The Distribution Function of True Sizes and Ages of Powerful Double Radio Sources. 1. Theory.

Astronomy and Astrophysics – Astronomy

Scientific paper

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Scientific paper

Two integral equations are derived for the distribution function of true sizes and ages of the classical double radio sources in an intrinsically symmetrical model, by using the distribution functions of known parameters that depend on the projected distances of the hotspots from the central engine. An analytical solution for the first equation is obtained, while the second equation can be evaluated using the Fredholm integral of the first kind; an isotropic orientation distribution of the radio axes is assumed. Simple analytical relations are derived for the initial moments of the true and observed distribution functions, and so the average true size,velocity and age of classical double radio sources, and the dispersion in these quantities are estimated. The solutions are considered in the light of a unified scheme, allowing us to make a new estimate of the viewing angle that separates quasars from radio galaxies.

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