There is increasing support for the idea that BL Lacertae objects are dominated by beamed emission from a relativistic jet aligned with the line of sight. If so, the most likely parent (i.e., misaligned) objects are Fanaroff-Riley type I (F-R I) radio galaxies. We test this hypothesis by determining the ratio of number densities of the two populations in a manner appropriate for flux-limited samples. Through a direct comparison of predicted and observed luminosity functions, we show that available radio samples of F-R I galaxies and BL Lac objects are fully consistent with the beaming hypothesis. Our model makes specific predictions about the luminosity function of BL Lacertae objects and their radio counts below currently observed levels. A distribution of Lorentz factors is required, covering roughly the range 5 <~γ<~35 but skewed toward the low end. These Lorentz factors are higher than the estimate produced via a similar calculation for X-ray samples, although the different quality of the observational data in the two bands makes the significance of this increase hard to assess. Still, a relation between Lorentz factor and wavelength could be explained in conventional inhomogeneous jet models if the Lorentz factor increased along the jet. This is supported by the lower surface density of radio-selected BL Lac objects relative to X-ray-selected BL Lac objects seen directly In the observed counts.
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Urry et al. (1991) studied this question.