Anchoring z>6 Galaxy Metallicities Using T_e and n_e Diagnostics Enabled by JWST and ALMA Spectroscopy

We propose deep NIRSpec and MIRI IFU spectroscopy targeting 3 galaxies at z=6.0-7.2 covered by ALMA [OIII]88um observations in order to derive gas-phase metallicities at z>6 using the reliable direct electron temperature method. Accurate gas-phase metallicities are crucial for understanding the formation and growth of early galaxies, but diagnostic calibrations to infer metallicity from strong-line ratios have not yet been established at high redshifts. Obtaining temperature-based metallicities of z>6 sources represents the most direct and robust solution to this problem. Although the direct method usually relies on temperature-sensitive auroral lines that are too faint to detect at z>6, we will accomplish this goal by combining measures of the temperature-sensitive far-infrared fine structure line [OIII]88um (from ALMA) with rest-frame optical lines (Ha, Hb, [OIII]4959,5007, and density-sensitive [OII]3726,3729 from JWST). Our program will deliver robust measures of the mass-metallicity relation to z~6-7 along with accompanying constraints on dynamical and gas masses, ionization parameter, and ionizing spectral shape. These constraints will allow us to understand the formation of luminous z~6 sources, the role of feedback in governing their growth, and their impact on cosmic reionization. Most significantly, direct-method metallicities derived from this program will serve as the first calibrating `anchor'''' for statistical studies of metallicities and ionization parameters for galaxies in GTO/ERS and other samples, derived using the strong-line method. The combination will provide robust data for understanding early galaxy formation and the sources of cosmic reionization.