Testing cold dark matter with the low-mass Tully-Fisher relation

In most cosmological theories, the galaxy mass function at small masses is related to the small-scale matter power spectrum. The circular velocity function (closely related to the mass function) is well studied for Local Group dwarfs. However, predictions and measurements are difficult for satellite galaxies because of ram pressure and tidal stripping. By contrast, isolated dwarf galaxies are less affected by these processes and almost always have 21 cm emission to trace their dynamics. Here we use isolated low-mass dwarf galaxies from the SDSS, with measured 21 cm widths, to test CDM cosmology. We find consistency between the predicted and observed number density of isolated galaxies down to V-max similar to 50 km s(-1). Our technique yields a direct test of small-scale cosmology that is independent of but weaker than the Ly alpha forest: warm dark matter particles heavier than 0.5 keV cannot be ruled out (for the case of thermal gravitinos). New, blind H I surveys are expected to uncover a much larger number of isolated low-mass galaxies and will increase the power of our constraints at small scales. Using our sample, we also find that the Tully-Fisher relation for dwarfs is a strong function of environment, and that the baryon fraction is only a weak function of galaxy mass. Together with the strong dependence of gas fraction on environment, these results indicate that for dwarf galaxies, gas loss and the end of star formation are dominated by external, not internal, processes.