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We study the dynamical evolution of the TRAPPIST-1 system under the influenceof orbital circularization through tidal interaction with the central star. Wefind that systems with parameters close to the observed one evolve into a statewhere consecutive planets are linked by first order resonances and consecutivetriples, apart from planets c, d and e, by connected three body Laplaceresonances. The system expands with period ratios increasing and meaneccentricities decreasing with time. This evolution is largely driven by tidesacting on the innermost planets which then influence the outer ones. In orderthat deviations from commensurability become significant only on $Gy$ timescales or longer, we require that the tidal parameter associated with theplanets has to be such that $Q' > \sim 10^{2-3}.$ At the same time, if we startwith two subsystems, with the inner three planets comprising the inner one,$Q'$ associated with the planets has to be on the order (and not significantlyexceeding) $10^{2-3}$ for the two subsystems to interact and end up in theobserved configuration. This scenario is also supported by modelling of theevolution through disk migration which indicates that the whole system cannothave migrated inwards together. Also in order to avoid large departures fromcommensurabilities, the system cannot have stalled at a disk inner edge forsignificant time periods. We discuss the habitability consequences of the tidaldissipation implied by our modelling, concluding that planets d, e and f arepotentially in habitable zones.

The TRAPPIST-1 system: Orbital evolution, tidal dissipation, formation and habitability