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. 
B. P. Venemans (1,2), H. J. A. Rottgering (1), G. K. Miley (1), W. J.   M. van Breugel (3,8), C. De Breuck (4), J. D. Kurk (...