A simple and general method for solving detailed chemical evolution with delayed production of iron and other chemical elements

Abstract: We present a theoretical method for solving the chemical evolution of galaxies, by assuming an instantaneous recycling approximation for chemical elements restored by massive stars and the Delay Time Distribution formalism for the delayed chemical enrichment by Type Ia Supernovae. The galaxy gas mass assembly history, together with the assumed stellar yields and initial mass function, represent the starting point of this method. We derive a simple and general equation which closely relates the Laplace transforms of the galaxy gas accretion history and star formation history, which can be used to simplify the problem of retrieving these quantities in the galaxy evolution models assuming a linear Schmidt-Kennicutt law. We find that - once the galaxy star formation history has been reconstructed from our assumptions - the differential equation for the evolution of the chemical element $X$ can be suitably solved with classical methods. We apply our model to reproduce the [O/Fe] and [Si/Fe] vs. [Fe/H] chemical abundance patterns as observed at the solar neighborhood, by assuming a decaying exponential infall rate of gas and different delay time distributions for Type Ia Supernovae; we also explore the effect of assuming a nonlinear Schmidt-Kennicutt law, with the index of the power law being $k=1.4$. Although approximate, we conclude that our model with the single degenerate scenario for Type Ia Supernovae provides the best agreement with the observed set of data. Our method can be used by other complementary galaxy stellar population synthesis models to predict also the chemical evolution of galaxies.