GOODS-ALMA: Optically dark ALMA galaxies shed light on a cluster in formation at z = 3.5

In this paper we study the properties of the six optically dark galaxies detected in the 69 arcmin^2 GOODS-ALMA 1.1mm continuum survey. While none of them are listed in the deepest H-band based CANDELS catalog in the GOODS-South field down to H=28.16AB, we were able to de-blend two of them from their bright neighbor and measure an $H$-band flux for them. We note that AGS4 and AGS15 have H=25.23, 27.11AB respectively. Their extreme proximity (0.50", 0.27") to a bright optical source and their extreme faintness prevented them from being included in the H-band catalog. We present the spectroscopic scan follow-up of five of the six sources with ALMA band 4. All are detected in the 2mm continuum with signal-to-noise ratios higher than eight. One emission line is detected in AGS4 (\nu_{obs} =151.44GHz with a S/N=8.58) and AGS17 (\nu_{obs} =154.78GHz with a S/N=10.23), which we interpret in both cases as being due to the CO(6-5) line at z^{AGS4}_{spec}=3.556 and z^{AGS4}_{spec}=3.467, respectively. These redshifts match both the probability distribution of the photometric redshifts derived from the UV to near-infrared spectral energy distributions (SEDs) and the far-infrared SEDs for typical dust temperatures of galaxies at these redshifts. We present evidence that nearly 70% (4/6 of galaxies) of the optically dark galaxies belong to the same overdensity of galaxies at z~3.5. overdensity The most massive one, AGS24 (M_{\star} = 10^{11.32^{+0.02}_{-0.19}} M_{\odot}), is the most massive galaxy without an active galactic nucleus (AGN) at $z$\,>\,3 in the GOODS-ALMA field. It falls in the very center of the peak of the galaxy surface density, which suggests that the surrounding overdensity is a proto-cluster in the process of virialization and that AGS24 is the candidate progenitor of the future brightest cluster galaxy (BCG).