通过共振链将行星推入内腔
Pushing planets into an inner cavity by a resonant chain
摘要：
上下文系外行星的轨道分布表明，在紧凑的系统中，有超地球大小的行星聚集在它们的主星附近。当假设它们的形成是向内的圆盘驱动的迁移场景时，这些行星可能已经停止，可能已经停在圆盘的内边缘，或者被共振链推过内部圆盘腔。这一主题尚未得到适当和广泛的研究。利用数值模拟，我们调查的可能性，在一个共振链内的行星可以被推入光盘内腔的外行星。我们进行了流体动力学和N体模拟的行星系嵌入在他们的新生盘。椎间盘的内边缘以两种不同的方式表示，类似于死区内边缘（DZ）或椎间盘内边界（IB）。主要区别在于表面密度分布的陡度。最里面的行星总是有一个10 M地球的质量，与其他外部行星相等或更高的质量。较陡的轮廓能够比较浅的轮廓更有效地阻止行星链。我们的DZ模型中的最终构型通常比IB模型中的构型更紧，因此更容易不稳定。我们推导出解析表达式的停止条件的基础上的权力平衡，并表明，最终的偏心转矩平衡的结果。对于较薄圆盘中的行星，我们第一次在流体动力学模拟中发现了过稳定振动的明显迹象，导致非常紧凑的系统。我们还发现，流行的N体模拟可能高估了盘内腔中的行星数量。
英文摘要：
Context. The orbital distribution of exoplanets indicates an accumulation of super-Earth sized planets close to their host stars in compact systems. When an inward disc-driven migration scenario is assumed for their formation, these planets could have been stopped and might have been parked at an inner edge of the disc, or be pushed through the inner disc cavity by a resonant chain. This topic has not been properly and extensively studied. Using numerical simulations, we investigate the possibility that the inner planets in a resonant chain can be pushed into the disc inner cavity by outer planets. We performed hydrodynamical and N-body simulations of planetary systems embedded in their nascent disc. The inner edge of the disc was represented in two different ways, resembling either a dead zone inner edge (DZ) or a disc inner boundary (IB). The main difference lies in the steepness of the surface density profile. The innermost planet always has a mass of 10 M Earth , with additional outer planets of equal or higher mass. A steeper profile is able to stop a chain of planets more efficiently than a shallower profile. The final configurations in our DZ models are usually tighter than in their IB counterparts, and therefore more prone to instability. We derive analytical expressions for the stopping conditions based on power equilibrium, and show that the final eccentricities result from torque equilibrium. For planets in thinner discs, we found, for the first time, clear signs for over-stable librations in the hydrodynamical simulations, leading to very compact systems. We also found that the popular N-body simulations may overestimate the number of planets in the disc inner cavity.
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