Compartmental description of the cosmological baryonic matter cycle

I. Competition of spontaneous star formation, stellar feedback, and stellar evolution

¹ Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany
² Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstr. 15, D-24118 Kiel, Germany
³ Magnetism and Interface Physics & Computational Polymer Physics, Department of Materials, ETH Zurich, Leopold-Ruzicka-Weg 4, CH-8093 Zurich, Switzerland

^⋆ Corresponding authors; mk@mat.ethz.ch; rsch@tp4.rub.de

Received: 14 August 2024
Accepted: 26 September 2024

Abstract

Context. The compartmental description, well-known as the description of infection diseases and epidemics, was applied here to describe the temporal evolution of the baryonic matter in interstellar gas and stars. The introduction of gaseous and stellar fractions of the total baryonic matter as the basic dynamical variables is advantageous because it allows us to apply the description to a variety of astrophysical systems.

Aims. We aimed to theoretically investigate the competition of spontaneous star formation, stellar feedback, and stellar evolution to understand the baryonic matter cycle including luminous baryonic matter in main-sequence stars and weakly luminous matter in white dwarfs, neutron stars, and black holes (referred to as locked-in matter). Of particular interest was the understanding of cosmic star formation history and the present-day gas fraction with compartmental models.

Methods. We derived exact analytical solutions for the time evolution of the fractions of gaseous, luminous stellar, and locked-in stellar matter for stationary rates of spontaneous star formation, continuous stellar feedback, and stellar evolution. The accuracy of the analytical solutions was proven by comparison with the exact numerical solutions of the dynamical equations.

Results. The observed cosmological star formation rate and the integrated stellar density as a function of redshift are reasonably well explained by the compartmental model without triggered star formation by the competition of spontaneous star formation and stellar evolution, whereas the influence of stellar feedback is less important. The action of stellar evolution provides a significant redshift-dependent reduction factor when calculating the integrated stellar density from the star formation rate. Without stellar evolution, the observations could not be reproduced very well. Then, the fits to the observation provided conclusions on the relative importance of spontaneous star formation, stellar evolution, and feedback in the early Universe after the recombination era until today. The gas, luminous star, and locked-in stellar matter fractions indicated that the vast majority of the baryons in the present-day Universe reside in the form of locked-in stellar matter in white dwarfs, neutron stars, and black holes.