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Observations of the radio galaxy MRC 0316-257 at z=3.13 and the surroundingfield are presented. Using narrow- and broad-band imaging obtained with theVLT, 77 candidate Ly-alpha emitters with a rest-frame equivalent width of > 15A were selected in a ~7'x7' field around the radio galaxy. Spectroscopy of 40candidate emitters resulted in the discovery of 33 emission line galaxies ofwhich 31 are Ly-alpha emitters with redshifts similar to that of the radiogalaxy, while the remaining two galaxies turned out to be [OII] emitters. TheLy-alpha profiles have widths (FWHM) in the range of 120-800 km/s, with amedian of 260 km/s. Where the signal-to-noise was large enough, the Ly-alphaprofiles were found to be asymmetric, with apparent absorption troughs bluewardof the profile peaks, indicative of absorption along the line of sight of an HImass of at least 2x10^2 - 5x10^4 M_sun. The properties of the Ly-alpha galaxies(faint, blue and small) are consistent with young star forming galaxies whichare still nearly dust free. The volume density of Ly-alpha emitting galaxies inthe field around MRC 0316-257 is a factor of 3.3+0.5-0.4 larger compared withthe density of field Ly-alpha emitters at that redshift. The velocitydistribution of the spectroscopically confirmed emitters has a FWHM of 1510km/s, which is substantially smaller than the width of the narrow-band filter(FWHM ~ 3500 km/s). The peak of the velocity distribution is located within 200km/s of the redshift of the radio galaxy. We conclude that the confirmedLy-alpha emitters are members of a protocluster of galaxies at z~3.13. The sizeof the protocluster is larger than 3.3x3.3 Mpc^2. The mass of this structure isestimated to be > 3-6x10^14 M_sun and could be the progenitor of a cluster ofgalaxies similar to e.g. the Virgo cluster. (Abridged)Comment: 23 Pages, including 20 PostScript figures. Publiced in Astronomy &  Astrophysics. v2: typo fixed and Journal reference adde

Properties of Lyα emitters around the radio galaxy MRC 0316–257