Strong environmental AGN enhancement among DSFGs in z > 2 protoclusters

Galaxy protoclusters (PCs) at z > 2 are dense regions in which cold gas availability and elevated galaxy interaction rates trigger intense, often dust-obscured, star formation. These mechanisms are also expected to promote super-massive black hole (SMBH) growth, but this effect remains unclear, largely due to heterogeneous galaxy selections and active galactic nuclei (AGN) identification methods in previous studies. We quantitatively assess the impact of PC environment on SMBH growth by measuring the incidence of X-ray AGN among dusty star-forming galaxies (DSFGs) in PCs and in a homogeneously selected control field sample, and investigate the physical mechanisms driving any difference. We consider ALMA-detected DSFGs in sub-mm/mm continuum of seven PCs at 2 < z < 4.5, and construct a selection-matched control sample from the COSMOS survey. We statistically compare X-ray AGN incidence and host galaxy physical properties obtained through uniform spectral energy distribution fitting. We find a significant enhancement of X-ray AGN fraction in PCs by ~2.7x (Poisson significance p = 3e-4). Similar values are found in two redshift bins: ~2.7x at z = 2-3 (p = 0.003) and ~2.6x at z = 3-4.5 (p = 0.03). PC and field DSFG samples are well matched in stellar mass, star-formation rate, and dust mass, ruling out selection effects or systematically higher host masses as the driver. Our results provide quantitative evidence that the dense PC environment enhances AGN incidence and SMBH growth in DSFGs beyond what host galaxy properties alone predict, likely through increased gas availability and interaction-driven fueling. This work is a first step toward a homogeneous assessment of environmental effects on SMBH growth across cosmic time.