The Planck clusters in the LOFAR sky. IV. LoTSS-DR2: Statistics of radio haloes and re-acceleration models

Context. Diffuse cluster-scale synchrotron radio emission is discovered in an increasing number of galaxy clusters in the form of radio haloes, probing the presence of relativistic electrons and magnetic fields in the intra-cluster medium (ICM). The favoured scenario to explain their origin is that they trace turbulent regions that are generated during cluster-cluster mergers, where particles are re-accelerated. In this framework, radio haloes are expected to probe cluster dynamics and are predicted to be more frequent in massive systems, in which more energy becomes available for the re-acceleration of relativistic electrons. For these reasons, statistical studies of galaxy cluster samples have the power to derive fundamental information on the radio haloes populations and on their connection with cluster dynamics, and hence to constrain theoretical models. Furthermore, low-frequency cluster surveys have the potential to shed light on the existence of radio haloes with very steep radio spectra, which are a key prediction of turbulent models and are thought to be generated in less energetic merger events and thus be more common in the Universe.
Aims: The main question we address is whether we can explain the observed properties of the radio halo population within the framework of current models.
Methods: We study the occurrence and properties of radio haloes from clusters of the second catalogue of Planck Sunyaev Zel'dovich-detected sources that lie within the 5634 deg² that are covered by the second data release (DR2) of the LOFAR Two-meter Sky Survey. We derive their integral number, flux density, and redshift distributions. We compare these observations with expectations of theoretical models. We also study the connection between radio haloes and cluster mergers by using cluster morphological parameters derived through Chandra and/or XMM-Newton data.
Results: We find that the number of observed radio haloes, their radio flux density, and their redshift distributions agree with what is expected in the framework of the re-acceleration scenario. In line with model expectations, the fraction of clusters with radio haloes increases with the cluster mass, confirming the leading role of the gravitational process of cluster formation in the generation of radio haloes. These models predict a large fraction of radio haloes with very steep spectra in the DR2 Planck sample. This will be tested in future studies, but a comparison of the occurrence of haloes in GMRT and LOFAR samples indeed shows a more frequent occurrence of haloes at lower frequencies, suggesting the presence of a population of haloes with very steep spectra that is preferentially detected by LOFAR. Using morphological information, we confirm that radio haloes are preferentially located in merging systems, and that the fraction of newly LOFAR-discovered radio haloes is larger in less strongly disturbed systems.