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.