A Uniform Analysis of Gas-phase Metallicity Evolution with 1-3 Gyr Time Sampling over the Past 12 Billion Years

We present a systematic investigation of the evolution of the mass-metallicity relation (MZR) and fundamental metallicity relation (FMR) using uniform metallicity diagnostics across redshifts $z\sim0$ to $z\sim3.3$. We present new Keck/DEIMOS measurements of the [OII]$λ\lambda3726,3729$ emission line doublet for star-forming galaxies at $z\sim1.5$ with existing measurements of redder rest-optical lines from the MOSDEF survey. These new observations enable uniform estimation of the gas-phase oxygen abundance using ratios of the [OII], H$β$, and [OIII] lines for mass-binned samples of star-forming galaxies in 6 redshift bins, employing strong-line calibrations that account for the distinct interstellar medium ionization conditions at $z<1$ and $z>1$. We find that the low-mass power law slope of the MZR remains constant over this redshift range with a value of $γ=0.28\pm0.01$, implying the outflow metal loading factor ($ζ_\text{out}=\frac{Z_{\text{out}}}{Z_{\text{ISM}}}\frac{\dot{M}_{\text{out}}}{\text{SFR}}$) scales approximately as $\rm ζ_{out}\propto M_*^{-0.3}$ out to at least $z\sim3.3$. The normalization of the MZR at $10^{10}\ \text{M}_\odot$ decreases with increasing redshift at a rate of $d\log(\text{O/H})/dz =-0.11\pm0.01$ across the full redshift range. We find that any evolution of the FMR is smaller than 0.1 dex out to $z\sim3.3$. We compare to cosmological galaxy formation simulations, and find that IllustrisTNG matches our measured combination of a nearly-invariant MZR slope, rate of MZR normalization decrease, and constant or very weakly evolving FMR. This work provides the most detailed view of MZR and FMR evolution from the present day through Cosmic Noon with a fine time sampling of $1-3$ Gyr, setting a robust baseline for metallicity evolution studies at $z>4$ with JWST.