Most galaxies in clusters have supermassive black holes at their center, and a fraction of those supermassive black holes show strong activity. These active galactic nuclei(AGNs) are an important probe of environmental dependence of galaxy evolution, intra-cluster medium, and cluster-scale feedback. We investigated AGN fraction in one of the largest samples of X-ray selected clusters from the ROSAT and their immediate surrounding field regions below z < 0.5. We found lower average AGN fraction in clusters, (2.37+-0.39)% than for the fields (5.12+-0.16)%. The lower AGN fractions in clusters were measured, after dividing the clusters into five redshift intervals between 0.0 and 0.5, in each redshift interval, and we found an increase in the fraction for both cluster and field galaxies with redshift below z < 0.5, which clearly indicates an environment and redshift dependence. We further divided the clusters into low-mass and high-mass objects using a mass cut at log(M500/Msun) = 13.5, finding comparable AGN fractions for both classifications, while a significantly higher AGN fraction in field. We also measured increasing AGN fractions with clustercentric distance for all redshift bins, further confirming the environmental dependence of AGN activities. In addition, we did not find an obvious trend between AGN fraction and SDSS-R absolute magnitudes among different redshift bins. We conclude that the lower AGN fraction in clusters relative to fields indicate that factors, such as inefficient galaxy mergers and ram pressure stripping cause a deficit of cold gas available in high density regions to fuel the central super-massive black hole. Clusters and fields in present universe have lost more gas relative to their high redshift counterparts resulting in a lower AGN fraction observed today.
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