  GJ 1132 b is a nearby Earth-sized exoplanet transiting an M dwarf, and is
amongst the most highly characterizable small exoplanets currently known. In
this paper we study the interaction of a magma ocean with a water-rich
atmosphere on GJ 1132b and determine that it must have begun with more than 5
wt% initial water in order to still retain a water-based atmosphere. We also
determine the amount of O2 that can build up in the atmosphere as a result of
hydrogen dissociation and loss. We find that the magma ocean absorbs at most
~10% of the O2 produced, whereas more than 90% is lost to space through
hydrodynamic drag. The most common outcome for GJ 1132 b from our simulations
is a tenuous atmosphere dominated by O2, although for very large initial water
abundances atmospheres with several thousands of bars of O2 are possible. A
substantial steam envelope would indicate either the existence of an earlier H2
envelope or low XUV flux over the system's lifetime. A steam atmosphere would
also imply the continued existence of a magma ocean on GJ 1132 b. Further
modeling is needed to study the evolution of CO2 or N2-rich atmospheres on GJ
1132 b.
