The seven planets orbiting TRAPPIST-1 in a compact near-resonant chain offer a unique case to study in planet formation theory. We demonstrate in this paper that the remarkable flatness of the system, exceeding that of any other known planetary system, is an important constraint on the mass of the gaseous disk in which it formed and attained its current configuration. We use three-dimensional hydrodynamic simulations of the gas and planets to study specific formation models. In particular, we report simulations motivated by the model proposed by Ormel et al.—in this model, the dispersal of the gas disk pushes the planets from an initial resonant chain into their present configuration. We find that a disk with the mass used in this model is consistent with the flatness of the TRAPPIST-1 system, but a more massive disk is not, with the transition occurring between 15 and 50 times the mass of the Ormel et al. disk. This upper limit on mass rules out certain models of the formation of the system, namely in situ formation and disk migration on long timescales.

在紧凑的近共振链中围绕 TRAPPIST-1 运行的七颗行星提供了一个独特的案例来研究行星形成理论。我们在本文中证明，该系统显着的平坦度，超过任何其他已知行星系统的平坦度，是对其形成并获得其当前配置的气态盘质量的重要约束。我们使用气体和行星的三维流体动力学模拟来研究特定的形成模型。特别是，我们报告了由 Ormel 等人提出的模型激发的模拟——在这个模型中，气体盘的扩散将行星从初始共振链推到它们目前的配置。我们发现该模型中使用的质量与 TRAPPIST-1 系统的平坦度一致的圆盘，但质量更大的圆盘则不然，过渡发生在 Ormel 等人质量的 15 到 50 倍之间。盘。这个质量上限排除了系统形成的某些模型，即长时间尺度上的原位形成和盘迁移。