The baryon budget of galaxies across the first billion years

Theoretical predictions for gas phases, depletion times, stellar return fractions

¹ INAF-Italian National Institute of Astrophysics, Observatory of Trieste, Via G. Tiepolo 11, 34143 Trieste, Italy
² Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
³ European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching bei Muenchen, Germania
⁴ Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille, France

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 October 2025
Accepted: 15 February 2026

Abstract

Context. ALMA and JWST observations of galaxies in the first billion years of the Universe provide key constraints on the baryon cycle during the epoch of reionisation. A complete census of the baryonic phases in early galaxies is essential to understand the efficiency and timescales of star formation.

Aims. In this work, we study cosmic matter at redshift z > 5 to investigate the different phases in which early gas and stars reside, their corresponding mass budgets, the resulting depletion times, and the expected stellar return fraction as a function of stellar age.

Methods. We used the COLDSIM hydrodynamical time-dependent non-equilibrium chemistry simulations to perform a detailed analysis of the cold, warm, hot, and stellar phases for both bound structures (galaxies and their circumgalactic medium) and the diffuse intergalactic medium. We further investigated the cold HI and H₂ components, explicitly computed in our simulations, and examined their relations with the host mass, star formation, metallicity, and depletion timescales. We also provide observational insights and discuss the implications for stellar mass functions, Population III star formation, and changes in the initial mass function.

Results. Cosmic gas prior to reionisation is mostly cold, while at later epochs the warm phase becomes dominant as a consequence of enhanced star formation activity and increasing UV reionising radiation. Stellar return fractions at these times are ∼0.15–0.20, a factor of two lower than the values usually adopted. Mass functions and mass density parameters in bound objects increase with cosmic time, closely tracing the overall structure formation process. Cold, warm, and hot gas masses as well as HI and H₂ components show increasing trends with mass and star formation rate, while HI and H₂ depletion times decrease down to 0.01–0.1 Gyr with a weak dependence on metallicity. The resulting star formation efficiency remains at the level of a few percent independently of z and gas-to-star fractions decline with mass, influenced by local feedback and environment. Our findings are consistent with ALMA, VLA and IRAM surveys at later epochs, including ALFALFA, xCOLDGASS, GASS, xGASS, EDGE-CALIFA, PHIBBS, and ASPECS.

Conclusions. Gas phases are quantitatively related to the underlying stellar populations and can be used to infer unknown quantities. In the appendix, we provide fit functions describing the trends of the stellar return fraction, the main sequence, phase mass relations, gas-to-star fractions, and depletion timescales.