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 (M = M*), average potential (Φ=M*/R_e), and average surface mass density (ε = M*/R²_e, where 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 R_e. We find that between 0.5 and 1.5 R_e, the gas-phase metallicity correlates more tightly with Φ than with either M* or ε 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 R_e than either themass-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, amore natural explanation for our findings is a local relation between the gas-phase metallicity and the escape velocity.