Annu. Rev. Astron. Astrophys. 1997. 35: 607-36
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4.1. Helical Jets

Superluminal motion requires that the jet must be relativistic and viewed at a narrow angle to the line of sight so that projection effects are likely to be significant. It is possible to reconstruct the three-dimensional trajectory of a moving feature if an assumption is made for the Lorentz factor, gamma, of the motion. If, for example, a constant pattern speed is assumed, the motion of the outer components in 3C 345 can be reconciled with one fixed curved trajectory where the apparent acceleration is due to changes in angle to the line of sight (Wardle et al 1994). For component C4, the observed curvature and acceleration, and the modest decline in (Doppler-boosted) flux density, are consistent with a curved jet of constant Lorentz factor of gamma about 10 (Zensus et al 1995a). The derived intrinsic jet curvature is small, but it is greatly amplified by projection effects, and the angle of the jet to the line of sight increases smoothly with radius from the core from ~ 1 to ~ 4°.

The observed apparently bent jets with components moving on different ballistic trajectories found in a number of sources can be explained by precession in the region of the nucleus (Blandford 1987): for example, caused by gravitational interaction between galaxies, binary black holes, or black-hole/disk systems. However, the required periods are typically short and cannot easily be reconciled with realistic models (Linfield 1981, Roos 1988). On parsec scales, orbital motion may be a better explanation for the origin of the observed jet structure and kinematics (Roos et al 1993).

A number of models have also been proposed based on helical motion of some sort to explain the curved quasiperiodic trajectories seen in 3C 345, 1803+78, 4C39.25, and similar sources (Camenzind & Krockenberger 1992, Hardee 1987, Königl & Choudhuri 1985, Camenzind 1986, Qian et al 1991, 1996). Helical features in jets are also readily explained from three-dimensional Kelvin-Helmholtz jet simulations (Hardee et al 1995). For the case of 3C 345, the basic properties of component trajectories and apparent velocities for components C4 and C5 have been explained by a simple helical jet with a straight jet axis, which is based on the conservation of physical quantities (Steffen et al 1995). No clear case for a common helix for all components in this source could be made, perhaps because effects in addition to the helical motion are at work. Again, orbital motion at the base of the jet may be the natural explanation for the lack of a unique helix describing the kinematics of all components (Qian et al 1993).

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