The effect of out-of-equilibrium outgassing on the cooling of planetary magma oceans

Abstract

Rocky planet mantles likely experienced at least one global magma ocean stage. These magma oceans cooled and solidified rapidly, setting the conditions under which rocky planet mantles evolved in the long-term. Upon magma ocean solidification, vigorous convective motions are commonly thought to efficiently outgas dissolved volatiles, progressively forming a secondary atmosphere. Through the atmospheric blanketing effect, exsolved volatiles can then significantly slow down the solidification of magma oceans, which can alter the final thermo-chemical state of the mantles and their long-term evolution. While the efficient outgassing is a common hypothesis in magma ocean evolution models, the outgassing efficiency may be limited by the fact that fluid parcels containing dissolved volatiles need to reach small pressures corresponding to shallow exsolution depths, $d_{\mathrm{exsol}}$, allowing bubbles to form and volatiles to be outgassed. A recent numerical study (Salvador and Samuel, 2023) revealed that small exsolution depths can delay exsolution of volatiles beyond the solidification time of the mantle, in the case of a magma ocean of constant extent and for a constant exsolution depth.

Here, we extended this work by performing computational fluid dynamics and analog experiments at various Rayleigh and Prandtl numbers, which govern convective motions. We derived for the first time a general law that describes the flux of exsolved volatiles for a magma ocean of evolving thickness, $D$, and exsolution depth, $d_{\mathrm{exsol}}$. For sufficiently high Reynolds numbers, in a magma ocean, convecting with velocities $v$, the time evolution of the fraction of exsolved volatiles $\chi$ obeys a first order differential equation $\dot{\chi }=v{C}_b{d}_{\mathrm{exsol}}(1-\chi )/D^2$, with $C_b=6.6$.

We implemented this parameterized flux into a coupled magma ocean–atmosphere evolution model to more realistically assess the effect of convective motions on the formation of secondary atmospheres, along with their mantle evolution.

We found that for a broad range of parameters (e.g., high rotation rates, large planetary masses, or relatively low initial volatile contents) inefficient outgassing can lead to a mantle solidification more than one order of magnitude faster than in the case with an atmosphere in equilibrium with the magma ocean. This may impact not only the thermal state but also the composition of the solidified mantle in major and trace elements, and the subsequent billions of years of evolution of terrestrial planets.