Analytic solution of Chemical Evolution Models with Type Ia SNe

Context: In the last years, a significant number of works have focused on finding analytic solutions for the chemical enrichment models of galactic systems, including the Milky Way. Some of these solutions, however, cannot account for the enrichment produced by Type Ia SNe due to the presence of the delay time distributions (DTDs) in the models. Aims: We present a new analytic solution for the chemical evolution model of the Galaxy. This solution can be used with different prescriptions of the DTD, including the single and double degenerate scenarios, and allows the inclusion of an arbitrary number of pristine gas infalls. Methods: We integrate the chemical evolution model by extending the instantaneous recycling approximation with the contribution of 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. Results: We obtain the exact solution for a chemical model with Type Ia SNe widely used in previous works. 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. Conclusions: 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.
Comment: Accepted for publication in A&A. 22 pages, 16 figures. ChEAP code available at https://bitbucket.org/pedroap/cheap/src/master/