标题： 原行星巨大撞击的合并准则 显示英文标题

标题： Merging Criteria for Giant Impacts of Protoplanets

摘要： 在地行星形成过程的最后阶段，即巨大撞击阶段，几十个火星大小的原行星相互碰撞以形成地行星。 几乎所有关于此阶段原行星轨道和吸积演化的先前研究都基于完美吸积的假设，即两个碰撞的原行星总是会合并。 然而，最近的撞击模拟显示，原行星之间的碰撞并不总是合并事件，也就是说，两个碰撞的原行星有时会在碰撞后分开（撞击逃逸碰撞）。 作为研究这种不完美吸积对地行星形成影响的第一步，我们研究了岩石原行星碰撞的合并条件。 使用平滑粒子流体动力学（SPH）方法，我们进行了超过1000次不同参数集的巨大撞击模拟，例如原行星的质量比，$\gamma$，两个原行星的总质量，$M_{\rm T}$，撞击角度，$\theta$，以及撞击速度，$v_{\rm imp}$。 我们研究了在合并和撞击逃逸碰撞之间转换的临界撞击速度，$v_{\rm cr}$。 我们发现归一化的临界撞击速度，$v_{\rm cr}/v_{\rm esc}$，取决于$\gamma$和$\theta$，但不取决于$M_{\rm T}$，其中$v_{\rm esc}$是双体逃逸速度。 我们推导出了$v_{\rm cr}/v_{\rm esc}$的一个简单公式，作为$\gamma$和$\theta$的函数，并将其应用于之前研究中通过\textit{N}-体计算得到的巨大小行星碰撞事件。 我们发现这些事件中有 40% 不应是合并事件。 显示英文摘要

摘要： At the final stage of terrestrial planet formation, known as the giant impact stage, a few tens of Mars-sized protoplanets collide with one another to form terrestrial planets. Almost all previous studies on the orbital and accretional evolution of protoplanets in this stage have been based on the assumption of perfect accretion, where two colliding protoplanets always merge. However, recent impact simulations have shown that collisions among protoplanets are not always merging events, that is, two colliding protoplanets sometimes move apart after the collision (hit-and-run collision). As a first step towards studying the effects of such imperfect accretion of protoplanets on terrestrial planet formation, we investigated the merging criteria for collisions of rocky protoplanets. Using the smoothed particle hydrodynamic (SPH) method, we performed more than 1000 simulations of giant impacts with various parameter sets, such as the mass ratio of protoplanets, $\gamma$, the total mass of two protoplanets, $M_{\rm T}$, the impact angle, $\theta$, and the impact velocity, $v_{\rm imp}$. We investigated the critical impact velocity, $v_{\rm cr}$, at the transition between merging and hit-and-run collisions. We found that the normalized critical impact velocity, $v_{\rm cr}/v_{\rm esc}$, depends on $\gamma$ and $\theta$, but does not depend on $M_{\rm T}$, where $v_{\rm esc}$ is the two-body escape velocity. We derived a simple formula for $v_{\rm cr}/v_{\rm esc}$ as a function of $\gamma$ and $\theta$, and applied it to the giant impact events obtained by \textit{N}-body calculations in the previous studies. We found that 40% of these events should not be merging events.