Annu. Rev. Astron. Astrophys. 1999. 37: 409-443
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4.3. Doppler Boosting

The ratios of observed to emitted flux density S0, from a twin pair of optically-thin, isotropically emitting jets are:

Equation 8 (8)

Equation 9 (9)

where alpha is the spectral index of the emission (S propto nu), and k is a parameter that accounts for the geometry of the ejecta, with k = 2 for a continuous jet and k = 3 for discrete condensations. Then, the ratio of observed flux densities (measured at equal separations from the core) will be given by

Equation 10 (10)

Since for the 1994 March 19 event beta cos theta = 0.323 and alpha = -0.8 the flux ratio in the case of discrete condensations would be 12, whereas for a continuous jet it would be 6. For a given angular separation it was found that the observed flux ratio between the approaching and receding condensations is 8 ± 1. Similar results were found using the MERLIN observations by Fender et al (1999). Therefore, irrespective of the distance to the source, the flux ratios for equal angular separations from the core are consistent with the assumption of a twin ejection at relativistic velocities. Atoyan & Aharonian (1997) have considered the observable effects in the flux density ratio of asymmetries between the jet and counterjet. Bodo & Ghisellini (1995) have proposed that there could be a contribution of wave propagation in the pattern motions, but that most of the observed displacements are true bulk plasma velocities.

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