CHEX-MATE: Scaling relations of radio halo profiles for clusters in the LoTSS DR2 area

¹ INAF – IASF Milano, Via A. Corti 12, 20133 Milano, Italy
² DiSAT, Università degli Studi dell’Insubria, Via Valleggio 11, I-22100 Como, Italy
³ DIFA – Università di Bologna, Via Gobetti 93/2, I-40129 Bologna, Italy
⁴ INAF, Osservatorio di Astrofisica e Scienza dello Spazio, Via Piero Gobetti 93/3, 40129 Bologna, Italy
⁵ INFN, Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁶ INAF – IRA, Via Gobetti 101, I-40129 Bologna, Italy
⁷ Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy
⁸ Laboratoire d’Astrophysique de Marseille, CNRS, Aix-Marseille Université, CNES, Marseille, France
⁹ Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98bis boulevard Arago, 75014 Paris, France
¹⁰ HH Wills Physics Laboratory, University of Bristol, Tyndall, Bristol BS8 1TL, UK
¹¹ IRAP, Université de Toulouse, CNRS, CNES, UT3-UPS, Toulouse, France
¹² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
¹³ INAF – Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34143 Trieste, Italy
¹⁴ Department of Physics, University of Michigan, 450 Church St, Ann Arbor, MI 48109, USA
¹⁵ Dipartimento di Fisica, Universitá degli Studi di Milano, Via G. Celoria 16, 20133 Milano, Italy
¹⁶ Leiden Observatory, Leiden University, PO Box 9513 2300 RA Leiden, The Netherlands
¹⁷ California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA

^⋆ Corresponding author; marco.balboni@inaf.it

Received: 26 November 2024
Accepted: 14 February 2025

Abstract

The thermal and non-thermal components in galaxy clusters have properties that, although shaped from different physical phenomena, can share some similarities, mainly driven by their halo mass and the accretion processes. Scaling relations have been proven to exist for both components and studied in X-ray (thermal) and radio (non-thermal) bands. On the X-ray side, both integrated and spatially resolved profiles have shown a predictable and correlated behaviour. At the radio wavelength, such investigations are so far limited to the integrated quantities (e.g. total power and mass). We aimed to investigate the scaling relations between the mass of a galaxy cluster and its radio emission at low frequencies, treating both the integrated and the spatially resolved quantities for a sample of well-selected objects in a self-consistent analysis. We crossmatched LoTSS DR2 and CHEX-MATE datasets in order to get the deepest and most homogeneous radio data of a representative sample of objects. Among the 40 CHEX-MATE objects in the LOFAR DR2 area, we investigated the 18 objects showing radio halo emission, which span a broad mass range, by extracting and analysing their radio emission profiles. We analytically derived the expected relation between the radio power (P_ν) and radio surface brightness profile (I_R(r)), and performed a comparison with observational results. We obtained that properly accounting for the mass and redshift dependence in the radio profile can reduce the overall scatter by a factor of ∼4, with an evident residual dependence on the cluster dynamical status. We show that assuming the halo size R_H ∼ R₅₀₀ did not allow us to reconcile the expected (from our analytical derivations) and observed mass profile scaling. Instead, accounting for no R_H − M relation, allowed us to reconcile the observed radio profile mass scaling and the one predicted starting from the P_ν − M relation. We discuss the implications of a lack of R_H − M relation, assessing possible systematics and biases in the analyses, and interpreting it as a natural consequence of the structure formation process, where the halo size depends on both the cluster dynamical status, related to the strength of the merger, and mass. Finally, we also considered the role of the magnetic field in the P_ν − M relation, putting constraints on its dependence upon the cluster mass and finding consistent results with expectations from our radio power mass scaling.