Effect of core–mantle and tidal torques on Mercury’s spin axis orientation

Abstract

The rotational evolution of Mercury’s mantle plus crust and its core under conservative and dissipative torques is important for understanding the planet’s spin state. Dissipation results from tidal torques and viscous, magnetic, and topographic torques contributed by interactions between the liquid core and solid mantle. For a spherically symmetric core–mantle boundary (CMB), the system goes to an equilibrium state wherein the spin axes of the mantle and core are fixed in the frame precessing with the orbit, and in which the mantle and core are differentially rotating. This equilibrium exhibits a mantle spin axis that is offset from the Cassini state by larger amounts for weaker core–mantle coupling for all three dissipative core–mantle coupling mechanisms, and the spin axis of the core is separated farther from that of the mantle, leading to larger differential rotation. Relatively strong core–mantle coupling is necessary to bring the mantle spin axis to a position within the uncertainty in its observed position, which is close to the Cassini state defined for a completely solid Mercury. Strong core–mantle coupling means that Mercury’s response is closer to that of a solid planet. Measured or inferred values of parameters in all three core–mantle coupling mechanisms for a spherically symmetric CMB appear not to accomplish this requirement. For a hydrostatic ellipsoidal CMB, pressure coupling dominates the dissipative effects on the mantle and core positions, and dissipation with pressure coupling brings the mantle spin solidly to the Cassini state. The core spin goes to a position displaced from that of the mantle by about 3.55arcmin nearly in the plane containing the Cassini state. The core spin lags the precessing plane containing the Cassini state by an increasing angle as the core viscosity is increased. With the maximum viscosity considered of ν∼15.0cm2/s if the coupling is by the circulation through an Ekman boundary layer or ν∼8.75×105cm2/s for purely viscous coupling, the core spin lags the precessing Cassini plane by 23arcsec, whereas the mantle spin lags by only 0.055arcsec. Larger, non-hydrostatic values of the CMB ellipticity also result in the mantle spin at the Cassini state, but the core spin is moved closer to the mantle spin. Current measurement uncertainties preclude using the mantle offset to constrain the internal core viscosity.