In this paper, we investigate the relativistic beaming effects in a well-defined sample of core-dominated quasars using the correlation between the relative prominence of the core with respect to the extended emission (defined as the ratio of core-to lobe-flux density measured in the rest frame of the source) and the projected linear size as an indicator of relativistic beaming and source orientation. Based on the orientation-dependent relativistic beaming and unification paradigm for high luminosity sources in which the Fanaroff-Riley class-II radio galaxies form the unbeamed parent population of both the lobe- and core-dominated quasars which are expected to lie at successively smaller angles to the line of sight, we find that the flows in the cores of these core-dominated quasars are highly relativistic, with optimum bulk Lorentz factor,γ_opt∼ 6–16, and also highly anisotropic, with an average viewing angle, ∼ 9°–16°. Furthermore, the largest boosting occurs within a critical cone angle of ≈ 4°–10°.

We use the correlation between the core-to-lobe radio luminosity ratio (𝑅) and the linear size (𝐷) of a sample of BL Lacertae objects to investigate the relativistic beaming and radio source orientation paradigm for high peaked and low-peaked BL Lacs (X-ray and radio selected BL Lacs respectively) and to constrain relativistic beaming model for this extreme class of active galactic nuclei. We show that the 𝑅 - 𝐷 distributions of the BL Lac populations contradict blazar orientation sequence, with the X-ray selected BL Lacs (XBLs) being more consistent with the beaming and orientation model. On the premise that Fanaroff-Riley Type I radio galaxies are the unbeamed parent population of these objects, we derive the bulk Lorentz factor of the jets, 𝛾 ∼ 7-20 corresponding to a critical cone angle for optimum boosting, 𝜙_c of ∼ 1° - 4°, while on average, these objects are inclined at 5° - 12° to the line-of-sight. The implications of these results for the blazar unification sequence are discussed.

We have presented an alternative interpretation for the absence of correlation in the relationship between the core radio power (𝑃_C) and core-dominance parameter (𝑅) for a sample of BL Lacs and radio galaxies found in Fan & Zhang (Astron. Astrophys. 407, 899 (2003)). This is contrary to the predictions of the relativistic beaming and radio source orientation models in which the core luminosity is expected to be Doppler-boosted relative to the extended luminosity which is generally assumed to be isotropic. Our analysis of the 𝑃_C - 𝑅 data indicates a strong luminosity selection effect (reminiscent of bright source samples due to Malmquist bias) in the sample. In particular, we showed that a strong 𝑃_C - 𝑅 correlation exists above some redshift cut-off which may correspond to the flux limit of the sample used.

We utilize the distributions of fractional separation difference (𝑥) as asymmetry parameter, linear size (𝐷) and core-to lobe luminosity ratio (𝑅) as orientation indicators, to investigate a consequence of radio source orientation and relativistic beaming effects in a sample of powerful non-symmetric extragalactic radio sources. In this scenario, radio sources viewed at small orientation angles to the line-of-sight are expected to show a high degree of asymmetry in observed radio structures due to relativistic beaming, with foreshortened projected linear sizes. A simple consequence of this is the 𝑥 - 𝐷 anti-correlation. Results show a tight correlation (𝑟 > 0.8) between the total and core radio luminosities and a clear 𝑥 - 𝐷 anti-correlation (𝑟 ∼ -0.5). The observed 𝑥 - 𝐷 anti-correlation is consistent with average orientation angle 𝜙 ≈ 48° and a maximum Lorentz factor 𝛾 ∼ 2 for the sample, with minimum angular separation of 26° between radio galaxies and quasars. However, there is no clear 𝑥 - 𝑅 correlation. While the results are consistent with quasar/galaxy unification via orientation, intrinsic asymmetry also seems to play a major role.

In this paper, we use the distributions of luminosity ($P$) and radio size ($D$) to re-examine the consistency of the unified scheme of high-excitation radio galaxies and quasars in the recently updated 3CRR sample. Based on a standard cosmology, we derive theoretically and show from observed data, the luminosity limit above which the 3CRR objects are well-sampled. We find, on average, a quasar fraction $\sim$0.44 and galaxy-to-quasar size ratio $\approx$2. Assuming a relativistic outflow of jet materials, we find a mean angle to the line of sight in the range 35$^{\circ} \leq \phi \leq 44^{\circ}$ for the quasars. On supposition of luminosity and orientation-dependent linear size evolution, expressed in a general functional form $D_{\rm (P,z,\phi)} \approx P^{\pm q}(1+z)^{−w} \sin \phi$, we show that above the flux detection threshold of the 3CRR sample, high-excitation galaxies and quasars undergo similar evolutionwith $q = −0.5$; $w = −0.27$ and luminosity independent evolution parameter $x = 2.27$, when orientation effect is accounted for. The results are consistent with orientation-based unified scheme for radio galaxies and quasars.