The optically-selected 1.4-GHz quasar luminosity function below 1 mJy
We present the radio luminosity function (RLF) of optically-selected quasars below 1~mJy, constructed by applying a Bayesian-fitting stacking technique to objects well below the nominal radio flux-density limit. We test the technique using simulated data, confirming that we can reconstruct the RLF over three orders of magnitude below the typical $5σ$ detection threshold. We apply our method to 1.4-GHz flux-densities from the Faint Images of the Radio Sky at Twenty-cm survey (FIRST), extracted at the positions of optical quasars from the Sloan Digital Sky Survey (SDSS) over seven redshift bins up to $z=2.15$ {and measure the RLF down to two orders of magnitude below the FIRST detection threshold}. In the lowest redshift bin ($0.2<z<0.45$), we find that our measured RLF agrees well with deeper data from the literature. The RLF for the radio-loud quasars flattens below $\log_{10}[L_{1.4}/{\rm W\,Hz}^{-1}] \approx 25.5$ and becomes steeper again below $\log_{10}[L_{1.4}/{\rm W\,Hz}^{-1}] \approx 24.8$, where radio-quiet quasars start to emerge. The radio luminosity where radio-quiet quasars emerge coincides with the luminosity where star-forming galaxies are expected to start to dominate the radio source counts. This implies that there could be a significant contribution from star formation in the host galaxies, but additional data is required to investigate this further. The higher-redshift bins show a similar behaviour as for the lowest-$z$ bin, implying that the same physical process may be responsible.