Physical constraints on the likelihood of accreting a non-chondritic Earth

地球是一个分化的行星。在它的演化过程中，熔融的铁下沉到它的中心形成了地核，在它的表面产生了一个地壳，在中间留下了一层残留的地幔。考虑到地球被分成几个不同的、无法进入的层，试图确定地球的组成是一个困难的问题。事实上，一种常见的方法是假设地球的组成，并利用这一点通过质量平衡来推断关于内层的信息。这就引出了一个问题，那就是如何估计地球的整体组成呢？就像陨石和太阳系中的所有其他行星一样，地球是由气体和尘埃组成的圆盘形成的，它含有太多的角动量，不可能直接落到年轻的太阳上。对于一些感兴趣的元素来说，这个由气体和尘埃组成的圆盘足够均匀，以至于地球的组成应该与从它生长出来的其他行星体相同。一些较小的小行星从未变得足够大，无法经历融化和分化，因此来自这些同质的未分化小行星的样本可以为整个地球提供一个成分估计。这样的样品以球粒陨石的形式存在。因此，这些珍贵的岩石在制约整个地球及其组成层的化学成分方面起到了关键作用。然而，地球的球粒陨石模型最近受到了密切关注。地球上和球粒陨石中的142Nd/144Nd的同位素比值应该是相同的，但测量结果却明显不同。为了解释这一令人震惊的观测结果，人们提出了两种截然不同的地球模型。第一个调用了一个隐藏的储集层，在规模和组成上与整个地球历史上一直被困在地幔底部的大陆地壳相媲美。另一种选择是，行星生长的吸积过程导致行星壳优先损失，从而导致非球粒陨石地球。这两个模型对地球的结构、行为和组成有着截然不同的影响。因此，确定这些情景中的哪一种是正确的具有至关重要的意义。虽然其他人已经(没有成功地)尝试确定隐藏的储存库的特征，但在这里，我们建议使用一种新的动力学模拟来解决吸积非球粒地球的物理可能性。在这项研究中，我们将运行一个代码，跟踪行星通过吸积增长的过程，同时也跟踪在这个过程中从撞击天体中丢失的物质。这项工作之所以成为可能，是因为皮莱因哈特和合作者斯图尔特最近开发了一个详细的碰撞模型。我们将进一步确定在这一过程中小行星的哪些部分会丢失。最后，将使用简单的熔化/结晶模型计算小行星不同部分的组成，熔化量由碰撞能量确定。这种模拟以前从未尝试过，用来绘制吸积行星的化学演化图。地壳的优先损失将导致富含在行星外部的一些关键元素(例如，产热元素Th和U)的枯竭。同样，其他影响可能会导致地幔而不是地核的移动，从而导致一个更富铁的行星。通过运行大量的模拟，我们可以评估一个地球大小的天体相对于地幔具有正确数量的核心和整体球粒组成的可能性。例如，我们可能会发现，地球不是软骨病几乎是不可避免的，或者恰好相反。无论是哪种情况，这项工作都将对地球的整体组成和行星吸积过程提供重要的启示。

The Earth is a differentiated planet. During its evolution, molten iron sank to its centre to form the core and a crust was produced at its surface, leaving a residual layer of mantle in between. Trying to determine the composition of the Earth is a difficult problem, given this division into several different, inaccessible layers. Indeed a common approach has been to assume a composition for the Earth and use this to deduce information about the interior layers by mass balance. This then begs the question, how is it possible to estimate the bulk composition of the Earth?The Earth, like the meteorites and all other planets in our solar system, formed from a disk of gas and dust that contained too much angular momentum to fall directly onto the young Sun. For some elements of interest this disk of gas and dust was sufficiently homogeneous that the Earth should be the same composition as other planetary bodies that grew from it. Some of the smaller asteroid bodies never grew large enough to undergo melting and differentiation, so samples from these homogenous undifferentiated planetesimals can provide a compositional estimate for bulk Earth. Such samples exist in the form of the chondritic meteorites. These precious rocks have therefore been critical in constraining the chemical composition of the Earth as a whole and also its constituent layers.However, the chondrite model for the Earth has recently come under close scrutiny. Measurements of the isotope ratio 142Nd/144Nd, which ought to be the same on Earth and in chondrites are notably divergent. To account for this alarming observation, two contrasting models of the Earth have been proposed. The first invokes a hidden reservoir, comparable in magnitude and composition to the continental crust that has been trapped at the bottom of the mantle throughout Earth History. The alternative is that the process of accretion, by which planets grow, leads to the preferential loss of planetary crust and so results in a non-chondritic Earth. These two models have very different implications for the structure, behaviour and composition of the Earth. Determining which of these scenarios is correct is therefore of fundamental importance. Whilst others have (unsuccessfully) attempted to identify a signature of the hidden reservoir, here we propose to address the physical plausibility of accreting a non-chondritic Earth using a novel dynamical simulations.In this study we will run a code that follows the growth of planets by accretion but also tracks material that is lost from impacting bodies during this process. This work has become possible due to the recent development of a detailed collision model developed by PI Leinhardt and collaborator Stewart. We will further determine what portions of the planetesimal are lost during this process. Finally, the composition of the different portions of the planetesimal will be calculated using simple melting/crystallization models following an amount of melting determined by the energy of collision. Such simulations, to chart the chemical evolution of accreting planets, have not previously been attempted.Preferential loss of crust will result in the depletion of some key elements (e.g. the heat producing elements Th and U) that are enriched in this outer portion of the planet. Likewise, other impacts may result in removal of mantle but not core, resulting in a more iron rich planet. By running a large number of simulations, we can assess the likelihood that a body the size of the Earth has the correct amount of core relative to mantle and an overall chondritic composition. For example, we may find that it is almost inevitable that the Earth is non-chondritic, or indeed the opposite. In either case this work will shed important light of the bulk composition of the Earth and the process of planetary accretion.