The Mass-Metallicity Relation at z=8: Direct-Method Metallicity
  Constraints and Near-Future Prospects
  Physical properties of galaxies at z>7 are of interest for understanding both
the early phases of star formation and the process of cosmic reionization.
Chemical abundance measurements offer valuable information on the integrated
star formation history, and hence ionizing photon production, as well as the
rapid gas accretion expected at such high redshifts. We use reported
measurements of [O III] 88$\mu$m emission and star formation rate to estimate
gas-phase oxygen abundances in five galaxies at z=7.1-9.1 using the direct T_e
method. We find typical abundances 12+log(O/H) = 7.9 ($\sim$0.2 times the solar
value) and an evolution of 0.9$\pm$0.5 dex in oxygen abundance at fixed stellar
mass from z$\simeq$8 to 0. These results are compatible with theoretical
predictions, albeit with large (conservative) uncertainties in both mass and
metallicity. We assess both statistical and systematic uncertainties to
identify promising means of improvement with the Atacama Large Millimeter Array
(ALMA) and the James Webb Space Telescope (JWST). In particular we highlight [O
III] 52$\mu$m as a valuable feature for robust metallicity measurements.
Precision of 0.1-0.2 dex in T_e-based O/H abundance can be reasonably achieved
for galaxies at z$\approx$5-8 by combining [O III] 52$\mu$m with rest-frame
optical strong lines. It will also be possible to probe gas mixing and mergers
via resolved T_e-based abundances on kpc scales. With ALMA and JWST, direct
metallicity measurements will thus be remarkably accessible in the reionization
epoch.
