The Gravity Signal of Mercury's Inner Core

Abstract

In a reference frame rotating with Mercury's mantle and crust, the inner core and fluid core precess in a retrograde sense with a period of 58.646 days. The precession of a triaxial inner core with a different density than the fluid core induces a periodic gravity variation of degree 2, order 1. Elastic deformations from the pressure that the precessing fluid core exerts on the core‐mantle boundary also contribute to this gravity signal. We show that the periodic change in Stokes coefficients ΔC21 and ΔS21 for this signal of internal origin is of the order of 10−10, similar in magnitude to the signal from solar tides. The relative contribution from the inner core increases with inner core radius and with the amplitude of its tilt angle with respect to the mantle. The latter depends on the strength of electromagnetic coupling at the inner core boundary which in turn depends on the radial magnetic field Br; a larger Br generates a larger tilt. The inner core signal features a contrast between ΔC21 and ΔS21 due to its triaxial shape, discernible for an inner core radius >500 km if Br > 0.1 mT, or for an inner core radius >1100 km if Br < 0.01 mT. A detection of this contrast would confirm the presence of an inner core and place constraints on its size and the strength of the internal magnetic field. These would provide key constraints for the thermal evolution of Mercury and for its dynamo mechanism.