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© 2005 American Association of Physics Teachers. We derive an expression for the velocity valid for the currently favored cosmological model: a flat universe with a nonzero cosmological constant. The apparent velocity of a source can be estimated from its redshift and proper motion using the values of the Hubble constant and the mean densities of different energy components in the universe. There is a positive correlation (correlation coefficient r0.45) between the flux density of the VLBI core and the -ray flux and a moderate correlation (partial correlation coefficient r0.31) between -ray apparent luminosity and superluminal velocities of jet components, as expected if the -ray emission originates in a very compact. The cause of this reduction is recession of the distant source due to the expansion of the universe. The apparent velocity of the source is reduced by a factor of 1+z compared to that of a similar nearby source.
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The cosmological expanding effect would play no part in the superluminal motion of radio galaxies, BL Lacertae objects as well as quasars. We derive the prediction of the standard model of superluminal radio sources for the apparent transverse velocity of a radio source located at redshift z. Apparent superluminal motion of different radio-loud AGNs are similarly related with beaming effect. Apparent speeds comparable with the maximum yvsyc should occur only if 8 1/y, i.e. Superluminal apparent motions in distant radio sources Superluminal apparent motions in distant radio sources EXPLANATIONS OF SUPERLUMINAL MOTION 199 This has been the favourite model ever since the one-sided VLBI structure (Item B) was discovered, and was worked out in considerable depth by Blandford and Konigl (1979).