Protoclusters associated with z > 2 radio galaxies. I. Characteristics of high redshift protoclusters

[Abridged] We present the results of a large program conducted with the Very Large Telescope and Keck telescope to search for forming clusters of galaxies near powerful radio galaxies at 2.0 < z < 5.2. We obtained narrow- and broad-band images of nine radio galaxies and their surroundings. The imaging was used to select candidate Lyman alpha emitting galaxies in ~3x3 Mpc^2 areas near the radio galaxies. A total of 337 candidate emitters were found with a rest-frame Lyman alpha equivalent width of EW_0 > 15 A and Sigma = EW_0/Delta EW_0 > 3. Follow-up spectroscopy confirmed 168 Lyman alpha emitters near eight radio galaxies. The success rate of our selection procedure is 91%. At least six of our eight fields are overdense in Lyman alpha emitters by a factor 3-5. Also, the emitters show significant clustering in velocity space. In the overdense fields, the width of the velocity distributions of the emitters is a factor 2-5 smaller than the width of the narrow-band filters. Taken together, we conclude that we have discovered six forming clusters of galaxies (protoclusters). We estimate that roughly 75% of powerful (L_2.7GHz > 10^33 erg/s/Hz/sr) high redshift radio galaxies reside in a protocluster, with a sizes of at least 1.75 Mpc. We estimate that the protoclusters have masses in the range 2-9 x 10^14 Msun and they are likely to be progenitors of present-day (massive) clusters of galaxies. For the first time, we have been able to estimate the velocity dispersion of cluster progenitors from z~5 to ~2. The velocity dispersion of the emitters increases with cosmic time, in agreement with the dark matter velocity dispersion in numerical simulations of forming massive clusters.