The cosmic web of X-ray active galactic nuclei seen through the eROSITA Final Equatorial Depth Survey (eFEDS)

Which galaxies in the general population turn into active galactic nuclei (AGNs) is a keystone of galaxy formation and evolution. Thanks to SRG/eROSITA's contiguous 140 square degree pilot survey field, we constructed a large, complete, and unbiased soft X-ray flux-limited ($F_X>6.5\times 10^{-15}$ erg s$^{-1}$ cm$^{-2}$) AGN sample at low redshift, $0.05<z<0.55$. Two summary statistics, the clustering using spectra from SDSS-V and galaxy-galaxy lensing with imaging from HSC, are measured and interpreted with halo occupation distribution and abundance matching models. Both models successfully account for the observations. We obtain an exceptionally complete view of the AGN halo occupation distribution. The population of AGNs is broadly distributed among halos with a mean mass of $3.9 _{- 2.4 }^{+ 2.0 }\times10^{12}M_\odot$. This corresponds to a large-scale halo bias of $b(z=0.34)= 0.99 ^{+0.08}_{-0.10}$. The central occupation has a large transition parameter, $\sigma_{\log_{10}(M)}=1.28\pm0.2$. The satellite occupation distribution is characterized by a shallow slope, $\alpha_{{\rm sat}}=0.73\pm0.38$. We find that AGNs in satellites are rare, with $f_{{\rm sat}}<20\%$. Most soft X-ray-selected AGNs are hosted by central galaxies in their dark matter halo. A weak correlation between soft X-ray luminosity and large-scale halo bias is confirmed (3.3$\sigma$). We discuss the implications of environmental-dependent AGN triggering. This study paves the way toward fully charting, in the coming decade, the coevolution of X-ray AGNs, their host galaxies, and dark matter halos by combining eROSITA with SDSS-V, 4MOST, DESI, LSST, and \textit{Euclid} data.