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.     

Quantitative magnetospheric magnetic field modelling with toroidal and poloidal vector fields

Toroidal and poloidal vector fields allow divergence free magnetic field representations in regions where currents flow. We derive general magnetospheric magnetic fields using combinations of spherical harmonic expansions of the toroidal and poloidal fields. Adding restrictive conditions like the field line topology symmetry or the magnetic field measurements, more specific magnetospheric magnetic field models can be derived. Two examples of this technique are given : an axisymmetric model with a ring current in the equatorial region and a time-dependent model of the Earth's magnetosphere. Our results are compared with the Olson-Pfitzer model.     

A three-ring circuit model of the magnetosphere

We have modeled the magnetosphere by superimposing a dipole field, a uniform field and a perturbation field due to a simple current system. This current system consists of a ring current in the neutral line of the dipole plus uniform fields, together with vertical currents representing field-aligned currents to the neutral line. The current circuit is closed by two additional ring currents above and below the equatorial plane representing distributed adiabatic perpendicular currents. This system produces many magnetospheric features including a magnetopause, bending of magnetic field lines in the anti-solar direction, a magnetotail, and cusps on the day-side of the Earth. Our aim is to demonstrate that it is not necessary to think of the magnetic field topology as being caused by the flowing plasma carrying field lines. The fundamental physical problem is to derive the current system from the self-consistent interaction of the solar-wind and magnetospheric plasmas and fields.     

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.     

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.     

Remote sensing of Mercury's magnetospheric plasma environment via energetic neutral atoms imaging

The potentiality of exploring the plasma dynamical behavior of Mercury via energetic neutral atom (ENA) analysis is briefly discussed. The analysis of the Hermean ENA would give clues to the global magnetospheric configuration, clarifying crucial issues like the existence of radiation belts. In order to demonstrate the feasibility of ENA imaging in the Hermean environment, an empirical model of the equatorial proton distributions, originally developed for the Earth's magnetosphere, is here modified in order to be applicable to the expected conditions, according to the present knowledge of the planet. Simulations of the ENA radiation are then presented and discussed. It is shown that the simulated radiation is significantly high, especially when pointing the field of view towards the Hermean surface. The way of determining the proton flux distributions and the cross-tail electric field characteristics by using the ENA signal is discussed. Finally, a preliminary design of an ENA detector suitable for the ESA mission to Mercury ‘BepiColombo’ is proposed and discussed.     

Observations of Magnetic Fields on T Tauri Stars

We present measurements of magnetic field strength and geometry on the surfaces of T Tauri stars (TTS) with and without circumstellar disks. We use these measurements to argue that magnetospheric accretion models should not assume that a fixed fraction of the stellar surface contains magnetic field lines that couple with the disk. We predict the fractional area of accretion footpoints, using magnetospheric accretion models and assuming field strength is roughly constant for all TTS. Analysis of Zeeman broadened infrared line profiles shows that individual TTS each have a distribution of surface magnetic field strengths extending up to 6 kG. Averaging over this distribution yields mean magnetic field strengths of 1-3 kG for all TTS, regardless of whether the star is surrounded by a disk. These strong magnetic fields suggest that magnetic pressure dominates gas pressure in TTS photospheres, indicating the need for new model atmospheres. The He I 5876 Å emission line in TTS can be strongly polarized, so that magnetic field lines at the footpoints of accretion have uniform polarity. The circular polarization signal appears to be rotationally modulated, implying that accretion and perhaps the magnetosphere are not axisymmetric. Time series spectropolarimetry is fitted reasonably well by a simple model with one magnetic spot on the surface of a rotating star. On the other hand, spectropolarimetry of photospheric absorption lines rules out a global dipolar field at the stellar surface for at least some TTS.     

A hybrid simulation of Mercury’s magnetosphere for the MESSENGER encounters in year 2008

The latest measurements from the two encounters of the MESSENGER spacecraft in year 2008 have discovered several interesting features of the magnetosphere of Mercury. We have performed high-resolution 3D hybrid model calculations to simulate the solar wind interaction with the Hermean magnetosphere during the first two Mercury encounters of the MESSENGER spacecraft in 2008. It is found that the global structure of the Hermean magnetosphere is significantly controlled by the direction of the interplanetary magnetic field. The bow shock size and shape and the magnetotail configuration have very large differences in these two encounters with northward-pointing and southward-pointing interplanetary magnetic field, respectively. Comparisons are also given with the observed magnetic field profiles and the computational results. In general, good agreement can be found including the interesting feature of the relatively thick magnetopause current layer at outbound measurements. Our work shows that 3D hybrid simulation is a promising method to study in detail the Hermean magnetosphere in parallel with the post-MOI observations of the MESSENGER spacecraft and the Bepi-Colombo mission in future.     

Jovian magnetosphere-ionosphere current system characterized by diurnal variation of ionospheric conductance

We developed a new numerical model of the Jovian magnetosphere-ionosphere coupling current system in order to investigate the effects of diurnal variation of ionospheric conductance. The conductance is determined by ion chemical processes that include the generation of hydrogen and hydrocarbon ions by solar EUV radiation and auroral electrons precipitation. The model solves the torque equations for magnetospheric plasma accelerated by the radial currents flowing along the magnetospheric equator. The conductance and magnetospheric plasma then change the field-aligned currents (FACs) and the intensity of the electric field projected onto the ionosphere. Because of the positive feedback of the ionospheric conductance on the FAC, the FAC is the maximum on the dayside and minimum just before sunrise. The power transferred from the planetary rotation is mainly consumed in the upper atmosphere on the dayside, while it is used for magnetospheric plasma acceleration in other local time (LT) sectors. Further, our simulations show that the magnetospheric plasma density and mass flux affect the temporal variation in the peak FAC density. The enhancement of the solar EUV flux by a factor of 2.4 increases the FAC density by 30%. The maximum density of the FAC is determined not only by the relationship between the precipitating electron flux and ionospheric conductance, but also by the system inertia, i.e., the inertia of the magnetospheric plasma. A theoretical analysis and numerical simulations reveal that the FAC density is in proportion to the planetary angular velocity on the dayside and to the square of the planetary angular velocity on the nightside. When the radial current at the outer boundary is fixed at values above 30 MA, as assumed in previous model studies, the peak FAC density determined at latitude 73°-74° is larger than the diurnal variable component. This result suggests large effects of this assumed radial current at the outer boundary on the system.     

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.     

A mathematical magnetospheric field model with independent physical parameters

A quantitative magnetospheric magnetic field model has been calculated in three dimensions. The model is based on an analytical solution of the Chapman-Ferraro problem. For this solution, the magnetopause was assumed to be an infinitesimally thin discontinuity with given geometry. The shape of the dayside magnetopause is in agreement with measurements derived from spacecraft boundary crossings.The magnetic field of the magnetopause currents can be derived from scalar potentials. The scalar potentials result from solutions of Laplace's equation with Neumann's boundary conditions. The boundary values and the magnetic flux through the magnetopause are determined by all magnetic sources which are located inside and outside the magnetospheric cavity. They include the Earth's dipole field, the fields of the equatorial ring current and tail current systems, and the homogeneous interplanetary magnetic field. In addition, the flux through the magnetopause depends on two constants of interconnection which provide the possibility of calculating static interconnection between magnetospheric and interplanetary field lines. Realistic numerical values for both constants have been derived empirically from observed displacements of the polar cusps which are due to changes in the orientation of the interplanetary field. The transition from a closed to an open magnetosphere and vice versa can be computed in terms of a change of the magnetic boundary conditions on the magnetopause. The magnetic field configuration of the closed magnetosphere is independent of the amount and orientation of the interplanetary field. In contrast, the configuration of the open magnetosphere confirms the observational finding that field line interconnection occurs primarily in the polar cusp and high latitude tail regions.The tail current system reflects explicitly the effect of dayside magnetospheric compression which is caused by the solar wind. In addition, the position of the plasma sheet relative to the ecliptic plane depends explicitly on the tilt angle of the Earth's dipole. Near the tail axis, the tail field is approximately in a self-consistent equilibrium with the tail currents and the isotropic thermal plasma.The models for the equatorial ring current depend on the D_st-parameter. They are self-consistent with respect to measured energy distributions of ring current protons and the axially symmetric part of the magnetospheric field.     

Electric fields and currents in the ionosphere generated by field-aligned currents observed by TRIAD

On the basis of the experimental data on the ionospheric conductivities and field-aligned currents the electric fields and currents in the ionosphere generated by the field-aligned currents were computated for various magnetic activity conditions. The model of the ionospheric conductivities by Vanyan and Osipova (1975) was used taking into account the influence of the universal time seasons and magnetic activity. The field-aligned current patterns and their change with magnetic activity was set on the basis of the TRIAD data. It is shown that the calculated patterns of the ionospheric electric fields and currents are in agreement with the measured electric fields and the equivalent current systems of the magnetic disturbances in high latitudes. The conclusion is made that the magnetospheric field-aligned currents are the main sources of the presently known polar magnetic disturbances.     

The role of rotation in the evolution of dynamo-generated magnetic fields in Super Earths

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_⊕). Using the most recent thermal evolution models of Super Earths (Gaidos, E., Conrad, C.P., Manga, M., Hernlund, J. [2010]. Astrophys. J. 718, 596–609; Tachinami, C., Senshu, H., Ida, S. [2011]. Astrophys. J. 726, 70) and updated scaling laws for convection-driven dynamos, we predict the evolution of the local Rossby number. This quantity is one of the proxies for core magnetic field regime, i.e. non-reversing dipolar, reversing dipolar and multipolar. We study the dependence of the local Rossby number and hence the core magnetic field regime on planetary mass and rotation rate. Previous works have focused only on the evolution of core magnetic fields assuming rapidly rotating planets, i.e. planets in the dipolar regime. In this work we go further, including the effects of rotation in the evolution of planetary magnetic field regime and obtaining global constraints to the existence of intense protective magnetic fields in rapidly and slowly rotating Super Earths. We find that the emergence and continued existence of a protective planetary magnetic field is not only a function of planetary mass but also depend on rotation rate. Low-mass Super Earths (M ? 2 M_⊕) develop intense surface magnetic fields but their lifetimes will be limited to 2–4 Gyrs for rotational periods larger than 1–4 days. On the other hand and also in the case of slowly rotating planets, more massive Super Earths (M ? 2 M_⊕) have weak magnetic fields but their dipoles will last longer. Finally we analyze tidally locked Super Earths inside and outside the habitable zone of GKM stars. Using the results obtained here we develop a classification of Super Earths based on the rotation rate and according to the evolving properties of dynamo-generated planetary magnetic fields.     

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.     

Emergence of magnetic field due to spin-polarized baryon matter in neutron stars

A model of the ferromagnetic origin of magnetic fields of neutron stars is considered. In this model, the magnetic phase transition occurs inside the core of neutron stars soon after formation. However, owing to the high electrical conductivity the core magnetic field is initially fully screened. We study how this magnetic field emerges for an outside observer. After some time, the induced field that screens the ferromagnetic field decays enough to uncover a detectable fraction of the ferromagnetic field. We calculate the time-scale of decay of the screening field and study how it depends on the size of the ferromagnetic core. We find that the same fractional decay of the screening field occurs earlier for larger cores. We conjecture that weak fields of millisecond pulsars, B ∼10⁸–10⁹ G, could be identified with ferromagnetic fields of unshielded fraction ε ∼10⁻⁴–10⁻³ resulting from the decay of screening fields by a factor 1− ε in ∼10⁸ yr since their birth.     

Effect of finite parallel conductivity on the magnetospheric convection

The magnetospheric plasma convection is studied, taking into account the finite conductivity along magnetic field lines. Field-aligned currents flowing at the inner boundary of the magnetospheric plasma sheet give rise to parallel electric fields which insignificantly affect the convection on the ionospheric level but change drastically the convection system in the magnetosphere. Intense azimuthal convective streams arise along both sides of the plasma sheet boundary. A part of convection lines appears to be completely closed in the inner magnetosphere.     

Predictions on the application of the Hanle effect to map the surface magnetic field of Jupiter

In this paper we evaluate the possibility of detecting, for the first time, the surface magnetic field of Jupiter (∼1 bar level) by observing the change of linear polarization induced by the Hanle effect on the H Lyman-alpha (Lyα) emission line of the planet. We find that, indeed, the Hanle effect, which results from the interaction between a local magnetic field and the atomic polarization induced by absorption of anisotropic radiation, is sensitive to relatively weak values of the strength of the magnetic fields expected on planets. First, we show that for the Lyα emission backscattered by atomic H in the presence of a magnetic field, the Hanle effect is polarizing. This new result is in total contrast to the depolarizing effect predicted and observed for emission lines scattered at right angles in solar prominences. Additionally, to estimate the polarization rate for the case of Jupiter, we have considered three magnetic field models: a dipole field for reference, an O₄ based model [Connerney, J.E.P., 1981. The magnetic field of Jupiter—A generalized inverse approach. J. Geophys. Res. 86, 7679-7693], and finally, an O₆ based model [Khurana, K.K., 1997. Euler potential models of Jupiter's magnetospheric field. J. Geophys. Res. 102, 11295-11306]. In all models, we show that for the jovian backscattered Lyα line, the Hanle effect does enhance the Lyα linear polarization; the polarization rate may exceed 2% at specific regions of the jovian disc, making detection possible either remotely or from an orbiter around Jupiter. In general, depending on the instrumental sensitivity and the observing strategy used, we show that accurate mapping of the linear polarization rate at the planetary surface (thermosphere) or off-disc (corona) may provide a rather accurate estimate of the jovian total magnetic field strength on large area scales.     

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)     

Modelling of magnetic field measurements at Mercury

Mapping Mercury's internal magnetic field with a magnetometer in closed orbit around the planet will provide valuable information about its internal structure. By measuring magnetic field multipoles of order higher than the dipole we could, in principle, determine some properties, such as size and location, of the internal source. Here we try to quantify these expectations. Using conceptual models, we simulate the actual measurement during the BepiColombo mission, and then we analyze the simulated data in order to estimate the measurement errors due to the limited spatial sampling. We also investigate our ability to locate the field generating current system within the planet. Finally, we address the main limitation of our model, due to the presence of time-varying external magnetospheric currents.     

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.