Contents List of Figures

CONTENTS 265
Contents
6 Macro– and Micro–Jets Driven by Black Holes 267
6.1 DRAG(o)Ns – FR I and FR II . . . . . . . . . . . . . . . . . . . . . . 268
6.2 Jets as Super(magneto)sonic Collimated Plasma Flows . . . . . . . . 275
6.3 Fundamental Parameters for Jets . . . . . . . . . . . . . . . . . . . . 278
6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters . . . . . . . . 283
6.5 Relativistic Jet Propagation . . . . . . . . . . . . . . . . . . . . . . . 288
6.6 Structure and Emission of Micro–Jets . . . . . . . . . . . . . . . . . . 291
6.6.1 Core–Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
6.6.2 Emission Properties . . . . . . . . . . . . . . . . . . . . . . . . 293
6.7 Formation of Micro–Jets . . . . . . . . . . . . . . . . . . . . . . . . . 301
6.7.1 The Stationary MHD Model . . . . . . . . . . . . . . . . . . . 304
6.7.2 The Collimation Zone . . . . . . . . . . . . . . . . . . . . . . 307
6.7.3 Nondiffusive Relativistic MHD Approach . . . . . . . . . . . . 309
6.7.4 Knot Ejection Mechanisms . . . . . . . . . . . . . . . . . . . . 312
7 The First Black Holes in the Universe 318
7.1 The Dark Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
7.2 The First Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
7.3 The First Quasars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
List of Figures
122 VLA Radio interferometer . . . . . . . . . . . . . . . . . . . . . . . . 267
123 Space VLBI VSOP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
124 M 87 – the first Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
125 Structure of the DRAGN Cygnus A . . . . . . . . . . . . . . . . . . . 271
126 Host galaxies of FR I and II . . . . . . . . . . . . . . . . . . . . . . . 272
127 DRAGN M 84 in the Virgo cluster . . . . . . . . . . . . . . . . . . . 273
128 FR I versus FR II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
129 Jet Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
130 Fundamental plane for hydro jets . . . . . . . . . . . . . . . . . . . . 278
131 Luminosity of radio galaxies . . . . . . . . . . . . . . . . . . . . . . . 280
132 Electron density in the Hydra cluster . . . . . . . . . . . . . . . . . . 283
133 Simulated dark matter and gas profiles . . . . . . . . . . . . . . . . . 284
134 Cyg A in X–rays and radio . . . . . . . . . . . . . . . . . . . . . . . . 285
135 Bipolar jets in the cluster gas . . . . . . . . . . . . . . . . . . . . . . 286
136 Jet evolution of 3C galaxies . . . . . . . . . . . . . . . . . . . . . . . 288
137 The radio halo of M 87 . . . . . . . . . . . . . . . . . . . . . . . . . . 289
138 Electron positron jet . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

266 LIST OF FIGURES
139 VLBA image of 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . . 292
140 RXTE light curves of 3C 273 . . . . . . . . . . . . . . . . . . . . . . 293
141 Global spectrum for 3C 273 . . . . . . . . . . . . . . . . . . . . . . . 294
142 Dust emission in 3C 273 . . . . . . . . . . . . . . . . . . . . . . . . . 295
143 VLBA image at 8.4 GHz of NGC 4261 . . . . . . . . . . . . . . . . . 298
144 Disk geometry in the center of NGC 4261 . . . . . . . . . . . . . . . . 299
145 Magnetic jet formation . . . . . . . . . . . . . . . . . . . . . . . . . . 303
146 Black Hole magnetospheres . . . . . . . . . . . . . . . . . . . . . . . 308
147 Particle density along flux tube . . . . . . . . . . . . . . . . . . . . . 310
148 Koide disk–jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
149 3C 120 sequence of images . . . . . . . . . . . . . . . . . . . . . . . . 313
150 RXTE light curves of 3C 120 . . . . . . . . . . . . . . . . . . . . . . 315
151 Knot formation in Jets . . . . . . . . . . . . . . . . . . . . . . . . . . 316
152 Dark ages of the Universe . . . . . . . . . . . . . . . . . . . . . . . . 319
153 Mass range for Black Hole formation . . . . . . . . . . . . . . . . . . 321
154 Cloud formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

6 Macro– and Micro–Jets Driven by Black Holes
267
Active galaxies were first identified in the 1950s when early radio telescopes found
that certain galaxies emit strong radio signals. Something very exotic had to be
going on in those galaxies to produce the energies needed to emit the signals. As
researchers developed new tools that made it possible to see across the entire electromagnetic
spectrum - infrared and ultraviolet emissions, X-ray and gamma ray
sources - astronomers found active galaxies also to be strong emitters of other radiation.
This was more evidence that some kind of extremely energetic process
had to be at work. Scientists have long thought that matter falling into supermassive
black holes might be the power source of active galaxies. That hypothesis
Figure 122: The structure of kiloparsec–scale jets has mainly been investigated by
the VLA radio interferometer.
was strengthened by astronomers’ recent understanding of microquasars, objects
that show characteristics similar to active galaxies but which are less massive and
also much closer to the earth. Being closer - only thousands of light years away -
microquasars have been observed with greater resolution and detail than has been
possible with active galaxies up until now. The active galaxy 3C 120 is 450 million
light years away. The supermassive black hole the researchers expected to be at its

268 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
core would have the mass of at least 30 million suns, yet would be squeezed into
a region smaller than the distance between the earth and the sun. The tremendous
gravitational force of this mass would continuously attract more matter, which
would spiral around the black hole into a thin doughnut-shape called an accretion
disk. A jet was first observed in the radio galaxy M 87 in 1917 by Heber Curtis using
Figure 123: Space VLBI VSOP provides the highest spatial resolution down to 0.1
mas.
an optical telescope. However, it was not until the 1970’s, when observations with
large, high resolution radio telescopes, like the Very Large Array in New Mexico,
revealed the nature of the ”curious straight ray” connected to the nucleus of M 87.
Jets are present in many, if not all, quasars and can extend millions of light years
from the central core of the galaxy.
6.1 DRAG(o)Ns – FR I and FR II
The jets of quasars and Radio galaxies are certainly the most spectacular collimated
plasma flows in the Universe. Their plasma is probably very exotic and is only

6.1 DRAG(o)Ns – FR I and FR II 269
visible in non–thermal emission. In contrast to these objects, jets of normal stellar
objects (young stellar objects, protostars and White Dwarfs) can be detected in
line emission of a normal gas. As such one has a much more direct observational
evidence for the flow velocities, they are moderate a few hundred to a few thousand
kilometers per second in stellar objects.
What are DRAGNs ? DRAGNs are large–scale double radio sources
produced by outflows (jets) that are launched by processes in active
galactic nuclei (AGN). They are clouds of radio-emitting plasma which have
been shot out of active galactic nuclei via narrow jets. The term DRAGN is an
acronym for ”Double Radio Source Associated with a Galactic Nucleus” . It was
coined by Patrick Leahy in 1993 [17].
Most of the extragalactic sources detected by early radio surveys were DRAGNs,
but modern deep radio surveys also detect many sources produced by ”starbursts”
in galaxies. Starbursts can produce radio emission throughout an extended region
of a galaxy, but do not produce significant radio emission in regions far from the
stars that have formed. DRAGNs fundamentally involve the mass concentration in
the nucleus of the galaxy and produce radio emission throughout regions that are
much larger than the host galaxies themselves.
DRAGNs are formed when an active galactic nucleus produces two persistent,
oppositely-directed plasma outflows that contain cosmic ray electrons and magnetic
fields. We do not know exactly what these ”jet” outflows contain, but they clearly
include fast-moving electrons and partially ordered magnetic fields which make them
visible at radio (and higher) frequencies by their synchrotron radiation (emission
that occurs when electrons move across a magnetic field at almost the velocity of
light). To preserve overall charge neutrality, there must also be either protons or
positrons in the outflows.
DRAGNs are made, so it seems, of the stuff that flows down the jets, the socalled
”synchrotron plasma”. We do not know exactly what this is. It radiates in the
radio band (and sometimes at higher frequencies) via the synchrotron process, from
which we can tell that it contains magnetic fields and cosmic-ray electrons. Since
cosmic plasmas must be neutral, there must be also protons or positrons in the jet.
Near the AGN the jets are supersonic, in the sense that the flow speed is faster than
the speed of sound in the jet plasma. As a result, shockwaves form easily, giving rise
to small regions with high pressure, which radiate intensely. Further away from the
AGN, the weaker jets become subsonic and turbulent. Both shocks and turbulence
may help to give the cosmic rays their high energies, via the Fermi mechanism.
Structure of DRAGNs: The main radio structures in a powerful DRAGN whose
jets stay supersonic to great distances are illustrated above with the VLA image of
the radio galaxy 3C 405 (Cygnus A, Fig. 125). A compact radio source usually de-

270 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Figure 124: M 87 in the Virgo cluster is historically the first jet detected in optical
emission (Curtis 1918). With HST the structure of this jet is nicely visible, the jet
ends beyond the extension of the core region of the optical galaxy (top). This jet
has been imaged in radio, optical and X–ray emission (bottom). M 87 is however
not a typical DRAGN.

6.1 DRAG(o)Ns – FR I and FR II 271
Figure 125: Structure of the archetypical DRAGN Cygnus A.
scribed as the ”core” coincides with the galactic nucleus. Most of the radio emission
does not come directly from the well-collimated ”jets”, but from the broader ”lobes”
that are found around the jet paths. The plasma in the lobes is believed to have been
supplied by the jets over millions of years. In the more powerful DRAGNs, there
are usually small, bright radio ”hot spots” near the boundaries of each lobe. These
hot spots thought to be where strong shocks form near the ends of the supersonic
jet outflows in the powerful DRAGNs.
The environs of a galaxy are not a perfect vacuum. The jets must travel first
through the atmosphere of the galactic nucleus, then through the interstellar medium
of the host galaxy, then (if they get that far without being slowed down by interaction)
through the successively lower densities and pressures of the outer halo of
the galaxy, the intra-cluster medium (ICM) of any surrounding group or cluster of
galaxies, and finally into the low-density inter-galactic medium. The jets do not flow
freely away from the AGN, but must push their way through these external media.
Fanaroff–Riley Classification: A landmark in the study of extragalactic radio
sources was the demonstration by Fanaroff and Riley (1974) of the existence of a
relatively sharp morphological transition at a radio luminosity P178 MHz 2.5 ×

272 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
10 26 h −2
50 W Hz −1 . The great majority of sources below this luminosity (FR I type)
are characterized by having diffuse radio lobes, with their brightest region within
the inner half of the radio source (edge–dimmed). On the contrary, more powerful
sources are usually straighter, exhibit edge–brightened (FR II) morphology, and
typically contain hotspots near the outer edges of their radio lobes. Most recently,
Figure 126: Correlation between radio luminosity, absolute optical red magnitude
and Fanaroff–Riley class. 1’s are FR I’s, 2’s are FR II’s and F’s are fat doubles.
[Ledlow et al. 2000]
it was realized that the critical radio luminosity separating the FR I and FR II
actually increases with the optical luminosity of the host galaxy, P ∗ R ∝ L1.65 opt (Fig.
126). The more luminous the host galaxy is, the more powerful the radio source
must be in order to attain the FR II morphology.
There is good evidence that the outflow speeds in DRAGNs are initially relativistic,
i.e. that the material travels outwards at a large fraction of the velocity of light,
often with Lorentz factors of order 10. The velocities appear to decrease along many
of the the jets, however. In the less powerful sources, it appears that the jets are
slowed down enough on the scale of the galaxy to become subsonic and turbulent.

6.1 DRAG(o)Ns – FR I and FR II 273
These FR Type I sources form large-scale plumes that meander across the sky at
the mercy of pressure gradients, shocks and winds in the large–scale intracluster or
intergalactic media. An example is 3C 31 (identified with the galaxy NGC 383),
shown below with the DRAGN in red and the optical field in blue:
In more powerful (FR Type II) sources, it appears that the jets remain at least
mildly relativistic (and supersonic) out to great distances from their host galaxies,
to form the ”classical” double–lobed structures like that shown above for 3C 405
(Cygnus A). In the Type II sources the ends of the jets move outwards more slowly
than material flows along the jet. The plasma arriving at the end of their jets is
then deflected back around them to form the lobes, large ”bubbles” in the medium
surrounding the galaxy.
Sizes of DRAGNs: Individual DRAGNs will tend to grow while their central
engine remains active. The smallest DRAGNs known are only a few tens of parsecs
across, contained within in the active nucleus. An example of a weak, small DRAGN
on a galactic scale is 3C 272.1, associated with the Virgo Cluster elliptical galaxy
M 84 (NGC 4374), shown in Fig. 127 with the DRAGN in red and the optical field
in blue.
Figure 127: DRAGN of FR type I associated with the Virgo cluster elliptical M 84
(elliptical galaxy in blue, radio structure in red).
At the other extreme, giant DRAGNs are the largest known objects, up to several

274 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Megaparsecs from end to end. The lobes of the radio source shown below were
discovered by a low-resolution all-sky survey made with the VLA. They were later
shown to be a single DRAGN by observations that revealed the radio core and the
jets connecting it to these lobes (left panel). The core coincides (central panel)
with a galaxy (right panel) whose redshift is z=0.154. This reveals the double radio
source to be over 4 Mpc in extent, and the second largest DRAGN known. The
largest of them all, 3C236, is about 6 Mpc across. Typical powerful DRAGNs are
Figure 128: Difference in morphology between FR I jet of 3C 31 and a typical quasar
jet (3C 175 at redshift 0.768). Quasars show the most luminous jets with double
sided lobe structure, but only one–sided jets.

6.2 Jets as Super(magneto)sonic Collimated Plasma Flows 275
hundreds of kiloparsecs across, several times bigger than their host galaxies. 1
DRAGNs are almost invariably associated with elliptical galaxies, rather than
with spirals. There appears to be a strong connection, still to be explained in detail,
between the processes that determine the bulge-to-disk ratio of the host galaxy and
the ability to form (and maintain) the active nuclear engine for the time it takes to
build up a large-scale DRAGN.
Ages of DRAGNs: Powerful DRAGNs have estimated lifetimes of order 20 million
years (estimated from synchrotron ages); this makes them a brief outburst in
the life of a galaxy (compare the 100 million years a star may take to orbit the
galaxy’s hub). On the other hand, weak DRAGNs are so common in the largest
elliptical galaxies that the jets must be ”on” essentially all the time. Most of the
radio emission from typical DRAGNs comes not from the jets themselves but from
twin lobes, which are much broader clouds around and near the inferred path of
the two jets. The synchrotron plasma in the lobes is believed to have been supplied
over a long period through the jets. The jets themselves can sometimes be seen as
narrow features threading the lobes. In powerful DRAGNs, small, bright hotspots
are found near the end of each lobe; these are thought to mark the ends of the jets.
6.2 Jets as Super(magneto)sonic Collimated Plasma Flows
The standard interpretation of DRAGNs was proposed independently by Scheuer
(1974) and Blandford & Rees (1974), and the underlying physical mechanism was
broadly confirmed by numerical fluid dynamics in the 1980’s. To understand DRAGNs,
it is crucial to bear in mind that space is not a perfect vacuum. The jets travel out
first through the atmosphere of the galactic nucleus, then through the interstellar
medium of the host galaxy, then (if they get that far) through the successively lower
densities and pressures of the outer halo of the galaxy, the intra-cluster medium of
any surrounding group or cluster of galaxies, and out into the inter-galactic medium.
Although much of this gas is pretty tenuous even by astronomical standards, it is
always denser than the jet plasma. This means the jets cannot flow freely away from
the AGN, but must push their way through the external medium (Fig. 129). As
a result, the ends of the jets move outwards much more slowly than material flows
up the jet. As envisaged by Scheuer and Blandford & Rees, the plasma arriving at
the end of the jet is deflected back to form the lobe, which can be thought of as
a large bubble surrounding the jet. The ”end of the jet” is just the point where
1 Patrick Leahy and Richard Strom have collected an Atlas of DRAGNs that includes images,
vital statistics and brief descriptions of each object. The atlas is served from Patrick’s web site at
Jodrell Bank http://www.jb.man.ac.uk/atlas/. The Atlas is a complete sample of all the DRAGNs
from the Third Cambridge Catalogue of Radio Sources (Second Revision, known as 3CRR), out
to a redshift of z=0.5.

276 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
the jet collides with the surface of the lobe. If the jet is still supersonic at this
point, this collision will take place through a system of strong shockwaves, and the
resulting high–pressure region will be seen as the hotspot. Over the past 20 years,
Figure 129: Structural elements of propagating jets: beam, cocoon, hotspot, contact
discontinuity (which is unstable against Kelvin–Helmholtz instabilities) and bow
shock. Parameters: M = 6, η = 0.01, vB = 0.28c, ΓB = 1.04, resolution = 6 ppb.
[Hughes 1996].
numerical simulations of time–dependent jet flows have progressed enormously from
the earliest two–dimensional axisymmetric gasdynamical flows (Smith et al. 1985)
to three–dimensional flows (e.g., Cox, Gull & Scheuer 1991) until now fully three
dimensional flows incorporating self-consistent MHD are relatively straightforward,
if not yet easy, to model with modest resolution (Krause 2002 [11]; Krause 2003
[12]). These simulation methods have also been extended to include flows in either
2D or 3D with relativistic bulk motions (see review by Marti & Müller 1999 [15]).
Simultaneously, physical models of particle acceleration physics, especially as it relates
to the formation of collisionless shocks, have become much better developed
(e.g., Jones 2001), even if that cannot yet be called a solved problem.
Most of our information about RGs currently derives from radio synchrotron
emissions reflecting the spatial and energy distributions of relativistic electrons convolved
with the spatial distribution of magnetic fields. X-ray observations, especially
of non–thermal Compton emissions, depending on the electron and ambient photon
distributions, are now beginning to add crucial information, as well. Using these
connections, much effort has been devoted to interpreting observed brightness, spectral
and polarization properties of the non–thermal emissions for estimates of the
key physical source properties, such as the energy and pressure distributions and

6.2 Jets as Super(magneto)sonic Collimated Plasma Flows 277
kinetic power, as well as to find self-consistent models for the particle acceleration
and flow patterns. As telescopes and analysis techniques have improved the level of
detail obtained, it has become apparent, however, that the observed properties are
not very simple and much harder to interpret than most simple models predict.
Radiative MHD with NIRVANA C: In the following we work in the one–
component approximation for the dynamical part, but include cooling for the evolution
of different atomic species [11]. The evolution of the jet plasma is given by the
continuity equation for the density ρ, the Euler equations for the momenta ρ V which
have pressure gradient and Lorentz forces as source terms. The magnetic fields B
evolve according to the induction equation, and the time evolution of the internal
energy e is determined by advection, compression and cooling (the K–term)
∂ρ
∂t + ∇ · (ρ V ) = 0 (673)
∂ρ V
∂t + ∇ · (ρ V ⊗ V ) = −∇P − 1
8π ∇ B 2 + 1
4π ( B · ∇) B (674)
∂e
∂t + ∇ · (e V ) = −P (∇ · V ) − K (675)
∂ B
∂t = ∇ × ( V × B) (676)
P = (Γ − 1)e . (677)
These equations are implemented in codes such as ZEUS3D and NIRVANA C [22],
or more modern versions based on shock capturing methods [23].
Cooling Functions for Low–Density Plasmas: Sutherland & Dopita [21] have
presented the equilibrium cooling functions for optically thin plasmas. These can
easily built into the code NIRVANA C. Some functions are terminated before reaching
10 4 K when the internal photoionization halts the cooling. The functions represent
a self-consistent set of curves covering a wide grid of temperature and metallicities
using recently published atomic data and processes. The results have implications
for phenomena such as cooling flows and for hydrodynamic modelling which
include gas components. NIRVANA C can however also handle non–equilibrium
cooling for an entire set of atomic species. Then the above equations must be supplemented
with a network of time evolution for various species. In cases, where
cooling is very rapid compared to dynamical time–scales, this network has to be
solved by means of time–implicit methods.

278 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
6.3 Fundamental Parameters for Jets
Already in early simulations, it turned out that one of the fundamental parameters
for jet propagation is the density contrast η = ρB/ρ0, where ρB denotes the beam
density and ρ0 the external density of the surrounding medium. For relativistic
beams propagating with a Lorentz bulk factor ΓB, the density contrast is given by
η = ρBhBΓ 2 B
ρ0
, (678)
with hB as the specific enthalpy of the beam plasma (= 1 for cold plasma) and ΓB
as the Lorentz factor of the beam propagation. For Quasar jets we typically find
ΓB 5 − 10 from superluminal motion on the parsec–scale. The third parameter
which determines the morphology of a jet is the internal Mach number M = VB/cS
5−10 for the beam plasma. The Mach number is not an independent quantity, since
the beam is steadily heated up by means of internal shocks. In addition, the ratio
Figure 130: Fundamental plane for hydro jets.
between external pressure and internal pressure is also important for the initial
launch of the jet. Overpressured jets will initially expand and then recollimate.
The density contrast determines the hot spot advance speed over momentum
balance at the working surface
vHS = vB
√
ηɛ
1 + √ , (679)
ηɛ

6.3 Fundamental Parameters for Jets 279
provided M >> 1. ɛ < 1 is the ratio of beam to head cross–section. For heavy
jets, η > 1, we find therefore vHS vB, i.e. the hot spot advances with the beam
speed. For light jets, η

280 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Cyg A
L_R = 10^45 erg/s
L_J = 10^46 erg/s
_________________________________________
3C295
___________ FR II / FR I Transition ___________
Figure 131: Luminosity of radio galaxies as a function of redshift. Open circles:
galaxies in the 3C catalog. The radio power varies over many orders of magnitude.
At high redshifts, only the most luminous sources with power comparable to Cyg A
can be detected.
On the FR I – FR II Transition: Many explanations have been given for the
explanation of the FR I / FR II transition. The most widely known explanation is
that, while the jets in both cases start out moving at very high (relativistic speeds),
those in FR II sources remain that way out to multi–kpc distances, while those in
FR I’s decelerate to much slower speeds within a few kpc of the galaxy core. Bicknell
(1995) developed detailed models for decelerating relativistic jets.
An alternative approach assumes that the FR I and FR II sources differ primarily
in the importance of the beam thrust relative to the basic parameters of the ambient
medium (Gopal–Krishna & Wiita 1988; 2001). In this version, the emphasis is on
the slowing down of the advance of the hotspot at the end of the jet, rather than
the slowing down of the bulk flow of the beam. In this scenario, the hotspots of FR
II’s have supersonic advance speed with respect to the ambient medium. When this
advance speed becomes transonic relative to the ambient medium, its Mach disk
weakens due to the fall in ram pressure, and the jet becomes decollimated.

6.3 Fundamental Parameters for Jets 281
The critical density contrast ηcrit can be estimated from the condition that the
bow shock becomes transonic, vHS = cS. For relativistic beams vB c, we find
ηcrit 10 −5 . For η < ηcrit, no bow shock will be found.
For a more quantitative formulation one needs certain empirical relations between
the elliptical’s blue magnitude MB, its soft X–ray emission LX, the stellar
velocity dispersion σ∗ (the Faber–Jackson relation), and the core radius Rc (Kormendy
relation), assuming H0 = 75 (Bicknell 1995)
log LX = 22.3 − 0.872 MB (685)
log σ∗ = 5.412 − 0.0959 MB (686)
log Rc = 11.7 − 0.436 MB . (687)
We furthermore assume a density scaling for the ISM of the elliptical
n(d) =
n0
[1 + (d/Rc) 2 ] δ
(688)
with δ 0.75 typically. Then the hotspot advance speed follows from pressure
balance
vHS(d) = vB
X[1 + (d/Rc) 2 ] δ/2
d/Rc + X[1 + (d/Rc) 2 . (689)
] δ/2
Here X =
4LB/πΘ 2 R 2 cn0µmpc 3 with LB as the beam power, Θ the effective opening
angle for the beam. A reasonable number is Θ 0.1 rad, at least for the inner
jet regions. X corresponds to the above quantity √ χη for cylindrical beams. The
temperature of the X–ray gas is not independent, but tied to the central stellar velocity
dispersion, kT = 2.2µmpσ 2 ∗/δ (Falle 1987). There is evidence that the central
gas density n0 is somewhat higher than the X–ray gas density nX, n0 = κnX with
κ 3. The interstellar density declines quite rapidly at distances beyond a few kpc,
observationally Rc 1 kpc. Hence the most likely regime for the jet’s decollimation
due to hotspots having slowed down to subsonic speeds lies within roughly 10 kpc
of the core.
Gopal–Krishna & Wiita (2001) now evaluate the critical beam power L ∗ B for
which the hotspot deceleration to subsonic velocities occurs at a distance d ∗ 3−10
kpc from the core. 10 kpc is a typical distance at which jets flare in a sample of
radio galaxies. Laing et al. (1999) have studied a sample of 38 FR I sources giving
a mean projected value of 3.5 kpc for the radial distance of the point where the
kpc–scale jet first becomes visible, after passing through an emission gap.
Now X can be scaled to
X = C2
√
LB/ n0Rc
(690)

282 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
where C2 =
4/πΘc 3 µmp = 2.14 × 10 −3 for µ = 0.620. LX can be expressed over
the Bremsstrahlung cooling function, sot hat
log LX = log C1 + log n0 + 3 log aX (691)
log nX = log n0 − log κ = 4.188 + 0.218 MB (692)
log X = −0.109 MB + log C2 + 0.25 log C1 + 3.20 + 0.5 log LB . (693)
We next impose the transonic condition
vHS(d ∗
) = cS = 2.2γ/δ σ∗ 1.5 σ∗ . (694)
For γ = 5/3 and δ = 0.75 this becomes
log vHS(d ∗ ) = 0.345 + log σ∗ = −4.720 − 0.0959 MB . (695)
Equating this to the original expression for vHS gives
dex(−4.720 − 0.0959 MB) =
X
(d/Rc)/[1 + (d/Rc) 2 ] δ/2 . (696)
+ X
This is the relation which must be solved for the critical beam power L ∗ B as a
function of MB. The resulting values are given in the following table (GKW 2001).
For MB > −23.5 this corresponds to a scaling L ∗ B ∝ L 1.6
opt, in good agreement with
MB Rc n0 L ∗ B β ∗
[kpc] [cm −3 ] [erg/s]
-19.5 0.052 2.82 4.35(41) 1.74
-20.0 0.085 2.02 8.28(41) 1.40
-20.5 0.141 1.57 1.71(42) 1.57
-21.0 0.233 1.22 3.57(42) 1.60
-21.5 0.384 0.951 7.23(42) 1.56
-22.0 0.635 0.741 1.49(43) 1.58
-22.5 1.05 0.576 3.06(43) 1.55
-23.0 1.73 0.447 6.21(43) 1.55
-23.5 2.86 0.348 1.23(44) 1.47
Table 8: Galaxy and jet parameters for given elliptical galaxy.
the dividing line in Fig. 126 with β ∗ = 1.65. The actual position for the dividing line
follows from the efficiency of conversion of beam power into synchrotron radiation
of about 10%.

6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters 283
Research Project: The ultimate reason for the FR II/FR I transition is still not
yet clear–cut. The density distribution of the hot gas around elliptical galaxies embedded
into a cluster background is more complex than discussed here. It consists
of two β–laws, one with the core radius of the galactic nucleus, and a second one
with the much bigger core radius of the cluster medium (see recent Chandra measurements).
This produces a jump in the pressure gradients where the two density
laws cross each other. The flaring of the radio jet in FR I sources could just occur
at this pronounced radius.
6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters
Many of the bright 3C galaxies are members of clusters. The density profile is therefore
an important ingredient into the modelling of jet propagation. The observed
electron density distribution for the Hydra cluster is shown in Fig. 132.
Figure 132: Density distribution in the Hydra cluster, as measured with Chandra.
Beyond 200 kpc, the density distribution considerably steepens, ne ∝ r −3 , as expected
from cosmological simulations. [Chandra observation]

284 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
The Archetype Cyg A: Cyg A is the central galaxy of a cluster. The ambient
density is therefore not constant, but follows typically a β–law
ρ0(r) =
ρc
(1 − r2 /r2 . (697)
3β/2
c)
rc 20 − 50 kpc is the core radius for the cluster gas. The Cygnus A radio source
Figure 133: Density profiles for dark matter and baryonic gas as obtained from
simulations. Inside 100 kpc, the gas density profile is quite shallow, beyond 200 kpc
it adjust to the density profile of dark matter.
is situated at the center of a dense cluster atmosphere that extends to a radius of
at least 0.5 Mpc (Smith et al. 2002). The total X–ray luminosity of the cluster is
LX = 1. × 10 45 erg/s at an average temperature of 8 keV, and an electron density at
the position of the radio hotspots (70 kpc from the center) of 0.006 cm −3 . The total
gas mass is 2 × 10 13 M⊙ and the total gravitational mass is 2 × 10 14 M⊙. A number
of signatures in X–rays are expected from the interaction between the jet and the

6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters 285
cluster gas, including emission from the unperturbed atmosphere, excess emission
from the shocked ICM surrounding the radio lobes, and a deficit of emission from
the evacuated radio lobes themselves. X–ray observations provide direct constraints
Figure 134: A low frequency radio image (VLA at 330 MHz, blue to red) superposed
on the Chandra image (yellow–red) of the inner 200 kpc of the Cygnus A cluster.
This shows for the first time the interaction of the radio source and the cluster gas.
on the physical conditions in the emitting regions. In contrast, observations of the
non–thermal radio synchrotron emission provide only information on the properties
of the cocoon and beam plasma. The pressure following from X–ray observations
is 1 × 10 10 dyne cm −2 . Fig. 134 also reveals X–ray emission coincident with radio
hot spots. This is non–thermal IC emission from the same population of electrons
emitting the radio synchrotron photons (SSC emission). While the radio emissivity
is a function of the relativistic electron density and the magnetic field strength, IC
X–ray emissivity constrains the number density alone. From this Wilson derives
magnetic fields of 150 µG for the radio hot spots, the minimum energy field would
be 250 µG.
(i) The Sedov–Phase of Jet Evolution: For density contrasts η < 0.01, the
initial expansion of the bow shock can be described in terms of a Sedov wave propagating
into a medium with decreasing density n(r) = n0(Rrc/r) κ with κ 1.4. The
energy in the bubble increases steadily, E = LBt, as long as the jet power does not
fade away. Similarly to the analysis for supernovae, the expansion of the blast wave

286 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Figure 135: Bipolar jets propagating in the cluster medium. The light blue color
traces the bow shock and the shocked cluster medium, only visible in X–ray emission;
the dark blue marks the shocked cocoon plasma with the contact discontinuity
(visible in synchrotron emission). The cocoon plasma is extremely hot and thin,
typical temperatures are ≥ 10 11 K. The dark colors mark bow shock plasma mixed
into the cocoon via KH instabilities. The core region stays more or less round, while
the accelerating bow shocks lead to a cigar–shape, once the hot spots left the core
region of the cluster atmosphere. [Krause 2002].

6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters 287
is given by [11]
R(t) =
For rc = 10 kpc, this leads to
(3 − κ)(5 − κ)
12πρ0r κ c
1/(5−κ)
t 3/(5−κ) . (698)
R(t) = 3.3 kpc (t/Myr) 1/1.2 . (699)
It is interesting, how accurate this simple formula is when compared to complicated
numerical simulations [11]. For a synchrotron age of Cyg A of 27 Myr, this exactly
corresponds to the radius of the X–ray bubble measured with Chandra (Fig. 134).
Jets must be considered as bipolar outflows working against the background gas of
the cluster medium. For a density contrast η < 0.01, the initial phase is similar to a
supernova explosion. We call therefore this phase the Sedov–phase. As shown by
Cyg A, the bow shock advances only slightly supersonically, the typical sonic speed
in the cluster medius is about 0.5 kpc/Myr, while the bow shock advance speed is
a few kpc/Myr.
(ii) The Cigar–Phase of Jet Evolution: Cygnus A just terminates the Sedov–
phase. The hot spots are on the way to break out of the roundish bow shock due
to acceleration in the decaying cluster atmosphere. In a few million years, Cyg A
will appear as 3C 132 (Fig. 136) consisting of a central cylindrical cocoon filled
with synchrotron plasma and two jets breaking out from this bubble and forming
a cigar–like feature, such as seen in 3C 341. The long cylindrical jets visible in
synchrotron light trace the cocoon plasma which appears highly collimated. The
surrounding bow shock could only be detected in X–rays, is however fairly weak at
distances of a few hundred kpc from the central source.
(iii) The Late Phase Evolution: Since the central activity decays after typically
20 – 50 million years, the radio lobes are no longer fuelled with high pressure
material. The synchrotron plasma gets mixed up with the cluster gas. This leads
to the formation of radio haloes in clusters of galaxies. In Fig. 137 we show the full
extent of the radio source in the Virgo cluster at 327 MHz, about 80 kpc end–to–end.
The inner lobes and jet can just be seen as the red structures in the center (and
the nuclear black hole sits in the center of this inner structure). This picture thus
covers an area larger than the optical galaxy; we are studying the inner region of the
Virgo cluster. The galaxy, and its radio halo, sit in a large atmosphere of hot, X–ray
loud gas (as already detected by the EINSTEIN and ROSAT satellites). From this
image of M 87 we can see that the radio halo is a bubble, with a well–defined outer
edge, sitting inside the X-ray emitting atmosphere. The bright plumes emanating
from the inner lobes tell us that the halo is still ”alive”, being supplied with energy
from the black hole. From our knowledge of the radio jet, we can tell that the jet is

288 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
3C295
3C132
3 Phase Evolution
of Jets
3C341
Figure 136: Time evolution of 3C galaxies as seen by computer simulations. Bright
3C galaxies show various types of morphology, from the Cyg A type (3C 295),
through break–out geometry (3C 132) and the typical cigar–shape (3C 341). These
different forms are the result of a time–evolution of jets in the background of the
inhomogeneous cluster medium.
pumping at least at much energy into the local atmosphere, as is being lost by that
atmosphere to X–rays. This and other evidence tells us, indirectly, that the core
of the Virgo cluster is a complex, turbulent, magnetized region. It is anything but
well-understood.
6.5 Relativistic Jet Propagation
In the last years, the Newtonian approach has been generalized to include relativistic
propagation of the beam fluid. In Minkowski spacetime and Cartesian coordinates
(t, x 1 , x 2 , x 3 ), the conservation equations can be written in conservative form as
(Marti & Müller 1999)
∂ U
∂t + ∂F i ( U)
= 0 . (700)
∂xi

6.5 Relativistic Jet Propagation 289
Figure 137: The kpc–scale jet of M 87 is embedded into a much more extended faint
radio halo (VLA image at 327 MHz). Such extended radio halos are now found in
many clusters of galaxies.
The state vector is defined by
and the flux vector F i as
U = (D, S 1 , S 2 , S 3 , τ) T
(701)
F i = (Dv i , S 1 v i + P δ 1i , S 2 v i + P δ 2i , S 3 v i + P δ 3i , S i − Dv i ) T . (702)
The five conserved quantities D, S 1 , S 2 , S 3 and τ are the rest–mass density, the three
components of the momentum density, and the energy density (measured relative to
the rest mass energy density), respectively. They are all measured in the laboratory
frame, and are related to quantities in the local rest frame of the fluid (primitive
variables) through
D = ρΓb (703)

290 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
S i = ρhΓ 2 bv i
(704)
τ = ρhΓ 2 b − D − P . (705)
v i = u i /u t is the three velocity and Γb the Lorentz factor. The system of equations
is closed by means of an equation of state (EOS), which we shall assume to be given
in the form P = P (ρ, ɛ).
In the non-relativistic limit D, S i and τ approach their Newtonian counterparts
ρ, ρv i and ρE = ρɛ + ρv 2 /2, and the equations of system reduce to the classical
ones. In the relativistic case the equations of are strongly coupled via the Lorentz
factor and the specific enthalpy, which gives rise to numerical complications.
An important property of system (5) is that it is hyperbolic for causal EOS.
For hyperbolic systems of conservation laws, the Jacobians have real eigenvalues
and a complete set of eigenvectors. Information about the solution propagates at
finite velocities given by the eigenvalues of the Jacobians. Hence, if the solution is
known (in some spatial domain) at some given time, this fact can be used to advance
the solution to some later time (initial value problem). However, in general, it is
not possible to derive the exact solution for this problem. Instead one has to rely
on numerical methods which provide an approximation to the solution. Moreover,
these numerical methods must be able to handle discontinuous solutions, which are
inherent to non-linear hyperbolic systems.
The simplest initial value problem with discontinuous data is called a Riemann
problem, where the one dimensional initial state consists of two constant states separated
by a discontinuity. The majority of modern numerical methods, the so-called
Godunov–type methods, are based on exact or approximate solutions of Riemann
problems [23, 20].
Although MHD and general relativistic effects seem to be crucial for a successful
launch of the jet, purely hydrodynamic, special relativistic simulations are adequate
to study the morphology and dynamics of relativistic jets at distances sufficiently far
from the central compact object (i.e., at parsec scales and beyond). The development
of relativistic hydrodynamic codes based on HRSC techniques has triggered the
numerical simulation of relativistic jets at parsec and kilo–parsec scales [18]. In Fig.
138 we show the time evolution of a light, relativistic (beam flow velocity equal to
0.99) jet with large internal energy. The logarithm of the proper rest-mass density is
plotted in grey scale, the maximum value corresponding to white and the minimum
to black.
Highly supersonic models, in which kinematic relativistic effects due to high
beam Lorentz factors dominate, have extended over-pressured cocoons. These overpressured
cocoons can help to confine the jets during the early stages of their evolution
and even cause their deflection when propagating through non-homogeneous
environments. The cocoon overpressure causes the formation of a series of oblique
shocks within the beam in which the synchrotron emission is enhanced. In long term

6.6 Structure and Emission of Micro–Jets 291
Figure 138: Structure of a relativistic electron positron jet. [Scheck et al. 2002]
simulations, the evolution is dominated by a strong deceleration phase during which
large lobes of jet material (like the ones observed in many FR II’s (e.g., Cyg A)
start to inflate around the jet’s head. These simulations reproduce some properties
observed in powerful extragalactic radio jets (lobe inflation, hot spot advance speeds
and pressures, deceleration of the beam flow along the jet) and can help to constrain
the values of basic parameters (such as the particle density and the flow speed) in
the jets of real sources.
Research Project: Relativistic jet simulations have to be adapted to real cluster
profiles. In previous simulations, the jets always propagate in a background medium
of constant pressure and density.
6.6 Structure and Emission of Micro–Jets
There is a wealth of information on the structure of jets on the parsec–scale in
galaxies. In the following we only a few aspects relevant for modelling jet acceleration
and collimation.

292 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
6.6.1 Core–Jets
Parsec–scale jets can only be detected by means of VLBI techniques. Since the jets
are obviously relativistic on this scale, they appear as one–sided (due to relativistic
Doppler beaming), including a stationary core and knots moving away from this
core at superluminal speeds.
Figure 139: A VLBA image of 3C 120 at a frequency of 22 GHz (Walker et al. 1996).
The scale is in milliarcseconds (mas). (At the distance of 3C 120, 1 mas corresponds
to a length of 0.7 parsecs = 2.3 light-years.)
3C 120: In Fig. 139 we show the structure of the parsec–scale jet of the radio
galaxy 3C 120 at 22 GHz (1 mas = 0.7 parsecs for a Hubble constant of 65
km/s/Mpc). There is an unresolved stationary feature on the left (eastern) end,
customarily called the core. Bright spots (termed blobs by experts) move down the
jet. Of particular interest is a bright blob that emerges from the core after a major
outburst in brightness (flux density) in early 1998 (Fig. 149). The speeds of the
superluminally moving components range from 3.5 to 8.3 times the speed of light.
The magnetic field behavior is complex, changing with both position and time. The

6.6 Structure and Emission of Micro–Jets 293
core, however, is usually unpolarized. 2
6.6.2 Emission Properties
As the brightest and nearest quasar (z = 0.158), 3C 273 is an ideal laboratory to
study emission processes for jets in quasars. This source displays significant flux
variations, has a well measured wide band spectral energy distribution and has
a relativistic jet emanating from the central part in a galaxy. This collimated jet
structure extends up to 150 kpc from the core, depending on the unknown inclination
towards the observer. 3C 273 is classified as a blazar – though I find this notion
somewhat misleading – and is also a prominent gamma–ray source.
3C 273 and the hard X–ray emission: Recently, the results of a long–term
monitoring of 3C 273 with RXTE have been published (Kataoka et al. 2002). This
covers the longest observation period in the hard X–rays (about 835 ksec, Fig. 140).
Most of the 3C 273 photon spectra observed between 1996 and 2000 can be fitted
Figure 140: RXTE light curves of 3C 273 in the hard X–rays (Katakoa et al. 2002).
The data are binned in 10 days intervals.
by a power–law spectrum with spectral index αX = 1.6 ± 0.1. This is consistent
with previously published data. Multifrequency spectra provide information for
physical quantities relevant to the jet physics, e.g. the magnetic field, the size of
the emission region, the maximum energy and the density of relativistic electrons.
2 For a movie see http://www.bu.edu/blazars/3C120.html

294 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
von Montigny et al. (1997) examined 3 models to reproduce the multifrequency
spectrum of 3C 273: (i) the synchrotron–self Compton model (SSC model); (ii) the
external radiation Compton model (ERC model; Sikora, Begelman and Rees 1994),
and, (iii) the proton induced cascade model (PIC model; Mannheim & Biermann
1992). At that time, the authors concluded that the data were still insufficient to
discriminate between the models. In Fig. 141, a simple one–zone model is shown to
explain the spectrum. In this simple model, the radiation is due to a homogeneous
jet component moving with a bulk Lorentz factor ΓBLK at an angle of line of sight
Θ 1/ΓBLK. It is assumed that the peak emission of the low–energy synchrotrn
component (LE) and the high energy inverse Compton components (HE) arise from
the same electron population with Lorentz factor γp. The peak frequencies of LE
and HE are related by
νHE,p = 4
(706)
3 γ2 pνLE,p
with νLE,p = 10 13.5 Hz, and νHE,p = 10 20 Hz. This requires a γp = 2 × 10 3 . The
Figure 141: Global spectrum for 3C 273 with X–rays as explained by SSC–emission
(Katakoa et al. 2002).
synchrotron peak frequency νLE,p is given by
νLE,p = 3.7 × 10 6 B γ 2 p
D
Hz (707)
1 + z

6.6 Structure and Emission of Micro–Jets 295
where B is the magnetic field strength in Gauss and D = Γ −1
B (1 − β cos Θ) −1 ΓB
is the relativistic Doppler factor. From the above numbers we get then a magnetic
field strength
and a corresponding energy density
B 0.4 × 10
ΓB
UB 6.7 × 10 −3
10
ΓB
2
G (708)
erg/cm 3 . (709)
The ratio of the synchrotron luminosity and the inverse Compton luminosity
Figure 142: Global IR spectra for 3C 273 and similar quasars with possible dust
emission in the mid–infrared (Meisenheimer et al. 2001).
LSSC
LS
= US
UB
(710)

296 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
is independent of the bulk motion. US is the energy density in the synchrotron
photons measured in the comoving frame of the jet. With LHE = 10 47.1 erg/s and
LS = 10 46.8 erg/s we obtain
US 0.02
2 10
erg/cm
D
3
Assuming a spherical geometry for the emission region of radius R
providing a radius
(711)
LS = 4πR 2 cD 4 US erg/s , (712)
R 2 × 10 16 cm 10
. (713)
D
The SSC spectrum is then calculated self–consistently from these numbers for an
electron distribution of the form N(γ) ∝ γ−2 exp(−γ/γp). This would indicate that
the inverse Compton emission is radiated in an extremely compact region near the
collimation region. The spectrum in the radio band can usually not be fitted by
simple one–zone models, since this low–frequency emission occurs on much larger
scales in the jet.
An ERC model can however also fit the observed spectra. Part of the mid–IR
and far–IR radiation is in fact emitted by warm dust in a dusty torus located on the
parsec–scale in the center of the bulge of the host galaxy of 3C 273 (Meisenheimer et
al. 2001, Fig. 142). This is a common feature for strong radio galaxies (Cyg A e.g.)
and radio–loud quasars. This dust emission zone can roughly be approximated by a
shell of radius RD 10 pc, so that the energy density inside the shell as measured
in the comoving frame of the jet is
UD = LD
4πR 2 Dc Γ2 BLK 10 −3 Γ 2 B erg/cm 3 ξDLUV X
10 47 erg/s
10 pc
RD
2
. (714)
The factor ξD 0.5 represents the fraction of the UV–bump luminosity reprocessed
by dust emission. This factor is quite high in Quasars. In particular, all photons
directed inwards towards the central source are blue–shifted, and enhanced by a
factor ΓB with respect to the comoving frame of the jet. On the parsec–scale,
this external photon density is the dominant source for inverse Compton
scattering. With such an ERC model the frequencies are now interrelated as
νHE,e = 4
3 γ2 eΓ 2 B νIR . (715)
The dust spectrum also peaks at νIR 10 13.5 Hz (warm dust). For ΓJ 10, this
only requires a γe 100. This is the typical Lorentz factor for the electrons in an

6.6 Structure and Emission of Micro–Jets 297
ion jet and corresponds to the minimal electron Lorentz factor required by global
spectra (Ghisellini et al. 2001).
Relativistic electrons are a natural consequence in relativistic jets. The plasma
in such jets is automatically heated to high temperatures by internal shocks (see
previous sections). The ion component essentially stays hot and can only cool over
adiabatic expansion. The electrons stay probably extremely hot since the jet material
passes through various shocks. In quasars, inverse Compton cooling is probably
the fastest mechanism on the parsec–scale with a cooling time given by
tIC =
mec 2
(4/3) σT cUphγe
10 yrs (716)
for γe = 1000 and Uph 10 −3 erg/cm 3 . Without reheating, the electrons would cool
down to a mean Lorentz factor γmin 50−100, when traversing the dust shell. The
heat carried by the electrons is therefore a rough measure for the inverse Compton
luminosity
LIC Lheat,e = ˙ MBc 2 < γe > (me/mp) < LB . (717)
The magnetic field structure can essentially be probed by means of Faraday
rotation
8.1 × 105
RM =
< γe > 2
neB dl[pc] rad m −2 , (718)
where the electron density ne is given in units of particles per cc and < γe >
is the mean energy of the relativistic electrons. The classical expression of the
rotation measure has to be corrected by the square of the Lorentz factor for the
electrons, since the rotation measure is proportional to the plasma frequency and the
cyclotron frequency. The parsec–scale jet of 3C 273 has a typical rotation measure
RM 300 rad m−2 . This indicates that the internal Faraday rotation is negligible.
It is probably produced by the electrons in the ISM of the galactic nucleus.
NGC 4261 and the state of the disk at 0.1 pc: The structure of the inner
disk in nearby radio galaxies can be probed by synchrotron emission from the jets
over free–free absorption. The nearby low–luminosity FRI–galaxy NGC 4261 (3C
270, Fig. 143) is a good candidate for detecting free–free absorption by ionized gas
in the inner disk [9, 24]. The galaxy is known to contain a Black Hole with a mass of
MH = 7×10 8 M⊙ (Ferrarese, Ford and Jaffe 1996), a nearly edge–on disk of gas and
dust with a diameter of about 100 pc. The large–scale symmetric radio structure
implies that the radio axis is close to the plane of the sky. First VLBA observations
revealed a parsec-scale radio jet and counter–jet aligned with the kiloparsec–scale
jet [9]. The opening angle is less than 20 degrees within 0.2 pc from the core and
less than 5 degrees within 0.8 pc. The free–free optical depth is given by
τff = 9.8 × 10 −3 Ln 2 e T −3/2 ν −2 (17.7 + ln(T 3/2 /ν)) , (719)

298 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Figure 143: The radio galaxy NGC 4261 and its nuclear disk (HST, top panel) with
a VLBA image at 8.4 GHz (bottom panel, Jones et al. 2001). At a distance of 40
Mpc, 1 mas corresponds to 0.2 pc. A 700 Mio solar mass Black Hole in the center
generates the jets in this radio galaxy.

6.6 Structure and Emission of Micro–Jets 299
where the path length L is in cm, and the electron density in cm−3 . From this we
can estimate the electron density
ne 3.4 τ/L νT 3/4
(720)
For a path–length L 0.3 pc, τff 3 and a temperature T 10 4 K, this corresponds
to an electron density ne 3 × 10 4 cm −3 . Since the temperature decays in a
Figure 144: Disk geometry in the center of NGC 4261 [Jones et al. 2001; Wehrle et
al. 2002].
SAD very rapidly with increasing radius, accretion disks around supermassive Black
Holes are expected to have a partial ionization zone, as in Galactic binaries, and
therefore to be subject of a similar thermal instability. This zone forms at a distance
of a few hundred Schwarzschild radii from the center (Lin and Shields 1986; Clarke

300 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
1989). Depending on the viscosity, the instability can develop in a very narrow
unstable zone and propagate over the entire disk resulting in this way in a large–
amplitude outburst on time–scales of the order of a few 10 5 years (Siemiginowska et
al. 1996).
In standard disk models one finds a local equilibrium relationship between a
steady state accretion rate ˙ M and the surface density Σ for given mass, viscosity
parameter α and radius R. This relationship has a characteristic S–shape for an
optically thick, geometrically thin disk. Three characteristic regions on the S–curve
describe different physical conditions. The lower branch is thermally stable, cool,
and neutral hydrogen dominates the chemical composition, molecules also contribute
to the opacity. A disk on the upper branch is also thermally stable, but is hot, and
hydrogen is fully ionized. Bound–free transitions in heavy metals, free–free transitions
and electron scattering determine the opacity. The middle branch corresponds
to a partially ionized disk that is thermally unstable due to the rapid increase of the
opacity with temperature. The instability strip is located at an effective temperature
of TA 4000 K, and its radius RA can be derived from the local values of ΣA
and TA (Siemiginowska et al. 1996)
RA 10 3 Rg M −0.6
H,8
˙M 0.4 α −0.05
−1 . (721)
This corresponds to a radius of about 100 Schwarzschild radii in the core of NGC
4261. Local accretion occurs then on the viscous time–scale, tvisc R/v r , or
tvisc 2 × 10 5 yr α −0.8
−1 M 1/4
8
˙M −0.3 R 1.25
16 . (722)
The disk beyond RA is optically thin (Clarke 1988). All the energy produced
dissipatively is radiated away by free–free emission. Under these conditions, the
ionisation instability requires the disk to be either in an optically thin hot state
or an optically thick cool state. These values are consistent with the particle
densities obtained for a standard accretion disk at a distance of 10 4 gravitational
radii (Camenzind 1997),
n 24 cm −3 α −1 ˙m −2 M −1
H,9
R
10 4 Rg
−3/2
. (723)
For a turbulence parameter α 0.1 and a relative mass accretion rate ˙m =
˙M/ ˙ MEd 0.01 this gives a particle density n 10 6 cm −3 with an ionisation fraction
of about 10%. The temperature of the disk at this position is in fact about 10000 K
TD(R) 10 4 K α −1/4 M −1/4
H,9
R
10 4 Rg
−3/8
. (724)
This absorption through the disk produces a gap in the low–frequency emission
detected from the counter–jet (Fig. 143, Jones et al. 2001).

6.7 Formation of Micro–Jets 301
6.7 Formation of Micro–Jets
In accretion and jet production theory the principal parameters determining the
appearance and behavior of the system are the black hole mass MH, the mass accretion
rate ˙ M, and the black hole angular momentum J, expressed in dimensionless
form as m9 = MH/10 9 M⊙ (where M⊙ represents one solar mass), ˙m = ˙ M/ ˙ MEdd
(where ˙ MEdd = 4GMH/ɛHκesc = 22 M⊙ yr −1 m9 is the accretion rate that produces
one Eddington luminosity for an efficiency ɛH = 0.1 and electron scattering opacity
κes), and j = J/Jmax (where Jmax = GM 2 H/c is the angular momentum of a maximal
Kerr black hole). For most AGN and quasar models typical ranges of the parameters
are 10 −3 < m9 < 10, 10 −5 < ˙m < 1, and 0 < j < 1. While all parameters will affect
the properties of an AGN to a certain extent, the purpose here is to identify the
principal observable effects of each.
The accretion paradigm states that most, and perhaps all, AGN are powered
by accretion onto a supermassive black hole. Within this model ˙m plays the most
important role, determining the emission properties, and therefore the appearance,
of the central source. Objects with high accretion rate ( ˙m > 0.1) appear as an “optical”
quasar (of course, equally bright, if not brighter, in X-rays as well), while low
sub-Eddington accretion ( ˙m ≤ 10 −2 ) produces a weak “radio” core with substantially
less optical emission. A zero accretion rate produces a “dead” quasar - a black
hole detectable only through its gravitational influence on the galactic nucleus. For
a given level, the black hole mass determines mainly the luminosity scaling.
The spin paradigm states that, to first order, it is the normalized black hole
angular momentum j that determines whether or not a strong radio jet is produced
(Wilson & Colbert 1995, Blandford 1999). If correct, this hypothesis has significant
implications for how we should view the jets and lobes in radio sources: the jet radio
and kinetic energy comes directly from the rotational energy of a (perhaps formerly)
spinning black hole. Radio sources are not powered (directly) by accretion.
There is significant theoretical basis for this paradigm as well. Several models of
relativistic jet formation indicate that the jet power should increase as the square
of the black hole angular momentum
Ljet 10 44 erg s −1
2
BH
m9j
1000 G
2 . (725)
where BH is the strength of the poloidal (vertical/radial) magnetic field threading
the ergospheric and horizon region of the rotating hole. In this model rotational
energy is extracted via a Penrose-like process: the frame-dragged accretion disk is
coupled to plasma above and outside the ergosphere via the poloidal magnetic field;
some plasma is pinched and accelerated upward while some disk material is diverted
into negative energy (retrograde) orbits inside the ergosphere, removing some of
the hole’s rotational energy. The key parameter determining the efficiency of this

302 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
process is the strength of the poloidal magnetic field. The standard approach (e.g.,
Moderski & Sikora 1996) to estimating BH is to set it equal to Bφ, the dominant
azimuthal magnetic field component given by the disk structure equations, yielding
and
Ljet,B = 2 × 10 45 erg s −1 m9 ˙m−2 j 2
(726)
Ljet,A = 3 × 10 49 erg s −1 m 0.8
9 ˙m−1 j 2 . (727)
for Class B (radio galaxy/ADAF) and Class A (quasar/standard disk) objects, respectively.
Note that, while the jet is not accretion-powered in this model, the
efficiency of extraction is still essentially linear in ˙m.
Basic physics of MHD acceleration and collimation: Though many models
have been proposed to generate jets, the magnetohydrodynamic (MHD) model is still
the leading one (Fig. 145). In this picture, the plasma is simplified in terms of a one–
component approximation and the conductivity is assumed to be very high so that
electric fields in the plasma are shorted out. In a first approximation, plasma is not
allowed to cross field lines, it can only flow parallel to them. In regions where the field
is weak or the plasma is dense, the rotating field will be bent backward. To accelerate
and collimate a jet with magnetic fields, all that is needed is a gravitating body to
collect the material which should be ejected, a poloidal magnetic field threading that
material, and some differential rotation, which produces a helical structure in the
field. This rotating field structure drives the confined plasma upwards and outwards
along the field lines. As this twist propagates outwards, the toroidal field pinches
the plasma towards the rotational axis. Depending on the relative importance of
the magnetic field, the plasma density and rotation, a variety of configurations are
possible from spherical winds, slowly collimated and highly collimated outflows.
Poloidal magnetic field strengths are estimated from equation disk pressure, but
(H/R) is of order unity for the low cases, and also for the high Kerr case due to
Lens-Thirring bloating of the inner disk. Otherwise (H/R) is calculated from the
electron scattering/gas pressure disk model of Shakura & Sunyaev (1973), and disk
field strengths are computed from that paper or from Narayan et al. (1998), as
appropriate. The logarithms of the resulting poloidal field strengths, and corresponding
jet powers, are represented as field line and jet arrow widths. In the Kerr
cases, the inner disk magnetic field is significantly enhanced over the Schwarzschild
cases, due in part to the smaller last stable orbit (flux conservation) and in part to
the large (H/R) of the bloated disks. The high accretion rate, Schwarzschild case has
the smallest field - and the weakest jet - because the disk is thin, the last stable orbit
is relatively large, and the Keplerian rotation rate of the field there is much smaller
than it would be in a Kerr hole ergosphere. Enhancement of the poloidal field due
to the buoyancy process suggested by Krolik (1999) is ignored here because we find

6.7 Formation of Micro–Jets 303
Figure 145: Essential elements for magnetic jet formation. A torus of hot gas is
initially magnetized by vertical magnetic fields. The differential rotation of the
torus drags the field lines in the azimuthal direction, angular momentum is thereby
carried away from the disk material which allows the material to accrete inwards
towards the horizon. This exerts a torque on the external field with a kind of
torsional Alfvèn wave. This carries away angular momentum and energy from the
system. [Meier et al., Science 291 (2001)].

304 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
it not to be a factor in the simulations discussed below. If it were important, then
the grand scheme proposed here would have to be re-evaluated, as the effect could
produce strong jets (up to the accretion luminosity in power) even in the plunging
region of Schwarzschild holes. Then even the latter would be expected to be radio
loud as well (Ljet 10 43−46 erg s −1 ).
6.7.1 The Stationary MHD Model
For BHs the above processes must be modelled with relativistic MHD. The time–
dependent analysis of this theory is however not yet fully developed. One can get
some insight from considerations of the plasma confinement analogue.
Plasma flow near the horizon is presently not observable due to the limited spatial
resolution of VLBI. So we cannot test directly the jet formation scenarios. The only
viable model for the generation of relativistic jets is however MHD models, where
collimation occurs on scales of a few hundred Schwarzschild radii. Such collimated
plasma beams will have therefore a kind of conical structure on scales of a few
thousand Schwarzschild radii (fraction of parsecs) to scales of a few hundred parsecs.
We can describe these plasma beams as a stationary equilibrium between various
forces (Appl & Camenzind [1])
κ B2 p
4π (1 − M 2 − x 2 ) = (1 − x 2 B
)∇⊥
2 p B
+ ∇⊥
8π 2 φ
+ ∇⊥P
8π
− B2 pΩF 4πc2 ∇⊥(Ω F R 2
2 µnj I2
) + −
R3 4πR3
(−∇⊥R) . (728)
Pressure gradients acting perpendicularly to the magnetic surfaces are in equilibrium
with electric forces, centrifugal forces, pinch forces generated by the poloidal currents
(I), as well as with curvature forces expressed on the left hand side. This is the
correct generalisation of well known pressure forces in Newtonian plasma pinches.
This equilibrium assumes a particualr simple form for cylindrical configurations,
κ = 0
(1 − x 2 ) d B
dR
2 p
8π
d B
+
dR
2 φ
8π
− B2 pR
2πR2 −
L
µnj 2
I2
−
R3 4πR3
= 0 . (729)
This can be written for the dimensionless variables, x = R/RL, y = B 2 p/B 2 0 and
I = RBφ → I/RLB0 as
(1 − x 2 ) dy 1
− 4xy +
dx x2 dI2 8π
+
dx B2 0
dP
dx
− 8πµn
B 2 0
j2 (cRL) 2 = 0 . (730)
x3

6.7 Formation of Micro–Jets 305
This is an extension of the force–free equation discussed by [1]. Pressure and tension
due to the toroidal field are combined into one expression for the variation of the
current, or the pinch force. The electric field also contributes a positive pinch
force, −x 2 dy/dx, which is opposite to the usual pressure force. These two forces
can therefore compensate for all pressure forces and lead to a pinch equilibrium.
Outside the light cylinder, R > RL the current assumes the simple expression
I = −Ω F (R 2 Bp) 1
βJ
(731)
and the specific angular momentum j of the plasma stays constant, i.e. the rotational
velocity of the plasma decreases as 1/R. This shows that the centrifugal force has a
negligible influence on the plasma equilibrium outside the light cylinder. Under this
condition we get a core–halo structure for the distribution of the poloidal magnetic
field
Bp
with the core radius Rc = ΓJβJRL and
Bφ − B0
βJ
B0
1 + R 2 /R 2 c
R/RL
1 + R 2 /R 2 L
(732)
. (733)
The beam radius RJ is probably larger than the core radius and given by pressure
equilibrium with external pressure. The plasma in the beam is rotating with nearly
the speed of light at the light cylinder.
The total electron density in the beam is
ne =
˙MJ
πR 2 Jmpc
100 cm−3
˙MJ
0.1 M⊙ yr −1
3 × 10 9 M⊙
MH
2 1000 2
Rg
The mass–flow in the beam is also related to the total jet kinetic energy
LJ = ˙ MJc 2 (ΓJ − 1) 5 × 10 46 erg s −1
˙MJ
0.1 M⊙ yr −1
RJ
. (734)
ΓJ
. (735)
10
This is a reasonable number for the outflow rate of bright quasars, since about a
few percent of the inflow is probably converted to outflows. The outflow rate in M
87 is estimated to be about a factor 100 lower than this number (Camenzind 1999).
These numbers tell us that the Alfven speed in the beam is about the speed of light
for
VA c B0/0.3 G
. (736)
n/10 cm−3 So one has to use the correct expression for the Alfven speed.

306 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Physical Parameter Symbol 3C 273 M 87
Black Hole mass MH [M⊙] 3 × 10 9 3 × 10 9
Gravitational radius Rg [AU] 30 30
Black Hole spin a 0.9 MH 0.8
Light cylinder RL/Rg 20 20
Bulk Lorentz factor ΓJ 10 6
Inclination ΘJ [deg] 8 20
Jet core radius Rc = ΓJRL 0.1 lyr 0.01 lyr
Beam Radius RJ 0.1 pc 0.03 pc
Ion number density nJ 6 cm −3
Ion temperature Ti 100 MeV 100 MeV
Beam sonic Mach number M = ΓJβJ/cS 30
Mass flux ˙ MJ 0.1 M⊙ yr −1
Magnetic field B0 0.1 Gauss 0.03 G
Magnetic flux ΨJ B0R 2 c 10 33 G cm 2
Total current IJ cRcB0 10 18 Amp
Alfvèn Mach number MA = ΓJβJ/VA 10 10
Fast magnetos. M number MF M 5 5
Mean e − Lorentz factor γe 100 50
Cutoff e − Lorentz factor γp 2000 2000
Table 9: Parameters of the MHD parsec–scale jet in 3C 273 and M 87. The Black
Hole mass in 3C 273 is estimated from the similarity of its host galaxy with M 87,
the mass in M 87 has been derived from the HST disk. The spin parameters are
essentially unknown.

6.7 Formation of Micro–Jets 307
VLBI jets are extreme plasma pipes, where all communication occurs
over the speed of light – the Alfven speed and the fast magnetosonic speed
are relativistic. The plasma in these pipes is also exotic: it is permanently heated
to high temperatures of the order of 10 12 K by means of internal shocks. The ions
are probably still non–relativistic, while the electrons always assume relativistic
temperatures with < γe > 100, which are then subject to acceleration to even
higher energies by various mechanisms.
6.7.2 The Collimation Zone
I am still convinced that jets in quasars are launched by complete MHD processes
and that this will be modelled some day within General Relativistic MHD. The
following elements should be included
• a dipolar magnetosphere that closes radially towards the horizon;
• hot plasma is launched from the innermost part (probably within the ergosphere
region) in radial direction;
• Along the axis, higly relativsitic plasma is injected from a polar gap. This
plasma is energetically not important, but it carries the closure currents.
• The gap is feeded by a pair plasma created from photoproduction in the ion
torus near the horizon.
• The toroidal field amplified by the frame–dragging effect leads to additional
J × B–forces near the ergosphere.
Structure of the magnetosphere: The calculation of the magnetosphere in the
stationary approach is very cumbersome (Beskin 1996; Camenzind [6]; Fendt &
Greiner [7]), since the current distribution has to be found self–consistently (this
exercise is in fact better done within a time–dependent approach). The transition
from the highly diffusive disk towards the ideal outflow conditions has however
hampered down all modelling so far. What is urgently needed for this process is a
realisation of the GR MHD equations on the background of compact objects. The
form of the magnetosphere shown in Fig. 146 is a first guess.
The Plasma Outflow: It has been shown that the stationary axisymmetric and
polytropic plasma flow along an axisymmetric magnetic flux tube Ψ(r, θ) can be
described by means of an algebraic wind equation (Camenzind [6]; Fendt & Greiner
[7]). The essential quantity which determines the asymptotic plasma flow is the

308 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Figure 146: The Black Hole magnetosphere consist of a family of nested magnetic
surfaces, and plasma can only flow along the flux surfaces. Currents can however
cross the flux surfaces. Only in the force–free approximation, currents are also force
to flow along the flux surfaces. This is in general violated near the Alfven points.
[Fendt 2001]
magnetissation parameter σ∗ at the injection point
σ∗ =
Φ∗
4πmpIp;∗
(737)
measuring the Poynting–flux in terms of the particle flux Ip = √ −gnup, where up
is the poloidal velocity along the flux–tube. The form of the flux–tube is expressed
in terms of the dimensionless flux–tube function Φ, Φ ≡ 1 is a pure monopole
flux surface. The other wind parameters are the total energy E and total angular
momentum L carried by the plasma. At the magnetosonic points the wind equation
becomes singular, and this fixes two parameters (for more details, see Lecture by
Beskin). In terms of astrophysical quantities, the magnetization parameter is given

6.7 Formation of Micro–Jets 309
as (Camenzind [6])
σ∗
Ψ 2 ∗
2c ˙ MJ(Ψ)R 2 L
= B2 p,∗R 2 L
c ˙ MJ(Ψ)
4
R∗
RL
. (738)
˙MJ(Ψ) denotes the jet mass flux carried by the flux surface Ψ, and RL = c/Ω F is the
light cylinder radius of the flux surface. With an idea on the maximal flux provided
by the disk near the horizon,
Ψ∗ ˙ MaccR 2 ∗
αT
Rg
R∗
we can estimate the value of the magnetization
−1
H
R
(739)
σ∗ (740)
The outflow starts hot, cS,∗ 0.3c and is then continuously accelerated, until collimation
is reached (Fig. 147). thereby, the particle number decreases rapidly and
also the temperature decreases adiabatically.
6.7.3 Nondiffusive Relativistic MHD Approach
Recent work by Koide, Shibata and Kudoh on general relativistic simulations of the
accretion of magnetized material by black holes is beginning to provide a clearer
picture of the development and evolution of a black hole magnetosphere and the
resulting jet. Initial indications are that rapid rotation of the black hole and rapid
infall of the magnetized plasma into this rotating spacetime both contribute to
powerful, collimated, relativistic jet outflows. We find no evidence for buoyant
poloidal field enhancement in the plunging region and, therefore, no reason to expect
Schwarzschild holes to have a jet any more powerful than that estimated in Figure
148. Figure 148 shows the initial and final state of a Kerr (j = 0.95) black hole
simulation with a weak (VA = Bp/ √ 4πρdisk = 0.01c) magnetic field and an inner
edge at Rin = 4.5GMH/c 2 . For more details see Koide et al. (1999a). In this first
simulation the disk was non-rotating, and so began to free-fall into the ergosphere
(at Rergo = 2GMH/c 2 ) as the calculation proceeded. As with other MHD disk
simulations, the field lines were wound up by differential rotation and a hollow jet
of material was ejected along the poloidal field lines by the J × B forces; here the
jet velocity was rather relativistic (vJ 0.93c or 2.7). However, as the disk was
initially non-rotating, all the action was due to the differential dragging of frames by
the rotating black hole. Little or no jet energy was derived from the binding energy
of the accreting material or its Keplerian rotation.
As a control experiment, the same simulation was also run with a Schwarzschild
(j = 0) hole. The collapse developed a splash outflow due to tidal focusing and
shocking of the inflowing disk, but no collimated MHD jet occurred.

310 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Figure 147: Poloidal flow velocity along a collimated flux tube (top panel) and
particle density (bottom panel) (Fendt & Greiner 2001). x = R/Rg

6.7 Formation of Micro–Jets 311
Figure 148: General relativistic simulation of a magnetized flow accreting onto a
Kerr black hole (after Koide et al. 1999a). Left panel shows one quadrant of
the initial model with the j = 0.95 hole at lower left, freely-falling corona, and
non-rotating disk. The hole rotation axis (Z) is along the left edge. The initial
magnetic field (vertical lines) is weak compared to the matter rest energy density
(VA = 0.01c). Right panel shows final model at t = 130GMH/c 3 . Some of the disk
and corona have been accreted into the hole, threading the ergosphere and horizon
with magnetic field lines that develop a significant radial component, and hence an
azimuthal component as well, due to differential frame dragging. The resulting jet
outflow is accelerated by J × B forces to a Lorentz factor of 2.7. [Koide et al. 2001]
The authors also studied counter-rotating and co-rotating Keplerian disks with
otherwise similar initial parameters (Koide et al. 1999b). The counter-rotating
case behaved nearly identically to the non-rotating case: because the last stable
retrograde orbit is at Rms = 9GMH/c 2 , the disk began to spiral rapidly into the
ergosphere, ejecting a strong, black-hole-spin-driven MHD jet. On the other hand,
for prograde orbits Rms = GMH/c 2 , so the co-rotating disk was stable, accreting
on a slow secular time scale. At the end of the calculation (tmax = 94GMH/c 3 ),
when the simulation had to be stopped because of numerical problems, the disk
had not yet accreted into the ergosphere and had produced only a weak MHD jet.
Future evolution of this case is still uncertain. The Keplerian Schwarzschild case was
previously reported by Koide et al. (1998) and developed a moderate sub-relativistic
MHD jet similar to the aforementioned simulations of magnetized Keplerian flows
around normal stars, plus a pressure-driven splash outflow internal to the MHD jet.
In the Kerr cases, significant magnetic field enhancement over the Schwarzschild

312 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
cases occurs due to compression and differential frame dragging. It is this increase
that is responsible for the powerful jets ejected from near the horizon. In the
Schwarzschild cases, on the other hand, - particularly in the Keplerian disk case
in Koide et al. (1998) - we do not see any MHD jet ejected from well inside Rms.
That is, we do not see any increase in jet power that could be attributed to buoyant
enhancement of the poloidal field in the plunging region. While there is a jet
ejected from inside the last stable orbit, it is pressure-driven by a focusing shock
that develops in the accretion flow. The magnetically-driven jet that does develop
in the Schwarzschild case emanates from near the last stable orbit as expected, not
well inside it. It is therefore concluded that a powerful MHD jet will be produced
near the horizon if and only if the hole is rotating rapidly.
The spin paradigm even offers an explanation for why present-day giant radio
sources occur only in elliptical galaxies. The e-folding spindown time (Erot/Ljet) is
of the order of the Hubble–time (Camenzind 1997)
tspindown = JH
dJH/dt
4 MHc 2
B 2 Hr 3 H
rH
c 1011 yr
−2 9
BH 10 M⊙
. (741)
kG MH
As a result, all AGN should be radio quiet at the present epoch, their black holes
having spun down when the universe was very young. In order to continually produce
radio sources up to the present epoch, there must be periodic input of significant
amounts of angular momentum from accreting stars and gas, or from a merger with
another supermassive black hole (see also Wilson & Colbert 1995). Such activity
is triggered most easily by violent events such as galaxy mergers. Since only elliptical
galaxies undergo significant mergers (the merging process is believed to be
responsible for their elliptical shape), only ellipticals are expected to be giant radio
sources in the present epoch. With little merger activity, spiral galaxies are
expected to be relatively radio quiet. Since merging and non-merging galaxies will
fuel and re-kindle their black hole’s spin in very different ways, bi-modality in the
radio luminosity distribution is to be expected.
6.7.4 Knot Ejection Mechanisms
According to theoretical models (see, for example, computer simulations by Meier,
Koide, et al.), this drives jets of ultra-high-energy particles (including electrons) at
speeds of about 98% the speed of light. (The spiral swirling of the jet corresponds to
the expected spiral pattern of the magnetic field.) About once every 10 months, an
instability in the accretion disk causes a chunk of the inner portion to break off and
fall into the black hole. Although most of the matter falls past the event horizon
and disappears, a small amount of the mass and energy is injected into the jet. This
causes a bright spot to appear about 0.41 parsecs (1.3 light-years) downstream of
the black hole. The bright spot appears to be moving at almost 5 times the speed

6.7 Formation of Micro–Jets 313
Figure 149: A sequence of VLBA images (year of observation in decimal form marked
on the left) at a frequency of 43 GHz. The scale is in milliarcseconds (mas). The
apparent diameter of the moon in the sky is about 1.8 million mas, which means
that the resolution of the VLBA is extraordinarily fine. There is a stationary core
at the left. One can see bright spots coming out at speeds of about 1.8 mas per
year, or between 4 and 5 times the speed of light. (At the distance of 3C 120, 1 mas
corresponds to a length of 0.7 parsecs = 2.3 light-years.) The diagonal lines pass
through the centers of the bright spots.

314 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
of light. This is an illusion that occurs when a jet moving at slightly less than the
speed of light is pointing nearly at us. Why the jet is invisible between the black
hole and 0.41 parsecs is not yet understood. (Marscher thinks that the jet expands
too fast until its pressure falls below that of the interstellar medium, which causes
a stationary shock wave to form. The shock wave then energizes electrons and
amplifies the magnetic field, which makes the jet shine from synchrotron radiation
and inverse Compton scattering. But, he admits that the evidence in favor of this is
pretty thin.) The top panel in Fig. 150 shows the X-ray flux as a function of time
measured with RXTE. The red points correspond to what we call the X-ray dips,
when the flux was low for at least 4 consecutive observations. The blue arrows show
the times when a bright spot first showed up on the VLBA radio images, about 0.1
years after each X-ray dip. The middle panel is the slope of the X-ray spectrum;
a low value means that the higher frequency X-rays are more prominent relative to
the lower frequency X-rays. The bottom panel shows the flux at 3 radio frequencies
(green is 14.5 GHz, red is 22 GHz, and blue is 43 GHz) obtained at the University
of Michigan Radio Astronomy Observatory and the Metsahovi Radio Observatory
in Finland. The black points on the bottom indicate the flux of the radio core as
seen on our 43 GHz VLBA images.
It is apparent from this Figure that each X–ray dip is followed by the appearance
of a superluminal knot at the side of the radio core. The mean time–delay between
the minimum in the X–ray flux and the appearance of the knot ejection is 0.1 ± 0.03
yr. At a typical superluminal apparent speed of 4.7 c, a knot moves a distance of
0.14 pc in 0.1 year, projected on the plane of the sky (the real distance is about 0.5
pc for an inclination of 20 degrees). The jet probably starts as a broad wind until it
gets collimated at the radio core on the scale of a few 100 Schwarzschild radii (see
M 87, Junor, Biretta and Livio, Nature 1999). this would correspond to a minimu
distance of 0.3 pc from the X-ray source to the radio core. The core of the radio
jet is therefore not coincident with the position of the Black Hole. The jet might be
invisible between the site of the origin and the radio core far downstream where the
electrons are reaccelerated (e.g. by a recollimation shock).
This correlated radio and X–ray behaviour is similar to the microquasar GRS
1915+105: here, X–ray dips, where the spectrum hardens, are followed by the ejection
of a bright superluminal radio knot. This is seen as resulting from an instability
where a piece of the inner disk breaks off. Most of this matter is accreted towards
the horizon, but a smaller amount is ejected from the inner region and accelerated
by magnetic forces to high velocities. The X–ray flux is due to Compton scattering
in the inner accretion torus. The bulk velocity of the jets in 3C 120 and GRS
1915+105 are also similar, about 0.98 c in each case (i.e. a Lorentz factor of about
5). The jet in the microquasar is however seen at a much higher inclination of 66
degrees. Therefore, the counterjet is also visible.
Nakamura et al. (2001) investigated the wiggled structure of AGN radio

6.7 Formation of Micro–Jets 315
Figure 150: RXTE light curves of 3C 120 in the hard X–rays (top panel, Marscher
et al. 2002). The middle panel is the slope of the X-ray spectrum. The bottom
panel shows the flux at 3 radio frequencies (green is 14.5 GHz, red is 22 GHz, and
blue is 43 GHz). The blue arrows show the times when a bright spot first showed
up on the VLBA radio images. [Marscher et al. 2002]

316 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
Figure 151: Knot formation in rotating magnetized jets. [Nakamura et al. 2001].
jets by performing 3-dimensional magnetohydrodynamic (MHD) simulations based
on the ‘Sweeping Magnetic-Twist’ model. The correlation between the wiggled
structures of AGN radio jets and tails and the distribution of magnetic field in them
suggests that the magnetic field plays an essential role, not only in the emission of
synchrotron radiation, but also in the dynamics of the production of the AGN–jets–
lobes systems (core, jets, tails, lobes, and hotspots) themselves. In order to produce
such a systematic magnetic configuration, a supply of a huge amount of energy, in an
organized form, is necessary. The supply of this energy must come from AGN core.
The most natural means of carrying this energy is in the form of the Poynting flux
of torsional Alfven wave train (TAWT) produced in the interaction of the rotating
accretion disk and the large scale magnetic field brought into it by the gravitational
contraction. The propagation of the TAWT can produce a slender jet shape by the
sweeping pinch effect from the initial large scale magnetic field. Further, wiggles of
the jet can be produced by the MHD processes due to the TAWT. Our numerical
results reveal that the structure of the magnetic jet can be distorted due to the
helical kink instability. This results in the formation of wiggled structures in the
jets as the TAWT encounters a domain of reduced Alfven velocity (either towards

6.7 Formation of Micro–Jets 317
the boundary of the ‘cavity’ from which the mass contracted to the central core, or
encounting smaller and denser clouds in the domain). The toroidal component of the
field accumulates due to the lowered Alfven velocity, and produces a strongly pinched
region, as well as the deformation of the jet into a writhed structure. The condition
for this to occur corresponds to the Kruskal–Shafranov criterion of the linear case.
If the intrinsic relationship between the wiggled structure of the jet shape and the
magnetic field in the jets and tails as proposed in this paper is confirmed, it will
influence the understandings of the AGN jets in a vital way.

318 7 THE FIRST BLACK HOLES IN THE UNIVERSE
7 The First Black Holes in the Universe
Recent ground- and space-based observations over the course of the last decade have
directly measured the kinematic signature of supermassive black holes at the centers
of approximately forty nearby galaxies. Even more interesting than this confirmation
of the existence of these black holes, however, is the fact that black holes have been
found in all of the galaxies which have a substantial spheroid component (i.e. they
are ellipticals or are spirals with a substantial bulge) and these black holes are
millions to billions of times as massive as our sun. This 100% success rate strongly
suggests that all galaxies have supermassive black holes at their centers. Present
research focuses on how these black holes have grown to their present size.
Black holes are known to form during the death throes of certain massive stars.
However, the black holes that form during the end stages of stellar evolution are
typically only a few times as massive as the sun, rather than millions to billions of
times greater. The main focus of this section on black hole evolution is how the
supermassive black holes at the centers of galaxies grew to their present size.
Most of this research is therefore aimed at identifying and understanding different
mechanisms that can ”feed” these black holes, determining which mechanisms are
more or less important, and how long these phases of black hole evolution last. If the
black hole at the center of a galaxy is growing relatively ”quickly,” which means it
may double in mass in a few tens of millions of years. In this case, the host galaxy is
said to have a high-luminosity active galactic nucleus (AGN), or quasar, due to the
great amount of radiation that is emitted as material falls onto the black hole. At
a more moderate growth rate, the emitted radiation is not as intense, and the host
galaxy would more likely appear to be a low-luminosity AGN, such as a Seyfert or
LINER galaxy. For very low growth rates, no emission from the host galaxy nucleus
may be visible at all, and in this case the galaxy may not be classified as an AGN.
7.1 The Dark Age
After its creation 10 – 15 billion years ago in the mother of all explosions, called the
Big Bang, the universe was a homogenous sea of cooling gas. Slight fluctuations in
gravity rippled this smoothness, however, and gravity’s force pulled the ripples into
waves of matter that condensed into the first objects with separate identities.
The Universe literally entered a dark age about 300,000 years after the big bang,
when the primordial radiation cooled below 3000K and shifted into the infrared.
Unless there were some photon input from (for instance) decaying particles, or string
loops, darkness would have persisted until the first non-linearities developed into
gravitationally-bound systems, whose internal evolution gave rise to stars, or perhaps
to more massive bright objects.
Spectroscopy from the new generation of 8 – 10 metre telescopes now comple-

7.1 The Dark Age 319
Figure 152: Dark age and reionization of the Universe.

320 7 THE FIRST BLACK HOLES IN THE UNIVERSE
ments the sharp imaging of the Hubble Space Telescope (HST); these instruments
are together elucidating the history of star formation, galaxies and clustering back,
at least, to redshifts z = 5. Our knowledge of these eras is no longer restricted to
‘pathological’ objects such as extreme AGNs - this is one of the outstanding astronomical
advances of recent years. In addition, quasar spectra (the Lyman forest,
etc) are now observable with much improved resolution and signal-to-noise; they offer
probes of the clumping, temperature, and composition of diffuse gas on galactic
(and smaller) scales over an equally large redshift range, rather as ice cores enable
geophysicists to probe climatic history.
7.2 The First Stars
Currently, we do not have direct observational constraints on how the first stars
(Population III stars) formed at the end of the cosmic dark age. What we know
is how Population I stars form out of cold, dense molecular gas. The molecular
clouds are supported against gravity by turbulent velocity fields and are pervaded
by large–scale magnetic fields. Stars tend to form in clusters, ranging from a few
hundred to one million stars. The IMF of Pop I stars is observed to have about the
Salpeter form
dN
d ln M ∝ M x , (742)
where x −1.35 for M ≥ 0.5 M⊙. For lower masses it turns over. The lower limit
corresponds roughly to the opacity limit for fragmentation. Therefore, 1 M⊙ is
the typical mass–scale of Pop I star formation, in the sense that most of the mass
goes into stars with masses close to this value.
How did the first stars form ? The simplest thing we can do is estimate the corresponding
characteristic mass–scale. To investigate the collapse and fragmentation
of primordial gas, one has to carry out complicated simulations (Bromm et al. 2002
[4]). In primordial gas clumps, molecular cooling, H2, in a metal–free environment
provides characteristic temperatures of 200 K and densities 10 4 cm −3 . Evaluating
the Jeans mass for these characteristic values results in MJ 10 3 M⊙. These
masses can still grow by accretion processes.
Current simulations indicate that the first stars were predominantly
very massive, and therefore rather different from star formation in the
local Universe. These very massive stars would rapidly explode and form seed
Black Holes which can grow by accretion.
7.3 The First Quasars
The brightest quasars at z ≥ 6 are most likely hosted by rare galaxies, more massive
than 10 12 M⊙. They would end up today as the most massive elliptical galaxies.

7.3 The First Quasars 321
Figure 153: Formation of compact objects in stellar evolution (adapted from Heger
et al. (2001)). In the mass range from 140 - 250 M⊙, no Black Holes are left over
(pair creation instability).

322 7 THE FIRST BLACK HOLES IN THE UNIVERSE
There are essentially two routes towards the formation of supermassive BHs in the
center of galaxies:
1. Black Holes with masses of a few hundred solar masses, left over from the
collapse of very massive stars, could grow by accretion.
2. Black Holes with masses in the range of 10 5 − 10 6 M⊙ are formed in a direct
collapse of primordial gas clouds at high redshifts. It has been shown that
without a pre–existing central point mass, this direct collapse is difficult by
the negative feedback resulting from star formation in the collapsing cloud
(Loeb & Rasio 1994). The input of kinetic energy from supernovae explosions
prevents the gas from assembling in the center of the dark matter potential.
If however star formation can be suppressed in a cloud that undergoes overall
collapse, such a negative feedback would not occur.
Figure 154: Formation of a cloud at redshift 10.3. The box size is 200 pc. One
compact object has formed in the center with a mass of 2.7 Mio solar masses.
[Bromm 2002]

7.3 The First Quasars 323
Bromm & Loeb (2003) [4] have carried out SPH simulations of isolated peaks in
the dark matter fluctuations with total masses of 10 8 M⊙ that collapse at z 10 3 .
The virial temperature of these dwarf galaxies exceeds 10 4 K, which allows collapse
of their gas through cooling by atomic hydrogen H2. Such a scenario would include
lower–mass halos that would have collapsed earlier on. Those lower mass systems
would have virial temperatures below 10 4 K, and consequently rely on the presence
of molecular hydrogen for cooling. This H2 is however fragile and readily destroyed
by photons in the energy bands of 11 – 13.6 ev (Werner bands), just below the
Lyman limit.
What is the future fate of the central object ? Once the gas has collapsed to
densities above 10 7 cm −3 and radii les than 0.01 light year, Thomson scattering traps
the photons, and the cooling time becomes now much larger than both the free–fall
time and the viscous time–scales. The gas cloud settles into a radiation–pressure
supported configuration resembling a rotating supermassive star. Fully relativistic
calculations of the collapse of such stars have recently been done by Baumgarte et al.
(1999) [3]. These objects are expected to collapse towards a supermassive spinning
Black Hole. A substantial fraction of the mass is expected to end up in the Black
Hole.
The main question is whether a complete destruction of molecular hydrogen
will occcur. The effective suppresion of H2 formation will crucially depend on the
presence of a stellar–like radiation background. It is therefore likely that stars
precede the first quasars. The above discussion shows that there is only a small
window in redshift where supermassive stars could be formed at redshifts around
10. At later times, the strong UV radiation field will certainly destroy molecular
hydrogen. Another question is whether there is some initial spin in the collapsing
cloud. This would lead to a binary system with a typical separation of one parsec.
3 see homepage http://www.ukaff.ac.uk/starcluster/

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