The XXL Survey: IX. Optical overdensity and radio continuum analysis of
  a supercluster at $z=0.43$
  We present observations with the Karl G. Jansky Very Large Array (VLA) at 3
GHz toward a sub-field of the XXL-North 25 deg$^{2}$ field targeting the first
supercluster discovered in the XXL Survey. The structure has been found at a
spectroscopic redshift of 0.43 and extending over $0.35\times0.1$ deg$^{2}$ on
the sky. We present the 3 GHz VLA radio continuum observations, the radio
mosaic and radio source catalogue, and, perform an analysis of the supercluster
in the optical and radio regimes using photometric redshifts from the CFHTLS
survey and our new VLA data. Our 3 GHz radio mosaic has a resolution of
$3.2\times1.9$ arcsec$^2$, and covers an area of $41\times41$ arcmin$^2$ with
rms noise level below $\sim20 \mu$Jy beam$^{-1}$ ($\sim11\mu$Jy beam$^{-1}$ in
central $15\times15$ arcmin$^2$). We extract a catalogue of 155 radio sources
$\geq6\sigma$, 8 of which are multicomponent sources, and 123 ($79\%$) can be
associated with optical sources in the CFHTLS W1 catalogue. Applying Voronoi
tessellation analysis (VTA) in the area around the X-ray identified
supercluster we identify a total of 17 overdensities at $z=0.35-0.50$, 7 of
which are associated with clusters detected in the $XMM-Newton$ XXL data. We
find a mean photometric redshift of 0.43 for our overdensities, consistent with
the spectroscopic redshifts of 7 X-ray detected clusters. The full
VTA-identified structure extends over $\sim0.6\times0.2$ deg$^2$ on the sky,
($\sim12\times4$ Mpc$^{2}$ at $z=0.43$). We associate 8 radio sources with
potential group/cluster member galaxies none of which are large radio galaxies.
The spatial distribution of the red and blue potential group member galaxies
suggests that the clusters are dynamically young and not virialised yet, as
expected for hierarchical structure growth in a $\Lambda$CDM universe. Further
spectroscopic data are required to analyze the dynamical state of the groups.
