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We present a comparative study of the relation between the aperture-basedgas-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 avolume-limited sample drawn from the publicly available SDSS DR7, and base ouranalysis on aperture-matched sampling by selecting sets of galaxies where theSDSS fibre probes a fixed fraction of $\mathrm{R_e}$. We find that between 0.5and 1.5 $\mathrm{R_e}$, the gas-phase metallicity correlates more tightly with$\Phi$ than with either $\mathrm{M}$ or $\Sigma$, in that for allaperture-matched samples, the potential-metallicity relation has (i) lessscatter, (ii) higher Spearman rank correlation coefficient and (iii) lessresidual trend with $\mathrm{R_e}$ than either the mass-metallicity relationand the average surface density-metallicity relation. Our result is broadlyconsistent with the current models of gas enrichment and metal loss. However, amore natural explanation for our findings is a local relation between thegas-phase metallicity and escape velocity.

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