Internal Structure and CO$_2$ Reservoirs of Habitable Water-Worlds

Abstract: Water-worlds are water-rich (>1 wt% H$_2$O) exoplanets. The classical models of water-worlds considered layered structures determined by the phase boundaries of pure water. However, water-worlds are likely to possess comet-like compositions, with between ~3 mol% to 30 mol% CO$_2$ relative to water. In this study, we build an interior structure model of habitable (i.e. surface-liquid-ocean-bearing) water-worlds using the latest results from experimental data on the CO$_2$-H$_2$O system, to explore the CO$_2$ budget and to localize the main CO$_2$ reservoirs inside of these planets. We show that CO$_2$ dissolved in the ocean and trapped inside of a clathrate layer cannot accommodate a cometary amount of CO$_2$ if the planet accretes more than 11 wt% of volatiles (CO$_2$ + H$_2$O) during its formation. We propose a new, potentially dominant, CO$_2$ reservoir for water-worlds: CO$_2$ buried inside of the high-pressure water ice mantle as CO$_2$ ices or (H$_2$CO$_3$ . H$_2$O), monohydrate of carbonic acid. If insufficient amounts of CO$_2$ are sequestered either in this reservoir or the planet's iron core, habitable zone water-worlds could generically be stalled in their cooling before liquid oceans have a chance to condense.