Jet evolution, flux ratios, and light-travel time effects

Studies of the knotty jets in both quasars and microquasars frequently make use of the ratio of the intensities of corresponding knots on opposite sides of the nucleus to infer the product of the intrinsic jet speed (beta(jet)) and the cosine of the angle that the jet axis makes with the line of sight (cos theta), via the formalism I-a/I-r [(1 + beta(jet) cos theta)/(1 - beta(jet) cos theta)](3+alpha), where alpha relates the intensity I-nu as a function of frequency nu as I-nu proportional to nu(-alpha). In the cases in which beta(jet) cos theta is determined independently, it is found that the intensity ratio of a given pair of jet to counterjet knots is overpredicted by the above formalism compared with that actually measured from radio images. As an example, in the case of the microquasar Cygnus X-3, the original formalism predicts an intensity ratio of similar to185, whereas the observed ratio at one single epoch is similar to3. Mirabel & Rodriguez have presented a refined approach to the original formalism that involves measuring the intensity ratio of knots when they are at equal angular separations from the nucleus. This method is, however, only applicable where there is sufficient time- sampling (with sufficient physical resolution) of the fading of the jet-knots so that interpolation of their intensities at equal distances from the nucleus is possible. It can therefore be difficult to apply to microquasars and is impossible to apply to quasars. We demonstrate that inclusion of two indisputable physical effects, (1) the light- travel time between the knots and (2) the simple evolution of the knots themselves (e. g., via adiabatic expansion), reconciles this overprediction (in the case of Cygnus X-3 quoted above, an intensity ratio of similar to3 is predicted) and renders the original formalism obsolete.