Variations of Heat Flux and Elastic Thickness of Mercury derived from Thermal Evolution Modeling

Introduction:

The very low obliquity of Mercury causes important surface temperature variations between its polar and equatorial regions (Margot et al., 2012). Additionally, its atypical 3:2 spin-orbit resonance also leads to longitudinal temperature variations (Siegler et al 2013). The combination of these effects creates a peculiar surface temperature distribution with equatorial hot and warm poles, and cold poles at the geographic poles of the planet (Fig.1a). Models that considered the insolation pattern were found compatible with the low-degree shape and geoid from MESSENGER (Tosi et al., 2015). These models showed that the insolation pattern imposes a long-wavelength thermal perturbation throughout the mantle.

Variations in crustal thickness can also influence the temperature distribution across the lithosphere and mantle, as previously shown for Mars (Plesa et al., 2016, 2018). Models ofMercury's crustal thickness obtained from MESSENGER’s gravity and topography data depend heavily on the assumed density differences between the crust and mantle. Recently, Beuthe et al. (2020) introduced several models of crustal thickness that use either a uniform crustal density (Fig. 1b) or a variable one (Fig. 1c), based on data of surface composition under the assumption that this  remains constant with depth throughout the whole crust.

In this study, we investigate the impact of variations in surface temperature and crustal thickness on the thermal evolution of Mercury's interior. We compute the distribution of surface and core-mantle boundary (CMB) heat flux, as well as variations in the thickness of the elastic lithosphere, and compare these calculations with independent estimates of elastic thickness obtained from local analyses of gravity and topography.

Model:

We include crustal thickness and surface temperature variations of Mercury in the mantle convection code GAIA (Hüttig et al., 2013). Similar to Plesa et al. (2016), we assume that the whole crust was emplaced early and remains unchanged for the entire evolution. The surface temperature pattern is also kept constant for the whole evolution, implicitly assuming that the 3:2 resonance was established early on. All simulations are performed in a 3D spherical shell geometry, use the extended Boussinesq Approximation, and consider core cooling and radioactive decay. The pressure- and temperature-dependent viscosity follows an Arrhenius law of diffusion creep. We model the entire thermal evolution of Mercury to determine the variations of surface and CMB heat fluxes in addition to the temporal evolution and distribution of the elastic lithosphere thickness.

Our models include surface temperature variations (Fig. 1a) following Vasavada et al. (1999). In addition, we test several crustal thickness models from Beuthe et al. (2020), namely model U0 (Fig. 1b), assuming a constant crustal density, and V0 (Fig. 1c), V3, and V4, all of which account for laterally-varying crustal density and assume mean crustal thicknesses of 35, 25, and 45 km, respectively. The crust is enriched in heat producing elements (HPEs) by a fixed factor λ compared to the primitive mantle, for which we assume a chondritic HPE abundance (Padovan et al., 2017).

The thermal conductivity of the crust is set to 1.761 Wm^-1K^-1 and includes the insulating effect of the overlying 3-km thick megaregolith.

Results:

The surface temperature distribution imposes a long-wavelength pattern on the present-day distribution of CMB and surface heat fluxes,  which is locally modified by the variations of crustal thickness. Positive thermal anomalies induced by the combination of the hot poles and thick crust propagate through the entire mantle and heat up the base of the mantle near the CMB. The impact of the crustal thickness on the heat flux variations depends on the crustal enrichment in HPE, becoming more significantfor a higher crustal enrichment.

Alongside the surface and CMB heat flux maps, Fig. 2 also displays temperature profiles at specific locations (Northern Volcanic Plains, Caloris basin, High-Magnesium region) in comparison to both the global average temperature profile and the solidus profile from Namur et al. (2016) at various stages of evolution. We note distinct differences in the thermal state across different geological zones on Mercury, especially in models employing a variable crustal density, which results in pronounced variations in crustal thickness.

Fig. 3 presents maps of the elastic thickness at various stages of the evolution, utilizing the crustal thickness model V0. Similar to the current heat fluxes shown in Fig. 2, the surface temperature creates a predominant degree 2 distribution, with thicker elastic lithosphere at the poles and thinner at the equatorial hot poles throughout Mercury's evolution. The crustal distribution leads to  smaller scale changes in the elastic lithospheric thickness, where regions with a thin crust, such as the Caloris basin and the Northern Volcanic Plains, are outlined as areas with greater lithospheric thickness.

Conclusion:

Our models indicate that the lateral variations of Mercury's surface heat flux is primarily influenced by its unique surface temperature pattern. However, variations in crustal thickness and the distribution of HPEs between the crust and mantle also locally modify the surface heat flux. Our findings reveal that elastic thickness values at Discovery Rupes align with previous studies, whereas consistently lower values are observed for the Caloris basin. Our model also provides an accurate distribution of the present-day CMB heat flux that should be used as boundary conditions to test future dynamo models. Finally, we find that different geochemical terrains, such as the Northern Volcanic Plains and the High-Magnesium Region, may have undergone significantly different thermal histories during Mercury's evolution.