  Despite very high temperatures accompanying lunar origin, indigenous water in
the form of OH has been unambiguously observed in Apollo samples in recent
years. Such observations have prompted questions about the abundance and
distribution of lunar hydrogen. Here, we investigate the related question of
the origin of lunar H: is the hydrogen observed a remnant of a much larger
initial inventory that was inherited from a wet Earth but partly depleted
during the process of origin, or was hydrogen quantitatively lost from the
lunar material, with water being delivered to lunar reservoirs via subsequent
impacts after the origins sequence? Motivated by recent results pointing to a
limited extent of hydrogen escape from the gravity field of the Earth during
lunar origin, we apply a newly developed thermodynamic model of liquid-vapor
silicates to the proto-lunar disk to interrogate the behavior of H as a trace
element in the energetic aftermath of the giant impact. We find that: (1)
pre-existing H-bearing molecules are rapidly dissociated at the temperatures
considered (3,100-4,200 K) and vaporized hydrogen predominantly exists as
OH(v), H(v) and MgOH(v) for nearly the full range of thermal states encountered
in the proto-lunar disk, (2) despite such a diversity in the vapor speciation,
which reduces the water fugacity and favors hydrogen exsolution from
co-existing liquids, the equilibration of the vapor atmosphere with the disk
liquid results in significant dissolution of H into proto-lunar magmas, and (3)
equilibrium H isotopic fractionation in this setting is limited to < 10 per mil
and the terrestrial character of lunar D/H recently inferred should extend to
such a precision if liquid-vapor equilibration in the proto-lunar disk is the
process that gave rise to lunar hydrogen. Taken together, these results
implicate dissolution as the process responsible for establishing lunar H
abundances.
