The thermal history of the Moon caused by transport of heat and heat producing elements by migrating magma

Geological and geophysical observations of the Moon indicate that it expanded by a few km for the first several hundred million years, then that mare volcanism actively took place, and then finally that it contracted by cooling of its interior. Given the hot origin of the Moon expected from the Giant Impact hypothesis, early expansion is too large to account for by thermal expansion only. In this study, we numerically calculated the thermal history of the internally heated one-dimensional spherically symmetric mantle of the Moon, taking account of its radial expansion by magma generation. Magma is generated, when the temperature exceeds the melting temperature. The generated magma migrates upward as a permeable flow driven by the density difference between the solid and liquid phases. The migrating magma transports incompatible heat-producing elements (HPEs) that decay with time. The initial temperature at depth in the mantle is 1400 K to 1700 K, which implies that the shallow mantle is partially molten at the beginning of the calculation. The calculated mantle expands for the first several hundred million years due to melting caused by internal heating. The generated magma migrates upward to the surface and extracts HPEs from the deep mantle. Consequently, the Moon becomes colder and thermally contracts. The time when the Moon expands most coincides with that when the volcanism is most active. We find that the radial expansion does not occur, when the initial temperature in the mantle is too high (more than 1700K), because an extensive magmatism extracts HPEs from the entire mantle within the first few tens of millions of years. We obtain thermal history model of the Moon that is compatible with its observed features, only when the lunar interior temperature is initially 1450 K to 1650 K, and there are HPEs-rich regions above the core-mantle boundary. These results constrain the earliest history of the Moon dominated by the magma ocean and mantle overturn.