A search for clusters at high redshift -: IV.: Spectroscopy of Hα 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 Lyalpha emitting galaxies in this field, consistent with a proto-cluster structure associated with the radio galaxy. Recently, we have discovered forty candidate Halpha emitters by their excess near infrared narrow band flux. Here, we present infrared spectroscopy of nine of the brightest candidate Halpha emitters. All these candidates show an emission line at the expected wavelength. The identification of three of these lines with Halpha is confirmed by accompanying [N II] emission. The spectra of the other candidates are consistent with Ha emission at zsimilar to2.15, one being a QSO as indicated by the broadness of its emission line. The velocity dispersion of the emitters (360 km s(-1)) is significantly smaller than that of the narrow band filter used for their selection (1600 km s(-1)). We therefore conclude that the emitters are associated with the radio galaxy. The star formation rates (SFRs) deduced from the Ha flux are in the range 6-44 M-circle dot yr(-1) 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.