![]() | Annu. Rev. Astron. Astrophys. 1984. 22:
319-58 Copyright © 1984 by Annual Reviews. All rights reserved |
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
with angle
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
d
/
d
=
2(dRj / dz)sec(i), where
i is the angle of the jet to the plane of the sky, nonlinearities in
(
) reflect changes in the balance between
pj and pe with distance z. The
(
) 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
d /
d
0.1 (e.g.
27,
48,
198). Between
1 and 10 kpc, these jets "flare", with
d
/
d
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),
d
/
d
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 +
B2
/ 8
, where
pet is the thermal pressure and
B
2
/ 8
represents confinement by
J × B forces of toroidal
magnetic fields B
on any current carried by the jet
(11,
14,
16,
28,
53,
61,
207,
208).
Recollimation requires
pj
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
j
50
(18).
Nevertheless, its first kiloparsec
expands at a constant rate, but the expansion slows beyond knot A; the
B
term has
been invoked
(18)
to explain this behavior.
If the longer rapidly expanding segments of these jets are free, the
observed
d /
d
<< 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
d /
d
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
(
) 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
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
B must also be
supposed to lie (frustratingly unobserved) outside the main
synchrotron-emitting regions.
Jet name | log10Pcore5 |
<d![]() ![]() |
[d![]() ![]() |
[d![]() ![]() |
1321+31 SE | 21.77 | 0.30 | ![]() |
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 | ![]() |
0.58 |
4C T74.17 | 23.26 | 0.12 | - | - |
Her A W | 23.61 | < 0.1 | - | - |
NGC 6251 NW | 23.66 | 0.08 | ![]() |
0.17 |
3C 33.1 | 23.76 | 0.06 | ![]() |
0.09 |
Cyg A | 24.12 | 0.03 | - | - |
3C 219 | 24.18 | 0.07 | ![]() |
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 | ![]() |
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
> 5". At what level
of brightness (if any) in such sources does the synchrotron expansion rate
d
/
d
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
B
required for
magnetic confinement of the jets, by detecting radial changes in
Ba or transverse
rotation measure gradients
(183).
About 40% of jets have spectra between
-0.6 and
-0.7
near 1.4 GHz, and
90% have spectra between
-0.5 and
-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).
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
-0.65 spectrum
(Section 4.2) both expands
laterally and responds to variations in its flow velocity
vj, then the jet's central brightness
I
will vary as
Rj-5.2 vj-1.4 in
B||-dominated regions, or
Rj-3.5 vj-3.1
in
B
-dominated
regions (88,
183). Note that
neither B|| varying as
Rj-2 nor
B
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
I
to decline as a
Rj-4.1 vj-0.9
for a
-0.65 spectrum. Actual
variations of I
with jet FWHM
(assumed
proportional to Rj) are often much slower
than these "adiabats" over large regions of the jets
(27,
118,
183,
278).
Near the core, I
often increases with
- 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
I
declines as
~
-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
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
(d /
d
)n
with 1.5
n
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
B
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
B 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
B
-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
I
(
) evolution. Models of jet
propagation are not yet sufficiently versatile to confront the data at
all of these points self-consistently, however.