Opacity, variability and kinematics of AGN jets

Synchrotron self-absorption in active galactic nuclei (AGN) jets manifests itself as a time delay between flares observed at high and low radio frequencies. It is also responsible for the observing frequency dependent change in size and position of the apparent base of the jet, aka the core shift effect, detected with very long baseline interferometry (VLBI). We measure the time delays and the core shifts in 11 radio-loud AGN to estimate the speed of their jets without relying on multi-epoch VLBI kinematics analysis. The 15$-$8 GHz total flux density time lags are obtained using Gaussian process regression, the core shift values are measured using VLBI observations and adopted from the literature. A strong correlation is found between the apparent core shift and the observed time delay. Our estimate of the jet speed is higher than the apparent speed of the fastest VLBI components by the median coefficient of 1.4. The coefficient ranges for individual sources from 0.5 to 20. We derive Doppler factors, Lorentz factors and viewing angles of the jets, as well as the corresponding de-projected distance from the jet base to the core. The results support evidence for acceleration of the jets with bulk motion Lorentz factor $\Gamma\propto R^{0.52\pm0.03}$ on de-projected scales $R$ of 0.5$-$500 parsecs.