  Magma oceans are episodes of large-scale melting of the mantle of terrestrial
planets. The energy delivered by the Moon-forming impact induced a deep magma
ocean on the young Earth, corresponding to the last episode of core-mantle
equilibration. The crystallization of this magma ocean led to the outgassing of
volatiles initially present in the Earth's mantle, resulting in the formation
of a secondary atmosphere. During outgassing, the magma ocean acts as a
chemical buffer for the atmosphere via the oxygen fugacity, set by the
equilibrium between ferrous- and ferric-iron oxides in the silicate melts. By
tracking the evolution of the oxygen fugacity during magma ocean
solidification, we model the evolving composition of a C-O-H atmosphere. We use
the atmosphere composition to calculate its thermal structure and radiative
flux. This allows us to calculate the lifetime of the terrestrial magma ocean.
We find that, upon crystallizing, the magma ocean evolves from a mildly
reducing to a highly oxidized redox state, thereby transiting from a CO- and
H2-dominated atmosphere to a CO2- and H2O-dominated one. We find the overall
duration of the magma ocean crystallization to depend mostly on the bulk H
content of the mantle, and to remain below 1.5 millions years for up to 9
Earth's water oceans' worth of H. Our model also suggests that reduced
atmospheres emit lower infrared radiation than oxidized ones, despite of the
lower greenhouse effect of reduced species, resulting in a longer magma ocean
lifetime in the former case. Although developed for a deep magma ocean on
Earth, the framework applies to all terrestrial planet and exoplanet magma
oceans, depending on their volatile budgets.
