Bubble stability in vigorous convection: Ramifications for magma-ocean degassing and formation of an early atmosphere

The heat provided by energetic impacts, radioactive decay and core formation during the early stages in terrestrial planet evolution is sufficient to melt a silicate mantle partially or entirely. Thus, magma-ocean models provide an interesting hypothetical starting point for understanding mantle evolution of terrestrial planets. A key constraint in these models is the formation of an early atmosphere, because it exerts a strong control over the heat flux from the planetary surface. One open question in the task of developing a model of early atmosphere formation is related to when volatiles begin to exsolve from the magma ocean and in what quantities. Even magma oceans with initial minute water or carbon contents will eventually, as they solidify, become saturated and begin to exsolve volatiles as gases. The bubble size distribution in the magma is likely to exert a strong control over this process: small gas bubbles will tend to remain entrained in vigorous convection while large bubbles decouple from the surrounding flow field and rise to the surface under their own buoyancy. In this paper, we use numerical simulations of two-phase flow to investigate how the size distribution of gas bubbles in a magma ocean depends on its physical characteristics, such as composition, magma viscosity and volatile content. The numerical technique couples a level-set-based representation of the interface to a Navier-Stokes solver through the construction of extension velocities. Preliminary results indicate that gas bubbles in superliquidus magma oceans with low viscosity remain small. In fact, current estimates of the radius at which gas bubbles cease to be entrained in flow and begin to rise to the free surface under their buoyancy might exceed the radius of stable gas bubbles. This observation implies that the earliest atmospheres might form only during the final stages of magma-ocean solidification and possibly through very rapid degassing of oversaturated magma. Late, rapid degassing from a putative terrestrial magma ocean, for example following a Moon-forming impact, implies that solidification of magma oceans would have been exceptionally fast. Rapid interior cooling in turn makes the time to clement surface conditions rapid, preparing the planetary surface for liquid water.