The XXL Survey: XVI. The clustering of X-ray selected galaxy clusters at
  z~0.3
  Galaxy clusters trace the highest density peaks in the large-scale structure
of the Universe. Their clustering provides a powerful probe that can be
exploited in combination with cluster mass measurements to strengthen the
cosmological constraints provided by cluster number counts. We investigate the
spatial properties of a homogeneous sample of X-ray selected galaxy clusters
from the XXL survey, the largest programme carried out by the XMM-Newton
satellite. The measurements are compared to $\Lambda$-cold dark matter
predictions, and used in combination with self-calibrated mass scaling
relations to constrain the effective bias of the sample, $b_{eff}$, and the
matter density contrast, $\Omega_{\rm M}$. We measured the angle-averaged
two-point correlation function of the XXL cluster sample. The analysed
catalogue consists of $182$ X-ray selected clusters from the XXL second data
release, with median redshift $\langle z \rangle=0.317$ and median mass
$\langle M_{500} \rangle\simeq1.3\cdot10^{14} M_\odot$. A Markov chain Monte
Carlo analysis is performed to extract cosmological constraints using a
likelihood function constructed to be independent of the cluster selection
function. Modelling the redshift-space clustering in the scale range
$10<r\,[$\Mpch$]<40$, we obtain $\Omega_{\rm M}=0.27_{-0.04}^{+0.06}$ and
$b_{eff}=2.73_{-0.20}^{+0.18}$. This is the first time the two-point
correlation function of an X-ray selected cluster catalogue at such relatively
high redshifts and low masses has been measured. The XXL cluster clustering
appears fully consistent with standard cosmological predictions. The analysis
presented in this work demonstrates the feasibility of a cosmological
exploitation of the XXL cluster clustering, paving the way for a combined
analysis of XXL cluster number counts and clustering.
