The influence of the jet opening angle on the appearance of relativistic jets

Abstract : We reinvestigate the problem of the appearance of relativistic jets when geometrical opening is taken into account. We propose a new criterion to define apparent velocities and Doppler factors, which we think being determined by the brightest zone of the jet. We numerically compute the apparent velocity and the Doppler factor of a non-homokinetic jet using different velocity profiles. We argue that if the motion is relativistic, the high superluminal velocities β_app≃γ, expected in the case of a homokinetic jet, are only possible for geometrical collimation smaller than the relativistic beaming angle γ^-1. This is relatively independent of the jet velocity profile. For jet collimation angles larger than γ^-1, the apparent image of the jet will always be dominated by parts of the jet travelling directly towards the observer at Lorentz factors <γ resulting in maximal apparent velocities smaller than γ. Furthermore, getting rid of the homokinetic hypothesis yields a complex relation between the observing angle and the Doppler factor, resulting in important consequences for the numerical computation of the active galactic nucleus population and unification scheme model.