Counting quasar--radio source pairs to derive the millijansky radio luminosity function and clustering strength to z=3.5

We apply a cross-correlation technique to infer the $S>3$mJy radio luminosity function (RLF) from the NRAO VLA sky survey (NVSS) to $z\sim3.5$. We measure $\Sigma$ the over density of radio sources around spectroscopically confirmed quasars. $\Sigma$ is related to the space density of radio sources at the distance of the quasars and the clustering strength between the two samples, hence knowledge of one constrains the other. Under simple assumptions we find $\Phi\propto (1+z)^{3.7\pm0.7}$ out to $z\sim2$. Above this redshift the evolution slows and we constrain the evolution exponent to $<1.01$ ($2\sigma$). This behaviour is almost identical to that found by previous authors for the bright end of the RLF potentially indicating that we are looking at the same population. This suggests that the NVSS is dominated by a single population; most likely radio sources associated with high-excitation cold-mode accretion. Inversely, by adopting a previously modelled RLF we can constrain the clustering of high-redshift radio sources and find a clustering strength consistent with $r_0=15.0\pm 2.5$ Mpc up to $z\sim3.5$. This is inconsistent with quasars at low redshift and some measurements of the clustering of bright FRII sources. This behaviour is more consistent with the clustering of lower luminosity radio galaxies in the local universe. Our results indicate that the high-excitation systems dominating our sample are hosted in the most massive galaxies at all redshifts sampled.