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Fig. 2

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Mass-radius relationships for various interior compositions and water content, assuming water is in the condensed form (left panel) and water forms an atmosphere (right panel). The silicate composition mass-radius relationship assumes a pure MgSiO3 interior and was taken from Zeng et al. (2016). The water-rich mass-radius relationships for water in condensed form (left panel) were derived using the data from Zeng et al. (2016). The water-rich mass-radius relationships for water in gaseous form (right panel) are the result of the present work. All mass-radius relationships with water were built assuming a pure MgSiO3 interior. For comparison, we added the measured positions of the seven TRAPPIST-1 planets measured from Grimm et al. (2018), with their associated 95% confidence ellipses. Based on the irradiation they receive compared to the theoretical runaway greenhouse limit (Kopparapu et al. 2013; Wolf 2017; Turbet et al. 2018), TRAPPIST-1 e, f, g, and h should be compared with mass-radius relationships on the left, while TRAPPIST-1b, c, and d should be compared with those on the right. To emphasize this, we indicated, on each panel and in black (and solid line ellipses), the planets (and their associated 95% confidenceellipses) for which mass-radius relationships (with water) are appropriate. In contrast, we indicated on each panel in gray (and dashed line ellipses) the planets (and their associated 95% confidence ellipses) for which mass-radius relationships (with water) are not appropriate. For reference, we also added a terrestrial composition that resembles that of the Earth, but also that of Mars and Venus. We note that mass-radiusrelationships for steam planets (right panel) can be easily built following the procedure described in Appendix D.

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