I'm not familar with "the self-ionization of water". My guess is that an energy source like ultra violet light or other radiation "tuned" to the binding energy of water molecules, or cell chemistry, is required to produce the ionization you speak of. Are these ions very short lived..say milliseconds per individual?
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After answering this question, how does this affect what we're searching for on/in other planets?
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We should look for the spectral signatures of O, O2, O+, and O2+ in planetary atmospheres when we get good enough. If life is not present, free oxygen won't hang around very long.