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CONTENTS 265<br />
<strong>Contents</strong><br />
6 Macro– and Micro–Jets Driven by Black Holes 267<br />
6.1 DRAG(o)Ns – FR I and FR II . . . . . . . . . . . . . . . . . . . . . . 268<br />
6.2 Jets as Super(magneto)sonic Collimated Plasma Flows . . . . . . . . 275<br />
6.3 Fundamental Parameters for Jets . . . . . . . . . . . . . . . . . . . . 278<br />
6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters . . . . . . . . 283<br />
6.5 Relativistic Jet Propagation . . . . . . . . . . . . . . . . . . . . . . . 288<br />
6.6 Structure and Emission <strong>of</strong> Micro–Jets . . . . . . . . . . . . . . . . . . 291<br />
6.6.1 Core–Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292<br />
6.6.2 Emission Properties . . . . . . . . . . . . . . . . . . . . . . . . 293<br />
6.7 Formation <strong>of</strong> Micro–Jets . . . . . . . . . . . . . . . . . . . . . . . . . 301<br />
6.7.1 The Stationary MHD Model . . . . . . . . . . . . . . . . . . . 304<br />
6.7.2 The Collimation Zone . . . . . . . . . . . . . . . . . . . . . . 307<br />
6.7.3 Nondiffusive Relativistic MHD Approach . . . . . . . . . . . . 309<br />
6.7.4 Knot Ejection Mechanisms . . . . . . . . . . . . . . . . . . . . 312<br />
7 The First Black Holes in the Universe 318<br />
7.1 The Dark Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318<br />
7.2 The First Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320<br />
7.3 The First Quasars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320<br />
<strong>List</strong> <strong>of</strong> <strong>Figures</strong><br />
122 VLA Radio interferometer . . . . . . . . . . . . . . . . . . . . . . . . 267<br />
123 Space VLBI VSOP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268<br />
124 M 87 – the first Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270<br />
125 Structure <strong>of</strong> the DRAGN Cygnus A . . . . . . . . . . . . . . . . . . . 271<br />
126 Host galaxies <strong>of</strong> FR I and II . . . . . . . . . . . . . . . . . . . . . . . 272<br />
127 DRAGN M 84 in the Virgo cluster . . . . . . . . . . . . . . . . . . . 273<br />
128 FR I versus FR II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274<br />
129 Jet Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276<br />
130 Fundamental plane for hydro jets . . . . . . . . . . . . . . . . . . . . 278<br />
131 Luminosity <strong>of</strong> radio galaxies . . . . . . . . . . . . . . . . . . . . . . . 280<br />
132 Electron density in the Hydra cluster . . . . . . . . . . . . . . . . . . 283<br />
133 Simulated dark matter and gas pr<strong>of</strong>iles . . . . . . . . . . . . . . . . . 284<br />
134 Cyg A in X–rays and radio . . . . . . . . . . . . . . . . . . . . . . . . 285<br />
135 Bipolar jets in the cluster gas . . . . . . . . . . . . . . . . . . . . . . 286<br />
136 Jet evolution <strong>of</strong> 3C galaxies . . . . . . . . . . . . . . . . . . . . . . . 288<br />
137 The radio halo <strong>of</strong> M 87 . . . . . . . . . . . . . . . . . . . . . . . . . . 289<br />
138 Electron positron jet . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
266 LIST OF FIGURES<br />
139 VLBA image <strong>of</strong> 3C 120 . . . . . . . . . . . . . . . . . . . . . . . . . . 292<br />
140 RXTE light curves <strong>of</strong> 3C 273 . . . . . . . . . . . . . . . . . . . . . . 293<br />
141 Global spectrum for 3C 273 . . . . . . . . . . . . . . . . . . . . . . . 294<br />
142 Dust emission in 3C 273 . . . . . . . . . . . . . . . . . . . . . . . . . 295<br />
143 VLBA image at 8.4 GHz <strong>of</strong> NGC 4261 . . . . . . . . . . . . . . . . . 298<br />
144 Disk geometry in the center <strong>of</strong> NGC 4261 . . . . . . . . . . . . . . . . 299<br />
145 Magnetic jet formation . . . . . . . . . . . . . . . . . . . . . . . . . . 303<br />
146 Black Hole magnetospheres . . . . . . . . . . . . . . . . . . . . . . . 308<br />
147 Particle density along flux tube . . . . . . . . . . . . . . . . . . . . . 310<br />
148 Koide disk–jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311<br />
149 3C 120 sequence <strong>of</strong> images . . . . . . . . . . . . . . . . . . . . . . . . 313<br />
150 RXTE light curves <strong>of</strong> 3C 120 . . . . . . . . . . . . . . . . . . . . . . 315<br />
151 Knot formation in Jets . . . . . . . . . . . . . . . . . . . . . . . . . . 316<br />
152 Dark ages <strong>of</strong> the Universe . . . . . . . . . . . . . . . . . . . . . . . . 319<br />
153 Mass range for Black Hole formation . . . . . . . . . . . . . . . . . . 321<br />
154 Cloud formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
6 Macro– and Micro–Jets Driven by Black Holes<br />
267<br />
Active galaxies were first identified in the 1950s when early radio telescopes found<br />
that certain galaxies emit strong radio signals. Something very exotic had to be<br />
going on in those galaxies to produce the energies needed to emit the signals. As<br />
researchers developed new tools that made it possible to see across the entire electromagnetic<br />
spectrum - infrared and ultraviolet emissions, X-ray and gamma ray<br />
sources - astronomers found active galaxies also to be strong emitters <strong>of</strong> other radiation.<br />
This was more evidence that some kind <strong>of</strong> extremely energetic process<br />
had to be at work. Scientists have long thought that matter falling into supermassive<br />
black holes might be the power source <strong>of</strong> active galaxies. That hypothesis<br />
Figure 122: The structure <strong>of</strong> kiloparsec–scale jets has mainly been investigated by<br />
the VLA radio interferometer.<br />
was strengthened by astronomers’ recent understanding <strong>of</strong> microquasars, objects<br />
that show characteristics similar to active galaxies but which are less massive and<br />
also much closer to the earth. Being closer - only thousands <strong>of</strong> light years away -<br />
microquasars have been observed with greater resolution and detail than has been<br />
possible with active galaxies up until now. The active galaxy 3C 120 is 450 million<br />
light years away. The supermassive black hole the researchers expected to be at its
268 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
core would have the mass <strong>of</strong> at least 30 million suns, yet would be squeezed into<br />
a region smaller than the distance between the earth and the sun. The tremendous<br />
gravitational force <strong>of</strong> this mass would continuously attract more matter, which<br />
would spiral around the black hole into a thin doughnut-shape called an accretion<br />
disk. A jet was first observed in the radio galaxy M 87 in 1917 by Heber Curtis using<br />
Figure 123: Space VLBI VSOP provides the highest spatial resolution down to 0.1<br />
mas.<br />
an optical telescope. However, it was not until the 1970’s, when observations with<br />
large, high resolution radio telescopes, like the Very Large Array in New Mexico,<br />
revealed the nature <strong>of</strong> the ”curious straight ray” connected to the nucleus <strong>of</strong> M 87.<br />
Jets are present in many, if not all, quasars and can extend millions <strong>of</strong> light years<br />
from the central core <strong>of</strong> the galaxy.<br />
6.1 DRAG(o)Ns – FR I and FR II<br />
The jets <strong>of</strong> quasars and Radio galaxies are certainly the most spectacular collimated<br />
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<br />
visible in non–thermal emission. In contrast to these objects, jets <strong>of</strong> normal stellar<br />
objects (young stellar objects, protostars and White Dwarfs) can be detected in<br />
line emission <strong>of</strong> a normal gas. As such one has a much more direct observational<br />
evidence for the flow velocities, they are moderate a few hundred to a few thousand<br />
kilometers per second in stellar objects.<br />
What are DRAGNs ? DRAGNs are large–scale double radio sources<br />
produced by outflows (jets) that are launched by processes in active<br />
galactic nuclei (AGN). They are clouds <strong>of</strong> radio-emitting plasma which have<br />
been shot out <strong>of</strong> active galactic nuclei via narrow jets. The term DRAGN is an<br />
acronym for ”Double Radio Source Associated with a Galactic Nucleus” . It was<br />
coined by Patrick Leahy in 1993 [17].<br />
Most <strong>of</strong> the extragalactic sources detected by early radio surveys were DRAGNs,<br />
but modern deep radio surveys also detect many sources produced by ”starbursts”<br />
in galaxies. Starbursts can produce radio emission throughout an extended region<br />
<strong>of</strong> a galaxy, but do not produce significant radio emission in regions far from the<br />
stars that have formed. DRAGNs fundamentally involve the mass concentration in<br />
the nucleus <strong>of</strong> the galaxy and produce radio emission throughout regions that are<br />
much larger than the host galaxies themselves.<br />
DRAGNs are formed when an active galactic nucleus produces two persistent,<br />
oppositely-directed plasma outflows that contain cosmic ray electrons and magnetic<br />
fields. We do not know exactly what these ”jet” outflows contain, but they clearly<br />
include fast-moving electrons and partially ordered magnetic fields which make them<br />
visible at radio (and higher) frequencies by their synchrotron radiation (emission<br />
that occurs when electrons move across a magnetic field at almost the velocity <strong>of</strong><br />
light). To preserve overall charge neutrality, there must also be either protons or<br />
positrons in the outflows.<br />
DRAGNs are made, so it seems, <strong>of</strong> the stuff that flows down the jets, the socalled<br />
”synchrotron plasma”. We do not know exactly what this is. It radiates in the<br />
radio band (and sometimes at higher frequencies) via the synchrotron process, from<br />
which we can tell that it contains magnetic fields and cosmic-ray electrons. Since<br />
cosmic plasmas must be neutral, there must be also protons or positrons in the jet.<br />
Near the AGN the jets are supersonic, in the sense that the flow speed is faster than<br />
the speed <strong>of</strong> sound in the jet plasma. As a result, shockwaves form easily, giving rise<br />
to small regions with high pressure, which radiate intensely. Further away from the<br />
AGN, the weaker jets become subsonic and turbulent. Both shocks and turbulence<br />
may help to give the cosmic rays their high energies, via the Fermi mechanism.<br />
Structure <strong>of</strong> DRAGNs: The main radio structures in a powerful DRAGN whose<br />
jets stay supersonic to great distances are illustrated above with the VLA image <strong>of</strong><br />
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<br />
Figure 124: M 87 in the Virgo cluster is historically the first jet detected in optical<br />
emission (Curtis 1918). With HST the structure <strong>of</strong> this jet is nicely visible, the jet<br />
ends beyond the extension <strong>of</strong> the core region <strong>of</strong> the optical galaxy (top). This jet<br />
has been imaged in radio, optical and X–ray emission (bottom). M 87 is however<br />
not a typical DRAGN.
6.1 DRAG(o)Ns – FR I and FR II 271<br />
Figure 125: Structure <strong>of</strong> the archetypical DRAGN Cygnus A.<br />
scribed as the ”core” coincides with the galactic nucleus. Most <strong>of</strong> the radio emission<br />
does not come directly from the well-collimated ”jets”, but from the broader ”lobes”<br />
that are found around the jet paths. The plasma in the lobes is believed to have been<br />
supplied by the jets over millions <strong>of</strong> years. In the more powerful DRAGNs, there<br />
are usually small, bright radio ”hot spots” near the boundaries <strong>of</strong> each lobe. These<br />
hot spots thought to be where strong shocks form near the ends <strong>of</strong> the supersonic<br />
jet outflows in the powerful DRAGNs.<br />
The environs <strong>of</strong> a galaxy are not a perfect vacuum. The jets must travel first<br />
through the atmosphere <strong>of</strong> the galactic nucleus, then through the interstellar medium<br />
<strong>of</strong> the host galaxy, then (if they get that far without being slowed down by interaction)<br />
through the successively lower densities and pressures <strong>of</strong> the outer halo <strong>of</strong><br />
the galaxy, the intra-cluster medium (ICM) <strong>of</strong> any surrounding group or cluster <strong>of</strong><br />
galaxies, and finally into the low-density inter-galactic medium. The jets do not flow<br />
freely away from the AGN, but must push their way through these external media.<br />
Fanar<strong>of</strong>f–Riley Classification: A landmark in the study <strong>of</strong> extragalactic radio<br />
sources was the demonstration by Fanar<strong>of</strong>f and Riley (1974) <strong>of</strong> the existence <strong>of</strong> a<br />
relatively sharp morphological transition at a radio luminosity P178 MHz 2.5 ×
272 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
10 26 h −2<br />
50 W Hz −1 . The great majority <strong>of</strong> sources below this luminosity (FR I type)<br />
are characterized by having diffuse radio lobes, with their brightest region within<br />
the inner half <strong>of</strong> the radio source (edge–dimmed). On the contrary, more powerful<br />
sources are usually straighter, exhibit edge–brightened (FR II) morphology, and<br />
typically contain hotspots near the outer edges <strong>of</strong> their radio lobes. Most recently,<br />
Figure 126: Correlation between radio luminosity, absolute optical red magnitude<br />
and Fanar<strong>of</strong>f–Riley class. 1’s are FR I’s, 2’s are FR II’s and F’s are fat doubles.<br />
[Ledlow et al. 2000]<br />
it was realized that the critical radio luminosity separating the FR I and FR II<br />
actually increases with the optical luminosity <strong>of</strong> the host galaxy, P ∗ R ∝ L1.65 opt (Fig.<br />
126). The more luminous the host galaxy is, the more powerful the radio source<br />
must be in order to attain the FR II morphology.<br />
There is good evidence that the outflow speeds in DRAGNs are initially relativistic,<br />
i.e. that the material travels outwards at a large fraction <strong>of</strong> the velocity <strong>of</strong> light,<br />
<strong>of</strong>ten with Lorentz factors <strong>of</strong> order 10. The velocities appear to decrease along many<br />
<strong>of</strong> the the jets, however. In the less powerful sources, it appears that the jets are<br />
slowed down enough on the scale <strong>of</strong> the galaxy to become subsonic and turbulent.
6.1 DRAG(o)Ns – FR I and FR II 273<br />
These FR Type I sources form large-scale plumes that meander across the sky at<br />
the mercy <strong>of</strong> pressure gradients, shocks and winds in the large–scale intracluster or<br />
intergalactic media. An example is 3C 31 (identified with the galaxy NGC 383),<br />
shown below with the DRAGN in red and the optical field in blue:<br />
In more powerful (FR Type II) sources, it appears that the jets remain at least<br />
mildly relativistic (and supersonic) out to great distances from their host galaxies,<br />
to form the ”classical” double–lobed structures like that shown above for 3C 405<br />
(Cygnus A). In the Type II sources the ends <strong>of</strong> the jets move outwards more slowly<br />
than material flows along the jet. The plasma arriving at the end <strong>of</strong> their jets is<br />
then deflected back around them to form the lobes, large ”bubbles” in the medium<br />
surrounding the galaxy.<br />
Sizes <strong>of</strong> DRAGNs: Individual DRAGNs will tend to grow while their central<br />
engine remains active. The smallest DRAGNs known are only a few tens <strong>of</strong> parsecs<br />
across, contained within in the active nucleus. An example <strong>of</strong> a weak, small DRAGN<br />
on a galactic scale is 3C 272.1, associated with the Virgo Cluster elliptical galaxy<br />
M 84 (NGC 4374), shown in Fig. 127 with the DRAGN in red and the optical field<br />
in blue.<br />
Figure 127: DRAGN <strong>of</strong> FR type I associated with the Virgo cluster elliptical M 84<br />
(elliptical galaxy in blue, radio structure in red).<br />
At the other extreme, giant DRAGNs are the largest known objects, up to several
274 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
Megaparsecs from end to end. The lobes <strong>of</strong> the radio source shown below were<br />
discovered by a low-resolution all-sky survey made with the VLA. They were later<br />
shown to be a single DRAGN by observations that revealed the radio core and the<br />
jets connecting it to these lobes (left panel). The core coincides (central panel)<br />
with a galaxy (right panel) whose redshift is z=0.154. This reveals the double radio<br />
source to be over 4 Mpc in extent, and the second largest DRAGN known. The<br />
largest <strong>of</strong> them all, 3C236, is about 6 Mpc across. Typical powerful DRAGNs are<br />
Figure 128: Difference in morphology between FR I jet <strong>of</strong> 3C 31 and a typical quasar<br />
jet (3C 175 at redshift 0.768). Quasars show the most luminous jets with double<br />
sided lobe structure, but only one–sided jets.
6.2 Jets as Super(magneto)sonic Collimated Plasma Flows 275<br />
hundreds <strong>of</strong> kiloparsecs across, several times bigger than their host galaxies. 1<br />
DRAGNs are almost invariably associated with elliptical galaxies, rather than<br />
with spirals. There appears to be a strong connection, still to be explained in detail,<br />
between the processes that determine the bulge-to-disk ratio <strong>of</strong> the host galaxy and<br />
the ability to form (and maintain) the active nuclear engine for the time it takes to<br />
build up a large-scale DRAGN.<br />
Ages <strong>of</strong> DRAGNs: Powerful DRAGNs have estimated lifetimes <strong>of</strong> order 20 million<br />
years (estimated from synchrotron ages); this makes them a brief outburst in<br />
the life <strong>of</strong> a galaxy (compare the 100 million years a star may take to orbit the<br />
galaxy’s hub). On the other hand, weak DRAGNs are so common in the largest<br />
elliptical galaxies that the jets must be ”on” essentially all the time. Most <strong>of</strong> the<br />
radio emission from typical DRAGNs comes not from the jets themselves but from<br />
twin lobes, which are much broader clouds around and near the inferred path <strong>of</strong><br />
the two jets. The synchrotron plasma in the lobes is believed to have been supplied<br />
over a long period through the jets. The jets themselves can sometimes be seen as<br />
narrow features threading the lobes. In powerful DRAGNs, small, bright hotspots<br />
are found near the end <strong>of</strong> each lobe; these are thought to mark the ends <strong>of</strong> the jets.<br />
6.2 Jets as Super(magneto)sonic Collimated Plasma Flows<br />
The standard interpretation <strong>of</strong> DRAGNs was proposed independently by Scheuer<br />
(1974) and Blandford & Rees (1974), and the underlying physical mechanism was<br />
broadly confirmed by numerical fluid dynamics in the 1980’s. To understand DRAGNs,<br />
it is crucial to bear in mind that space is not a perfect vacuum. The jets travel out<br />
first through the atmosphere <strong>of</strong> the galactic nucleus, then through the interstellar<br />
medium <strong>of</strong> the host galaxy, then (if they get that far) through the successively lower<br />
densities and pressures <strong>of</strong> the outer halo <strong>of</strong> the galaxy, the intra-cluster medium <strong>of</strong><br />
any surrounding group or cluster <strong>of</strong> galaxies, and out into the inter-galactic medium.<br />
Although much <strong>of</strong> this gas is pretty tenuous even by astronomical standards, it is<br />
always denser than the jet plasma. This means the jets cannot flow freely away from<br />
the AGN, but must push their way through the external medium (Fig. 129). As<br />
a result, the ends <strong>of</strong> the jets move outwards much more slowly than material flows<br />
up the jet. As envisaged by Scheuer and Blandford & Rees, the plasma arriving at<br />
the end <strong>of</strong> the jet is deflected back to form the lobe, which can be thought <strong>of</strong> as<br />
a large bubble surrounding the jet. The ”end <strong>of</strong> the jet” is just the point where<br />
1 Patrick Leahy and Richard Strom have collected an Atlas <strong>of</strong> DRAGNs that includes images,<br />
vital statistics and brief descriptions <strong>of</strong> each object. The atlas is served from Patrick’s web site at<br />
Jodrell Bank http://www.jb.man.ac.uk/atlas/. The Atlas is a complete sample <strong>of</strong> all the DRAGNs<br />
from the Third Cambridge Catalogue <strong>of</strong> Radio Sources (Second Revision, known as 3CRR), out<br />
to a redshift <strong>of</strong> z=0.5.
276 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
the jet collides with the surface <strong>of</strong> the lobe. If the jet is still supersonic at this<br />
point, this collision will take place through a system <strong>of</strong> strong shockwaves, and the<br />
resulting high–pressure region will be seen as the hotspot. Over the past 20 years,<br />
Figure 129: Structural elements <strong>of</strong> propagating jets: beam, cocoon, hotspot, contact<br />
discontinuity (which is unstable against Kelvin–Helmholtz instabilities) and bow<br />
shock. Parameters: M = 6, η = 0.01, vB = 0.28c, ΓB = 1.04, resolution = 6 ppb.<br />
[Hughes 1996].<br />
numerical simulations <strong>of</strong> time–dependent jet flows have progressed enormously from<br />
the earliest two–dimensional axisymmetric gasdynamical flows (Smith et al. 1985)<br />
to three–dimensional flows (e.g., Cox, Gull & Scheuer 1991) until now fully three<br />
dimensional flows incorporating self-consistent MHD are relatively straightforward,<br />
if not yet easy, to model with modest resolution (Krause 2002 [11]; Krause 2003<br />
[12]). These simulation methods have also been extended to include flows in either<br />
2D or 3D with relativistic bulk motions (see review by Marti & Müller 1999 [15]).<br />
Simultaneously, physical models <strong>of</strong> particle acceleration physics, especially as it relates<br />
to the formation <strong>of</strong> collisionless shocks, have become much better developed<br />
(e.g., Jones 2001), even if that cannot yet be called a solved problem.<br />
Most <strong>of</strong> our information about RGs currently derives from radio synchrotron<br />
emissions reflecting the spatial and energy distributions <strong>of</strong> relativistic electrons convolved<br />
with the spatial distribution <strong>of</strong> magnetic fields. X-ray observations, especially<br />
<strong>of</strong> non–thermal Compton emissions, depending on the electron and ambient photon<br />
distributions, are now beginning to add crucial information, as well. Using these<br />
connections, much effort has been devoted to interpreting observed brightness, spectral<br />
and polarization properties <strong>of</strong> the non–thermal emissions for estimates <strong>of</strong> the<br />
key physical source properties, such as the energy and pressure distributions and
6.2 Jets as Super(magneto)sonic Collimated Plasma Flows 277<br />
kinetic power, as well as to find self-consistent models for the particle acceleration<br />
and flow patterns. As telescopes and analysis techniques have improved the level <strong>of</strong><br />
detail obtained, it has become apparent, however, that the observed properties are<br />
not very simple and much harder to interpret than most simple models predict.<br />
Radiative MHD with NIRVANA C: In the following we work in the one–<br />
component approximation for the dynamical part, but include cooling for the evolution<br />
<strong>of</strong> different atomic species [11]. The evolution <strong>of</strong> the jet plasma is given by the<br />
continuity equation for the density ρ, the Euler equations for the momenta ρ V which<br />
have pressure gradient and Lorentz forces as source terms. The magnetic fields B<br />
evolve according to the induction equation, and the time evolution <strong>of</strong> the internal<br />
energy e is determined by advection, compression and cooling (the K–term)<br />
∂ρ<br />
∂t + ∇ · (ρ V ) = 0 (673)<br />
∂ρ V<br />
∂t + ∇ · (ρ V ⊗ V ) = −∇P − 1<br />
8π ∇ B 2 + 1<br />
4π ( B · ∇) B (674)<br />
∂e<br />
∂t + ∇ · (e V ) = −P (∇ · V ) − K (675)<br />
∂ B<br />
∂t = ∇ × ( V × B) (676)<br />
P = (Γ − 1)e . (677)<br />
These equations are implemented in codes such as ZEUS3D and NIRVANA C [22],<br />
or more modern versions based on shock capturing methods [23].<br />
Cooling Functions for Low–Density Plasmas: Sutherland & Dopita [21] have<br />
presented the equilibrium cooling functions for optically thin plasmas. These can<br />
easily built into the code NIRVANA C. Some functions are terminated before reaching<br />
10 4 K when the internal photoionization halts the cooling. The functions represent<br />
a self-consistent set <strong>of</strong> curves covering a wide grid <strong>of</strong> temperature and metallicities<br />
using recently published atomic data and processes. The results have implications<br />
for phenomena such as cooling flows and for hydrodynamic modelling which<br />
include gas components. NIRVANA C can however also handle non–equilibrium<br />
cooling for an entire set <strong>of</strong> atomic species. Then the above equations must be supplemented<br />
with a network <strong>of</strong> time evolution for various species. In cases, where<br />
cooling is very rapid compared to dynamical time–scales, this network has to be<br />
solved by means <strong>of</strong> time–implicit methods.
278 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
6.3 Fundamental Parameters for Jets<br />
Already in early simulations, it turned out that one <strong>of</strong> the fundamental parameters<br />
for jet propagation is the density contrast η = ρB/ρ0, where ρB denotes the beam<br />
density and ρ0 the external density <strong>of</strong> the surrounding medium. For relativistic<br />
beams propagating with a Lorentz bulk factor ΓB, the density contrast is given by<br />
η = ρBhBΓ 2 B<br />
ρ0<br />
, (678)<br />
with hB as the specific enthalpy <strong>of</strong> the beam plasma (= 1 for cold plasma) and ΓB<br />
as the Lorentz factor <strong>of</strong> the beam propagation. For Quasar jets we typically find<br />
ΓB 5 − 10 from superluminal motion on the parsec–scale. The third parameter<br />
which determines the morphology <strong>of</strong> a jet is the internal Mach number M = VB/cS <br />
5−10 for the beam plasma. The Mach number is not an independent quantity, since<br />
the beam is steadily heated up by means <strong>of</strong> internal shocks. In addition, the ratio<br />
Figure 130: Fundamental plane for hydro jets.<br />
between external pressure and internal pressure is also important for the initial<br />
launch <strong>of</strong> the jet. Overpressured jets will initially expand and then recollimate.<br />
The density contrast determines the hot spot advance speed over momentum<br />
balance at the working surface<br />
vHS = vB<br />
√<br />
ηɛ<br />
1 + √ , (679)<br />
ηɛ
6.3 Fundamental Parameters for Jets 279<br />
provided M >> 1. ɛ < 1 is the ratio <strong>of</strong> beam to head cross–section. For heavy<br />
jets, η > 1, we find therefore vHS vB, i.e. the hot spot advances with the beam<br />
speed. For light jets, η
280 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
Cyg A<br />
L_R = 10^45 erg/s<br />
L_J = 10^46 erg/s<br />
_________________________________________<br />
3C295<br />
___________ FR II / FR I Transition ___________<br />
Figure 131: Luminosity <strong>of</strong> radio galaxies as a function <strong>of</strong> redshift. Open circles:<br />
galaxies in the 3C catalog. The radio power varies over many orders <strong>of</strong> magnitude.<br />
At high redshifts, only the most luminous sources with power comparable to Cyg A<br />
can be detected.<br />
On the FR I – FR II Transition: Many explanations have been given for the<br />
explanation <strong>of</strong> the FR I / FR II transition. The most widely known explanation is<br />
that, while the jets in both cases start out moving at very high (relativistic speeds),<br />
those in FR II sources remain that way out to multi–kpc distances, while those in<br />
FR I’s decelerate to much slower speeds within a few kpc <strong>of</strong> the galaxy core. Bicknell<br />
(1995) developed detailed models for decelerating relativistic jets.<br />
An alternative approach assumes that the FR I and FR II sources differ primarily<br />
in the importance <strong>of</strong> the beam thrust relative to the basic parameters <strong>of</strong> the ambient<br />
medium (Gopal–Krishna & Wiita 1988; 2001). In this version, the emphasis is on<br />
the slowing down <strong>of</strong> the advance <strong>of</strong> the hotspot at the end <strong>of</strong> the jet, rather than<br />
the slowing down <strong>of</strong> the bulk flow <strong>of</strong> the beam. In this scenario, the hotspots <strong>of</strong> FR<br />
II’s have supersonic advance speed with respect to the ambient medium. When this<br />
advance speed becomes transonic relative to the ambient medium, its Mach disk<br />
weakens due to the fall in ram pressure, and the jet becomes decollimated.
6.3 Fundamental Parameters for Jets 281<br />
The critical density contrast ηcrit can be estimated from the condition that the<br />
bow shock becomes transonic, vHS = cS. For relativistic beams vB c, we find<br />
ηcrit 10 −5 . For η < ηcrit, no bow shock will be found.<br />
For a more quantitative formulation one needs certain empirical relations between<br />
the elliptical’s blue magnitude MB, its s<strong>of</strong>t X–ray emission LX, the stellar<br />
velocity dispersion σ∗ (the Faber–Jackson relation), and the core radius Rc (Kormendy<br />
relation), assuming H0 = 75 (Bicknell 1995)<br />
log LX = 22.3 − 0.872 MB (685)<br />
log σ∗ = 5.412 − 0.0959 MB (686)<br />
log Rc = 11.7 − 0.436 MB . (687)<br />
We furthermore assume a density scaling for the ISM <strong>of</strong> the elliptical<br />
n(d) =<br />
n0<br />
[1 + (d/Rc) 2 ] δ<br />
(688)<br />
with δ 0.75 typically. Then the hotspot advance speed follows from pressure<br />
balance<br />
vHS(d) = vB<br />
X[1 + (d/Rc) 2 ] δ/2<br />
d/Rc + X[1 + (d/Rc) 2 . (689)<br />
] δ/2<br />
Here X = <br />
4LB/πΘ 2 R 2 cn0µmpc 3 with LB as the beam power, Θ the effective opening<br />
angle for the beam. A reasonable number is Θ 0.1 rad, at least for the inner<br />
jet regions. X corresponds to the above quantity √ χη for cylindrical beams. The<br />
temperature <strong>of</strong> the X–ray gas is not independent, but tied to the central stellar velocity<br />
dispersion, kT = 2.2µmpσ 2 ∗/δ (Falle 1987). There is evidence that the central<br />
gas density n0 is somewhat higher than the X–ray gas density nX, n0 = κnX with<br />
κ 3. The interstellar density declines quite rapidly at distances beyond a few kpc,<br />
observationally Rc 1 kpc. Hence the most likely regime for the jet’s decollimation<br />
due to hotspots having slowed down to subsonic speeds lies within roughly 10 kpc<br />
<strong>of</strong> the core.<br />
Gopal–Krishna & Wiita (2001) now evaluate the critical beam power L ∗ B for<br />
which the hotspot deceleration to subsonic velocities occurs at a distance d ∗ 3−10<br />
kpc from the core. 10 kpc is a typical distance at which jets flare in a sample <strong>of</strong><br />
radio galaxies. Laing et al. (1999) have studied a sample <strong>of</strong> 38 FR I sources giving<br />
a mean projected value <strong>of</strong> 3.5 kpc for the radial distance <strong>of</strong> the point where the<br />
kpc–scale jet first becomes visible, after passing through an emission gap.<br />
Now X can be scaled to<br />
X = C2<br />
√ <br />
LB/ n0Rc<br />
(690)
282 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
where C2 = <br />
4/πΘc 3 µmp = 2.14 × 10 −3 for µ = 0.620. LX can be expressed over<br />
the Bremsstrahlung cooling function, sot hat<br />
log LX = log C1 + log n0 + 3 log aX (691)<br />
log nX = log n0 − log κ = 4.188 + 0.218 MB (692)<br />
log X = −0.109 MB + log C2 + 0.25 log C1 + 3.20 + 0.5 log LB . (693)<br />
We next impose the transonic condition<br />
vHS(d ∗ <br />
) = cS = 2.2γ/δ σ∗ 1.5 σ∗ . (694)<br />
For γ = 5/3 and δ = 0.75 this becomes<br />
log vHS(d ∗ ) = 0.345 + log σ∗ = −4.720 − 0.0959 MB . (695)<br />
Equating this to the original expression for vHS gives<br />
dex(−4.720 − 0.0959 MB) =<br />
X<br />
(d/Rc)/[1 + (d/Rc) 2 ] δ/2 . (696)<br />
+ X<br />
This is the relation which must be solved for the critical beam power L ∗ B as a<br />
function <strong>of</strong> MB. The resulting values are given in the following table (GKW 2001).<br />
For MB > −23.5 this corresponds to a scaling L ∗ B ∝ L 1.6<br />
opt, in good agreement with<br />
MB Rc n0 L ∗ B β ∗<br />
[kpc] [cm −3 ] [erg/s]<br />
-19.5 0.052 2.82 4.35(41) 1.74<br />
-20.0 0.085 2.02 8.28(41) 1.40<br />
-20.5 0.141 1.57 1.71(42) 1.57<br />
-21.0 0.233 1.22 3.57(42) 1.60<br />
-21.5 0.384 0.951 7.23(42) 1.56<br />
-22.0 0.635 0.741 1.49(43) 1.58<br />
-22.5 1.05 0.576 3.06(43) 1.55<br />
-23.0 1.73 0.447 6.21(43) 1.55<br />
-23.5 2.86 0.348 1.23(44) 1.47<br />
Table 8: Galaxy and jet parameters for given elliptical galaxy.<br />
the dividing line in Fig. 126 with β ∗ = 1.65. The actual position for the dividing line<br />
follows from the efficiency <strong>of</strong> conversion <strong>of</strong> beam power into synchrotron radiation<br />
<strong>of</strong> about 10%.
6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters 283<br />
Research Project: The ultimate reason for the FR II/FR I transition is still not<br />
yet clear–cut. The density distribution <strong>of</strong> the hot gas around elliptical galaxies embedded<br />
into a cluster background is more complex than discussed here. It consists<br />
<strong>of</strong> two β–laws, one with the core radius <strong>of</strong> the galactic nucleus, and a second one<br />
with the much bigger core radius <strong>of</strong> the cluster medium (see recent Chandra measurements).<br />
This produces a jump in the pressure gradients where the two density<br />
laws cross each other. The flaring <strong>of</strong> the radio jet in FR I sources could just occur<br />
at this pronounced radius.<br />
6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters<br />
Many <strong>of</strong> the bright 3C galaxies are members <strong>of</strong> clusters. The density pr<strong>of</strong>ile is therefore<br />
an important ingredient into the modelling <strong>of</strong> jet propagation. The observed<br />
electron density distribution for the Hydra cluster is shown in Fig. 132.<br />
Figure 132: Density distribution in the Hydra cluster, as measured with Chandra.<br />
Beyond 200 kpc, the density distribution considerably steepens, ne ∝ r −3 , as expected<br />
from cosmological simulations. [Chandra observation]
284 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
The Archetype Cyg A: Cyg A is the central galaxy <strong>of</strong> a cluster. The ambient<br />
density is therefore not constant, but follows typically a β–law<br />
ρ0(r) =<br />
ρc<br />
(1 − r2 /r2 . (697)<br />
3β/2<br />
c)<br />
rc 20 − 50 kpc is the core radius for the cluster gas. The Cygnus A radio source<br />
Figure 133: Density pr<strong>of</strong>iles for dark matter and baryonic gas as obtained from<br />
simulations. Inside 100 kpc, the gas density pr<strong>of</strong>ile is quite shallow, beyond 200 kpc<br />
it adjust to the density pr<strong>of</strong>ile <strong>of</strong> dark matter.<br />
is situated at the center <strong>of</strong> a dense cluster atmosphere that extends to a radius <strong>of</strong><br />
at least 0.5 Mpc (Smith et al. 2002). The total X–ray luminosity <strong>of</strong> the cluster is<br />
LX = 1. × 10 45 erg/s at an average temperature <strong>of</strong> 8 keV, and an electron density at<br />
the position <strong>of</strong> the radio hotspots (70 kpc from the center) <strong>of</strong> 0.006 cm −3 . The total<br />
gas mass is 2 × 10 13 M⊙ and the total gravitational mass is 2 × 10 14 M⊙. A number<br />
<strong>of</strong> 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<br />
cluster gas, including emission from the unperturbed atmosphere, excess emission<br />
from the shocked ICM surrounding the radio lobes, and a deficit <strong>of</strong> emission from<br />
the evacuated radio lobes themselves. X–ray observations provide direct constraints<br />
Figure 134: A low frequency radio image (VLA at 330 MHz, blue to red) superposed<br />
on the Chandra image (yellow–red) <strong>of</strong> the inner 200 kpc <strong>of</strong> the Cygnus A cluster.<br />
This shows for the first time the interaction <strong>of</strong> the radio source and the cluster gas.<br />
on the physical conditions in the emitting regions. In contrast, observations <strong>of</strong> the<br />
non–thermal radio synchrotron emission provide only information on the properties<br />
<strong>of</strong> the cocoon and beam plasma. The pressure following from X–ray observations<br />
is 1 × 10 10 dyne cm −2 . Fig. 134 also reveals X–ray emission coincident with radio<br />
hot spots. This is non–thermal IC emission from the same population <strong>of</strong> electrons<br />
emitting the radio synchrotron photons (SSC emission). While the radio emissivity<br />
is a function <strong>of</strong> the relativistic electron density and the magnetic field strength, IC<br />
X–ray emissivity constrains the number density alone. From this Wilson derives<br />
magnetic fields <strong>of</strong> 150 µG for the radio hot spots, the minimum energy field would<br />
be 250 µG.<br />
(i) The Sedov–Phase <strong>of</strong> Jet Evolution: For density contrasts η < 0.01, the<br />
initial expansion <strong>of</strong> the bow shock can be described in terms <strong>of</strong> a Sedov wave propagating<br />
into a medium with decreasing density n(r) = n0(Rrc/r) κ with κ 1.4. The<br />
energy in the bubble increases steadily, E = LBt, as long as the jet power does not<br />
fade away. Similarly to the analysis for supernovae, the expansion <strong>of</strong> the blast wave
286 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
Figure 135: Bipolar jets propagating in the cluster medium. The light blue color<br />
traces the bow shock and the shocked cluster medium, only visible in X–ray emission;<br />
the dark blue marks the shocked cocoon plasma with the contact discontinuity<br />
(visible in synchrotron emission). The cocoon plasma is extremely hot and thin,<br />
typical temperatures are ≥ 10 11 K. The dark colors mark bow shock plasma mixed<br />
into the cocoon via KH instabilities. The core region stays more or less round, while<br />
the accelerating bow shocks lead to a cigar–shape, once the hot spots left the core<br />
region <strong>of</strong> the cluster atmosphere. [Krause 2002].
6.4 A 3–Phase Model for Kiloparsec–Scale Jets in Clusters 287<br />
is given by [11]<br />
R(t) =<br />
For rc = 10 kpc, this leads to<br />
(3 − κ)(5 − κ)<br />
12πρ0r κ c<br />
1/(5−κ)<br />
t 3/(5−κ) . (698)<br />
R(t) = 3.3 kpc (t/Myr) 1/1.2 . (699)<br />
It is interesting, how accurate this simple formula is when compared to complicated<br />
numerical simulations [11]. For a synchrotron age <strong>of</strong> Cyg A <strong>of</strong> 27 Myr, this exactly<br />
corresponds to the radius <strong>of</strong> the X–ray bubble measured with Chandra (Fig. 134).<br />
Jets must be considered as bipolar outflows working against the background gas <strong>of</strong><br />
the cluster medium. For a density contrast η < 0.01, the initial phase is similar to a<br />
supernova explosion. We call therefore this phase the Sedov–phase. As shown by<br />
Cyg A, the bow shock advances only slightly supersonically, the typical sonic speed<br />
in the cluster medius is about 0.5 kpc/Myr, while the bow shock advance speed is<br />
a few kpc/Myr.<br />
(ii) The Cigar–Phase <strong>of</strong> Jet Evolution: Cygnus A just terminates the Sedov–<br />
phase. The hot spots are on the way to break out <strong>of</strong> the roundish bow shock due<br />
to acceleration in the decaying cluster atmosphere. In a few million years, Cyg A<br />
will appear as 3C 132 (Fig. 136) consisting <strong>of</strong> a central cylindrical cocoon filled<br />
with synchrotron plasma and two jets breaking out from this bubble and forming<br />
a cigar–like feature, such as seen in 3C 341. The long cylindrical jets visible in<br />
synchrotron light trace the cocoon plasma which appears highly collimated. The<br />
surrounding bow shock could only be detected in X–rays, is however fairly weak at<br />
distances <strong>of</strong> a few hundred kpc from the central source.<br />
(iii) The Late Phase Evolution: Since the central activity decays after typically<br />
20 – 50 million years, the radio lobes are no longer fuelled with high pressure<br />
material. The synchrotron plasma gets mixed up with the cluster gas. This leads<br />
to the formation <strong>of</strong> radio haloes in clusters <strong>of</strong> galaxies. In Fig. 137 we show the full<br />
extent <strong>of</strong> the radio source in the Virgo cluster at 327 MHz, about 80 kpc end–to–end.<br />
The inner lobes and jet can just be seen as the red structures in the center (and<br />
the nuclear black hole sits in the center <strong>of</strong> this inner structure). This picture thus<br />
covers an area larger than the optical galaxy; we are studying the inner region <strong>of</strong> the<br />
Virgo cluster. The galaxy, and its radio halo, sit in a large atmosphere <strong>of</strong> hot, X–ray<br />
loud gas (as already detected by the EINSTEIN and ROSAT satellites). From this<br />
image <strong>of</strong> M 87 we can see that the radio halo is a bubble, with a well–defined outer<br />
edge, sitting inside the X-ray emitting atmosphere. The bright plumes emanating<br />
from the inner lobes tell us that the halo is still ”alive”, being supplied with energy<br />
from the black hole. From our knowledge <strong>of</strong> the radio jet, we can tell that the jet is
288 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
3C295<br />
3C132<br />
3 Phase Evolution<br />
<strong>of</strong> Jets<br />
3C341<br />
Figure 136: Time evolution <strong>of</strong> 3C galaxies as seen by computer simulations. Bright<br />
3C galaxies show various types <strong>of</strong> morphology, from the Cyg A type (3C 295),<br />
through break–out geometry (3C 132) and the typical cigar–shape (3C 341). These<br />
different forms are the result <strong>of</strong> a time–evolution <strong>of</strong> jets in the background <strong>of</strong> the<br />
inhomogeneous cluster medium.<br />
pumping at least at much energy into the local atmosphere, as is being lost by that<br />
atmosphere to X–rays. This and other evidence tells us, indirectly, that the core<br />
<strong>of</strong> the Virgo cluster is a complex, turbulent, magnetized region. It is anything but<br />
well-understood.<br />
6.5 Relativistic Jet Propagation<br />
In the last years, the Newtonian approach has been generalized to include relativistic<br />
propagation <strong>of</strong> the beam fluid. In Minkowski spacetime and Cartesian coordinates<br />
(t, x 1 , x 2 , x 3 ), the conservation equations can be written in conservative form as<br />
(Marti & Müller 1999)<br />
∂ U<br />
∂t + ∂F i ( U)<br />
= 0 . (700)<br />
∂xi
6.5 Relativistic Jet Propagation 289<br />
Figure 137: The kpc–scale jet <strong>of</strong> M 87 is embedded into a much more extended faint<br />
radio halo (VLA image at 327 MHz). Such extended radio halos are now found in<br />
many clusters <strong>of</strong> galaxies.<br />
The state vector is defined by<br />
and the flux vector F i as<br />
U = (D, S 1 , S 2 , S 3 , τ) T<br />
(701)<br />
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)<br />
The five conserved quantities D, S 1 , S 2 , S 3 and τ are the rest–mass density, the three<br />
components <strong>of</strong> the momentum density, and the energy density (measured relative to<br />
the rest mass energy density), respectively. They are all measured in the laboratory<br />
frame, and are related to quantities in the local rest frame <strong>of</strong> the fluid (primitive<br />
variables) through<br />
D = ρΓb (703)
290 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
S i = ρhΓ 2 bv i<br />
(704)<br />
τ = ρhΓ 2 b − D − P . (705)<br />
v i = u i /u t is the three velocity and Γb the Lorentz factor. The system <strong>of</strong> equations<br />
is closed by means <strong>of</strong> an equation <strong>of</strong> state (EOS), which we shall assume to be given<br />
in the form P = P (ρ, ɛ).<br />
In the non-relativistic limit D, S i and τ approach their Newtonian counterparts<br />
ρ, ρv i and ρE = ρɛ + ρv 2 /2, and the equations <strong>of</strong> system reduce to the classical<br />
ones. In the relativistic case the equations <strong>of</strong> are strongly coupled via the Lorentz<br />
factor and the specific enthalpy, which gives rise to numerical complications.<br />
An important property <strong>of</strong> system (5) is that it is hyperbolic for causal EOS.<br />
For hyperbolic systems <strong>of</strong> conservation laws, the Jacobians have real eigenvalues<br />
and a complete set <strong>of</strong> eigenvectors. Information about the solution propagates at<br />
finite velocities given by the eigenvalues <strong>of</strong> the Jacobians. Hence, if the solution is<br />
known (in some spatial domain) at some given time, this fact can be used to advance<br />
the solution to some later time (initial value problem). However, in general, it is<br />
not possible to derive the exact solution for this problem. Instead one has to rely<br />
on numerical methods which provide an approximation to the solution. Moreover,<br />
these numerical methods must be able to handle discontinuous solutions, which are<br />
inherent to non-linear hyperbolic systems.<br />
The simplest initial value problem with discontinuous data is called a Riemann<br />
problem, where the one dimensional initial state consists <strong>of</strong> two constant states separated<br />
by a discontinuity. The majority <strong>of</strong> modern numerical methods, the so-called<br />
Godunov–type methods, are based on exact or approximate solutions <strong>of</strong> Riemann<br />
problems [23, 20].<br />
Although MHD and general relativistic effects seem to be crucial for a successful<br />
launch <strong>of</strong> the jet, purely hydrodynamic, special relativistic simulations are adequate<br />
to study the morphology and dynamics <strong>of</strong> relativistic jets at distances sufficiently far<br />
from the central compact object (i.e., at parsec scales and beyond). The development<br />
<strong>of</strong> relativistic hydrodynamic codes based on HRSC techniques has triggered the<br />
numerical simulation <strong>of</strong> relativistic jets at parsec and kilo–parsec scales [18]. In Fig.<br />
138 we show the time evolution <strong>of</strong> a light, relativistic (beam flow velocity equal to<br />
0.99) jet with large internal energy. The logarithm <strong>of</strong> the proper rest-mass density is<br />
plotted in grey scale, the maximum value corresponding to white and the minimum<br />
to black.<br />
Highly supersonic models, in which kinematic relativistic effects due to high<br />
beam Lorentz factors dominate, have extended over-pressured cocoons. These overpressured<br />
cocoons can help to confine the jets during the early stages <strong>of</strong> their evolution<br />
and even cause their deflection when propagating through non-homogeneous<br />
environments. The cocoon overpressure causes the formation <strong>of</strong> a series <strong>of</strong> oblique<br />
shocks within the beam in which the synchrotron emission is enhanced. In long term
6.6 Structure and Emission <strong>of</strong> Micro–Jets 291<br />
Figure 138: Structure <strong>of</strong> a relativistic electron positron jet. [Scheck et al. 2002]<br />
simulations, the evolution is dominated by a strong deceleration phase during which<br />
large lobes <strong>of</strong> jet material (like the ones observed in many FR II’s (e.g., Cyg A)<br />
start to inflate around the jet’s head. These simulations reproduce some properties<br />
observed in powerful extragalactic radio jets (lobe inflation, hot spot advance speeds<br />
and pressures, deceleration <strong>of</strong> the beam flow along the jet) and can help to constrain<br />
the values <strong>of</strong> basic parameters (such as the particle density and the flow speed) in<br />
the jets <strong>of</strong> real sources.<br />
Research Project: Relativistic jet simulations have to be adapted to real cluster<br />
pr<strong>of</strong>iles. In previous simulations, the jets always propagate in a background medium<br />
<strong>of</strong> constant pressure and density.<br />
6.6 Structure and Emission <strong>of</strong> Micro–Jets<br />
There is a wealth <strong>of</strong> information on the structure <strong>of</strong> jets on the parsec–scale in<br />
galaxies. In the following we only a few aspects relevant for modelling jet acceleration<br />
and collimation.
292 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
6.6.1 Core–Jets<br />
Parsec–scale jets can only be detected by means <strong>of</strong> VLBI techniques. Since the jets<br />
are obviously relativistic on this scale, they appear as one–sided (due to relativistic<br />
Doppler beaming), including a stationary core and knots moving away from this<br />
core at superluminal speeds.<br />
Figure 139: A VLBA image <strong>of</strong> 3C 120 at a frequency <strong>of</strong> 22 GHz (Walker et al. 1996).<br />
The scale is in milliarcseconds (mas). (At the distance <strong>of</strong> 3C 120, 1 mas corresponds<br />
to a length <strong>of</strong> 0.7 parsecs = 2.3 light-years.)<br />
3C 120: In Fig. 139 we show the structure <strong>of</strong> the parsec–scale jet <strong>of</strong> the radio<br />
galaxy 3C 120 at 22 GHz (1 mas = 0.7 parsecs for a Hubble constant <strong>of</strong> 65<br />
km/s/Mpc). There is an unresolved stationary feature on the left (eastern) end,<br />
customarily called the core. Bright spots (termed blobs by experts) move down the<br />
jet. Of particular interest is a bright blob that emerges from the core after a major<br />
outburst in brightness (flux density) in early 1998 (Fig. 149). The speeds <strong>of</strong> the<br />
superluminally moving components range from 3.5 to 8.3 times the speed <strong>of</strong> light.<br />
The magnetic field behavior is complex, changing with both position and time. The
6.6 Structure and Emission <strong>of</strong> Micro–Jets 293<br />
core, however, is usually unpolarized. 2<br />
6.6.2 Emission Properties<br />
As the brightest and nearest quasar (z = 0.158), 3C 273 is an ideal laboratory to<br />
study emission processes for jets in quasars. This source displays significant flux<br />
variations, has a well measured wide band spectral energy distribution and has<br />
a relativistic jet emanating from the central part in a galaxy. This collimated jet<br />
structure extends up to 150 kpc from the core, depending on the unknown inclination<br />
towards the observer. 3C 273 is classified as a blazar – though I find this notion<br />
somewhat misleading – and is also a prominent gamma–ray source.<br />
3C 273 and the hard X–ray emission: Recently, the results <strong>of</strong> a long–term<br />
monitoring <strong>of</strong> 3C 273 with RXTE have been published (Kataoka et al. 2002). This<br />
covers the longest observation period in the hard X–rays (about 835 ksec, Fig. 140).<br />
Most <strong>of</strong> the 3C 273 photon spectra observed between 1996 and 2000 can be fitted<br />
Figure 140: RXTE light curves <strong>of</strong> 3C 273 in the hard X–rays (Katakoa et al. 2002).<br />
The data are binned in 10 days intervals.<br />
by a power–law spectrum with spectral index αX = 1.6 ± 0.1. This is consistent<br />
with previously published data. Multifrequency spectra provide information for<br />
physical quantities relevant to the jet physics, e.g. the magnetic field, the size <strong>of</strong><br />
the emission region, the maximum energy and the density <strong>of</strong> relativistic electrons.<br />
2 For a movie see http://www.bu.edu/blazars/3C120.html
294 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
von Montigny et al. (1997) examined 3 models to reproduce the multifrequency<br />
spectrum <strong>of</strong> 3C 273: (i) the synchrotron–self Compton model (SSC model); (ii) the<br />
external radiation Compton model (ERC model; Sikora, Begelman and Rees 1994),<br />
and, (iii) the proton induced cascade model (PIC model; Mannheim & Biermann<br />
1992). At that time, the authors concluded that the data were still insufficient to<br />
discriminate between the models. In Fig. 141, a simple one–zone model is shown to<br />
explain the spectrum. In this simple model, the radiation is due to a homogeneous<br />
jet component moving with a bulk Lorentz factor ΓBLK at an angle <strong>of</strong> line <strong>of</strong> sight<br />
Θ 1/ΓBLK. It is assumed that the peak emission <strong>of</strong> the low–energy synchrotrn<br />
component (LE) and the high energy inverse Compton components (HE) arise from<br />
the same electron population with Lorentz factor γp. The peak frequencies <strong>of</strong> LE<br />
and HE are related by<br />
νHE,p = 4<br />
(706)<br />
3 γ2 pνLE,p<br />
with νLE,p = 10 13.5 Hz, and νHE,p = 10 20 Hz. This requires a γp = 2 × 10 3 . The<br />
Figure 141: Global spectrum for 3C 273 with X–rays as explained by SSC–emission<br />
(Katakoa et al. 2002).<br />
synchrotron peak frequency νLE,p is given by<br />
νLE,p = 3.7 × 10 6 B γ 2 p<br />
D<br />
Hz (707)<br />
1 + z
6.6 Structure and Emission <strong>of</strong> Micro–Jets 295<br />
where B is the magnetic field strength in Gauss and D = Γ −1<br />
B (1 − β cos Θ) −1 ΓB<br />
is the relativistic Doppler factor. From the above numbers we get then a magnetic<br />
field strength<br />
and a corresponding energy density<br />
B 0.4 × 10<br />
ΓB<br />
UB 6.7 × 10 −3<br />
<br />
10<br />
ΓB<br />
2<br />
G (708)<br />
erg/cm 3 . (709)<br />
The ratio <strong>of</strong> the synchrotron luminosity and the inverse Compton luminosity<br />
Figure 142: Global IR spectra for 3C 273 and similar quasars with possible dust<br />
emission in the mid–infrared (Meisenheimer et al. 2001).<br />
LSSC<br />
LS<br />
= US<br />
UB<br />
(710)
296 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
is independent <strong>of</strong> the bulk motion. US is the energy density in the synchrotron<br />
photons measured in the comoving frame <strong>of</strong> the jet. With LHE = 10 47.1 erg/s and<br />
LS = 10 46.8 erg/s we obtain<br />
US 0.02<br />
2 10<br />
erg/cm<br />
D<br />
3<br />
Assuming a spherical geometry for the emission region <strong>of</strong> radius R<br />
providing a radius<br />
(711)<br />
LS = 4πR 2 cD 4 US erg/s , (712)<br />
R 2 × 10 16 cm 10<br />
. (713)<br />
D<br />
The SSC spectrum is then calculated self–consistently from these numbers for an<br />
electron distribution <strong>of</strong> the form N(γ) ∝ γ−2 exp(−γ/γp). This would indicate that<br />
the inverse Compton emission is radiated in an extremely compact region near the<br />
collimation region. The spectrum in the radio band can usually not be fitted by<br />
simple one–zone models, since this low–frequency emission occurs on much larger<br />
scales in the jet.<br />
An ERC model can however also fit the observed spectra. Part <strong>of</strong> the mid–IR<br />
and far–IR radiation is in fact emitted by warm dust in a dusty torus located on the<br />
parsec–scale in the center <strong>of</strong> the bulge <strong>of</strong> the host galaxy <strong>of</strong> 3C 273 (Meisenheimer et<br />
al. 2001, Fig. 142). This is a common feature for strong radio galaxies (Cyg A e.g.)<br />
and radio–loud quasars. This dust emission zone can roughly be approximated by a<br />
shell <strong>of</strong> radius RD 10 pc, so that the energy density inside the shell as measured<br />
in the comoving frame <strong>of</strong> the jet is<br />
UD = LD<br />
4πR 2 Dc Γ2 BLK 10 −3 Γ 2 B erg/cm 3 ξDLUV X<br />
10 47 erg/s<br />
10 pc<br />
RD<br />
2<br />
. (714)<br />
The factor ξD 0.5 represents the fraction <strong>of</strong> the UV–bump luminosity reprocessed<br />
by dust emission. This factor is quite high in Quasars. In particular, all photons<br />
directed inwards towards the central source are blue–shifted, and enhanced by a<br />
factor ΓB with respect to the comoving frame <strong>of</strong> the jet. On the parsec–scale,<br />
this external photon density is the dominant source for inverse Compton<br />
scattering. With such an ERC model the frequencies are now interrelated as<br />
νHE,e = 4<br />
3 γ2 eΓ 2 B νIR . (715)<br />
The dust spectrum also peaks at νIR 10 13.5 Hz (warm dust). For ΓJ 10, this<br />
only requires a γe 100. This is the typical Lorentz factor for the electrons in an
6.6 Structure and Emission <strong>of</strong> Micro–Jets 297<br />
ion jet and corresponds to the minimal electron Lorentz factor required by global<br />
spectra (Ghisellini et al. 2001).<br />
Relativistic electrons are a natural consequence in relativistic jets. The plasma<br />
in such jets is automatically heated to high temperatures by internal shocks (see<br />
previous sections). The ion component essentially stays hot and can only cool over<br />
adiabatic expansion. The electrons stay probably extremely hot since the jet material<br />
passes through various shocks. In quasars, inverse Compton cooling is probably<br />
the fastest mechanism on the parsec–scale with a cooling time given by<br />
tIC =<br />
mec 2<br />
(4/3) σT cUphγe<br />
10 yrs (716)<br />
for γe = 1000 and Uph 10 −3 erg/cm 3 . Without reheating, the electrons would cool<br />
down to a mean Lorentz factor γmin 50−100, when traversing the dust shell. The<br />
heat carried by the electrons is therefore a rough measure for the inverse Compton<br />
luminosity<br />
LIC Lheat,e = ˙ MBc 2 < γe > (me/mp) < LB . (717)<br />
The magnetic field structure can essentially be probed by means <strong>of</strong> Faraday<br />
rotation<br />
8.1 × 105<br />
RM =<br />
< γe > 2<br />
<br />
neB dl[pc] rad m −2 , (718)<br />
where the electron density ne is given in units <strong>of</strong> particles per cc and < γe ><br />
is the mean energy <strong>of</strong> the relativistic electrons. The classical expression <strong>of</strong> the<br />
rotation measure has to be corrected by the square <strong>of</strong> the Lorentz factor for the<br />
electrons, since the rotation measure is proportional to the plasma frequency and the<br />
cyclotron frequency. The parsec–scale jet <strong>of</strong> 3C 273 has a typical rotation measure<br />
RM 300 rad m−2 . This indicates that the internal Faraday rotation is negligible.<br />
It is probably produced by the electrons in the ISM <strong>of</strong> the galactic nucleus.<br />
NGC 4261 and the state <strong>of</strong> the disk at 0.1 pc: The structure <strong>of</strong> the inner<br />
disk in nearby radio galaxies can be probed by synchrotron emission from the jets<br />
over free–free absorption. The nearby low–luminosity FRI–galaxy NGC 4261 (3C<br />
270, Fig. 143) is a good candidate for detecting free–free absorption by ionized gas<br />
in the inner disk [9, 24]. The galaxy is known to contain a Black Hole with a mass <strong>of</strong><br />
MH = 7×10 8 M⊙ (Ferrarese, Ford and Jaffe 1996), a nearly edge–on disk <strong>of</strong> gas and<br />
dust with a diameter <strong>of</strong> about 100 pc. The large–scale symmetric radio structure<br />
implies that the radio axis is close to the plane <strong>of</strong> the sky. First VLBA observations<br />
revealed a parsec-scale radio jet and counter–jet aligned with the kiloparsec–scale<br />
jet [9]. The opening angle is less than 20 degrees within 0.2 pc from the core and<br />
less than 5 degrees within 0.8 pc. The free–free optical depth is given by<br />
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<br />
Figure 143: The radio galaxy NGC 4261 and its nuclear disk (HST, top panel) with<br />
a VLBA image at 8.4 GHz (bottom panel, Jones et al. 2001). At a distance <strong>of</strong> 40<br />
Mpc, 1 mas corresponds to 0.2 pc. A 700 Mio solar mass Black Hole in the center<br />
generates the jets in this radio galaxy.
6.6 Structure and Emission <strong>of</strong> Micro–Jets 299<br />
where the path length L is in cm, and the electron density in cm−3 . From this we<br />
can estimate the electron density<br />
<br />
ne 3.4 τ/L νT 3/4<br />
(720)<br />
For a path–length L 0.3 pc, τff 3 and a temperature T 10 4 K, this corresponds<br />
to an electron density ne 3 × 10 4 cm −3 . Since the temperature decays in a<br />
Figure 144: Disk geometry in the center <strong>of</strong> NGC 4261 [Jones et al. 2001; Wehrle et<br />
al. 2002].<br />
SAD very rapidly with increasing radius, accretion disks around supermassive Black<br />
Holes are expected to have a partial ionization zone, as in Galactic binaries, and<br />
therefore to be subject <strong>of</strong> a similar thermal instability. This zone forms at a distance<br />
<strong>of</strong> a few hundred Schwarzschild radii from the center (Lin and Shields 1986; Clarke
300 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
1989). Depending on the viscosity, the instability can develop in a very narrow<br />
unstable zone and propagate over the entire disk resulting in this way in a large–<br />
amplitude outburst on time–scales <strong>of</strong> the order <strong>of</strong> a few 10 5 years (Siemiginowska et<br />
al. 1996).<br />
In standard disk models one finds a local equilibrium relationship between a<br />
steady state accretion rate ˙ M and the surface density Σ for given mass, viscosity<br />
parameter α and radius R. This relationship has a characteristic S–shape for an<br />
optically thick, geometrically thin disk. Three characteristic regions on the S–curve<br />
describe different physical conditions. The lower branch is thermally stable, cool,<br />
and neutral hydrogen dominates the chemical composition, molecules also contribute<br />
to the opacity. A disk on the upper branch is also thermally stable, but is hot, and<br />
hydrogen is fully ionized. Bound–free transitions in heavy metals, free–free transitions<br />
and electron scattering determine the opacity. The middle branch corresponds<br />
to a partially ionized disk that is thermally unstable due to the rapid increase <strong>of</strong> the<br />
opacity with temperature. The instability strip is located at an effective temperature<br />
<strong>of</strong> TA 4000 K, and its radius RA can be derived from the local values <strong>of</strong> ΣA<br />
and TA (Siemiginowska et al. 1996)<br />
RA 10 3 Rg M −0.6<br />
H,8<br />
˙M 0.4 α −0.05<br />
−1 . (721)<br />
This corresponds to a radius <strong>of</strong> about 100 Schwarzschild radii in the core <strong>of</strong> NGC<br />
4261. Local accretion occurs then on the viscous time–scale, tvisc R/v r , or<br />
tvisc 2 × 10 5 yr α −0.8<br />
−1 M 1/4<br />
8<br />
˙M −0.3 R 1.25<br />
16 . (722)<br />
The disk beyond RA is optically thin (Clarke 1988). All the energy produced<br />
dissipatively is radiated away by free–free emission. Under these conditions, the<br />
ionisation instability requires the disk to be either in an optically thin hot state<br />
or an optically thick cool state. These values are consistent with the particle<br />
densities obtained for a standard accretion disk at a distance <strong>of</strong> 10 4 gravitational<br />
radii (Camenzind 1997),<br />
n 24 cm −3 α −1 ˙m −2 M −1<br />
H,9<br />
R<br />
10 4 Rg<br />
−3/2<br />
. (723)<br />
For a turbulence parameter α 0.1 and a relative mass accretion rate ˙m =<br />
˙M/ ˙ MEd 0.01 this gives a particle density n 10 6 cm −3 with an ionisation fraction<br />
<strong>of</strong> about 10%. The temperature <strong>of</strong> the disk at this position is in fact about 10000 K<br />
TD(R) 10 4 K α −1/4 M −1/4<br />
H,9<br />
R<br />
10 4 Rg<br />
−3/8<br />
. (724)<br />
This absorption through the disk produces a gap in the low–frequency emission<br />
detected from the counter–jet (Fig. 143, Jones et al. 2001).
6.7 Formation <strong>of</strong> Micro–Jets 301<br />
6.7 Formation <strong>of</strong> Micro–Jets<br />
In accretion and jet production theory the principal parameters determining the<br />
appearance and behavior <strong>of</strong> the system are the black hole mass MH, the mass accretion<br />
rate ˙ M, and the black hole angular momentum J, expressed in dimensionless<br />
form as m9 = MH/10 9 M⊙ (where M⊙ represents one solar mass), ˙m = ˙ M/ ˙ MEdd<br />
(where ˙ MEdd = 4GMH/ɛHκesc = 22 M⊙ yr −1 m9 is the accretion rate that produces<br />
one Eddington luminosity for an efficiency ɛH = 0.1 and electron scattering opacity<br />
κes), and j = J/Jmax (where Jmax = GM 2 H/c is the angular momentum <strong>of</strong> a maximal<br />
Kerr black hole). For most AGN and quasar models typical ranges <strong>of</strong> the parameters<br />
are 10 −3 < m9 < 10, 10 −5 < ˙m < 1, and 0 < j < 1. While all parameters will affect<br />
the properties <strong>of</strong> an AGN to a certain extent, the purpose here is to identify the<br />
principal observable effects <strong>of</strong> each.<br />
The accretion paradigm states that most, and perhaps all, AGN are powered<br />
by accretion onto a supermassive black hole. Within this model ˙m plays the most<br />
important role, determining the emission properties, and therefore the appearance,<br />
<strong>of</strong> the central source. Objects with high accretion rate ( ˙m > 0.1) appear as an “optical”<br />
quasar (<strong>of</strong> course, equally bright, if not brighter, in X-rays as well), while low<br />
sub-Eddington accretion ( ˙m ≤ 10 −2 ) produces a weak “radio” core with substantially<br />
less optical emission. A zero accretion rate produces a “dead” quasar - a black<br />
hole detectable only through its gravitational influence on the galactic nucleus. For<br />
a given level, the black hole mass determines mainly the luminosity scaling.<br />
The spin paradigm states that, to first order, it is the normalized black hole<br />
angular momentum j that determines whether or not a strong radio jet is produced<br />
(Wilson & Colbert 1995, Blandford 1999). If correct, this hypothesis has significant<br />
implications for how we should view the jets and lobes in radio sources: the jet radio<br />
and kinetic energy comes directly from the rotational energy <strong>of</strong> a (perhaps formerly)<br />
spinning black hole. Radio sources are not powered (directly) by accretion.<br />
There is significant theoretical basis for this paradigm as well. Several models <strong>of</strong><br />
relativistic jet formation indicate that the jet power should increase as the square<br />
<strong>of</strong> the black hole angular momentum<br />
Ljet 10 44 erg s −1<br />
2<br />
BH<br />
m9j<br />
1000 G<br />
2 . (725)<br />
where BH is the strength <strong>of</strong> the poloidal (vertical/radial) magnetic field threading<br />
the ergospheric and horizon region <strong>of</strong> the rotating hole. In this model rotational<br />
energy is extracted via a Penrose-like process: the frame-dragged accretion disk is<br />
coupled to plasma above and outside the ergosphere via the poloidal magnetic field;<br />
some plasma is pinched and accelerated upward while some disk material is diverted<br />
into negative energy (retrograde) orbits inside the ergosphere, removing some <strong>of</strong><br />
the hole’s rotational energy. The key parameter determining the efficiency <strong>of</strong> this
302 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
process is the strength <strong>of</strong> the poloidal magnetic field. The standard approach (e.g.,<br />
Moderski & Sikora 1996) to estimating BH is to set it equal to Bφ, the dominant<br />
azimuthal magnetic field component given by the disk structure equations, yielding<br />
and<br />
Ljet,B = 2 × 10 45 erg s −1 m9 ˙m−2 j 2<br />
(726)<br />
Ljet,A = 3 × 10 49 erg s −1 m 0.8<br />
9 ˙m−1 j 2 . (727)<br />
for Class B (radio galaxy/ADAF) and Class A (quasar/standard disk) objects, respectively.<br />
Note that, while the jet is not accretion-powered in this model, the<br />
efficiency <strong>of</strong> extraction is still essentially linear in ˙m.<br />
Basic physics <strong>of</strong> MHD acceleration and collimation: Though many models<br />
have been proposed to generate jets, the magnetohydrodynamic (MHD) model is still<br />
the leading one (Fig. 145). In this picture, the plasma is simplified in terms <strong>of</strong> a one–<br />
component approximation and the conductivity is assumed to be very high so that<br />
electric fields in the plasma are shorted out. In a first approximation, plasma is not<br />
allowed to cross field lines, it can only flow parallel to them. In regions where the field<br />
is weak or the plasma is dense, the rotating field will be bent backward. To accelerate<br />
and collimate a jet with magnetic fields, all that is needed is a gravitating body to<br />
collect the material which should be ejected, a poloidal magnetic field threading that<br />
material, and some differential rotation, which produces a helical structure in the<br />
field. This rotating field structure drives the confined plasma upwards and outwards<br />
along the field lines. As this twist propagates outwards, the toroidal field pinches<br />
the plasma towards the rotational axis. Depending on the relative importance <strong>of</strong><br />
the magnetic field, the plasma density and rotation, a variety <strong>of</strong> configurations are<br />
possible from spherical winds, slowly collimated and highly collimated outflows.<br />
Poloidal magnetic field strengths are estimated from equation disk pressure, but<br />
(H/R) is <strong>of</strong> order unity for the low cases, and also for the high Kerr case due to<br />
Lens-Thirring bloating <strong>of</strong> the inner disk. Otherwise (H/R) is calculated from the<br />
electron scattering/gas pressure disk model <strong>of</strong> Shakura & Sunyaev (1973), and disk<br />
field strengths are computed from that paper or from Narayan et al. (1998), as<br />
appropriate. The logarithms <strong>of</strong> the resulting poloidal field strengths, and corresponding<br />
jet powers, are represented as field line and jet arrow widths. In the Kerr<br />
cases, the inner disk magnetic field is significantly enhanced over the Schwarzschild<br />
cases, due in part to the smaller last stable orbit (flux conservation) and in part to<br />
the large (H/R) <strong>of</strong> the bloated disks. The high accretion rate, Schwarzschild case has<br />
the smallest field - and the weakest jet - because the disk is thin, the last stable orbit<br />
is relatively large, and the Keplerian rotation rate <strong>of</strong> the field there is much smaller<br />
than it would be in a Kerr hole ergosphere. Enhancement <strong>of</strong> the poloidal field due<br />
to the buoyancy process suggested by Krolik (1999) is ignored here because we find
6.7 Formation <strong>of</strong> Micro–Jets 303<br />
Figure 145: Essential elements for magnetic jet formation. A torus <strong>of</strong> hot gas is<br />
initially magnetized by vertical magnetic fields. The differential rotation <strong>of</strong> the<br />
torus drags the field lines in the azimuthal direction, angular momentum is thereby<br />
carried away from the disk material which allows the material to accrete inwards<br />
towards the horizon. This exerts a torque on the external field with a kind <strong>of</strong><br />
torsional Alfvèn wave. This carries away angular momentum and energy from the<br />
system. [Meier et al., Science 291 (2001)].
304 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
it not to be a factor in the simulations discussed below. If it were important, then<br />
the grand scheme proposed here would have to be re-evaluated, as the effect could<br />
produce strong jets (up to the accretion luminosity in power) even in the plunging<br />
region <strong>of</strong> Schwarzschild holes. Then even the latter would be expected to be radio<br />
loud as well (Ljet 10 43−46 erg s −1 ).<br />
6.7.1 The Stationary MHD Model<br />
For BHs the above processes must be modelled with relativistic MHD. The time–<br />
dependent analysis <strong>of</strong> this theory is however not yet fully developed. One can get<br />
some insight from considerations <strong>of</strong> the plasma confinement analogue.<br />
Plasma flow near the horizon is presently not observable due to the limited spatial<br />
resolution <strong>of</strong> VLBI. So we cannot test directly the jet formation scenarios. The only<br />
viable model for the generation <strong>of</strong> relativistic jets is however MHD models, where<br />
collimation occurs on scales <strong>of</strong> a few hundred Schwarzschild radii. Such collimated<br />
plasma beams will have therefore a kind <strong>of</strong> conical structure on scales <strong>of</strong> a few<br />
thousand Schwarzschild radii (fraction <strong>of</strong> parsecs) to scales <strong>of</strong> a few hundred parsecs.<br />
We can describe these plasma beams as a stationary equilibrium between various<br />
forces (Appl & Camenzind [1])<br />
κ B2 p<br />
4π (1 − M 2 − x 2 ) = (1 − x 2 B<br />
)∇⊥<br />
2 p B<br />
+ ∇⊥<br />
8π 2 φ<br />
+ ∇⊥P<br />
8π<br />
− B2 pΩF 4πc2 ∇⊥(Ω F R 2 <br />
2 µnj I2<br />
) + −<br />
R3 4πR3 <br />
(−∇⊥R) . (728)<br />
Pressure gradients acting perpendicularly to the magnetic surfaces are in equilibrium<br />
with electric forces, centrifugal forces, pinch forces generated by the poloidal currents<br />
(I), as well as with curvature forces expressed on the left hand side. This is the<br />
correct generalisation <strong>of</strong> well known pressure forces in Newtonian plasma pinches.<br />
This equilibrium assumes a particualr simple form for cylindrical configurations,<br />
κ = 0<br />
(1 − x 2 ) d B<br />
dR<br />
2 p<br />
8π<br />
d B<br />
+<br />
dR<br />
2 φ<br />
8π<br />
− B2 pR<br />
2πR2 −<br />
L<br />
µnj 2<br />
I2<br />
−<br />
R3 4πR3 <br />
= 0 . (729)<br />
This can be written for the dimensionless variables, x = R/RL, y = B 2 p/B 2 0 and<br />
I = RBφ → I/RLB0 as<br />
(1 − x 2 ) dy 1<br />
− 4xy +<br />
dx x2 dI2 8π<br />
+<br />
dx B2 0<br />
dP<br />
dx<br />
− 8πµn<br />
B 2 0<br />
j2 (cRL) 2 = 0 . (730)<br />
x3
6.7 Formation <strong>of</strong> Micro–Jets 305<br />
This is an extension <strong>of</strong> the force–free equation discussed by [1]. Pressure and tension<br />
due to the toroidal field are combined into one expression for the variation <strong>of</strong> the<br />
current, or the pinch force. The electric field also contributes a positive pinch<br />
force, −x 2 dy/dx, which is opposite to the usual pressure force. These two forces<br />
can therefore compensate for all pressure forces and lead to a pinch equilibrium.<br />
Outside the light cylinder, R > RL the current assumes the simple expression<br />
I = −Ω F (R 2 Bp) 1<br />
βJ<br />
(731)<br />
and the specific angular momentum j <strong>of</strong> the plasma stays constant, i.e. the rotational<br />
velocity <strong>of</strong> the plasma decreases as 1/R. This shows that the centrifugal force has a<br />
negligible influence on the plasma equilibrium outside the light cylinder. Under this<br />
condition we get a core–halo structure for the distribution <strong>of</strong> the poloidal magnetic<br />
field<br />
Bp <br />
with the core radius Rc = ΓJβJRL and<br />
Bφ − B0<br />
βJ<br />
B0<br />
1 + R 2 /R 2 c<br />
R/RL<br />
1 + R 2 /R 2 L<br />
(732)<br />
. (733)<br />
The beam radius RJ is probably larger than the core radius and given by pressure<br />
equilibrium with external pressure. The plasma in the beam is rotating with nearly<br />
the speed <strong>of</strong> light at the light cylinder.<br />
The total electron density in the beam is<br />
ne =<br />
˙MJ<br />
πR 2 Jmpc<br />
100 cm−3<br />
˙MJ<br />
0.1 M⊙ yr −1<br />
3 × 10 9 M⊙<br />
MH<br />
2 1000 2<br />
Rg<br />
The mass–flow in the beam is also related to the total jet kinetic energy<br />
LJ = ˙ MJc 2 (ΓJ − 1) 5 × 10 46 erg s −1<br />
˙MJ<br />
0.1 M⊙ yr −1<br />
RJ<br />
. (734)<br />
ΓJ<br />
. (735)<br />
10<br />
This is a reasonable number for the outflow rate <strong>of</strong> bright quasars, since about a<br />
few percent <strong>of</strong> the inflow is probably converted to outflows. The outflow rate in M<br />
87 is estimated to be about a factor 100 lower than this number (Camenzind 1999).<br />
These numbers tell us that the Alfven speed in the beam is about the speed <strong>of</strong> light<br />
for<br />
VA c B0/0.3 G<br />
. (736)<br />
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<br />
Physical Parameter Symbol 3C 273 M 87<br />
Black Hole mass MH [M⊙] 3 × 10 9 3 × 10 9<br />
Gravitational radius Rg [AU] 30 30<br />
Black Hole spin a 0.9 MH 0.8<br />
Light cylinder RL/Rg 20 20<br />
Bulk Lorentz factor ΓJ 10 6<br />
Inclination ΘJ [deg] 8 20<br />
Jet core radius Rc = ΓJRL 0.1 lyr 0.01 lyr<br />
Beam Radius RJ 0.1 pc 0.03 pc<br />
Ion number density nJ 6 cm −3<br />
Ion temperature Ti 100 MeV 100 MeV<br />
Beam sonic Mach number M = ΓJβJ/cS 30<br />
Mass flux ˙ MJ 0.1 M⊙ yr −1<br />
Magnetic field B0 0.1 Gauss 0.03 G<br />
Magnetic flux ΨJ B0R 2 c 10 33 G cm 2<br />
Total current IJ cRcB0 10 18 Amp<br />
Alfvèn Mach number MA = ΓJβJ/VA 10 10<br />
Fast magnetos. M number MF M 5 5<br />
Mean e − Lorentz factor γe 100 50<br />
Cut<strong>of</strong>f e − Lorentz factor γp 2000 2000<br />
Table 9: Parameters <strong>of</strong> the MHD parsec–scale jet in 3C 273 and M 87. The Black<br />
Hole mass in 3C 273 is estimated from the similarity <strong>of</strong> its host galaxy with M 87,<br />
the mass in M 87 has been derived from the HST disk. The spin parameters are<br />
essentially unknown.
6.7 Formation <strong>of</strong> Micro–Jets 307<br />
VLBI jets are extreme plasma pipes, where all communication occurs<br />
over the speed <strong>of</strong> light – the Alfven speed and the fast magnetosonic speed<br />
are relativistic. The plasma in these pipes is also exotic: it is permanently heated<br />
to high temperatures <strong>of</strong> the order <strong>of</strong> 10 12 K by means <strong>of</strong> internal shocks. The ions<br />
are probably still non–relativistic, while the electrons always assume relativistic<br />
temperatures with < γe > 100, which are then subject to acceleration to even<br />
higher energies by various mechanisms.<br />
6.7.2 The Collimation Zone<br />
I am still convinced that jets in quasars are launched by complete MHD processes<br />
and that this will be modelled some day within General Relativistic MHD. The<br />
following elements should be included<br />
• a dipolar magnetosphere that closes radially towards the horizon;<br />
• hot plasma is launched from the innermost part (probably within the ergosphere<br />
region) in radial direction;<br />
• Along the axis, higly relativsitic plasma is injected from a polar gap. This<br />
plasma is energetically not important, but it carries the closure currents.<br />
• The gap is feeded by a pair plasma created from photoproduction in the ion<br />
torus near the horizon.<br />
• The toroidal field amplified by the frame–dragging effect leads to additional<br />
J × B–forces near the ergosphere.<br />
Structure <strong>of</strong> the magnetosphere: The calculation <strong>of</strong> the magnetosphere in the<br />
stationary approach is very cumbersome (Beskin 1996; Camenzind [6]; Fendt &<br />
Greiner [7]), since the current distribution has to be found self–consistently (this<br />
exercise is in fact better done within a time–dependent approach). The transition<br />
from the highly diffusive disk towards the ideal outflow conditions has however<br />
hampered down all modelling so far. What is urgently needed for this process is a<br />
realisation <strong>of</strong> the GR MHD equations on the background <strong>of</strong> compact objects. The<br />
form <strong>of</strong> the magnetosphere shown in Fig. 146 is a first guess.<br />
The Plasma Outflow: It has been shown that the stationary axisymmetric and<br />
polytropic plasma flow along an axisymmetric magnetic flux tube Ψ(r, θ) can be<br />
described by means <strong>of</strong> an algebraic wind equation (Camenzind [6]; Fendt & Greiner<br />
[7]). The essential quantity which determines the asymptotic plasma flow is the
308 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
Figure 146: The Black Hole magnetosphere consist <strong>of</strong> a family <strong>of</strong> nested magnetic<br />
surfaces, and plasma can only flow along the flux surfaces. Currents can however<br />
cross the flux surfaces. Only in the force–free approximation, currents are also force<br />
to flow along the flux surfaces. This is in general violated near the Alfven points.<br />
[Fendt 2001]<br />
magnetissation parameter σ∗ at the injection point<br />
σ∗ =<br />
Φ∗<br />
4πmpIp;∗<br />
(737)<br />
measuring the Poynting–flux in terms <strong>of</strong> the particle flux Ip = √ −gnup, where up<br />
is the poloidal velocity along the flux–tube. The form <strong>of</strong> the flux–tube is expressed<br />
in terms <strong>of</strong> the dimensionless flux–tube function Φ, Φ ≡ 1 is a pure monopole<br />
flux surface. The other wind parameters are the total energy E and total angular<br />
momentum L carried by the plasma. At the magnetosonic points the wind equation<br />
becomes singular, and this fixes two parameters (for more details, see Lecture by<br />
Beskin). In terms <strong>of</strong> astrophysical quantities, the magnetization parameter is given
6.7 Formation <strong>of</strong> Micro–Jets 309<br />
as (Camenzind [6])<br />
σ∗ <br />
Ψ 2 ∗<br />
2c ˙ MJ(Ψ)R 2 L<br />
= B2 p,∗R 2 L<br />
c ˙ MJ(Ψ)<br />
4<br />
R∗<br />
RL<br />
. (738)<br />
˙MJ(Ψ) denotes the jet mass flux carried by the flux surface Ψ, and RL = c/Ω F is the<br />
light cylinder radius <strong>of</strong> the flux surface. With an idea on the maximal flux provided<br />
by the disk near the horizon,<br />
Ψ∗ ˙ MaccR 2 ∗<br />
αT<br />
<br />
Rg<br />
R∗<br />
we can estimate the value <strong>of</strong> the magnetization<br />
−1<br />
H<br />
R<br />
(739)<br />
σ∗ (740)<br />
The outflow starts hot, cS,∗ 0.3c and is then continuously accelerated, until collimation<br />
is reached (Fig. 147). thereby, the particle number decreases rapidly and<br />
also the temperature decreases adiabatically.<br />
6.7.3 Nondiffusive Relativistic MHD Approach<br />
Recent work by Koide, Shibata and Kudoh on general relativistic simulations <strong>of</strong> the<br />
accretion <strong>of</strong> magnetized material by black holes is beginning to provide a clearer<br />
picture <strong>of</strong> the development and evolution <strong>of</strong> a black hole magnetosphere and the<br />
resulting jet. Initial indications are that rapid rotation <strong>of</strong> the black hole and rapid<br />
infall <strong>of</strong> the magnetized plasma into this rotating spacetime both contribute to<br />
powerful, collimated, relativistic jet outflows. We find no evidence for buoyant<br />
poloidal field enhancement in the plunging region and, therefore, no reason to expect<br />
Schwarzschild holes to have a jet any more powerful than that estimated in Figure<br />
148. Figure 148 shows the initial and final state <strong>of</strong> a Kerr (j = 0.95) black hole<br />
simulation with a weak (VA = Bp/ √ 4πρdisk = 0.01c) magnetic field and an inner<br />
edge at Rin = 4.5GMH/c 2 . For more details see Koide et al. (1999a). In this first<br />
simulation the disk was non-rotating, and so began to free-fall into the ergosphere<br />
(at Rergo = 2GMH/c 2 ) as the calculation proceeded. As with other MHD disk<br />
simulations, the field lines were wound up by differential rotation and a hollow jet<br />
<strong>of</strong> material was ejected along the poloidal field lines by the J × B forces; here the<br />
jet velocity was rather relativistic (vJ 0.93c or 2.7). However, as the disk was<br />
initially non-rotating, all the action was due to the differential dragging <strong>of</strong> frames by<br />
the rotating black hole. Little or no jet energy was derived from the binding energy<br />
<strong>of</strong> the accreting material or its Keplerian rotation.<br />
As a control experiment, the same simulation was also run with a Schwarzschild<br />
(j = 0) hole. The collapse developed a splash outflow due to tidal focusing and<br />
shocking <strong>of</strong> the inflowing disk, but no collimated MHD jet occurred.
310 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
Figure 147: Poloidal flow velocity along a collimated flux tube (top panel) and<br />
particle density (bottom panel) (Fendt & Greiner 2001). x = R/Rg
6.7 Formation <strong>of</strong> Micro–Jets 311<br />
Figure 148: General relativistic simulation <strong>of</strong> a magnetized flow accreting onto a<br />
Kerr black hole (after Koide et al. 1999a). Left panel shows one quadrant <strong>of</strong><br />
the initial model with the j = 0.95 hole at lower left, freely-falling corona, and<br />
non-rotating disk. The hole rotation axis (Z) is along the left edge. The initial<br />
magnetic field (vertical lines) is weak compared to the matter rest energy density<br />
(VA = 0.01c). Right panel shows final model at t = 130GMH/c 3 . Some <strong>of</strong> the disk<br />
and corona have been accreted into the hole, threading the ergosphere and horizon<br />
with magnetic field lines that develop a significant radial component, and hence an<br />
azimuthal component as well, due to differential frame dragging. The resulting jet<br />
outflow is accelerated by J × B forces to a Lorentz factor <strong>of</strong> 2.7. [Koide et al. 2001]<br />
The authors also studied counter-rotating and co-rotating Keplerian disks with<br />
otherwise similar initial parameters (Koide et al. 1999b). The counter-rotating<br />
case behaved nearly identically to the non-rotating case: because the last stable<br />
retrograde orbit is at Rms = 9GMH/c 2 , the disk began to spiral rapidly into the<br />
ergosphere, ejecting a strong, black-hole-spin-driven MHD jet. On the other hand,<br />
for prograde orbits Rms = GMH/c 2 , so the co-rotating disk was stable, accreting<br />
on a slow secular time scale. At the end <strong>of</strong> the calculation (tmax = 94GMH/c 3 ),<br />
when the simulation had to be stopped because <strong>of</strong> numerical problems, the disk<br />
had not yet accreted into the ergosphere and had produced only a weak MHD jet.<br />
Future evolution <strong>of</strong> this case is still uncertain. The Keplerian Schwarzschild case was<br />
previously reported by Koide et al. (1998) and developed a moderate sub-relativistic<br />
MHD jet similar to the aforementioned simulations <strong>of</strong> magnetized Keplerian flows<br />
around normal stars, plus a pressure-driven splash outflow internal to the MHD jet.<br />
In the Kerr cases, significant magnetic field enhancement over the Schwarzschild
312 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
cases occurs due to compression and differential frame dragging. It is this increase<br />
that is responsible for the powerful jets ejected from near the horizon. In the<br />
Schwarzschild cases, on the other hand, - particularly in the Keplerian disk case<br />
in Koide et al. (1998) - we do not see any MHD jet ejected from well inside Rms.<br />
That is, we do not see any increase in jet power that could be attributed to buoyant<br />
enhancement <strong>of</strong> the poloidal field in the plunging region. While there is a jet<br />
ejected from inside the last stable orbit, it is pressure-driven by a focusing shock<br />
that develops in the accretion flow. The magnetically-driven jet that does develop<br />
in the Schwarzschild case emanates from near the last stable orbit as expected, not<br />
well inside it. It is therefore concluded that a powerful MHD jet will be produced<br />
near the horizon if and only if the hole is rotating rapidly.<br />
The spin paradigm even <strong>of</strong>fers an explanation for why present-day giant radio<br />
sources occur only in elliptical galaxies. The e-folding spindown time (Erot/Ljet) is<br />
<strong>of</strong> the order <strong>of</strong> the Hubble–time (Camenzind 1997)<br />
tspindown = JH<br />
dJH/dt<br />
4 MHc 2<br />
B 2 Hr 3 H<br />
rH<br />
c 1011 yr<br />
−2 9<br />
BH 10 M⊙<br />
. (741)<br />
kG MH<br />
As a result, all AGN should be radio quiet at the present epoch, their black holes<br />
having spun down when the universe was very young. In order to continually produce<br />
radio sources up to the present epoch, there must be periodic input <strong>of</strong> significant<br />
amounts <strong>of</strong> angular momentum from accreting stars and gas, or from a merger with<br />
another supermassive black hole (see also Wilson & Colbert 1995). Such activity<br />
is triggered most easily by violent events such as galaxy mergers. Since only elliptical<br />
galaxies undergo significant mergers (the merging process is believed to be<br />
responsible for their elliptical shape), only ellipticals are expected to be giant radio<br />
sources in the present epoch. With little merger activity, spiral galaxies are<br />
expected to be relatively radio quiet. Since merging and non-merging galaxies will<br />
fuel and re-kindle their black hole’s spin in very different ways, bi-modality in the<br />
radio luminosity distribution is to be expected.<br />
6.7.4 Knot Ejection Mechanisms<br />
According to theoretical models (see, for example, computer simulations by Meier,<br />
Koide, et al.), this drives jets <strong>of</strong> ultra-high-energy particles (including electrons) at<br />
speeds <strong>of</strong> about 98% the speed <strong>of</strong> light. (The spiral swirling <strong>of</strong> the jet corresponds to<br />
the expected spiral pattern <strong>of</strong> the magnetic field.) About once every 10 months, an<br />
instability in the accretion disk causes a chunk <strong>of</strong> the inner portion to break <strong>of</strong>f and<br />
fall into the black hole. Although most <strong>of</strong> the matter falls past the event horizon<br />
and disappears, a small amount <strong>of</strong> the mass and energy is injected into the jet. This<br />
causes a bright spot to appear about 0.41 parsecs (1.3 light-years) downstream <strong>of</strong><br />
the black hole. The bright spot appears to be moving at almost 5 times the speed
6.7 Formation <strong>of</strong> Micro–Jets 313<br />
Figure 149: A sequence <strong>of</strong> VLBA images (year <strong>of</strong> observation in decimal form marked<br />
on the left) at a frequency <strong>of</strong> 43 GHz. The scale is in milliarcseconds (mas). The<br />
apparent diameter <strong>of</strong> the moon in the sky is about 1.8 million mas, which means<br />
that the resolution <strong>of</strong> the VLBA is extraordinarily fine. There is a stationary core<br />
at the left. One can see bright spots coming out at speeds <strong>of</strong> about 1.8 mas per<br />
year, or between 4 and 5 times the speed <strong>of</strong> light. (At the distance <strong>of</strong> 3C 120, 1 mas<br />
corresponds to a length <strong>of</strong> 0.7 parsecs = 2.3 light-years.) The diagonal lines pass<br />
through the centers <strong>of</strong> the bright spots.
314 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
<strong>of</strong> light. This is an illusion that occurs when a jet moving at slightly less than the<br />
speed <strong>of</strong> light is pointing nearly at us. Why the jet is invisible between the black<br />
hole and 0.41 parsecs is not yet understood. (Marscher thinks that the jet expands<br />
too fast until its pressure falls below that <strong>of</strong> the interstellar medium, which causes<br />
a stationary shock wave to form. The shock wave then energizes electrons and<br />
amplifies the magnetic field, which makes the jet shine from synchrotron radiation<br />
and inverse Compton scattering. But, he admits that the evidence in favor <strong>of</strong> this is<br />
pretty thin.) The top panel in Fig. 150 shows the X-ray flux as a function <strong>of</strong> time<br />
measured with RXTE. The red points correspond to what we call the X-ray dips,<br />
when the flux was low for at least 4 consecutive observations. The blue arrows show<br />
the times when a bright spot first showed up on the VLBA radio images, about 0.1<br />
years after each X-ray dip. The middle panel is the slope <strong>of</strong> the X-ray spectrum;<br />
a low value means that the higher frequency X-rays are more prominent relative to<br />
the lower frequency X-rays. The bottom panel shows the flux at 3 radio frequencies<br />
(green is 14.5 GHz, red is 22 GHz, and blue is 43 GHz) obtained at the University<br />
<strong>of</strong> Michigan Radio Astronomy Observatory and the Metsahovi Radio Observatory<br />
in Finland. The black points on the bottom indicate the flux <strong>of</strong> the radio core as<br />
seen on our 43 GHz VLBA images.<br />
It is apparent from this Figure that each X–ray dip is followed by the appearance<br />
<strong>of</strong> a superluminal knot at the side <strong>of</strong> the radio core. The mean time–delay between<br />
the minimum in the X–ray flux and the appearance <strong>of</strong> the knot ejection is 0.1 ± 0.03<br />
yr. At a typical superluminal apparent speed <strong>of</strong> 4.7 c, a knot moves a distance <strong>of</strong><br />
0.14 pc in 0.1 year, projected on the plane <strong>of</strong> the sky (the real distance is about 0.5<br />
pc for an inclination <strong>of</strong> 20 degrees). The jet probably starts as a broad wind until it<br />
gets collimated at the radio core on the scale <strong>of</strong> a few 100 Schwarzschild radii (see<br />
M 87, Junor, Biretta and Livio, Nature 1999). this would correspond to a minimu<br />
distance <strong>of</strong> 0.3 pc from the X-ray source to the radio core. The core <strong>of</strong> the radio<br />
jet is therefore not coincident with the position <strong>of</strong> the Black Hole. The jet might be<br />
invisible between the site <strong>of</strong> the origin and the radio core far downstream where the<br />
electrons are reaccelerated (e.g. by a recollimation shock).<br />
This correlated radio and X–ray behaviour is similar to the microquasar GRS<br />
1915+105: here, X–ray dips, where the spectrum hardens, are followed by the ejection<br />
<strong>of</strong> a bright superluminal radio knot. This is seen as resulting from an instability<br />
where a piece <strong>of</strong> the inner disk breaks <strong>of</strong>f. Most <strong>of</strong> this matter is accreted towards<br />
the horizon, but a smaller amount is ejected from the inner region and accelerated<br />
by magnetic forces to high velocities. The X–ray flux is due to Compton scattering<br />
in the inner accretion torus. The bulk velocity <strong>of</strong> the jets in 3C 120 and GRS<br />
1915+105 are also similar, about 0.98 c in each case (i.e. a Lorentz factor <strong>of</strong> about<br />
5). The jet in the microquasar is however seen at a much higher inclination <strong>of</strong> 66<br />
degrees. Therefore, the counterjet is also visible.<br />
Nakamura et al. (2001) investigated the wiggled structure <strong>of</strong> AGN radio
6.7 Formation <strong>of</strong> Micro–Jets 315<br />
Figure 150: RXTE light curves <strong>of</strong> 3C 120 in the hard X–rays (top panel, Marscher<br />
et al. 2002). The middle panel is the slope <strong>of</strong> the X-ray spectrum. The bottom<br />
panel shows the flux at 3 radio frequencies (green is 14.5 GHz, red is 22 GHz, and<br />
blue is 43 GHz). The blue arrows show the times when a bright spot first showed<br />
up on the VLBA radio images. [Marscher et al. 2002]
316 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES<br />
Figure 151: Knot formation in rotating magnetized jets. [Nakamura et al. 2001].<br />
jets by performing 3-dimensional magnetohydrodynamic (MHD) simulations based<br />
on the ‘Sweeping Magnetic-Twist’ model. The correlation between the wiggled<br />
structures <strong>of</strong> AGN radio jets and tails and the distribution <strong>of</strong> magnetic field in them<br />
suggests that the magnetic field plays an essential role, not only in the emission <strong>of</strong><br />
synchrotron radiation, but also in the dynamics <strong>of</strong> the production <strong>of</strong> the AGN–jets–<br />
lobes systems (core, jets, tails, lobes, and hotspots) themselves. In order to produce<br />
such a systematic magnetic configuration, a supply <strong>of</strong> a huge amount <strong>of</strong> energy, in an<br />
organized form, is necessary. The supply <strong>of</strong> this energy must come from AGN core.<br />
The most natural means <strong>of</strong> carrying this energy is in the form <strong>of</strong> the Poynting flux<br />
<strong>of</strong> torsional Alfven wave train (TAWT) produced in the interaction <strong>of</strong> the rotating<br />
accretion disk and the large scale magnetic field brought into it by the gravitational<br />
contraction. The propagation <strong>of</strong> the TAWT can produce a slender jet shape by the<br />
sweeping pinch effect from the initial large scale magnetic field. Further, wiggles <strong>of</strong><br />
the jet can be produced by the MHD processes due to the TAWT. Our numerical<br />
results reveal that the structure <strong>of</strong> the magnetic jet can be distorted due to the<br />
helical kink instability. This results in the formation <strong>of</strong> wiggled structures in the<br />
jets as the TAWT encounters a domain <strong>of</strong> reduced Alfven velocity (either towards
6.7 Formation <strong>of</strong> Micro–Jets 317<br />
the boundary <strong>of</strong> the ‘cavity’ from which the mass contracted to the central core, or<br />
encounting smaller and denser clouds in the domain). The toroidal component <strong>of</strong> the<br />
field accumulates due to the lowered Alfven velocity, and produces a strongly pinched<br />
region, as well as the deformation <strong>of</strong> the jet into a writhed structure. The condition<br />
for this to occur corresponds to the Kruskal–Shafranov criterion <strong>of</strong> the linear case.<br />
If the intrinsic relationship between the wiggled structure <strong>of</strong> the jet shape and the<br />
magnetic field in the jets and tails as proposed in this paper is confirmed, it will<br />
influence the understandings <strong>of</strong> the AGN jets in a vital way.
318 7 THE FIRST BLACK HOLES IN THE UNIVERSE<br />
7 The First Black Holes in the Universe<br />
Recent ground- and space-based observations over the course <strong>of</strong> the last decade have<br />
directly measured the kinematic signature <strong>of</strong> supermassive black holes at the centers<br />
<strong>of</strong> approximately forty nearby galaxies. Even more interesting than this confirmation<br />
<strong>of</strong> the existence <strong>of</strong> these black holes, however, is the fact that black holes have been<br />
found in all <strong>of</strong> the galaxies which have a substantial spheroid component (i.e. they<br />
are ellipticals or are spirals with a substantial bulge) and these black holes are<br />
millions to billions <strong>of</strong> times as massive as our sun. This 100% success rate strongly<br />
suggests that all galaxies have supermassive black holes at their centers. Present<br />
research focuses on how these black holes have grown to their present size.<br />
Black holes are known to form during the death throes <strong>of</strong> certain massive stars.<br />
However, the black holes that form during the end stages <strong>of</strong> stellar evolution are<br />
typically only a few times as massive as the sun, rather than millions to billions <strong>of</strong><br />
times greater. The main focus <strong>of</strong> this section on black hole evolution is how the<br />
supermassive black holes at the centers <strong>of</strong> galaxies grew to their present size.<br />
Most <strong>of</strong> this research is therefore aimed at identifying and understanding different<br />
mechanisms that can ”feed” these black holes, determining which mechanisms are<br />
more or less important, and how long these phases <strong>of</strong> black hole evolution last. If the<br />
black hole at the center <strong>of</strong> a galaxy is growing relatively ”quickly,” which means it<br />
may double in mass in a few tens <strong>of</strong> millions <strong>of</strong> years. In this case, the host galaxy is<br />
said to have a high-luminosity active galactic nucleus (AGN), or quasar, due to the<br />
great amount <strong>of</strong> radiation that is emitted as material falls onto the black hole. At<br />
a more moderate growth rate, the emitted radiation is not as intense, and the host<br />
galaxy would more likely appear to be a low-luminosity AGN, such as a Seyfert or<br />
LINER galaxy. For very low growth rates, no emission from the host galaxy nucleus<br />
may be visible at all, and in this case the galaxy may not be classified as an AGN.<br />
7.1 The Dark Age<br />
After its creation 10 – 15 billion years ago in the mother <strong>of</strong> all explosions, called the<br />
Big Bang, the universe was a homogenous sea <strong>of</strong> cooling gas. Slight fluctuations in<br />
gravity rippled this smoothness, however, and gravity’s force pulled the ripples into<br />
waves <strong>of</strong> matter that condensed into the first objects with separate identities.<br />
The Universe literally entered a dark age about 300,000 years after the big bang,<br />
when the primordial radiation cooled below 3000K and shifted into the infrared.<br />
Unless there were some photon input from (for instance) decaying particles, or string<br />
loops, darkness would have persisted until the first non-linearities developed into<br />
gravitationally-bound systems, whose internal evolution gave rise to stars, or perhaps<br />
to more massive bright objects.<br />
Spectroscopy from the new generation <strong>of</strong> 8 – 10 metre telescopes now comple-
7.1 The Dark Age 319<br />
Figure 152: Dark age and reionization <strong>of</strong> the Universe.
320 7 THE FIRST BLACK HOLES IN THE UNIVERSE<br />
ments the sharp imaging <strong>of</strong> the Hubble Space Telescope (HST); these instruments<br />
are together elucidating the history <strong>of</strong> star formation, galaxies and clustering back,<br />
at least, to redshifts z = 5. Our knowledge <strong>of</strong> these eras is no longer restricted to<br />
‘pathological’ objects such as extreme AGNs - this is one <strong>of</strong> the outstanding astronomical<br />
advances <strong>of</strong> recent years. In addition, quasar spectra (the Lyman forest,<br />
etc) are now observable with much improved resolution and signal-to-noise; they <strong>of</strong>fer<br />
probes <strong>of</strong> the clumping, temperature, and composition <strong>of</strong> diffuse gas on galactic<br />
(and smaller) scales over an equally large redshift range, rather as ice cores enable<br />
geophysicists to probe climatic history.<br />
7.2 The First Stars<br />
Currently, we do not have direct observational constraints on how the first stars<br />
(Population III stars) formed at the end <strong>of</strong> the cosmic dark age. What we know<br />
is how Population I stars form out <strong>of</strong> cold, dense molecular gas. The molecular<br />
clouds are supported against gravity by turbulent velocity fields and are pervaded<br />
by large–scale magnetic fields. Stars tend to form in clusters, ranging from a few<br />
hundred to one million stars. The IMF <strong>of</strong> Pop I stars is observed to have about the<br />
Salpeter form<br />
dN<br />
d ln M ∝ M x , (742)<br />
where x −1.35 for M ≥ 0.5 M⊙. For lower masses it turns over. The lower limit<br />
corresponds roughly to the opacity limit for fragmentation. Therefore, 1 M⊙ is<br />
the typical mass–scale <strong>of</strong> Pop I star formation, in the sense that most <strong>of</strong> the mass<br />
goes into stars with masses close to this value.<br />
How did the first stars form ? The simplest thing we can do is estimate the corresponding<br />
characteristic mass–scale. To investigate the collapse and fragmentation<br />
<strong>of</strong> primordial gas, one has to carry out complicated simulations (Bromm et al. 2002<br />
[4]). In primordial gas clumps, molecular cooling, H2, in a metal–free environment<br />
provides characteristic temperatures <strong>of</strong> 200 K and densities 10 4 cm −3 . Evaluating<br />
the Jeans mass for these characteristic values results in MJ 10 3 M⊙. These<br />
masses can still grow by accretion processes.<br />
Current simulations indicate that the first stars were predominantly<br />
very massive, and therefore rather different from star formation in the<br />
local Universe. These very massive stars would rapidly explode and form seed<br />
Black Holes which can grow by accretion.<br />
7.3 The First Quasars<br />
The brightest quasars at z ≥ 6 are most likely hosted by rare galaxies, more massive<br />
than 10 12 M⊙. They would end up today as the most massive elliptical galaxies.
7.3 The First Quasars 321<br />
Figure 153: Formation <strong>of</strong> compact objects in stellar evolution (adapted from Heger<br />
et al. (2001)). In the mass range from 140 - 250 M⊙, no Black Holes are left over<br />
(pair creation instability).
322 7 THE FIRST BLACK HOLES IN THE UNIVERSE<br />
There are essentially two routes towards the formation <strong>of</strong> supermassive BHs in the<br />
center <strong>of</strong> galaxies:<br />
1. Black Holes with masses <strong>of</strong> a few hundred solar masses, left over from the<br />
collapse <strong>of</strong> very massive stars, could grow by accretion.<br />
2. Black Holes with masses in the range <strong>of</strong> 10 5 − 10 6 M⊙ are formed in a direct<br />
collapse <strong>of</strong> primordial gas clouds at high redshifts. It has been shown that<br />
without a pre–existing central point mass, this direct collapse is difficult by<br />
the negative feedback resulting from star formation in the collapsing cloud<br />
(Loeb & Rasio 1994). The input <strong>of</strong> kinetic energy from supernovae explosions<br />
prevents the gas from assembling in the center <strong>of</strong> the dark matter potential.<br />
If however star formation can be suppressed in a cloud that undergoes overall<br />
collapse, such a negative feedback would not occur.<br />
Figure 154: Formation <strong>of</strong> a cloud at redshift 10.3. The box size is 200 pc. One<br />
compact object has formed in the center with a mass <strong>of</strong> 2.7 Mio solar masses.<br />
[Bromm 2002]
7.3 The First Quasars 323<br />
Bromm & Loeb (2003) [4] have carried out SPH simulations <strong>of</strong> isolated peaks in<br />
the dark matter fluctuations with total masses <strong>of</strong> 10 8 M⊙ that collapse at z 10 3 .<br />
The virial temperature <strong>of</strong> these dwarf galaxies exceeds 10 4 K, which allows collapse<br />
<strong>of</strong> their gas through cooling by atomic hydrogen H2. Such a scenario would include<br />
lower–mass halos that would have collapsed earlier on. Those lower mass systems<br />
would have virial temperatures below 10 4 K, and consequently rely on the presence<br />
<strong>of</strong> molecular hydrogen for cooling. This H2 is however fragile and readily destroyed<br />
by photons in the energy bands <strong>of</strong> 11 – 13.6 ev (Werner bands), just below the<br />
Lyman limit.<br />
What is the future fate <strong>of</strong> the central object ? Once the gas has collapsed to<br />
densities above 10 7 cm −3 and radii les than 0.01 light year, Thomson scattering traps<br />
the photons, and the cooling time becomes now much larger than both the free–fall<br />
time and the viscous time–scales. The gas cloud settles into a radiation–pressure<br />
supported configuration resembling a rotating supermassive star. Fully relativistic<br />
calculations <strong>of</strong> the collapse <strong>of</strong> such stars have recently been done by Baumgarte et al.<br />
(1999) [3]. These objects are expected to collapse towards a supermassive spinning<br />
Black Hole. A substantial fraction <strong>of</strong> the mass is expected to end up in the Black<br />
Hole.<br />
The main question is whether a complete destruction <strong>of</strong> molecular hydrogen<br />
will occcur. The effective suppresion <strong>of</strong> H2 formation will crucially depend on the<br />
presence <strong>of</strong> a stellar–like radiation background. It is therefore likely that stars<br />
precede the first quasars. The above discussion shows that there is only a small<br />
window in redshift where supermassive stars could be formed at redshifts around<br />
10. At later times, the strong UV radiation field will certainly destroy molecular<br />
hydrogen. Another question is whether there is some initial spin in the collapsing<br />
cloud. This would lead to a binary system with a typical separation <strong>of</strong> one parsec.<br />
3 see homepage http://www.ukaff.ac.uk/starcluster/
324 REFERENCES<br />
References<br />
[1] Appl, S., Camenzind, M. 1993, The structure <strong>of</strong> relativistic MHD jets: a<br />
solution to the nonlinear Grad-Shafranov equation, A&A 274, 699.<br />
[2] Barkana, R., Loeb, A. 2001, The First Sources <strong>of</strong> Light and the Rionisation<br />
<strong>of</strong> the Universe, Phys. Reports 349, 125<br />
[3] Baumgarte, T.W., Shapiro, S.L. 1999, , ApJ 526, 941.<br />
[4] Bromm, V., Loeb, A. 2002, Formation <strong>of</strong> the First Supermassive Black<br />
Holes, ApJ<br />
[5] Bromm, V., Loeb, A. 2003, The first Sources <strong>of</strong> Light, astro–ph/0301406<br />
[6] Camenzind, M. 1998, Magnetohydrodynamics <strong>of</strong> Rtoating Black Holes, in<br />
Relativistic Astrophysics, eds. H. Riffert et al., Vieweg, pp 82–117.<br />
[7] Fendt, C., Greiner, J. 2001, Magnetically driven superluminal motion<br />
from rotating black holes. Solution <strong>of</strong> the magnetic wind equation in Kerr<br />
metric, A&A 369, 308.<br />
[8] Gopal–Krishna, Wiita, P. 2001, The Fanar<strong>of</strong>f–Riley Transition and the<br />
Optical Luminosity <strong>of</strong> the Host Elliptical Galaxy, A&A 373, 100.<br />
[9] Jones, et al. 2001, In the Shadow <strong>of</strong> the Accretion Disk: Higher Resolution<br />
Imaging <strong>of</strong> the Central Parsec in NGC 4261, ApJ 553, 968.<br />
[10] Kataoka, Jun et al. 2002, RXTE observations <strong>of</strong> 3C 273 between 1996<br />
and 2000: variability time-scale and jet power, MNRAS 336, 932.<br />
[11] Krause, M. 2002, On the interaction <strong>of</strong> jets with the dense medium <strong>of</strong> the<br />
early universe, PhD thesis, Univ. Heidelberg.<br />
[12] Krause, M. 2003, Very light jets. I. Axisymmetric parameter study and<br />
analytic approximation, A&A 398, 113.<br />
[13] Laing, R.A. et al. 1999, MNRAS 306, 513.<br />
[14] Ledlow, M.J., Owen, F.N., Eilek, J.A. 2001, Rich-cluster and non–cluster<br />
radio galaxies and the (P, D) diagram for a large number <strong>of</strong> FR I and<br />
FR II sources, New Astron. Rev. 46, 343.<br />
[15] Marti, J.M., Müller, E. 1999, Living Reviews in Relativity.<br />
[16] Marscher, A.P. et al. 2002, Observational evidence for the accretion-disk<br />
origin for a radio jet in an active galaxy, Nature 417, 625.
REFERENCES 325<br />
[17] Leahy, P. 1993, in Jets in Extragalactic Radio Sources, eds. Röser, H.-J.,<br />
Meisenheimer, K.; LNP, Springer-Verlag, Heidelberg.<br />
[18] Scheck, L. et al. 2002, Does the plasma composition affect the long term<br />
evolution <strong>of</strong> relativistic jets ?, MNRAS 331, 615.<br />
[19] Smith, D.A. et al. 2002, A Chandra X-Ray Study <strong>of</strong> Cygnus A. III. The<br />
Cluster <strong>of</strong> Galaxies, ApJ 565, 195.<br />
[20] Spindeldreher, S. 2002, The discontinous Galerkin method applied on the<br />
equations <strong>of</strong> ideal relativistic hydrodynamics, PhD Thesis, Univ. Heidelberg<br />
[21] Sutherland, R.S., Dopita, M.A. 1993, Cooling functions for low–density<br />
astrophysical plasmas, ApJSup 88, 253.<br />
[22] Thiele, M. 2000, Simulation protostellarer Jets, PhD thesis, Univ. Heidelberg.<br />
[23] Toro, E.F. 2001, Godunov Methods: Theory And Applications, Kluwer<br />
Academics.<br />
[24] Wehrle, A. et al. 2002, The radio jets and accretion disk in NGC 4261,<br />
New Astron. Rev. 46, 235.<br />
[25] Wilson, A. S., Yang, Y. 2002, Chandra X-Ray Imaging and Spectroscopy<br />
<strong>of</strong> the M87 Jet and Nucleus, ApJ 568, 133.