Probing particle acceleration in Abell 2256: from 16 MHz to gamma rays

Merging galaxy clusters often host spectacular diffuse radio synchrotron sources. These sources can be explained by a non-thermal pool of relativistic electrons that are accelerated by shocks and turbulence in the intracluster medium. The origin of the pool and details of the cosmic ray transport and acceleration mechanisms in clusters are still open questions. Due to the often extremely steep spectral indices of diffuse radio emission, it is best studied at low frequencies. However, the lowest frequency window available to ground-based telescopes (10-30 MHz) has remained largely unexplored as radio frequency interference and calibration problems related to the ionosphere become severe. Here, we present LOFAR observations from 16 to 168 MHz targeting the famous cluster Abell 2256. In the deepest-ever images at decametre wavelengths, we detected and resolved the radio halo, radio shock, and various steep spectrum sources. We measured standard single power-law behaviour for the radio halo and radio shock spectra, with spectral indices of $ from 24 to 1500 MHz and $ from 24 to 3000 MHz, respectively. Additionally, we found significant spectral index and curvature fluctuations across the radio halo, indicating an inhomogeneous emitting volume. In contrast to the straight power-law spectra of the large-scale diffuse sources, the various AGN-related sources showed extreme steepening towards higher frequencies and flattening towards low frequencies. We also discovered a new fossil plasma source with a steep spectrum between 23 and 144 MHz, with $ 0.1$. Finally, by comparing radio and gamma-ray observations, we ruled out purely hadronic models for the radio halo origin in Abell 2256, unless the magnetic field strength in the cluster is exceptionally high, which is unsupportable by energetic arguments and inconsistent with the knowledge of other cluster magnetic fields.