We present a study of the overdensity of X-ray-selected active galactic nuclei ( AGN ) in 33 galaxy clusters in the XMM-LSS field ( The XMM-Newton Large Scale Structure Survey ) , up to redshift z = 1.05 and further divided into a lower ( 0.14 \leq z \leq 0.35 ) and a higher redshift ( 0.43 \leq z \leq 1.05 ) subsample .
Previous studies have shown that the presence of X-ray-selected AGN in rich galaxy clusters is suppressed , since their number is significantly lower than what is expected from the high galaxy overdensities in the area .
In the current study we have investigated the occurrence of X-ray-selected AGN in low ( \langle L _ { x } ,bol \rangle = 2.7 \times 10 ^ { 43 } erg/s ) and moderate ( \langle L _ { x } ,bol \rangle = 2.4 \times 10 ^ { 44 } erg/s ) X-ray luminosity galaxy clusters in an attempt to trace back the relation between high-density environments and nuclear activity .
Owing to the wide contiguous XMM-LSS survey area , we were able to extend the study to the cluster outskirts .
We therefore determined the projected overdensity of X-ray point-like sources around each cluster out to 6 r _ { 500 } radius , within \delta r _ { 500 } = 1 annulus , with respect to the field expectations based on the X-ray source \log N - \log S of the XMM-LSS field .
To provide robust statistical results we also conducted a consistent stacking analysis separately for the two z ranges .
We investigated whether the observed X-ray overdensities are to be expected thanks to the obvious enhancement of galaxy numbers in the cluster environment by also estimating the corresponding optical galaxy overdensities , and we assessed the possible enhancement or suppression of AGN activity in clusters .

We find a positive X-ray projected overdensity in both redshift ranges at the first radial bin , which however has the same amplitude as that of optical galaxies .
Therefore , no suppression ( or enhancement ) of X-ray AGN activity with respect to the field is found , in sharp contrast to previous results based on rich galaxy clusters , implying that the mechanisms responsible for the suppression are not as effective in lower density environments .
After a drop to roughly the background level between 2 and 3 r _ { 500 } , the X-ray overdensity exhibits a rise at larger radii , significantly greater than the corresponding optical overdensity .
The radial distance of this overdensity “ bump ” , corresponding to \sim 1.5 - 3 Mpc , depends on the richness of the clusters , as well as on the overall X-ray overdensity profile .

Finally , using the redshift information , photometric or spectroscopic , of the optical counterparts , we derive the spatial overdensity profile of the clusters .
We find that the agreement between X-ray and optical overdensities in the first radial bin is also suggested in the 3-dimensional analysis .
However , we argue that the X-ray overdensity “ bump ” at larger radial distance is at least partially a result of flux boosting by gravitational lensing of background QSOs , confirming previous results .
For high-redshift clusters the enhancement of X-ray AGN activity in their outskirts appears to be intrinsic .
We argue that a spatial analysis is crucial for disentangling irrelevant phenomena affecting the projected analysis , but we are still not able to report statistically significant results on the spatial overdensity of AGN in clusters or their outskirts because we lack the necessary numbers .