In this data release from the ongoing LOw-Frequency ARray (LOFAR) Two-metre Sky Survey we present 120–168 MHz images covering 27% of the northern sky. Our coverage is split into two regions centred at approximately 12h45m +44°30′ and 1h00m +28°00′ and spanning 4178 and 1457 square degrees respectively. The images were derived from 3451 h (7.6 PB) of LOFAR High Band Antenna data which were corrected for the direction-independent instrumental properties as well as direction-dependent ionospheric distortions during extensive, but fully automated, data processing. A catalogue of 4 396 228 radio sources is derived from our total intensity (Stokes I) maps, where the majority of these have never been detected at radio wavelengths before. At 6″ resolution, our full bandwidth Stokes I continuum maps with a central frequency of 144 MHz have: a median rms sensitivity of 83 μJy beam⁻¹; a flux density scale accuracy of approximately 10%; an astrometric accuracy of 0.2″; and we estimate the point-source completeness to be 90% at a peak brightness of 0.8 mJy beam⁻¹. By creating three 16 MHz bandwidth images across the band we are able to measure the in-band spectral index of many sources, albeit with an error on the derived spectral index of > ± 0.2 which is a consequence of our flux-density scale accuracy and small fractional bandwidth. Our circular polarisation (Stokes V) 20″ resolution 120–168 MHz continuum images have a median rms sensitivity of 95 μJy beam⁻¹, and we estimate a Stokes I to Stokes V leakage of 0.056%. Our linear polarisation (Stokes Q and Stokes U) image cubes consist of 480 × 97.6 kHz wide planes and have a median rms sensitivity per plane of 10.8 mJy beam⁻¹ at 4′ and 2.2 mJy beam⁻¹ at 20″; we estimate the Stokes I to Stokes Q/U leakage to be approximately 0.2%. Here we characterise and publicly release our Stokes I, Q, U and V images in addition to the calibrated uv-data to facilitate the thorough scientific exploitation of this unique dataset.

The Low Frequency Array (LOFAR) is an ideal instrument to conduct deep extragalactic surveys. It has a large field of view and is sensitive to large-scale and compact emission. It is, however, very challenging to synthesize thermal noise limited maps at full resolution, mainly because of the complexity of the low-frequency sky and the direction dependent effects (phased array beams and ionosphere). In this first paper of a series, we present a new calibration and imaging pipeline that aims at producing high fidelity, high dynamic range images with LOFAR High Band Antenna data, while being computationally efficient and robust against the absorption of unmodeled radio emission. We apply this calibration and imaging strategy to synthesize deep images of the Boötes and Lockman Hole fields at ~150 MHz, totaling ~80 and ~100 h of integration, respectively, and reaching unprecedented noise levels at these low frequencies of ≲30 and ≲23μJy beam⁻¹in the inner ~3 deg². This approach is also being used to reduce the LOTSS-wide data for the second data release.

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 the 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 deg². For this, we developed a method to extract individual targets from LOFAR observations processed with the LoTSS DDF-pipeline software. This procedure enables improved calibration as well as the joint imaging and deconvolution of multiple pointings of selected targets. The calibration strategy can also be used for LOFAR low-band antenna and international-baseline observations. The fraction of Planck PSZ2 catalog clusters with any diffuse radio emission apparently associated with the ICM is 73 ± 17%. We detect a total of ten radio halos and twelve candidate halos in the HETDEX Spring Field. Of these ten radio halos, four are new discoveries, two of which are located in PSZ2 clusters. Five clusters host radio relics, two of which are new discoveries. The fraction of radio halos in Planck PSZ2 clusters is 31 ± 11%, or 62 ± 15% when including the candidate radio halos. Based on these numbers, we expect that there will be at least 183 ± 65 radio halos found in the LoTSS survey in PSZ2 clusters, in agreement with past 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 (M₅₀₀) and Compton Y parameter (Y₅₀₀) 150 MHz radio power (P_150 MHz) scaling relations for Planck PSZ2-detected radio halos. Using bivariate correlated errors and intrinsic scatter orthogonal regression, we find slopes of 6.13 ± 1.11 and 3.32 ± 0.65 for the M₅₀₀–P_150 MHz and M₅₀₀–P_150 MHz relations, respectively. These values are consistent with the results of previous works.

Context. Radio relics in galaxy clusters are giant diffuse synchrotron sources powered in cluster outskirts by merger shocks. Although the relic–shock connection has been consolidated in recent years by a number of observations, the details of the mechanisms leading to the formation of relativistic particles in this environment are still not well understood. Aims. The diffusive shock acceleration (DSA) theory is a commonly adopted scenario to explain the origin of cosmic rays at astrophysical shocks, including those in radio relics in galaxy clusters. However, in a few specific cases it has been shown that the energy dissipated by cluster shocks is not enough to reproduce the luminosity of the relics via DSA of thermal particles. Studies based on samples of radio relics are required to further address this limitation of the mechanism. Methods. In this paper, we focus on ten well-studied radio relics with underlying shocks observed in the X-rays and calculate the electron acceleration efficiency of these shocks that is necessary to reproduce the observed radio luminosity of the relics. Results. We find that in general the standard DSA cannot explain the origin of the relics if electrons are accelerated from the thermal pool with an efficiency significantly smaller than 10%. Our results show that other mechanisms, such as shock re-acceleration of supra-thermal seed electrons or a modification of standard DSA, are required to explain the formation of radio relics.

Source classifications, stellar masses and star formation rates are presented for ≈80,000 radio sources from the first data release of the Low Frequency Array Two-metre Sky Survey (LoTSS) Deep Fields, which represents the widest deep radio survey ever undertaken. Using deep multi-wavelength data spanning from the ultraviolet to the far-infrared, spectral energy distribution (SED) fitting is carried out for all of the LoTSS-Deep host galaxies using four different SED codes, two of which include modelling of the contributions from an active galactic nucleus (AGN). Comparing the results of the four codes, galaxies that host a radiative AGN are identified, and an optimised consensus estimate of the stellar mass and star-formation rate for each galaxy is derived. Those galaxies with an excess of radio emission over that expected from star formation are then identified, and the LoTSS-Deep sources are divided into four classes: star-forming galaxies, radio-quiet AGN, and radio-loud high-excitation and low-excitation AGN. Ninety-five per cent of the sources can be reliably classified, more than two-thirds of which are star-forming galaxies, ranging from normal galaxies in the nearby Universe to highly-starbursting systems at z > 4. Star-forming galaxies become the dominant population below 150-MHz flux densities of ≈1 mJy, accounting for 90 per cent of sources at S_150MHz ∼ 100μJy. Radio-quiet AGN comprise ≈10 per cent of the overall population. Results are compared against the predictions of the SKADS and T-RECS radio sky simulations, and improvements to the simulations are suggested.

Context. Relativistic electrons and magnetic fields permeate the intra-cluster medium (ICM) and manifest themselves as diffuse sources of synchrotron emission observable at radio wavelengths, namely radio halos and radio relics. Although there is broad consensus that the formation of these sources is connected to turbulence and shocks in the ICM, the details of the required particle acceleration, the strength and morphology of the magnetic field in the cluster volume, and the influence of other sources of high-energy particles are poorly known. Aims. Sufficiently large samples of radio halos and relics, which would allow us to examine the variation among the source population and pinpoint their commonalities and differences, are still missing. At present, due to the physical properties of the sources and the capabilities of existing facilities, large numbers of these sources are easiest to detect at low radio frequencies, where they shine brightly. Methods. We examined the low-frequency radio emission from all 309 clusters in the second catalog of Planck Sunyaev Zel’dovich detected sources that lie within the 5634 deg² covered by the Second Data Release of the LOFAR Two-meter Sky Survey (LoTSS-DR2). We produced LOFAR images at different resolutions, with and without discrete sources subtracted, and created overlays with optical and X-ray images before classifying the diffuse sources in the ICM, guided by a decision tree. Results. Overall, we found 83 clusters that host a radio halo and 26 that host one or more radio relics (including candidates). About half of them are new discoveries. The detection rate of clusters that host a radio halo and one or more relics in our sample is 30 ± 11% and 10 ± 6%, respectively. Extrapolating these numbers, we anticipate that once LoTSS covers the entire northern sky it will provide the detection of 251 ± 92 clusters that host a halo and 83 ± 50 clusters that host at least one relic from Planck clusters alone. All images and results produced in this work are publicly available via the project website.