The gas-phase metallicities of star-forming galaxies in aperture-matched SDSS samples follow potential rather than mass or average surface density

We present a comparative study of the relation between the aperture-based gas-phase metallicity and three structural parameters of star-forming galaxies: mass ($\mathrm{M \equiv M_*}$), average potential ($\Phi \equiv \mathrm{M_*/R_e}$) and average surface mass density ($\Sigma \equiv \mathrm{M_*/R_e^2}$; where $\mathrm{R_e}$ is the effective radius). We use a volume-limited sample drawn from the publicly available SDSS DR7, and base our analysis on aperture-matched sampling by selecting sets of galaxies where the SDSS fibre probes a fixed fraction of $\mathrm{R_e}$. We find that between 0.5 and 1.5 $\mathrm{R_e}$, the gas-phase metallicity correlates more tightly with $\Phi$ than with either $\mathrm{M}$ or $\Sigma$, in that for all aperture-matched samples, the potential-metallicity relation has (i) less scatter, (ii) higher Spearman rank correlation coefficient and (iii) less residual trend with $\mathrm{R_e}$ than either the mass-metallicity relation and the average surface density-metallicity relation. Our result is broadly consistent with the current models of gas enrichment and metal loss. However, a more natural explanation for our findings is a local relation between the gas-phase metallicity and escape velocity.