| Abstract
| - Context. Radio halos and relics are Mpc-scale diffuse radio sources in galaxy clusters, which have a steep spectral index α > 1 (defined as S ∝ ν− α). It has been proposed that halos and relics arise from particle acceleration induced by turbulence and weak shocks that are injected into the intracluster medium (ICM) during mergers. Aims. MACS J1149.5+2223 is a high-redshift ( z = 0.544) galaxy cluster possibly hosting a radio halo and a relic. We analysed LOw Frequency Array (LOFAR), Giant Metrewave Radio Telescope, and Karl G. Jansky Very Large Array (JVLA) radio data at 144, 323, and 1500 MHz, respectively. In addition, we analysed archival Chandra X-ray data to characterise the thermal and non-thermal properties of the cluster. Methods. We obtained radio images at different frequencies to investigate the spectral properties of the radio halo. We used Chandra X-ray images to constrain the thermal properties of the cluster and to search for discontinuities (due to cold fronts or shock fronts) in the surface brightness of the ICM. By combining radio and X-ray images, we carried out a point-to-point analysis to study the connection between the thermal and non-thermal emission. Results. We measured a steep spectrum of the halo, which can be described by a power-law with α = 1.49 ± 0.12 between 144 and 1500 MHz. The radio surface brightness distribution across the halo is found to correlate with the X-ray brightness of the ICM. The derived correlation shows a sub-linear slope in the range 0.4-0.6. We also report two possible cold fronts in north-east and north-west, but deeper X-ray observations are required to firmly constrain the properties of the upstream emission. Conclusions. We show that the combination of high-redshift, steep radio spectrum, and sub-linear radio-X scaling of the halo rules out hadronic models. An old (∼1 Gyr ago) major merger likely induced the formation of the halo through stochastic re-acceleration of relativistic electrons. We suggest that the two possible X-ray discontinuities may be part of the same cold front. In this case, the coolest gas pushed towards the north-west might be associated with the cool core of a sub-cluster involved in the major merger. The peculiar orientation of the south-east relic might indicate a different nature of this source and requires further investigation.
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