Local and global gas metallicity versus stellar age relation in MaNGA galaxies

The search for new global scaling relations linking physical properties of galaxies has a fundamental interest. Furthermore, their recovery from spatially resolved relations has been one of the spotlights of integral field spectroscopy (IFS). In this study we investigate the existence of global and local relations between stellar age ($Age_\star$) and gas-phase metallicity ($Z_g$). To this aim, we analyze IFS data for a sample of 736 star-forming disk galaxies from the MaNGA survey. We report a positive correlation between the global $Z_g$ and $D(4000)$ (an indicator of stellar age), with a slope that decreases with increasing galaxy mass. Locally, a similar trend is found when analyzing the $Z_g$ and $D(4000)$ of the star-forming regions, as well as the residuals resulting from removing the radial gradients of both parameters. The local laws have systematically smaller slopes than the global one. We ascribe this difference to random errors, that make the true slope of the $Age_\star-Z_g$ relation to be systematically underestimated when performing a least square fitting. The explored relation is intimately linked with the already known relation between gas metallicity and star formation rate at fixed mass, both presenting a common physical origin.