The XXL Survey. XLI. Radio AGN luminosity functions based on the GMRT
  $610 \ \mathrm{MHz}$ continuum observations
  We study the space density evolution of active galactic nuclei (AGN) using
the $610 \ \mathrm{MHz}$ radio survey of the XXL-North field, performed with
the Giant Metrewave Radio Telescope (GMRT). The survey covers an area of $30.4
\ \mathrm{deg}^2$, with a beamsize of $6.5 \ \mathrm{arcsec}$. The survey is
divided into two parts, one covering an area of $11.9 \ \mathrm{deg}^2$ with $1
\sigma$ rms noise of $200\ \mathrm{\mu Jy \ beam^{-1}}$ and the other spanning
$18.5 \ \mathrm{deg}^2$ with rms noise of $45\ \mathrm{\mu Jy \ beam^{-1}}$. We
extracted the catalog of radio components above $7 \sigma$. The catalog was
cross-matched with a multi-wavelength catalog of the XXL-North field (covering
about $80 \%$ of the radio XXL-North field) using a likelihood ratio method,
which determines the counterparts based on their positions and their optical
properties. The multi-component sources were matched visually with the aid of a
computer code: Multi-Catalog Visual Cross-Matching (MCVCM). A flux density cut
above $1\ \mathrm{mJy}$ selects AGN hosts with a high purity in terms of star
formation contamination based on the available source counts. After
cross-matching and elimination of observational biases arising from survey
incompletenesses, the number of remaining sources was $1150$. We constructed
the rest-frame $1.4 \ \mathrm{GHz}$ radio luminosity functions of these sources
using the maximum volume method. This survey allows us to probe luminosities of
$ 23 \lesssim \log(L_{1.4 \ \mathrm{GHz}}[\mathrm{W/Hz}]) \lesssim 28$ up to
redshifts of $z \approx 2.1$. Our results are consistent with the results from
the literature in which AGN are comprised of two differently evolving
populations, where the high luminosity end of the luminosity functions evolves
more strongly than the low-luminosity end.
