Observations of the radio galaxy MRC 0316–257 at z = 3.13 and the surrounding field are presented .
Using narrow- and broad-band imaging obtained with the VLT , 77 candidate Ly \alpha emitters with a rest-frame equivalent width of > 15 Å were selected in a \sim 7 ′ \times 7 ′ field around the radio galaxy .
Spectroscopy of 40 candidate emitters resulted in the discovery of 33 emission line galaxies of which 31 are Ly \alpha emitters with redshifts similar to that of the radio galaxy , while the remaining two galaxies turned out to be [ O ii ] emitters .
The Ly \alpha profiles have widths ( FWHM ) in the range of 120–800 km s ^ { -1 } , with a median of 260 km s ^ { -1 } .
Where the signal-to-noise was large enough , the Ly \alpha profiles were found to be asymmetric , with apparent absorption troughs blueward of the profile peaks , indicative of absorption along the line of sight of an H i mass of at least 2 \times 10 ^ { 2 } -5 \times 10 ^ { 4 } M _ { \sun } .
Besides that of the radio galaxy and one of the emitters that is a QSO , the continuum of the emitters is faint , with luminosities ranging from 1.3 L ^ { * } to < 0.03 L ^ { * } .
The colors of the confirmed emitters are , on average , very blue .
The median UV continuum slope is \beta = -1.76 , bluer than the average slope of LBGs with Ly \alpha emission ( \beta \sim - 1.09 ) .
A large fraction of the confirmed emitters ( \sim 2 / 3 ) have colors consistent with that of dust-free starburst galaxies .
Observations with the Advanced Camera for Surveys on the Hubble Space Telescope show that the emitters that were detected in the ACS image have a range of different morphologies .
Four Ly \alpha emitters ( \sim 25 % ) were unresolved with upper limits on their half light radii of r _ { h } < 0.6 - 1.3 kpc , three objects ( \sim 19 % ) show multiple clumps of emission , as does the radio galaxy , and the rest ( \sim 56 % ) are single , resolved objects with r _ { h } < 1.5 kpc .
A comparison with the sizes of Lyman break galaxies at z \sim 3 suggests that the Ly \alpha emitters are on average smaller than LBGs .
The average star formation rate of the Ly \alpha emitters is 2.6 M _ { \sun } yr ^ { -1 } as measured by the Ly \alpha emission line or < 3.9 M _ { \sun } yr ^ { -1 } as measured by the UV continuum .
The properties of the Ly \alpha galaxies ( faint , blue and small ) are consistent with young star forming galaxies which are still nearly dust free .

The volume density of Ly \alpha emitting galaxies in the field around MRC 0316–257 is a factor of 3.3 ^ { +0.5 } _ { -0.4 } larger compared with the density of field Ly \alpha emitters at that redshift .
The velocity distribution of the spectroscopically confirmed emitters has a dispersion of 640 km s ^ { -1 } , corresponding to a FWHM of 1510 km s ^ { -1 } , which is substantially smaller than the width of the narrow-band filter ( FWHM \sim 3500 km s ^ { -1 } ) .
The peak of the velocity distribution is located within 200 km s ^ { -1 } of the redshift of the radio galaxy .
We conclude that the confirmed Ly \alpha emitters are members of a protocluster of galaxies at z \sim 3.13 .
The size of the protocluster is unconstrained and is larger than 3.3 \times 3.3 Mpc ^ { 2 } .
The mass of this structure is estimated to be > 3–6 \times 10 ^ { 14 } M _ { \sun } and could be the progenitor of a cluster of galaxies similar to e.g .
the Virgo cluster .