Protoclusters associated with

We present the results of a large program conducted with the Very Large Telescope and augmented by observations with the Keck telescope to search for forming clusters of galaxies near powerful radio galaxies at $2.0 < z < 5.2$. Besides MRC 1138-262 at $z = 2.16$, the radio galaxy observed in our pilot program, we obtained narrow- and broad-band images of eight radio galaxies and their surroundings. The imaging was used to select candidate Lyα emitting galaxies in ~$3\times3$ Mpc2 areas near the radio galaxies. A total of 300 candidate emitters were found with a rest-frame Lyα equivalent width of EW$_0 > 15$ Å and significance $\Sigma \equiv {\it EW}_0/\Delta {\it EW}_0 > 3$. Follow-up spectroscopy was performed on 152 candidates in seven of the radio galaxy fields. Of these, 139 were confirmed to be Lyα emitters, four were low redshift interlopers and nine were non-detections. With the adopted criteria the success rate is $139/152 = 91$%. In addition, 14 objects with EW$_0 < 15$ and/or $\Sigma < 3$ were confirmed to be Lyα emitters. Combined with the 15 Lyα emitters near MRC 1138-262, we have determined Lyα redshifts for 168 objects near eight radio galaxies. At least six of our eight fields are overdense in Lyα emitters by a factor 3-5 as compared to the field density of Lyα emitters at similar redshifts, although the statistics in our highest redshift field ($z = 5.2$) are poor. 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 ($L_\mathrm{2.7\,GHz} > 10^{33}$ erg s-1 Hz-1 sr-1) high redshift radio galaxies reside in a protocluster. The protoclusters have sizes of at least 1.75 Mpc, which is consistent with the structure sizes found by other groups. By using the volume occupied by the overdensities and assuming a bias parameter of $b=3{-}6$, we estimate that the protoclusters have masses in the range $2{-}9 \times 10^{14}$ $M_{\odot}$. These protoclusters 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 $z\sim5$ 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