The Milky Way Radial Metallicity Gradient as an Equilibrium Phenomenon: Why Old Stars are Metal-Rich
Metallicities of both gas and stars decline toward large radii in spiral galaxies, a trend known as the radial metallicity gradient. We quantify the evolution of the metallicity gradient in the Milky Way as traced by APOGEE red giants with age estimates from machine learning algorithms. Stars up to ages of $\sim$9 Gyr follow a similar relation between metallicity and Galactocentric radius. This constancy challenges current models of Galactic chemical evolution, which typically predict lower metallicities for older stellar populations. Our results favor an equilibrium scenario, in which the gas-phase gradient reaches a nearly constant normalization early in the disk lifetime. Using a fiducial choice of parameters, we demonstrate that one possible origin of this behavior is an outflow that more readily ejects gas from the interstellar medium with increasing Galactocentric radius. A direct effect of the outflow is that baryons do not remain in the interstellar medium for long, which causes the ratio of star formation to accretion, $\dotΣ_\star / \dotΣ_\text{in}$, to quickly become constant. This ratio is closely related to the local equilibrium metallicity, since its numerator and denominator set the rates of metal production by stars and hydrogen gained through accretion, respectively. Building in a merger event results in a perturbation that evolves back toward the equilibrium state on $\sim$Gyr timescales. Under the equilibrium scenario, the radial metallicity gradient is not a consequence of the inside-out growth of the disk but instead reflects a trend of declining $\dotΣ_\star / \dotΣ_\text{in}$ with increasing Galactocentric radius.