Black hole mass, host galaxy mass, and dark matter halos: Testing the environmental connection

We investigate the connection between supermassive black holes (SMBHs), their host galaxies, and large-scale dark-matter halos using broad-line X-ray AGN from the XMM--XXL and Stripe\,82X surveys, together with galaxies from VIPERS and SDSS/Stripe\,82. Building on the homogeneous host-galaxy catalogue presented in Paper~I, we test whether AGN with a given black-hole mass, $M_{\rm BH}$, inhabit different large-scale environments from non-AGN galaxies with similar host properties. We first examine the empirical $M_{\rm BH}$--$M_{\star}$ relation of the AGN sample. We find a shallow trend with substantial scatter, likely driven by flux-limited selection effects and uncertainties in virial black-hole mass estimates. The ratio $M_{\rm BH}/M_{\star}$ decreases with increasing stellar mass, and AGN lying above and below the empirical relation show different median host properties, consistent with non-synchronous SMBH and stellar growth. We then divide the AGN into two black-hole mass bins, $8.0 \le \log(M_{\rm BH}/M_\odot) < 8.5$ and $8.5 \le \log(M_{\rm BH}/M_\odot) < 9.0$, and construct galaxy control samples matched in $M_{\star}$, SFR, and sSFR using a multivariate nearest-neighbour method. From AGN--galaxy cross-correlation functions, we infer the characteristic halo masses of AGN and matched galaxies. In the lower-$M_{\rm BH}$ bin, AGN occupy halos statistically indistinguishable from those of their controls. In the higher-$M_{\rm BH}$ bin, we find a mild indication that AGN may reside in somewhat more massive halos, with a difference of about 0.4 dex, although still consistent within the uncertainties. If confirmed with larger samples, this would suggest that halo-scale processes become important mainly at the highest $M_{\rm BH}$.