Radio halos are diffuse synchrotron sources on scales of ~1 Mpc that are found in merging clusters of galaxies, and are believed to be powered by electrons re-accelerated by the merger-driven turbulence. We present measurements of extended radio emission on similarly large scales in two clusters of galaxies hosting cool cores: Abell 2390 and Abell 2261. The analysis is based on interferometric imaging with the JVLA, VLA and GMRT. We present detailed radio images of the targets, subtract the compact emission components, and measure the spectral indices for the diffuse components. The radio emission in A2390 extends beyond a known sloshing-like brightness discontinuity, and has a very steep in-band spectral slope at 1.5 GHz that is similar to some known ultra-steep spectrum radio halos. The diffuse signal in A2261 is more extended than in A2390 but has lower luminosity. X-ray morphological indicators, derived from XMM-Newton X-ray data, place these clusters in the category of relaxed or regular systems, although some asymmetric features that can indicate past minor mergers are seen in the X-ray brightness images. If these two Mpc-scale radio sources are categorized as giant radio halos, they question the common assumption of radio halos occurring exclusively in clusters undergoing violent merging activity, in addition to commonly used criteria in distinguishing between radio halos and mini-halos.
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