The gas phase mass metallicity relation for dwarf galaxies: Dependence on star formation rate and HI gas mass

Using a sample of dwarf galaxies observed using the VIMOS IFU on the Very Large Telescope, we investigate the mass-metallicity relation (MZR) as a function of star formation rate (FMRSFR) as well as HI-gas mass (FMRHI). We combine our IFU data with a subsample of galaxies from the ALFALFA HI survey crossmatched to the Sloan Digital Sky Survey (SDSS) to study the FMRSFR and FMRHI across the stellar mass range 106.6-108.8 Mo, with metallicities as low as 12 + log(O/H) = 7.67. We find the 1σ mean scatter in the MZR to be 0.05 dex. The 1σ mean scatter in the FMRSFR (0.02 dex) is significantly lower than that of the MZR. The FMRSFR is not consistent between the IFU observed galaxies and the ALFALFA/SDSS galaxies for SFRs lower than 10-2.4 Mo yr-1, however, this could be the result of limitations of our measurements in that regime. The lowest mean scatter (0.01 dex) is found in the FMRHI. We also find that the FMRHI is consistent between the IFU observed dwarf galaxies and the ALFALFA/SDSS crossmatched sample. We introduce the fundamental metallicity luminosity counterpart to the FMR, again characterized in terms of SFR (FMLSFR) and HI-gas mass (FMLHI). We find that the FMLHI relation is consistent between the IFU observed dwarf galaxy sample and the larger ALFALFA/SDSS sample. However, the 1σ scatter for the FMLHI relation is not improved over the FMRHI scenario. This leads us to conclude that the FMRHI is the best candidate for a physically motivated fundamental metallicity relation.