As a planet transits its star, starlight grazes the planet's atmospheric limb. Gases absorb specific wavelengths, so the apparent planet radius grows slightly at those wavelengths — the transit gets a little deeper. The extra depth from one atmospheric scale height is:
H = k_B·T / (μ·m_H·g) (atmospheric scale height)
Δdepth ≈ 2·R_p·H / R_s² (per scale height of absorber)
For an Earth-radius planet around a Sun-like star, H ≈ 8 km gives only ~0.2 ppm per scale height — which is exactly why Earth's own atmosphere would be undetectable by transit spectroscopy at interstellar distances with current instruments; real surveys target smaller, cooler M-dwarf hosts where the same physics yields a far larger signal.
The sliders drive a simplified steady-state photochemistry model — production balanced by loss, dP/dt = 0:
O₂ production = 0.50·bio + 0.015·UV (photosynthesis + weak CO₂/H₂O photolysis)
O₂ loss = 0.05 + 0.04·UV (surface oxidation + UV-driven recombination)
CH₄ production = 0.35·bio + 0.15·volcanism (biogenic methanogenesis + geologic outgassing)
CH₄ loss = 0.08 + 0.20·UV (UV photolysis dominates)
steady state: [X]_ss = production_X / loss_X
Why simultaneous O₂ + CH₄ matters: the two gases react (CH₄ + 2O₂ → CO₂ + 2H₂O) on timescales far shorter than either persists alone. Finding both at once — as on modern Earth — means something is continuously replenishing them faster than they can react away. Abiotic photolysis alone rarely sustains meaningful O₂ without also destroying any CH₄, which is why real surveys (following Lovelock's 1965 disequilibrium argument, formalized by Krissansen-Totton et al. 2018) treat co-existing O₂ and CH₄ as a stronger biosignature than either gas alone, and why O₂ from CO₂/H₂O photolysis with no CH₄ is flagged as a possible false positive (Meadows 2017).
This toy model is illustrative, not a real atmospheric retrieval code — it captures the reasoning astrobiologists use, not literature rate constants.