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We revisit the relation between the stellar surface density, the gas surfacedensity, and the gas-phase metallicity of typical disk galaxies in the localUniverse with the SDSS-IV/MaNGA survey, using the star formation rate surfacedensity as an indicator for the gas surface density. We show that these threelocal parameters form a tight relationship, confirming previous works (e.g., bythe PINGS and CALIFA surveys), but with a larger sample. We present a new localleaky-box model, assuming star formation history and chemical evolution islocalized except for outflowing materials. We derive closed-form solutions forthe evolution of stellar surface density, gas surface density and gas-phasemetallicity, and show that these parameters form a tight relation independentof initial gas density and time. We show that, with canonical values of modelparameters, this predicted relation match the observed one well. In addition,we briefly describe a pathway to improving the current semi-analytic models ofgalaxy formation by incorporating the local leaky-box model in the cosmologicalcontext, which can potentially explain simultaneously multiple properties ofMilky Way-type disk galaxies, such as the size growth and the global stellarmass-gas metallicity relation.

A Local Leaky-box Model for the Local Stellar Surface Density - Gas Surface Density - Gas Phase Metallicity Relation