Abstract
A simple analytical model is formulated to study beam dynamics in powerful extragalactic radio sources. Two phases are considered for the beam propagation: first through the gaseous halo of the parent galaxy, and then through a much hotter intergalactic medium (IGM). These two media are conceived to be pressure-matched at their interface, which is expected to move closer to the parent galaxy with increasing redshift, owing to a steeply rising IGM pressure. It is argued that the advance of the beam can be ignored quantitatively (notwithstanding a continuing nuclear activity) once its rate has become subsonic relative to the ambient medium. For the input parameters to the model typical values for a powerful radio source, its associated X-ray emitting halo, and the IGM are adopted, and it is shown that the model can explain in a fairly natural way the observed linear sizes of the sources at small redshifts and also their cosmological evolution. The possible relevance of the model to the reported prevalence of subgalactic-sized sources at very high redshifts (z greater than about 2) is also discussed.
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