A 3.5 Mpc long radio relic in the galaxy cluster ClG 0217+70

Context. Megaparsec-scale radio sources in the form of halos and relics are often detected in dynamically disturbed galaxy clusters. Although they are associated with merger-induced turbulence and shocks, respectively, their formation is not fully understood. Aims. We aim to identify the mechanisms responsible for particle acceleration and magnetic field amplification in the halo and relics of the galaxy cluster ClG 0217+70. Methods. We observed ClG 0217+70 with LOFAR at 141 MHz and with VLA at 1.5 GHz, and we combined these observations with VLA 1.4 GHz archival data to study the morphological and spectral properties of the diffuse sources. We added Chandra archival data to examine the thermal and non-thermal properties of the halo. Results. Our LOFAR and VLA data confirm the presence of a giant radio halo in the cluster centre and multiple relics in the outskirts. The radio and X-ray emission from the halo are correlated, implying a tight relation between the thermal and non-thermal components. The diffuse radio structure in the south-east, with a projected size of 3.5 Mpc, is the most extended radio relic detected to date. The spectral index across the relic width steepens towards the cluster centre, suggesting electron ageing in the post-shock regions. The shock Mach numbers for the relics derived from the spectral index map range between 2.0 and 3.2. However, the integrated spectral indices lead to increasingly high Mach numbers for the relics farther from the cluster centre. This discrepancy could be because the relation between injection and integrated spectra does not hold for distant shocks, suggesting that the cooling time for the radio-emitting electrons is longer than the crossing time of the shocks. The variations in the surface brightness of the relics and the low Mach numbers imply that the radio-emitting electrons are re-accelerated from fossil plasma that could originate in active galactic nuclei.