Analytic solution of chemical evolution models with Type Ia supernovae

I. Disc bimodality in the [α/Fe] versus [Fe/H] plane and other applications^★

¹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice cedex 4, France
e-mail: pedro.alonso-palicio@oca.eu
² I.N.A.F., Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, 34131 Trieste, Italy
³ Dipartimento di Fisica, Sezione di Astronomia, Università di Trieste, via G.B. Tiepolo 11, I-34131, Trieste, Italy
⁴ I.N.F.N. Sezione di Trieste, via Valerio 2, 34134 Trieste, Italy
⁵ Sorbonne Université, CNRS, UMR7095, Institute d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
⁶ I.N.A.F., Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy

Received: 31 March 2023
Accepted: 22 July 2023

Abstract

Context. In recent years, a significant number of works have been focussed on finding analytic solutions for the chemical enrichment models of galactic systems, including the Milky Way. Some of these solutions, however, are not able to account for the enrichment produced by Type Ia supernovae (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 for the inclusion of an arbitrary number of pristine gas infalls.

Methods. We integrated the chemical evolution model by extending the instantaneous recycling approximation with the contribution of Type Ia SNe. This implies an extra term in the modelling that depends on the DTD. For 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 obtained the exact solution for a chemical model with Type Ia SNe widely used in previous works, while managing to avoid numerical integration errors. This solution is able to reproduce the expected chemical evolution of the α and iron-peak elements in less computing time than numerical integration methods. We compare the pattern in the [Si/Fe] versus [Fe/H] plane observed by APOGEE DR17 with that predicted by the model. We find the low α 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 has been released as a PYTHON package.

Conclusions. Our solution constitutes a promising tool for Galactic archaeology studies and it is able to model the observed trends in α element abundances versus [Fe/H] in the solar neighbourhood. We infer the chemical information of a simulated galaxy modelled without chemistry.