Coevolution of metallicity and star formation in galaxies to z=3.7: I. A fundamental plane

With the aim of understanding the coevolution of star formation rate (SFR), stellar mass (M*), and oxygen abundance (O/H) in galaxies up to redshift z=3.7, we have compiled the largest available dataset for studying Metallicity Evolution and Galaxy Assembly (MEGA); it comprises roughly 1000 galaxies with a common O/H calibration and spans almost two orders of magnitude in metallicity, a factor of 10^6 in SFR, and a factor of 10^5 in stellar mass. From a Principal Component Analysis, we find that the 3-dimensional parameter space reduces to a Fundamental Plane of Metallicity (FPZ) given by 12+log(O/H) = -0.14 log (SFR) + 0.37 log (M*) + 4.82. The mean O/H FPZ residuals are small (0.16 dex) and consistent with trends found in smaller galaxy samples with more limited ranges in M*, SFR, and O/H. Importantly, the FPZ is found to be redshift-invariant within the uncertainties. In a companion paper, these results are interpreted with an updated version of the model presented by Dayal et al. (2013).