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 similar or equal to 3.7, we have compiled the largest available data set for studying Metallicity Evolution and Galaxy Assembly (MEGA); it comprises similar to 1000 galaxies with a common O/H calibration and spans almost two orders of magnitude in metallicity, a factor of similar to 10(6) in SFR, and a factor of similar to 10(5) in stellar mass. From a principal component analysis, we find that the three-dimensional parameter space reduces to a Fundamental Plane in 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 approximately redshift invariant within the uncertainties. In a companion paper, these results are interpreted with an updated version of the model presented by Dayal, Ferrara & Dunlop.