Analytic solution of the CEM with Type Ia SNe

For those DTDs that lead to non-analytic integrals, we describe them as a superposition of Gaussian, exponential and 1/t functions using a restricted least-squares fitting method. We obtain the exact solution for a chemical model with Type Ia SNe widely used in previous works, avoiding numerical integration errors. This solution can reproduce the expected chemical evolution of the alpha and iron-peak elements in less computing time than numerical integration methods.

We compare the pattern in the [Si/Fe] vs. [Fe/H] plane observed by APOGEE DR17 with that predicted by the model. We find the low alpha sequence can be explained by a delayed gas infall. We exploit the applicability of our solution by modelling the chemical evolution of a simulated Milky Way-like galaxy from its star formation history.

The implementation of our solution is released as a Python package. Our solution constitutes a promising tool for the Galactic Archaeology and is able to model the observed trends in alpha element abundances versus [Fe/H] in the solar neighbourhood. We infer the chemical information of a simulated galaxy modelled without Chemistry.