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.
and A. Witzel
Radioastronomie, Auf dem Hügel 56, 53121 Bonn,
The University of Manchester, Dept. of Physics and Astronomy, Manchester M13 9PL, UNITED KINGDOM
The central engines of active galactic nuclei (AGN) are generally thought to contain a compact supermassive object surrounded by an accretion disc. A two-sided jet is ejected perpendicular to this accretion disc. The nature of the central mass and the existence of the accretion disc are subject to debate; however, jets are frequently observed in AGN. In the radio regime, VLBI observations have shown that jets and sub-regions of higher emission can be highly variable on time-scales as short as months, showing apparent superluminal motion and intensity variations of the emission regions. Due to relativistic Doppler boosting the receding jet is reduced in brightness and often unobservable, whereas the brightness of the approaching jet is enhanced.
Curved radio structures and moving emission regions of bent trajectories are frequently found in radio jets. In some cases they suggest that the underlying structure is helically twisted. Theoretical models for such oscillating, bent structures include helical modes in hydrodynamic jets (Hardee (1987),Owen et al. (1989)) or in magnetized jets (Königl & Choudhuri (1985)). Camenzind (1986) developed a model for compact jets with bulk plasma acceleration along internal helical magnetic field lines, based on magnetized accretion disc winds.
In this paper, we consider the BL-Lacertae type object 1803+78 (), which is one of a complete sample of flat spectrum radio sources described by Witzel et al. (1988). VLBI monitoring of the milliarcsecond scale structure shows stationary components at about 5, 1.4 and 0.4 mas separation from the core (Eckart et al. (1986),Schalinski (1990),Krichbaum et al. (1990),Krichbaum et al. (1993),Krichbaum et al. (1994a),Krichbaum et al. (1994b)). Observations at 22 and 43 GHz revealed moving features between the core and the 1.4 mas component. These exhibit superluminal motion up to approximately (), varying as a function of core distance. A blow up of the central 2.5 mas and an estimate of the velocity changes within this region is shown in Krichbaum et al. (1994a) and Krichbaum et al. (1994b). Preliminary maps at 2.3 and 8.4 GHz show a curved jet structure beyond the 1.4mas-component, up to at least 7 mas from the core (Ros & Witzel, private communication).
The accumulated VLBI data show that the observed components and the continuous jet structure are aligned along a curved, oscillating ridge line (see Figure 1). Apparent variations of the component speed and oscillations of the axis strongly indicate motion along a spatially bent path. Three complete oscillations of increasing wavelength can be followed along the jet. In this paper, we interpret the observed structure as the result of a helically bent, relativistic jet.
Figure 1: The oscillating ridge line of the mas-jet of 1803+78 after subtraction of a small overall parabolic curvature. The crosses mark observed components and their position uncertainty. Crosses with filled circles mark the ridgeline of the jet at around 5 mas from the core as found from the 8.4 GHz-map in Figure 2. The data points from 0-2.5 mas core separation are from Krichbaum et al. (1994a) and Krichbaum et al. (1994b), data at larger separations are from Britzen et al. (1994) and Ros & Witzel (private communication). The data were obtained at different epochs and frequencies, thus the image shows a ``timeaveraged'' mean jet ridge line. Superimposed on the data is a fit of a helical trajectory, which in Figure 2 was used to simulate the observed structure of the VLBI jet (Steffen (1994),Steffen et al. (1995)).
The stationary flux density distribution of 1803+78 is modeled as an adiabatically expanding, homogeneous plasma jet, taking into account differential relativistic Doppler boosting along the helical trajectory (Steffen (1994)). It consists of a succession of equidistant spherical synchrotron components. These components are assumed to expand adiabatically with their radius increasing linearly as a function of core distance (corresponding to a constant opening angle of the jet). In order to compare the simulations with the observations, the flux density distribution of the model is convolved with the beam of the observed images. The result is shown in Figure 2, which compares the simulations (left) with the observed flux density distribution at different frequencies (right). The frequency and resolution increases from top to bottom. The curved structure and the position of stationary components are well reproduced by the simulations. Note that the components at about 1.2 mas in the 22 GHz-image and at 0.8 mas in the 43 GHz-image are non-stationary, and have not been modeled in these simulations.
Figure 2: A comparison of our helical simulation (left) with the observed VLBI jet (right) of 1803+78 at different frequencies. The observing frequency and the resolution increase from top to bottom. The maps at 2.3, 8.4 GHz (Ros & Witzel, private communication) are preliminary results. The maps at 22 and 43 GHz are, respectively, taken from Krichbaum et al. (1993) and Krichbaum et al. (1994b).
Further evidence for a helical jet structure is found from an analysis of the change in wavelength of the oscillations along the jet. We find that the wavelength increases stepwise as shown in the lower diagram of Figure 3. Such a behaviour is expected from a helical structure whose axis is at a considerable angle to the sky plane. The upper panel of Figure 3 illustrates this interpretation.
Figure 3: The lower panel shows the wavelength of the jet oscillations as a function of core separation. The wavelength increases stepwise. Steps appear near the position of stationary components in the jet. As illustrated in the upper panel, such a behaviour is expected from a helically distorted jet viewed at an angle to the line of sight which is considerably smaller than . The arrows indicate positions of expected stationary components. A step or jump in the observed wavelength is expected shortly after these positions. Ellipses indicate the measured positions of zero and full elongation and their error-range. The local wavelength of the oscillation is determined by taking the distance between these points to be .
As a possible origin of these jet distortions, we consider Kelvin-Helmholtz instabilities of a relativistic jet as described by Hardee (1987). We assume that the conditions of those calculations, like a power-law decrease of density, pressure, and temperature with core distance also apply to the parsec scale. Evidence for such a behaviour in 3C 345 is found by Zensus et al. (1995). From the limit to the apparent velocity, (Krichbaum et al. (1994a)), of the overall structure produced by the instability, we deduce an upper limit of the angle between the jet axis and the line of sight. It is given by:
where is the radius of the jet, is the local wavelength of the oscillation, is the Mach number of the jet with respect to the external medium, c is the speed of light, and is the bulk speed of the jet. From this relation and using only the upper limit to the apparent velocity of the 1.4 mas-component, , we find . Taking the jet radius (assumed equal to the observed component radius) and the wavelength at 1.5 mas from the core, the limit is reduced to , where the jet velocity is c and the jet is assumed to be supersonic ().
The structure of the milliarcsecond radio jet of the BL-Lac object 1803+78 can be modeled by an expanding helical synchrotron jet. Assuming Kelvin-Helmholtz instabilities in a relativistic jet as the origin of the distorted structure, we deduced an upper limit for the angle to the line of sight of .