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.
Highlights
Understanding the evolution of the chemical abundances within the interstellar medium (ISM) of galaxies is fundamental for the development of a galaxy formation and evolution theory that aims at being complete
We present a simple and fast method to solve chemical evolution of galaxies by assuming an instantaneous recycling approximation (IRA)1 for chemical elements contributed by massive stars and the delay time distribution (DTD) formalism for chemical elements restored by Type Ia Supernovae (SNe)
By assuming a non-linear Schmidt-Kennicutt law, equation (10) becomes a Bernoulli differential equation with a source function, which is given by the infall term, I (r, t); the corresponding Green function is determined by the response of the system to a Dirac delta function in the infall term, which – as aforementioned – represents the source function in equation (10); from a physical point of view, the Green function corresponds to the solution of the so-called ‘closed-box model’, with all the gases being already present in the galaxy since the beginning of its evolution
Summary
Understanding the evolution of the chemical abundances within the interstellar medium (ISM) of galaxies is fundamental for the development of a galaxy formation and evolution theory that aims at being complete. The difficulty of building up a fast and accurate chemical evolution model – including chemical elements restored with a certain delay time from the star formation event – to couple with other population synthesis models has represented an obstacle for developing a complete galaxy formation and evolution model for different groups in. We aim at reproducing the [α/Fe] versus [Fe/H] chemical abundance patterns as observed in the Milky Way (MW) at the solar neighbourhood by exploring the effect of different prescriptions for the DTD of Type Ia SNe. The assumed galaxy gas mass assembly history represents the starting point of this model. The assumed galaxy gas mass assembly history represents the starting point of this model This can be incorporated in other stellar population synthesis models to better characterize, in a simple but effective way, the formation and evolution of galaxies from the observed properties of their stellar populations at the present time.
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