The XXL Survey. II. The bright cluster sample: catalogue and luminosity
  function
  Context. The XXL Survey is the largest survey carried out by the XMM-Newton
satellite and covers a total area of 50 square degrees distributed over two
fields. It primarily aims at investigating the large-scale structures of the
Universe using the distribution of galaxy clusters and active galactic nuclei
as tracers of the matter distribution.
  Aims. This article presents the XXL bright cluster sample, a subsample of 100
galaxy clusters selected from the full XXL catalogue by setting a lower limit
of $3\times 10^{-14}\,\mathrm{erg \,s^{-1}cm^{-2}}$ on the source flux within a
1$^{\prime}$ aperture.
  Methods. The selection function was estimated using a mixture of Monte Carlo
simulations and analytical recipes that closely reproduce the source selection
process. An extensive spectroscopic follow-up provided redshifts for 97 of the
100 clusters. We derived accurate X-ray parameters for all the sources. Scaling
relations were self-consistently derived from the same sample in other
publications of the series. On this basis, we study the number density,
luminosity function, and spatial distribution of the sample.
  Results. The bright cluster sample consists of systems with masses between
$M_{500}=7\times 10^{13}$ and $3\times 10^{14} M_\odot$, mostly located between
$z=0.1$ and 0.5. The observed sky density of clusters is slightly below the
predictions from the WMAP9 model, and significantly below the predictions from
the Planck 2015 cosmology. In general, within the current uncertainties of the
cluster mass calibration, models with higher values of $\sigma_8$ and/or
$\Omega_m$ appear more difficult to accommodate. We provide tight constraints
on the cluster differential luminosity function and find no hint of evolution
out to $z\sim1$. We also find strong evidence for the presence of large-scale
structures in the XXL bright cluster sample and identify five new
superclusters.
