Signs of environmental effects on star-forming galaxies in the Spiderweb protocluster at z=2.16

We use multi-object near-infrared (NIR) spectroscopy with VLT/KMOS to investigate the role of the environment in the evolution of the ionized gas properties of narrow-band selected H$\alpha$ emitters (HAEs) in the Spiderweb protocluster at $z=2.16$. Based on rest-frame optical emission lines, H$\alpha$ and [NII]$\lambda$6584, we confirm the cluster membership of 39 of our targets (i.e. 93% success rate), and measure their star-formation rates (SFR), gas-phase oxygen abundances and effective radius. We parametrize the environment where our targets reside by using local and global density indicators based on previous samples of spectroscopic and narrow-band cluster members. We find that star-forming galaxies embedded in the Spiderweb protocluster display SFRs compatible with those of the main sequence and morphologies comparable to those of late-type galaxies at $z=2.2$ in the field. We also report a mild gas-phase metallicity enhancement ($0.6\pm0.3$ dex) at intermediate stellar masses. Furthermore, we identify two UVJ-selected quiescent galaxies with residual H$\alpha$-based star formation and find signs of extreme dust obscuration in a small sample of SMGs based on their FIR and H$\alpha$ emission. Interestingly, the spatial distribution of these objects differs from the rest of HAEs, avoiding the protocluster core. Finally, we explore the gas fraction-gas metallicity diagram for 7 galaxies with molecular gas masses measured by ATCA using CO(1-0). In the context of the gas-regulator model, our objects are consistent with relatively low mass-loading factors, suggesting lower outflow activity than field samples at the cosmic noon and thus, hinting at the onset of environmental effects in this massive protocluster.