On the radio luminosity distribution of active galactic nuclei and the black hole fundamental plane

We have studied the dependence of the nuclear radio (1.4 GHz) luminosity of active galactic nuclei (AGN) on both 2-10 keV X-ray and host-galaxy K-band luminosities. A complete sample of 1268 X-ray-selected AGN (both type 1 and type 2) has been used, which is the largest catalogue of AGN belonging to statistically well-defined samples where radio, X-ray and K-band information exists. At variance with previous studies, radio upper limits have been taken into account statistically using a Bayesian maximum-likelihood fitting method. A good fit is obtained assuming a plane in 3D L-R-L-X-L-K space, namely log L-R = xi(X) log L-X + xi(K) log L-K + xi(0), with a similar to 1 dex wide (1 sigma) spread in radio luminosity. As already shown by La Franca, Melini & Fiore, no evidence of bimodality in the radio luminosity distribution was found and therefore any definition of radio-loudness in AGN is arbitrary. Using scaling relations between the black hole (BH) mass and the host galaxy K-band luminosity, we have also derived a new estimate of the BH fundamental plane (in L-5 (GHz)-L-X-M-BH space). Our analysis shows that previous measures of the BH fundamental plane are biased by similar to 0.8 dex in favour of the most luminous radio sources. Therefore, many AGN studies, where the BH fundamental plane is used to investigate how AGN regulate their radiative and mechanical luminosity as a function of the accretion rate, and many AGN/galaxy co-evolution models, where radio feedback is computed using the AGN fundamental plane, should revise their conclusions.