The magma ocean as an impediment to lunar plate tectonics

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Abstract
Potential for plate tectonics on a planet is determined by several factors besides the obvious one of temperature. One of the most important of these is the ratio zc/zl, where zc and zl are the thicknesses of the crust and tectonic lithosphere, respectively. A high zc/zl ratio imparts a low bulk density, and thus a high buoyancy, to the lithosphere. Cooling of the lithosphere can offset a limited degree of compositional buoyancy, but for realistic assumptions regarding crustal and mantle densities, lithosphere geotherms, and the spatial variability of the zc/zl ratio, systematic lithosphere subduction (i.e., plate tectonics) is unlikely on any planet with average zc/zl ratio greater than about 0.25. During a “magma ocean” phase, zc/zl must be ∼ 1, so systematic lithosphere subduction is impossible. In general, zl is closely linked to the average planet temperature, whereas zc is only weakly related to T but is sensitive to the planet's pressure‐depth gradient dP/dz (i.e., its size), which governs the fate of Al during deep melting/crystallization processes. The Moon has probably always had zc/zl too high, or in later times lithosphere thickness too high, to sustain plate tectonics. Conceivably, plate tectonics operated over the first few million years of lunar evolution, particularly if the early interior was cooler than generally assumed and a true magma “ocean” never developed, or only developed after gradual warming of the deep interior. However, weighing against this scenario, in addition to the wide array of evidence in favor of the magma ocean hypothesis, are the consistently moderate to young (by lunar standards) ages of geochemically evolved lunar rocks.