The core-mantle friction effect on the secular spin evolution of terrestrial planets

For planets having a liquid core, friction with the mantle results in an additional source of dissipating energy alternative to tides. As a consequence, the spin of the planet will slowly change: the rotation rate decreases while the equator is tilted toward the orbital plane. Here we revisit the theory of secular spin evolution due to core-mantle friction in a very general formulation. We are able to determine the core's spin vector as a function of the mantle's spin, which can be used to estimate the effective viscosity of the core as well as its ellipticity. Contrarily to previous studies, we also investigate the effect on an axially asymmetric planet (C22 ≠ 0), which becomes an important additional source of dissipation near spin-orbit resonances. The secular effect of core-mantle friction on the spin proves to be essential in the long-term studies of Mercury and Venus, while it can be neglected for the Earth or Mars.