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Future Directions in High Resolution Astronomy: The 10th Anniversary of the VLBA
ASP Conference Series, Vol. ***, 2003
J. D. Romney & M. J. Reid (eds.)
Where has all the polarization gone?
E. Middelberg, A. L. Roy, U. Bach
Max­Planck­Institut f˜ur Radioastronomie, Bonn, Germany
D. C. Gabuzda
Physics Department, University College Cork, Ireland
T. Beckert
Max­Planck­Institut f˜ur Radioastronomie
1. Introduction
Circumnuclear tori are a central ingredient in the unification of the AGN phe­
nomenon, but the conditions in the tori, the jet collimation, and the accretion
mechanisms are still poorly constrained. Magnetic fields are involved in jet col­
limation and probably in feeding material into the nucleus, but those that are
derived using equipartition are uncertain since equipartition conditions are not
known to hold.
A more direct measurement of magnetic field strength can be made using
Faraday rotation (FR) and free­free absorption (FFA). FR changes the electric
vector position angle of a polarized wave passing through a magnetized plasma
by an angle # = Rm # 2 , where the rotation measure Rm is the path integral over
the line­of­sight component of the magnetic field, B # , and the density of thermal
electrons, n e . FFA depends on n e , the path length, L, and the electron temper­
ature, T e . The value of L can be estimated by assuming it to be the same as the
width of the region of FFA in the VLBI images. Making reasonable assumptions
about T e , estimates of n e can also be derived from the FFA measurements. Thus,
a joint analysis of FR and FFA measurements can provide direct diagnostics of
the magnetic­field strength B # with minimum imposed assumptions.
2. Sample and Results
We selected all five AGNs that we found in the literature that had steeply rising
spectra across parts of the jet at pc scales. In all cases, the absorption was most
likely FFA due to a pc­scale foreground absorber, perhaps the ionized inner edge
of an obscuring torus or an accretion flow. The sample comprises NGC 1052
(LINER), NGC 4261 (FR I), Centaurus A (FR I), Hydra A (FR I) and Cygnus A
(FR II). Polarimetric observations were carried out with the VLBA 1 at 15.4 GHz
1 The National Radio Astronomy Observatory is a facility of the National Science Foundation,
operated under cooperative agreement by Associated Universities, Inc.
1

2 Middelberg et al.
Relative
Dec
/
mas
Relative RA / mas
4 2 0 ­2 ­4 ­6 ­8
3
2
1
0
­1
­2
­3
Figure 1. Uniformly weighted 15 GHz image of CygA with superim­
posed polarization vectors.
with 60 min to 240 min integration time per source to see whether polarized
emission is present before making FR observations.
Only Cyg A (Fig. 1) showed significant linear polarization, having 1.4 mJy beam -1
polarized emission at the position of the total intensity peak flux density of
315 mJy beam -1 (0.4 %). With a detection threshold of 0.3 %, all other sources
appeared entirely unpolarized, in the absorbed gaps as well as in all other lo­
cations along their jets. As the emission process is undoubtedly synchrotron
emission (given the high brightness temperatures), the lack of polarized emis­
sion in these sources needs explanation.
3. Discussion
We suggest several intrinsic and extrinsic mechanisms to depolarize the emission.
Tangled internal magnetic fields: Assume the source is optically thin
and its magnetic field is composed of a uniform component B 0 and a random
component B r . Provided that B r varies on scales much less than the source
diameter and that the electrons have a power­law energy distribution with index
#, the intrinsic degree of polarization p(#) will be averaged over the source
to p i = p(#)(B 2
0 )/(B 2
0 + B 2
r ) (Burn 1966). For # = 2, the intrinsic degree
of polarization is 70 %. To depolarize this below our detection threshold, the
magnetic field energy would need to be extremely dominated by the random
component, and so the jets would have to be turbulent, and very little ordering
of the magnetic fields by the overall outward motion of the jet flow would be
permitted. In case the source is optically thick, the maximum intrinsic degree
of polarization is 10 % to 12 %, and we receive emission only from the surface.
For the source to appear depolarized, the scale on which the surface magnetic
field is tangled must be much smaller (< 1/10) than the observing beam. This
explanation is unsatisfactory because the magnetic fields inside the jets must
be ordered to confine them, but the surface must be turbulent, and why the
transition occurs is unexplained.

APS Conf. Ser. Style 3
Internal Faraday rotation: In the transition region between optically
thick and optically thin source parts, internal FR could be significant. Polarized
emission from various depths along the line of sight through the source are Fara­
day rotated by the source itself, the degree of rotation depending on the depth
of the emitting region. However, internal FR is also unsatisfactory for explain­
ing our observed lack of polarization because it requires a significant fraction of
``cold'' (# min # 1 - 10) electrons in the jet. Internal FR produces a characteris­
tic dependence of polarization fraction on frequency, but unfortunately, we are
not able to test for the expected wavelength dependence because we lack the
required measurements of the polarization fraction at several wavelengths.
Bandwidth depolarization: This depolarization mechanism requires very
high, homogeneous RM (10 6 rad m -2 ), and such conditions should also produce
strong FFA which is not seen along most of the depolarized jets. A possible way
out is if the Faraday screen/absorber is very extended or hot, or both.
Beam depolarization: If the magnetic field in a foreground Faraday
screen is tangled on scales much smaller than the observing beam, regions with
similar degrees of polarization but opposite signs will average out and the ob­
served degree of polarization will be decreased. Thus, with spatially highly
variable RM, one could in principle depolarize the source, although the changes
in RM from region to region still need to be of the order of 10 4 rad m -2 to de­
polarize the 15 GHz band. If one requires at least 10 cells across the beam,
the typical cell sizes in NGC 1052, NGC 4261, Cen A, HydA and CygA need to
be 0.01 pc, 0.02 pc, 0.002 pc, 0.12 pc and 0.13 pc, respectively. Since these are
the least exotic conditions required by any of the mechanisms discussed, we feel
that beam depolarization in an external medium is the most likely mechanism
to depolarize the sources presented here.
4. Summary
Compact core­dominated AGN such as BL Lac objects and quasars typically
display linear polarization of a few to a few tens of percent on pc scales, with
the degree of polarization occasionally approaching the theoretical maximum
of 70 %. Thus, some AGN jets have comparatively modest depolarization. In
contrast, the pc­scale structures of the five radio sources considered here exhibit
strong depolarization at high frequencies. The weakness of their pc­scale polar­
ization indicates that most likely tangled jet magnetic fields on sub­pc scales in a
foreground screen causes beam depolarization, although we lack enough informa­
tion to conclusively decide among the discussed mechanisms. Why that screen
is present in these objects but absent in most core­dominated AGNs might be
an orientation­selection e#ect. Core­dominated objects are viewed preferentially
pole­on, and then the lack of depolarization means that the Faraday screen lies
in the equatorial plane. The sample of jets selected here is viewed preferentially
face­on, making the Faraday­screen viewed against the source.
References
Burn, B. J. 1966, MNRAS, 133, 67