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.
