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1803+78: A Helical Core Jet
By W. S t e f f enyz, T.P. K r i c hb a umy, S. B r i t z e ny
AND A. W i t z e ly
e­mail: wsteffen@ast.man.ac.uk
y Max­Planck­Institut f¨ur Radioastronomie, Auf dem H¨ugel 56, 53121 Bonn, GERMANY
z The University of Manchester, Dept. of Physics and Astronomy, Manchester M13 9PL,
UNITED KINGDOM
The plasma jets in active galactic nuclei propagate with velocities close to the speed of light
through the interstellar medium of their host galaxies. These jets are supersonic and highly
collimated. It is expected from theory and found from observations that the interaction between
the two fluids causes instabilities. This is common on kpc scales. However, new observations
show that as close as a few parsec from the central engine quasi­periodic oscillations of the jet
ridge line take place in a number of jets. Such oscillations can result from precession of the jet,
helical magnetic fields, or helical instabilities. Each of these processes presents characteristic
observable properties. In the present paper the jet distortions found in the BL Lac object
1803+78 are interpreted as the result of helical Kelvin­Helmholtz instabilities. Based on this
interpretation a model of the jet is presented and a limit to the angle between the jet axis and
the line of sight of ` ! 16 ffi is derived.
1. Introduction
The central engines of active galactic nuclei (AGN) are generally thought to contain a
compact supermassive object surrounded by an accretion disc. A two­sided 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 sub­regions of higher
emission can be highly variable on time­scales as short as months, showing apparent
superluminal motion and intensity variations of the emission regions. Due to relativ­
istic 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 (K¨onigl
& Choudhuri (1985)). Camenzind (1986) developed a model for compact jets with bulk
plasma acceleration along internal helical magnetic field lines, based on magnetized ac­
cretion disc winds.
In this paper, we consider the BL­Lacertae type object 1803+78 (z = 0:68), 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 4c (H 0 = 100 km s \Gamma1 Mpc \Gamma1 ), 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
1

2 W. Steffen et al.: 1803+78: A Helical Core Jet
Figure 1. The oscillating ridge line of the mas­jet 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 GHz­map 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)).
at 2.3 and 8.4 GHz show a curved jet structure beyond the 1.4 mas­component, 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.
2. Results
The stationary flux density distribution of 1803+78 is modeled as an adiabatically
expanding, homogeneous plasma jet, taking into account differential relativistic Dop­
pler boosting along the helical trajectory (Steffen (1994)). It consists of a succession of
equidistant spherical synchrotron components. These components are assumed to ex­
pand 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 sim­
ulations 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 struc­
ture and the position of stationary components are well reproduced by the simulations.
Note that the components at about 1.2 mas in the 22 GHz­image and at 0.8 mas in the
43 GHz­image are non­stationary, and have not been modeled in these simulations.
Further evidence for a helical jet structure is found from an analysis of the change

W. Steffen et al.: 1803+78: A Helical Core Jet 3
5 mas
5 mas
1 mas
1 mas
5 mas
5 mas
1 mas
1 mas
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).
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.
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 power­law 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, v app ! 0:3c (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:
tan ` ú
Ÿ
2ú R
–
M x
v j =c
+ 1
v app =c
– \Gamma1
! v app
c ; (2.1)
where R is the radius of the jet, – is the local wavelength of the oscillation, M x is the
Mach number of the jet with respect to the external medium, c is the speed of light, and
v j is the bulk speed of the jet. From this relation and using only the upper limit to the
apparent velocity of the 1.4 mas­component, v app ! 0:3c, we find ` ! 17 ffi . Taking the

4 W. Steffen et al.: 1803+78: A Helical Core Jet
q
Projection on Sky
Helix in Space
Observer z
z'
l2
l1
0.1 1.0 10.0
Core Distance [mas]
1
10
Wavelength
[mas]
Stationary Components
l1 l2
Jump Jump
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 90 ffi . 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 error­range. The local wavelength of
the oscillation is determined by taking the distance between these points to be –=4.
jet radius R = 0:17 \Sigma 0:03mas (assumed equal to the observed component radius) and
the wavelength –m = 2 \Sigma 1mas at 1.5 mas from the core, the limit is reduced to ` ! 16 ffi ,
where the jet velocity is v j ! 1c and the jet is assumed to be supersonic (M x ? 1).
3. Conclusions
The structure of the milliarcsecond radio jet of the BL­Lac object 1803+78 can be
modeled by an expanding helical synchrotron jet. Assuming Kelvin­Helmholtz instabil­
ities 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 ` ! 16 ffi .
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W. Steffen et al.: 1803+78: A Helical Core Jet 5
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