Asymmetric growth of planetary stagnant lids
Authors: Watson Callum , Neufeld Jerome , Michaut Chloé 
Published: March 2022

&lt;p&gt;Both the Moon&lt;sup&gt;1&lt;/sup&gt; and Mars&lt;sup&gt;2&lt;/sup&gt; 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&lt;sup&gt;3,4&lt;/sup&gt;, radiant heat from the Earth&lt;sup&gt;5&lt;/sup&gt; (in the case of the Moon), and large-scale volcanism&lt;sup&gt;6&lt;/sup&gt; (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.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;sup&gt;1&lt;/sup&gt; 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. &amp; Bussey, B. 2006 The Constitution and Structure of the Lunar Interior. &lt;em&gt;Reviews in Mineralogy and Geochemistry&lt;/em&gt; &lt;strong&gt;60&lt;/strong&gt;, 221&amp;#8211;364.&lt;/p&gt;&lt;p&gt;&lt;sup&gt;2&lt;/sup&gt; Thiriet, M., Michaut, C., Breuer, D. &amp; Plesa, A.-C. 2018 Hemispheric dichotomy in lithosphere thickness on mars caused by differences in crustal structure and composition. &lt;em&gt;Journal of Geophysical Research: Planets&lt;/em&gt; &lt;strong&gt;123&lt;/strong&gt; (4), 823&amp;#8211;848.&lt;br&gt;Weiss, Benjamin P. &amp; Tikoo, Sonia M. 2014 The lunar dynamo. Science 346 (6214), 1198&lt;/p&gt;&lt;p&gt;&lt;sup&gt;3 &lt;/sup&gt;Garrick-Bethell, I., Perera, V., Nimmo, F. &amp; Zuber, M.T. 2014 The tidal-rotational shape of the Moon and evidence for polar wander. &lt;em&gt;Nature&lt;/em&gt; &lt;strong&gt;512&lt;/strong&gt; (7513), 181&amp;#8211;184.&lt;/p&gt;&lt;p&gt;&lt;sup&gt;4&lt;/sup&gt; Andrews-Hanna, J.C., Zuber, M.T. &amp; Banerdt, W.B. 2008 The borealis basin and the origin of the martian crustal dichotomy. &lt;em&gt;Nature&lt;/em&gt; &lt;strong&gt;453&lt;/strong&gt; (7199), 1212&amp;#8211;1215.&lt;/p&gt;&lt;p&gt;&lt;sup&gt;5 &lt;/sup&gt;Roy, A., Wright, J.T. &amp; Sigur&amp;#240;sson, S. 2014 Earthshine on a young moon: Explaining the lunar farside highlands. &lt;em&gt;The Astrophysical Journal Letters&lt;/em&gt; &lt;strong&gt;788&lt;/strong&gt; (2), L42.&lt;/p&gt;&lt;p&gt;&lt;sup&gt;6 &lt;/sup&gt;Golabek, G.J., Keller, T., Gerya, T.V., Zhu, G., Tackley, P.J. &amp; Connolly, J.A.D. 2011 Origin of the martian dichotomy and tharsis from a giant impact causing massive magmatism. &lt;em&gt;Icarus&lt;/em&gt; &lt;strong&gt;215&lt;/strong&gt; (1), 346&amp;#8211;357.&lt;/p&gt;