arXiv 1011.02012010-11astro-ph.EP

行星形成期间的失控增长：解释大型柯伊伯带天体的尺寸分布

Runaway Growth During Planet Formation: Explaining the Size Distribution of Large Kuiper Belt Objects

Hilke E. Schlichting, Reem Sari

备注：: 13 pages, 7 figues
DOI：: 10.1088/0004-637X/728/1/68

摘要：

跑道生长是行星形成的一个重要阶段，在此期间，大型原行星形成，而大部分初始质量仍保留在小星子中。转换成大型原行星的质量数量及其产生的大小分布还没有很好的了解。在这里，我们使用通过凝聚模拟确认的分析工作来描述失控的生长和相应的速度弥散演变。我们发现，失控的增长过程如下：最初所有的质量都存在于小的星子中，质量表面密度为σ，大型原行星开始通过吸积小的星子形成。这种增长一直持续到合并大型原行星的增长变得与星子吸积的增长相当。当Σ/σ~α^{3/4} ~ 10^{-3}时，这一条件成立，其中Σ是原行星在给定对数质量区间内的质量表面密度，α是天体大小与希尔半径之比。从那时起，原行星的生长和速度色散的演变变得自相似，并且由于小微行星的吸积而增加的速度色散被由于与大原行星合并而减少的速度色散所平衡，因此速度色散大致保持不变。我们发现，这种增长导致原行星的大小分布由N（>R）\propto R^{-3}给出，其中N（>R）是半径大于R的物体的数量（即，微分幂律指数为4）。我们将我们的结果应用于柯伊伯带，这是一个失控增长的遗迹。我们的结果成功地匹配了观测到的柯伊伯带尺寸分布，它们阐明了形成它的物理过程，并解释了今天大型柯伊伯带天体（KBO）中存在的总质量。这项工作表明，目前在大型KBO的质量是原始的，它还没有被显着耗尽。删节

英文摘要：

Runway growth is an important stage in planet formation during which large protoplanets form, while most of the initial mass remains in small planetesimals. The amount of mass converted into large protoplanets and their resulting size distribution are not well understood. Here, we use analytic work, that we confirm by coagulation simulations, to describe runaway growth and the corresponding evolution of the velocity dispersion. We find that runaway growth proceeds as follows: Initially all the mass resides in small planetesimals, with mass surface density σ, and large protoplanets start to form by accreting small planetesimals. This growth continues until growth by merging large protoplanets becomes comparable to growth by planetesimal accretion. This condition sets in when Σ/σ~α^{3/4} ~ 10^{-3}, where Σis the mass surface density in protoplanets in a given logarithmic mass interval and αis the ratio of the size of a body to its Hill radius. From then on, protoplanetary growth and the evolution of the velocity dispersion become self-similar and Σremains roughly constant, since an increase in Σby accretion of small planetesimals is balanced by a decrease due to merging with large protoplanets. We show that this growth leads to a protoplanet size distribution given by N(>R) \propto R^{-3} where N(>R) is the number of objects with radii greater than R (i.e., a differential power-law index of 4). We apply our results to the Kuiper Belt, which is a relic of runaway growth. Our results successfully match the observed Kuiper belt size distribution, they illuminate the physical processes that shaped it and explain the total mass that is present in large Kuiper belt objects (KBOs) today. This work suggests that the current mass in large KBOs is primordial and that it has not been significantly depleted. Abridged

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