Do not forget the electrons: Extending moderately-sized nuclear networks for multidimensional hydrodynamic codes

¹ Departament de Física. Universitat Politècnica de Catalunya (UPC). Av. Eduard Maristany 16, 08019 Barcelona, Spain
e-mail: domingo.garcia@upc.edu
² Institut d’Estudis Espacials de Catalunya (IEEC), 08860 Castelldefels (Barcelona), Spain
³ Center for Scientific Computing – sciCORE, University of Basel, Klingelberstrasse 61, 4056 Basel, Switzerland
e-mail: ruben.cabezon@unibas.ch
⁴ Department of Astronomy and Astrophysics, University of Valencia, C/Dr. Moliner 50, 46100 Burjassot (Valencia), Spain
e-mail: moritz.reichert@uv.es
⁵ Triangle Universities Nuclear Laboratory, Duke University, Durham, North Carolina 27708, USA
⁶ Department of Physics, Duke University, Durham, North Carolina 27708, USA
⁷ Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstr. 2, Darmstadt 64289, Germany
⁸ GSI Helmholtzzentrum für Schwerionenforschung GmbH, PlanckStrs. 1, Darmstadt 64291, Germany
⁹ Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
¹⁰ Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland

Received: 5 March 2024
Accepted: 7 July 2024

Abstract

Context. Nuclear networks are widely used coupled with hydrodynamical simulations of explosive scenarios to account for the change of nuclear species and energy generation rate due to nuclear reactions. In this way, there is a feedback mechanism between the hydrodynamical state and the nuclear processes. Unfortunately, the timescale of nuclear reactions is orders of magnitude smaller than the dynamical timescale that drives hydrodynamical simulations. Therefore, these nuclear networks are usually very small, reduced in most cases to a dozen elements, especially when simulations are carried out in more than one dimension.

Aims. We present here an extended nuclear network, with 90 species, designed for being coupled with hydrodynamic simulations, which includes neutrons, protons, electrons, positrons, and the corresponding neutrino and anti-neutrino emission. This network is also coupled with temperature, making it extremely robust and, together with its size, unique of its kind. The inclusion of electron captures on free protons makes the network very appropriate for multidimensional studies of Type Ia supernova explosions, especially when the exploding object is a massive white dwarf.

Methods. We perform several tests that are relevant to simulate explosive scenarios, such as Type Ia supernovae and core-collapse supernovae. We compare the results of the 90 nuclei network with a standard α-chain network with 14 elements to evaluate the differences in the energy generation rate. We also evaluate the relevance of including the electrons in the network in terms of generated yields and how it affects the pressure of a degenerate fluid such as that of white dwarfs. The results obtained with the 90-nuclei network have been verified with a much larger 2000-nuclei network built from REACLIB (WinNet), in terms of nuclear energy generation rate, pressure, and produced yields.

Results. The results obtained with the proposed medium-sized network compare fairly well, to a few percent, with those computed with WinNet in scenarios reproducing the gross physical conditions of current Type Ia supernova explosion models. In those cases where the carbon and oxygen fuel ignites at high density, the high-temperature plateau typical of the nuclear statistical equilibrium regime is well defined and stable, allowing large integration time steps. We show that the inclusion of electron captures on free protons substantially improves the estimation of the electron fraction of the mixture. Therefore, the pressure is better determined than in networks where electron captures are excluded, which will ultimately lead to more reliable hydrodynamic models. Explosive combustion of helium at low density, occurring near the surface layer of a white dwarf, is also better described with the proposed network, which gives nuclear energy generation rates much closer to WinNet than typical reduced alpha networks.

Conclusions. A nuclear network with N = 90 species, including electrons, aimed at multidimensional calculations of supernova explosions is described and verified. The proposed network is suitable for the study of Type Ia supernova explosions because it provides better values of pressure and electron abundance than other existing networks with smaller or even a similar size but without including electron capture processes.