JWST MIRI detections of Hα and [O III] and direct metallicity measurement of the $z=10.17$ lensed galaxy MACS0647$-$JD

JWST spectroscopy has revolutionized our understanding of galaxies in the early universe. Covering wavelengths up to 5.3\, μ m, NIRSpec can detect rest-frame optical emission lines Hα out to $z = 7$ and [O III] to $z = 9.5$. Observing these lines in more distant galaxies requires longer wavelength spectroscopy with MIRI. Here we present MIRI MRS IFU observations of the lensed galaxy merger MACS0647$-$JD at $z = 10.165$. With exposure times of 4.2 hours in each of two bands, we detect Hα at 9σ, [O III]\,λ5008 at 11σ, and [O III]\,λ4960 at 3σ. Combined with previously reported NIRSpec spectroscopy that yields seven emission lines including the auroral line [O III]\,λ4363, we present the first direct metallicity measurement of a $z > 10$ galaxy: 12+ log(O/H)= 7.79±0.09, or 0.13+0.02-0.03\,Z_. This is similar to galaxies at z ~ 4 - 9 with direct metallicity measurements, though higher than expected given the high specific star formation rate log(sSFR / yr⁻¹) = -7.4 ± 0.3. We further constrain the ionization parameter log(U) = -1.9 ± 0.1, ionizing photon production efficiency log(ξᵢₒₙ) = 25.3±0.1, and star formation rate 5.0±0.6\,M_/ yr within the past 10\, Myr. These observations demonstrate the combined power of JWST NIRSpec and MIRI for studying galaxies in the first $500$ million years.