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The ultracool dwarf star TRAPPIST-1 hosts seven Earth-size transitingplanets, some of which could harbour liquid water on their surfaces. UVobservations are essential to measure their high-energy irradiation, and tosearch for photodissociated water escaping from their putative atmospheres. Ournew observations of TRAPPIST-1 Ly-$\alpha$ line during the transit ofTRAPPIST-1c show an evolution of the star emission over three months,preventing us from assessing the presence of an extended hydrogen exosphere.Based on the current knowledge of the stellar irradiation, we investigated thelikely history of water loss in the system. Planets b to d might still be in arunaway phase, and planets within the orbit of TRAPPIST-1g could have lost morethan 20 Earth oceans after 8 Gyr of hydrodynamic escape. However, TRAPPIST-1eto h might have lost less than 3 Earth oceans if hydrodynamic escape stoppedonce they entered the habitable zone. We caution that these estimates remainlimited by the large uncertainty on the planet masses. They likely representupper limits on the actual water loss because our assumptions maximize theXUV-driven escape, while photodissociation in the upper atmospheres should bethe limiting process. Late-stage outgassing could also have contributedsignificant amounts of water for the outer, more massive planets after theyentered the habitable zone. While our results suggest that the outer planetsare the best candidates to search for water with the JWST, they also highlightthe need for theoretical studies and complementary observations in allwavelength domains to determine the nature of the TRAPPIST-1 planets, and theirpotential habitability.

Temporal evolution of the high-energy irradiation and water content of TRAPPIST-1 exoplanets