Role of the acceleration in relativistically expanding objects and its significance for the intensity variations in quasi-stellar sources

Abstract

Rees has discussed the appearance of relativistically expanding objects as seen by distant observers, with a view to explaining the variation of flux from radio sources. There he considers a spherical shell expanding with a uniform radial velocity v~c. The apparent radius of the source at time t₀, measured from the moment when the expansion is seen to begin, is γvt₀, where γ=(1−v²/c²)^−½. The Doppler blue-shift, measured as the ratio of frequency observed to frequency emitted, varies from γ on the limb to γ[1+v/c] in the centre. The effect of special relativity in Rees's model is to cut down the apparent time scales, in the cases where γv is greater than c. The actual variation of flux is obtained from an astrophysical model. Such a model might work for radio variations, but not for optical variations of quasi-stellar sources.