Evolution of Planetesimal Velocities Based on Three-Body Orbital Integrations and Growth of Protoplanets
Evolution of Planetesimal Velocities Based on Three-Body Orbital Integrations and Growth of Protoplanets
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基于三体轨道整合和原行星生长的行星速度演化
DOI：
10.1006/icar.2001.6741
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发表时间：
2002
期刊：
影响因子：
3.2
通讯作者：
S. Ida
中科院分区：
文献类型：
--
作者：
K. Ohtsuki;G. Stewart;S. Ida
利用三体轨道积分和Ohtsuki(1999，Icarus 137,152)所描述的方法，我们得到了偏心和倾角为Rayleigh分布的行星体的粘性搅拌和动力摩擦率。Ohtsuki(1999，Icarus 137,152)估计了环形粒子的粘性搅拌和动力摩擦率。我们发现，这些基于轨道积分的速率在高速情况下与Stewart和Ida(2000，Icarus 143，28)的分析结果符合得很好。然而，在相对速度以开普勒剪切为主的低速情况下，三体计算与Stewart和Ida的公式有很大的偏差，他们没有详细研究低速的速率，只是在他们的高速公式和圆形轨道的数值结果之间给出了一个简单的内插公式。我们使用上述基于轨道积分的搅拌速率计算了均方根偏心率和倾角的演化，发现对于单组分和双组分系统，即使在低速情况下，也与N体模拟结果非常一致。基于我们的数值结果，我们导出了搅拌摩擦率和动摩擦率的半解析公式，并证实它们以足够的精度重现了N体模拟的结果。利用这些公式，我们计算了给定尺寸分布的行星体的平衡速度。在大型天体开始失控增长之前的一个阶段，用我们的新公式计算的速度分布与用Stewart和Ida或Wetherill和Stewart(1993，Icarus 106,190)公式得到的结果很好地吻合。然而，在后来的阶段，我们发现用我们的新公式计算的小碰撞碎片的倾角可以比用以前得到的公式计算的小得多，因此它们更容易被大物体吸积。这些结果基本上支持了之前的结果，如原行星的失控增长，但它们可以在早期失控增长后将其增长速度提高10%-30%，其中那些具有低随机速度的碎片可以显著地促进失控天体的快速增长。
Abstract We obtain the viscous stirring and dynamical friction rates of planetesimals with a Rayleigh distribution of eccentricities and inclinations, using three-body orbital integration and the procedure described by Ohtsuki (1999, Icarus 137 , 152), who evaluated these rates for ring particles. We find that these rates based on orbital integrations agree quite well with the analytic results of Stewart and Ida (2000, Icarus 143 , 28) in high-velocity cases. In low-velocity cases where Kepler shear dominates the relative velocity, however, the three-body calculations show significant deviation from the formulas of Stewart and Ida, who did not investigate the rates for low velocities in detail but just presented a simple interpolation formula between their high-velocity formula and the numerical results for circular orbits. We calculate evolution of root mean square eccentricities and inclinations using the above stirring rates based on orbital integrations, and find excellent agreement with N -body simulations for both one- and two-component systems, even in the low-velocity cases. We derive semi-analytic formulas for the stirring and dynamical friction rates based on our numerical results, and confirm that they reproduce the results of N -body simulations with sufficient accuracy. Using these formulas, we calculate equilibrium velocities of planetesimals with given size distributions. At a stage before the onset of runaway growth of large bodies, the velocity distribution calculated by our new formulas are found to agree quite well with those obtained by using the formulas of Stewart and Ida or Wetherill and Stewart (1993, Icarus 106 , 190). However, at later stages, we find that the inclinations of small collisional fragments calculated by our new formulas can be much smaller than those calculated by the previously obtained formulas, so that they are more easily accreted by larger bodies in our case. The results essentially support the previous results such as runaway growth of protoplanets, but they could enhance their growth rate by 10–30% after early runaway growth, where those fragments with low random velocities can significantly contribute to rapid growth of runaway bodies.