LOFAR observations of galaxy clusters in HETDEX: Extraction and self-calibration of individual LOFAR targets

Diffuse cluster radio sources, in the form of radio halos and relics, reveal the presence of cosmic rays and magnetic fields in the intracluster medium (ICM). These cosmic rays are thought to be (re-)accelerated through ICM turbulence and shock waves generated by cluster merger events. Here we characterize the presence of diffuse radio emission in known galaxy clusters in the HETDEX Spring Field, covering 424 deg$^2$. For this, we developed a method to extract individual targets from LOFAR observations processed with the LoTSS DDF-pipeline. This procedure enables improved calibration and joint imaging and deconvolution of multiple pointings of selected targets. The calibration strategy can also be used for LOFAR Low-Band Antenna (LBA) and international-baseline observations. The fraction of Planck PSZ2 clusters with any diffuse radio emission apparently associated with the ICM is $73\pm17\%$. We detect a total of 10 radio halos and 12 candidate halos in the HETDEX Spring Field. Five clusters host radio relics. The fraction of radio halos in Planck PSZ2 clusters is $31\pm11\%$, and $62\pm15\%$ when including the candidate radio halos. Based on these numbers, we expect that there will be at least $183 \pm 65$ radio halos found in the LoTSS survey in PSZ2 clusters, in agreement with predictions. The integrated flux densities for the radio halos were computed by fitting exponential models to the radio images. From these flux densities, we determine the cluster mass (M$_{500}$) and Compton Y parameter (Y$_{500}$) 150 MHz radio power (P$_{\rm{150 MHz}}$) scaling relations for Planck PSZ2-detected radio halos. We find that the slopes of these relations are steeper than those determined from the 1.4 GHz radio powers. However, considering the uncertainties this is not a statistically significant result.