared turbulence

Mechanisms of nonhelical large‐scale dynamos (shear‐current dynamo and effect of homogeneous kinetic helicity fluctuations with zero mean) in a homogeneous turbulence with large‐scale shear are discussed. We have found that the shearcurrent dynamo can act even in random flows with small Reynolds numbers. However, in this case mean‐field dynamo requires small magnetic Prandtl numbers (i.e., when Pm < Pm^cr < 1). The threshold in the magnetic Prandtl number, Pm^cr = 0.24, is determined using second order correlation approximation (or first‐order smoothing approximation) for a background random flow with a scale‐dependent viscous correlation time τ_c = (νk 2)^–1 (where ν is the kinematic viscosity of the fluid and k is the wave number). For turbulent flows with large Reynolds numbers shear‐current dynamo occurs for arbitrary magnetic Prandtl numbers. This dynamo effect represents a very generic mechanism for generating large‐scale magnetic fields in a broad class of astrophysical turbulent systems with large‐scale shear. On the other hand, mean‐field dynamo due to homogeneous kinetic helicity fluctuations alone in a sheared turbulence is not realistic for a broad class of astrophysical systems because it requires a very specific random forcing of kinetic helicity fluctuations that contains, e.g., low‐frequency oscillations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interest and design of magnetic properties measurements on planetary and asteroidal landers

Intrinsic magnetic properties, like susceptibility, provide a precise determination of the iron phases with a penetration depth not available with other chemical and mineralogical sensing tools, thus allowing to unravel space weathering effects. Systematic measurements of meteorites demonstrate that susceptibility measurements on asteroid surface could be a very efficient way to assign a meteorite class to a given asteroid. Another application could be the characterization of the highly magnetic Martian regolith. On the other hand, natural remanent magnetization (NRM) measurements are crucial to interpret magnetic field anomalies such as those found on Mars and Moon, and likely to be found on Mercury. NRM gives also access to past magnetic fields and extinct planetary dynamo. Rugged, light and low consumption systems already exist for such measurements on Earth and we present a scheme to integrate both magnetic susceptibility (using a LC oscillator) and NRM (using a 3 axis fluxgate or a gradiometer) to offer a versatile instrument package for any mission involving a lander. For the LC oscillator calibration of the geometric factor is presented. The fluxgate can be used both for making local magnetic anomaly maps, thus investigating subsurface structures, and for evaluating NRM of individual boulders.     

The MESSENGER mission to Mercury: scientific objectives and implementation

Mercury holds answers to several critical questions regarding the formation and evolution of the terrestrial planets. These questions include the origin of Mercury's anomalously high ratio of metal to silicate and its implications for planetary accretion processes, the nature of Mercury's geological evolution and interior cooling history, the mechanism of global magnetic field generation, the state of Mercury's core, and the processes controlling volatile species in Mercury's polar deposits, exosphere, and magnetosphere. The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission has been designed to fly by and orbit Mercury to address all of these key questions. After launch by a Delta 2925H-9.5, two flybys of Venus, and two flybys of Mercury, orbit insertion is accomplished at the third Mercury encounter. The instrument payload includes a dual imaging system for wide and narrow fields-of-view, monochrome and color imaging, and stereo; X-ray and combined gamma-ray and neutron spectrometers for surface chemical mapping; a magnetometer; a laser altimeter; a combined ultraviolet–visible and visible-near-infrared spectrometer to survey both exospheric species and surface mineralogy; and an energetic particle and plasma spectrometer to sample charged species in the magnetosphere. During the flybys of Mercury, regions unexplored by Mariner 10 will be seen for the first time, and new data will be gathered on Mercury's exosphere, magnetosphere, and surface composition. During the orbital phase of the mission, one Earth year in duration, MESSENGER will complete global mapping and the detailed characterization of the exosphere, magnetosphere, surface, and interior.     

Mercury’s magnetospheric magnetic field after the first two MESSENGER flybys

The “paraboloid” model of Mercury’s magnetospheric magnetic field is used to determine the best-fit magnetospheric current system and internal dipole parameters from magnetic field measurements taken during the first and second MESSENGER flybys of Mercury on 14 January and 6 October 2008. Together with magnetic field measurements taken during the Mariner 10 flybys on 29 March 1974 and 16 March 1975, there exist three low-latitude traversals separated in longitude and one high-latitude encounter. From our model formulation and fitting procedure a Mercury dipole moment of 196 nT ·  (where R_M is Mercury’s radius) was determined. The dipole is offset from Mercury’s center by 405 km in the northward direction. The dipole inclination to Mercury’s rotation axis is relatively small, ∼4°, with an eastern longitude of 193° for the dipole northern pole. Our model is based on the a priori assumption that the dipole position and the moment orientation and strength do not change in time. The root mean square (rms) deviation between the Mariner 10 and MESSENGER magnetic field measurements and the predictions of our model for all four flybys is 10.7 nT. For each magnetic field component the rms residual is ∼6 nT or about 1.5% of the maximum measured magnetic field, ∼400 nT. This level of agreement is possible only because the magnetospheric current system parameters have been determined separately for each flyby. The magnetospheric stand-off distance, the distance from the planet’s center to the inner edge of the tail current sheet, the tail lobe magnetic flux, and the displacement of the tail current sheet relative to the Mercury solar-magnetospheric equatorial plane have been determined independently for each flyby. The magnetic flux in the tail lobes varied from 3.8 to 5.9 MWb; the subsolar magnetopause stand-off distance from 1.28 to 1.43 R_M; and the distance to the inner edge of the current sheet from 1.23 to 1.32 R_M. The differences in the current systems between the first and second MESSENGER flybys are attributed to the effects of strong magnetic reconnection driven by southward interplanetary magnetic field during the latter flyby.     

Models of magnetic field generation in partly stable planetary cores: Applications to Mercury and Saturn

A substantial part of Mercury's iron core may be stably stratified because the temperature gradient is subadiabatic. A dynamo would operate only in a deep sublayer. We show that such a situation arises for a wide range of values for the heat flow and the sulfur content in the core. In Saturn the upper part of the metallic hydrogen core could be stably stratified because of helium depletion. The magnetic field is unusually weak in the case of Mercury and unusually axisymmetric at Saturn. We study numerical dynamo models in rotating spherical shells with a stable outer region. The control parameters are chosen such that the magnetic Reynolds number is in the range of expected Mercury values. Because of its slow rotation, Mercury may be in a regime where the dipole contribution to the internal magnetic field is weak. Most of our models are in this regime, where the dynamo field consists mainly of rapidly varying higher multipole components. They can hardly pass the stable conducting layer because of the skin effect. The weak low-degree components vary more slowly and control the structure of the field outside the core, whose strength matches the observed field strength at Mercury. In some models the axial dipole dominates at the planet's surface and in others the axial quadrupole is dominant. Differential rotation in the stable layer, representing a thermal wind, is important for attenuating non-axisymmetric components in the exterior field. In some models that we relate to Saturn the axial dipole is intrinsically strong inside the dynamo. The surface field strength is much larger than in the other cases, but the stable layer eliminates non-axisymmetric modes. The Messenger and Bepi Colombo space missions can test our predictions that Mercury's field is large-scaled, fairly axisymmetric, and shows no secular variations on the decadal time scale.     

Aurora on Uranus: A Faraday disc dynamo mechanism

We propose a mechanism whereby the solar wind flowing past the magnetosphere of Uranus causes a Faraday disc dynamo topology to be established and power to be extracted from the kinetic energy of rotation of Uranus. An immediate consequence of this dynamo is the generation of Birkeland currents that flow in and out of the sunlit polar cap with the accompanying production of polar aurora. We calculate the power extracted from planetary rotation as a function of planetary dipole magnetic moment and the ionospheric conductivity of Uranus. For plausible values of ionospheric conductivity, the observed auroral power requires a magnetic moment corresponding to a surface equatorial field of the order of 4 Gauss, slightly larger than the value 1.8 Gauss given by the empirical “magnetic Bodes law”.     

Quenching of Meridional Circulation in Flux Transport Dynamo Models

Guided by the recent observational result that the meridional circulation of the Sun becomes weaker at the time of the sunspot maximum, we have included a parametric quenching of the meridional circulation in solar dynamo models such that the meridional circulation becomes weaker when the magnetic field at the base of the convection zone is stronger. We find that a flux transport solar dynamo tends to become unstable on including this quenching of meridional circulation if the diffusivity in the convection zone is less than about 2×10¹¹ cm² s⁻¹. The quenching of α, however, has a stabilizing effect and it is possible to stabilize a dynamo with low diffusivity with sufficiently strong α-quenching. For dynamo models with high diffusivity, the quenching of meridional circulation does not produce a large effect and the dynamo remains stable. We present a solar-like solution from a dynamo model with diffusivity 2.8×10¹² cm² s⁻¹ in which the quenching of meridional circulation makes the meridional circulation vary periodically with solar cycle as observed and does not have any other significant effect on the dynamo.     

Dipolar magnetic moment of the bodies of the solar system and the Hot Jupiters

Context

The planets magnetic field has been explained based on the dynamo theory, which presents as many difficulties in mathematical terms as well as in predictions. It proves to be extremely difficult to calculate the dipolar magnetic moment of the extrasolar planets using the dynamo theory.

Objective

The aim is to find an empirical relationship (justifying using first principles) between the planetary magnetic moment, the mass of the planet, its rotation period and the electrical conductivity of its most conductive layer. Then this is applied to Hot Jupiters.

Method

Using all the magnetic planetary bodies of the solar system and tracing a graph of the dipolar magnetic moment versus body mass parameter, the rotation period and electrical conductivity of the internal conductive layer is obtained. An empirical, functional relation was constructed, which was adjusted to a power law curve in order to fit the data. Once this empirical relation has been defined, it is theoretically justified and applied to the calculation of the dipolar magnetic moment of the extra solar planets known as Hot Jupiters.

Results

Almost all data calculated is interpolated, bestowing confidence in terms of their validity. The value for the dipolar magnetic moment, obtained for the exoplanet Osiris (HD209458b), helps understand the way in which the atmosphere of a planet with an intense magnetic field can be eroded by stellar wind. The relationship observed also helps understand why Venus and Mars do not present any magnetic field.