Breaking the degeneracy between gas inflow and outflows with stellar metallicity: Insights on M101

An analytical chemical evolution model is constructed to investigate the radial distribution of gas-phase and stellar metallicity for star-forming galaxies. By means of the model, the gas-phase and stellar metallicity can be obtained from the stellar-to-gas mass ratio. Both the gas inflow and outflow processes play an important role in building the final gas-phase metallicity, and there exists degeneracy effect between the gas inflow and outflow rates for star-forming galaxies. On the other hand, stellar metallicity is more sensitive to the gas outflow rate than to the gas inflow rate, and this helps to break the parameter degeneracy for star-forming galaxies. We apply this analysis method to the nearby disc galaxy M\,101 and adopting the classical $\chi^{2}$ methodology to explore the influence of model parameters on the resulted metallicity. It can be found that the combination of gas-phase and stellar metallicity is indeed more effective for constraining the gas inflow and outflow rates. Our results also show that the model with relatively strong gas outflows but weak gas inflow describes the evolution of M\,101 reasonably well.