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_̊m BH, occupy the same or different large-scale environments as non-AGN galaxies with statistically indistinguishable host properties. We characterised the empirical M_̊m BH--M_⋆ distribution of the AGN sample. A shallow scaling between M_̊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_̊m BH intervals, 8.0 łe łog(M_ ̊m BH /M_⊙) < 8.5 and 8.5 łe łog(M_ ̊m BH /M_⊙) < 9.0, and constructed galaxy control samples matched in M_⋆, SFR, and sSFR ($= $) 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 łe łog(M_ SFR M_⋆ ̊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 łe łog(M_ ̊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 sim0.4,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_̊m BH, while at lower masses AGN environments remain indistinguishable from those of inactive galaxies with similar host properties.