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Presidential Address
Dynamos in planets,
stars and galaxies
Nigel Weiss discusses dynamos in settings as diverse as galaxies and planets in this his
2000 Presidential Address to the Ordinary (A&G) Meeting of the Royal Astronomical Society.
Abstract
Global magnetic fields in the Earth and
other major planets, in the Sun and other
active stars, and also in spiral galaxies
like the Milky Way, are apparently
maintained by hydromagnetic dynamos.
This lecture will contrast the various
dynamo models that have been put
forward. Powerful supercomputers have
now made it possible to simulate the
geodynamo in considerable detail. In the
case of the Sun, we have yet to explain its
internal rotation and models still have to
rely on mean field dynamo theory. There
are many features that can be explained
but extrapolation to other stars remains
uncertain. For galaxies, even the need for
a dynamo is still controversial.
1: The Sun’s dipolar magnetic field revealed by the
structure of the solar corona during an eclipse in
1998. (Courtesy of the High Altitude Observatory.)
2: The magnetic field in the Earth’s core. Magnetic
field lines showing the predominantly dipole field
in the insulating mantle and the tangled,
predominantly toroidal field in the conducting core.
(From Glatzmaier and Roberts 1995.)
L
ast year I spoke about small-scale turbulent magnetic fields in the Sun, but this
year I shall talk about the maintenance
of large-scale, global magnetic fields, like those
revealed by the structure of the Sun’s corona at
eclipses (as shown in figure 1). However, I shall
also discuss magnetic fields in the Earth, as
depicted from a theoretical model in figure 2,
and the fields revealed by radio astronomy in
galaxies like M51 (see figure 3), which raise
rather different problems. Large-scale fields
seem to be generated everywhere in the universe. Yet what Nature manages so easily has
proved surprisingly difficult to model.
About 100 years ago geophysicists identified
the Earth’s fluid core, containing molten iron
above the Curie point – and the naive assumption that the geomagnetic field was produced
by a permanent magnet could no longer be sustained. In 1908, Hale used the Zeeman effect
to measure magnetic fields in sunspots and
showed that these fields corresponded to an
azimuthal (or toroidal) field that was antisymmetric about the solar equator. Moreover,
the incidence of sunspots varies cyclically with
an average period of 11 years, as indicated by
the butterfly diagram in figure 4, and the fields
June 2002 Vol 43
3: The magnetic field of the spiral galaxy M51.
Total radio emission and magnetic field vectors of
polarized emission at 6 cm from the VLA combined
with extended emission observed with the
Effelsberg 100 m telescope (Beck 2000).
(Copyright: MPIfR Bonn, R Beck, C Horellou and
N Neininger.)
>0%
90N
>0.1%
>1%
30N
EQ
30S
90S
1880
1900
1920
1940
datex
1960
1980
2000
4: Cyclic activity on the Sun. Butterfly diagram showing the incidence of sunspots as a function of
latitude and time since 1875. Spots appear at latitudes of ±30° at sunspot minimum and spread
towards the equator by sunspot maximum. Then they dwindle away until the next cycle starts. The
toroidal field that emerges in active regions has opposite directions in each hemisphere and reverses
its direction after each cycle. (Courtesy of D H Hathaway, NASA/MSFC.)
3.9
Presidential Address
5: Meridian slices showing
axisymmetric components in an
azimuthally truncated
geodynamo model. The two
semicircles represent the
boundaries of the inner and
outer core. The top left panels
show the toroidal field and the
(Stokes) flux function, which is
constant along poloidal field
lines. The lower panels show
the angular velocity and the
stream function for the poloidal
flow. The top right panel shows
the density variations that drive
the flow, which are
concentrated on the inner core
boundary. (From Jones 2000.)
0
A r sinθ
–17.64
C
8984
.1098
0
ψ r sinθ
17.11
0
0
–8984
–17.11
(b)
(c)
6: Numerical modelling of the geodynamo. Comparisons
between the radial components of the magnetic field at the
surface (left) and at the core–mantle boundary (right) for
the geomagnetic field in 1980 (top) and the dynamo model
of Glatzmaier and Roberts, all smoothed to exclude
spherical harmonic components with degree greater than
12. (After Glatzmaier and Roberts 1995.)
(d)
CMB
surface
(a)
.2196
–.2123
v/r sinθ
reverse direction after each activity cycle, so
that the magnetic cycle has a 22-year period.
How can these fields be maintained?
Faraday had shown in 1831 that electric currents could be driven by the inductive effect of
a disk rotating in the field of a permanent magnet, and Werner Siemens produced the selfexcited dynamo in 1866. These devices rely on
circuits to guide the currents and it was by no
means obvious that electromagnetic induction
could generate currents by flow across magnetic field lines in a homogeneous fluid and so
maintain the field (see box “Can homogeneous
dynamos exist?” below). Now we know that
any motion that is sufficiently complex can act
as a self-exciting dynamo: for instance, turbulent convection can maintain a disordered
small-scale field (Cattaneo and Hughes 2001).
However, as Cowling insisted, “order does not
arise spontaneously out of chaos”. To generate
a large-scale field we rely on the order that is
introduced by rotation.
3.10
.2123
0
8: Development of instabilities driven by
magnetic buoyancy in an adiabatically stratified
compressible layer: isosurfaces of |B| in the
nonlinear regime. The figure is stretched
vertically to make the structure clear. (After
Matthews et al. 1995.)
mean
7: A simulated
reversal of the
geomagnetic field.
A sequence of
images showing
the surface field,
the field at the
core–mantle
boundary and the
azimuthally
averaged poloidal
and toroidal fields
at four successive
stages during a
reversal. (After
Glatzmaier and
Roberts 1995.)
B
17.64
In what follows, I shall provide a selective
review of the current state of dynamo theory,
biased inevitably towards my own particular
interests. I shall start by discussing the magnetic fields of the Earth and planets, then go on to
magnetism in the Sun and stars and finally conclude with fields in galaxies and accretion
disks. The status of theoretical models differs
in each case.
The geodynamo
The Earth’s electrically conducting core, of
radius R, is surrounded by the insulating mantle. At the centre of the liquid outer core is a
solid inner core and convection is driven primarily by the solidification process, rather
than by thermal buoyancy. The timescale for
ohmic decay of the magnetic field in the core is
given by τη = R2/η ≈ 7000 yr, where η is the
magnetic diffusivity. The field has, however,
been present for at least 3.5 Gyr, so a dynamo
must be there. We know from magnetohydro-
dynamics that, in a highly conducting fluid,
magnetic field lines are “frozen” into the fluid.
In the presence of differential rotation, field
lines in meridional planes are stretched out
azimuthally to give strong toroidal fields. This
process (the ω-effect) can, for instance, create
an antisymmetric toroidal field from an
axisymmetric dipole field if there is an equatorial acceleration. It is more difficult to generate
a poloidal field from the toroidal field, thereby
closing the circle. This step relies on the Coriolis force, which acts on rising plumes to produce systematic cyclonic (or gyrotropic)
motion, thereby twisting azimuthal field lines
so as to yield a poloidal component of the field
(the α-effect).
The whole process, including the backreaction of the Lorentz force on the motion, is
described by nonlinear partial differential
equations and is intrinsically three-dimensional. Direct numerical solution has now become
feasible for idealized models. Figure 5 shows
June 2002 Vol 43
Presidential Address
Can homogeneous
dynamos exist?
Dynamo theory began with a brief paper by
Larmor (1919), entitled “How could a rotating body such as the Sun become a magnet?”, in which he suggested that “it is possible for the internal cyclic motion to act
after the manner of the cycle of a self-exciting dynamo, and maintain a permanent
magnetic field from insignificant beginnings,
at the expense of some of the energy of the
internal circulation”. This proposal ran into
difficulties when Cowling (1933) showed
that an axisymmetric field could not be
maintained – and went on, rather characteristically, to say that “the theory proposed by
Sir Joseph Larmor, that the magnetic field of
a sunspot is maintained by the currents it
the results of such a calculation, with equatorial symmetry imposed (Jones 2000). It is immediately apparent that the role of the solid inner
core is extremely important. Rapid rotation
tends to constrain motion to be constant on
cylinders (through the Taylor-Proudman Theorem). As a result, the structures of the angular
velocity and the toroidal field are heavily influenced by the tangent cylinder that encloses the
inner core. Furthermore, the magnetic field is
stabilized by the “magnetic inertia” of the solid
inner core, where timescales are controlled by
diffusion.
More elaborate simulations (Glatzmaier and
Roberts 1995), requiring massively parallel
computers, have finally succeeded in reproducing many qualitative features of the geomagnetic field, as can be seen in figure 6, where the
measured field at the Earth’s surface and the
extrapolated field at the core–mantle boundary
are compared with corresponding fields in a
computation. The Earth’s magnetic field is naturally time-dependent and the dipole moment
does not even maintain a constant direction.
There are excursions (short-lived flips in sign)
and longer-term reversals. These features are
also reproduced in the numerical calculations,
as illustrated in figure 7. Such behaviour is
found to depend critically on the thermal
boundary conditions at the core–mantle
boundary (Glatzmaier et al. 1999). The palaeomagnetic record shows that the frequency of
reversals has varied over geological time. For
the last 10 Myr, the average interval between
reversals has been around 200 000 yr, but prior
to that reversals were less frequent; during the
Cretaceous “superchron”, between 83 Myr
and 118 Myr BP, there were no reversals at all.
This long-term modulation is probably due to
the effects of convection in the lower mantle on
the temperature at the core–mantle boundary.
June 2002 Vol 43
induces in moving matter, is examined and
shown to be faulty: the same result also
applies for the similar theory of the maintenance of the general field of Earth and Sun”.
As a glance at Larmor’s portrait would
lead one to expect, the old man was not
pleased and he responded indignantly: “The
view that I advanced briefly and tentatively
long ago, which has come to be referred to
as, perhaps too precisely, the self-exciting
dynamo analogy, is still, so far as I know,
the only foundation on which a gaseous
body such as the Sun could possess a magnetic field: so that if it is demolished there
could be no explanation of the Sun’s magnetism even remotely in sight,” (Larmor
1934). Others were less optimistic. When
the problem was explained to Einstein, he
commented that if such simple solutions
The relatively stable behaviour of the geomagnetic field over the past few hundred million
years, with a timescale for reversals that is
much longer than the resistive time τη , may be
due to the presence of the solid inner core.
Recent studies of the Earth’s thermal history
indicate, however, that the inner core is only
1–2 Gyr old. The magnetic field was there
much earlier but its behaviour may have been
quite different, though whether it was less or
more erratic is still controversial (Roberts and
Glatzmaier 2001).
Planetary dynamos
The geodynamo serves as a model for other
planets and their satellites (Jones 2002). A necessary ingredient for the generation of magnetic fields is the presence of an electrically conducting fluid core. The terrestrial planets have
metallic cores. Mercury exhibits a weak
dynamo-produced field, associated with the
presence of a vestigial liquid core, in the form
of a thin shell surrounding a solid inner core.
Venus remains somewhat mysterious and has
no current dynamo. The cores of the Moon
and Mars have solidified completely and their
remanent magnetism is a product of dynamos
that are now extinct. Among the satellites of
Jupiter and Saturn, only Ganymede and perhaps Titan have active dynamos.
The giant planets do not possess cores that
are composed predominantly of iron. Instead,
Jupiter and Saturn have cores with a liquid
metallic phase of hydrogen. Their rapid rotation leads to dynamo action and the production of comparatively strong magnetic fields.
Jupiter’s dipole axis, like that of the Earth, is
inclined at about 10° to its rotation axis, while
Saturn’s dipole field is almost perfectly aligned
with its rotation axis. The fields of Uranus and
Neptune, on the other hand, are strongly
were impossible, self-excited dynamos could
not exist. It turned out that Larmor was
right and Einstein was wrong, but it was not
until 1958 that the existence of self-exciting
homogeneous dynamos was proved by
Backus and Herzenberg.
Meanwhile, Cowling had been converted
as a result of an ambitious numerical treatment of the linear (kinematic) problem by
Bullard and Gellman (1954); later it
emerged that their procedure was not sufficiently accurate and it took another 20
years before dynamo action was firmly
established. So, in this instance, the Lord
God was not only subtle but also malicious!
Indeed, the controversy demonstrates how
dynamo theory raises deep mathematical
issues, which have made it a fascinating subject in its own right.
inclined to their rotation axes. The latter planets have ionic conductors in their cores and
their magnetic properties are not yet properly
understood.
The solar dynamo
Solar activity varies aperiodically with a welldefined mean period of 11 years, as shown in
figure 4. The toroidal field reverses at sunspot
minimum, while the poloidal field (which manifests itself in figure 1) reverses around sunspot
maximum. The ohmic timescale τη ≈ 1010 yr
and is far greater than the 22-year period of the
magnetic cycle. Since both fields reverse, we
need to seek an oscillatory dynamo (Weiss and
Tobias 2000) and several physical processes
are involved (Weiss 1994, Mestel 1999, Tobias
2002).
Once again, differential rotation is a key
ingredient: the pattern of rotation in the solar
interior has been revealed by helioseismology
(Schou et al. 1998). In the convection zone,
which occupies the outer 30% by radius, the
angular velocity is, to a good approximation, a
function of latitude only, while the radiative
interior rotates more or less uniformly. The
interface between these two regions is a thin
layer – the tachocline – with a strong radial
shear. It is generally accepted that the solar
dynamo is located in this region, where the
ω-effect leads to the generation of strong
toroidal fields.
Magnetic buoyancy drives instabilities at this
interface, which lead to buckling and twisting
of toroidal flux tubes, as depicted in figure 8
(Matthews, Hughes and Proctor 1995). Parts of
some flux tubes rise, eventually forming
Ω-shaped loops which intersect the surface to
produce active regions and sunspots; other flux
tubes will be twisted by Coriolis forces. They
can then be pumped downwards into the
3.11
Presidential Address
9: Downward pumping of magnetic flux by
turbulent compressible convection.
Results of a numerical experiment with an
unstably stratified layer superimposed on
one that is stably stratified. The magnetic
field was initially horizontal and confined
to a thin sheet near the top of the box.
The figures are stretched vertically to
make their structure clear. Panel (a)
shows the vertical velocity w (red
upwards, blue downwards). The vigorous
descending plumes penetrate into the
stable layer, as shown by the enstrophy
(the square of the vorticity) in panel (b).
Panel (c), which shows the magnetic
energy |B|2, demonstrates how the
magnetic field is pumped into the stably
stratified region. Panel (d), which shows
both enstrophy and magnetic energy,
confirms that the pumping is dominated
by the effects of rapidly descending
plumes. (From Tobias et al. 2001.)
(a) w
(b) ω2
(c) B 2
(d) ω2, B 2
(b)
x
(a)
t
(d)
x
(c)
t
t
t
10: Butterfly diagrams showing symmetries and symmetry-breaking for mean field dynamo models in
simplified cartesian geometry. Periodic cycles with (a) dipole symmetry and (b) quadrupole symmetry.
(c) A mixed-mode solution. (d) A modulated solution in which the solution flips from dipole to
quadrupole symmetry after a grand minimum. (After Knobloch et al. 1998.)
3.12
tachocline by turbulent compressible convection, an effect that is illustrated in figure 9
(Tobias et al. 2001). These processes, combined
perhaps with small-scale cyclonic convection,
provide the α-effect that generates a reversed
poloidal field – and so the cycle continues.
So far, almost all models of the solar dynamo
have relied on mean field electrodynamics. In
this approximation, the effect of small-scale
cyclonic turbulence is parametrized, so that the
problem is reduced to solving the coupled nonlinear partial differential equations
∂B/∂t = × [(U + u) × B] + × (αB) + η2B
and
ρ[∂u/∂t + (u ⋅)u] = –p + µ0–1 × B × B + G + Fvisc
for the magnetic field B and the velocity u,
where U is the imposed pattern of differential
rotation and meridional circulation and the spatial distribution of α is assumed. Here ρ is the
density, p the pressure, η the magnetic diffusivity, G the driving force (e.g. thermal buoyancy)
and Fvisc the viscous drag. Growth of the magnetic field is limited either by quenching the αeffect or by the action of the nonlinear Lorentz
force on the velocity. This procedure captures
the essential physics and it can be formally justified – though not for the conditions that prevail
in stellar interiors. With suitably chosen distributions of angular velocity and of α, these equations yield cyclic behaviour and produce butterfly diagrams that match the observations. To
that extent, we understand the solar dynamo.
The aperiodic cyclic activity in figure 4 is
modulated on a longer timescale. It is wellknown that sunspots virtually disappeared during the Maunder minimum, from 1645 to 1715.
Although this is the only such event that has
been directly observed, there is proxy evidence
from the abundances of cosmogenic elements
which confirms that similar grand minima have
recurred over at least the last 50 000 years.
Galactic cosmic rays impinging on the Earth’s
atmosphere lead to the production of 14C and
12
Be, which are preserved in trees and in polar
icecaps, respectively. Since cosmic rays are
deflected by magnetic fields in the solar wind,
the production rates of these unstable isotopes
are anticorrelated with solar activity. The abundances vary aperiodically but power spectra
show a clear peak corresponding to a period of
about 200 years (Wagner et al. 2000).
Such behaviour is characteristic of chaotic
oscillators. In nonlinear dynamo models the
macrodynamic effect of the Lorentz force on
differential rotation (which is seen at the solar
surface) is a key ingredient and this process has
been studied in some detail for idealized configurations. Figure 10 shows several butterfly diagrams for different choices of parameters
(Knobloch et al. 1998). The eigenfunctions of
the linear problem yield toroidal fields that are
either antisymmetric (dipole symmetry, as in
figure 10a) or symmetric (quadrupole symmeJune 2002 Vol 43
Presidential Address
time
11: Grand minima in a nonlinear dynamo
model. Note the temporary loss of symmetry
leading to “hemispheric” behaviour at the end
of the grand minimum. (After Beer et al. 1998.)
try, as in figure 10b) about the equator. Mixed
mode solutions (figure 10c) may also appear in
the nonlinear regime. Further bifurcations lead
to periodically modulated cycles and eventually
to chaotic modulation (Tobias 1996, 1997). Figure 11 shows such a modulated solution (Beer et
al. 1998). Although the active cycles maintain
dipole symmetry, this symmetry is broken as the
system emerges from a grand minimum, when
activity is concentrated in one hemisphere: this
is exactly what happened between 1680 and
1714, at the end of the Maunder minimum
(Ribes and Nesme-Ribes 1993).
Even more interesting is the behaviour shown
in figure 10d. Here the active cycles enter the
grand minimum with dipole symmetry but
emerge from it with quadrupole symmetry.
Although the solar magnetic field has maintained near-perfect dipole symmetry since 1715,
its symmetry may have flipped in the past. Furthermore, the symmetry may well have been
different at earlier stages in the Sun’s evolution,
and may change again in the future. Similarly,
there is no reason to suppose that the fields in
other stars must also exhibit dipole symmetry.
Mean field dynamos have been successful
despite their obvious limitations, but now we
need to ask where solar dynamo theory should
be going next. The subject will soon be ripe for
massive computation, whose power has been
demonstrated for the geodynamo. At the
moment, however, this would be premature.
First of all we have to understand the hydrodynamics of the convection zone and to
explain how the observed pattern of differential rotation is generated, together with the origin of the tachocline (Miesch 2000). Only then
will it be possible to model the full magnetohydrodynamic problem. Meanwhile, it is possible to go to the other extreme and to investigate nonlinear behaviour by studying minimal
systems (see box “Low-order models”) rather
than by massive computation.
There is an extreme alternative to massive
computation. Instead of solving the partial
differential equations, one constructs a loworder system of coupled ordinary differential
equations that captures the essential features
of the nonlinear problem. The aim here is to
seek generic behaviour which is robust,
though lacking any detailed predictive power.
The development of chaotic modulation in
stellar dynamos is encapsulated in the behaviour of a canonical third-order system, as
shown schematically in figure 12 (Tobias,
Weiss and Kirk 1995). As the appropriate
parameter (which depends on the star’s rotation rate) is varied there is a transition first to
cyclic dynamo action (with an attracting limit
cycle in the phase space of the system), then
to periodically modulated cycles (with an
attracting two-torus in the phase space, as
illustrated in figure 13a) and finally to chaotically modulated activity (with the chaotic
attractor shown in figure 13b). The last state
corresponds to what we see in the Sun. The
same bifurcation structure is found in nonlinear mean field dynamo models (Tobias 1996).
This approach can, moreover, be extended to
deal with symmetry changes like those in figures 10d and 11 (Knobloch et al. 1998).
chaos
latitude
Low-order models
H1
Ω
H2
12: Schematic diagram showing the transition from
periodic cycles to periodically modulated
(quasiperiodic) and then to chaotically modulated
behaviour in a nonlinear stellar dynamo. Dynamo
activity depends on the angular velocity Ω of the
star: as Ω increases there is an oscillatory (Hopf)
bifurcation H1 from the field-free state, leading to
periodic cycles that correspond to a limit cycle in
the phase space of the system. The second Hopf
bifurcation H2 leads to periodically modulated
cycles, with trajectories that lie on a two-torus in
phase space. This torus is followed by a chaotic
attractor. (After Tobias et al. 1995.)
(a)
(b)
Stellar dynamos
Magnetic fields appear in many other stars.
The early-type “magnetic stars” have only a
very shallow convective shell and are presumably oblique rotators, but provided a star
rotates sufficiently rapidly and possesses a subJune 2002 Vol 43
13: Attractors in the three-dimensional phase space of a canonical low-order model.
(a) Trajectory attracted to a two-torus, corresponding to periodically modulated cyclic behaviour.
(b) Trajectory on a chaotic attractor, corresponding to aperiodic modulation. (After Tobias et al. 1995.)
3.13
Presidential Address
stantial outer convection zone, a large-scale
dynamo will be present (Mestel 1999, Rosner
2000). Stars of type G, K and M with deep
convective zones can have interface dynamos,
like the Sun, but late M stars, which are fully
convective, are still magnetically active. If the
magnetic field is sufficiently strong it can be
measured by the Zeeman effect; otherwise
magnetic activity is detected indirectly, through
coronal X-ray emission, photometric variation
or from Ca II H and K emission, which is correlated with magnetic fields in the Sun. These
observations confirm that magnetic activity
increases the more rapidly a star rotates; that
the angular velocity of a star decreases with
age (owing to magnetic braking); and that
cyclic activity, interspersed with grand minima,
is characteristic of slow rotators like the Sun.
The youngest and most rapidly rotating stars
are much more active. Doppler imaging makes
it possible to map their surfaces and, like
AB Doradus in figure 14, they tend to have
large spots near their poles.
It is dangerous to extrapolate from the Sun in
order to model dynamos in such active stars.
Owing to their rapid rotation, the Taylor-Proudman constraint is much more important (as it is
in the Earth’s core). That almost certainly leads
to a different pattern of differential rotation,
which makes an interface dynamo less likely. As
yet, there is no adequate explanation for polar
spots and new theories are badly needed.
Galaxies and accretion disks
The first issue here is to determine whether a
dynamo is necessary. It is important to distinguish dynamo action from amplification of a
primordial field by turbulence or differential
rotation (Cattaneo, Hughes and Weiss 1991).
Only a dynamo is able to maintain a magnetic
field for timescales much longer than that for
ohmic decay – though it is not always feasible
to pursue a numerical calculation for that long.
The interstellar gas in galaxies rotates differentially and is subjected to turbulent motion, driven mainly by exploding supernovae and OB
associations, but whether turbulence in such a
viscously dominated medium can sustain a
large-scale field is still unclear (Kinney et al.
2000). The evidence for such an inverse cascade is fairly strong (Beck et al. 1996, Beck
2000). A primordial field might be expected to
have dipolar symmetry, whereas a dynamogenerated field would have quadrupolar symmetry, with the azimuthal and radial components of B symmetrical about the mid-plane.
The latest evidence suggests that the local
toroidal field in the Milky Way is indeed symmetrical, though it changes sign with radius,
while there is also a unidirectional magnetic
field in M31, as shown in figure 15. Mean field
dynamo models do give plausible results for
thin disks embedded in halos, though many
3.14
14: Reconstruction of starspots on the active star
AB Doradus, derived from Doppler imaging,
together with its coronal structure. (Courtesy of A
Collier Cameron.)
15: The toroidal magnetic field in the galaxy M31.
B vectors of polarized radio emission at 6 cm
wavelength and rotation measures between 6 cm
and 11 cm, obtained from the Effelsberg 100 m
telescope (Beck 2000). (Copyright: MPIfR Bonn, R
Beck, E M Berkhuijsen and P Hoernes.)
questions still remain (Kulsrud 1999).
Accretion disks raise an intriguing problem
(Brandenburg 2000). Accretion requires
enhanced diffusion, which is attributed to turbulence – but Keplerian disks are hydrodynamically stable. Magnetic fields can mediate
magneto-rotational instabilities – but a nonmagnetic disk is also stable to magnetic perturbations. Numerical calculations show, however,
that a finite magnetic field can cause instabilities
that develop into turbulent motion which is then
able to act as a dynamo and to sustain the field
itself (Brandenburg et al. 1995, Hawley et al.
1996a). This boot-strapping process is fascinating but bizarre: it depends on a nonlinear instability that requires further detailed investigation.
accretion disks raise issues that have still to be
explored. Although dynamo theory has been
around now for more than 80 years, there is
still plenty of scope for future research. ●
The current state of play
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Dynamos of one sort or another are required to
generate magnetic fields on all scales from planets like the Earth through stars like our Sun to
accretion disks around black holes in active
galactic nuclei. Up to a point, the associated
theory is convincing but it is intrinsically nonlinear. The mathematical and physical details
still raise formidable problems – with the result
that dynamo theory is still very much alive.
So far as the geodynamo is concerned, the
large-scale numerical models are convincing.
To be sure, they are still far from reproducing
the actual values of key parameters in the
Earth’s core, but there is no reason to doubt
that the models are becoming increasingly precise as they are gradually refined. The behaviour of the solar dynamo can only be explained
in terms of its bifurcation structure, which has
to be interpreted by reference to other stars.
The physics of these stellar dynamos is largely
understood but most models still rely on mean
field electrodynamics. This is a well-established
and thriving approach but one whose justification in an astrophysical context remains shaky.
What is needed now is a different attack,
through massive computations that will finally
clarify the interactions between convection,
rotation and magnetic fields in some detail.
When we come to galaxies, the models are still
primitive and the physics is less clear, while
Nigel Weiss, DAMTP, University of Cambridge.
Acknowledgments: I remain grateful both to Sir
Edward Bullard, who introduced me to the geodynamo, and to Leon Mestel, who diverted me into
astrophysics. Since then, I have learnt a lot from
my elders, Raymond Hide, Eugene Parker and Paul
Roberts, and from my colleagues Christopher
Jones, Keith Moffatt and Michael Proctor, as well
as from Paul Bushby, Fausto Cattaneo, David
Hughes, Gordon Ogilvie and Steven Tobias, whom
I first knew as students.
June 2002 Vol 43