TRAPPIST-1 hosts seven planets. The period ratios of neighbouring pairs are close to the 8:5, 5:3, 3:2, 3:2, 4:3 and 3:2 ratios in increasing distance from the star. The Laplace angles associated with neighbouring triplets are observed to be librating, proving the resonant nature of the system. This compact, resonant configuration is a manifest sign of disk-driven migration; however, the preferred outcome of such evolution is the establishment of first-order resonances, not the high-order resonances observed in the inner system. Here, we explain the observed orbital configuration with a model that is largely independent of the specific disk migration and orbital circularization efficiencies. Together with migration, the two key elements of our model are that the inner border of the protoplanetary disk receded with time and that the system was initially separated into two subsystems. Specifically, the inner b, c, d and e planets were initially placed in a 3:2 resonance chain and then evolved to the 8:5–5:3 commensurability between planets b, c and d due to the recession of the inner edge of the disk, whereas the outer planets migrated to the inner edge at a later time and established the remaining resonances. Our results pivot on the dynamical role of the presently unobservable recession of the inner edge of protoplanetary disks. They also reveal the role of recurring phases of convergent migration followed by resonant repulsion with associated orbital circularization when resonant chains interact with migration barriers.

TRAPPIST-1 拥有七颗行星。随着距恒星距离的增加，相邻对的周期比接近于 8:5、5:3、3:2、3:2、4:3 和 3:2。观察到与相邻三重态相关的拉普拉斯角是振动的，证明了系统的共振性质。这种紧凑、共振的配置是磁盘驱动迁移的明显标志。然而，这种进化的首选结果是建立一级共振，而不是在内部系统中观察到的高阶共振。在这里，我们用一个很大程度上独立于特定盘迁移和轨道环化效率的模型来解释观察到的轨道配置。与迁移一起，我们模型的两个关键要素是原行星盘的内边界随着时间的推移而后退，并且系统最初分为两个子系统。具体来说，内部b、c、d和e行星最初处于3:2共振链中，然后由于内边缘的退缩而演化为b、c、d行星之间的8:5–5:3可通约性盘的，而外行星后来迁移到内边缘并建立了剩余的共振。我们的结果以目前无法观察到的原行星盘内缘衰退的动力学作用为中心。他们还揭示了当共振链与迁移势垒相互作用时，会聚迁移的重复阶段的作用，随后是伴随相关轨道环化的共振排斥。