Constraints on Lunar Thermal-Rotational Evolution from the Fossil Shape of the Moon

The shape and gravity field of Earth's natural satellite have been a long-standing puzzle to geodynamicists. Measurements of the gravitational field and librations of the Moon show that the Moon's density distribution (as measured by its principal moments of inertia) is inconsistent with its present, synchronously rotating state, or with any past synchronous state. The Moon's degree-two gravity components can be explained, however, as a combination of a fossil synchronous state with a fossil non-synchronous (rapidly rotating) shape. The key to capturing both signatures is for the Moon to be cooling rapidly at the same time it is captured into synchronous rotation. Since the Moon's rotational evolution is expected to be rapid, this is not unreasonable. Coupled thermal-rotational evolution calculations are used to place bounds on the distance from the Earth at which the Moon becomes synchronous, based on a range of interior models, initial rotation rates, and initial thermal states. Two important points that have not been incorporated into previous treatments of this problem are the initial capture of the Moon into a high-obliquity Cassini state (which alters the tidal potential), and the coupling of the rotational evolution to the thermal evolution through a Maxwell viscoelastic tidal model. A key process controlling this evolution is the rapid transport of heat by volcanism while the upper part of the Moon's mantle is still partially molten, which allows the thermal evolution to keep pace with the rotational evolution.