Mercury's weak internal dipole field is subject to an intense solar wind; and thus, only a small magnetospheric cavity is created. The location of the outer boundary, the magnetopause, is mainly controlled by a pressure balance between the solar wind pressure outside and magnetic pressure inside, but during times of intense dayside reconnection the standoff distance may be reduced due to erosion. For the Hermean magnetosphere, different erosion mechanisms such as direct flux transport, neutral current sheet enhancement, field‐aligned currents, and interplanetary magnetic field penetration are compared. As any of these erosion mechanisms change the external field experienced by the planet, currents are induced within the electrically conductive planetary interior. Secondary magnetic fields from these induced currents counteract their source by temporarily increasing the planetary magnetic moment. The amplitude of this compensation depends on the interior electrical conductivity structure. Using a magnetospheric model, that is based on in situ MErcury Surface, Space ENvironment, GEochemistry, and Ranging data, as well as a simple conductivity model for the planetary interior, we give an estimate of the induced magnetic field range possible for various internal conductivity structures and external forcings. Considering the planetary response to the magnetospheric field changes opens a possibility to probe the planetary interior—a method especially suited for the upcoming BepiColombo mission to Mercury.

We present a new analytical method to derive steady-state magnetohydrodynamic (MHD) solutions of the magnetosheath in different levels of approximation. With this method, we calculate the magnetosheath's density, velocity, and magnetic field distribution as well as its geometry. Thereby, the solution depends on the geomagnetic dipole moment and solar wind conditions only. To simplify the representation, we restrict our model to northward IMF with the solar wind flow along the stagnation streamline. The sheath's geometry, with its boundaries, bow shock and magnetopause, is determined self-consistently. Our model is stationary and time relaxation has not to be considered as in global MHD simulations. Our method uses series expansion to transfer the MHD equations into a new set of ordinary differential equations. The number of equations is related to the level of approximation considered including different physical processes. These equations can be solved numerically; however, an analytical approach for the lowest-order approximation is also presented. This yields explicit expressions, not only for the flow and field variations but also for the magnetosheath thickness, depending on the solar wind parameters. Results are compared to THEMIS data and offer a detailed explanation of, e.g., the pile-up process and the corresponding plasma depletion layer, the bow shock and magnetopause geometry, the magnetosheath thickness, and the flow deceleration

Abstract. We present a new method to reconstruct solar wind conditions from spacecraft data taken during magnetosheath passages, which can be used to support, e.g., magnetospheric models. The unknown parameters of the solar wind are used as boundary conditions of an MHD (magnetohydrodynamics) magnetosheath model. The boundary conditions are varied until the spacecraft data matches the model predictions. The matching process is performed using a gradientbased minimization of the misfit between data and model. To achieve this time-consuming procedure, we introduce the adjoint of the magnetosheath model, which allows efficient calculation of the gradients. An automatic differentiation tool is used to generate the adjoint source code of the model. The reconstruction method is applied to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data to calculate the solar wind conditions during spacecraft magnetosheath transitions. The results are compared to actual solar wind data. This allows validation of our reconstruction method and indicates the limitations of the MHD magnetosheath model used.

Abstract. We present a statistical survey of current structures observed by the Cluster spacecraft at high-latitude day-side magnetopause encounters in the close vicinity of the polar cusps. Making use of the curlometer technique and the fluxgate magnetometer data, we calculate the 3-D current densities and investigate the magnetopause current direction, location, and magnitude during varying solar wind conditions. We find that the orientation of the day-side current structures is in accordance with existing magnetopause current models. Based on the ambient plasma properties, we distinguish five different transition regions at the magnetopause surface and observe distinctive current properties for each region. Additionally, we find that the location of currents varies with respect to the onset of the changes in the plasma environment during magnetopause crossings.

Abstract. The interaction of the solar wind with a planetary magnetic field causes electrical currents that modify the magnetic field distribution around the planet. We present an approach to estimating the planetary magnetic field from in situ spacecraft data using a magnetohydrodynamic (MHD) simulation approach. The method is developed with respect to the upcoming BepiColombo mission to planet Mercury aimed at determining the planet's magnetic field and its interior electrical conductivity distribution. In contrast to the widely used empirical models, global MHD simulations allow the calculation of the strongly time-dependent interaction process of the solar wind with the planet. As a first approach, we use a simple MHD simulation code that includes time-dependent solar wind and magnetic field parameters. The planetary parameters are estimated by minimizing the misfit of spacecraft data and simulation results with a gradient-based optimization. As the calculation of gradients with respect to many parameters is usually very time-consuming, we investigate the application of an adjoint MHD model. This adjoint MHD model is generated by an automatic differentiation tool to compute the gradients efficiently. The computational cost for determining the gradient with an adjoint approach is nearly independent of the number of parameters. Our method is validated by application to THEMIS (Time History of Events and Macroscale Interactions during Substorms) magnetosheath data to estimate Earth's dipole moment.

Abstract. Knowledge of planetary magnetic fields provides deep insights into the structure and dynamics of planets. Due to the interaction of a planet with the solar wind plasma, a rather complex magnetic environment is generated. The situation at planet Mercury is an example of the complexities occurring as this planet's field is rather weak and the magnetosphere rather small. New methods are presented to separate interior and exterior magnetic field contributions which are based on a dynamic inversion approach using a reduced magnetohydrodynamic (MHD) model and time-varying spacecraft observations. The methods select different data such as bow shock location information or magnetosheath magnetic field data. Our investigations are carried out in preparation for the upcoming dual-spacecraft BepiColombo mission set out to precisely estimate Mercury's intrinsic magnetic field. To validate our new approaches, we use THEMIS magnetosheath observations to estimate the known terrestrial dipole moment. The terrestrial magnetosheath provides observations from a strongly disturbed magnetic environment, comparable to the situation at Mercury. Statistical and systematic errors are considered and their dependence on the selected data sets are examined. Including time-dependent upstream solar wind variations rather than averaged conditions significantly reduces the statistical error of the estimation. Taking the entire magnetosheath data along the spacecraft's trajectory instead of only the bow shock location into account further improves accuracy of the estimated dipole moment.

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine-Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

Abstract. We present the first comprehensive statistical survey of the day-side terrestrial bow shock current system based on a large number of Cluster spacecraft bow shock crossings. Calculating the 3-D current densities using Fluxgate Magnetometer data and the Curlometer technique enables the investigation of current locations, directions and magnitudes in dependence on arbitrary IMF orientation. In case of quasi-perpendicular shock geometries we find that the current properties are in good accordance to theory and existing simulation results. However, currents at quasi-parallel shock geometries next to the foreshock 5 region underlie distinct variations regarding their directions.