Probing the Mpc-scale environment of hyperluminous infrared galaxies at 2<z<4

Protoclusters are important for studying how halo mass and stellar mass assemble in the early universe. Finding signposts of such over-dense regions is a popular method to identify protocluster candidates. Hyperluminous infrared galaxies (HLIRGs), are expected to reside in overdense regions with massive halos. We study the Mpc-scale environment of the largest HLIRG sample to date and investigate whether they predominantly live in overdense regions. We first explore the surface density of Herschel 250 $\mu$m sources around HLIRGs and compare with that around random positions. Then, we compare the spatial distribution of neighbours around HLIRGs with that around randomly selected galaxies using a deep IRAC-selected catalogue with good-quality photometric redshifts. We also use a redshift-matched quasar sample and submillimeter galaxy (SMG) sample to validate our method, as previous clustering studies have measured the host halo masses of these populations. Finally, we adopt a Friends of Friends (FOF) algorithm to seek (proto)clusters that host HLIRGs. We find that HLIRGs tend to have more bright star-forming neighbours (with 250 $\mu$m flux density >10 mJy) within 100$\arcsec$ projected radius than a random galaxy at a 3.7$\sigma$ significance. In our 3D analysis, we find relatively weak excess of IRAC-selected sources within 3 Mpc around HLIRGs compared with random galaxy neighbours, mainly influenced by photometric redshift uncertainty and survey depth. We find a more significant difference (at a 4.7$\sigma$ significance) in the number of Low Frequency Array (LOFAR)-detected neighbours in the deepest EN1 field. HLIRGs at 3 < z < 4 show stronger excess compared to HLIRGs at 2 < z < 3, consistent with cosmic downsizing. Finally, we select and present a list of 30 most promising protocluster candidates for future follow-up observations.