2025MNRAS.544.1779P

We present new methods to quantify the active galactic nucleus (AGN) population in terms of a multidimensional luminosity function that describes the space density of sources as a function of both X-ray and radio luminosity. We compile a sample of 1538 radio and X-ray detected extragalactic sources from the Boötes and COSMOS fields. First, we investigate the X-ray-radio luminosity correlation in the sample and find that an apparent correlation is introduced due to the sensitivity limits of the surveys; when considering individual redshift bins we find a wide range of radio luminosities associated with a given X-ray luminosity, and vice versa, indicating little direct connection between the emission processes. We then measure the X-ray luminosity function, radio luminosity function and multidimensional X-ray-radio luminosity function across redshift (0 < z < 6). We apply luminosity thresholds in X-ray and radio to restrict our sample to those in the AGN-dominated regime and explore how the fraction of radio-selected AGNs within the overall X-ray sample varies with increasing X-ray luminosity (and vice versa). We find that towards the highest X-ray and radio luminosities the fraction of sources with both an X-ray and radio detection increases towards 100 per cent, indicating that at the highest luminosities we are more likely to obtain a detection in both bands, though the source will not necessarily be bright in both bands. Thus, the most luminous accretion events are more likely to be associated with the production of a jet, despite the distinct physical structures that produce the emission and likely persist over very different time-scales.