Ultra-relativistic bulk motion and radio flux variability of Active Galactic Nuclei

We have analysed 10 published prominent events of metre-wavelength flux variability associated with seven extragalactic radio sources in terms of the hypothesis that the variable components in these sources have a bulk relativistic motion and radiate by the incoherent synchrotron process. The Doppler factor for each variable component is derived by considering that synchrotron self-absorption effects limit the surface brightness of the component, which is assumed to be homogeneous and spherical in shape and to have a magnetic energy density not much lower than the energy density due to relativistic electrons (as expected on theoretical grounds). Lower limits to the Doppler factors thus estimated for our sample of 10 variability events have a median value of δ∼70. A similarly high median value of δ∼45 is estimated for a large sample comprising all 35 events of metre-wavelength flux variability reported for the 23 sources of known redshift covered in the Bologna monitoring programme. On the other hand, the same approach yields a median Doppler factor of only ∼3.5 for a sample of 11 prominent centimetre-wavelength variable sources, which is consistent with the Doppler factors inferred in the past from observations of superluminal motion and also from the observed lack of X-ray emission from variable radio sources. It is noted, however, that even at centimetre wavelengths a small number of events of ultra-rapid but relatively large (≳10 per cent) flux variation have been reported in literature. For eight such rare events, with a variability time-scale of ∼1 day, the minimum values of Doppler factor are again inferred to be very large (δ∼50).