AQUA: A Collection of H$_2$O Equations of State for Planetary Models

Water is one of the key chemical elements in planetary structure modelling. Due to its complex phase diagram, equations of state cover often only parts of the pressure - temperature space needed in planetary modelling. We construct an equation of state of H$_2$O spanning a very wide range from 0.1 Pa to 400 TPa and 150 K to $10^{5}$ K, which can be used to model the interior of planets. We combine equations of state valid in localised regions to form a continuous equation of state spanning over said pressure and temperature range. We provide tabulated values for the most important thermodynamic quantities, i.e., density, adiabatic temperature gradient, entropy, internal energy and bulk speed of sound of water over this pressure and temperature range. For better usability we also calculated density - temperature and density - internal energy grids. We discuss further the impact of this equation of state on the mass radius relation of planets compared to other popular equation of states like ANEOS and QEOS. AQUA is a combination of existing equation of state useful for planetary models. We show that AQUA is in most regions a thermodynamic consistent description of water. At pressures above 10 GPa AQUA predicts systematic larger densities than ANEOS or QEOS. A feature which was already present in a previously proposed equation of state, which is the main underlying equation of this work. We show that the choice of the equation of state can have a large impact on the mass-radius relation, which highlights the importance of future developments in the field of equation of states and regarding experimental data of water at high pressures.