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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 VLT, we investigate the mass-metallicity relation (MZR) as a function of star formation rate (FMR$_{\text{SFR}}$) as well as HI-gas mass (FMR$_{\text{HI}}$). We combine our IFU data with a subsample of galaxies from the ALFALFA HI survey crossmatched to the Sloan Digital Sky Survey to study the FMR$_{\text{SFR}}$ and FMR$_{\text{HI}}$ across the stellar mass range 10$^{6.6}$ to 10$^{8.8}$ M$_\odot$, with metallicities as low as 12+log(O/H) = 7.67. We find the 1$σ$ mean scatter in the MZR to be 0.05 dex. The 1$σ$ mean scatter in the FMR$_{\text{SFR}}$ (0.02 dex) is significantly lower than that of the MZR. The FMR$_{\text{SFR}}$ is not consistent between the IFU observed galaxies and the ALFALFA/SDSS galaxies for SFRs lower than 10$^{-2.4}$ M$_\odot$ 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 FMR$_{\text{HI}}$. We also find that the FMR$_{\text{HI}}$ 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 (FML$_{\text{SFR}}$) and HI-gas mass (FML$_{\text{HI}}$). We find that the FML$_{\text{HI}}$ relation is consistent between the IFU observed dwarf galaxy sample and the larger ALFALFA/SDSS sample. However the 1$σ$ scatter for the FML$_{\text{HI}}$ relation is not improved over the FMR$_{\text{HI}}$ scenario. This leads us to conclude that the FMR$_{\text{HI}}$ is the best candidate for a physically motivated fundamental metallicity relation.