  Here we discuss the feasibility of photosynthesis on Earth-like rocky planets
in close orbit around ultra-cool red dwarf stars. Stars of this type have very
limited emission in the \textit{photosynthetically active} region of the
spectrum ($400 - 700$ nm), suggesting that they may not be able to support
oxygenic photosynthesis. However, photoautotrophs on Earth frequently exploit
very dim environments with the aid of highly structured and extremely efficient
antenna systems. Moreover, the anoxygenic photosynthetic bacteria, which do not
need to oxidize water to source electrons, can exploit far red and near
infrared light. Here we apply a simple model of a photosynthetic antenna to a
range of model stellar spectra, ranging from ultra-cool (2300 K) to Sun-like
(5800 K). We assume that a photosynthetic organism will evolve an antenna that
maximizes the rate of energy input while also minimizing fluctuations. The
latter is the 'noise cancelling' principle recently reported by Arp et al.
2020. Applied to the Solar spectrum this predicts optimal antenna
configurations in agreement with the chlorophyll Soret absorption bands.
Applied to cooler stars, the optimal antenna peaks become redder with
decreasing stellar temperature, crossing to the typical wavelength ranges
associated with anoxygenic photoautotrophs at $\sim 3300$ K. Lastly, we compare
the relative input power delivered by antennae of equivalent size around
different stars and find that the predicted variation is within the same order
of magnitude. We conclude that low-mass stars do not automatically present
light-limiting conditions for photosynthesis but they may select for anoxygenic
organisms.
