The soft X-ray cluster-AGN spatial cross-correlation function in the ROSAT-NEP survey

Context. X-ray surveys facilitate investigations of the environment of AGNs. Deep Chandra observations have revealed that the AGN source surface density rises near clusters of galaxies. The natural extension of this finding is the measurement of spatial clustering of AGNs around clusters and the investigation of relative biasing between active galactic nuclei and galaxies near clusters. Aims. We aim to measure the correlation length of AGNs around clusters and the average clustering properties of a complete sample of AGNs in a dense environment. Methods. We present the first measurement of the soft X-ray cluster-AGN cross-correlation function in redshift space using the data of the ROSAT-NEP survey. The survey covers 9 x 9 deg(2) around the North Ecliptic Pole where 442 X-ray sources were detected and almost completely spectroscopically identified. Results. We detected a > 3 sigma significant clustering signal on scales s <= 50 h(70)(-1) Mpc. We performed a classical maximum-likelihood power-law fit to the data and obtained a correlation length s(0) = 8.7(-0.3)(+1.2) h(70)(-1) Mpc and a slope gamma = 1.7(-0.7)(+0.2) (1 sigma errors). Conclusions. This is strong evidence that AGNs are good tracers of the large scale structure of the Universe. Our data were compared to the results obtained by cross-correlating X-ray clusters and galaxies. We observe, with a large uncertainty, a similar behaviour of AGN clustering around clusters similar to the clustering of galaxies around clusters.