Architecture of Planetary Systems: Solar and Extrasolar

如果我们任意地将多颗行星放在围绕一颗星星的轨道上，我们可能会发现这个系统是动态不稳定的：在几个轨道周期的时间尺度上，这些轨道将以指数方式偏离它们的原始路径。真实的行星系统，至少在数百万轨道上存活下来，并不是动态不稳定的。在这些长时间尺度上，行星的行为就好像它的质量围绕着它的轨道分布，就像一个椭圆环围绕着星星。这些环在引力作用下相互吸引，导致它们的形状和方向发生缓慢变化，这可能导致所谓的长期不稳定或长期混乱。该项目的主要研究者和合作者计划开发一个完整的长期不稳定性理论，使用分析技术以及相互作用的椭圆环和直接N体模拟的计算机模拟。他们的目标是确定长期不稳定性和长期混沌是否可以定量地解释和预测（1）内行星的长期轨道演化，（2）“热木星”系外行星的轨道特性和质量分布，以及（3）一般系外行星系统的特性。特别是，他们的目标是确定长期的混乱是否是一个可行的替代磁盘驱动的迁移形成的热彗星，这也可能能够占相对于恒星赤道的轨道倾角的广泛分布。他们将对太阳系外行星的偏心率和间距进行定量预测，并了解如何利用对系外行星系统的观测来约束行星形成物理学。该项目将支持和培训一名博士后研究员和两名本科暑期学生，首席研究员将公开介绍工作成果。

If one were to arbitrarily put multiple planets in orbit around a star, one might find the system to be dynamically unstable: the orbits would deviate exponentially from their original paths on time scales of a few orbital periods. Real planetary systems, which have survived for at least millions of orbits, are not dynamically unstable. On these long time scales, a planet behaves as if its mass were spread around its orbit, like an elliptical ring around the star. These rings pull on each other gravitationally, causing slow changes in their shapes and orientations, which may lead to so-called secular instability or secular chaos. The Principal Investigator and collaborators on this project plan to develop a complete theory of secular instability, using analytic techniques as well as computer simulations of interacting elliptical rings and direct N-body simulations. Their goal is to determine whether secular instability and secular chaos can quantitatively explain and predict (1) the long-term orbital evolution of the Inner Planets, (2) the distribution of orbital properties and masses of "hot Jupiter" exoplanets, and (3) the properties of exoplanet systems in general. In particular, they aim to determine whether secular chaos is a viable alternative to disk-driven migration for the formation of hot Jupiters which may be able also to account for the wide distribution of orbital inclinations with respect to the stellar equator. They will make quantitative predictions for the eccentricities and spacings of extrasolar planets, and build an understanding of how observations of exoplanet systems can be used to constrain planet formation physics. The project will support and train one postdoctoral researcher and two undergraduate summer students, and the Principal Investigator will give public presentations on the results of the work.