LOFAR detection of extended emission around a mini-halo in the galaxy cluster Abell 1413

The relation between giant radio halos and mini-halos in galaxy clusters is not understood. The former are usually associated with merging clusters, the latter are found in relaxed systems. In the last years, the advent of low-frequency radio observations has challenged this dichotomy, finding intermediate objects with a hybrid radio morphology. We aim to investigate the presence of diffuse radio emission in the cluster Abell 1413 and determine its dynamical status. We used LOFAR HBA observations centred at 144 MHz to study the diffuse emission hosted by this cluster.To investigate the dynamical state of the system, we complete our study with newly analysed XMM-Newton archival data. A1413 shows features that are typically present in both relaxed (e.g., peaked x-ray surface brightness distribution and little large-scale inhomogeneities) and disturbed (e.g., flatter temperature and metallicity profiles) clusters.This evidence supports the scenario that A1413 is neither a disturbed nor fully relaxed object. We argue that it is an intermediate-phase cluster.Using radio observations at 144 MHz, we discover the presence of a wider diffuse component surrounding the previously reported mini-halo at the cluster centre. By fitting the radio surface brightness profile with a double-exponential model, we can disentangle the two components. We find an inner mini-halo with an e-folding radius r_e1=28 kpc and the extended component with r_e2 = 290 kpc. We also performed point-to-point correlations between radio and X-ray surface brightness, finding a sub-linear relation for the outer emission and a super-linear relation for the mini-halo.The mini-halo and the diffuse emission extend over different scales and show different features, confirming the double nature of the radio emission and suggesting that the mechanisms responsible for the re-acceleration of the radio-emitting particle might be different.
Comment: 14 pages, 8 figures, accepted A&A