Implications of an improved water equation of state for water-rich planets

Abstract: Water (H$_{2}$O), in all forms, is an important constituent in planetary bodies, controlling habitability and influencing geological activity. Under conditions found in the interior of many planets, as the pressure increases, the H-bonds in water gradually weaken and are replaced by ionic bonds. Recent experimental measurements of the water equation of state (EOS) showed both a new phase of H-bonded water ice, ice-VII$_t$, and a relatively low transition pressure just above 30 GPa to ionic bonded ice-X, which has a bulk modulus 2.5 times larger. The higher bulk modulus of ice-X produces larger planets for a given mass, thereby either reducing the atmospheric contribution to the volume of many exoplanets or limiting their water content. We investigate the impact of the new EOS measurements on the planetary mass-radius relation and interior structure for water-rich planets. We find that the change in the planet mass-radius relation caused by the systematic differences between previous and new experimental EOS measurements are comparable to the observational uncertainties in some planet sizes -- an issue that will become more important as observations continue to improve.