EPOCHS Paper X: Environmental effects on Galaxy Formation and Protocluster Galaxy candidates at $4.5<z<10$ from JWST observations

In this paper we describe our search for galaxy protocluster candidates at $4.5< z < 10$ and explore the environmental and physical properties of their member galaxies identified through JWST wide-field surveys within the CEERS, JADES, and PEARLS NEP-TDF fields. Combining with HST data, we identify 2948 robust $z>4.5$ candidates within an area of 185.4 arcmin$^2$. We determine nearest neighbour statistics and galaxy environments. We find that high-$z$ galaxies in overdense environments exhibit higher star formation activity compared to those in underdense regions. Galaxies in dense environments have a slightly increased SFR at a given mass compared with galaxies in the lower density environments. At the high mass end we also find a gradual flattening of the $M_{\star}$-SFR slope. We find that galaxies in high-density regions often have redder UV slopes than those in low-density regions, suggesting more dust extinction, weaker Lyman-alpha emission and / or a higher damped Lyman-alpha absorption. We also find that the mass-size relation remains consistent and statistically similar across all environments. Furthermore, we quantitatively assess the probability of a galaxy belonging to a protocluster candidate. In total, we identified 26 overdensities at $z=5-7$ and estimate their dark matter halo masses. We find that all protocluster candidates could evolve into clusters with $M_{\rm halo} > 10^{14}M_{\odot}$ at $z = 0$, thereby supporting the theoretical and simulation predictions of cluster formation. Notably, this marks an early search for protocluster candidates in JWST wide field based on photometric data, providing valuable candidates to study cosmic structure formation at the early stages.