Astrophysical Background
Stirling A. Colgate and Hui Li, T-6, Los Alamos
National Lab
Radio astronomy aperture synthesis pictures of quasars or active
galactic nuclei (AGN) within the special environment of clusters of
galaxies reveal massive regions of coherent magnetic flux: Fig. 1,
3C465, 3C75, (Eilek and Owen, 1999) and Fig. 2, Hydra, (Taylor and
Perley, 1993). This magnetic field is inferred using the technique of
measuring the Faraday rotation by a foreground screen of the vector of
polarized emission of an underlying, highly polarized source. In order
for this effect to be observed, this screen must have: (1) a highly
polarized source, (2) with small internal Rm, (3)
lying behind, (4) a region of highly ordered Rm, (5)
without significant emission, and (6) further
requiring both a highly ordered field and (7) a uniform
electron density. A modification of any one of these seven
conditions rapidly averages a potentially large Rm
to a negligible value. The fact that the field can be measured and is so
strong, highly oriented, and uniform and furthermore that the electron
density is equally as uniform over dimensions of 100 kpc or 10 times the
size of our galaxy is truly extraordinary. The energy derived from the
size and therefore volume of coherent field is ~ 1059 to 1060 erg. This energy is so large, a million times that of the
field energy of our own galaxy and orders of magnitude larger than the
binding energy of typical galaxies, that an extraordinary source of
this energy is necessary (Colgate and Li, 1999). The underlying
highly polarized source is an AGN. This implies that the AGN is the
source of this immense magnetic energy. A massive black hole, ~ 108 Mʘ is presumed to power every AGN from the black hole
binding energy, ~ 1062 erg. A significant fraction of this
energy is therefore required to create the fields inferred from
Faraday measurements. Furthermore an even larger magnetic energy,
~ 1060 to 1061 erg is required to explain the
underlying polarized synchrotron source, which is also the giant radio
lobes of typical, average field AGN, (not in clusters). One
calculates this still larger energy by assuming that the radio
emission from the giant radio lobes is synchrotron radiation. This
emission requires both a magnetic field and highly energetic
electrons. The minimum energy is determined from the minimum sum of
the accelerated electrons (plus ions) and magnetic field strength
necessary to emit the observed synchrotron radiation. This minimum
occurs when the two energies are equal. If the energy in energetic
electrons is just a small fraction, ~ 1%, of the ion energy as
expected from our galactic cosmic ray spectrum, then the total energy is
an order of magnitude larger. The Faraday rotation measures indicate that
strong magnetic fields of immense energy are associated with AGN. This
substantiates the synchrotron radiation interpretation of still larger
energies implied for most sources. Finally, comparable field energies
are seen in the cluster as a whole (Clarke,Krönberg, & Böhringer
2000).
Figure 1:
Shows the emission measure maps and the Faraday rotation
measure maps of two galaxies 3C465 and 3C75 in two different Abell
clusters. The scale is of the order of 80 kpc, far larger than normal
galaxy size. The Faraday rotation proves the immense regions of
coherent magnetic fields. The minimum energy of the emission maps
interpreted as synchrotron emission implies a minimum energy ~ 1061 erg for the sum of magnetic and relativistic electrons plus ions,
more than an order of magnitude greater than the field energy implied by
Faraday rotation measures. This energy is so large that we believe
that only a massive black hole is a feasible energy source (courtesy
Eilek and Owen 2000).
Figure 2:
Shows the emission measure maps and the Faraday rotation
measure maps of a galaxy in the Hydra cluster of galaxies. The scale
is of the order of 100 kpc, far larger than normal galaxy size. The
Faraday rotation proves the immense regions of coherent magnetic
fields. The minimum energy of the emission maps interpreted as
synchrotron emission implies a minimum energy ~ 1061 erg for
the sum of magnetic and relativistic electrons plus ions, more than an
order of magnitude greater than the field energy implied by Faraday
rotation measures(courtesy Taylor and Perley 1993).
Most galaxies exist outside of clusters, i.e. field galaxies. Nearly
all galaxies go through an early phase of being an AGN (Richstone
1998). These field AGN also always emit synchrotron radiation from
their radio lobes, which are larger in dimension than in clusters.
The Faraday rotation cannot be observed in these field galaxies or
field AGN, because of the low, ~ 10-2 electron density, but
within the galaxy clusters a stronger gravity binds a thousand times
larger electron (and mass) density and so we can observe the Faraday
rotation. Thus we are led to conclude that all galaxies produced an
immense energy in magnetic flux during their brief, early AGN phase.
This magnetic energy may be so large as to explain the missing energy,
~ 90%, lost or not seen from the black hole formation,
(Richstone, 1998) aside from the background x-ray sources. In order
to explain the large fields requires a dynamo. In order to convert the
kinetic energy of the black hole accretion disk into magnetic energy
requires an efficient dynamo. In order to explain the missing
luminosity from AGN, the dynamo that produces this field would have to
be ~ 90% efficient. But this high efficiency is what we expect
of an α ω dynamo. If this magnetic energy were the
"missing" energy, it would then exceed that of star light emitted
during the lifetime of the galaxy.
The only feasible source of this magnetic energy is the gravitational
binding energy of forming the central galactic black hole. How can
one convert a significant fraction of this energy, 108 Mʘc2 = 2 × 1062 erg, into magnetic energy, B2/8π? Such a
conversion mechanism is called a dynamo. In order for this magnetic
energy to remain "dark" it must not be dissipated into heat at some
later point in time as is the case for most dynamos. We believe that
this magnetic energy remains as force-free magnetic fields of ~ 1μ G in the intergalactic space between galaxies, i.e. the "walls".
Matter is born with too much angular momentum. The initial
Lyman-α clouds, so called because of their UV hydrogen
absorption spectra, are the first signature of large density
fluctuations, galaxy size, in calculations of the emerging structure
of the universe (Zurek, et. al, 1994). The initial specific angular
momentum of the matter of these massive clouds, although small, ~ 5%, compared to that necessary for Keplerian support, is
nevertheless very large, ~ 3 × 106 greater than the
specific angular momentum of the same matter when it reaches the
"event horizon" of the black hole. Exchanging this angular momentum
with another fraction of matter not reaching the black hole is a
central problem in astrophysics. Initially matter and angular
momentum are exchanged equally by tidal torquing so that a "flat",
constant velocity, "rotation curve" is produced, where Minterior ∝ R. Thus one has a small mass at a small radius. This would
never lead to a massive central black hole. Instead at a critical
radius and critical condition a hydrodynamic instability is initiated
so that almost all the interior matter falls to form the black hole.
This process generally called an accretion disk, starts with fluid
dynamic processes when the disk is thick enough to remain adiabatic
during the growth of this instability (Lovelace, Li, and Colgate,
1999, Li, Lovelace, and Colgate 2000, Li, Wendroff, and Colgate,
2000). When a galaxy is being formed from the collapse of giant
Lyman-α clouds emerging from the growth of structure of the
universe, we predict that this instability, Fig. 3, is initiated at a
critical thickness, ~ 100 to 1000 g/cm2. At
this point ~ 108 Mʘ reside within a disk several parsecs
in radius. The matter in this accretion disk then evolves by these
instabilities into the black hole.
Figure 3:
Shows a calculation of the formation of co-rotating
"Rossby vortices" in a Keplerian flow. These vortices are calculated
as if they are just 2 dimensional. It is these vortices that
transport angular momentum. The interaction with the third dimension
sets the condition for minimum thickness and contributes to the
damping of the vortices (Li et al. 2000).
Figure 4: The α ω
dynamo in a galactic black hole accretion disk (ANIMATE ). The initial poloidal quadrupole field within the
disk (Panel A) is sheared by the differential rotation within the
disk, developing a strong toroidal component (Panel B). As a star
passes through the disk it heats by shock and by radiation a fraction
of the matter of the disk, which expands vertically and lifts a
fraction of the toroidal flux within an expanding plume (Panel C).
Due to the conservation of angular momentum, the expanding plume and
embedded flux rotate ~ π/2 radians before the
plume falls back to the disk (Panel D). (The Pulsed Jet Rotation Experiment explains
the relative counter-rotation of an expanding plume in a rotating
frame due to conserved angular momentum.) Reconnection allows the new
poloidal flux to merge with and augment the original poloidal flux
(Panel D).
This accretion disk we believe is a natural dynamo because of one
peculiar circumstance. A small fraction of the accreting matter must
be in the form of stars, Pop III stars, because of the metalicity
observed in the initial Lyman-α clouds, ~ 10-3 to 10-4. These stars, not in the orbit of the disk, plunge through
the disk many times, ~ 109, before falling into the black hole.
Each collision with the disk carries a fraction of the disk matter, as
well as entrained magnetic flux, to high altitude, like plumes, above
and below the disk. Remarkably these plumes rotate, actually
un-rotate, relative to the Keplerian rotation of the disk (Beckley et
al 2000). The differential rotation is in the same direction
regardless of their orbit. The twist is opposite to the rotation of
the disk, because the moment of inertia of the expanding plume always
increases and therefore the plume slows down relative to the frame.
Thus the translation and twist of the plumes is strikingly coherent.
It is this coherent motion, the helicity, (α = v • (∇ × v)) that is the basis of the
α-deformation of the dynamo. The differential rotation of
Keplerian motion of the disk will always wrap up the radial component
of an initial poloidal field provided it is immersed in a conducting
medium, the Ω-deformation. A field line wrapped up n turns
will be larger by n and, hence, for large n the toroidal field can
be much larger than an initial poloidal one. Then only a small
fraction of the enhanced toroidal field needs to be converted back to
poloidal field to result in a dynamo of positive gain. This
conversion of toroidal to poloidal is produced by the helicity of the
plume rotation. What is remarkable is that such a random phenomena as
star-disk collisions can convert a fraction of this wrapped up, now
larger toroidal field, back into the original poloidal field and
therefore give rise to a coherent amplification. We have simulated
this processes with a kinematic dynamo, vector potential code and are
proceeding to demonstrate it in the laboratory. As Paul Roberts and
Torkel Jensen, (1993) once lamented,
"And yet laboratory models of such dynamos, working under controlled
conditions, are still lacking! They are, at this time, merely sterile
fantasies of the armchair scientists: the theoreticians. This seems
to be a too unhealthy state to be allowed to persist. As Fermi once
warned, in magnetohydrodynamics one should not believe the product of
a long and complicated piece of mathematics if it is unsupported by
observation".
Now that the "α2" dynamo has been demonstrated in two
experiments, Karlsruhe (Rädler, 1988) and Riga (Gailitis et al.,
2000) we know that the basic principle of a dynamo is valid. Such an
α2 dynamo can not usefully create the magnetic fields of the
universe.
We need the experiment to substantiate our understanding of the the
α - Ω dynamo in the accretion disk, the largest energy
machine in the universe. Theory, mathematics, calculations, and some
experiments now agree.
Beckley, H.F., Colgate, S.A., Romero, V.D., Ferrel, R.,
2000, "
Rotation of a Pulsed Jet in a Rotating Annulus: A Source of Helicity for an
α - Ω Dynamo
", 2000, Submitted to
Physics of Fluids
Burbidge, G.R., 1958, ApJ, 129, 849
Clarke, T.E., Krönberg, P.P., and Böhringer, H., 2000,
ApJ., Letter in press
Colgate, S.A. & Hui Li, 1998, "The Galactic Dynamo, the
Helical Force Free Field and the Emissions of AGN", Proc of the
Conference on "Relativistic Jets in AGNs", ed. Michal Ostrowski,
Sikora, Madejski, and Begelman, Cracow, Poland, 27-30 May 1997,
pp. 170-179
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the Magnetic Fields of the Universe:The Plasma Astrophysics of the
Free Energy of the Universe" Physics of Plasmas, accepted
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vs. Observation, Ringberg workshop, Germany, MPE-Report
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Gailitis, A., Lielausis, O., Dement'ev, S., Platacis,
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Li, H., Colgate, S.A., Wendroff, B. and Liska, R., 2001,
"Rossby Wave Instability of Thin Accretion Disk-III. Nonlinear
Simulations", 2000, Astrophys. J. accepted
Li, H., Finn, J.M., Lovelace, R.V.E., and Colgate, S.A.,
2000 Astrophys. J. 533, 1023
Lovelace, R.V.E., Li, H., Colgate, S.A., and Nelson, A.F.,
1999,"Rossby Wave Instability of Keplerian Accretion Disks,"
Astrophys. J., 513, 805
Rädler, K.-H., Apstein, E., Rheinhardt, M., and Schüler,
M., 1998, "The Karlsruhe Dynamo Experiment; A Mean Field Approach",
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Taylor, G.B., & Perley, R.A., 1993, Astrophys. J., 416, 554
Zurek, W.H., Quinn, P.J., Salmon, J.K., and Warren, M.S.,
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