Mercury possesses an internally generated global magnetic field which significantly differs from Earth’s magnetic field in geometry and strength. While being much weaker (1% of Earth’s surface field strength), Mercury’s magnetic field is strongly aligned to the rotation axis and the magnetic equator is offset towards north. These characteristics of the field have been a challenging task for dynamo modelling. Current dynamo models for Mercury suggest that a stably stratified layer below the core-mantle boundary is necessary to explain the the weak, axisymmetric and offset dipole magnetic field. Although, having different geophysical measurements by NASA’s MESSENGER mission the inner core size of the planet is barely constrained. While interior models from geodetic measurements suggests an inner core sizes which can occupy half of the total core, dynamo models which generate a Mercury-like magnetic field have mostly a rather small inner core of around 400 km. In this study we performed dynamo simulations with a stably stratified layer below the core-mantle boundary which are able to reproduce Mercury’s magnetic field characteristics and we vary the inner core size in these models systematically. First results of the study reveal, that only dynamo models with a small inner core well below 750 km radius are capable of reproducing a Mercury-like magnetic field, while models with a larger inner cores cannot reproduce the offset magnetic equator.

The reconstruction of Mercury's internal magnetic field enables us to take a look into the inner heart of Mercury. In view of the BepiColombo mission, Mercury's magnetosphere is simulated using a hybrid plasma code, and the multipoles of the internal magnetic field are estimated from the virtual spacecraft data using three distinct reconstruction methods: the truncated singular value decomposition, the Tikhonov regularization and Capon's minimum variance projection. The study shows that a precise determination of Mercury's internal field beyond the octupole up to the dotriacontapole is possible and that Capon's method provides the same high performance as the Tikhonov regularization, which is superior to the performance of the truncated singular value decomposition.

Since the discovery of Mercury’s peculiar magnetic field it has raised questions about the underlying dynamo process in its fluid core. The global magnetic field at the surface is rather weak compared to other planetary magnetic fields, strongly aligned to the planet's rotation axis and its magnetic equator is shifted towards north. Especially the latter characteristic is difficult to explain using common dynamo model setups. One promising model suggests that a thermal stably stratified layer right underneath the core-mantle boundary is present. As a consequence the magnetic field deep inside the core is efficiently damped by passing through the stably stratified layer due to the skin effect. Additionally, the non-axisymmetric parts of the magnetic field are vanishing, too, such that a dipole dominated magnetic is left at the planet’s surface. In this study we present new direct numerical simulations of the magnetohydrodynamical dynamo problem which include a stably stratified layer on top of the outer core, which can also reproduce the shift of the magnetic equator towards north. We revisit a model configuration for Mercury’s dynamo action, which successfully reproduced the magnetic field features, in which core convection is driven by thermal buoyancy as well as compositional buoyancy (double-diffusive convection). While we find that this model configuration produces Mercury-like magnetic field only in a limited parameter range (Rayleigh and Ekman number), we show that also a simple codensity model is sufficient over a wide parameter range to produce Mercury-like magnetic fields.

Since the discovery of Mercury’s peculiar magnetic field it has raised questions about the underlying dynamo process in its fluid core. The global magnetic field at the surface is rather weak compared to other planetary magnetic fields, strongly aligned to the planet's rotation axis and its magnetic equator is shifted towards north. Especially the latter characteristic is difficult to explain using common dynamo model setups. One promising model suggests that a thermal stably stratified layer right underneath the core-mantle boundary is present. As a consequence the magnetic field deep inside the core is efficiently damped by passing through the stably stratified layer due to the skin effect. Additionally, the non-axisymmetric parts of the magnetic field are vanishing, too, such that a dipole dominated magnetic is left at the planet’s surface. In this study we present new direct numerical simulations of the magnetohydrodynamical dynamo problem which include a stably stratified layer on top of the outer core, which can also reproduce the shift of the magnetic equator towards north. We revisit a model configuration for Mercury’s dynamo action, which successfully reproduced the magnetic field features, in which core convection is driven by thermal buoyancy as well as compositional buoyancy (double-diffusive convection). While we find that this model configuration produces Mercury-like magnetic field only in a limited parameter range (Rayleigh and Ekman number), we show that also a simple codensity model is sufficient over a wide parameter range to produce Mercury-like magnetic fields.

The internal magnetic field of Mercury is best described by a northward offset dipole with almost zero obliquity. Its offset, weakness, axisymmetry and lack of secular variation still poses a challenge to dynamo theory. After NASA’s Mariner 10 flybys in the 1970’s and MESSENGER’s orbital mission in 2011-2015, BepiColombo performed a flyby at Mercury in October 2021. For the first time, magnetic field measurements are obtained from the southern hemisphere by the fluxgate magnetometer MPO-MAG. We will present an overview of the flyby data and compare the new in-situ data to magnetospheric models obtained from the previous missions to the innermost terrestrial planet. Does the flyby data reveal any secular variation? Has the dipole offset changed? These are some of the questions we will discuss with this unprecedented magnetometer data. We will close with a discussion on what is to be expected from the orbital phase of BepiColombo.

The Childress-Soward model, consisting of a an electrically conducting RayleighBenard layer rotating about a vertical axis, is the conceptually simplest model configuration that captures all essentials of convectively driven dynamos. Here we study the effects of different boundary conditions on this type of dynamo. This closes a gap in the existing literature, which has primarily focused on simple, but geophysically not very realistic, cases. Furthermore, the extensive literature on boundary layers in nonrotating and rotating Rayleigh-Benard convection makes the Childress-Soward model an ideal test bed for illuminating the fundamental effects that the boundary conditions have on convection-driven dynamos. In this study we systematically vary the thermal, mechanical, and electrical boundary conditions in direct numerical simulations, with a focus on flow regimes characterized by geostrophic turbulence. One key result applies to both dynamos and nonmagnetic, rotating convection. We show that for no-slip boundaries, the Nusselt number increases significantly when a fixed heat flux is imposed instead of a given temperature difference. This effect can be explained by an interplay of Ekman pumping and the internal structure of the thermal boundary layer, which is very sensitive to thermal boundary conditions. Dynamical changes are shown to exist only within the boundary layers, such that the bulk dynamics remains largely unaffected. In the dynamo case, we argue that care needs to be taken in order to ensure comparable energetics when changing from fixed-temperature to fixed-flux conditions. If done properly, no significant differences in the leading order features of the resulting dynamos are observed. In particular, the thermal boundary conditions have no noticeable influence on the horizontal flow scales, as might have been expected from studies in spherical geometry. In contrast, the mechanical boundary conditions largely control whether or not large-scale flows and fields can be generated. For no-slip boundaries, Ekman friction strongly suppresses upscale transport and eliminates the large-scale vortex dynamos that exist in the stress-free case. Finally, the magnetic boundary conditions are shown to strongly affect the topology of the generated magnetic fields. For an insulating exterior, the magnetic field is most intense in the central part of the fluid layer, whereas we observe a strong magnetic field buildup close to perfectly conducting boundaries. For large magnetic Reynolds numbers, we further observe thin layers of intense horizontal field attached to perfect conductors. The horizontal flow scales, however, remain largely unaffected in the investigated parameter regime.

In preparation for the ESA/JAXA BepiColombo mission to Mercury, thematic working groups had been established for coordinating the activities within the BepiColombo Science Working Team in specific fields. Here we describe the scientific goals of the Geodesy and Geophysics Working Group (GGWG) that aims at addressing fundamental questions regarding Mercury’s internal structure and evolution. This multidisciplinary investigation will also test the gravity laws by using the planet Mercury as a proof mass. The instruments on the Mercury Planetary Orbiter (MPO), which are devoted to accomplishing the GGWG science objectives, include the BepiColombo Laser Altimeter (BELA), the Mercury orbiter radio science experiment (MORE), and the MPO magnetometer (MPO-MAG). The onboard Italian spring accelerometer (ISA) will greatly aid the orbit reconstruction needed by the gravity investigation and laser altimetry. We report the current knowledge on the geophysics, geodesy, and evolution of Mercury after the successful NASA mission MESSENGER and set the prospects for the BepiColombo science investigations based on the latest findings on Mercury’s interior. The MPO spacecraft of the BepiColombo mission will provide extremely accurate measurements of Mercury’s topography, gravity, and magnetic field, extending and improving MESSENGER data coverage, in particular in the southern hemisphere. Furthermore, the dual-spacecraft configuration of the BepiColombo mission with the Mio spacecraft at higher altitudes than the MPO spacecraft will be fundamental for decoupling the internal and external contributions of Mercury’s magnetic field. Thanks to the synergy between the geophysical instrument suite and to the complementary instruments dedicated to the investigations on Mercury’s surface, composition, and environment, the BepiColombo mission is poised to advance our understanding of the interior and evolution of the innermost planet of the solar system.

The magnetometer instrument MPO-MAG on-board the Mercury Planetary Orbiter (MPO) of the BepiColombo mission en-route to Mercury is introduced, with its instrument design, its calibration and scientific targets. The instrument is comprised of two tri-axial fluxgate magnetometers mounted on a 2.9 m boom and are 0.8 m apart. They monitor the magnetic field with up to 128 Hz in a $\pm 2048$  nT range. The MPO will be injected into an initial $480 \times 1500$  km polar orbit (2.3 h orbital period). At Mercury, we will map the planetary magnetic field and determine the dynamo generated field and constrain the secular variation. In this paper, we also discuss the effect of the instrument calibration on the ability to improve the knowledge on the internal field. Furthermore, the study of induced magnetic fields and field-aligned currents will help to constrain the interior structure in concert with other geophysical instruments. The orbit is also well-suited to study dynamical phenomena at the Hermean magnetopause and magnetospheric cusps. Together with its sister instrument Mio-MGF on-board the second satellite of the BepiColombo mission, the magnetometers at Mercury will study the reaction of the highly dynamic magnetosphere to changes in the solar wind. In the extreme case, the solar wind might even collapse the entire dayside magnetosphere. During cruise, MPO-MAG will contribute to studies of solar wind turbulence and transient phenomena.

Poloidal–toroidal magnetic field decomposition is a useful application of the Mie representation and the decomposition method enables us to determine the current density observationally and unambiguously in the local region of magnetic field measurement. The application and the limits of the decomposition method are tested against the Mercury magnetic field simulation in view of BepiColombo’s arrival at Mercury in 2025. The simulated magnetic field data are evaluated along the planned Mercury Planetary Orbiter (MPO) trajectories and the current system that is crossed by the spacecraft is extracted from the magnetic field measurements. Afterwards, the resulting currents are classified in terms of the established current system in the vicinity of Mercury. Graphical Abstract

Minimum variance distortionless projection, the so-called Capon method, serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. The method has not only successfully been applied to multipoint wave and turbulence studies in the context of seismics and space plasma physics, but it is also currently being considered as a technique to perform the multipole expansion of planetary magnetic fields from a limited data set, such as Mercury’s magnetic field analysis. The mathematical foundations and the practical application of the Capon method are discussed in a rigorous fashion by extending its linear algebraic derivation in view of planetary magnetic field studies. Furthermore, the optimization of Capon’s method by making use of diagonal loading is considered.

The parameterization of the magnetospheric field contribution, generated by currents flowing in the magnetosphere is of major importance for the analysis of Mercury’s internal magnetic field. Using a combination of the Gauss and the Mie representation (toroidal–poloidal decomposition) for the parameterization of the magnetic field enables the analysis of magnetic field data measured in current carrying regions in the vicinity of Mercury. In view of the BepiColombo mission, the magnetic field resulting from the plasma interaction of Mercury with the solar wind is simulated with a hybrid simulation code and the internal Gauss coefficients for the dipole, quadrupole and octupole field are reconstructed from the data, evaluated along the prospective trajectories of the Mercury Planetary Orbiter (MPO) using Capon’s method. Especially, it turns out that a high-precision determination of Mercury’s octupole field is expectable from the future analysis of the magnetic field data measured by the magnetometer on board MPO. Furthermore, magnetic field data of the MESSENGER mission are analyzed and the reconstructed internal Gauss coefficients are in reasonable agreement with the results from more conventional methods such as the least-square fit.

In the 1970’s the flybys of NASA’s Mariner 10 spacecraft confirmed the existence of an internally generated magnetic field at Mercury. The measurements taken during its flybys already revealed, that Mercury‘s magnetic field is unique along other planetary magnetic fields, since the magnetic dipole moment of ~190 nT ∙ RM3 is very weak, e.g. compared to Earth’s magnetic dipole moment. The following MESSENGER mission from NASA investigated Mercury and its magnetic field more precisely and exposed additional interesting properties about the planet’s magnetic field. The tilt of its dipole component is less than 1°, which indicates a strong alignment of the field along the planet’s rotation axis. Additionally the measurement showed that the magnetic field equator is shifted roughly 0.2 ∙ RM towards north compared to Mercury‘s actual geographic equator.Since its discovery Mercury‘s magnetic field has puzzled the community and modelling the dynamo process inside the planet’s interior is still a challenging task. Adapting the typical control parameters and the geometry in the models of the geodynamo for Mercury does not lead to the observed field morphology and strength. Therefore new non-Earth-like models were developed over the past decades trying to match Mercury’s peculiar magnetic field. One promising model suggests a stably stratified layer on the upper part of Mercury’s core. Such a layer divides the fluid core in a convecting part and a non-convecting part, where the magnetic field generation is mainly inhibited. As a consequence the magnetic field inside the outer core is damped very efficiently passing through the stably stratified layer by a so-called skin effect. Additionally, the non-axisymmetric parts of the magnetic field are vanishing, too, such that a dipole dominated magnetic is left at the planet’s surface.In this study we present new direct numerical simulations of the magnetohydrodynamical dynamo problem which include a stably stratified layer on top of the outer core. We explore a wide parameter range, varying mainly the Rayleigh and Ekman number in the model under the aspect of a strong stratification of the stable layer. We show which conditions are necessary to produce a Mercury-like magnetic field and give a inside about the planets interior structure.

Minimum variance distortionless projection, the so-called Capon method, serves as a powerful and robust data analysis tool when working on various kinds of ill-posed inverse problems. The method has not only successfully been applied to multipoint wave and turbulence studies in the context of space plasma physics, but it is also currently being considered as a technique to perform the multipole expansion of planetary magnetic fields from a limited data set, such as Mercury's magnetic field analysis. The practical application and limits of the Capon method are discussed in a rigorous fashion by formulating its linear algebraic derivation in view of planetary magnetic field studies. Furthermore, the optimization of Capon's method by making use of diagonal loading is considered.