Final Stages of Planet Formation
Final Stages of Planet Formation
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行星形成的最后阶段
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
R. Sari
中科院分区：
文献类型：
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作者：
P. Goldreich;Y. Lithwick;R. Sari
我们探讨有关太阳系行星的三个问题：是什么决定了它们的数量？为什么它们的轨道几乎是圆形且共面？它们形成需要多长时间？在一个小天体盘中的失控吸积导致极少数天体变得比其他所有天体都大得多。这些大天体主导了所有天体的粘性搅动。小天体产生的动力摩擦冷却了大天体的随机速度。小天体的随机速度通过相互碰撞和/或气体阻力得以冷却。当大天体的轨道间距变得和它们的吸积区一样宽时，失控吸积终止。随后是寡头生长阶段，在此期间大天体保持相似的质量以及均匀间隔的半长轴。随着寡头天体的增长，它们的数密度降低，但它们的面质量密度增加。我们与行星形成的标准理论不同，我们假设随着大天体变大，小天体由于经历碰撞破碎级联而变小。由此可知，寡头阶段是太阳系演化中的一个短暂阶段。当寡头天体的面质量密度与小天体的面质量密度相匹配时，动力摩擦不再能够平衡粘性搅动，所以它们的速度弥散增加到轨道交叉的程度。这标志着寡头阶段的结束。接下来在内行星系和外行星系发生的情况不同。在内行星系，行星表面逃逸速度与轨道逃逸速度之比小于1，当大天体的随机速度变得与它们的逃逸速度相当时，大天体发生碰撞并合并。在外行星系，这个比值大于1，一些大天体的随机速度继续上升直到它们被弹出。在这两个区域，大天体的数密度最终降低到它们之间的引力相互作用不再产生大规模混沌的程度。之后，它们的轨道偏心率和倾角被剩余小天体的动力摩擦所阻尼。行星形成的最后也是最长的阶段是小天体的清除。我们对这个阶段的理解充满了不确定性。幸存的原行星在其轨道周围清除出很宽的空隙，这抑制了它们吸积小天体的能力。然而，在内行星系，小天体中的所有物质最终都进入了行星内部。外行星系的小天体可能在太阳系的年龄内无法被吸积。第二代小行星体可能在小天体盘中通过碰撞凝聚或引力不稳定性形成。在外行星系，千米级或更大的天体其随机速度会被激发，直到它们的轨道与相邻原行星的轨道交叉。最终它们要么逃离太阳，要么成为奥尔特云的成员。一个重要的区别是内行星的生长在清除阶段持续进行，而外行星的组装在寡头阶段结束时基本完成。这些结论意味着原行星盘的面密度在内行星区域是最小太阳质量星云的面密度，但在外行星区域要大几倍。清除阶段的时间尺度由内行星区域几何截面的吸积率和外行星区域引力增强截面的弹出率决定。前者是几亿年，后者是几十亿年。然而，由于天王星和海王星在寡头阶段结束时就获得了它们大部分的质量，它们可能在地球之前形成！上述情景有几个值得注意的含义。在内行星系，大小相当的原行星之间的碰撞很常见，但在外行星系则不然。外行星系的弹出包括寡头阶段之后几个质量超过地球的天体以及在清除阶段足够数量的千米级天体来填充奥尔特彗星云。除了在清除阶段的最后，碰撞阻止了天王星和海王星弹出千米级物体。只有木星，以及在较小程度上的土星，能够用千米级的彗星填充奥尔特云。
We address three questions regarding solar system planets: What determined their number? Why are their orbits nearly circular and coplanar? How long did they take to form? Runaway accretion in a disk of small bodies resulted in a tiny fraction of the bodies growing much larger than all the others. These big bodies dominated the viscous stirring of all bodies. Dynamical friction by small bodies cooled the random velocities of the big ones. Random velocities of small bodies were cooled by mutual collisions and/or gas drag. Runaway accretion terminated when the orbital separations of the big bodies became as wide as their feeding zones. This was followed by oligarchic growth during which the big bodies maintained similar masses and uniformly spaced semimajor axes. As the oligarchs grew, their number density decreased, but their surface mass density increased. We depart from standard treatments of planet formation by assuming that as the big bodies got bigger, the small ones got smaller as the result of undergoing a collisional fragmentation cascade. It follows that oligarchy was a brief stage in solar system evolution. When the oligarchs' surface mass density matched that of the small bodies, dynamical friction was no longer able to balance viscous stirring, so their velocity dispersion increased to the extent that their orbits crossed. This marked the end of oligarchy. What happened next differed in the inner and outer parts of the planetary system. In the inner part, where the ratios of the escape velocities from the surfaces of the planets to the escape velocities from their orbits are smaller than unity, big bodies collided and coalesced after their random velocities became comparable to their escape velocities. In the outer part, where these ratios are larger than unity, the random velocities of some of the big bodies continued to rise until they were ejected. In both parts, the number density of the big bodies eventually decreased to the extent that gravitational interactions among them no longer produced large-scale chaos. After that their orbital eccentricities and inclinations were damped by dynamical friction from the remaining small bodies. The last and longest stage in planet formation was the cleanup of small bodies. Our understanding of this stage is fraught with uncertainty. The surviving protoplanets cleared wide gaps around their orbits that inhibited their ability to accrete small bodies. Nevertheless, in the inner planet system, all of the material in the small bodies ended up inside planets. Small bodies in the outer planet system probably could not have been accreted in the age of the solar system. A second generation of planetesimals may have formed in the disk of small bodies, by either collisional coagulation or gravitational instability. In the outer planet system, bodies of kilometer size or larger would have had their random velocities excited until their orbits crossed those of neighboring protoplanets. Ultimately they would have either escaped from the Sun or become residents of the Oort Cloud. An important distinction is that growth of the inner planets continued through cleanup, whereas assembly of the outer planets was essentially complete by the end of oligarchy. These conclusions imply that the surface density of the protoplanetary disk was that of the minimum solar mass nebula in the inner planet region but a few times larger in the outer planet region. The timescale through cleanup was set by the accretion rate at the geometrical cross section in the inner planet region and by the ejection rate at the gravitationally enhanced cross section in the outer planet region. It was a few hundred million years in the former and a few billion years in the latter. However, since Uranus and Neptune acquired most of their mass by the end of oligarchy, they may have formed before Earth! A few implications of the above scenario are worth noting. Impacts among protoplanets of comparable size were common in the inner planet system but not in the outer. Ejections from the outer planet system included several bodies with masses in excess of Earth after oligarchy and an adequate number of kilometer-size bodies to populate the Oort comet cloud during cleanup. Except at the very end of cleanup, collisions prevented Uranus and Neptune from ejecting kilometer-size objects. Only Jupiter and, to a much lesser extent, Saturn were capable of populating the Oort Cloud with comets of kilometer size.