Comparison of H-alpha and UV Star Formation Rates in the Local Volume: Systematic Discrepancies for Dwarf Galaxies

(abridged) Using a complete sample of ~300 star-forming galaxies within 11 Mpc, we evaluate the consistency between star formation rates (SFRs) inferred from the far ultraviolet (FUV) non-ionizing continuum and H-alpha nebular emission, assuming standard conversion recipes in which the SFR scales linearly with luminosity at a given wavelength. Our analysis probes SFRs over 5 orders of magnitude, down to ultra-low activities on the order of ~0.0001 M_sun/yr. The data are drawn from the 11 Mpc H-alpha and Ultraviolet Galaxy Survey (11HUGS), which has obtained H-alpha fluxes from ground-based narrowband imaging, and UV fluxes from imaging with GALEX. For normal spiral galaxies (SFR~1 M_sun/yr), our results are consistent with previous work which has shown that FUV SFRs tend to be lower than H-alpha SFRs before accounting for internal dust attenuation, but that there is relative consistency between the two tracers after proper corrections are applied. However, a puzzle is encountered at the faint end of the luminosity function. As lower luminosity dwarf galaxies, roughly less active than the Small Magellanic Cloud, are examined, H-alpha tends to increasingly under-predict the SFR relative to the FUV. Although past studies have suggested similar trends, this is the first time this effect is probed with a statistical sample for galaxies with SFR~<0.1 M_sun/yr. A range of standard explanations does not appear to be able to account for the magnitude of the systematic. Some recent work has argued for an IMF which is deficient in high mass stars in dwarf and low surface brightness galaxies, and we also consider this scenario.