LOFAR 150-MHz observations of the Bo\"otes field: Catalogue and Source
  Counts
  We present the first wide area (19 deg$^2$), deep ($\approx120-150$ {\mu}Jy
beam$^{-1}$), high resolution ($5.6 \times 7.4$ arcsec) LOFAR High Band Antenna
image of the Bo\"otes 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 6276 sources
detected over an area of $19$\,deg$^2$, with a peak flux density threshold of
$5\sigma$. 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
radio-quiet AGN.
