We present spectra of 14 A-type supergiants in the metal-rich spiral galaxy M83. We derive stellar parameters and metallicities, and measure a spectroscopic distance modulus m-M = 28.47 +- 0.10 (4.9 +- 0.2 Mpc), in agreement with other methods. We use the stellar characteristic metallicity of M83 and other systems to discuss a version of the galaxy mass-metallicity relation that is independent of the analysis of nebular emission lines and the associated systematic uncertainties. We reproduce the radial metallicity gradient of M83, which flattens at large radii, with a chemical evolution model, constraining gas inflow and outflow processes. We carry out a comparative analysis of the metallicities we derive from the stellar spectra and published HII region line fluxes, utilizing both the direct, Te-based method and different strong-line abundance diagnostics. The direct abundances are in relatively good agreement with the stellar metallicities, once we apply a modest correction to the nebular oxygen abundance due to depletion onto dust. Popular empirically calibrated strong-line diagnostics tend to provide nebular abundances that underestimate the stellar metallicities above the solar value by ~0.2 dex. This result could be related to difficulties in selecting calibration samples at high metallicity. The O3N2 method calibrated by Pettini and Pagel gives the best agreement with our stellar metallicities. We confirm that metal recombination lines yield nebular abundances that agree with the stellar abundances for high metallicity systems, but find evidence that in more metal-poor environments they tend to underestimate the stellar metallicities by a significant amount, opposite to the behavior of the direct method.
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