Probing cluster magnetism with embedded and background radio sources in Planck clusters

¹ Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada
² Leiden Observatory, Leiden University, PO Box 9513 NL-2300 RA Leiden, The Netherlands
³ Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St SE, Minneapolis, MN 55455, USA
⁴ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
⁵ Department of Liberal Arts and Sciences, Berklee College of Music, 7 Haviland Street, Boston, MA 02215, USA
⁶ Clay Center Observatory, Dexter Southfield, 20 Newton Street, Brookline, MA 02445, USA
⁷ DIFA – Università di Bologna, Via Gobetti 93/2, I-40129 Bologna, Italy
⁸ INAF – IRA, Via Gobetti 101, I-40129 Bologna, Italy
⁹ IRA – INAF, Via P. Gobetti 101, I-40129 Bologna, Italy
¹⁰ Naval Research Laboratory, 4555 Overlook Avenue SW, Code 7213, Washington, DC 20375, USA
¹¹ Institute for Astronomy, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

^⋆ Corresponding author; erik.osinga@utoronto.ca

Received: 13 August 2024
Accepted: 10 December 2024

Abstract

Magnetic fields remain an elusive part of the content of galaxy clusters. Faraday rotation and depolarisation of extragalactic radio sources are useful probes, but the limited availability of polarised radio sources necessitates the stacking of clusters to study average magnetic field properties. We recently presented a Karl G. Jansky Very Large Array survey of the 124 most massive Planck clusters at low redshift (z < 0.35), finding a clear depolarisation trend with the cluster impact parameter, with sources at smaller projected distances to the cluster centre showing more depolarisation. In this study, we combine the depolarisation information with the observed rotation measure (RM) and present an investigation of the average magnetic field properties of the sample, using both background sources and sources embedded in clusters. We observe a significant increase in the RM scatter, σ_RRM, closer to the cluster centres. Averaging all 124 clusters, we find a scatter within R₅₀₀ of σ_RRM = 209 ± 37 rad m⁻², with background sources and cluster members showing similar values (200 ± 33 and 219 ± 66 rad m⁻², respectively). In the simple assumption of a uniform amplitude magnetic field with a single fluctuation scale Λ_c, this translates to an average magnetic field strength of 2 (Λ_c/10 kpc)^−0.5 μG. The profile of σ_RRM as a function of the projected radius is inconsistent with a model that has a simple scaling B ∝ n_e^η, with an observed deficit near the centre of clusters possibly caused by the fact that the highest RM sources near the centre of clusters are depolarised. Combining depolarisation and RM in a full forward model, we find that the magnetic field power spectrum roughly agrees with the Kolmogorov value, but that none of the Gaussian random field models can fully explain the observed relatively flat profiles. This implies that more sophisticated models of cluster magnetic fields in a cosmological context are needed.