Asymmetric growth of planetary stagnant lids

Both the Moon¹ and Mars² are known to have significant degree-1 variations in their crustal thicknesses, with the Moon's far side and Mars's southern hemisphere having far thicker crusts than their respective opposing hemispheres. A number of potential mechanisms have been proposed to explain these dichotomies, including large impacts in both cases^3,4, radiant heat from the Earth⁵ (in the case of the Moon), and large-scale volcanism⁶ (in the case of Mars). However, the effectiveness of these mechanisms are limited by the difficulty of sustaining a large hemispheric difference during the tens to hundreds of Ma of crustal formation. Both planets' lithospheres are examples of a fluid-dynamical boundary layer known as a stagnant lid, caused by temperature-dependent viscosity in a convecting system. We consider the effect of pressure on the viscosity of magma oceans and mantles, finding that under certain circumstances a spherically-symmetric stagnant lid is linearly unstable to asymmetric perturbations. The fastest-growing wavenumbers of this instability is degree 1, meaning that a small initial asymmetry may grow into a full-scale hemispherical dichotomy. We then numerically examine the stability of these asymmetric states, finding that they may last for hundreds of Ma. We also compare to the case of Mercury, a similarly-sized planet with no such crustal dichotomy, to determine if our analysis matches observations.

 

¹ Wieczorek, M.A., Jolliff, B.L., Khan, A., Pritchard, M.E., Weiss, B.P., Williams, J.G., Hood, L.L., Righter, K., Neal, C.R., Shearer, C.K., McCallum, I.S., Tompkins, S., Hawke, B.R., Peterson, C., Gillis, J.J. & Bussey, B. 2006 The Constitution and Structure of the Lunar Interior. Reviews in Mineralogy and Geochemistry 60, 221–364.

² Thiriet, M., Michaut, C., Breuer, D. & Plesa, A.-C. 2018 Hemispheric dichotomy in lithosphere thickness on mars caused by differences in crustal structure and composition. Journal of Geophysical Research: Planets 123 (4), 823–848.
Weiss, Benjamin P. & Tikoo, Sonia M. 2014 The lunar dynamo. Science 346 (6214), 1198

³ Garrick-Bethell, I., Perera, V., Nimmo, F. & Zuber, M.T. 2014 The tidal-rotational shape of the Moon and evidence for polar wander. Nature 512 (7513), 181–184.

⁴ Andrews-Hanna, J.C., Zuber, M.T. & Banerdt, W.B. 2008 The borealis basin and the origin of the martian crustal dichotomy. Nature 453 (7199), 1212–1215.

⁵ Roy, A., Wright, J.T. & Sigurðsson, S. 2014 Earthshine on a young moon: Explaining the lunar farside highlands. The Astrophysical Journal Letters 788 (2), L42.

⁶ Golabek, G.J., Keller, T., Gerya, T.V., Zhu, G., Tackley, P.J. & Connolly, J.A.D. 2011 Origin of the martian dichotomy and tharsis from a giant impact causing massive magmatism. Icarus 215 (1), 346–357.