Galaxy protoclusters as drivers of cosmic reionization. II. Te-based metallicities of Lyman-α emitters

Protoclusters in the epoch of reionization are believed to host a significant fraction of the total cosmic star formation rate density, which makes them crucial in determining the timing and topology of reionization. Understanding the physical properties of galaxies within them is thus essential. A key property to trace the evolutionary stage of a galaxy, the gas-phase metallicity, can now be directly measured in the early Universe thanks to JWST. We aim to measure the gas-phase metallicity of Lyman-α emitters (LAEs) in the LAGER-z7OD1 protocluster at z ≈ 6.93 via the direct (T_e-based) method using the O III łambda4363 auroral line. By combining these metallicities with stellar masses, we aim to constrain the mass--metallicity relation (MZR) in dense environments and determine how the chemical buildup of protocluster LAEs compares to other early galaxy populations. We used deep JWST-NIRSpec/MSA G395H spectroscopy to measure the rest-frame optical emission lines of our sample. We derived metallicities using self-consistent analytic prescriptions, with the systematic uncertainty from dust extinction fully propagated into an asymmetric error budget via Monte Carlo simulations based on the observed Balmer decrements. Stellar masses were derived from BEAGLE spectral energy distribution fitting using JWST/NIRCam and UltraVISTA photometry. We also created a weighted spectral stack to study the high signal-to-noise mean properties of the sample. We obtain five secure detections of the O III łambda4363 line and one upper limit, yielding individual metallicities in the range of 12+łog(̊m O/H) ≈ 7.2 - 8.0. Our weighted spectral stack yields 12+łog(̊m O/H) = 7.76^ +0.06 _ -0.05 , which is ∼ 0.26 dex higher than stacks of LAEs at similar redshifts from JWST spectroscopic surveys. However, fitting the MZR yields a slope of γ = 0.232 ± 0.214 and a normalization of Z_0 = 7.888 ± 0.199, which demonstrates that our sources lie systematically below the MZR of lower-redshift galaxies and the recently reported protocluster relations at z ∼ 5-7. The enhancement in absolute metallicity relative to general population LAEs suggests an accelerated early assembly driven by the overdensity. However, the offset below the MZR seen in recent high-redshift studies indicates a complex interplay between mass buildup and gas accretion. Because our selection strictly targets actively star-forming LAEs, we are probably capturing a violent phase of pristine gas accretion from the intergalactic medium. This massive influx fuels star formation but overpowers normal environmental metal retention, thereby systematically diluting the interstellar media of these specific protocluster members.