has been suggested as a mechanism for producing significant amounts of O$_2$ in an atmosphere (@WordsworthPierrehumbert14; @LugerBarnes15). In this scenario, a planet with a large amount of atmospheric H$_2$O orbiting a very active star will undergo rapid escape but with much of the O remaining, leading to O$_2$ build-up. For potentially habitable planets, it is expected that this build-up might be more significant for planets orbiting M dwarfs since these stars spend a very long time on the pre-main-sequence, meaning that planets that will eventually be in the habitable zones when the star reaches the main-sequence spend a long time inside the inner edge of the habitable zone where they are too hot for liquid surface water (@RamirezKaltenegger14).

The build-up of O$_2$ can be prevented if oxygen is absorbed into the surface, which @Wordsworth18 showed could significantly reduce the build-up of O$_2$ during a planet’s early magma ocean phase. In this case the absorbed oxygen can still be released into the atmosphere later in the planet’s lifetime. Alternatively, as the O$_2$ accumulates, the mixing ratio of O in the upper atmosphere will increase, leading to a decrease in the difference between the H and O loss rates (@Tian15). The loss 