Young M dwarfs stay locked in a high-activity phase for up to a billion years, bathing close-in habitable-zone planets in strong XUV radiation. That radiation photolyses upper-atmosphere H2O into H and O. Because H is 16× lighter than O, it escapes to space far more readily — and if the heavier O is left behind, it can build up into a thick abiotic O2 atmosphere that mimics a photosynthesis biosignature with no life involved (Luger & Barnes 2015; Wordsworth & Pierrehumbert 2014).
Escape rate (energy-limited, XUV-driven hydrodynamic loss):
dM/dt = ε · F_XUV · π R_p³ / (G M_p)
Whether O is dragged out with the escaping H, or left behind to accumulate, is set by the Hunten (1973) crossover mass — the heaviest species the outflow can still carry:
m_c = m_H + (k_B T φ_H) / (b · g)
φ_H is the hydrogen number flux at the exobase, b is the H–O binary diffusion parameter, g is surface gravity, and T is the exobase temperature. If m_c > m_O (16 amu), oxygen is entrained in the outflow and escapes with the hydrogen — no buildup. If m_c < m_O, oxygen is left behind and accumulates.
- XUV flux — sets the photolysis and escape rate. Too low and almost nothing photolyses; too high and the outflow becomes strong enough to drag oxygen out too — the false-positive risk peaks in between.
- Planet mass — sets surface gravity and escape radius; a deeper gravity well raises the crossover mass needed to entrain oxygen.
- Water inventory — the O2 source runs out once the ocean is fully photolysed; buildup then stops.
- Time speed — this plays out over 10s–100s of millions of years in reality; the slider fast-forwards it.
Simplification: this model tracks only the water-derived O–H photolysis branch and ignores crustal/magma-ocean oxygen sinks, which real planets likely have and which would cap the buildup below what's shown here.