Contents List of Figures

lsw.uni.heidelberg.de

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


− 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


d B

+

dR

2 φ


− 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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