In hot water: effects of temperature-dependent interiors on the radii of water-rich super-Earths

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Observational advancements are leading to increasingly precise measurements of super-Earth masses and radii. Such measurements are used in internal structure models to constrain interior compositions of super-Earths. It is now critically important to quantify the effect of various model assumptions on the predicted radii. In particular, models often neglect thermal effects, a choice justified by noting that the thermal expansion of a solid Earth-like planet is small. However, the thermal effects for water-rich interiors may be significant. We have systematically explored the extent to which thermal effects can influence the radii of water-rich super-Earths over a wide range of masses, surface temperatures, surface pressures and water mass fractions. We developed temperature-dependent internal structure models of water-rich super-Earths that include a comprehensive temperature-dependent water equation of state. We found that thermal effects induce significant changes in their radii. For example, for super-Earths with 10 per cent water by mass, the radius increases by up to 0.5$\,$R$_\oplus$ when the surface temperature is increased from 300 to 1000$\,$K, assuming a surface pressure of 100$\,$bar and an adiabatic temperature gradient in the water layer. The increase is even larger at lower surface pressures and/or higher surface temperatures, while changing the water fraction makes only a marginal difference. These effects are comparable to current super-Earth radial measurement errors, which can be better than 0.1$\,$R$_\oplus$. It is therefore important to ensure that the thermal behaviour of water is taken into account when interpreting super-Earth radii using internal structure models.