The Planck clusters in the LOFAR sky III. LoTSS-DR2: Dynamic states and density fluctuations of the intracluster medium?

Context. The footprint of the recent second data release of the LOFAR Two-metre Sky Survey (LoTSS-DR2) covers 309 Planck Sunyaev-Zeldovich (SZ) selected galaxy clusters, 83 of which host a radio halo and 26 host a radio relic(s). It provides an excellent opportunity to statistically study the properties of extended cluster radio sources, especially their connection with merging activities. Aims. We quantify cluster dynamic states to investigate their relation with the occurrence of extended radio sources. We also search for connections between intracluster medium (ICM) turbulence and nonthermal characteristics of radio halos in the LoTSS-DR2. Methods. We analyzed XMM-Newton and Chandra archival X-ray data of all Planck SZ clusters in the footprint of LoTSS-DR2. We computed concentration parameters and centroid shifts that indicate the dynamic states of the clusters. We also performed a power spectral analysis of the X-ray surface brightness fluctuations to investigate large-scale density perturbations and estimate the turbulent velocity dispersion. Furthermore, we searched for the relation between radio halo power and the turbulent dissipation flux channeled to particle acceleration. Results. The concentration parameters measured by the two telescopes agree well, but the centroid shift has a larger scatter. The surface brightness power spectral analysis results in a large scatter of the surface brightness and density fluctuation amplitudes. We therefore only found a marginal anticorrelation between density fluctuations and cluster relaxation state, and we did not find a correlation between density fluctuations and radio halo power. Nevertheless, the injected power for particle acceleration calculated from turbulent dissipation is correlated with the radio halo power, where the best-fit unity slope supports the turbulent (re)acceleration scenario. Two different acceleration models, transit-time damping and adiabatic stochastic acceleration, cannot be distinguished due to the large scatter of the estimated turbulent Mach number. We introduced a new quantity [k(B)T center dot Y-X](rRH), which is proportional to the turbulent acceleration power assuming a constant Mach number. This quantity is strongly correlated with radio halo power, where the slope is also unity.