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

We investigate the relation between supermassive black holes (SMBHs), their host galaxies, and large-scale dark-matter halos by combining broad-line X-ray active galactic nuclei (AGNs) from the XMM–XXL and Stripe 82X surveys with galaxies from VIPERS and SDSS/Stripe 82. Building on the homogeneous host-galaxy catalogue developed in Paper I, we test whether AGNs with a given black-hole mass, M BH , occupy the same or different large-scale environments as non-AGN galaxies with statistically indistinguishable host properties. We characterised the empirical M BH − M ★ distribution of the AGN sample. A shallow scaling between M BH and stellar mass, M ★ , is present, but with a large intrinsic scatter influenced by flux-limited selection and virial-mass uncertainties. The ratio M BH / M ★ declines with increasing M ★ over the sampled range. Overmassive and undermassive AGN subsets, defined relative to this empirical trend, exhibit distinct median host properties consistent with partially non-synchronous SMBH and M ★ growth. We then selected AGNs in two M BH intervals, 8.0 ≤ log( M BH / M ⊙ ) < 8.5 and 8.5 ≤ log( M BH / M ⊙ ) < 9.0, and constructed galaxy control samples matched in M ★ , SFR, and sSFR (SFR/ M ★ ) using a multivariate nearest-neighbour procedure. Using AGN–galaxy cross-correlation functions, we inferred characteristic halo masses for AGNs and matched galaxies in each bin. The AGNs with 8.0 ≤ log( M BH / M ⊙ ) < 8.5 occupy halos statistically indistinguishable from those of their controls, indicating no detectable environmental dependence at these masses once host properties are controlled. In the higher-mass bin, 8.5 ≤ log( M BH / M ⊙ ) < 9.0, we find a mild indication that AGNs may reside in more massive halos than the matched non-AGN galaxies. The inferred difference is ∼0.4 dex but remains formally consistent within the uncertainties. If confirmed with larger samples, this may indicate that halo-scale processes become increasingly relevant only at the highest M BH , while at lower masses AGN environments remain indistinguishable from those of inactive galaxies with similar host properties.