Which non-biological processes can mimic oxygen or methane biosignatures?
In plain words
Oxygen and methane can sometimes be made by sunlight splitting water or by volcanic and rock-water chemistry, without life. A sign of life must be distinguishable from these.
Precise statement
Enumerate and quantify abiotic pathways that produce detectable $\mathrm{O_2}$, $\mathrm{O_3}$ or $\mathrm{CH_4}$ plus $\mathrm{CO_2}$ disequilibrium on rocky planets: $\mathrm{H_2O}$ photolysis with hydrogen escape, $\mathrm{CO_2}$ photolysis in dry atmospheres, serpentinization and volcanic outgassing. For each, derive spectral discriminants (CO, O4, $\mathrm{H_2O}$ abundance, redox state) measurable by a Habitable Worlds Observatory-class telescope. The answer is a classified list with abundance ranges and discriminants.
What would settle it
Coupled photochemical, geochemical and escape models over the plausible parameter range, with synthetic spectra at expected telescope resolution and signal to noise.
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