Apparent superluminal expansion velocities in the dipole magnetic field model

Abstract

VERY long baseline interferometry (VLBI) observations of compact radio sources have shown that the components of some radio sources seem to move apart with relative velocities more than twice the speed of light. These observations and many interpretations have been reviewed by Cohen et al.¹ and Blanford et al.². Sanders has presented a model for compact extragalactic radio sources in which apparent superluminal expansion arises naturally. In this model, radiating particles move at relativistic velocities along dipole magnetic field lines. Sanders discusses the relationship of this proposal to other explanations of superluminal velocities in compact radio sources. However, he incorrectly evaluated the consequences of the dipole field model, obtaining results both for the magnitude of the expansion velocity and its time dependence that are in conflict with observations. We present here the valid geometrical consequences of the model, show that they agree with available observations, and make some additional predictions. A detailed derivation of the equations used here, the plasma-physics aspects of the model, and the possible relation to extended radio sources will be discussed in detail elsewhere.