Despite the existence of well-defined relationships between cold gas and star formation, there is evidence that some galaxies contain large amounts of HI that do not form stars efficiently. By systematically assessing the link between HI and star formation within a sample of galaxies with extremely high HI masses (log M_HI/M_sun > 10), we uncover a population of galaxies with an unexpected combination of high HI masses and low specific star formation rates that exists primarily at stellar masses greater than log M_*/M_sun ~ 10.5. We obtained HI maps of 20 galaxies in this population to understand the distribution of the HI and the physical conditions in the galaxies that could be suppressing star formation in the presence of large quantities of HI. We find that all of the galaxies we observed have low HI surface densities in the range in which inefficient star formation is common. The low HI surface densities are likely the main cause of the low sSFRs, but there is also some evidence that AGN or bulges contribute to the suppression of star formation. The samples agreement with the global star formation law highlights its usefulness as a tool for understanding galaxies that do not always follow expected relationships.
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