Around active M dwarfs, stellar UV/XUV photons split (photolyse) water vapor high in a planet's atmosphere into hydrogen and oxygen. Hydrogen (1 amu) is 16× lighter than atomic oxygen, so it escapes to space via thermal (Jeans) escape vastly faster — and any oxygen left behind builds up into an O2 atmosphere that looks like a photosynthesis biosignature even though no life is involved.
Photolysis supply rate (UV-driven):
R_phot = k · F_UV (g H2O/s)
Per-species thermal (Jeans) escape is mass-selective — this engine computes it independently for H and O2 every frame from their actual atomic masses:
λ = m · g · R_exo / (k_B · T_exo)
f_esc = (1 + λ) · exp(−λ)
Because O2 is 32× more massive than atomic H, λ_O2 = 32·λ_H — so f_esc(O2) is smaller than f_esc(H) by dozens of orders of magnitude across every slider setting: hydrogen leaks away efficiently while oxygen is essentially trapped. The net water-splitting rate actually sustained is throttled by how fast the escaping species (H) can actually leave (the standard escape-limited/diffusion-limited regime from the photochemical-escape literature):
R_net = R_phot · f_esc(H)
2 H2O → O2 + 4 H(escaped)
Both mass balance and the H/O2 inventories are integrated forward in simulated Myr:
- Stellar UV flux — sets R_phot directly and heats the exobase (higher T raises escape efficiency too). Weak, Sun-like UV never drives meaningful abiotic O2; only sustained high XUV (young, active M dwarfs) does.
- Planetary gravity — sets λ for both species. Lower gravity lowers λ_H sharply, letting hydrogen stream away efficiently and driving more net water loss and more O2 buildup; λ_O2 (32× larger) stays enormous across the whole slider range, so oxygen is essentially never dragged away with it.
- Water inventory — the O2 source runs out once the ocean is fully photolysed; buildup then stops.
Simplification: O2's own Jeans sink is computed and shown (usually negligible, occasionally measurable at extreme low gravity) but water loss is not capped by anything except escape efficiency — real planets also have crustal/magma-ocean oxygen sinks that would cap buildup below what is shown here.