Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mrao.cam.ac.uk/yerac/kovalev/kovalev.ps Äàòà èçìåíåíèÿ: Wed Feb 22 22:33:05 1995 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 02:39:23 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: jet

Structure of Active Galactic Nuclei in a
model with the radial magnetic field
By Yu r i Y. K o v a l e v
e­mail: yyk@dpc.asc.rssi.ru
Astro Space Center of the Lebedev Physical Institute, Moscow State University, Moscow,
RUSSIA
Sternberg Astronomical Institute, Universitetskiy pr. 13, 119899 Moscow, RUSSIA
Synchrotron emission of a jet in the strong radial magnetic field of an AGN is analyzed. Variable
radio spectra of some quasars and galaxies had been earlier explained by this model. A next
interesting step is a simulation of a theoretical structure for such objects in the model and com­
parison of it with the VLBI observations. First results for such model maps are presented here.
It is shown that jet maps depend strongly on the observed angle of the jet axis, opening angle of
a cone jet in the picture plane, frequency, as well as on the time variability of geometrical and
physical parameters of a relativistic plasma flow across the jet entrance. Preliminary qualitative
comparing shows that the obtained model maps may be similar with the typical observed VLBI
structure of AGNs. Often observed multi­component structures can be explained by the single
jet in the model, if the flow of relativistic particles from the active nucleus varies in time.
1. Introduction
Observed radio images of extragalactic sources (see, for example, Mutel & Phillips
(1987), Unwin et al. (1989), Gabuzda et al. (1989), Gabuzda et al. (1992), Bšašath et
al. (1992)) --- such as QSO, BL Lac's and radio galaxies --- stimulated great scientific
interest always. Carrying a lot of new information, radio images are very important
for interpretation, but are very difficult material to be successfully compared with the
model images. Only a few works to this moment are known with more or less successful
comparison of the observed and simulated maps for variable sources.
One of the first studies on this topic is one by Hughes et al. (1989a) and Hughes et al.
(1991), where the interpretations of the variable flux densities of BL Lac (at 6 frequencies
from 0.4 to 14.5 GHz), 3C 279 and OT 081 (at 3 frequencies --- 4.8, 8.0 and 14.5 GHz)
had been conducted using the shock relativistic beaming model (Hughes et al. (1989b)).
In the same work the model images for BL Lac (Hughes et al. (1989a)) and 3C 279
(Hughes et al. (1991)) had been obtained. The model structures of BL Lac and 3C 279
are compared with the results of observations Mutel & Phillips (1987) and Unwin et al.
(1989) respectively.
Calculations of the structure in some particular cases had been done by Gomez et
al. (1993a) for a shock relativistic curve jet model with the synchrotron emission. On
the base of numerical simulations by Gomez et al. (1993a), the maps of the angular
distribution for the total and polarized flux density of the quasars 3C 273B by Gomez et
al. (1993b) and 3C 295 by Lara et al. (1993) was studied.
The common characteristics of the variable spectra of radio emission for extragalactic
objects had been explained earlier by synchrotron emission in the model of a narrow jet
of relativistic particles in a strong radial magnetic field of a source nucleus (the Hedgehog
model, see Kardashev (1969), Kurilchik (1972), Ozernoy & Ulanovskiy (1974), Kovalev
& Mikhailutsa (1980)) In particular, a comparison of this model with combined spectra
of the sources 3C 345, 3C 454.3, 2134+00, 1510 \Gamma 08 and 4C 39.25 as well as with 3­years
1

2 Y.Y. Kovalev: Model structure of AGN
evolution of the instantaneous 1--22 GHz spectra of BL Lac at 7 frequencies had been
carried out by Kovalev (1984). 0.3--15 GHz spectra during 1.5 years set of bursts in a
quasar 0235+16 are explained by the Hedgehog model in Kovalev & Larionov (1994). A
study of `quiet' spectra and spectra of bursts for extragalactic objects with the strong
millimeter emission were conducted in Nesterov et al. (1994), and the emission of 11
sources were interpreted by the same model.
Thus, this success in explanation of spectra observations by this model leads to a
wish to study the jet's structure in the same model. The main aim of this work is a
numerical analysis of the model images of the angular distribution of the radio brightness
in dependence on some physical and spatial parameters of a jet, as well as a qualitative
comparison of them with the typical VLBI­images.
2. Calculation Procedure
The task can be in short formulated as follows (see Kovalev & Mikhailutsa (1980)
for more details). Let us consider a radial magnetic field of an active nucleus and a
narrow jet of relativistic particles. The particles move from the nucleus because of the
longitudinal components of their velocities and emit by the synchrotron mechanism in
quasi vacuum conditions. It is assumed that the density of the magnetic field energy
is much more than the density of the jet particles energy. The adiabatic invariant and
the energy of the emitted particles are conserved. Other emissions, excluding by the
synchrotron emission, are neglected. It is required to make numerical simulations of the
angular distribution of the observed intensity in typical VLBI­measurements.
I calculate maps of the observed (visible) intensity I obs
š (¸ 0 ; j 0 ) on the formulae:
I obs
š (¸ 0 ; j 0 ) =
Z
\Omega j
I š (¸; j) D(¸ 0 \Gamma ¸; j 0 \Gamma j)
d\Omega =\Omega b ; (2.1)
where I š (¸; j) is the emitted intensity (brightness) in the model (see Kovalev & Mik­
hailutsa (1980), Kovalev & Larionov (1994) for more details), D(¸; j) is the synthesized
pattern diagram of a radio interferometer, which is approximated by the Gaussian func­
tion
here,\Omega j is the spatial angle of the jet
and\Omega b is the VLBI­beam.
Calculations have been done by setting the pattern diagram of the VLBI, the geomet­
rical and physical parameters of the jet to obtain I š (¸; j)
and\Omega j in the model.
3. Discussion
All maps of the fully evaluated stationary jet in the radial magnetic field --- see Fig­
ures 1 and 2 --- can be considered as a result of a superposition of two main components
(relatively compact and extent), but their relative contribution to a total emission depend
in a complicated way on the exponent fl in the energy distribution of emitted relativistic
particles, normalized frequency š=šm0 , the angle # between the jet axis and the direction
to an observer, the cone angle of the jet in the picture plan ' and the angle dimension
of the jet ff. A weak third component at the end of the jet appears at some narrow
frequency interval (š=šm0 ú 1=4 \Xi 1=8). It should be pointed out that a mean value of
šm0 was earlier estimated as šm0 ¸ 30 GHz by Kovalev (1994).
The dependence of structure on the frequency š=šm0 and on the angle of observation #
is the following. The changes of the observational brightness distribution with increasing
the angle # at the fixed frequency š=šm0 are qualitative similar to the changes of one
with decreasing the frequency at the fixed angle # --- the importance of an extended

Y.Y. Kovalev: Model structure of AGN 3
Figure 1. The structure of the fully evaluated stationary jet in the radial magnetic field: a
dependence of visible intensity on the relative frequency š=šm0 with fixed values of the exponent
fl = 1:8 in the energy distribution of emitted particles, the angle to an observer # = 2 ffi , and the
cone angle of the jet in the picture plan ' = 30 ffi . The contours are at 1, 3, 5, 10, 20, 30, 50, 70,
and 90 % of the maximum value.
component is increasing (see Figure 1 for the dependence on the frequency). Moreover, a
weak third component of the images (at the level of several percent of the maximum) at
frequencies of approximately the average of the flattened part of the flux density spectra
appears (see Figure 1) as a result of increasing the emitted intensity at the end of the jet.
This increase in the emission is explained by increasing the number of particles, emitted
along to the direction of observation because of the pitch­angles evolution in the model
(see Kovalev & Mikhailutsa (1980) for more details).
The maximum of the compact component shifts to the middle from the start of the jet,
and width of it increases with increasing the frequency or the angle of the observation.
This tendency is weak or absent at higher frequencies (š=šm0 ? 1) and is most observed
at lower frequency (š=šm0 ! 1=16) --- see the visible brightness distribution on Figure 1.

4 Y.Y. Kovalev: Model structure of AGN
Figure 2. The structure of the fully evaluated stationary jet emitting in the radial magnetic
field in a particular case, defined by the following parameters: š=šm0 = 3=32, # = 2 ffi , fl = 1:8,
' = 35 ffi , ff = 2:7 milli arcseconds. The relative right ascension and declination are shown on the
horizontal and vertical axes, respectively, to compare with Figure 1a in Gabuzda et al. (1989).
Contours are at 2, 2.8, 4, 5.6, 8, 11, 16, 23, 32, 45, 64, and 90 % of the maximum value.
4. Comparison with Observations
It should be emphasized that the quantitative comparison of the model maps with
results of observations is not the aim of the presented work. This is planned to be done
in the future, but here some main results are pointed out only.
Even the particular case of a fully evaluated stationary emitting jet in the model is
in qualitative agreement with the typical VLBI­images by Gabuzda et al. (1989) and
Gabuzda et al. (1992). Unfortunately, the real diagram patterns of the VLBI meas­
urement influence the resultant maps, and often distort of them essentially (it concerns
particular to the diagram patterns with the elliptical cross­sections).
Let us consider in more detail a map of the source 0454+84 (see Figure 1a in Gabuzda
et al. (1989)). A qualitative result of the fitting the structure of the fully evaluated
stationary jet in the model to this image is shown on Figure 2. The diagram pattern has
been used as in Gabuzda et al. (1989). The values obtained for the model parameters
are shown in the caption of Figure 2. Contours are the same as in Gabuzda et al. (1989)
in Figure 1a. One can see a good agreement between the observed and model maps by
visual comparison.
Let us also consider also the image of the fully evolved model jets, if the flux of the
number of emitted particles at the base of the jet is varied in time. One of the infinite
possible cases is presented on Figure 3. Some important parameters are shown in the
caption. The angle between the jet's axis and the right ascension axis is equal to 20 ffi .
The radio image on Figure 3 is a typical image of a multi­component structure, and

Y.Y. Kovalev: Model structure of AGN 5
Figure 3. The structure of the fully evaluated non­stationary jet in the radial magnetic field
for the fixed values of the relative frequency š=šm0 = 3=16, the angle to an observer # = 3 ffi , the
exponent fl = 1:8 in the energy distribution of emitted particles and the angle dimension of the
jet ff = 2 milli arcseconds. Values of the angle ' are varied in time. Contours are at 1, 2, 3, 4,
5, 7, 10, 20, 30, 40, 50, 60, 70, 80, and 90 % of the maximum value.
has an objective to show to skeptics that a multi­component source must not always have
several jets or clouds. An influence of the non circle cross­section of the pattern diagram
can be also seen on Figure 3. If the angle dimension ff of the jet would be equal to or
less than the dimension of the main lobe of the pattern diagram, then the contours of
the model map in the form of ellipses for an any jet would be obtained, in accordance
with observations (see, an example, Figure 1 in Gabuzda et al. (1992)).
5. Summary
It is obtained that the visible structure of the jet in the discussed model strongly
depends on some physical and geometrical parameters of the jet and on the used syn­
thesized pattern diagram of the VLBI. Calculated maps are in qualitative agreement with
the typical VLBI­images. The multi­component sources can be explained by this model
in a case of a nonstationary flow of the jet. It is concluded that a narrow jet of relativistic
particles emitted by the synchrotron mechanism in the strong radial magnetic field of an
active galactic nucleus can be a real model for variable extragalactic radio sources.
I wish to thank the Cavendish Laboratory and the Russian Foundation for Funda­
mental Researches for the support of my travel to YERAC'94, as well as Priya Shah for
the help in preparation of this paper.

6 Y.Y. Kovalev: Model structure of AGN
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