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3.1. Density

It was conventional to estimate internal densities in radio sources using measurements of Faraday rotation and depolarization, on the assumption that thermal matter and relativistic electrons are uniformly mixed and that the observed polarization is due to an isotropic, random component superimposed on a uniform one (Burn 1966). It has subsequently been recognized that these assumptions are either incorrect or unsubstantiated:

  1. In almost all of the cases which have been studied in sufficient detail, the Faraday effects appear to arise from fluctuations in rotation measure in a foreground medium. In sources such as NGC 6251 (Perley, Bridle & Willis 1984), M 84 (Laing & Bridle 1987), Cygnus A (Dreher, Carilli & Perley 1987), 3C 295 (Perley & Taylor 1991) and Hydra A (Taylor et al. 1990), the fluctuations are resolved on scales of 0.5 - 5 kpc and are probably due to magnetic-field variations in a fairly smooth medium, most plausibly the galaxy and/or cluster halo. A good case can also be made that extended emission-line regions are directly responsible for the depolarization in some objects (e.g. 3C 305; Heckman et al. 1982).

  2. The degree of polarization is not affected by the number of reversals in the magnetic field, but the depolarization for uniformly mixed thermal matter and relativistic electrons is proportional to N-1/2, where N is the number of reversals along the line of sight. It is therefore possible to hide a significant amount of thermal matter if the field is disordered on a small scale (a lower limit to the scale is presumably set by field-line reconnection).

  3. The assumption that the field is a superposition of uniform and isotropic disordered components is not necessary. Laing (1980, 1981) and Hughes, Aller & Aller (1985) have considered various partially ordered field configurations which can show high degrees of polarization when viewed from appropriate angles.

The only observations which may have detected internal depolarization are those of Jägers (1987). He showed that the tails of wide-angle tail sources such as 3C 130 depolarize significantly more at their centers than at their edges (as expected from the greater path length if the Faraday effects are internal). The Faraday depths are slight, and the effect is only detected at low frequency (and therefore poor resolution). With these exceptions, existing observations are consistent with the hypothesis that all Faraday effects occur in front of the synchrotron-emitting regions. The resulting constraints on the internal density of thermal matter are almost worthless.

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