  To understand the evolution of the Moon, we numerically modeled mantle
convection and magmatism in a two-dimensional polar rectangular mantle.
Magmatism occurs as an upward permeable flow of magma generated by
decompression melting through the convecting matrix. The mantle is assumed to
be initially enriched in heat-producing elements (HPEs) and compositionally
dense ilmenite-bearing cumulates (IBC) at its base. Here, we newly show that
magma generation and migration play a crucial role in the calculated volcanic
and radial expansion/contraction history. Magma is generated in the deep mantle
by internal heating for the first several hundred million years. A large volume
of the generated magma ascends to the surface as partially molten fingers and
plumes driven by melt-buoyancy to cause a volcanic activity and radial
expansion of the planet with the peak at 3.5-4 Gyr ago. Eventually, however,
the planet begins to radially contract when the mantle solidifies by cooling
from the surface boundary. As the mantle is cooled, the activity of partially
molten plumes declines but continues for billions of years after the peak
because some basal materials enriched in the dense IBC components hold HPEs.
The calculated volcanic and radial expansion/contraction history is consistent
with the observed history of the Moon. Our simulations suggest a substantial
fraction of the mantle was solid, and there was a basal layer enriched in HPEs
and the IBC components at the beginning of the history of the Moon.
