Chemical-Evolution Models in Galaxies

• Chemical-evolution models are theoretical frameworks that simulate the temporal and spatial evolution of chemical abundances in galaxies using mass- and metal-conservation equations.
• They integrate key processes such as star formation, nucleosynthesis, gas infall, outflow, and internal redistribution to reproduce observed metallicity gradients.
• Applications include interpreting abundance patterns in environments from molecular clouds and circumstellar disks to spiral galaxies, aiding in stellar population diagnostics.

Chemical-evolution models are theoretical and computational frameworks designed to predict the temporal and spatial evolution of chemical abundances in galaxies and interstellar environments. These models underpin the quantitative interpretation of observed abundance patterns, metallicity gradients, and stellar population diagnostics across a wide range of astronomical systems, from early molecular clouds and circumstellar disks to massive spiral galaxies and cosmological volumes.

1. Theoretical Foundations and Model Ingredients

At their core, chemical-evolution models apply mass- and metal-conservation equations to one or more spatial zones, tracking the exchange of baryons and heavy elements between gas, stars, and galactic reservoirs. The standard formulation includes terms for star formation, nucleosynthetic enrichment from dying stars, gas infall and outflow, and internal redistribution of material:

$\frac{dM_g}{dt} = -\psi(t) + E(t) + f(t) - w(t)$

$$\frac{d[M_i(t) M_g(t)]}{dt} = -X_i(t)\psi(t) + E_i(t) + X_{i,f}f(t) - X_i(t)w(t)$$

Where $M_g$ is the total gas mass, $M_i$ the mass (or surface density) of element $i$, $\psi(t)$ the star-formation rate (SFR), $E(t)$ the total stellar ejecta, $f(t)$ the infall rate, and $w(t)$ the outflow (wind) rate. $X_i(t)$ denotes the mass fraction of element $i$ in the ISM; yields and recycling fractions are parameterized via the initial mass function (IMF), stellar lifetimes, and metallicity- and mass-dependent nucleosynthetic tables (e.g., Woosley &