The COSMOS-Web ring: Spectroscopic confirmation of the background source at z = 5.1

We report the spectroscopic confirmation of the background source of the most distant Einstein ring known to date, the COSMOS-Web ring. This system consists of a complete Einstein ring at $z=5.1$, lensed by a massive early-type galaxy at $z\sim2$. The redshift $z=5.1043\pm0.0004$ is unambiguously identified with our NOEMA and Keck/MOSFIRE spectroscopy, where the NOEMA observations reveal the CO(4-3) and CO(5-4) lines at $>8\,\sigma$, and the MOSFIRE data detect [O\textsc{ii}] at $\sim 6\,\sigma$. Using multi-wavelength photometry spanning near-infrared to radio bands, we find that the lensed galaxy is a dust-obscured starburst ($M_{\star} \sim 1.8\times10^{10}\,{\rm M_{\odot}}$, ${\rm SFR_{IR}\sim 60\,{\rm M_{\odot}} ~yr^{-1}}$) with high star-formation efficiency (gas depletion time $\tau_{\rm dep}<100~$Myr) as indicated by the [C\textsc{i}](1-0) non-detection. The redshift confirmation revalidates that the total lens mass budget within the Einstein radius is fully accounted for by the stellar and dark matter components, without the need of modifying the initial mass function or dark matter distribution profile. This work paves the way for detailed studies and future follow-ups of this unique lensing system, providing an ideal laboratory for studying mass distribution at $z\sim2$ and physical conditions of star formation at $z\sim5$.