Crystal Distribution in a Solidifying Lunar Magma Ocean
Authors: Wiesner Nikolas , Schwinger Sabrina 
Published: October 2020

&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;&lt;strong&gt;Introduction: &lt;/strong&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;During its early history, the Moon experienced a phase of planetary-scale melting that is commonly referred to as the Lunar Magma Ocean (LMO). Progressive crystallization of the LMO lead to differentiation of the lunar interior into a crust and a stratified mantle. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;The composition of the crystallizing solids strongly depends on the degree of crystal fractionation. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;However, the degree of crystal fractionation in the magma ocean and its evolution with time is still poorly constrained since it depends on multiple factors, including the initial thermal state of the LMO, the ability of the magma to suspend crystals by vigorous convection or the kinetics of crystal growth and dissolution during transport in the LMO and the resulting distribution of crystals in the LMO.&lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;In this study we combine multiple modeling approaches to investigate the distribution of crystals in a solidifying magma ocean and the evolution of the crystal budget during LMO solidification. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;&lt;strong&gt;Methods:&lt;/strong&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;In our model we &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;assumed&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; that two processes contribute to the total crystal budget of the early LMO: the formation of crystals in regions where the temperature drops below the liquidus and the introduction of solid material by impacts. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;&lt;em&gt;&lt;strong&gt;Crystal formation in the LMO: &lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;We assumed an initially 1350 km deep LMO that progressively cools from its liquidus temperature. The thermochemical evolution of the solidifying LMO was modeled using the phase equilibria software packages alphaMELTS and SPICE&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;S [1,2]. The results were used to calculate the temperature and composition dependent viscosity of the evolving magma as well as the solidus and liquidus temperatures at different stages of LMO evolution. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;We used the convection code GAIA &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;[3] &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;to model the temperature distribution in the convecting L&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;MO at distinct stages of LMO evolution, assuming a 2D &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;box&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; geometry&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;. We assumed that the time &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;scale &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;required for significant changes in the thermochemical properties is many orders of magnitude &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;larger&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; than the relaxation time of the convecting magma&lt;/span&gt;,&lt;span lang=&quot;en-US&quot;&gt; so that the convection is in a steady state at any given stage of the LMO evolution. Therefore, we modeled each stage of the evolution separately, using the results from our solidification model to define the initial temperature profile and the physical properties of the LMO. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;By comparing the steady state temperature distribution with the solidus and liquidus temperatures of the LMO, we determined the local &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;equilibrium &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;crystal fractions for each grid point of the 2D model. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;&lt;em&gt;&lt;strong&gt;Crystal introduction by impacts: &lt;/strong&gt;&lt;/em&gt;&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;We assumed that the LMO is impacted by a population of spherical impactor&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;s with bulk Moon composition an&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;d varying initial sub-solidus temperatures of&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; 0-1360 K&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;. The size distributio&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;n of the impactor population was assumed as suggested by [4]. The&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; impact velocity was not considered as a model parameter and was assumed not to affect the properties and sinking behavior of the impactors. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;Individual impactors were assumed to sink with their Stokes&amp;#8217; velocities, considering their sizes and densities as well as the density and viscosity of the surrounding magma. This velocity and the LMO depth were used to calculate the residence time of the impactors in the LMO before reaching the LMO bottom. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;We applied a 1D heat diffusion model to calculate the temperature distribution in the sinking impactor. Thereby we assumed time dependent boundary temperatures depending on the radial position of the impactor during sinking. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;S&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;olidus and liquidus temperatures of the impactors as well as the latent heat of melting were calculated with alphaMELTS and used to calculate the degree of melting of the impactor. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;&lt;strong&gt;Results:&lt;/strong&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;We &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;found&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; that &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;the &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;temperatures in &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;the &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;early LMO are close to the mean temperature with deviations of only a few K due to vigorous convection. The local deviations from the mean temperature increase as the LMO evolves, since&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; the liquid viscosity increases due to the compositional evolution and progressive cooling of the liquid. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;Subliquidus temperatures are reached only within a region close to the LMO bottom, while cold downwellings at shallower depths are not cold enough to facilitate crystal formation. The thickness of this crystal bearing region decreases from 250 km to 20 km as the LMO solidifies from an initial depth of 1350 km to a depth of &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;200&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; km. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;Nevertheless, the shallower regions are not completely free of crystals due to the introduction of impacting material. Our results indicate that impactors with a size of more than ~1m will reach the bottom of the LMO without melting completely. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;&lt;strong&gt;Discussion: &lt;/strong&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;The preliminary results of our models indicate that both the growth of crystals from the magma ocean liquid and the introduction of solid material from impacts contribute to the crystal budget of the LMO. This has implications for the magma ocean dynamics as the crystal budget influences magma viscosity. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;The surface of impacting solid material reaching the crystallization region &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;also &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;provides nucleation sites that facilitate the heterogeneous nucleation of crystals. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;H&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;eterogeneous nucleation on pre-existing solid aggregates requires less &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;undercooling than &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;homogeneous nucleation from the LMO liquid. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;Thus&lt;/span&gt; &lt;span lang=&quot;en-US&quot;&gt;the presence of impacted material might lead to an increased average size of crystals or crystal aggregates in the LMO&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; and hence &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;facilitate&lt;/span&gt; &lt;span lang=&quot;en-US&quot;&gt;the&lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt; fractionation of &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;solid &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;material from the LMO. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;&lt;strong&gt;References:&lt;/strong&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;[1] &lt;/span&gt;&lt;span lang=&quot;en-GB&quot;&gt;Smith and Asimow (2005), G&amp;#179;, 6.2.&lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;[2] &lt;/span&gt;&lt;span lang=&quot;en-GB&quot;&gt;Davenport (2013), Planet. Sci Res. Disc. Report 1, 173. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;[3] H&amp;#252;ttig et al. (2013), PEPI 220, 11-18. &lt;/span&gt;&lt;/p&gt;
&lt;p class=&quot;western&quot; align=&quot;justify&quot;&gt;&lt;span lang=&quot;en-US&quot;&gt;[4] Perera et al. &lt;/span&gt;&lt;span lang=&quot;en-US&quot;&gt;(2018), GJR: Planets, 123(5), 1168-1191. &lt;/span&gt;&lt;/p&gt;