Chemical separation of stellar populations: analytic solutions for chemical evolution models with metallicity-dependent yields

Abstract

Stellar abundances of elements with production channels that are metallicity-dependent (most notably aluminium) have provided an empirical route for separating different Galactic components. We present 'single-zone' analytic solutions for the chemical evolution of galaxies when the stellar yields are metallicity-dependent. Our solutions assume a constant star formation efficiency, a constant mass-loading factor and that the yields are linearly dependent on the interstellar medium abundance (with the option of a saturation of the yields at high metallicity). We demonstrate how the metallicity dependence of the yields can be mathematically considered as a system-dependent delay time (approximately equal to the system's depletion time) that, when combined with system-independent delay times arising from stellar evolutionary channels, produces the separation of different systems based on their star formation efficiency and mass-loading factor. The utility of the models is highlighted through comparisons with data from the APOGEE spectroscopic survey. We provide a comprehensive discussion of the chemical evolution models in the [Al/Fe]-[Mg/Fe] plane, a diagnostic plane for the separation of in-situ and accreted Galactic components. Extensions of the models are presented, allowing for the modelling of more complex behaviours largely through the linear combination of the presented simpler solutions.