We revisit the relation between the stellar surface density, the gas surface density and the gas-phase metallicity of typical disc galaxies in the local Universe with the SDSS-IV/MaNGA survey, using the star formation rate surface density as an indicator for the gas surface density. We show that these three local parameters form a tight relationship, confirming previous works (e.g. by the PINGS and CALIFA surveys), but with a larger sample. We present a new local leaky-box model, assuming star-formation history and chemical evolution is localized except for outflowing materials. We derive closed-form solutions for the evolution of stellar surface density, gas surface density and gas-phase metallicity, and show that these parameters form a tight relation independent of initial gas density and time. We show that, with canonical values of model parameters, this predicted relation match the observed one well. In addition, we briefly describe a pathway to improving the current semi-analytic models of galaxy formation by incorporating the local leaky-box model in the cosmological context, which can potentially explain simultaneously multiple properties of Milky Way-type disc galaxies, such as the size growth and the global stellar mass–gas metallicity relation.

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Published in Monthly Notices of the Royal Astronomical Society, v. 468, issue 4, p. 4494-4501.

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2017 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.

The copyright holders have granted the permission for posting the article here.

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GBZ acknowledges support provided by NASA through Hubble Fellowship grant #HST-HF2-51351 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under contract NAS 5-26555.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. The SDSS web site is www.sdss.org.