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We present the spectroscopic confirmation of a galaxy cluster at $z=2.095$ inthe COSMOS field. This galaxy cluster was first reported in the ZFOURGE surveyas harboring evolved massive galaxies using photometric redshifts derived withdeep near-infrared (NIR) medium-band filters. We obtain medium resolution ($R\sim$ 3600) NIR spectroscopy with MOSFIRE on the Keck 1 telescope and secure180 redshifts in a $12'\times12'$ region. We find a prominent spike of 57galaxies at $z=2.095$ corresponding to the galaxy cluster. The cluster velocitydispersion is measured to be $\sigma_{\rm v1D}$ = 552 $\pm$ 52 km/s. This isthe first study of a galaxy cluster in this redshift range ($z \gt 2.0$) withthe combination of spectral resolution ($\sim$26 km/s) and the number ofconfirmed members (${>}50$) needed to impose a meaningful constraint on thecluster velocity dispersion and map its members over a large field of view. Our$\Lambda$CDM cosmological simulation suggests that this cluster will mostlikely evolve into a Virgo-like cluster with ${\rm M_{vir}}{=}10^{14.4\pm0.3}{\rm M_\odot}$ ($68\%$ confidence) at $z\sim$ 0. The theoretical expectation offinding such a cluster is $\sim$ $4\%$. Our results demonstrate the feasibilityof studying galaxy clusters at $z > 2$ in the same detailed manner usingmulti-object NIR spectrographs as has been done in the optical in lowerredshift clusters.

KECK/MOSFIRE spectroscopic confirmation of a Virgo-like cluster ancestor at z=2.095