We investigate extremely luminous dusty galaxies in the environments around Wide-field Infrared Survey Explorer (WISE)-selected hot dust-obscured galaxies (Hot DOGs) and WISE/radio-selected active galactic nuclei (AGNs) at average redshifts of z=2.7 and 1.7, respectively. Previous observations have detected overdensities of companion submillimetre-selected sources around 10 Hot DOGs and 30 WISE/radio AGNs, with overdensities of ~2-3 and ~5-6, respectively. We find that the space densities in both samples to be overdense compared to normal star-forming galaxies and submillimetre galaxies (SMGs) in the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) Cosmology Legacy Survey (S2CLS). Both samples of companion sources have consistent mid-infrared (mid-IR) colours and mid-IR to submm ratios as SMGs. The brighter population around WISE/radio AGNs could be responsible for the higher overdensity reported. We also find that the star formation rate densities are higher than the field, but consistent with clusters of dusty galaxies. WISE-selected AGNs appear to be good signposts for protoclusters at high redshift on arcmin scales. The results reported here provide an upper limit to the strength of angular clustering using the two-point correlation function. Monte Carlo simulations show no angular correlation, which could indicate protoclusters on scales larger than the SCUBA-2 1.5-arcmin scale maps.

Cone search capability for table J/MNRAS/469/4565/table1 (Coordinates and photometry of the 17 companion SMG sources found around 10 Hot DOGs)

Cone search capability for table J/MNRAS/469/4565/tab2-5 (*Coordinates and photometry of the 81 companion SMG sources found around 30 WISE/radio AGNs)