Photosynthesis on habitable planets around low-mass stars

We show that planets around M-dwarfs with $M_\star \lesssim 0.2 M_\odot$ may not receive enough photons in the photosynthetically active range of $400$-$750$ nm to sustain Earth-like biospheres. As a result of the lower biological productivity, it is likely that biotic molecular oxygen would not build up to detectable levels in the atmospheres of habitable planets orbiting low-mass stars, consistent with prior work by Lehmer et al. (2018). We also estimate the minimum flaring rate for sustaining biospheres with Earth-like productivity and permitting the build-up of atmospheric oxygen, and find that the overwhelming majority of M-dwarfs are unlikely to exceed this threshold.