The LOFAR Two-metre Sky Survey -- V. Second data release
  In this data release from the LOFAR Two-metre Sky Survey (LoTSS) we present
120-168MHz images covering 27% of the northern sky. Our coverage is split into
two regions centred at approximately 12h45m +44$^\circ$30' and 1h00m
+28$^\circ$00' and spanning 4178 and 1457 square degrees respectively. The
images were derived from 3,451hrs (7.6PB) of LOFAR High Band Antenna data which
were corrected for the direction-independent instrumental properties as well as
direction-dependent ionospheric distortions during extensive, but fully
automated, data processing. A catalogue of 4,396,228 radio sources is derived
from our total intensity (Stokes I) maps, where the majority of these have
never been detected at radio wavelengths before. At 6" resolution, our full
bandwidth Stokes I continuum maps with a central frequency of 144MHz have: a
median rms sensitivity of 83$\mu$Jy/beam; a flux density scale accuracy of
approximately 10%; an astrometric accuracy of 0.2"; and we estimate the
point-source completeness to be 90% at a peak brightness of 0.8mJy/beam. By
creating three 16MHz bandwidth images across the band we are able to measure
the in-band spectral index of many sources, albeit with an error on the derived
spectral index of +/-0.2 which is a consequence of our flux-density scale
accuracy and small fractional bandwidth. Our circular polarisation (Stokes V)
20" resolution 120-168MHz continuum images have a median rms sensitivity of
95$\mu$Jy/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 x 97.6
kHz wide planes and have a median rms sensitivity per plane of 10.8mJy/beam at
4' and 2.2mJy/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.
