The RAdio Galaxy Environment Reference Survey (RAGERS): Evidence of an anisotropic distribution of submillimeter galaxies in the 4C 23.56 protocluster at z=2.48

High-redshift radio(-loud) galaxies (H$z$RGs) are massive galaxies with powerful radio-loud active galactic nuclei (AGNs) and serve as beacons for protocluster identification. However, the interplay between H$z$RGs and the large-scale environment remains unclear. To understand the connection between H$z$RGs and the surrounding obscured star formation, we investigated the overdensity and spatial distribution of submillimeter-bright galaxies (SMGs) in the field of 4C\,23.56, a well-known H$z$RG at $z=2.48$. We used SCUBA-2 data ($\sigma\,{\sim}\,0.6$\,mJy) to estimate the $850\,{\rm \mu m}$ source number counts and examine the radial and azimuthal overdensities of the $850\,{\rm \mu m}$ sources in the vicinity of the H$z$RG. The angular distribution of SMGs is inhomogeneous around the H$z$RG 4C\,23.56, with fewer sources oriented along the radio jet. We also find a significant overdensity of bright SMGs (${\rm S}_{850\rm\,\mu m}\geq5\,$mJy). Faint and bright SMGs exhibit different spatial distributions. The former are concentrated in the core region, while the latter prefer the outskirts of the H$z$RG field. High-resolution observations show that the seven brightest SMGs in our sample are intrinsically bright, suggesting that the overdensity of bright SMGs is less likely due to the source multiplicity.