tokens: 2018 ; Barr et al. 2018 ; Wang et al. 2017 ; Grimm et al. 2018 ), and we also find the vast majority of the possible structures for planet b have substantial quantities of water (~ 20−70%). The remaining planets are also probably water-rich, most notably planet d, where a volume fraction of H 2 O ≳ 0.25 is required by the mass and radius data. Table 2 summarises the values of T eq , F tidal , F RG , and F glob for planets b through e. Planets d and e have a total heat flux from tidal heating and insolation that is below the critical heat flux for a runaway greenhouse effect, and could be potentially habitable from a geophysical point of view. Planet d avoids a runaway greenhouse effect only if its Bond albedo is greater than or approximately equal to 0.3, indicating a surface at least as reflective as the surface of the Earth, which could be possible if the planet has a thick atmosphere with highly reflective clouds ( Turbet et al. 2018 ). In this case, planet d could have liquid water at its surface at the substellar point provided it is tidally locked in a 1:1 spin–orbit resonance ( Turbet et al. 2018 ). It is not clear whether TRAPPIST-1d is synchronously rotating because perturbations from the other planets may prevent tidal locking which results in a larger illuminated area where surface ice can melt ( Vinson Hansen 2017 ). Since the planet is close to the runaway greenhouse state due tothe received stellar irradiation, the moderate tidal heating rate that is present in the body might transform itinto a “tidal Venus” ( Barnes et al. 2013 ). We find that planet e avoids a runaway greenhouse effect regardless of its albedo, bolstering the already strong case for its habitability based solely on climate modelling ( Wolf 2017 ; Turbet et al. 2018 ). Planet e can maintain global surface oceans through greenhouse warming from H 2 O alone ( Turbet et al. 2018 ); alternatively, Earth-like temperatures can be maintained with an atmosphere of 1 bar of N 2 and 0.4 bar CO 2 , or a pure CO 2 atmosphere with a pressure of 1.3 bar ( Wolf 2017 ). If planets d or e were ice-covered, they could still sustain biospheres fueled by the planet’s interior tidal dissipation, for example clustered around hydrothermal vents at the top of the internally heated rock layer, as has been suggested for Jupiter’s moon Europa ( Vance et al. 2007 ). Since both planets have equilibrium rock mantle temperatures greater than the melting point of silicate minerals, heat dissipation from the rock layer can locally melt the high-pressure ice to provide a warmer environment where the rock interacts with water through the vents and might support simple chemoautolithotropic life ( Vance et al. 2007 ). The surface ice layer would shield the biosphere from the strong stellar flare activity of the TRAPPIST-1 star ( Vida et al. 2017 ; Garraffo et al. 2017 ), but would serve as a barrier to detection of the biosphere through telescopic observations. Hydrothermal activity would be more
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