3. DIAGNOSTICS OF PHYSICAL CONDITIONS
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:
- 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).
- 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).
- 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.