Influence of the jet opening angle on the derived kinematical parameters of blazar jets having uniform and stratified bulk motion

TL;DR

This study analytically models conical relativistic jets to understand how the jet opening angle influences key observed parameters like orientation, apparent speed, and Doppler factor, especially in ultra-relativistic blazar jets.

Contribution

It provides a comparative analysis of the impact of jet opening angles on kinematical parameters for uniform and stratified jet velocity profiles.

Findings

Jet orientation angle decreases with increasing Lorentz factor but stabilizes at a fraction of the opening angle.

Apparent speeds and Doppler factors decline with larger opening angles, especially in ultra-relativistic jets.

Highly relativistic, less collimated jets may explain the scarcity of superluminal components in TeV blazars.

Abstract

We present analytical modelling of conical relativistic jets, in order to evaluate the role of the jet opening angle on certain key parameters that are inferred from VLBI radio observations of blazar nuclear jets. The key parameters evaluated are the orientation angle (i.e., the viewing angle) of the jet and the apparent speed and Doppler factor of the radio knots on parsec scales. Quantitative comparisons are made of the influence of the jet opening angle on the above parameters of the radio knots, as would be estimated for two widely discussed variants of relativistic nuclear jets, namely, those having uniform bulk speed and those in which the bulk Lorentz factor of the flow decreases with distance from the jet axis (a `spine--sheath' flow). Our analysis shows that for both types of jet velocity distributions the expectation value of the jet orientation angle at first falls dramatically with increases in the (central) jet Lorentz factor, but it levels off at a fraction of the opening angle for extremely relativistic jets. We also find that the effective values of the apparent speeds and Doppler factors of the knots always decline substantially with increasing jet opening angle, but that this effect is strongest for ultra-relativistic jets with uniform bulk speed. We suggest that the paucity of highly superluminal parsec-scale radio components in TeV blazars can be understood if their jets are highly relativistic and, being intrinsically weaker, somewhat less well collimated, in comparison to the jets in other blazars.