An X-ray Census of Active Galactic Nuclei in the Virgo and Fornax Clusters of Galaxies with SRG/eROSITA

We present a uniform and sensitive X-ray census of active galactic nuclei (AGNs) in the two nearest galaxy clusters, Virgo and Fornax, utilizing the newly released X-ray source catalogs from the first all-sky scan of SRG/eROSITA. A total of 50 and 10 X-ray sources are found positionally coincident with the nuclei of member galaxies in Virgo and Fornax, respectively, down to a 0.2-2.3 keV luminosity of $\sim10^{39}\rm~erg~s^{-1}$ and reaching out to a projected distance well beyond the virial radius of both clusters. The majority of the nuclear X-ray sources are newly identified. There is weak evidence that the nuclear X-ray sources are preferentially found in late-type hosts. Several hosts are dwarf galaxies with a stellar mass below $\sim10^{9}\rm~M_\odot$. We find that contamination by non-nuclear X-ray emission can be neglected in most cases, indicating the dominance of a genuine AGN. In the meantime, no nuclear X-ray source exhibits a luminosity higher than a few times $10^{41}\rm~erg~s^{-1}$. The X-ray AGN occupation rate is only $\sim$ 3% in both clusters, apparently much lower than that in field galaxies inferred from previous X-ray studies. Both aspects suggest that the cluster environment effectively suppresses AGN activity. The findings of this census have important implications on the interplay between galaxies and their central massive black holes in cluster environments.