Luminosity functions, relativistic beaming, and unified theories of high-luminosity radio sources

Abstract

If relativistically beamed emission dominates the observed radio flux from flat-spectrum radio quasars, as suggested by their rapid variability, polarization, and superluminal motion, then there must be counterpart sources whose emission is beamed at larger angles to the line of sight. We evaluate such unified schemes quantitatively, with steep-spectrum radio quasars and high-luminosity radio galaxies constituting the misaligned sources. Our procedure compares the number densities and luminosities of the separate populations, taking into account the strong selection effects introduced by relativistic beaming. First, we derive the local luminosity functions of high-luminosity (i.e., Fanaroff-Riley type II) radio galaxies, flat-spectrum quasars, and steep-spectrum quasars. Then we calculate the luminosity functions predicted by a relativistic beaming model and compare them to the observed ones. We find very good agreement both for flat- and steep-spectrum quasars for a distribution of Lorentz factors 5 ≲ γ ≲ 40 (skewed toward lower values) that was estimated from the observed distribution of superluminal speeds for flat-spectrum quasars. Our model predicts that flat-spectrum quasars have their radio axes within θ ∼ 14° of the line of sight, steep-spectrum quasars are in the range 14° ≲ θ ≲ 40°, and high-luminosity radio galaxies occupy the remaining angles. The alternative hypothesis that flat-spectrum quasars are simply the beamed version of steep-spectrum ones, with Fanaroff-Riley type II radio galaxies belonging to a separate class, does not give as good a fit to the data.