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8.2.3 Parameterization of Relativistic Beaming

The adopted beaming model (Sec. 5.6; Appendix B) is undoubtedly too simple. Jets are almost certainly complicated, more so than usually assumed in the statistical tests (Lind and Blandford 1985; Bridle et al. 1994). They are likely to be bent, have variable bulk Lorentz factors, have hot spots at local shocks, and so on, rather than being a well-behaved, ideal confluence of particles, photons, and fields in equipartition. This is borne out by the complex morphologies and trajectories of superluminal components in blazars. Jet velocities probably decrease or increase with increasing distance from the nucleus, whereas we have assumed they are fixed; observed superluminal motion in well-monitored sources is definitely complex (e.g., Biretta et al. 1986). Finally, there is always the problem of flow versus pattern velocity (Sec. 4.2), with only the former causing Doppler boosting.

Moreover, it is not clear how jets form and propagate. By what physical process is matter accelerated to Lorentz factors ~ 5, and sometimes as much as an order of magnitude higher? How is the balance between kinetic and radiative energy determined? Jet formation and motion is almost certainly affected by the local gas environment, which might explain in part the differences between FR I and FR II radio galaxies (De Young 1993; Bicknell 1994), and perhaps why the parsec-scale magnetic field configurations differ in quasars and BL Lac objects. Jet motion is probably also affected by competition between gravitational force and radiation pressure, which moderates the accretion rate. If so, the Lorentz factor could depend on the source Eddington ratio (dotmEdd propto L / M, where M is the mass of the central black hole; Abramowicz 1992).

Unified schemes for radio-loud objects can also be complicated if the beaming is wavelength-dependent. Although this is probably not the case for BL Lacs (Sambruna 1994), it could be important in quasars (Impey et al. 1991, but see also Hough and Readhead 1989). The dependence of beaming on wavelength occurs naturally for an obscuring torus because its transparency is wavelength dependent or for an inhomogeneous jet model with variable Lorentz factor along its length.