NOEMA Redshift Measurements of the Brightest Submillimeter Galaxies in the GOODS-N.

We report spectroscopic redshift measurements for three bright submillimeter galaxies (SMGs) in the GOODS-N field, each with SCUBA-2 850 micron fluxes > 10 mJy, using the Northern Extended Millimeter Array (NOEMA). Our molecular linescan observations of these sources, which occupy a ~7 arcmin$^2$ area outside of the HST/ACS region of the field, reveal that two lie at $z \sim$ 3.14 and thus likely belong to a previously-unknown overdensity of rare galaxies, which we shall refer to as a protocluster. In the remaining object, which is the brightest SCUBA-2 source in the entire GOODS-N, we detect line emission consistent with CO(7-6), [C I], and H2O at $z$ = 4.42. The far-infrared spectral energy distributions of these galaxies, constrained by SCUBA-2, NOEMA, and Herschel/SPIRE, indicate instantaneous SFRs $\sim4000 ~{\rm M_{\odot}~yr^{-1}}$ in the $z$ = 4.42 galaxy and $\sim 2500~{\rm M_{\odot}~yr^{-1}}$ in the two $z \sim$ 3 galaxies. These occupy a co-moving volume ~30 Mpc$^3$, making the protocluster one of the most compact, spectroscopically-confirmed episodes of simultaneous dusty starbursts. Based on our sources' CO line luminosities, we estimate $M_{{\rm gas}}\sim10^{11} M_{\odot}$ and find gas depletion timescales of $\tau_{{\rm depl}}\sim 50$ Myr, consistent with findings in other high-redshift SMG protoclusters.