The influence of a fluid core and a solid inner core on the Cassini sate of Mercury

TL;DR

This study models Mercury's Cassini state considering an inner core, fluid core, and mantle, revealing that interior coupling causes minimal obliquity deviations, making Mercury's spin axis behavior similar to a rigid planet.

Contribution

It introduces a comprehensive model of Mercury's interior including inertial, gravitational, viscous, and electromagnetic couplings, highlighting their effects on the planet's obliquity.

Findings

Interior coupling causes less than 0.01 arcmin obliquity deviation.

Electromagnetic coupling dominates viscous effects at the core boundary.

Inner core size influences the alignment and obliquity of Mercury's spin axis.

Abstract

We present a model of the Cassini state of Mercury that comprises an inner core, a fluid core and a mantle. Our model includes inertial and gravitational torques between interior regions, and viscous and electromagnetic (EM) coupling at the boundaries of the fluid core. We show that the coupling between Mercury's interior regions is sufficiently strong that the obliquity of the mantle spin axis deviates from that of a rigid planet by no more than 0.01 arcmin. The mantle obliquity decreases with increasing inner core size, but the change between a large and no inner core is limited to 0.015 arcmin. EM coupling is stronger than viscous coupling at the inner core boundary and, if the core magnetic field strength is above 0.3 mT, locks the fluid and solid cores into a common precession motion. Because of the strong gravitational coupling between the mantle and inner core, the larger the inner core is, the more this co-precessing core is brought into an alignment with the mantle, and the more the obliquity of the polar moment of inertia approaches that expected for a rigid planet. The misalignment between the polar moment of inertia and mantle spin axis increases with inner core size, but is limited to 0.007 arcmin. Our results imply that the measured obliquities of the mantle spin axis and polar moment of inertia should coincide at the present-day level of measurement errors, and cannot be distinguished from the obliquity of a rigid planet.