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

地球是一个分化的星球。在它的演化过程中，熔融的铁下沉到它的中心形成地核，在它的表面形成地壳，中间留下一层地幔。考虑到地球分为几个不同的、难以接近的层，试图确定地球的组成是一个难题。事实上，一种常见的方法是假设地球的组成，并利用它通过质量平衡来推断有关内层的信息。这就引出了一个问题，怎样才能估计出地球的总体组成？地球，就像我们太阳系中的陨石和所有其他行星一样，是由气体和尘埃组成的圆盘形成的，这些圆盘的角动量太大，无法直接落在年轻的太阳上。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是足够均匀的，以至于地球应该与从它生长出来的其他行星体具有相同的组成。一些较小的小行星体从未长大到足以经历融化和分化的程度，因此从这些均匀的未分化的星子中提取的样本可以为整体地球提供成分估计。这些样本以球粒陨石的形式存在。因此，这些珍贵的岩石在限制整个地球及其组成层的化学成分方面起着至关重要的作用。然而，地球的球粒陨石模型最近受到了密切关注。在地球和球粒陨石中应该相同的同位素比率142 /144Nd的测量结果明显不同。为了解释这一令人震惊的观察结果，人们提出了两种截然不同的地球模型。第一种方法需要一个隐藏的储层，其规模和组成可与地球历史上一直被困在地幔底部的大陆地壳相媲美。另一种说法是，行星生长的吸积过程导致行星地壳优先丧失，从而导致地球非球粒质。这两个模型对地球的结构、行为和组成有着非常不同的含义。因此，确定哪一种情况是正确的是至关重要的。虽然其他人（不成功）试图识别隐藏储层的特征，但在这里，我们建议使用一种新的动力学模拟来解决非球粒地球吸积的物理合理性。在这项研究中，我们将运行一个代码来跟踪行星通过吸积的增长，但也跟踪在这个过程中从撞击体中丢失的物质。由于最近由PI Leinhardt和合作者Stewart开发的详细碰撞模型的发展，这项工作成为可能。我们将进一步确定在这个过程中丢失了哪些部分的星子。最后，根据碰撞能量确定的熔化量，使用简单的熔化/结晶模型计算小行星不同部分的组成。这种模拟是为了绘制吸积行星的化学演化图，以前从未有人尝试过。地壳的优先损失将导致一些关键元素（例如产热元素Th和U）的消耗，这些元素在地球的外层富集。同样，其他影响可能导致地幔的移除，但不会导致地核的移除，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，地球几乎不可避免地是非球粒质的，或者恰恰相反。无论哪种情况，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.