The mass-metallicity relations for gas and stars in star-forming
  galaxies: strong outflow vs variable IMF
  We investigate the mass-metallicity relations for the gaseous (MZRgas) and
stellar components (MZRstar) of local star-forming galaxies based on a
representative sample from SDSS DR12. The mass-weighted average stellar
metallicities are systematically lower than the gas metallicities. This
difference in metallicity increases toward galaxies with lower masses and
reaches 0.4-0.8 dex at 10^9 Msun (depending on the gas metallicity
calibration). As a result, the MZRstar is much steeper than the MZRgas. The
much lower metallicities in stars compared to the gas in low mass galaxies
implies dramatic metallicity evolution with suppressed metal enrichment at
early times. The aim of this paper is to explain the observed large difference
in gas and stellar metallicity and to infer the origin of the mass-metallicity
relations. To this end we develop a galactic chemical evolution model
accounting for star formation, gas inflow and outflow. By combining the
observed mass-metallicity relation for both gas and stellar components to
constrain the models, we find that only two scenarios are able to reproduce the
observations. Either strong metal outflow or a steep IMF slope at early epochs
of galaxy evolution is needed. Based on these two scenarios, for the first time
we successfully reproduce the observed MZRgas and MZRstar simultaneously,
together with other independent observational constraints in the local
universe. Our model also naturally reproduces the flattening of the MZRgas at
the high mass end leaving the MZRstar intact, as seen in observational data.
