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In this work, we investigate how the central stellar metallicity ([Z/H]) of1363 galaxies from the SAMI galaxy survey is related to their stellar mass anda proxy for the gravitational potential, $\Phi$ = log10(M/M*) -log10($r_e$/kpc). In agreement with previous studies, we find that passive andstar-forming galaxies occupy different areas of the [Z/H]-M* plane, withpassive galaxies having higher [Z/H] than star-forming galaxies at fixed mass(a difference of 0.23 dex at log10(M/M*)=10.3). We show for the first time thatall galaxies lie on the same relation between [Z/H] and $\Phi$, and show thatthe offset in [Z/H] between passive and star-forming galaxies at fixed $\Phi$is smaller than or equal to the offset in [Z/H] at fixed mass (an average$\Delta$[Z/H] of 0.11 dex at fixed $\Phi$ compared to 0.21 dex at fixed mass).We then build a simple model of galaxy evolution to explain and understand ourresults. By assuming that [Z/H] traces $\Phi$ over cosmic time and that theprobability that a galaxy quenches depends on both its mass and size, we areable to reproduce these offsets in stellar metallicity with a model containinginstantaneous quenching. We therefore conclude that an offset in metallicity atfixed mass cannot by itself be used as evidence of slow quenching processes, incontrast to previous studies. Instead, our model implies that metal-richgalaxies have always been the smallest objects for their mass in a population.Our findings reiterate the need to consider galaxy size when studying stellarpopulations.

The SAMI galaxy survey: galaxy size can explain the offset between star-forming and passive galaxies in the mass-metallicity relationship