The implications of the maps and models from these sources are considered in the second study. Observations of the central components provide the obvious way to determine the existence of this energy pipeline. The assumed intrinsic jet curvature is caused by a precession-like motion of the base of the jet.
Resource features produced by this model are compared to features in real resources.
CHAPTER 1
This telescope was unable to measure the central component of Cyg A due to the large flux from the outer lobes. The fit of the b-functions that make up this map to the data is shown in Figure 3. This source has not been investigated as well as the other three, and there is no evidence for or against variability.
The cross is on the position of the optical galaxy. Reprinted with permission from Bridle et al.
CHAPTER 2
IMPLICATIONS OF OBSERVED JET-COUNTEIUET RATIOS
The exact value of the flux ratio is frequency dependent and is difficult to determine due to the range of angular scales present in these sources.). This large-scale symmetry is in sharp contrast to the asymmetry observed on a msec scale. The observations in Chapter 1 showed extensions only on one side of the core in each source.
This msec asymmetry may be due to an intrinsic asymmetry between the jet and the (assumed) contrail. This seems likely in the case of 0055+30, where the flux of the bow and arc current, and of the NW diffuse lobe, is 10 times greater than that of the flux from the corresponding structures on the other side (the msec flux points in the same direction as the stronger of the two oversized ones). In 3C 111 and 3C 390.3 there is some evidence of jet/counter-jet asymmetry in that in each source one of the two outer lobes is significantly more compact than the other.
The internal asymmetry could be in the form of a difference in time-averaged power, but this is unlikely except in 0055+30 due to similar lobe currents. This is certainly possible, but the fact that the msec jets in 3C 111 and 3C 390.3 point towards a more compact lobe argues against it. This is in contrast to the value given by Hargrave and Ryle (1974) based on the broad but sharp end of the southern hotspot.
They allow the possibility that the northern lobe has a lower inclination to the line of sight than the southern lobe, but the high symmetry of this source makes such a possibility seem unlikely. It therefore seems almost certain that in Cyg A the jet and counterjet must have intrinsic differences, notwithstanding the similarity of the two lobes.
PHYSICAL CONDITIONS FROM SYNCHROTRON THEORY
The energy of relativistic protons has been assumed by various people to be from 0 to 100 times that of relativistic electrons. A value of 0 is assumed here, so that a fixed lower limit can be calculated for the total energy and pressure in the source. This source is a third of the distance from the other three; a given angular resolution therefore corresponds to a volume.
From the time scale of the variation in 3C 111 (several years) and the Umin value for the core. The lifetimes of electrons in nuclei are not much longer than the travel times of light through them, indicating at least slightly relativistic outflow velocities. The lifetime of electrons in jets is several times longer than the travel times of light from the nucleus.
In Table 5, the optical depths calculated at 10.6 GHz and the frequencies at which ~=1 are given. These values are for the homogeneous components whose dimensions are the FWHM of the Gaussian patterns. Because of this, sources will begin to show optical depth effects at higher frequencies than predicted by these calculations.
PRESSURE CONFINEMENT OF THE JET IN CYGNUS A
From HEAO-A X-ray observations, preliminary results indicate that the flux from a point source centered on the core of Cyg A is less than 1042. There will be some local mechanical heating on shorter timescales, but this will result in temperature inhomogeneities, which will significantly increase the emission measure. The constraints imposed by equations (1)-(4) on the outer jet component of Cyg A are shown in Figure 1.
However, it is possible that there is a black hole powering the radio source; this would dominate the potential at the distance of the jet. If there were a large outflow of gas from the core, this limitation would not apply, but this outflow gas would have to be hotter than 109 K. If the jet is not limited by external pressure, it is either itself limited by its own magnetic field, or is a free ray.
If it expands freely, the observations of Chapter 1 indicate a full opening angle ~i10°, implying a Mach number ill.~6. The model of two identical but oppositely directed jets (Blandford and Rees, 1978) does not apply to these sources. The jet in Cyg A (the best studied of the four sources) is almost certainly not constrained by external pressure.
A better measurement of its width at different distances from the core could help determine whether it is a free jet or not. 6 1 AX is the FWHM along the major axis of the elliptic Gaussian component 2 AY is the FWHM along the minor axis of the elliptic Gaussian component.
CHAPTER 3
CHOICE OF JET PARAMETERS
In order to limit the region in the parameter space to be investigated, the source luminosity function (both in the intrinsic flux, .so· and in the jet y factor, y=l/ {i-~:;_1) was chosen and the distribution in angle of view for the extent of the observed current calculated by S and 'Y wa~. This is necessary because the central components of a large number of symmetric sources are visible, the jets of which should be almost in the plane of the sky. Typical values of o and that meet these criteria are o=l.8 and r =10, but quite a wide range of values.
The very different Doppler excitation for different viewing angles was used by Scheuer and Readhead (1979) to explain the large range in the ratio of radio to optical flux from quasars. However, some properties of compact radio sources are well explained by the simple geometric model and it is used here. First, the mean of the distribution in 1 is larger for fixed s than for fixed so· (ie the sources being viewed are biased towards those with large y).
The spectral index for the optically thin part of the jet was -.6. The precession period varied from values so long that no curvature was observed in the size range covered by VLBI observations to values so short that curvature would be visible in several directions. The value of ~ that causes this depends on the radius at which the jet becomes optically thin.
RESULTS
They are up to 8 times brighter than the surrounding regions of the jet, and retain their identity for from one to many precession periods (depending on the parameters). They result from a 'build-up' of material along the line, rather than from an increased Doppler enhancement during part of the precession cycle. 'P (the usual case, given the small values of 'fJ used here), then hot spots will only form on one side of the precession cone.
In both cases, the motion of the hotspots is almost linear, with both Tobs a and . The position of the unresolved nucleus on a VLBI map of a jet corresponds approximately to the point at which the jet becomes optically thin (R = R . ); this. These changes would be very difficult to observe, and any deviation from a purely precessional motion of the jet nozzle would further increase the difficulty of the measurement.
The radio beam of the quasar 4C 32.69 has two sharp bends, around which the intensity remains constant (Potash and Wardle, 1980). The constant intensity around the twists also implies that the twists cannot be caused by a precession-like motion of the jet nozzle, regardless of the jet velocity. The most likely explanation for the twists is a translation of the nozzle perpendicular to the direction of the jet flow (eg due to a close encounter between the quasar and a companion object).
The main problem with explaining nodes in this way is that only one hot spot (node) forms for each precession cycle. Therefore, you should resort to the more conventional nodal origin, unless 1) the real motion of the jet source is much more complicated than precession, and produces several or many hotspots in the 1000 year 'period', or 2) vibration random at the base of the plane is accompanied by explosive events, which cause a disparity. Because of the different time dilation factors for the plane and counter-life, the counter-plane is much more curved than it.
CONCLUSIONS
Counter-jets are not proJllinent in the maps produced from this model, since at a distance R~min(jet) from the core the jet/counter-jet flux ratio is -r4-20• For ri2, the counter-jet would be visible with the currently achievable dynamic range , although for symmetric sources, where y is probably so small, no antijet is seen in msec (Linfield 1981). If the curvature in asymmetric sources is indeed caused by the motion of the jet source, this motion is unlikely to be pure precession. The required precession ages (-1000 years) are too short to be easily explained by known mechanisms.
A more likely situation is an irregular motion of the rotation axis of an accretion disk (caused by stochastic events in the surrounding accretion disk, such as infall from either stars or interstellar gas clouds.). A dynamic range of 30:1 was assumed when making this map, so that it can be compared with current VI.BI maps. The flux of this beam is increased by a factor of 130 above the flux seen by a comoving observer.
The structure in the sky bends 8° from the core to the furthest point visible on this map; the intrinsic bending angle in the beam up to that point is 0.7so. The PA change shown on this map is 37°. compared to an intrinsic bend angle of 4°. The scale on this figure is smaller than in a) - the horizontal bars in a) and b) represent the same distance on the sky.
The distance from the brightest part of the beam (R;:R . ) to the hot spot is indicated. The dynamic ranges of the four maps (contour distances are different on each map) are 100:1.
