We investigate the nature of the star formation law at low gas surface densities using a sample of 19 low surface brightness (LSB) galaxies with existing HI maps in the literature, UV imaging from the Galaxy Evolution Explorer satellite, and optical images from the Sloan Digital Sky Survey. All of the LSB galaxies have (NUV-r) colors similar to those for higher surface brightness star-forming galaxies of similar luminosity indicating that their average star formation histories are not very different. Based upon four LSB galaxies with both UV and FIR data, we find FIR/UV ratios significantly less than one, implying low amounts of internal UV extinction in LSB galaxies. We use the UV images and HI maps to measure the star formation rate and hydrogen gas surface densities within the same region for all of the galaxies. The LSB galaxy star formation rate surface densities lie below the extrapolation of the power law fit to the star formation rate surface density as a function of the total gas density for higher surface brightness galaxies. Although there is more scatter, the LSB galaxies also lie below a second version of the star formation law in which the star formation rate surface density is correlated with the gas density divided by the orbital time in the disk. The downturn seen in both star formation laws is consistent with theoretical models that predict lower star formation efficiencies in LSB galaxies due to the declining molecular fraction with decreasing density.
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