Present-day surface heat flux variations on the Moon from global geodynamic and crustal thickness models

High resolution gravity field measurements from GRAIL 1, in-situ heat flux 2 and seismic measurements from Apollo 3,4, surface composition from Clementine and Lunar Prospector 5,6, and the analysis of lunar samples have provided a wealth of information about the thermal evolution of the Moon 7. Constraints on the present-day thermal state of the lunar interior come from the Apollo surface heat flux measurements: 213 mW m-2 at the Apollo 15 and 142 mW m-2 at the Apollo 17 landing sites 2. A peak heat flux of ~180 mW m-2 was recently inferred by 8 from the ChangE 1 and 2 data at the Compton-Belkovich location, a Thorium anomaly feature on the lunar farside. A lower bound for the lunar heat flux of only ~6 mW m-2 has been suggested, for the so-called Region 5, by measurements of the Diviner Lunar Radiometer Experiment onboard LRO 9. Additionally, thermal expansion/contraction estimates 10 provide secondary constraints on the thermal state of the interior throughout lunar history. Here, we model the interior dynamics of the Moon to infer plausible distributions of heat producing elements (HPEs) that, in turn, are directly linked to surface heat flux variations. To this end, we compare the present-day surface heat flux obtained in our models with the above constraints. Similar to 11, we combine global geodynamical models 12 with crustal thickness models derived from gravity and topography data 13. We include higher HPEs abundances in the Procellarum KREEP Terrane (PKT) and crust compared to the mantle, and a mantle rheology similar to 14. We test both constant and pressure/temperature dependent thermal conductivity scenarios. In addition to present-day heat flux, we compute the thermal expansion/contraction based on the interior thermal state obtained from our models at different times during lunar evolution and compare these values with available estimates to select best-fit models. We find that variations in crustal thickness and the distribution of HPEs in the crust, mantle, and PKT region predominantly affect the convection pattern in the lunar interior and the surface heat flux. Models best compatible with the heat fluxes in the Apollo regions and Region 5 show an average Thorium abundance in the PKT region of ~2.4 ppm, smaller than the observed surface values 6, suggesting a strong Thorium enrichment close to the surface. These models have a crustal thermal conductivity of ~1.2 W/(mK), ~3 times lower than that of the mantle. None of our models matches the heat flux estimated at the Compton-Belkovich location, indicating either specific local processes 8 or large measurement uncertainties. References: 1 Zuber et al., 2013; 2 Langseth et al., 1976; 3 Garcia et al., 2019; 4 Nunn et al., 2020; 5 McEwen et al., 1997; 6 Lawrence at al., 2003; 7 Jaumann et al., 2012; 8 Siegler et al., 2023; 9 Paige Siegler, 2016; 10 Andrews-Hanna et al. 2013; 11 Plesa et al., 2016; 12 Httig et al., 2013; 13 Broquet Andrews-Hanna, 2023; 14 Laneuville et al., 2013.