Synchrotron emission from shocked relativistic jets. I - The theory of radio-wavelength variability and its relation to superluminal motion

Abstract

We summarize the theory of the transfer of polarized radiation in a synchrotron plasma of arbitrary optical depth, and the theory of plane shock waves with relativistic flow velocity and equation of state. We then describe the construction of a computer code that utilizes these theories to study the properties of the radiation from shocked, parsec-scale extragalactic jets. Runs of this code with "example" shock patterns show that both the appearance of superluminal VLBI sources and the characteristics of the total and polarized flux evolution of variable compact sources may be understood in terms of one shock, or a sequence of closely spaced shocks, propagating along a diverging flow. We argue that multiple-shock events may be a common feature of such sources. The interpretation of VLBI maps is discussed. We note that, in this model, the "core-knot" separation is frequency-dependent, the knot may sometimes be brighter than the core, and, because of the multiplicity of components, infrequent mapping can lead to apparent contractions and accelerations.