LoTSS

The LOw Frequency ARray (LOFAR; \citealt{vanHaarlem_2013}) Two-metre Sky Survey (LoTSS; \citealt{Shimwell_2017}) is one of several ongoing very wide area deep radio wavelength sky surveys. Other similar projects with different instruments include the Evolutionary Map of the Universe (EMU; \citealt{Norris_2011,Norris_2021}), the Polarization Sky Survey of the Universe's Magnetism (POSSUM; \citealt{Gaensler_2010}), the APERture Tile In Focus surveys (APERTIF surveys; Hess et al. in prep), the GaLactic and Extragalactic All-Sky MWA-eXtended survey (GLEAM-X; Hurley Walker et al. in prep), the Karl G. Jansky Very Large Array Sky Survey (VLASS; \citealt{Lacy_2020}) and the Global Magneto-Ionic Medium Survey (GMIMS; \citealt{Wolleben_2019}, \citealt{Wolleben_2021}). LoTSS also forms part of a broader LOFAR Surveys Key Science Project (LSKSP; \citealt{Rottgering_2011}) that is striving to map the low-frequency ($<200$\,MHz) northern sky with a series of surveys spanning a range of depths, frequencies, and areas. The 120-168\,MHz LoTSS survey is the highest frequency very wide-area LOFAR surveys project and is complemented by the ongoing very wide area 42-66\,MHz LOFAR Low Band Antenna Sky Survey (LoLSS; \citealt{deGasperin_2021}) and the even lower frequency 14-30\,MHz LOFAR Decametre Sky Survey (LoDSS) which has recently started. Furthermore, narrower area, but far deeper surveys of several fields with exceptionally high quality auxiliary data are also being carried out, namely the LoTSS and LoLSS Deep Fields (\citealt{Tasse_2021}, \citealt{Sabater_2021}, \citealt{Kondapally_2021}, \citealt{Duncan_2021}, Best et al. in prep and \citealt{Williams_2021})
as well as moderate depth observations (or otherwise tailored data processing) towards targets of particular scientific interest (the H-ATLAS North Galactic Pole, North Ecliptic Pole, Virgo cluster, Coma cluster, Corona Borealis supercluster, Abell 2255, Abell 399-401, GJ 1151, GJ 412 and others).

The capabilities of LOFAR, and the amount of observing time secured to date, have enabled LoTSS to achieve a unique combination of sensitivity ($\sim$100$\mu$Jy/beam) coupled with high resolution ($\sim$6$\arcsec$) and an accurate recovery of very extended (up to degree scales) objects -- all at a low radio frequency of 144\,MHz.
The emission mechanism for radio sources is generally synchrotron and the sources
typically increase in integrated flux density ($S_{I}$) with decreasing frequency ($\nu$), with the emission often characterised by $S_\nu \propto \nu^{\alpha}$ where the conventional spectral index ($\alpha$) is $-0.7$ (e.g. \citealt{Condon_2002}).
With its properties, LoTSS is therefore able to detect, and precisely characterise, an exceptionally high density of radio sources. The source density far exceeds ($>$ 8 times) that of pioneering very wide-area higher-frequency surveys such as the NRAO VLA Sky Survey (NVSS; \citealt{Condon_1998}), Faint Images of the Radio Sky at Twenty-Centimeters (FIRST; \citealt{Becker_1995}), Sydney University Molonglo Sky Survey (SUMSS; \citealt{Bock_1999} and \citealt{Mauch_2003}), WEsterbork Northern Sky Survey (WENSS; Rengelink et al. 1997) and Westerbork In the Southern Hemisphere (WISH; \citealt{DeBreuck_2002}) as well as that of current state-of-the-art low-frequency surveys such as the TIFR GMRT Sky Survey alternative data release (TGSS-ADR1; \citealt{Intema_2017}), GaLactic and Extragalactic All-sky MWA (GLEAM; \citealt{Wayth_2015} and \citealt{HurleyWalker_2017}), LOFAR Multifrequency Snapshot Sky Survey (MSSS; \citealt{Heald_2015}) and the Very Large Array Low-frequency Sky Survey Redux (VLSSr; \citealt{Lane_2014}). Thus, LoTSS, and other forthcoming radio surveys with significantly improved sensitivities, resolutions, or other unique properties such as fractional bandwidth, frequency- or time-resolution, are dramatically enriching our view of the radio Universe. Specifically, the suite of ongoing LOFAR surveys will enable us to probe the 14-168\,MHz northern sky over very wide areas with a sensitivity of $\sim0.1\times \left(\frac{\nu}{144\,\textrm{MHz}}\right)^{-2.5}$\,mJy/beam and a resolution of $\sim 6 \times \left(\frac{144\,\textrm{MHz}}{\nu}\right)$\,arcsec whilst narrow areas will be mapped with a factor of up to ten improved sensitivity.

To realise LoTSS, extensive development has been required to build
strategies that correct the severe ionospheric distortions which vary
rapidly with both time and direction on the sky. If uncorrected, these effects
prohibit high fidelity imaging at low frequencies (see e.g. \citealt{Lonsdale_2005} and \citealt{Intema_2009}).
Furthermore, each individual LoTSS pointing (of which there are 3168 across the Northern sky) corresponds to a very large dataset (8.8\,TB) and
thus such strategies
must be able to run routinely and efficiently in order to produce the
desired maps within a reasonable time period.

A further challenge,
common to all radio surveys, is that even once high fidelity maps are produced,
to increase the scientific value
of the radio catalogues we need procedures that
carefully associate the detected sources and cross-match them with
other auxiliary catalogues to deduce information that is vital to
understand the nature of the detected radio sources. Over time our
methods have improved. For example, in the preliminary LoTSS data
release (LoTSS-PDR; \citealt{Shimwell_2017}) we presented a catalogue
of 44,500 radio sources but at that time we were unable to routinely
correct for ionospheric errors over very wide areas of the sky and
were thus limited in resolution, sensitivity and fidelity. This was
followed by the first LoTSS data release (LoTSS-DR1; \citealt{Shimwell_2019}) that mapped the same area but utilised an automated and robust direction dependent calibration pipeline to produce a much larger radio catalogue of 325,694 components. In LoTSS-DR1 we also performed significant post processing of the radio catalogues to enhance their scientific potential. The 325,694 components were carefully grouped into 318,520 distinct radio sources and 73\% of these were matched to optical or infrared host galaxies (\citealt{Williams_2019}) and, where possible, photometric redshifts were estimated (\citealt{Duncan_2019}).

Our aims within the LSKSP are not only to provide
publicly available radio images and catalogues of the sky but also to increase our understanding of the detected sources through a coordinated scientific exploitation of the images and auxiliary data.
To date, with this approach, the LOFAR surveys have facilitated numerous scientific studies\footnote{https://lofar-surveys.org/publications.html} in core areas of radio astronomy such as the physics of active galactic nuclei, particle acceleration in galaxy clusters, large scale structure and star formation.
Furthermore, the breadth of scientific studies continues to expand to include topics ranging from cosmological studies (\citealt{Siewert_2020}) through to pulsars (\citealt{Tan_2018}), supernovae remnants (\citealt{Arias_2019}) and even exoplanets (\citealt{Vedantham_2020}). Meanwhile, valuable synergies are being established such as those with the LOFAR Magnetism Key Science Project\footnote{https://lofar-mksp.org/}, APERTIF imaging surveys, Extended Baryon Oscillation Spectroscopic Survey (eBOSS; \citealt{Dawson_2016}), extended ROentgen Survey with an Imaging Telescope Array (eROSITA; \citealt{Predehl_2021}) and the William Herschel Telescope Enhanced Area Velocity Explorer survey of LOFAR selected sources (WEAVE-LOFAR; \citealt{Smith_2016}) which are each enabling new scientific studies (e.g. \citealt{Ghirardini_2021}, \citealt{Morganti_2021}, \citealt{OSullivan_2020}, \citealt{Wolf_2021}). Finally, the LOFAR surveys are also having a large technical impact with studies of calibration and imaging techniques (e.g. \citealt{deGasperin_2019}, \citealt{Tasse_2021} and \citealt{vanWeeren_2021}, \citealt{Morabito_prep} and \citealt{Sweijen_2022}), efficient distributed processing
(\citealt{Drabent_2019} and \citealt{Mechev_2019}), photometric
redshift estimators (\citealt{Duncan_2019}) and automated source classification
(e.g. \citealt{Mostert_2021} and \citealt{Mingo_2019}). Excitingly, despite all
of these advances, the LOFAR surveys data still retain vast, and largely untapped, potential. For example, 96\% of existing LoTSS observations have been conducted with the full international LOFAR telescope which now includes 14 stations outside of the Netherlands and are archived at high (1\,s) time and frequency (12.1875\,kHz) resolution. Presently, due to resource limitations and ongoing technical developments, during regular LoTSS processing we significantly average the data and remove the international stations. We thus do not yet fully realise the higher sensitivity sub-arcsecond wide-field imaging (e.g. \citealt{Morabito_prep}, \citealt{Sweijen_2022}), source variability (e.g. \citealt{Vedantham_2020,callingham2021}) and spectral line (see e.g. \citealt{Emig_2020}, \citealt{Salas_2019}) capabilities of the data.

In this publication we present our second LoTSS data release (LoTSS-DR2) and a characterisation of the associated images. This builds significantly upon our previous work by making use of our enhanced direction dependent calibration and imaging processing pipeline (see \citealt{Tasse_2021}) as well as improved processing efficiency and automation (see e.g. \citealt{Drabent_2019} and \citealt{Mechev_2019}).
These improvements enable us to present images spanning 5,634 square degrees (27\%) of the Northern sky, and a catalogue containing 4,396,228 radio sources -- the largest catalogue of radio sources released to date. In addition to radio continuum catalogues and images at multiple resolutions, we also release polarisation images and calibrated $uv$-datasets. All data products associated with this release have the Digital Object Identifier (DOI) 10.25606/SURF.LoTSS-DR2 and are available via the collaboration's webpage\footnote{\url{https://www.lofar-surveys.org/}}, the ASTRON Virtual Observatory\footnote{\url{https://vo.astron.nl}} and the SURF Data Repository\footnote{\url{https://repository.surfsara.nl/}}.