Galaxy Protoclusters as Drivers of Cosmic Reionization: II. Te-Based Metallicities of Lyman-α Emitters

Abstract: Context. Protoclusters at reionization are thought to host a significant fraction of the cosmic star formation rate density, making them crucial for the timing and topology of reionization. The gas-phase metallicity, a key tracer of galaxy evolutionary stage, can now be measured directly in the early Universe with JWST. Aims. We measure the gas-phase metallicity of Lyman-$α$ emitters (LAEs) in the LAGER-z7OD1 protocluster at $z\approx6.93$ via the direct ($T_e$-based) method using the [O III]$λ$4363 auroral line, and combine it with stellar masses to constrain the mass-metallicity relation (MZR) in dense environments. Methods. We use JWST/NIRSpec MSA G395H spectroscopy, derive metallicities with self-consistent analytic prescriptions, and propagate the dust-extinction uncertainty into an asymmetric error budget via Monte Carlo simulations based on the observed Balmer decrements. Stellar masses come from BEAGLE SED fitting of JWST/NIRCam and UltraVISTA photometry. Results. We obtain five secure [O III]$λ$4363 detections and one upper limit, with 12+log(O/H) $\approx$ 7.2-8.0. The weighted spectral stack yields 12+log(O/H) = $7.76<sup>{+0.06}_{-0.05}$, ~0.26 dex higher than stacks of LAEs at similar redshifts from JWST surveys. However, the MZR fit gives a slope $γ$ = 0.232 +/- 0.214 and normalization $Z_0$ = 7.888 +/- 0.199, placing our sources below the established MZR of normal galaxies and recent protocluster baselines at $z\sim5-7$. Conclusions. The higher metallicity relative to general LAEs suggests accelerated assembly driven by the overdensity, while the offset below the MZR points to a complex interplay between mass build-up and gas accretion. Since we target actively star-forming LAEs, we are likely capturing a phase of pristine gas inflow from the intergalactic medium that fuels star formation but dilutes the interstellar media of these protocluster members.