Non-thermal emission in galaxy groups at extremely low frequency: The case of A1213

Galaxy clusters and groups are the last link in the chain of hierarchical structure formation. Their environments can be significantly affected by outbursts from active galactic nuclei (AGN), especially in groups where the medium density is lower and the gravitational potential is shallower. Thus, interaction between AGN and group weather can greatly affect their evolution. We investigate the non-thermal radio emission in Abell 1213, a galaxy group that is part of a larger sample of sim 50 systems (X-GAP) recently explored in XMM-Newton observations. We exploited proprietary LOFAR 54 MHz and uGMRT 380 MHz observations, complementing them with 144 MHz LOFAR survey and XMM-Newton archival data. A1213 hosts a bright AGN associated with one of the central members, 4C\,29.41, which was previously optically identified as a dumb-bell galaxy. Observations at 144 MHz at a resolution of 0.3$''$ have allowed us to resolve the central radio galaxy. From this source, a $ 500$ kpc-long tail extends in the north-east direction. Our analysis suggests that the tail likely originated from a past outburst of 4C\,29.41 and its current state might be the result of the interaction with the surrounding environment. The plateau of the spectral index distribution in the easternmost part of the tail suggests mild particle re-acceleration, which could have re-energised seed electrons from the past activity of the AGN. While we do observe a spatial and physical correlation of the extended, central emission with the thermal plasma (which might hint at a mini-halo), the current evidence cannot prove this conclusively. A1213 is only the first group among the X-GAP sample that we have been able to investigate via low-frequency radio observations. Its complex environment once again demonstrates the significant impact that the interplay between thermal and non-thermal processes can exert on galaxy groups.