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Context: A number of merging galaxy clusters show the presence of large-scale radio emission associated with the intra-cluster medium (ICM). These synchrotron sources are generally classified as radio haloes and radio relics. Aims. Whilst it is commonly accepted that mergers play a crucial role in the formation of radio haloes and relics, not all the merging clusters show the presence of giant diffuse radio sources and this provides important information concerning current models. The Abell 781 complex is a spectacular system composed of an apparent chain of clusters on the sky. Its main component is undergoing a merger and hosts peripheral emission that is classified as a candidate radio relic and a disputed radio halo. Methods. We used new LOw Frequency ARay (LOFAR) observations at 143 MHz and archival Giant Metrewave Radio Telescope (GMRT) observations at 325 and 610 MHz to study radio emission from non-thermal components in the ICM of Abell 781. Complementary information came from XMM-Newton data, which allowed us to investigate the connection with the thermal emission and its complex morphology. Results. The origin of the peripheral emission is still uncertain. We speculate that it is related to the interaction between a head tail radio galaxy and shock. However, the current data allow us only to set an upper limit of M < 1.4 on the Mach number of this putative shock. Instead, we successfully characterise the surface brightness and temperature jumps of a shock and two cold fronts in the main cluster component of Abell 781. Their positions suggest that the merger is involving three substructures. We do not find any evidence for a radio halo either at the centre of this system or in the other clusters of the chain. We place an upper limit to the diffuse radio emission in the main cluster of Abell 781 that is a factor of 2 below the current radio power-mass relation for giant radio haloes.

Centrally located diffuse radio emission has been observed in both merging and non-merging galaxy clusters. Depending on their morphology and size, we distinguish between giant radio haloes, which occur predominantly in merging clusters, and mini haloes, which are found in non-merging, cool-core clusters. In recent years, cluster-scale radio emission has also been observed in clusters with no sign of major mergers, showing that our knowledge of the mechanisms that lead to particle acceleration in the intra-cluster medium (ICM) is still incomplete. Low-frequency sensitive observations are required to assess whether the emission discovered in these few cases is common in galaxy clusters or not. With this aim, we carried out a campaign of observations with the LOw Frequency ARay (LOFAR) in the frequency range 120-168 MHz of nine massive clusters selected from the Planck SZ catalogue, which had no sign of major mergers. In this paper, we discuss the results of the observations that have led to the largest cluster sample studied within the LOFAR Two-metre Sky Survey, and we present Chandra X-ray data used to investigate the dynamical state of the clusters, verifying that the clusters are currently not undergoing major mergers, and to search for traces of minor or off-axis mergers. We discover large-scale steep-spectrum emission around mini haloes in the cool-core clusters PSZ1G139.61+24 and RXJ1720.1+2638, which is not observed around the mini halo in the non-cool-core cluster A1413. We also discover a new 570 kpc-halo in the non-cool-core cluster RXCJ0142.0+2131. We derived new upper limits to the radio power for clusters in which no diffuse radio emission was found, and we discuss the implication of our results to constrain the cosmic-ray energy budget in the ICM. We conclude that radio emission in non-merging massive clusters is not common at the sensitivity level reached by our observations and that no clear connection with the cluster dynamical state is observed. Ou

Massive, merging galaxy clusters often host giant, diffuse radio sources that arise from shocks and turbulence; hence, radio observations can be useful for determining the merger state of a cluster. In preparation for a larger study, we selected three clusters - Abell 1319, Abell 1314, and RXC J1501.3+4220 (Z7215) - making use of the new LOFAR Two-Metre Sky Survey (LoTSS) at 120-168 MHz, and together with archival data, show that these clusters appear to be in pre-merging, merging, and post-merging states, respectively. We argue that Abell 1319 is likely in its pre-merging phase, where three separate cluster components are about to merge. There are no radio haloes nor radio relics detected in this system. Abell 1314 is a highly disturbed, low-mass cluster that is likely in the process of merging. This low-mass system does not show a radio halo, however, we argue that the merger activates mechanisms that cause electron re-acceleration in the large 800 kpc radio tail associated with IC 711. In the cluster Z7215 we discover diffuse radio emission at the cluster centre, and we classify this emission as a radio halo, although it is dimmer and smaller than expected by the radio halo power versus cluster mass correlation. We suggest that the disturbed cluster Z7215 is in its post-merging phase. Systematic studies of this kind over a larger sample of clusters observed with LoTSS will help to constrain the timescales involved in turbulent re-acceleration and the subsequent energy losses of the underlying electrons.