Comparative analysis of the diffuse radio emission in the galaxy clusters A1835, A2029, and Ophiuchus

Aims. We recently performed a study of a sample of relaxed, cooling core galaxy clusters with deep Very Large Array observations at 1.4 GHz. We find that in the central regions of A1835, A2029, and Ophiuchus the dominant radio galaxy is surrounded by a diffuse low-brightness radio emission that takes the form of a mini-halo. Here we present the results of the analysis of the extended diffuse radio emission in these mini-halos. Methods. In order to investigate the morphological properties of the diffuse radio emission in clusters of galaxies we propose to fit their azimuthally averaged brightness profile with an exponential, obtaining the central brightness and the e-folding radius from which the radio emissivity can be calculated. We investigate the radio properties of the mini-halos in A1835, A2029, and Ophiuchus in comparison with the radio properties of a representative sample of mini-halos and halos already known in the literature. Results. We find that radio halos can have quite different length-scales but their emissivity is remarkably similar from one halo to the other. In contrast, mini-halos span a wide range of radio emissivity. Some of them, like the Perseus mini-halos, are characterized by a radio emissivity which is more than 100 times greater than that of radio halos. On the other hand, the new mini-halos in cooling core clusters analyzed in this work, namely A2029, Ophiuchus, and A1835, have a radio emissivity which is much more typical of halos in merging clusters rather than similar to that of the other mini-halos previously known.