2.6. Collimation

All the suggestions that have been made for collimating the beams involve the supposition that the required buoyant fluid of hot (possibly relativistic) plasma escapes along the direction of least resistance, which is likely to be the rotation axis of some central object, disc or gas cloud. We mention three classes of mechanism.

2.6.1 De Laval nozzles. These were first discussed in detail by Blandford and Rees [7]. Aside from uncertainty about the stability of the configuration to Kelvin-Helmholtz and Rayleigh-Taylor instabilities, there are observational constraints on the properties of the gas cloud, which has to be in pressure balance with the outflowing fluid. Blandford and Rees, who considered the specific example of Cygnus A, envisaged a gas cloud with scale height R_* 100 pc supported by gas pressure. This cloud would be a strong X-ray emitter, and the X-ray emission would have been enacceptably high if the scale height R_* were decreased. This question was discussed by Wiita [22], who showed that a somewhat smaller scale was possible. (The required density R_*^-2, so the emission, which depends on ² R_*³, varies as R_*^-1). The assumption that the external pressure is provided by the ram pressure of infalling matter, rather than the thermal pressure, eases the X-ray constraint, but free-free absorption ( T^-3/2) then becomes important. These values of R_* are larger than (or comparable with) the sizes of compact sources, and the parameters are insensitive to the character of the central energy source, provided that its size does not exceed a few parsecs.

As argued by one of us elsewhere in these proceedings, there now seem good reasons for identifying the energy source with a massive accreting black hole. One can then envisage the nozzle as being established on a much smaller scale (maybe 100 Schwarzschild radii). The confinement would then be provided by an optically-thick cloud of infalling material supported primarily by radiation pressure, and the X-ray constraint is then irrelevant. In this model the timescale for variations in the collimation, and for changes in the external cloud, may be as short as a few days.

2.6.2. Flaring disc If the relativistic plasma were generated by magnetic flares in the inner region of an accretion disc [23], or by some exotic process such as e⁺ - e^- pair production near a Kerr black hole [24], (and perhaps channelled by large-scale poloidal magnetic fields), then it may already be sufficiently collimated to make its mean speed along the axis > c_s. There is then no need for a nozzle, though external pressure would refine the collimation as the beam penetrated further from the nucleus.

2.6.3. Radiation-pressure-driven outflow A third possibility, not necessarily completely distinct from (i), is that the beam consists of material accelerated out along the axis solely by the pressure of thermal radiation. If the accretion flow near the hole resembles a "settling solution", then the effective sound speed is ~ c(r / r_s)^-1/2. If angular momentum causes rotational flattening, then material blown off from near the hole will attain terminal velocities comparable with the escape velocity from its starting-point.

There is an appealing advantage to models in which the collimation is established very close to the black hole. The data on extended sources requires that the beam orientation should remain steady for 10⁸ yr, apart from the slow wandering or precession indicated by the apparent "mirror symmetry" in some extended source components (see maps of Cygnus A, 3C 192 and NGC 315 in Dr Willis's contribution). If the confining gas comes from disrupted stars, random infall of gaseous debris, etc, there is no guarantee (and not necessarily any likelihood) that the orientation would achieve this long-term constancy. But near a rotating (Kerr) black hole, Lense-Thirring precession would cause the accreted material to acquire symmetry with respect to the hole's rotation axis (which can change only on the timescale ~ 10⁸ yr on which its mass doubles by accretion). The details of this essentially relativistic effect have been discussed by Bardeen and Petterson [25], with application to compact X-ray sources; but in the present context, the effect would ensure constant beam orientation in any model where collimation occurred in the relativistic domain.

Note that, if the collimation is set up on scales 100r_s, even the most compact radio structure accessible to VLBI observations is very much a "secondary" phenomena, being on scales several orders of magnitude larger. The compact radio components may nevertheless provide important clues to the nature of the (much smaller) object that energises them, and we now turn to consider their properties in more detail.