Tidal Heating of the Lunar Magma Ocean

TL;DR

This study tackles the puzzling timing of the Moon's magma-ocean (LMO) solidification, where most LMO-derived rocks cluster around $4.35\pm0.05$ Ga after an initial formation epoch. It proposes that tidal heating within the LMO, driven by Earth–Moon tidal forcing during orbital recession, creates a high-energy thermal plateau (stable equilibrium) followed by a rapid temperature drop (thermal cliff) near $4.35$ Ga, naturally delaying the final crystallization for $\sim$100 Myr and then driving a rapid solidification as dissipation wanes. The model predicts a transient nearside–farside temperature contrast of $20$–$100^{\circ}{\rm C}$ during the final solidification, offering a mechanism for asymmetric crystallization that aligns with observed nearside-dominant KREEP, mare volcanism, and Mg# differences. Overall, tidal heating emerges as a robust, intrinsic control on LMO evolution and potentially on broader lunar differentiation, including long-lived asymmetries between the hemispheres.

Abstract

The timing of the lunar magma ocean (LMO) solidification is governed by its thermal evolution. A key geochronological observation is that all analyzed products of LMO solidification have ages (or age peaks) near 4.35 +/- 0.05 billion years ago (Ga), suggesting rapid solidification of the last ~40% of the LMO at that time. The ages raise two questions: (1) how was the final solidification of the LMO delayed for over 100 Myr (million years) from the Moon's formation, and (2) after such a delay, how did it solidify so quickly? These two aspects of the ages are inconsistent with models of early-fast solidification or slow-prolonged solidification, controlled by radiogenic heat production and convective cooling (even if slowed by a conductive lithosphere). We propose that both aspects can not only be explained by tidal heating of the LMO but are in fact robust and expected thermal evolution features of a magma ocean cooling while being tidally heated and, in the Moon's case, receding from the Earth. The delay in solidification is due to the LMO being trapped at a stable equilibrium between the enhanced tidal heating rate and the decreasing cooling rate. The rapid solidification at ~4.35 Ga occurs when the Moon retreats to the point where an unstable equilibrium is reached, where tidal heating is drastically reduced, rapidly cooling the Moon. Moreover, an unanticipated outcome of our modeling is that the farside of the Moon is predicted to be 20-60 deg C cooler than the nearside for ~10-100 Myr during the final solidification stage. This is consistent with previous studies indicating asymmetric crystallization of the LMO from the farside to the nearside, which leads to an older and less evolved farside crust than the nearside, consistent with the observed higher Mg# of farside anorthositic crust and the nearside concentration of H2O, KREEP, and high Fe-Ti components.

Figures (13)

• Figure 1: LMO crystallization geochronology predicted by different thermal evolution models. (A) Ages of mare-basalt mantle sources (pyroxenites, orange), Ferroan Anorthosites (FANs, green), urKREEP (purple), and Mg-suite rocks (blue) cluster near $\sim4.35$ Ga. These represent the last 30--50% of LMO solidification and post-solidification overturn (Mg-suite). The light-gray curve shows the age distribution of early detrital zircons, which also peaks at $\sim4.35$ Ga. Data are from Borg and Carlson (2023) borg2023evolving and references therein. The red curve shows the modeled LMO tidal-heating rate, featuring a prolonged thermal plateau followed by a thermal cliff at $\sim4.35$ Ga. The green near-horizontal curve indicates the radiogenic heating rate for comparison. White numerals in black squares mark stages 1--4 of the LMO thermal evolution. (B) End-member cooling histories with different total cooling rates. A fast-cooling case (leftmost curve) produces clustered ages but much older ages than observed, whereas slower cooling (right two curves) extends LMO solidification and yields a more dispersed age distribution than observed. (C) In reheating models, the LMO solidifies early, and a later post-solidification event (e.g., the South Pole--Aitken (SPA) impact or the Laplace Plane Transition (LPT) event) reheats and resets the ages of all LMO products. Symbols in panels (B) and (C) match the four lithologies and colors in panel (A).
• Figure 2: Tidal heating evolution of the LMO. Coevolution of LMO temperature, tidal heating, and total energy. Temperature on the lower axis decreases from left to right; two vertical gray lines mark the liquidus and solidus. The upper axis shows melt fraction, partitioning the diagram into liquid, mush, and solid regimes. Energy (watts) is plotted on a logarithmic scale. The blue curve is total cooling power (convection + conduction). The red curves are tidal-heating power for different assumed Earth--Moon distances. The red arrows show that as the Earth--Moon distance increases, the peak tidal-heating power (red dots) decreases. The green curve traces the tidal heating rate within the LMO. Tidal power is small at very high and very low temperatures and rises by orders of magnitude across the rheological transition, peaking near an intermediate melt fraction of $\sim0.4$. Because the initial energy is high, the LMO cools rapidly at first. It then enters a regime where tidal heating and cooling nearly balance; intersections of the red and blue curves (black points) are stable equilibria, and the system moves through a sequence of these as tidal power wanes with increasing Earth--Moon distance. The sequence ends at a tangency (gray point), an unstable equilibrium. Between the first stable intersection and this unstable tangency, strong tidal heating buffers energy loss, producing a gentler net-cooling slope---a high-energy plateau in the LMO's evolution. Beyond the unstable point, tidal power collapses, total cooling exceeds heating, and the system descends a sharp cliff.
• Figure 3: Duration of LMO tidal heating as a function of eccentricity and Earth's tidal parameters. The x-axis is Earth's tidal quality factor over Love number, $Q_{\mathrm{E}}/k_{2\mathrm{E}}$, which varies inversely with the rate of Earth--Moon distance expansion; the y-axis is the lunar orbital eccentricity $e$. The color map gives the "cliff age"---the first time at which LMO tidal heating drops below radiogenic heating following the high-energy plateau---and thus scales inversely with the duration of the high tidal-heating interval. Three dashed curves mark contours at cliff ages of 4.40, 4.35, and 4.30 Ga. The corresponding $(e,Q_{\mathrm{E}}/k_{2\mathrm{E}})$ combinations along these contours are, to first order, consistent with the available geochronological constraints on sample ages. The green star denotes the parameter choice used in Fig. 1A ($e=0.05$, $Q_{\mathrm{E}}/k_{2\mathrm{E}}=400$), consistent with prior early Earth--Moon distance evolution models farhat2022resonant.
• Figure 4: Asymmetric tidal heating of the LMO. Tidal heating rates for the lunar nearside and farside are computed by perturbing the tidal amplitude (for methods, see the Supplementary Materials) relative to the baseline case in Fig. 1A. Other parameters, such as eccentricity and viscosity are held fixed. (A) Tidal-heating histories for the nearside (red) and farside (blue). The curves track closely through stable-equilibrium stage 2, then diverge as the farside reaches the unstable equilibrium earlier because its forcing distance is larger ($+R_{\mathrm{M}}$). The nearside-to-farside tidal-heating ratio (purple, right axis) is shown with a dashed reference line at 1.2. The ratio peaks at 7.9 at 4.36 Ga; at most other times before 4.35 Ga, it remains $\leq1.2$. (B) Temperature evolution. The temperature difference between the nearside and farside is minimal during the stable-equilibrium stage 2, and peaks in the time between the farside and nearside reaching the unstable point. The purple curve shows $T_{\mathrm{near}}-T_{\mathrm{far}}$, peaking at $\sim20$$^\circ$C near 4.35 Ga. White numerals in black squares mark stages 1--4 of the LMO thermal evolution. Results based on additional orbital parameter choices can be found in the Supplementary Materials.
• Figure 5: Asymmetric crystallization of the LMO driven by differential tidal heating. (A) Nearside-hot / farside-cold state at $\sim4.35$ Ga, just as the farside has passed the unstable point and is cooling rapidly. Enhanced tidal/thermal input on the nearside keeps the LMO warmer and delays the plagioclase flotation process there, while the farside cools faster and forms a thicker, earlier anorthositic crust. Early mafic cumulates (olivine $\pm$ orthopyroxene) deposited before $\sim4.35$ Ga are compositionally similar on both sides. (B) Post-4.35 Ga cumulates. Continued crystallization and asymmetric cooling concentrate late Fe--Ti--rich melts and urKREEP beneath the thinner nearside crust, enriching the nearside in Fe, Ti, incompatible elements, and H$_2$O. The farside retains older, higher-Mg# anorthosite and thicker crust; dashed horizons schematically illustrate the nearside-ward tilting of mafic cumulates. Figure is not to scale.