The LOFAR Two-metre Sky Survey (LoTSS) is a deep 120-168 MHz imaging survey that will eventually cover the entire northern sky. Each of the 3170 pointings will be observed for 8 h, which, at most declinations, is sufficient to produce ∼5 resolution images with a sensitivity of ∼100 µJy/beam and accomplish the main scientific aims of the survey, which are to explore the formation and evolution of massive black holes, galaxies, clusters of galaxies and large-scale structure. Owing to the compact core and long baselines of LOFAR, the images provide excellent sensitivity to both highly extended and compact emission. For legacy value, the data are archived at high spectral and time resolution to facilitate subarcsecond imaging and spectral line studies. In this paper we provide an overview of the LoTSS. We outline the survey strategy, the observational status, the current calibration techniques, a preliminary data release, and the anticipated scientific impact. The preliminary images that we have released were created using a fully automated but direction-independent calibration strategy and are significantly more sensitive than those produced by any existing large-area low-frequency survey. In excess of 44 000 sources are detected in the images that have a resolution of 25 , typical noise levels of less than 0.5 mJy/beam, and cover an area of over 350 square degrees in the region of the HETDEX Spring Field (right ascension 10h45m00s to 15h30m00s and declination 45• 00 00 to 57• 00 00 ).

We present the first wide area (19 deg 2 ), deep (≈ 120-150 µJy beam −1 ), high resolution (5.6× 7.4 arcsec) LOFAR High Band Antenna image of the Boötes field made at 130-169 MHz. This image is at least an order of magnitude deeper and 3 − 5 times higher in angular resolution than previously achieved for this field at low frequencies. The observations and data reduction, which includes full direction-dependent calibration, are described here. We present a radio source catalogue containing 6 276 sources detected over an area of 19 deg 2 , with a peak flux density threshold of 5σ . As the first thorough test of the facet calibration strategy, introduced by van Weeren et al., we investigate the flux and positional accuracy of the catalogue. We present differential source counts that reach an order of magnitude deeper in flux density than previously achieved at these low frequencies, and show flattening at 150 MHz flux densities below 10 mJy associated with the rise of the low flux density star-forming galaxies and radioquiet AGN.

In this data release from the ongoing LOw-Frequency ARray (LOFAR) Two-metre Sky Survey (LoTSS) 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 3,451 hrs (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; 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. 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, 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 at 4 and 2.2 mJy/beam 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.

Recent high-resolution N-body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matter haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the Sérsic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.

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 ≲23 μJy beam−1 in the inner ~3 deg2. This approach is also being used to reduce the LOTSS-wide data for the second data release.