根据2D模拟计算的碰撞参数统计
Statistics of collision parameters computed from 2D simulations
摘要：
有两种常用的方法通过增加碰撞概率来加速行星形成的模拟：（{ \it i}）将运动限制在2D，（{ \it ii}）通过膨胀因子人为地增加天体的物理半径。在本文中，我已经进行了100次模拟，每个模拟包含$10^4$相互作用的机构，并从运行的结果计算碰撞参数。针对较低和较高准确度参数执行每次运行。主要目的是确定碰撞参数的概率分布函数及其对膨胀因子的依赖性。设计了一种简单的方法，以提高从模拟数据的碰撞参数的确定。结果表明，碰撞参量的分布是均匀的，与膨胀因子无关。对于真实碰撞，碰撞速度大于1个相互逃逸速度，这一发现可以用两体问题来解释。这一结果对假设合并的类地行星最终吸积的模拟提出了一些质疑。采用\cite{Leinhardt2012}的碎裂模型绘制了碰撞结果图，以估计不同类型碰撞的数量。与早期作品的详细比较表明，不同作品之间既有相似之处，也有显着差异。结果表明，随着行星盘的成熟和机构的质量逐渐不同，比大多数碰撞导致质量增长通过部分吸积或通过擦合并碰撞。
英文摘要：
There are two popular ways to speed up simulations of planet formation via increasing the collision probability: ({\it i}) confine motion to 2D, ({\it ii}) artificially enhance the physical radii of the bodies by an expansion factor. In this paper I have performed 100 simulations each containing $10^4$ interacting bodies and computed the collision parameters from the results of the runs. Each run was executed for a lower and a higher accuracy parameter. The main goal is to determine the probability distribution functions of the collision parameters and their dependence on the expansion factor. A simple method is devised to improve the determination of the collision parameters from the simulation data. It was shown that the distribution of the impact parameter is uniform and independent of the expansion factor. For real collisions the impact velocity is greater than 1 mutual escape velocity, a finding that can be explained using the two-body problem. The results casts some doubts on simulations of the terrestrial planets' final accretion that have assumed merge. Collision outcome maps were created adopting the fragmentation model of \cite{Leinhardt2012} to estimate the number of different types of collisions. A detailed comparison with earlier works indicates that there are similarities as well as significant differences between the different works. The results indicate that as the planetary disc matures and the masses of the bodies differs progressively than the majority of collisions lead to mass growth either via partial accretion or via graze-and-merge collision.
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