  We present the results of a study of the AGN density in a homogeneous and
well-studied sample of 167 bona fide X-ray galaxy clusters ($0.1<z<0.5$) from
the XXL Survey. The results can provide evidence of the physical mechanisms
that drive AGN and galaxy evolution within clusters. The XXL cluster sample
mostly comprises poor and moderately rich structures ($M=10^{13} -
4\times10^{14} M_{\rm o}$). Our aim is to statistically study the demographics
of cluster AGNs as a function of cluster mass and host galaxy position. To
investigate the effect of the environment on AGN activity, we computed the
fraction of spectroscopically confirmed X-ray AGNs ($L_{\rm X
[0.5-10\,keV]}>10^{42}$ erg cm$^{-1}$) in bright cluster galaxies, up to
$6r_{500}$ radius. To study the mass dependence and the evolution of the AGN
population, we further divided the sample into low- and high-mass clusters and
two redshift bins (0.1-0.28 and 0.28-0.5). We detect a significant excess of
X-ray AGNs, at the 95% confidence level, in low-mass clusters between
$0.5r_{500}$ and 2$r_{500}$, which drops to the field value within the cluster
cores ($r<0.5r_{500}$). In contrast, high-mass clusters present a decreasing
AGN fraction towards the cluster centres. The high AGN fraction in the
outskirts is caused by low-luminosity AGNs. It can be explained by a higher
galaxy merging rate in low-mass clusters, where velocity dispersions are not
high enough to prevent galaxy interactions and merging. Ram pressure stripping
is possible in the cores of all our clusters, but probably stronger in deeper
gravitational potentials. Compared with previous studies of massive or
high-redshift clusters, we conclude that the AGN fraction in cluster galaxies
anti-correlates strongly with cluster mass. The AGN fraction also increases
with redshift, but at the same rate with the respective fraction in field
galaxies.
