Revisiting the Slichter mode of Mercury in the context of differentiated models

Abstract

We revisit the Slichter mode of a set of differentiated Mercury models that were considered previously. We apply a different and independent formalism, based on variational principles of mechanics, to analytically model the internal translations of a body with a global internal perfect fluid layer limited by two differentiated rigid solid constituents that have a spherical symmetric mass distribution. The Slichter mode is specified by providing the time evolution of the barycenters of the solid constituents, the amplitude ratio of the mantle to the inner core, and the period of the oscillatory motion. All these parameters only depend on the mass of the body, the mass of the inner core, the density of the fluid, and the mean density of the inner core. For previously developed Mercury models we find, in contrast to other results, that there are no discontinuities in the Slichter period when passing from undifferentiated to differentiated inner cores. Hence, in a general situation, a potential detection of the Slichter mode cannot determine the differentiation of the inner core. We also find that the BepiColombo mission may be able to detect the Slichter mode caused by an impactor meteroid with a mass of about 10 12 kg in the most favorable of circumstances. This shows that a measurable excitation of the mode by this mechanism is even more unlikely than was previously established, where a mass about 10 10 kg was found.