  Recent observations of the potentially habitable planets TRAPPIST-1 e, f, and
g suggest that they possess large water mass fractions of possibly several tens
of wt% of water, even though the host star's activity should drive rapid
atmospheric escape. These processes can photolyze water, generating free oxygen
and possibly desiccating the planet. After the planets formed, their mantles
were likely completely molten with volatiles dissolving and exsolving from the
melt. In order to understand these planets and prepare for future observations,
the magma ocean phase of these worlds must be understood. To simulate these
planets, we have combined existing models of stellar evolution, atmospheric
escape, tidal heating, radiogenic heating, magma ocean cooling, planetary
radiation, and water-oxygen-iron geochemistry. We present MagmOc, a versatile
magma ocean evolution model, validated against the rocky Super-Earth GJ 1132b
and early Earth. We simulate the coupled magma ocean-atmospheric evolution of
TRAPPIST-1 e, f, and g for a range of tidal and radiogenic heating rates, as
well as initial water contents between 1 and 100 Earth oceans. We also
reanalyze the structures of these planets and find they have water mass
fractions of 0-0.23, 0.01-0.21, and 0.11-0.24 for planets e, f, and g,
respectively. Our model does not make a strong prediction about the water and
oxygen content of the atmosphere of TRAPPIST-1 e at the time of mantle
solidification. In contrast, the model predicts that TRAPPIST-1 f and g would
have a thick steam atmosphere with a small amount of oxygen at that stage. For
all planets that we investigated, we find that only 3-5% of the initial water
will be locked in the mantle after the magma ocean solidified.
