Can Bioluminescence drive photosynthesis?

I'm trying to construct an anaerobic kitchen-waste digester at home.

The major output from the digester is methane - with a significant component of carbon dioxide. To scrub/reduce the CO2 I was thinking of passing the methane through a freshwater container charged with algae ... then it occurred to me to also think of introducing some bioluminescent algae to drive the photosynthesis & absorb some of the oxygen released by the other algae. Understandably this would be an unbalanced system.

But ... can bioluminescence drive photosynthesis?

Answer

Yes and no. Yes as in the energetics do work out and you will be going down a small but non-trivial driving force as long as you continue to provide the luciferin to the algae.

However, the wavelengths of light by which photosynthesis absorbs its energy are well defined and narrow. As a result, light sources for photosynthetic organisms have to be fairly strong and bright to cover the whole spectrum to provide the necessary light. As a result, your bioluminescent algae will also have to emit light at the desired wavelength to achieve a high photochemical efficiency and provide light to both Photosystem II and Photosystem I which have different wavelength requirements.

_{(source: gsu.edu)}