Ultra-low-frequency LOFAR spectral indices of cluster radio halos

Context. A fraction of galaxy clusters harbor diffuse radio sources known as radio halos. The prevailing theory regarding their formation is based on second-order Fermi reacceleration of seed electrons caused by merger-driven turbulence in the intra-cluster medium. This mechanism is expected to be inefficient, which implies that a significant fraction of halos should have very steep energy spectra (alpha < -1.5). Aims. We start investigating the potential and current limitations of the combination of the two surveys conducted by LOFAR, LoTSS (144 MHz) and LoLSS (54 MHz), to probe the origin of radio halos. Methods. We followed up the 20 radio halos detected in Data Release 1 of LoTSS, which covers the HETDEX field, with the LoLSS survey, and we studied their spectral properties between 54 and 144 MHz. Results. After removing compact sources, nine halos were excluded due to unreliable halo flux density measurements at 54 MHz. Our main finding is that 7 out of 11 (similar to 64%) exhibit an ultra-steep spectrum (alpha < -1.5), which is a key prediction of turbulent reacceleration models. We also note a tentative trend for more massive systems to host flatter halos, although the currently poor statistics do not allow for a deeper analysis. Conclusions. Our sample suffers from low angular resolution at 54 MHz, which limits the accuracy of the compact-source subtraction. Nevertheless, this study is the first step toward providing compelling evidence for the existence of a large fraction of radio halos with a very steep spectrum, which is a fundamental prediction of turbulent reacceleration models. In this regard, the forthcoming second data release of LoLSS, along with the integration of LOFAR international stations and the instrumental upgrade to LOFAR2.0, will improve both the statistics and the low-frequency angular resolution, allowing us to determine the origin of radio halos in galaxy clusters conclusively.