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Abell 1033 is a merging galaxy cluster of moderate mass($M_{500}=3.2\times10^{14} \mathrm{M}_\odot$). It hosts a broad variety ofdiffuse radio sources linked to different astrophysical phenomena. The mostpeculiar one is an elongated feature with an ultra-steep spectrum that is theprototype of the category of gently reenergized tails (GReET). Furthermore, thecluster hosts sources that were previously classified as a radio phoenix and aradio halo. We aim to improve the understanding of the cosmic-ray accelerationmechanisms in galaxy clusters in a frequency and mass range that has beenpoorly explored so far. To investigate the ultra-steep synchrotron emission inthe cluster, we performed a full calibration of a LOFAR observation centered at54 MHz. We analyzed this observation together with re-calibrated data of LoTSSat 144 MHz and an archival GMRT observation at 323 MHz. We performed a spectralstudy of the radio galaxy tail connected to the GReET to test if the currentinterpretation of the source is in agreement with observational evidence below100 MHz. Additionally, we studied the radio halo at different frequencies. Wereport an extreme spectral curvature for the GReET, the spectral index flattensfrom $\alpha_{144}^{323} = -4$ to $\alpha_{54}^{144} = -2$. This indicates thepresence of a cut-off in the electron energy spectrum. At the cluster center,we detect the radio halo at 54, 144 and at lower significance at 323 MHz. Wecategorize it as an ultra-steep spectrum radio halo with a spectral index$\alpha = -1.65 \pm 0.17$. Additionally, it is found to be significantly abovethe radio power-to-cluster mass correlations reported in the literature.Furthermore, the synchrotron spectrum of the halo is found to further steepenbetween 144 and 323 MHz, in agreement with the presence of a break in theelectron spectrum, which is a prediction of homogeneous re-acceleration models.

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