The Local Star Formation Rate Surface Density and Metallicity Relation for Star-forming Galaxies

We study the relations between gas-phase metallicity (Z), local stellar mass surface density (sigma(*)), and the local star formation surface density (sigma(SFR)) in a sample of 1120 star-forming galaxies from the MaNGA survey. At fixed sigma(*)the local metallicity increases as sigma(SFR)decreases or vice versa for metallicity calibrators of N2 and O3N2. Alternatively, at fixed sigma(SFR)metallicity increases as sigma(*)increases, but in the high mass region, the trend is flatter. However, the dependence of metallicity on sigma(SFR)nearly disappears for N2O2 and N2S2 calibrators. We investigate the local metallicity against sigma(SFR)with different metallicity calibrators and find negative/positive correlations depending on the choice of the calibrator. We demonstrate that the O32 ratio (or ionization parameter) is probably dependent on star formation rate at fixed local stellar mass surface density. Additionally, the shape of sigma(*)-Z-sigma(SFR)(fundamental metallicity relation; FMR) depends on metallicity calibrator and stellar mass range. Due to the large discrepancy between the empirical fitting-based (N2, O3N2) electronic temperature metallicity and the photoionization model-dependent (N2O2, N2S2) metallicity calibrations, we conclude that the selection of metallicity calibration affects the existence of FMR on sigma(SFR).