2022A&A...659A..20I

Context. Radio observations represent a powerful probe of the physics occurring in the intracluster medium (ICM) because they trace the relativistic cosmic rays in the cluster magnetic fields, or within galaxies themselves. By probing the low-energy cosmic rays, low-frequency radio observations are especially interesting because they unveil emission powered by low-efficiency particle acceleration processes, which are believed to play a crucial role in the origin of diffuse radio emission. Aims. We investigate the origin of the radio mini-halo at the centre of the galaxy cluster 2A0335+096 and its connection to the central galaxy and the sloshing cool core. We also study the properties of the head-tail galaxy GB6 B0335+096 hosted in the cluster to explore the life cycle of the relativistic electrons in its radio tails. Methods. We used new LOw Frequency ARray (LOFAR) observations from the LOFAR Two-meter Sky Survey at 144 MHz to map the low-frequency emission with a high level of detail. The new data were combined with archival Giant Metrewave Radio Telescope and Chandra observations to carry out a multi-wavelength study. Results. We have made the first measurement of the spectral index of the mini-halo (α = -1.2 ± 0.1 between 144 MHz and 1.4 GHz) and the lobes of the central source (α ≃ -1.5 ± 0.1 between 144 and 610 MHz). Based on the low-frequency radio emission morphology with respect to the thermal ICM, we propose that the origin of the diffuse radio emission is linked to the sloshing of the cool core. The new data reveal the presence of a megaparsec-long radio tail associated with GB6 B0335+096. The observed projected length is a factor 3 longer than the expected cooling length, with evidence of flattening in the spectral index trend along the tail. Therefore, we suggest that the electrons towards the end of the tail are kept alive by the ICM gentle re-acceleration.