A modified Equivalent Source Dipole method to model partially distributed magnetic field measurements, with application to Mercury

Hermean magnetic field measurements acquired over the northern hemisphere by the MErcury Surface Space ENvironment GEochemistry, and Ranging (MESSENGER) spacecraft provide crucial information on the magnetic field of the planet. We develop a new method, the Time Dependent Equivalent Source Dipole, to model a planetary magnetic field and its secular variation over a limited spatial region. Tests with synthetic data distributed on regular grids as well as at spacecraft positions show that our modeled magnetic field can be upward or downward continued in an altitude range of -300 to 1460km for regular grids and in a narrower range of 10 to 970km for spacecraft positions. They also show that the method is not sensitive to a very weak secular variation along MESSENGER orbits. We then model the magnetic field of Mercury during the first four individual sidereal days as measured by MESSENGER using the modified Equivalent Source Dipoles scheme and excluding the secular variation terms. We find a dominantly zonal field with small-scale nonaxisymmetric features corotating with the Sun in the Mercury Body Fixed system and repeating under similar local time, suggestive of external origin. When modeling the field during one complete solar day, these small-scale features decrease and the field becomes more axisymmetric. The lack of any coherent nonaxisymmetric feature recovered by our method, which was designed to allow for such small-scale structures, provides strong evidence for the large-scale and close-to-axisymmetry structure of the internal magnetic field of Mercury.