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

In this work, we investigate how the central stellar metallicity ([Z/H]) of 1363 galaxies from the SAMI galaxy survey is related to their stellar mass and a proxy for the gravitational potential, Phi = log(10)(M-*/M-circle dot)-log(10)(r(e)/kpc) . In agreement with previous studies, we find that passive and star-forming galaxies occupy different areas of the [Z/H]-M-* plane, with passive galaxies having higher [Z/H] than star-forming galaxies at fixed mass (a difference of 0.23 dex at log(10)(M-*/M-circle dot) = 10.3). We show for the first time that all galaxies lie on the same relation between [Z/H] and Phi, and show that the 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 our results. By assuming that [Z/H] traces Phi over cosmic time and that the probability that a galaxy quenches depends on both its mass and size, we are able to reproduce these offsets in stellar metallicity with a model containing instantaneous quenching. We therefore conclude that an offset in metallicity at fixed mass cannot by itself be used as evidence of slow quenching processes, in contrast to previous studies. Instead, our model implies that metal-rich galaxies have always been the smallest objects for their mass in a population. Our findings reiterate the need to consider galaxy size when studying stellar populations.