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 α emitters with a rest-frame equivalent width of >15 A were selected in a ∼ 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 α emitters with redshifts similar to that of the radio galaxy, while the remaining two galaxies turned out to be [$\ion{O}{ii}$] emitters. The Ly α 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 α 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 $\ion{H}{i}$ mass of at least $2 \times 10^2 {-} 5 \times 10^4$ M $_{\odot}$. 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 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 α emission ($\beta \sim -1.09$). A large fraction of the confirmed emitters ( ∼ 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 α emitters ( ∼ 25%) were unresolved with upper limits on their half light radii of $r_{\rm h} ∼ 19%) show multiple clumps of emission, as does the radio galaxy, and the rest ( ∼ 56%) are single, resolved objects with $r_{\rm h} α emitters are on average smaller than LBGs. The average star formation rate of the Ly α emitters is 2.6 M $_{\odot}\;{\rm yr}^{-1}$ as measured by the Ly α emission line or M $_{\odot}\;{\rm yr}^{-1}$ as measured by the UV continuum. The properties of the Ly α galaxies (faint, blue and small) are consistent with young star forming galaxies which are still nearly dust free. The volume density of Ly α 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 α 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 (${\it FWHM} \sim 3500$ 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 α 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 $_{\odot}$ and could be the progenitor of a cluster of galaxies similar to e.g. the Virgo cluster.
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