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comment Why didn't the polar bear change its color from white to black during evolution to absorb heat?
@Chris - The amount of energy in UV is utterly negligible compared to the bear's metabolism. See for instance (where you get numbers of under a watt per square meter even at noon in the tropics). It might be useful for vitamin D production (if bears need it), but not for warmth.
comment Can Bioluminescence drive photosynthesis?
@shigeta - Refrigerators are reasonably efficient air conditioners. The key is not how much energy you expend, it's the configuration of the heat cycle (i.e. cooling coils and open door not in the same room if you want to reduce the mean temperature in one room). It's really not analogous at all--here the issue is that you need the methane processed, and providing light input (and methane as the carbon source) is one way to accomplish it.
comment Can Bioluminescence drive photosynthesis?
@shigeta - No, opening a refrigerator in the kitchen can only warm the kitchen. The more energy you put in, the warmer it will get. You can cool the kitchen if you put the refrigerator half in the kitchen and half in some other room (or outside).