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.

We study the distributions of $\gamma$-ray properties of a sample of $\gamma$-ray loud blazars taken from the third catalogue of blazars detected by Fermi-Large Area Telescope (Fermi-LAT).We compute the $\gamma$-ray dominance ($D_{\rm g}$) of the sample which includes 415 flat spectrum radio quasars (FSRQs) and 535 BL Lacertae objects (BL Lacs). We find that BL Lacs and FSRQs are highly dominated by $\gamma$-ray emission, which is consistent with diffuse high-energy neutrino flux associated with $\gamma$-ray loud blazars. The $\gamma$-ray dominance fairly scales with $\gamma$-ray luminosity ($r \sim +0.5$) in both BL Lacs and FSRQs, but shows little or no correlation ($r \leq 0.2$) with radio luminosity in either sample. BL Lacs and FSRQs occupy separate and parallel regions on the $D_{\rm g}$-luminosity plane. There is a fairly significant correlation ($r \sim 0.5$) between $\gamma$-ray dominance and frequency at synchrotron peak ($\nu_{\rm pk}$) in BL Lacs, which disappears in FSRQs. On the other hand, there is a tight correlation ($r \geq +0.8$) between $\gamma$-ray and radio luminosity with a smooth transition from BL Lacs at low luminosities to FSRQs at high luminosities. Nevertheless, the presence of few BL Lac-like FSRQs is noted. These results suggest that while there may be intrinsic differences between BL Lacs and FSRQs, some form of a unified scheme can also be relevant.