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The TRAPPIST-1 system has 7 known terrestrial planets arranged compactly in amean motion resonant chain around an ultra-cool central star, some within theestimated habitable zone. Given their short orbital periods of just a few days,it is often presumed that the planets are tidally locked such that the spinrate is equal to that of the orbital mean motion. However, the compact, andresonant, nature of the system implies that there can be significant variationsin the mean motion of these planets due to their mutual interactions. We showthat such fluctuations can then have significant effects on the spin states ofthese planets. In this paper, we analyze, using detailed numerical simulations,the mean motion histories of the three planets that are thought to lie withinor close to the habitable zone of the system: planets d, e, and f. Wedemonstrate that, depending on the strength of the mutual interactions withinthe system, these planets can be pushed into spin states which are effectivelynon-synchronous. We find that it can produce significant libration of the spinstate, if not complete circulation in the frame co-rotating with the orbit. Wealso show that these spin states are likely to be unable to sustain long-termstability, with many of our simulations suggesting that the spin evolves, underthe influence of tidal synchronization forces, into quasi-stable attractorstates, which last on timescales of thousands of years.

The Chaotic Nature of TRAPPIST-1 Planetary Spin States