Luminosity function, sizes and FR dichotomy of radio-loud AGN

The radio luminosity function (RLF) of radio galaxies and radio-loud quasars is often modelled as a broken power law. The break luminosity is close to the dividing line between the two Fanaroff-Riley (FR) morphological classes for the large-scale radio structure of these objects. We use an analytical model for the luminosity and size evolution of FR type II (FR II) objects together with a simple prescription for FR type I (FR I) sources to construct the RLF. We postulate that all sources start out with a FR II morphology. Weaker jets subsequently disrupt within the quasi-constant density cores of their host galaxies and develop the turbulent lobes of FR I. With this model, we recover the slopes of the power laws and the break luminosity of the RLF determined from observations. The rate at which active galactic nuclei (AGN) with jets of jet power Q appear in the universe is found to be proportional to Q(-1.6). The model also roughly predicts the distribution of the radio lobe sizes for FR II objects, if the radio luminosity of the turbulent jets drops significantly at the point of disruption. We show that our model is consistent with recent ideas of two distinct accretion modes in jet-producing AGN if radiative efficiency of the accretion process is correlated with jet power.