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Ultracool dwarfs (UCD; $T_{\rm eff}<\sim3000~$K) cool to settle on the mainsequence after $\sim$1 Gyr. For brown dwarfs, this cooling never stops. Theirhabitable zone (HZ) thus sweeps inward at least during the first Gyr of theirlives. Assuming they possess water, planets found in the HZ of UCDs haveexperienced a runaway greenhouse phase too hot for liquid water prior toentering the HZ. It has been proposed that such planets are desiccated by thishot early phase and enter the HZ as dry worlds. Here we model the water lossduring this pre-HZ hot phase taking into account recent upper limits on the XUVemission of UCDs and using 1D radiation-hydrodynamic simulations. We addressthe whole range of UCDs but also focus on the planets recently found around the$0.08~M_\odot$ dwarf TRAPPIST-1.  Despite assumptions maximizing the FUV-photolysis of water and the XUV-drivenescape of hydrogen, we find that planets can retain significant amounts ofwater in the HZ of UCDs, with a sweet spot in the $0.04$-$0.06~M_\odot$ range.We also studied the TRAPPIST-1 system using observed constraints on theXUV-flux. We find that TRAPPIST-1b and c may have lost as much as 15 EarthOceans and planet d -- which might be inside the HZ -- may have lost less than1 Earth Ocean. Depending on their initial water contents, they could haveenough water to remain habitable. TRAPPIST-1 planets are key targets foratmospheric characterization and could provide strong constraints on the watererosion around UCDs.

Water loss from Earth-sized planets in the habitable zones of ultracool dwarfs: Implications for the planets of TRAPPIST-1