Environmental dependence of the Mass-Metallicity Star Formation Relations at z=4-10 with JWST
We study how environment affects the mass-metallicity relation (MZR) at $z=4$-$10$ using deep imaging and spectroscopy from the James Webb Space Telescope (JWST). Combining CEERS and JADES, we compile a sample of 225 galaxies with stellar masses, star-formation rates, and gas-phase metallicities. We characterize environment using the projected fifth-nearest-neighbour surface density, $Σ_{5}$, within $Δz=\pm0.25$. At $4.5<z<7$, we find that galaxies in dense regions are more metal-rich at fixed $M_\star$ by $\sim0.1$-0.2 dex, while the slopes of the MZR remain similar across environments. Including SFR increases the separation, suggesting more efficient chemical enrichment in overdense regions. Compared to the local $T_e$-based FMR, our full sample lies $\simeq0.2$-0.3 dex below the $z\sim0$ relation, with a smaller deficit in overdense environments. We also examine how metallicity relates to galaxy size using NIRCam-based effective radii. Metallicity increases weakly with size up to $R_e\sim1$ kpc and then flattens, with only a modest residual trend at fixed $M_\star$ and little environmental dependence. Using mass-weighted stellar ages at $5<z<10$, we find a positive age-metallicity relation in both environments, steeper in the field. Finally, we find that the star-formation rate density is higher in overdense regions at $z\simeq6$-9 by a factor of $\sim2$-3. Overall, our results suggest that environment accelerates both star formation and chemical enrichment during the epoch of reionization. Future wide-area JWST spectroscopy, combined with ALMA and Euclid, will better constrain the role of environment in early galaxy evolution.