Deep LOFAR 150 MHz imaging of the Bo\"otes field: Unveiling the faint
  low-frequency sky
  We have conducted a deep survey (with a central rms of $55\mu\textrm{Jy}$)
with the LOw Frequency ARray (LOFAR) at 120-168 MHz of the Bo\"otes field, with
an angular resolution of $3.98^{''}\times6.45^{''}$, and obtained a sample of
10091 radio sources ($5\sigma$ limit) over an area of $20\:\textrm{deg}^{2}$.
The astrometry and flux scale accuracy of our source catalog is investigated.
The resolution bias, incompleteness and other systematic effects that could
affect our source counts are discussed and accounted for. The derived 150 MHz
source counts present a flattening below sub-mJy flux densities, that is in
agreement with previous results from high- and low- frequency surveys. This
flattening has been argued to be due to an increasing contribution of
star-forming galaxies and faint active galactic nuclei. Additionally, we use
our observations to evaluate the contribution of cosmic variance to the scatter
in source counts measurements. The latter is achieved by dividing our Bo\"otes
mosaic into 10 non-overlapping circular sectors, each one with an approximate
area of $2\:\textrm{deg}^{2}.$ The counts in each sector are computed in the
same way as done for the entire mosaic. By comparing the induced scatter with
that of counts obtained from depth observations scaled to 150MHz, we find that
the $1\sigma$ scatter due to cosmic variance is larger than the Poissonian
errors of the source counts, and it may explain the dispersion from previously
reported depth source counts at flux densities $S<1\,\textrm{mJy}$. This work
demonstrates the feasibility of achieving deep radio imaging at low-frequencies
with LOFAR.
