The correlation between active galactic nuclei (AGN) and environment provides important clues to AGN fueling and the relationship of black hole growth to galaxy evolution. In this paper, we analyze the fraction of galaxies in clusters hosting AGN as a function of redshift and cluster richness for X-ray detected AGN associated with clusters of galaxies in Dark Energy Survey (DES) Science Verification data. The present sample includes 33 AGN with L_X > 10^43 ergs s^-1 in non-central, host galaxies with luminosity greater than 0.5 L* from a total sample of 432 clusters in the redshift range of 0.1<z<0.95. Analysis of the present sample reveals that the AGN fraction in red-sequence cluster members has a strong positive correlation with redshift such that the AGN fraction increases by a factor of ~8 from low to high redshift, and the fraction of cluster galaxies hosting AGN at high redshifts is greater than the low-redshift fraction at 3.6 sigma. In particular, the AGN fraction increases steeply at the highest redshifts in our sample at z>0.7. This result is in good agreement with previous work and parallels the increase in star formation in cluster galaxies over the same redshift range. However, the AGN fraction in clusters is observed to have no significant correlation with cluster mass. Future analyses with DES Year 1 through Year 3 data will be able to clarify whether AGN activity is correlated to cluster mass and will tightly constrain the relationship between cluster AGN populations and redshift.
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