1. Abstract

1
1. Abstract Lobanov (1998) developed an approach
for deriving the local magnetic (B) fields in
Active Galactic Nuclei (AGN) from the observed
local frequency of the spectrum peak (?m) and
corresponding peak flux density (Sm), based on a
Blandford-Konigl jet model. Determining ?m and Sm
in individual regions of the source requires VLBI
images encompassing, or nearly encompassing, the
frequencies at which the spectral peaks lie,
which have been accurately aligned relative to
each other we have used the 5-43GHz data of
O'Sullivan Gabuzda (2009) for the three AGN
1418546, 2007777, and 2200420 (BL Lac),
aligned using the cross-correlation algorithm of
Croke Gabuzda (2008). Our results suggest the
presence of enhancements in the B field both in
the core region and somewhat upstream of the
observed core we also find the B field to be
enhanced in bright jet components well resolved
from the core, consistent with the possibility
that these are shocks. The jet B field of BL Lac
falls off smoothly and monotonically with
distance from the core, suggesting that the jet
emission does not include a significant
contribution from shocks.
2. Turnover Frequency We approximated the shape
of the synchrotron spectrum at a given point in
the VLBI images from a 4th order polynomial fit
of the flux density against the frequency for
that point, for the eight frequencies (4.6, 5.1,
7.9, 8.9, 12.9, 15.4, 22.2, and 43.1 GHz). We
estimated lower and upper cutoff frequencies from
fits in optically thick core regions, where a
clear peak was observed. The spectral maximum, or
turnover flux density Sm, was determined from the
fit and the corresponding turnover frequency ?m
obtained. This process yielded distributions of
Sm and ?m throughout the source.
4. Results


1418546
Frequency vs Flux Density in the VLBI Core of
2200420
The derived Sm values are magnified by a factor
of ten to show clear peaks near the core and a
bright knot in the jet. The B field is strongest
in the knot, and peaks slightly downstream and
upstream of the core.
Turnover Map of 2007777

2007777
Frequency vs Flux Density in the Jet of 2200420
3. Magnetic Field Strength The turnover
frequency can be sensitive to changes in the jet
namely velocity, particle density and magnetic
field strength. For any point in the jet p, the
magnetic field strength at that point Bp, is
given by Lobanov (1998), where Bcore, ?m,core
and Sm,core are the magnetic field strength,
turnover frequency, and spectral maximum of the
VLBI core, and rp and rcore are the distances of
the point and the VLBI core from the black hole.
Since this cannot be determined, the distance of
the points to the sonic point is used as a good
approximation. Here ?m is measured in GHz, Sm is
in Jy, r in parsecs, and B in Gauss. We consider
the case where m1, since the core regions of
these AGN are close to equipartition, O'Sullivan
and Gabuzda (2009) the values of Bcore and rcore
were taken from O'Sullivan and Gabuzda
(2009). The profiles were constructed through the
VLBI core region and along the jet, passing
through any bright features in the jet these
show profiles of ?m, Sm, and B along the jets.

The derived Sm values are magnified again by a
factor of ten to show clear peaks near the core
and a bright knot in the jet. The B field has
peaks slightly downstream and upstream of the
core, and in the bright jet knot.

2200420
5. Discussion The turnover frequency, turnover
flux density and B field are smooth and
physically plausible functions along the derived
profiles. In all three AGN, the B field peaks
slightly downstream from the core, possibly
indicating strong B fields in emerging jet
components the B field also has a peak upstream
from the observed core, possibly marking some
region physically associated with the base of the
jet. The jets 1418546 and 2007777 also have
bright compact features with strong B fields,
suggestive of shocks, whereas there is no
evidence for shocks in the smooth B field
distribution of the jet of 2200420 (BL Lac). The
B fields in the core-regions and bright knots of
1418546 and 2007777 are 5-10 G, whereas the B
fields in BL Lac are lower, less than 1 G.

The derived Sm shows only one peak near the
core. The B field is magnified by a factor of a
hundred the B field is dominated by one peak
slightly downstream from the core, and falls off
smoothly in the jet.
6. Reference Lobanov, A.P. 1998AAS, 132,
261L O'Sullivan, S.P. Gabuzda, D.C. 2009MNRAS,
400, 26O Croke, S.M. Gabuzda D.C. 2008MNRAS,
386, 619C