Parabolic jet shape on parsec scales in high redshift AGN

Geometry of relativistic jets in active galaxies provides important information about mechanisms of launching, collimation and acceleration of plasma flow. We propose a new method to probe a boundary shape of a jet on parsec scales -- in the vicinity of its radio core. Apparent speed of an outflow is derived from variability time delays and core shifts measured at the same jet region, providing a self-consistent estimate of the Lorentz factor $\Gamma$. We link together the distance along the jet $z$ with its transverse size assuming a constant flow acceleration. Our results indicate that jets have parabolic shape and sustain an effective acceleration in the core region, consistent with the Lorentz factor dependency $\Gamma\propto z^{0.5}$. The proposed method can be applied to the sources observed at small viewing angles as well as to the distant sources when direct measurements are impossible due to a limited angular resolution.