Forming the Trappist-1 system in two steps during the recession of the disc inner edge

Abstract

Trappist-1 hosts 7 planets where 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 disc-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 in a model that is largely independent on the specific disc migration and orbital circularisation efficiencies. Together with migration, the two key elements of our model are: i) the inner border of the protoplanetary disc receded with time; and ii) the system was initially separated in two sub-systems. 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 under the effect of the recession of the inner edge of the disc, whereas the outer planets migrated to the inner edge at a later time, establishing the remaining resonances. Our results pivot on the dynamical role of the presently unobservable recession of the inner edge of protoplanetary discs. They also reveal the role of recurring phases of convergent migration followed by resonant repulsion with associated orbital circularisation when resonant chains interact with migration barriers.