Effect of core--mantle and tidal torques on Mercury's spin axis orientation

Abstract

The rotational evolution of Mercury's mantle and its core under conservative and dissipative torques is important for understanding the planet's spin state. Dissipation results from tides and viscous, magnetic and topographic core--mantle interactions. The dissipative core--mantle torques take the system to an equilibrium state wherein both spins 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. The relatively strong core--mantle coupling necessary to bring the mantle spin axis to its observed position close to the Cassini state is not obtained by any of the three dissipative core--mantle coupling mechanisms. For a hydrostatic ellipsoidal core--mantle boundary, pressure coupling dominates the dissipative effects on the mantle and core positions, and dissipation together 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 3.55 arcmin nearly in the plane containing the Cassini state. With the maximum viscosity considered of $\nu \sim 15.0\mathrm{c}{\mathrm{m}}^2/s$ if the coupling is by the circulation through an Ekman boundary layer or $\nu \sim 8.75\times 10^5\mathrm{c}{\mathrm{m}}^2/s$ for purely viscous coupling, the core spin lags the precessing Cassini plane by 23 arcsec, whereas the mantle spin lags by only 0.055 arcsec. 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.

35 pages, 7 figures

References in corpus (1)

• Mercury's capture into the 3/2 spin-orbit resonance including the effect of core-mantle friction

Cited by in corpus (10)

• Early Excitation of Spin-Orbit Misalignments in Close-in Planetary Systems
• Magnetic Origins of the Stellar Mass-Obliquity Correlation in Planetary Systems
• Obliquity of Mercury: influence of the precession of the pericenter and of tides
• Mercury's resonant rotation from secular orbital elements
• Cassini states of a rigid body with a liquid core
• Librations of a body composed of a deformable mantle and a fluid core
• The influence of a fluid core and a solid inner core on the Cassini sate of Mercury
• Rotation of a synchronous viscoelastic shell
• Deviation of Mercury's spin axis from an exact Cassini state induced by dissipation
• A Simplified Model for the Forced Libration of Icy Moons with Subsurface Oceans: Application to Enceladus and Mimas