Deep low-frequency radio observations of Abell 2256 II: The ultra-steep spectrum radio halo

We present the first detailed analysis of the radio halo in the merging galaxy cluster Abell 2256 using the LOFAR, uGMRT, and VLA. These observations combined with archival X-ray data allowed us to study the halo emission with unprecedented detail. The integrated radio emission from the entire halo is characterized by an ultra-steep spectrum, which can be described by a power law with $\alpha_{144 \rm MHz}^{1.5 \rm GHz}=-1.63\pm0.03$, and a radial steepening in the outer regions. The halo is significantly underluminous according to the scaling relations between radio power and mass at 1.4 GHz but not at 150 MHz; ultra-steep spectrum halos are predicted to be statistically underluminous. Despite the complex structure of this system, the radio halo morphology is remarkably similar to that of the X-ray emission. The radio surface brightness distribution across the halo is strongly correlated with the X-ray brightness of the intracluster medium. The derived correlations show sublinear slopes and there are distinct structures: the core is $\rm I_{R}\propto I_{X}^{1.51}$, the outermost region $\rm I_{R}\propto I_{X}^{0.41}$, and we find radio morphological connections with X-ray discontinuities. We also find a strong anti-correlation between the radio spectral index and the X-ray surface brightness, implying radial steepening. We suggests that the halo core is either related to old plasma from previous AGN activity, being advected, compressed and re-accelerated by mechanisms activated by the cold front or less turbulent with strong magnetic field in the core. The change in the radio vs X-ray correlation slopes in the outer regions of the halo could be due to a radial decline of magnetic field, increase in the number density of seed particles or increasing turbulence. Our findings suggest that that the emitting volume is not homogenous according to turbulence re-acceleration models.