The Three Hundred Project: Modeling baryon and hot-gas fraction evolution in simulated clusters

¹ INAF – Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131 Trieste, Italy
² IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
³ Department of Physics, University of Michigan, Ann Arbor, MI, 48109 USA
⁴ University of Ljubljana, Faculty of Mathematics and Physics, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia
⁵ Dipartimento di Fisica dell’Università di Trieste, Sez. di Astronomia, via Tiepolo 11, I-34131 Trieste, Italy
⁶ Center on High Performance Computing, Big Data and Quantum Computing, via Magnanelli 2, 40033 Casalecchio di Reno, Italy
⁷ INFN, Instituto Nazionale di Fisica Nucleare, Via Valerio 2, I-34127 Trieste, Italy
⁸ Departamento de Física Teórica, M-8, Universidad Autónoma de Madrid, Cantoblanco, E-28049 Madrid, Spain
⁹ Centro de Investigación Avanzada en Física Fundamental (CIAFF), Universidad Autńoma de Madrid, Cantoblanco, E-28049 Madrid, Spain
¹⁰ Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy
¹¹ Universitäts-Sternwarte, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstr.1, 81679 München, Germany
¹² Max-Plank-Institut für Astrophysik, Karl-Schwarzschild Strasse 1, D-85740 Garching, Germany
¹³ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, CH-1290 Versoix, Switzerland
¹⁴ INAF, Osservatorio di Astrofisica e Scienza dello Spazio, via Piero Gobetti 93/3, 40129 Bologna, Italy
¹⁵ INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy
¹⁶ Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy

^⋆ Corresponding author: elena.rasia@inaf.it

Received: 26 February 2025
Accepted: 9 July 2025

Abstract

Context. The baryon fraction of galaxy clusters, expressed as the ratio between the mass in baryons (including both stars and cold or hot gas) and the total mass, is a powerful tool to provide information on the cosmological parameters, while the hot-gas fraction provides indications on the physics of the intracluster plasma and its interplay with the processes that drive galaxy formation.

Aims. Using cosmological hydrodynamical simulations of about 300 simulated massive galaxy clusters with a median mass M₅₀₀ ≈ 7 × 10¹⁴ M_⊙ at z = 0, we model the relations between total mass and either baryon fraction or the hot gas fractions at overdensities Δ = 2500, 500, and 200 with respect to the cosmic critical density, and their evolution from z ∼ 0 to z ∼ 1.3.

Methods. We utilized the simulated galaxy clusters from the Three Hundred project, which include star formation and feedback from both supernovae and active galactic nuclei. We fit the simulation results for such scaling relations against three analytic forms (linear, quadratic, and logarithmic in a logarithmic plane) and three forms for the redshift dependence, and we considered as a variable both the inverse of the cosmic scale factor, (1 + z), and the Hubble expansion rate, E(z).

Results. We show that power-law dependencies on cluster mass poorly describe the investigated relations. A power law fails to simultaneously capture the flattening of the total baryon and gas fractions at high masses, their drop at low masses, and the transition between these two regimes. The other two functional forms provide a more accurate description of the curvature in mass scaling. The fractions measured within smaller radii exhibit a stronger evolution than those measured within larger radii.

Conclusions. From the analysis of these simulations, we evince that as long as we include systems in the mass range herein investigated, the baryon or gas fraction can be accurately related to the total mass through either a parabola or a logarithm in the logarithmic plane. The trends are common to all modern hydro simulations, although the amplitude of the drop at low masses might differ. Being able to observationally determine the gas fraction in groups will thus provide constraints on the baryonic physics.