Please Note: the e-mail address(es) and any external links in this paper were correct when it was written in 1995, but may no longer be valid.
Astro Space Center of the Lebedev Physical Institute, Moscow State
University, Moscow, RUSSIA
Sternberg Astronomical Institute, Universitetskiy pr. 13, 119899 Moscow, RUSSIA
Observed radio images of extragalactic sources (see, for example, Mutel & Phillips (1987),Unwin et al. (1989),Gabuzda et al. (1989),Gabuzda et al. (1992),Bååth 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, , and 4C 39.25 as well as with 3-years 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 VLBI-images.
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 VLBI-measurements.
I calculate maps of the observed (visible) intensity on the formulae:
where is the emitted intensity (brightness) in the model (see Kovalev & Mikhailutsa (1980),Kovalev & Larionov (1994) for more details), is the synthesized pattern diagram of a radio interferometer, which is approximated by the Gaussian function here, is the spatial angle of the jet and is the VLBI-beam.
Calculations have been done by setting the pattern diagram of the VLBI, the geometrical and physical parameters of the jet to obtain and in the model.
Figure 1: The structure of the fully evaluated stationary jet in the radial magnetic field: a dependence of visible intensity on the relative frequency with fixed values of the exponent in the energy distribution of emitted particles, the angle to an observer , and the cone angle of the jet in the picture plan . The contours are at 1, 3, 5, 10, 20, 30, 50, 70, and 90 % of the maximum value.
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: , , , , 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.
All maps of the fully evaluated stationary jet in the radial magnetic field - see Figures 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 in the energy distribution of emitted relativistic particles, normalized frequency , 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 . A weak third component at the end of the jet appears at some narrow frequency interval (). It should be pointed out that a mean value of was earlier estimated as by Kovalev (1994).
The dependence of structure on the frequency and on the angle of observation is the following. The changes of the observational brightness distribution with increasing the angle at the fixed frequency are qualitative similar to the changes of one with decreasing the frequency at the fixed angle - the importance of an extended 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 pitch-angles 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 () and is most observed at lower frequency () - see the visible brightness distribution on Figure 1.
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 VLBI-images by Gabuzda et al. (1989) and Gabuzda et al. (1992). Unfortunately, the real diagram patterns of the VLBI measurement influence the resultant maps, and often distort of them essentially (it concerns particular to the diagram patterns with the elliptical cross-sections).
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.
Figure 3: The structure of the fully evaluated non-stationary jet in the radial magnetic field for the fixed values of the relative frequency , the angle to an observer , the exponent in the energy distribution of emitted particles and the angle dimension of the jet 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.
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 .
The radio image on Figure 3 is a typical image of a multi-component structure, and has an objective to show to skeptics that a multi-component source must not always have several jets or clouds. An influence of the non circle cross-section of the pattern diagram can be also seen on Figure 3. If the angle dimension 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)).
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 synthesized pattern diagram of the VLBI. Calculated maps are in qualitative agreement with the typical VLBI-images. The multi-component 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.