The Competition Between Thermal Contraction and Differentiation in the Stress History of the Moon

Abstract

The scarcity of both extension and compression features on the Moon strongly constrains the history of the lunar radius—to variations of less than ±1 km over the past 3.8 Gyr. This limit has traditionally been interpreted as requiring a delicate balance between thermal contraction of the near-surface and expansion of a substantial cold interior region. Recent theories of lunar origin (e.g., giant impact), in contrast, favor a “hot” initial state. We propose that a reconciliation may be possible by taking account of the volume change ΔV/V|_d due to differentiation. We calculate STP densities based on simplified normative mineralogies for a suite of estimates of the bulk lunar composition, of primary lunar basalt, and of the residuum left when the maximum amount of the latter is extracted from the former. Typically ΔV/V|_d ≃ 2 to 5%—an expansion equivalent to heating by ∼10^(3)K. Provided the timing of differentiation is correct, one might offset the cooling of a magma ocean as much as 630 km deep by differentiation of the remainder of the Moon (which need not start much below the solidus temperature). A large but not impossible amount of gabbroic melt production is implied: ∼100 times the volume of mare basalts known to have been extruded. We do not address the detailed genetic relationship of this melt to the basalts observed on the lunar surface but point out that it need not have reached the surface directly or even have entered the crust in order for the expansion to have occurred. To assess the timing of melt formation, we investigate a simple conductive lunar thermal model which takes account of both ΔV/V|_d and thermal contraction. Our initial state is characterized by a central temperature T_c and a depth Z_0 above which the material (derived from the magma ocean) is already at the solidus and is not suceptible to volume changes upon further differentiation. We find a range of models satisfying the limits on radius increase and decrease. The hottest has T_c = 1210 K, Z_0 = 400 km; without ΔV/V|d, we would need a larger or colder (or both) core, e.g., T_c ≲ 700 K for Z0 = 200–400 km, in agreement with previous investigators. Our modeling thus lends credence to the idea that the Moon could have been initially ≳50% molten (with the remainder relatively close to the solidus) and yet experienced little volume change over the last 3.8 Gyr.