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Radio observations represent a powerful probe of the physics occurring in theintracluster medium (ICM) because they trace the relativistic cosmic rays inthe cluster magnetic fields, or within galaxies themselves. By probing thelow-energy cosmic rays, low-frequency radio observations are especiallyinteresting because they unveil emission powered by low-efficiency particleacceleration processes, which are believed to play a crucial role in the originof diffuse radio emission. We investigate the origin of the radio mini-halo atthe center of the galaxy cluster 2A0335+096 and its connection to the centralgalaxy and the sloshing cool core. We also study the properties of thehead-tail galaxy GB6 B0335+096 hosted in the cluster to explore the lifecycleof the relativistic electrons in its radio tails. We use new LOw FrequencyARray (LOFAR) observations from the LOFAR Two-meter Sky Survey at 144 MHz tomap the low-frequency emission with a high level of detail. The new data werecombined with archival Giant Metrewave Radio Telescope and Chandra observationsto carry out a multi-wavelength study. We have made the first measurement ofthe spectral index of the mini-halo ($\alpha=-1.2\pm0.1$ between 144 MHz and1.4 GHz) and the lobes of the central source ($\alpha\simeq-1.5\pm0.1$ between144 and 610 MHz). Based on the low-frequency radio emission morphology withrespect to the thermal ICM, we propose that the origin of the diffuse radioemission is linked to the sloshing of the cool core. The new data revealed thepresence of a Mpc-long radio tail associated with GB6 B0335+096. The observedprojected length is a factor 3 longer than the expected cooling length, withevidence of flattening in the spectral index trend along the tail. Therefore,we suggest that the electrons toward the end of the tail are kept alive by theICM gentle re-acceleration.

A LOFAR view into the stormy environment of the galaxy cluster 2A0335+096