巨行星散射和碰撞：流体动力学、合并-抛射分支比和残留物的性质
Giant Planet Scatterings and Collisions: Hydrodynamics, Merger-Ejection Branching Ratio, and Properties of the Remnants
摘要：
轨道间距足够小的行星系会经历行星合并和抛射。合并与喷射的分支比敏感地依赖于行星近距离接触的处理。以往的研究都采用简单的“粘球”处方，其有效性值得怀疑。我们应用光滑粒子流体动力学和$N$体积分来研究气体巨星之间近距离相遇的流体效应和紧密堆积的行星系的长期演化。通过对$M_J$和$2M_J$的抛物碰撞的研究，我们发现当碰撞参量$r_p$（行星间近心点间距）小于$2R_J$时，会发生快速合并，合并后的质量保持了初始质量的97%.当$r_p$处于$2R_J$和$4R_J$之间时，强潮汐效应会影响“双行星”轨道。我们量化这些影响，使用一组拟合公式，可以实现$N$体代码。我们运行了一套$N$体模拟的公式和两个巨行星系统最初在不稳定的，近圆形共面轨道。流体（潮汐）效应通过使有效碰撞半径加倍，显著增加了行星合并相对于抛射的分支比。虽然流体效应不会改变每种类型的残留行星的半长轴和偏心率的分布（合并与喷射中的幸存行星），但由于分支比的变化，行星散射残留物的整体轨道特性受到强烈影响。我们还发现并合产物的自旋大小和自旋密度分布很宽。
英文摘要：
Planetary systems with sufficiently small orbital spacings can experience planetary mergers and ejections. The branching ratio of mergers vs ejections depends sensitively on the treatment of planetary close encounters. Previous works have adopted a simple "sticky-sphere" prescription, whose validity is questionable. We apply both smoothed particle hydrodynamics and $N$-body integrations to investigate the fluid effects in close encounters between gas giants and the long-term evolution of closely-packed planetary systems. Focusing on parabolic encounters between Jupiter-like planets with $M_J$ and $2M_J$, we find that quick mergers occur when the impact parameter $r_p$ (the pericenter separation between the planets) is less than $2R_J$, and the merger conserved 97% of the initial mass. Strong tidal effects can affect the "binary-planet" orbit when $r_p$ is between $2R_J$ and $4R_J$. We quantify these effects using a set of fitting formulae that can be implemented in $N$-body codes. We run a suite of $N$-body simulations with and without the formulae for systems of two giant planets initially in unstable, nearly circular coplanar orbits. The fluid (tidal) effects significantly increase the branching ratio of planetary mergers relative to ejections by doubling the effective collision radius. While the fluid effects do not change the distributions of semi-major axis and eccentricity of each type of remnant planets (mergers vs surviving planets in ejections), the overall orbital properties of planet scattering remnants are strongly affected due to the change in the branching ratio. We also find that the merger products have broad distributions of spin magnitudes and obliquities.
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