Global MHD modeling of Mercury's magnetosphere with applications to the MESSENGER mission and dynamo theory

We use a global magnetohydrodynamic (MHD) model to simulate Mercury's space environment for several solar wind and interplanetary magnetic field (IMF) conditions in anticipation of the magnetic field measurements by the MESSENGER spacecraft. The main goal of our study is to assess what characteristics of the internally generated field of Mercury can be inferred from the MESSENGER observations, and to what extent they will be able to constrain various models of Mercury's magnetic field generation. Based on the results of our simulations, we argue that it should be possible to infer not only the dipole component, but also the quadrupole and possibly even higher harmonics of the Mercury's planetary magnetic field. We furthermore expect that some of the crucial measurements for specifying the Hermean internal field will be acquired during the initial fly-bys of the planet, before MESSENGER goes into orbit around Mercury.     

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.     

Numerical simulations of type I planetary migration in non-turbulent magnetized discs

Using 2D magnetohydrodynamic (MHD) numerical simulations performed with two different finite-difference Eulerian codes, we analyse the effect that a toroidal magnetic field has on low-mass planet migration in non-turbulent protoplanetary discs. The presence of the magnetic field modifies the waves that can propagate in the disc. In agreement with a recent linear analysis, we find that two magnetic resonances develop on both sides of the planet orbit, which contribute to a significant global torque. In order to measure the torque exerted by the disc on the planet, we perform simulations in which the latter is either fixed on a circular orbit or allowed to migrate. For a     planet, when the ratio β between the square of the sound speed and that of the Alfven speed at the location of the planet is equal to 2, we find inward migration when the magnetic field   B _φ  is uniform in the disc, reduced migration when   B _φ  decreases as   r ⁻¹  and outward migration when   B _φ  decreases as   r ⁻²  . These results are in agreement with predictions from the linear analysis. Taken as a whole, our results confirm that even a subthermal stable field can stop inward migration of an earth-like planet.     

The fate of sub-micron circumplanetary dust grains I: Aligned dipolar magnetic fields

We study the stability of charged dust grains orbiting a planet and subject to gravity and the electromagnetic force. Our numerical models cover a broad range of launch distances from the planetary surface to beyond synchronous orbit, and the full range of charge-to-mass ratios from ions to rocks. Treating the spinning planetary magnetic field as an aligned dipole, we map regions of radial and vertical instability where dust grains are driven to escape or crash into the planet. We derive the boundaries between stable and unstable trajectories analytically, and apply our models to Jupiter, Saturn and the Earth, whose magnetic fields are reasonably well represented by aligned dipoles.     

Magnetic cycles of the planet-hosting star τ Bootis – II. A second magnetic polarity reversal

In this paper, we present new spectropolarimetric observations of the planet-hosting star τ Bootis, using ESPaDOnS and Narval spectropolarimeters at Canada–France–Hawaii Telescope and Telescope Bernard Lyot, respectively.
We detected the magnetic field of the star at three epochs in 2008. It has a weak magnetic field of only a few gauss, oscillating between a predominant toroidal component in January and a dominant poloidal component in June and July. A magnetic polarity reversal was observed relative to the magnetic topology in 2007 June. This is the second such reversal observed in 2 years on this star, suggesting that τ Boo has a magnetic cycle of about 2 years. This is the first detection of a magnetic cycle for a star other than the Sun. The role of the close-in massive planet in the short activity cycle of the star is questioned.
τ Boo has a strong differential rotation, a common trend for stars with shallow convective envelope. At latitude 40°, the surface layer of the star rotates in 3.31 d, equal to the orbital period. Synchronization suggests that the tidal effects induced by the planet may be strong enough to force at least the thin convective envelope into corotation.
τ Boo shows variability in the Ca  ii H & K and Hα throughout the night and on a night-to-night time-scale. We do not detect enhancement in the activity of the star that may be related to the conjunction of the planet. Further data are needed to conclude about the activity enhancement due to the planet.     

Analytical Estimation of the Scale of Earth-Like Planetary Magnetic Fields

In this paper we analytically estimate the magnetic field scale of planets with physical core conditions similar to that of Earth from a statistical physics point of view. We evaluate the magnetic field on the basis of the physical parameters of the center of the planet, such as density, temperature, and core size. We look at the contribution of the Seebeck effect on the magnetic field, showing that a thermally induced electrical current can exist in a rotating fluid sphere. We apply our calculations to Earth, where the currents would be driven by the temperature difference at the outer-inner core boundary, Jupiter and the Jupiter’s satellite Ganymede. In each case we show that the thermal generation of currents leads to a magnetic field scale comparable to the observed fields of the considered celestial bodies.     

Magnetized Mars: Transformation of Earth-like magnetosphere to Venus-like induced magnetosphere

Using a global numerical model, we have studied how the present Martian magnetosphere may have looked in the past when the planet had a global intrinsic magnetic field. A Mars version (HYB-Mars) of the self-consistent quasi-neutral hybrid model was used which treats the ions as particles and the electrons as a massless charge-neutralizing fluid. We compare four cases where an intrinsic dipole magnetic field was 0 nT (the present situation), 10, 30, and 60 nT at the surface of Mars along the magnetic equator. We find that the 10 nT dipolar magnetic field already results in a magnetosphere which in many respects is more Earth-like than, a non-magnetized, “induced” magnetosphere. However, the 10 nT dipole magnetosphere is still relatively strongly connected to the interplanetary magnetic field, while the 30 nT dipole case, and especially the 60 nT dipole case, results in a magnetosphere whose morphology is determined predominantly by the Martian intrinsic magnetic field. A change of the magnetosphere due to a decreasing dipole magnetic field strength from 60 to 0 nT could have happened during the history of Mars when a globally magnetized Mars turned into the present, globally non-magnetized, planet.     

Plasma interactions of exoplanets with their parent star and associated radio emissions

The relatively high contrast between planetary and solar low-frequency radio emissions suggests that the low-frequency radio range may be well adapted to the direct detection of exoplanets. We review the most significant properties of planetary radio emissions (auroral as well as satellite induced) and show that their primary engine is the interaction of a plasma flow with an obstacle in the presence of a strong magnetic field (of the flow or of the obstacle). Scaling laws have been derived from solar system planetary radio emissions that relate the emitted radio power to the power dissipated in the various corresponding flow–obstacle interactions. We generalize these scaling laws into a “radio-magnetic” scaling law that seems to relate output radio power to the magnetic energy flux convected on the obstacle, this obstacle being magnetized or unmagnetized. Extrapolating this scaling law to the case of exoplanets, we find that hot Jupiters may produce very intense radio emissions due to either magnetospheric interaction with a strong stellar wind or to unipolar interaction between the planet and a magnetic star (or strongly magnetized regions of the stellar surface). In the former case, similar to the magnetosphere–solar wind interactions in our solar system or to the Ganymede–Jupiter interaction, a hecto-decameter emission is expected in the vicinity of the planet with an intensity possibly 10³–10⁵ times that of Jupiter's low frequency radio emissions. In the latter case, which is a giant analogy of the Io–Jupiter system, emission in the decameter-to-meter wavelength range near the footprints of the star's magnetic field lines interacting with the planet may reach 10⁶ times that of Jupiter (unless some “saturation” mechanism occurs). The system of HD179949, where a hot spot has been tentatively detected in visible light near the sub-planetary point, is discussed in some details. Radio detectability is addressed with present and future low-frequency radiotelescopes. Finally, we discuss the interests of direct radio detection, among which access to exoplanetary magnetic field measurements and comparative magnetospheric physics.     

MHD simulation scenarios of the stellar wind interaction with Hot Jupiter magnetospheres

We present three-dimensional numerical simulations of the interaction between a Hot Jupiter and the stellar wind plasma of its host star in the framework of resistive magnetohydrodynamics (MHD). In a first step, we investigate the numerical realization of the plasma flow around the planet and the planetary magnetic field using a simplified model, before we simulate more realistic scenarios on the basis of the stellar wind model by Weber and Davis. A main goal is to understand the magnetic interaction between star and planet. In analogy to the well-known Jupiter Io scenario, we study the development of a magnetic field-aligned current system in different parameter regimes.     

Gravity field and rotation state of Mercury from the BepiColombo Radio Science Experiments

The ESA mission BepiColombo will include a Mercury Planetary Orbiter equipped with a full complement of instruments to perform Radio Science Experiments. Very precise range and range-rate tracking from Earth, on-board accelerometry, altimetry and accurate angular measurements with optical instruments will provide large data sets. From these it will be possible to study (1) the global gravity field of Mercury and its temporal variations due to tides, (2) the medium to short scale (down do 300400 km) gravity anomalies, (3) the rotation state of the planet, in particular the obliquity and the libration with respect to the 3/2 spin orbit resonance and (4) the orbit of the center of mass of the planet.With the global gravity field and the rotation state it is possible to tightly constrain the internal structure of the planet, in particular to determine whether the solid surface of the planet is decoupled from the inner core by some liquid layer, as postulated by dynamo theories of Mercury's magnetic field. With the gravity anomalies and altimetry it is possible to study the geophysics of the planet's crust, mantle and impact basins. With the orbit of the planet closest to the Sun it is possible to constrain relativistic theories of gravitation.The possibility of achieving these scientific goals has been tested with a full cycle numerical simulation of the Radio Science Experiments. It includes the generation of simulated tracking and accelerometer data, and the determination, by least squares fit, of a long list of variables including the initial conditions for each observed arc, calibration parameters, gravity field harmonic coefficients, and corrections to the orbit of Mercury. An error budget has been deduced both from the formal covariance matrices and from the actual difference between the nominal values used in the data simulation and the solution. Thus the most complete error budget contains the effect of systematic measurement errors and is by far more reliable than a formal one. For the rotation experiment an error budget has been computed on the basis of dedicated studies on each separate error source.The results of the full cycle simulation are positive, that is the experiments are feasible at the required level of accuracy. However, the extraction of the full accuracy results from the data will be by no means trivial, and there are a number of open problems, both in the data processing (e.g., the selection of the orbital arc length) and in the mission scheduling (e.g., the selection of the target areas for the rotation experiment).     

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)     

Variations of the magnetic field near Mars caused by magnetic crustal anomalies

The possible avenues for photoelectron transport were determined during southern hemisphere winter at Mars by using a mapping analysis of the theoretical magnetic field. Magnetic field line tracing was performed by superposing two magnetic field models: (1) magnetic field derived from a three-dimensional (3D) self-consistent quasi-neutral hybrid model which does not contain the Martian crustal magnetic anomalies and (2) a 3D map of the magnetic field associated with the magnetic anomalies based on Mars Global Surveyor magnetic field measurements. It was found that magnetic field lines connected to the nightside of the planet are mainly channeled within the optical shadow of the magnetotail whereas magnetic field lines connected to the dayside of the planet are observed to form the remainder of the magnetosphere. The simulation suggests that the crustal anomalies create “a magnetic shield” by decreasing the region near Mars which is magnetically connected to the Martian magnetosphere. The rotation of Mars causes periodic changes in magnetic connectivity, but not to qualitative changes in the overall magnetic field draping around Mars.     

Modeling of major martian magnetic anomalies: Further evidence for polar reorientations during the Noachian

Maps of the vector components of the Mars crustal magnetic field are constructed at the mapping altitude (360 to 410 km) using a selected set of data obtained with the Mars Global Surveyor magnetometer during 2780 orbits of the planet in 1999. Forward modeling calculations are then applied to six relatively strong and isolated, dominantly dipolar, magnetic anomalies for the primary purpose of estimating bulk directions of magnetization. Assuming that the magnetizing field was a (dipolar) core dynamo field centered in the planet, paleomagnetic pole positions are calculated for the six primary source bodies together with that for a seventh anomaly analyzed earlier. In agreement with several previous studies, it is found that six of the seven pole positions are clustered in what is now the northern lowlands in a region centered northwest of Olympus Mons (mean pole position: 34°±10° N, 202°±58° E). Assuming that the dynamo dipole moment vector was approximately parallel to the rotation axis, the modeling results therefore suggest a major reorientation of Mars relative to its rotation axis after magnetization was acquired. Such a reorientation may have been stimulated by internal mass redistributions associated with the formation of the northern lowlands and Tharsis, for example. A comparison of the mean paleo (magnetic) equator to the global distribution of crustal fields shows that magnetic anomalies tend to occur at low paleolatitudes. The same appears to be true for the Noachian-aged valley networks, which exhibit a broad spatial correlation with the magnetic anomalies. A possible interpretation is that the formation of magnetic anomalies and the valley networks was favored in the tropics where melting of water ice and snow was a stronger source of both surface valley erosion and groundwater recharge during the earliest history of the planet. This would be consistent with models in which hydrothermal alteration of crustal rocks played a role in producing the unusually strong martian magnetic anomalies.     

Mapping of the cusp plasma precipitation on the surface of Mercury

The presence of a magnetosphere around Mercury plays a fundamental role on the way the solar wind plasma interacts with the planet. Since the observations suggest that Mercury should occupy a large fraction of its magnetosphere and because of lack of an atmosphere, significant differences in solar wind-magnetosphere coupling are expected to exist with respect to the Earth case. On the basis of a modified Tsyganenko T96 model we describe the geometry of the magnetic field that could characterize Mercury, and its response to the variations of the impinging solar wind and of the interplanetary magnetic field. The investigation is focused on the shape and dimension of the open magnetic field regions (cusps) that allow the direct penetration of magnetosheath plasma through the exosphere of Mercury, down to its surface. The precipitating particle flux and energy are evaluated as a function of the open field line position, according to different solar wind conditions. A target of this study is the evaluation of the sputtered particles from the crust of the planet, and their contribution to the exospheric neutral particle populations. Such estimates are valuable in the frame of a neutral particle analyser to be proposed on board of the ESA/BepiColombo mission.     

Multi-frequency electromagnetic sounding of the Galilean moons

Induced magnetic fields provide the unique possibility to sound the conductive interior of planetary bodies. Such fields are caused by external time-variable magnetic fields. We investigate temporal variations of the jovian magnetospheric field at multiple frequencies at the positions of the Galilean moons and analyze possible responses due to electromagnetic induction within multi-layered interior models of all four satellites. At the jovian satellites the magnetic field varies with the synodic rotation period of Jupiter’s internal field (about 10 h), fractions of this period (e.g., 1/2 and 1/3) due to higher order harmonics of the internal field, the orbital periods of the satellites (∼40 h at Io to ∼400 h at Callisto) and the solar rotation period (about 640 h) and its harmonics due to variabilities of the magnetopause field. To analyze these field variations, we use a magnetospheric model that includes the jovian internal field, the current sheet field and fields due to the magnetopause boundary currents. With this model we calculate magnetic amplitude spectra for each satellite orbit. These spectra provide the strengths of the inducing signals at the different frequencies for all magnetic components. The magnetic fields induced in the interiors of the satellites are then determined from response functions computed for different multi-layer interior models including conductive cores and ocean layers of various conductivities and thicknesses. Based on these results we discuss what information about the ocean and core layers can be deduced from the analysis of induction signals at multiple frequencies. Even moderately thick and conductive oceans produce measurable signal strengths at several frequencies for all satellites. The conductive cores cause signals which will be hardly detectable. Our results show that mutual induction occurs between the core and the ocean. We briefly address this effect and its implications for the analysis of induced field data. We further note that close polar orbits are preferable for future Jupiter system missions to investigate the satellites interiors.     

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.     

Equatorial orbits in superposed dipole and uniform magnetic fields

In the present work we study the equatorial motions of charged par ticles that are performed within a field consisting of the superposition of a dipole field—that could represent the magnetic field of a planet — and of a uniform magnetic field normal to the dipole's equator. We use a non-dimensional coordinate system in which the velocity of the charged particle is unit. The model depends on two parameters: the constant of the generalized momentum and the parameter of the interplanetary magnetic field. It is proved that the motion is always bounded. The regions of the motion and the corresponding orbits are studied with respect to the constant of the generalized momentum. We also, investigate numerically conditional periodic and asymptotic orbits.     

Dynamo-generated magnetic fields at the surface of a massive star

Spruit has shown that an astrophysical dynamo can operate in the non-convective material of a differentially rotating star as a result of a particular instability in the magnetic field (the Tayler instability). By assuming that the dynamo operates in a state of marginal instability, Spruit has obtained formulae which predict the equilibrium strengths of azimuthal and radial field components in terms of local physical quantities. Here, we apply Spruit's formulae to our previously published models of rotating massive stars in order to estimate Tayler dynamo field strengths. There are no free parameters in Spruit's formulae. In our models of 10- and  50-M_⊙  stars on the zero-age main sequence, we find internal azimuthal fields of up to 1 MG, and internal radial components of a few kG. Evolved models contain weaker fields. In order to obtain estimates of the field strength at the stellar surface, we examine the conditions under which the Tayler dynamo fields are subject to magnetic buoyancy. We find that conditions for Tayler instability overlap with those for buoyancy at intermediate to high magnetic latitudes. This suggests that fields emerge at the surface of a massive star between magnetic latitudes of about 45° and the poles. We attempt to estimate the strength of the field which emerges at the surface of a massive star. Although these estimates are very rough, we find that the surface field strengths overlap with values which have been reported recently for line-of-sight fields in several O and B stars.     

Induced magnetic field effects at planet Mercury

At Mercury's surface external magnetic field contributions caused by magnetospheric current systems play a much more important role than at Earth. They are subjected to temporal variations and therefore will induce currents in the large conductive iron core. These currents give rise to an additional magnetic field superposing the planetary field. We present a model to estimate the size of the induced fields using a magnetospheric magnetic field model with time-varying magnetopause position. For the Hermean interior we assume a two-layer conductivity distribution. We found out that about half of the surface magnetic field is due to magnetospheric or induced currents. The induced fields achieve 7-12% of the mean surface magnetic intensity of the internal planetary field, depending on the core size. The magnetic field was also modeled for a satellite moving along a polar orbit in the Hermean magnetosphere, showing the importance of a careful separation of the magnetic field measurements.     

Further investigations of Jupiter models

In our previous investigation of Jupiter models, subject to the constraint that the hydrogen-to-helium ratio is solar, we found a need to include considerable additional mass in the form of volatilized condensates in the atmosphere and excess mass in a central core. The stricter constraints imposed by the measurement of the gravitational moments of the planet as a result of the Pioneer 10 flyby indicate that the mass of the excess volatilized condensates, assumed to be water, relative to the core mass, assumed to be rock, exceeds the ratio of the relevant elements in the solar composition. In this paper we have tested the sensitivity of this conclusion to varying assumptions about the constraints and the equation of state: in particular, to variations in the hydrogen-to-helium ratio, in the softness of the equation of state for water, in the treatment of the internal adiabat, in departures from an internal adiabat, and to variations in the temperature at the 1 bar level. The above conclusion is not changed if any of these alterations are made within reasonable limits.