Cosmic evolution of the Faraday rotation measure in the intracluster medium of galaxy clusters

¹ Institute of Physics, Laboratory of Astrophysics, École Polytechnique Fédérale de Lausanne (EPFL), 1290 Sauverny, Switzerland
² Argelander Institute für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
³ Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy
⁴ Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia
⁵ Australian Research Council Centre of Excellence in All Sky Astrophysics (ASTRO3D), Canberra, ACT 2611, Australia

^★ Corresponding author; yoan.rappaz@epfl.ch

Received: 14 June 2024
Accepted: 9 September 2024

Abstract

Context. Radio observations have revealed magnetic fields in the intracluster medium (ICM) of galaxy clusters, and their energy density is nearly in equipartition with the turbulent kinetic energy. This suggests magnetic field amplification by dynamo processes during cluster formation. However, observations are limited to redshifts ɀ ≲ 0.7, and the weakly collisional nature of the ICM complicates studying magnetic field evolution at higher redshifts through theoretical models and simulations.

Aims. Using a model of the weakly collisional dynamo, we modelled the evolution of the Faraday rotation measure (RM) in galaxy clusters of different masses, up to ɀ ≃ 1.5, and investigated its properties such as its radial distribution up to the virial radius r₂₀₀. We compared our results with radio observations of various galaxy clusters.

Methods. We used merger trees generated by the modified GALFORM algorithm to track the evolution of plasma quantities during galaxy cluster formation. Assuming the magnetic field remains in equipartition with the turbulent velocity field, we generated RM maps to study their properties.

Results. We find that both the standard deviation of RM, σ_RM, and the absolute average |µ_RM| increase with cluster mass. Due to redshift dilution, RM values for a fixed cluster mass remain nearly constant between ɀ = 0 and ɀ = 1.5. For r/r₂₀₀ ≳ 0.4, σ_RM does not vary significantly with ℒ/r₂₀₀, with ℒ being the size of the observed RM patch. Below this limit, σ_RM increases as ℒ decreases. We find that radial RM profiles have a consistent shape, proportional to 10^{−1.2(r/r₂₀₀)}, and are nearly independent of redshift. Our ɀ ≃ 0 profiles for M_clust = 10¹⁵ M_⊙ match RM observations in the Coma cluster but show discrepancies with Perseus, possibly due to high gas mixing. Models for clusters with M_clust = 10¹³ and 10¹⁵ M_⊙ at ɀ = 0 and ɀ = 0.174 align well with Fornax and A2345 data for r/r₂₀₀ ≲ 0.4. Our model can be useful for generating mock polarization observations for current and next-generation radio telescopes.