The origin of long-wavelength variations in crustal thickness on telluric planet
Authors: Bonnet Gibet Valentin , michaut chloe 
Published: July 2024

Long-wavelength topography variations are observed on telluric planets. They are often associated with long-wavelength crustal thickness variations and define different geological provinces. Mars and the Moon both display a hemispherical dichotomy in topography. The Southern Hemisphere of Mars and the far side of the Moon constitute the highlands of the planets, while the opposite hemispheres concentrate topographic lows: the Martian plains and the Lunar mare. Venus also shows highlands surrounded by volcanic plains, but no hemispheric dichotomy. On Earth, the present-day difference in topography between continents and oceans is not hemispheric either and is, in this case, the result of plate tectonics. Mercury seems to be an exception, as it does not present long-wavelength variations in topography. However, a thick crustal province associated with a denser crust has been proposed.&#160;On one-plate planets, a positive feedback mechanism exists between crustal thickness and melt extraction. Thicker crusts contain more radioelements, which leads to hotter temperature profiles and hence thinner lid thicknesses. Because of the pressure-dependence of the solidus, thinner lids are associated to more partial melt in the mantle below the lid and, hence, larger crustal extraction rates where the crust is thicker. This mechanism enables the spontaneous formation of thick crustal regions (Bonnet Gibet et al. 2022). A linear stability analysis on a simplified setup that does not account for planetary cooling shows that long-wavelength variations in crustal thickness, the hemispherical one (degree l = 1) in particular, are favoured by this mechanism. Shorter wavelengths are more efficiently attenuated by lateral diffusion of heat within the conductive lid (Figure 1, left panel).&#160; Additionally, as the planetary radius gets smaller, the growth rate becomes more peaked towards the degree l=1 mode (Figure 1, left panel). A hemispherical difference, or dichotomy, in crustal thickness is thus even more likely to grow on a smaller planet. The growth of a perturbation in crustal thickness necessitates, however, the presence of partial melt and is thus dampened by planetary cooling and lid thickening. Therefore, if the timescale for crustal extraction is too short, i.e. shorter than the characteristic timescale for the growth of this perturbation, long wavelength variations in crustal thickness cannot grow through this mechanism (Figure 1, right panel).Figure 1 : Left panel, growth rate of a perturbation normalised by the growth rate l=1 (&#955;(l)/&#955;(1)) as a function of spherical harmonic degree (l) for different planet sizes. Right panel, characteristic timescale for the growth of a perturbation (1/&#955;(l)) as a function of planetary radius.&#160;We use a parametrised, asymmetric, thermal evolution model accounting for crustal extraction. We assume a thermally well-mixed convective mantle topped by a stagnant lid divided into two different hemispheres that evolve independently. This model allows us to calculate the temporal evolution of the lid thickness, the mantle melt fraction and the crustal thickness for each hemisphere. Assuming a very small initial thermal anomaly between the two hemispheres, we monitor the thermal evolution of the planet to see whether this small difference grows into a crustal thickness dichotomy or decays. We apply our model to Mercury, Mars, and Venus, with an initial thermal state corresponding to the end of the crystallisation of a magma ocean.&#160;Our results show that this positive feedback mechanism can explain by itself the formation of the Martian dichotomy for a large range of parameters (Bonnet Gibet et al. 2022). For Mars, the crust extraction time is indeed larger than 1 Gyr and hence larger than the characteristic time for the growth of the initial thermal perturbation. For Venus, as the planet's secular cooling is very small, crustal extraction can proceed throughout the planet's evolution, but at a lower mantle melt fraction because of the larger internal pressure gradient. Variations in the crustal thickness can thus develop on Venus during an episode of stagnant lid convection with this mechanism. It is, however, not clear whether the degree l=1 mode could be selected, given the very flat growth rate curve at a small spherical harmonic degree (Figure 1). On the contrary, for Mercury, which has a thin silicate shell (~400 km) and a high Urey ratio, cooling is too fast for this mechanism to produce a significant dichotomy in crustal thickness. Mars seems therefore to present the optimal size for the growth of a hemispheric crustal dichotomy.