LOFAR discovery of an ultra-steep radio halo and giant head-tail radio galaxy in Abell 1132

LOFAR observations at 144 MHz have revealed large-scale radio sources in the unrelaxed galaxy cluster Abell 1132. The cluster hosts diffuse radio emission on scales of $\sim$650 kpc near the cluster center and a head-tail (HT) radio galaxy, extending up to 1 Mpc, South of the cluster center. The central diffuse radio emission is not seen in NVSS, FIRST, WENSS, nor in C & D array VLA observations at 1.4 GHz, but is detected in our follow-up GMRT observations at 325 MHz. Using LOFAR and GMRT data, we determine the spectral index of the central diffuse emission to be $\alpha=-1.75\pm0.19$ ($S\propto\nu^{\alpha}$). We classify this emission as an ultra-steep spectrum radio halo and discuss the possible implications for the physical origin of radio halos. The HT radio galaxy shows narrow, collimated emission extending up to 1 Mpc and another 300 kpc of more diffuse, disturbed emission, giving a full projected linear size of 1.3 Mpc - classifying it as a giant radio galaxy (GRG) and making it the longest HT found to date. The head of the GRG coincides with an elliptical galaxy (SDSS J105851.01$+$564308.5) belonging to Abell 1132. In our LOFAR image, there appears to be a connection between the radio halo and the GRG. The turbulence that may have produced the halo may have also affected the tail of the GRG. In turn, the GRG may have provided seed electrons for the radio halo.