Modelling radio luminosity functions of radio-loud AGN by the cosmological evolution of supermassive black holes

Aims. We develop a formalism to model the luminosity functions (LFs) of radio-loud active galactic nuclei (AGN) at GHz frequencies by the cosmological evolution of the supermassive black hole (SMBH) hosted in their nuclei. The mass function and Eddington ratio distributions of SMBHs computed in a previous work published by one of the authors have been taken as the starting point for this analysis. Methods. Our approach is based on physical and phenomenological relations that allow us to statistically calculate the radio luminosity of AGN cores, corrected for beaming effects, by linking it with the SMBH at their centre, through the fundamental plane of black hole activity. Moreover, radio luminosity from extended jets and lobes is also computed through a power-law relationship that reflects the expected correlation between the inner radio core and the extended jets and lobes. By following a classification scheme well established in the field, radio-loud AGN are further divided into two classes, characterized by different accretion modes onto the central BH. If the Eddington ratio, λ, is ≤0.01 they are called low-kinetic (LK) mode AGN; if λ ≥ 0.01, they are called high-kinetic (HK) mode AGN, this critical value roughly corresponding to the transition between radiatively inefficient and efficient accretion flows. The few free parameters used in the present model are determined by fitting two different types of observational data sets: local (or low-redshift) LFs of radio-loud AGN at 1.4 GHz and differential number counts of extragalactic radio sources at 1.4 and 5 GHz. Results. Our present model fits well almost all published data on LFs of LK mode AGN and of the total AGN population up to redshifts z ≤ 1.5 and also in the full range of luminosities currently probed by data. On the other hand, it tends to underestimate some recent measures of the LF of HK mode AGN at low redshifts, but only at low radio luminosities. All in all, the good performance of our model in this redshift range is remarkable, considering that all the free parameters used but the fraction of HK mode AGN are redshift independent. The present model is also able to provide a very good fit to almost all data on number counts of radio-loud sources at 1.4 and 5 GHz