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4.1. Collimation, Freedom, and Confinement

The jets in over a dozen radio galaxies (but in few QSRs) have been resolved transversely well enough to show their lateral expansions directly. They are generally center brightened, supporting the view that jets radiate by dissipation in the energy transport region itself, not in a static cocoon around it. The variation of (deconvolved) synchrotron FWHM Phi with angle Theta from the radio core may then track the variation of flow radius Rj with distance z from the nucleus. A steady free jet (whose pressure pj >> pe, the sum of all external pressures) would expand with a constant lateral velocity vr equal to its internal sound speed cs where it first became free. It would widen at a constant rate dRj / dz = vr / vj, unless the flow velocity vj is slowed by gravity. If dPhi / dTheta = 2(dRj / dz)sec(i), where i is the angle of the jet to the plane of the sky, nonlinearities in Phi(Theta) reflect changes in the balance between pj and pe with distance z. The Phi(Theta) data for well-resolved jets show that few are free at all z. Their expansion rates are not set once and for all on parsec scales, even though VLBI jets are first collimated on such scales.

4.1.1   WEAK RADIO GALAXIES   The first kiloparsec or so of well-resolved jets in weak radio galaxies typically expand with dPhi / dTheta leq 0.1 (e.g. 27, 48, 198). Between 1 and 10 kpc, these jets "flare", with dPhi / dTheta reaching values of 0.25 to ~ 0.6 (e.g. 27, 32, 48, 183). On still larger scales they may recollimate (27, 32, 33, 88, 183, 214, 220, 278). In NGC 315 (278) and NGC 6251 (33, 183), dPhi / dTheta oscillates where the jets recollimate; these jets re-expand > 100 kpc from their cores.

The jet pressure is given by pj = pjt + pjr + pjm, where pjt and pjr are the pressures of the jet's thermal and relativistic particles and pjm is the pressure of its magnetic field Bj. The external pressure is pe = pet + Bphi2 / 8pi, where pet is the thermal pressure and Bphi2 / 8pi represents confinement by J × B forces of toroidal magnetic fields Bphi on any current carried by the jet (11, 14, 16, 28, 53, 61, 207, 208). Recollimation requires pj approx pe over many kiloparsecs, but it is unclear which component of pe dominates. Both halves of two-sided jets tend to recollimate at similar distances from their cores (32, 88, 186, 278).

Those in 2354+47 decollimate as they descend intensity gradients in its soft X-ray halo (49). The synchrotron properties of weak radio galaxy jets set lower limits to pj ranging from ~ 10-10 dyne cm-2 in the inner few kiloparsecs to ~ 10-13 dyne cm-2 - 100 kpc from the galactic nuclei. These data suggest, but do not confirm, that weak radio galaxy jets can be collimated solely by pet in hot galactic haloes. Confinement by gas at ~ 1 - 3 × 107 K [cf. the M87 halo (85)] is (just) compatible with the Einstein IPC detections of, or upper limits to, extended soft X-ray sources around several jets, e.g. NGC 315 (278), 3C 66B (152, 168), Cen A (48), and NGC 6251 (183). The contribution of compact nuclear X-ray sources to the IPC data is unclear in some cases, however. Einstein and VLA data for M87 (18, 85) show that the minimum pj in the knots (in this case a few times 10-9 dyne cm-2) exceeds pet at their projected distances in the X-ray halo by least factor of 10; only the first few hundred parsecs of this jet can be thermally confined by the X-ray halo, unless the jet is relativistic with gammaj geq 50 (18). Nevertheless, its first kiloparsec expands at a constant rate, but the expansion slows beyond knot A; the Bphi term has been invoked (18) to explain this behavior.

If the longer rapidly expanding segments of these jets are free, the observed dPhi / dTheta << 1 implies that they are supersonic. The data suggest the jets are collimated initially (and become transonic) < 1 kpc from the nuclei, and that they then escape into regions where pe drops rapidly. If pe falls faster than ~ z-2, continued confinement of a supersonic jet eventually requires that vr > cs (236), so the jet becomes free by "detaching" from pe at an oblique shock (219). If pe again falls slower than z-2 farther out, as in the X-ray halo of M87 (85, 230), the free jet may be reconfined. Conical shocks would propagate into it from its surface, where it first "feels" the declining gradient of pe, reheating it and possibly (re)accelerating relativistic particles in it (76, and references therein). The shock structure downstream from the reconfinement may be quasi-periodic, leading (a) to oscillations in the jet's expansion rate and (b) to regularly spaced knots along it (219). These phenomena may have been observed in NGC 315 (278) and particularly in NGC 6251 (33, 183; Figure 2), whose jet is limb brightened near its first reconfinement, consistent with particle acceleration in the conical shocks.

4.1.2   POWERFUL RADIO GALAXIES AND QUASARS   The jets in more powerful sources expand more slowly than those in weaker radio galaxies - Table 3 gives the average, minimum, and maximum expansion rates dPhi / dTheta for 25 transverse-resolved jets. Several in powerful sources show little systematic expansion, e.g. 3C 33.1 (Table 1, ref. R1), 3C 111 (145), and 3C 219 (184). The small median angle (< 1°) subtended at the radio cores by "hot spots" in powerful doubles (e.g. 238) supports the trend, if the sizes of the hot spots indicate (roughly) the diameters of Mach disks where jets terminate (166, 167). The narrower collimation of the jets in stronger sources, coupled with their greater distances, means that their Phi(Theta) forms are only crudely known. The data are adequate to show, however, that jets in powerful sources must be either (a) free with Mach numbers geq 50, (b) confined by much larger external pressures than those in nearby radio galaxies, or (c) the approaching sides of relativistic twin jets, whose minimum pj is overestimated by the conventional calculation due to Doppler boosting (Section 6.1.7); they are all one sided (Section 3.1), so this interpretation is permitted.

Thermal confinement of the parsec-scale jets in several powerful radio galaxies (but not in Cyg A) is compatible with the X-ray data (144), but for several large-scale QSR jets (271) the Einstein data rule out pure thermal confinement at ~ 1 - 3 × 107 K unless the jets are Doppler boosted. Wardle & Potash (271) argue that freedom is inconsistent with energy and thrust balance (Section 6.1). Eichler (78, 79) discusses balancing pet against the inertia of low-entropy jets to collimate them. Magnetic confinement is also frequently invoked (11, 14, 16, 53, 191, 207, 208). It requires jet currents of ~ 1017 - 18 A if the fields are near equipartition; the return currents are assumed to lie outside the observed radio emission regions. The QSR jets are B||-dominated (Section 3.2), so the toroidal Bphi must also be supposed to lie (frustratingly unobserved) outside the main synchrotron-emitting regions.

Table 3. Expansion data for radio jets

Jet name log10Pcore5 <dPhi / dTheta> [dPhi / dTheta]min [dPhi / dTheta]max

1321+31 SE 21.77 0.30 approx 0 0.4
1321+31 NW 21.77 0.25 < 0.07 0.27
3C 449 N 22.07 0.20 0.1 0.80
3C 449 S 22.07 0.20 0.1 0.45
3C 129 E 22.19 0.13 0.1 0.35
Cen A 22.20 0.19 0.05 0.20
3C 31 N 22.45 0.30 0.08 0.38
3C 31 S 22.45 0.28 0.18 0.36
3C 296 (mean) 22.67 0.16 - -
0326+39 E 22.70 0.22 0.10 0.34
0326+39 W 22.70 0.25 0.10 0.26
M87 22.92 0.07 - -
NGC 315 SE 23.24 0.11 0.06 0.6
NGC 315 NW 23.24 0.11 approx 0 0.58
4C T74.17 23.26 0.12 - -
Her A W 23.61 < 0.1 - -
NGC 6251 NW 23.66 0.08 approx 0 0.17
3C 33.1 23.76 0.06 approx 0 0.09
Cyg A 24.12 0.03 - -
3C 219 24.18 0.07 approx 0 0.15
3C 111 24.47 0.04 0.01 0.06
4C 32.69 25.15 0.06 - -
3C 280.1 26.21 0.05 - -
3C 273 26.92 0.013 approx 0 0.018
3C 279 27.56 < 0.02 - -

4.1.3   COCOONS   The study of jet collimation is complicated by sources such as M84 (Figure 1), 3C 341 (Figure 6), 1321+31 (88), 4C 32.69 (75), and 2354+47 (49) with faint emission "cocoons" around brighter jets. The collimation properties of cocoons may differ radically from those of their jets, e.g. that in M84 (Figure 1) expands much faster than the jets at Theta > 5". At what level of brightness (if any) in such sources does the synchrotron expansion rate dPhi / dTheta indicate streamline shapes in an underlying flow? The minimum cocoon pressures are only ~ 0.1pj (if the jets are unbeamed), so thermal confinement of the jets should crush the cocoons (75). The relationship of cocoons to the brighter structure - whether they are faint "outer jets," static sheaths, or backflows such as those in simulations of thermal matter flows in jets (166, 167) - is unclear. Polarimetry of the cocoons may test whether they contain the Bphi required for magnetic confinement of the jets, by detecting radial changes in Ba or transverse rotation measure gradients (183).

4.2. Radio Spectra

About 40% of jets have spectra between nu-0.6 and nu-0.7 near 1.4 GHz, and geq 90% have spectra between nu-0.5 and nu-0.9. Spectral gradients along most jets are small, but where they have been detected the spectra steepen away from the cores (48, 54, 70, 75, 245), consistent with synchrotron depletion of the higher-energy electrons in the outer jets (277).

4.3. Intensity Evolution

Both the magnetic field strengths and the relativistic particle energies will decrease along an expanding laminar jet, with no magnetic flux amplification or particle reacceleration. If (a) magnetic flux is conserved and (b) the radiating particles do work, as a jet with the typical nu-0.65 spectrum (Section 4.2) both expands laterally and responds to variations in its flow velocity vj, then the jet's central brightness Inu will vary as Rj-5.2 vj-1.4 in B||-dominated regions, or Rj-3.5 vj-3.1 in Bperp-dominated regions (88, 183). Note that neither B|| varying as Rj-2 nor Bperp as Rj-1 vj-1 to conserve magnetic flux are compatible with equipartition of energy between radiating particles and Bj in a confined jet if the particles do work and are not reaccelerated; equipartition requires Bj to vary as Rj-4/3 vj-0.3 and Inu to decline as a Rj-4.1 vj-0.9 for a nu-0.65 spectrum. Actual variations of Inu with jet FWHM Phi (assumed proportional to Rj) are often much slower than these "adiabats" over large regions of the jets (27, 118, 183, 278). Near the core, Inu often increases with Phi - the jets "turn on" following regions of diminished emission, or "gaps" (19, 29, 186, 277; Figures 1, 3, 6). The "turn-on" is often followed by regimes many kiloparsecs long in which Inu declines as ~ Phi-x, with x = 1.2 - 1.6; the value of x reaches ~ 4 in the outer regions of some jets (33, 117, 183, 278), but in NGC 6251 the "adiabatic" decline geq 100 kpc (200") from the core is repeatedly interrupted by the "turning on" of bright knots (see Figure 2 and 183).

It is likely that some of the bulk kinetic energy of the jets (which is not lost by adiabatic expansion) is converted to magnetic flux and relativistic particles through dissipative interactions with the surrounding ISM. Indeed, if Bj is near equipartition on kiloparsec scales, B|| must be amplified locally (instead of falling as Rj-2) or else long B||-dominated jets would have unreasonably high fields on parsec scales. Models for "reheating" of jets include shock formation (24, 66, 167, 219) and various mechanisms following the development of large-scale vortical turbulence (8, 13, 15, 17, 73, 82, 94, 112, 118) from the growth of instabilities at the jet surface. Some models based on large-scale turbulence link the synchrotron emissivity directly to the turbulent power, and hence to the jet spreading rate as (dPhi / dTheta)n with 1.5 leq n leq 3 (17, 82, 118). They can thereby explain why the rapidly expanding jets in weak sources (Table 3) are so conspicuous, and why a jet's most rapidly expanding segments are often those of its most "subadiabatic" intensity evolution (118, 183). Initially laminar jets may also propagate far from their sources before becoming turbulent; rapid fading in the laminar ("adiabatic") regime (as in parsec-scale VLBI jets; Figure 4) can be followed by "turning on" of a large-scale jet in the same direction once turbulence becomes well developed. This may explain the "gap" phenomenon (8, 13, 17, 118, 129). Velocity variations may also keep jets bright in two distinct ways. Fluctuations in vj at the core can produce strong shocks that locally enhance the synchrotron emissivity (206). Entrainment of surrounding material will decrease vj along a jet - the resulting axial compression may partly compensate the effects of lateral expansion, particularly where Bperp dominates (88, 183).

Detailed understanding of what keeps large-scale jets lit up requires self-consistent modeling of their collimation, intensity evolution, and magnetic field configurations. Abrupt changes in Ba from B|| to Bperp at bright knots (Section 3.2) may indicate particle acceleration at oblique shocks, particularly if the knots have their sharpest brightness gradients on their coreward sides, as in M87 (18, 54) and NGC 6251 (183). The degrees of linear polarization in, and the depths of, B|| edges on Bperp-dominated jets may indicate the extent of viscous interactions with the surrounding ISM. The observations provide copious constraints for the models: jet expansion rates, "turn-on" heights, transverse intensity profiles, field orderliness and orientation, as well as the Inu(Phi) evolution. Models of jet propagation are not yet sufficiently versatile to confront the data at all of these points self-consistently, however.

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