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.     

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.     

Highly reducing conditions during core formation on Mercury: Implications for internal structure and the origin of a magnetic field

The high average density and low surface FeO content of the planet Mercury are shown to be consistent with very low oxygen fugacity during core segregation, in the range 3-6 log units below the iron-wüstite buffer. These low oxygen fugacities, and associated high metal content, are characteristic of high-iron enstatite (EH) and Bencubbinite (CB) chondrites, raising the possibility that such materials may have been important building blocks for this planet. With this idea in mind we have explored the internal structure of a Mercury sized planet of EH or CB bulk composition. Phase equilibria in the silicate mantle have been modeled using the thermodynamic calculator p-MELTS, and these simulations suggest that orthopyroxene will be the dominant mantle phase for both EH and CB compositions, with crystalline SiO₂ being an important minor phase at all pressures. Simulations for both compositions predict a plagioclase-bearing “crust” at low pressure, significant clinopyroxene also being calculated for the CB bulk composition. Concerning the core, comparison with recent high pressure and high temperature experiments relevant to the formation of enstatite meteorites, suggest that the core of Mercury may contain several wt.% silicon, in addition to sulfur. In light of the pressure of the core-mantle boundary on Mercury (∼7 GPa) and the pressure at which the immiscibility gap in the system Fe-S-Si closes (∼15 GPa) we suggest that Mercury’s core may have a complex shell structure comprising: (i) an outer layer of Fe-S liquid, poor in Si; (ii) a middle layer of Fe-Si liquid, poor in S; and (iii) an inner core of solid metal. The distribution of heat-producing elements between mantle and core, and within a layered core have been quantified. Available data for Th and K suggest that these elements will not enter the core in significant amounts. On the other hand, for the case of U both recently published metal/silicate partitioning data, as well as observations of U distribution in enstatite chondrites, suggest that this element behaves as a chalcophile element at low oxygen fugacity. Using these new data we predict that U will be concentrated in the outer layer of the mercurian core. Heat from the decay of U could thus act to maintain this part of Mercury’s core molten, potentially contributing to the origin of Mercury’s magnetic field. This result contrasts with the Earth where the radioactive decay of U represents a negligible contribution to core heating.     

Comments on the origin of Mercury

Mercury is not only highly refractory, but remarkably small. Both properties may have been affected by planetesimal scattering and collisions, as well as by solar activity.     

The origin of our galactic magnetic field

A serious difficulty with the standard alpha‐omega theory of the origin of galactic magnetic fields involves the question of flux expulsion. This is intimately related to flux freezing. The alpha‐omega theory is shown in the context of the giant superbubble explosions that have a large impact on the physics of the interstellar medium. It is shown that superbubbles alone can duplicate the processes of the alpha‐omega dynamo and produce exponential growth of the galactic magnetic field. The possibility of the blow‐out of pieces of the magnetic field is discussed and it is shown that they have the potential to solve the flux‐expulsion problem. However, such an explanation must lead to apparent ‘gaps’ in the field in the galactic disc. These gaps are probably unavoidable in any dynamo theory and should have important observable consequences, one of which is an explanation for the escape of cosmic rays from the disc (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Recurrency and the origin of the vertical component of the interplanetary magnetic field

The autocorrelation functions of the solar wind velocity and of the IMF components as well as of the geomagnetic activity indices are studied for two periods: August–December, 1965 and January–May, 1974. The vertical component of the IMF is shown to exhibit a rather definite recurrency relatively independent of the recurrency of the solar wind velocity.The daily mean values of the Z-component of the IMF are shown to correlate ( = -0.5) with the intensity of the meridional component of the large scale solar magnetic field with time delay of about 5 days with respect to the latter. This result is interpreted as an evidence for the Z- component of the IMF to be carried away by the solar wind from the Sun.     

Iron/silicate fractionation and the origin of Mercury

Compared with the other terrestrial planets, Mercury has anomalously low mass and high iron content. Equilibrium condensation and inhomogeneous accretional models are not compatible with these properties, unless the solar nebula's thermal structure and history meet stringent conditions. Also, such models predict a composition which does not allow a presently molten core. It appears that most of the solid matter which originally condensed in Mercury's zone has been removed. The planet's composition may be explained if the removal process was only slightly more effective for silicates than for iron. It is proposed that planetesimal orbits in the inner solar nebula decayed because of gas drag. This process is a natural consequence of the non-Keplerian rotation of a centrally condensed nebula. A simple quantitative model shows good agreement with the observed mass distribution of the terrestrial planets. The rate of orbital decay is slower for larger and/or denser bodies, because of their smaller area-to-mass ratios. With plausible assumptions as to planetesimal sizes and compositions, this process can produce fractionation of the sense required to produce an iron-rich planet. Cosmogonical implications are discussed.     

The origin of the 28- to 29-day recurrent patterns of the solar magnetic field

Numerical simulations of the Sun's mean line-of-sight magnetic field suggest an origin for the 28-to 29-day recurrent patterns of the field and its associated interplanetary phenomena. The patterns are caused by longitudinal fluctuations in the eruption of new magnetic flux, the transport of this flux to mid latitudes by supergranular diffusion and meridional flow, and the slow rotation of the resulting flux distributions at the 28- to 29-day periods characteristic of those latitudes.E. O. Hulburt Center for Space Research.Laboratory for Computational Physics.     

Comparison of the mean photospheric magnetic field and the interplanetary magnetic field

The mean photospheric magnetic field of the sun seen as a star has been compared with the interplanetary magnetic field observed with spacecraft near the earth. Each change in polarity of the mean solar field is followed about 4 1/2 days later by a change in polarity of the interplanetary field (sector boundary). The scaling of the field magnitude from sun to near earth is within a factor of two of the theoretical value, indicating that large areas on the sun have the same predominant polarity as that of the interplanetary sector pattern. An independent determination of the zero level of the solar magnetograph has yielded a value of 0.1±0.05 G. An effect attributed to a delay of approximately one solar rotation between the appearance of a new photospheric magnetic feature and the resulting change in the interplanetary field is observed.     

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.     

On the origin of galactic magnetic fields

We discuss the properties of the large-scale galactic magnetic fields which can help to discriminate between theories of their origin. We argue that the mean-field dynamo theory in its simplest form is unique in that it can explain most of the known features from a single conceptual viewpoint. This revised version was published online in September 2006 with corrections to the Cover Date.     

Constraints on the magnetic field geometry of magnetars

We study the effect of the magnetic field geometry on the oscillation spectra of strongly magnetized stars. We construct a configuration of magnetic field where a toroidal component is added to the standard poloidal one. We consider a star with a type I superconductor core so that both components of the magnetic field are expelled from the core and confined in the crust. Our results show that the toroidal contribution does not influence significantly the torsional oscillations of the crust. On the contrary, the confinement of the magnetic field in the crust drastically affects the torsional oscillation spectrum. A comparison with estimations for the magnetic field strength, from observations, excludes the possibility that magnetars will have a magnetic field solely confined in the crust, that is, our results suggest that the magnetic field in whatever geometry has to permeate the whole star.     

Evolution of the magnetic field imbalance on the Sun

The time and latitude change of the flux and rotation of magnetic-field imbalance structures with various strengths has been determined from observations at the Kitt-Peak observatory for 26 years. The regularities revealed during the work allow this change to be explained as follows. The structure of the imbalance of the magnetic field of a particular strength emerges at the photosphere surface while possessing a rotation typical for the area of this structure formation. After this, the structure begins to drift along the meridian (toward the pole or toward the equator) while rotating at the same velocity and occupying several interval of latitudes. Having displaced to the poles from the emerging latitude by about 20° (or more, depending on the rotation period), structures that have a certain significant period cease to exist as a whole, giving rise to other structures with other significant rotation periods. From here it follows that the differential rotation of the layers responsible for forming the imbalance structures of fields with various strengths can be determined from the dependence of the rotation period on the latitude of the emergence of the imbalance structure.     

The influence of a flow field on the stability of the force-free magnetic field

In order to analyse the convective instability of the force-free magnetic field, an exact solution of the MHD equation for the magnetic field (1) together with the flow field (2) of constant speed V₀ making an angle θ with the magnetic field, was chosen as the unperturbed state. The stability of the fields between two parallel conducting walls of seperation d was studied by a linear perturbation method, which led to the eigenvalue problem (12), X being given by (13). It was shown by an approximate variational method that instability will set in by the flow field if V₀ is greater than 1/ $\text{3}$ times Alfven velocity V_A. For , the stability of the force-free field (1) is not influenced by the flow field, which may still be significant in other respects. Perturbations transverse to the magnetic field were found to be the most unstable modes.     

On the origin of ancient lunar magnetic fields

The maximum value of possible lunar dynamo-field in our epoch is estimated in the scheme of precession dynamo model. In the light of our notions on the evolution of the Earth-Moon system this scheme may account for the size and character of ancient lunar fields that resulted in magnetization of surface lunar rocks, as well as for the absence of lunar dipole field of paleomagnetic origin in our epoch.     

Measurement of the prominences magnetic field

A new type of magnetograph has been built capable to measure weak magnetic fields in the chromosphere and corona. Measurements of magnetic field in two prominences are demonstrated as examples.