Annu. Rev. Astron. Astrophys. 1981. 19: 373-410
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4.2 Implications of the Observed Flux Density Variations

Although the dependence of flux density on wavelength and time can generally be adequately described by an expanding cloud of relativistic particles, with suitably chosen initial conditions and rates of particle energy gain and loss, there are no VLBI observations that can directly relate the assumed expansion to a flux density outburst. Probably this is the result of the complex source structure and component motions, which obscure small changes in the size of components. Direct confirmation of component expansion combined with multi-frequency flux density observations would contribute substantially to our understanding of the fundamental source of energy in quasars and galactic nuclei.

The observed flux density variations alone, although complex, do not present any fundamental problem; but, at distances inferred from the conventional cosmological interpretation of the red shifts, the sometimes very rapid variability often leads to an apparent conflict with the generally accepted synchrotron models. Since it is usually supposed that the time scale for variations cannot be less than the light travel time across the source, an upper limit on the linear dimensions of the variable region can be estimated. When combined with the distance calculated in the usual way from the red shift, this often indicates angular dimensions that are so small that it appears the inverse Compton limit is exceeded, and that the required energy in the radio outburst is uncomfortably large, with total energies ~ 1060 ergs required on a time scale of a year or so (Pauliny-Toth & Kellermann 1966, Hoyle et al. 1966, Ledden et al. 1976). This problem is particularly serious when rapid variations are observed at the longer decimeter wavelengths, which suggest brightness temperatures up to 1016 K (Fanti et al. 1979, Condon et al. 1979, Cotton & Spangler 1979). The apparently extreme conditions required by conventional synchrotron models have led to the speculation that the compact variable sources are either closer than indicated by the cosmological interpretation of the red shift (Jones & Burbidge 1973, Burbidge & Stein 1975), or that they are not conventional incoherent synchrotron sources but radiate by some coherent process (Cocke & Pacholczyk 1975, Benford 1977, Cocke et al. 1978, Colgate & Petschek 1978).

These problems were first recognized, at least in a qualitative way, when the radio variations were first reported by Sholomitskii (1965), at about the same time that the quasars were found to have unprecedented large red shifts, and it was suggested that the observations might be incorrect or that the variable sources might be transmissions from extraterrestrial civilizations (Kardashev 1964). When the observational evidence for rapid flux density variations became firmly established (Dent 1965), even at wavelengths as long as 20 and 40 cm, the consequences for conventional synchrotron theory and cosmological red shifts were discussed by Hoyle et al. (1966) and Pauliny-Toth & Kellermann (1966).

The limitations of inverse Compton scattering and the observation that the outbursts are sometimes optically thin even at long wavelengths lead to lower limits on the angular size which are up to 100 times greater than those deduced by the simple light-travel-time arguments. Additional evidence that the sizes of variable radio sources exceed the light-travel size is suggested by X-ray observations in the band 3 to 17 keV which have been made during radio outbursts in several sources with the HEAO-A satellite. In no case are X rays observed, although if the source dimensions are smaller than those suggested by the time scale of the radio flux density variations, inverse Compton scattering is expected to give rise to an X-ray flux many orders of magnitude greater than the observed upper limit (Marscher et al. 1979).

It has also been noted that if the radio source dimensions are as small as implied by the light-travel time, then, as in the case of pulsars, interstellar scintillations should be observable. Attempts to detect the scintillations give negative results implying brightness temperatures up to a factor of 104 smaller than those given by the light-travel-time arguments (Condon & Backer 1975, Armstrong et al. 1977, Condon & Dennison 1978, Ozernoi & Sheshov 1980, Dennison & Condon 1981).

There is thus no direct evidence for the small dimensions that would require coherent emission mechanisms. In particular, the absence of scintillations during a strong radio outburst in the BL Lac object 0235 + 16 appears to place a lower limit to the size that is considerably greater than the light-travel size (Scheuer 1976). This is a critical observation, since intergalactic absorption lines from an intervening galaxy appear to confirm the cosmological distance of 0235 + 16 (Wolfe et al. 1978), although it has been noted that scattering in the intervening galaxy might cause an apparent increase in the observed dimensions (Condon & Dennison 1978).

The large flux density variations, the absence of Compton X-ray flux, and the large dimensions deduced from the scintillation observations can all be interpreted within the framework of conventional synchrotron theory and cosmology as due to "Doppler beaming" if the radiating region is moving nearly along the line of sight, with a velocity close to that of light. There is direct observational evidence for this bulk relativistic motion from VLBI observations, and this is discussed further in Section 6.

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