A search for clusters at high redshift - IV. Spectroscopy of H-alpha emitters in a proto-cluster at z=2.16

Radio galaxy PKS 1138-262 is a massive galaxy at z=2.16, located in a dense environment. We have found an overdensity of Ly-alpha emitting galaxies in this field, consistent with a proto-cluster structure associated with the radio galaxy. Recently, we have discovered forty candidate H-alpha emitters by their excess near infrared narrow band flux. Here, we present infrared spectroscopy of nine of the brightest candidate H-alpha emitters. All these candidates show an emission line at the expected wavelength. The identification of three of these lines with H-alpha is confirmed by accompanying [NII] emission. The spectra of the other candidates are consistent with H-alpha emission at z~2.15, one being a QSO as indicated by the broadness of its emission line. The velocity dispersion of the emitters (360 km/s) is significantly smaller than that of the narrow band filter used for their selection (1600 km/s). We therefore conclude that the emitters are associated with the radio galaxy. The star formation rates (SFRs) deduced from the H-alpha flux are in the range 6-44 M_solar/yr and the SFR density observed is 5-10 times higher than in the HDF-N at z=2.23. The properties of the narrow emission lines indicate that the emitters are powered by star formation and contain very young (< 100 Myr) stellar populations with moderately high metallicities.