Abell 1033: Radio halo and gently reenergized tail at 54 MHz

Context. Abell 1033 is a merging galaxy cluster of moderate mass (M500 = 3.24 × 1014 M⊙). It hosts a broad variety of diffuse radio sources that are linked to different astrophysical phenomena. The most peculiar phenomenon is an elongated feature with an ultra-steep spectrum that is the prototype of the category of gently reenergized tails (GReET). Furthermore, the cluster hosts sources that were previously classified as a radio phoenix and a radio halo. Aims: We aim to improve the understanding of the cosmic-ray acceleration mechanisms in galaxy clusters in a frequency and mass range that has been poorly explored so far. Methods: To investigate the ultra-steep synchrotron emission in the cluster, we performed a full direction-dependent calibration of a LOFAR observation centered at 54 MHz. We analyzed this observation together with recalibrated data of the LOFAR Two-meter Sky Survey at 144 MHz and an archival GMRT observation at 323 MHz. We performed a spectral study of the radio galaxy tail that is connected to the GReET to test whether the current interpretation of the source agrees with observational evidence below 100 MHz. Additionally, we employed a Markov chain Monte Carlo code to fit the halo surface brightness profile at different frequencies. Results: We report an extreme spectral curvature for the GReET. The spectral index flattens from α144 MHz323 MHz ≈ -4 to α144 MHz54 MHz ≈ -2