Download Planetary magnetic fields: Observations and models

Physics of the Earth and Planetary Interiors 187 (2011) 92–108
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Physics of the Earth and Planetary Interiors
journal homepage: www.elsevier.com/locate/pepi
Planetary magnetic fields: Observations and models
G. Schubert ⇑, K.M. Soderlund
Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095, USA
a r t i c l e
i n f o
Article history:
Available online 12 June 2011
Edited by Keke Zhang
Keywords:
Planetary magnetic fields
Planetary cores
Spacecraft observations
Numerical dynamo models
a b s t r a c t
The state of knowledge and understanding of planetary magnetic fields is reviewed. All of the planets,
with the possible exception of Venus, have had active dynamos at some time in their evolution. The properties and characteristics of the dynamos are as diverse as the planets themselves. Even within the subclasses of terrestrial and giant planets, the contrasting compositions, sizes, and internal pressures and
temperatures of the planets result in strikingly different dynamos. As an example, the dynamos in Mercury and Ganymede are likely driven by compositional buoyancy distributions different from that in the
Earth’s core. Dynamo models operate far from the parameter regimes appropriate to the real planets, yet
provide insight into the dynamics of their interiors. While Boussinesq models are generally adequate for
simulating terrestrial planet dynamos, anelastic models that also account for large density and electrical
conductivity variations are needed to simulate the dynamos in giant planets. Future spacecraft missions
to planets with active dynamos are needed to learn about the character and temporal variability of the
planetary magnetic fields.
Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
With the possible exception of Venus, all planets in the solar
system have or once had internally generated magnetic fields.
The Moon also had its own magnetic field in the past, and Jupiter’s satellite Ganymede has a magnetic field at present. Undoubtedly, other bodies in the solar system have generated magnetic
fields in the past, e.g., the angrite meteorite parent body (Weiss
et al., 2008) and possibly some outer solar system objects other
than Ganymede have a magnetic field at present. It is expected
that many of the extrasolar planets now being detected have
magnetic fields and some observations support this conjecture
(e.g., Sanchez-Lavega, 2004; Shkolnik et al., 2005, 2008).
While many planets, satellites, and small bodies generate magnetic fields by dynamo action in their interiors, not all objects with
the requisite electrically conducting fluid layers have a dynamo.
Prominent among such bodies in our own solar system are Venus
and Io, which are likely to have completely or at least partially
molten metallic cores (e.g., Konopliv and Yoder, 1996; McEwen
et al., 1989; Khurana et al., 2011). The cores in Mars and the Moon
are also likely partially molten at present (e.g., Yoder et al., 2003;
Khan et al., 2004), yet the dynamos that once existed in these
bodies have ceased to function.
A planetary magnetic field, or the absence of such a field, informs us about the internal structure of a body and its thermal evo⇑ Corresponding author. Tel.: +1 310 825 4577; fax: +1 310 825 2779.
E-mail addresses: [email protected] (G. Schubert), [email protected] (K.M.
Soderlund).
0031-9201/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.pepi.2011.05.013
lution. Together with the gravitational field, the magnetic field
provides a window into the interiors of bodies that we can only
probe from a distance. The magnetic fields recorded and preserved
in the crusts of planets and satellites also provide a window into
the histories of the bodies.
Planetary magnetism therefore merits study from many perspectives, including that of understanding the physics of how
dynamos work and what they imply about the past and present
properties of the body containing the dynamo. In this paper we review what is known about magnetic fields in the solar system,
what attempts have been made to simulate the working dynamos,
and what we learn about the host bodies from their magnetic
fields.
2. Survey of planetary magnetism
The planets in our solar system can be classified into three types
– terrestrial, gas giant, or ice giant – based on their physical properties, and the magnetic fields show a large diversity in structure and
strength. Table 1 summarizes the physical properties and magnetic
field characteristics of the planets and select satellites. The mean
density and moment of inertia (MOI) of a planet provide constraints
on the internal composition and structure. All of the planets and
many of the satellites show evidence of differentiation into layers.
The terrestrial planets have an outer rocky crust, an intermediate
silicate mantle, and a central iron-alloy core (e.g., Riner et al.,
2008; Zharkov, 1983; Dziewonski and Anderson, 1981; Longhi
et al., 1992). The gas giants, Jupiter and Saturn, have outer molecular envelopes of hydrogen and helium, fluid mantles that are largely
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G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
Table 1
Summary of physical properties and magnetic field characteristics. Overbars indicate mean values. Physical property data taken from 1Lodders and Fegley (1998), 2de Pater and
Lissauer (2001), 3Schubert et al. (2007) for the MOI of the Galilean satellites, and 4Iess et al. (2010) for the MOI of Titan. Magnetic field characteristics are calculated using Eqs. (2)–
(4) and data in Uno et al. (2009) for Mercury, IAGA Division V-MOD geomagnetic field modeling website for Earth, Yu et al. (2010) for Jupiter, Kivelson et al. (2002) for Ganymede,
Burton et al. (2009) for Saturn, and Holme and Bloxham (1996) for the ice giants. MOI is normalized with respect to the product of the mass and the square of the radius of the body.
Planet
Mercury
Venus
Earth
Moon
Mars
Jupiter
Io
Europa
Ganymede
Callisto
Saturn
Titan
Uranus
Neptune
Mass1
Radius1
(km)
Density1
(kg/m3)
MOI24
(1024 kg)
0.33
4.87
5.97
0.07
0.64
1900
0.09
0.05
0.15
0.11
570
0.13
87
100
2440
6052
6371
1738
3390
69,911
1821
1565
2634
2403
58,232
2575
25,362
24,624
5.4
5.2
5.5
3.3
3.9
1.3
3.5
3.0
1.9
1.9
0.7
1.9
1.3
1.6
0.33
0.33
0.33
0.39
0.37
0.25
0.38
0.35
0.31
0.35
0.21
0.34
0.23
0.23
composed of metallic hydrogen and helium, and perhaps central
rocky cores (Guillot, 1999a). The ice giants, Uranus and Neptune,
have outer molecular envelopes of hydrogen, helium, and ices,
intermediate ionic oceans of water, methane, and ammonia, and
possibly central rocky cores (Guillot, 1999a). However, the layer
thicknesses are not well-constrained for planets other than the
Earth. Outer solar system satellites exhibit a wide variety of sizes,
from tens of kilometers to larger than the planet Mercury, and have
mean densities that are icy to rocky. Ganymede is the largest satellite in the solar system and also has the lowest moment of inertia of
all known planetary bodies (Schubert et al., 2007). This indicates
that the satellite is fully differentiated, with a thick water-ice shell
overlying an intermediate rocky mantle and a central metallic core
(Schubert et al., 2007). Thus, Ganymede has a terrestrial-style internal structure beneath the ice shell.
Magnetic fields originate in the electrically conducting fluid regions of planets and satellites and are likely driven by dynamo action (e.g., Elsasser, 1939; Bullard, 1949; Stevenson, 2003). These
regions are expected to be unstable to thermochemical convection
in order to remove the heat of formation and radioactive decay
(Stevenson, 2010). Convection of an electrically conducting fluid
drives electrical currents and generates a magnetic field; the process whereby kinetic energy is converted into magnetic energy is
known as dynamo action. While convection is the most probable
dynamo driver, it has been argued that precession, libration, nutation, and tidal interactions may also promote dynamo action
(Malkus, 1994; Tilgner, 2007; Dwyer et al., 2010).
Intrinsic planetary magnetic fields diffuse as a potential field
through the overlying electrically insulating or less electrically
conducting regions. This field can be expressed as B = rU, where
the magnetic potential U can be decomposed into spherical
harmonics:
( lþ1
1 X
l
X
m
RP
Uðr; h; /Þ ¼ RP
g l cosðm/Þ
r
l¼1 m¼0
m
þhl sinðm/Þ Pm
ðcoshÞ
l
ð1Þ
where r is radius, h is colatitude, / is longitude, RP is the planet radius, l is spherical harmonic degree, m is spherical harmonic order,
Pm
l are associated Legendre polynomials with partial Schmidt normalization (see Appendix B of Merrill et al. (1996)), and g m
l and
m
hl are the gauss coefficients. The gauss coefficients are used to describe planetary magnetic fields. The radial magnetic field for a given radius r is obtained through
Br ðrÞ ¼ rU ^r ¼
Surface jBr j
(lT)
Dipolarity
0.30
–
38
[100
[0.1
550
–
–
0.91
–
28
–
32
27
0.71
–
0.61
–
–
0.61
–
–
0.95
–
0.85
–
0.42
0.31
lmax X
l
X
(
ðl þ 1Þ
l¼1 m¼0
m
þhl sinðm/Þ Pm
l ðcoshÞ
Dipole
tilt (°)
3
–
10
–
–
9
–
–
4
–
<0.5
–
59
45
lþ2
m
RP
g l cosðm/Þ
r
ð2Þ
where lmax is the maximum harmonic degree of the observations.
The two radial levels most frequently considered are the planet surface, r = RP, and the top of the dynamo-generating region, r = RD. The
strength of the dipole relative to the total field strength is the
dipolarity,
P1 m
m jg 1 j þ jh1 j
:
f ¼ Plmaxm¼0
Pl m
m m¼0 jg l j þ jhl j
l¼1
ð3Þ
Perfectly-dipolar magnetic fields have f = 1. The fields are considered to be dipole-dominated when f > 0.5. The tilt of the dipole relative to the rotation axis, hd, is given by
0
1
1 2 1 2 1=2
g
þ
h
B
C
1
1
B
C
hd ¼ tan1 B
C:
0
@
A
jg 1 j
ð4Þ
2.1. Active dynamos
2.1.1. Earth
Earth’s magnetic field is at least 3.5 billion years old as recorded
by crustal rocks that were magnetized as they cooled (Hale and
Dunlop, 1984). These paleomagnetic records indicate that the dynamo has almost always had a strong axial dipole component with
a field strength that has not significantly varied over time (Hulot
et al., 2010). The present field has a mean surface strength of about
40 lT and the dominant dipole component is offset 10° from the
rotation axis. However, episodic reversals in field polarity have
been recorded as magnetic stripes in oceanic crust over the past
hundred million years (Johnson et al., 2003). During the 10,000
years over which reversals occur, the total field strength decreases
and the field becomes multipolar (Bogue and Merrill, 1992).
Observatories and satellites have greatly improved our understanding of the Earth’s magnetic field and its evolution over short
timescales. The Magsat (1979–1980), Ørsted (1999–), CHAMP
(2000–2010), and SAC-C (2000–2004) satellites have provided continuous measurements of the field over a range of altitudes for
more than ten years. The SWARM satellite constellation will be
launched in 2011 to continue these efforts. Fig. 1 shows the radial
magnetic field at the surface and the core-mantle boundary plotted
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G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
up to spherical harmonic degree 13. Higher order harmonics of the
internal field are masked by crustal remnant magnetism. The dynamic nature of the geodynamo is revealed through secular variation, where changes in the strength and spatial structure of the
field occur over timescales of months (Olsen and Mandea, 2008)
to centuries (Bloxham et al., 1989) to millenia (Cande and Kent,
1995). The most notable aspects of secular variation are polarity
reversals, westward drift of the non-axisymmetric field, anticyclonic field motions at high latitudes, growth of the South Atlantic
anomaly where the field is unusually weak, and geomagnetic jerks
(Finlay et al., 2010). The physical mechanisms that lead to these
behaviors, however, are not yet understood.
2.1.2. Mercury
Mercury has the weakest intrinsic magnetic field in the solar
system with a mean surface strength of only about 0.3 lT. This
field was first measured during the Mariner 10 flybys in 1974
and 1975 (Ness et al., 1975, 1976) and again during the MESSENGER flybys in 2008 and 2009 (Anderson et al., 2008, 2010; Uno
et al., 2009; McNutt et al., 2010; Solomon, 2011). These observations suggest that the field is dipole-dominated and nearly aligned
with the rotation axis. The surface radial magnetic field plotted up
to spherical harmonic degree three is shown in Fig. 2a. Compared
to the Earth, the field is about 100 times weaker at the surface
and about 500 times weaker at the core-mantle boundary, assuming Mercury’s core has a radius of 1900 km. It is not yet understood
why Mercury has such a weak magnetic field.
The source of the field is not agreed upon in the literature (e.g.,
Schubert et al., 1988; Stevenson, 2010), although dynamo action is
the general consensus because libration measurements by Margot
et al. (2007), gravity measurements of MESSENGER (Smith et al.,
2010), and thermodynamic phase equilibrium simulations of
Malavergne et al. (2010) support the presence of a liquid core. Other
possibilities include remnant magnetism (Aharonson et al., 2005) or
thermoelectric currents (Stevenson, 1987; Giampieri and Balogh,
2002). Further, MESSENGER found that the internal field interacts
with currents in the planet’s magnetosphere (McNutt et al., 2010),
but the dynamical implications of this coupling are not well constrained (Glassmeier et al., 2007; Kabin et al., 2008; Gomez-Perez
and Solomon, 2010; Gomez-Perez and Wicht, 2010).
2.1.3. Ganymede
The Galileo spacecraft revealed that the Jovian satellite Ganymede also has an intrinsic magnetic field (Kivelson et al., 1996).
As shown in Fig. 2b, these measurements suggest that the field is
nearly axially-aligned and dipole-dominated with a mean surface
strength of about 1 lT. However, it might also be appropriate to
consider the value of Ganymede’s magnetic field at the ice-rock
boundary since the body has a terrestrial-style internal structure
beneath the ice shell. Assuming an ice shell thickness of about
900 km (Schubert et al., 2007), the mean magnetic field is 3 lT at
the ice-rock boundary. This is about an order of magnitude larger
(smaller) than Mercury’s (Earth’s) surface field. The field resolution, however, is limited to the dipole and quadrupole components
and additional data are needed to further characterize the magnetic field. Since Ganymede is thought to have a metallic core with
a fluid component, the field is likely driven by dynamo action
(Schubert et al., 1996; Sarson et al., 1997; Kivelson et al., 2002).
The size of the core is poorly constrained, and the energy source
for maintaining a liquid or partially liquid core in such a small body
is not fully understood.
2.1.4. Jupiter
The magnetic field of Jupiter was discovered when Burke and
Franklin (1955) showed that the planet was a strong radio source.
This was the first detection of a planetary magnetic field besides
that of the Earth. The existence of the field was confirmed when
the planet was visited by the Pioneer 10 flyby in 1973 (Smith
et al., 1974). Additional measurements were obtained by the Pioneer 11 flyby in 1974 (Smith et al., 1975), the Voyager 1 and 2 flybys in 1979 (Ness et al., 1979), the Ulysses flybys in 1992 and 2004
(Balogh et al., 1992), the Galileo orbiter between 1995 and 2003
(e.g., Connerney, 1993; Yu et al., 2010), and the New Horizons flyby
in 2007 (e.g., McComas et al., 2007; McNutt et al., 2007). These
measurements show that the magnetic field is dominated by the
axial dipole component and is the strongest field in the solar system with a mean surface strength of 550 lT. The surface of gaseous
planets is taken to be the 1 bar pressure level. The surface radial
magnetic field including up to the octupole component is shown
in Fig. 2c. The spatial and temporal resolution of the field is a significant limitation. While Jupiter’s magnetic field has been
measured by several missions, the orbits do not extend inward of
1.6 Jupiter radii and have longitudinal data gaps (Russell and
Dougherty, 2010). Consequently, the observations are only resolved to spherical harmonic degree three. Jupiter has not exhibited unambiguous secular variations in field strength or dipole
tilt in the 20 years between the Pioneer and Galileo missions (Yu
et al., 2010).
(b) Earth CMB
(a) Earth surface
-80 µT
0
80 µT
-800 µT
0
800 µT
Fig. 1. Radial magnetic field of Earth at (a) the surface and (b) the core-mantle boundary (CMB). The colors represent field intensity where purple (green) indicates outward
(inward) directed field. A mollweide projection is used in which the horizontal lines indicate constant latitude. IGRF-11 coefficients are used and are available on the IAGA
Division V-MOD geomagnetic field modeling website.
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G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
The magnetic field is produced by convectively-driven dynamo
action in the highly electrically conducting metallic hydrogen
mantle and in the less electrically conducting region near the base
of the molecular envelope (Stanley and Glatzmaier, 2010). The exact location and extent of the dynamo region is poorly constrained.
Nellis (2000) argues that the dynamo can extend up to 95% of the
planet radius. Consequently, the dynamo region is expected to exhibit significant changes in density and electrical conductivity, the
effects of which are relatively unknown. The upcoming Juno mission will critically improve our understanding of Jupiter by resolving the magnetic field up to spherical harmonic degree 14,
detecting short timescale secular variation, and constraining the
planet’s internal structure (Connerney, private communication).
2.1.5. Saturn
Saturn was revealed to have a magnetic field during the Pioneer
11 flyby in 1979 (Smith et al., 1980), and subsequent observations
were made by Voyager 1 in 1980 (Ness et al., 1981) and Voyager 2
in 1981 (Ness et al., 1982). The Cassini spacecraft arrived at Saturn
in 2004 and is still collecting data (Dougherty et al., 2005; Burton
et al., 2009). These observations have mapped the large-scale radial
magnetic field, shown in Fig. 2d, and suggest that no resolved
(b) Ganymede
(a) Mercury
-0.6 µT
0
0.6 µT
-1.5 µT
(c) Jupiter
-1200 µT
0
0
1.5 µT
(d) Saturn
1200 µT
-60 µT
(e) Uranus
-100 µT
0
0
60 µT
(f) Neptune
100 µT
-100 µT
0
100 µT
Fig. 2. Radial magnetic field at the surfaces of (a) Mercury, (b) Ganymede, (c) Jupiter, (d) Saturn, (e) Uranus, and (f) Neptune. Data taken from Uno et al. (2009) for Mercury
(with spectral resolution l, m 6 3), Kivelson et al. (2002) for Ganymede (l, m 6 2), Yu et al. (2010) for Jupiter (l, m 6 3), Burton et al. (2009) for Saturn (l, m 6 3), and Holme and
Bloxham (1996) for the ice giants (l, m 6 3).
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G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
surface field strengths near 30 lT, comparable to that of the Earth
and Saturn. These multipolar magnetic fields were a surprise to
many scientists, and it is still not understood why these bodies
produce remarkably different fields from the other planets. The
fields are thought to be generated in the planets’ ionic oceans
(Cavazzoni et al., 1999; Lee et al., 2006). However, the internal
structures and dynamics of the ice giants are poorly constrained.
(a) Mars
60
Latitude
30
0
-30
2.2. Extinct dynamos: Mars and the Moon
-60
0
90
-200 nT
180
Longitude
270
0
0
200 nT
(b) Moon
60
Latitude
30
0
-30
-60
0
90
-10 nT
180
Longitude
0
270
0
10 nT
Fig. 3. Radial magnetic fields of (a) Mars and (b) the Moon. The colors represent
field intensity where red (blue) indicates outward (inward) directed field. A
Mercator projection is used, and circles indicate impact basins. Adapted from
Langlais et al. (2010).
secular variation has occurred (Burton et al., 2009). The spatial resolution is limited to spherical harmonic degree three. However,
this is due to uncertainty in the planet’s rotation rate (see Gurnett
et al. (2007) and Anderson and Schubert (2007)) rather than insufficient measurements (Burton et al., 2009). The field is strongly
dipole-dominated with a mean surface (1 bar) strength of about
30 lT and has a remarkably small offset of less than 1°. No other
observed magnetic field has such a small dipole tilt. According to
Cowling’s theorem, no axisymmetric magnetic field can be generated by dynamo action, so the field must have unresolved nonaxisymmetric components. It has also been proposed that a
secondary mechanism operating in the overlying regions may be
responsible for axisymmetrizing the field (e.g., Stevenson, 1980,
1982, 1983). The mechanisms that lead to a strongly axisymmetric
magnetic field, however, are not yet well-understood.
2.1.6. Uranus and Neptune
The magnetic fields of Uranus and Neptune were discovered by
the Voyager 2 flybys in 1986 and 1989, respectively (Ness et al.,
1986, 1989; Holme and Bloxham, 1996). The spacecraft passed
within 4.2 Uranian radii and 1.2 Neptunian radii, allowing their dipole, quadrupole, and octupole components to be mapped as
shown in Fig. 2e and f. The ice giants’ magnetic fields are fundamentally different from other known planetary fields since they
are multipolar, with f = 0.42 for Uranus and f = 0.31 for Neptune.
The dipole component is tilted about 59° and 47° from the rotation
axis for Uranus and Neptune, respectively. Both planets have mean
Mars Global Surveyor (MGS) showed that Mars does not presently have an active magnetic field, yet discovered magnetic anomalies associated with the magnetization of crustal rocks due to an
ancient dynamo (e.g., Ness et al., 1999; Acuña et al., 1998, 1999;
Connerney et al., 1999, 2001; Purucker et al., 2000; Langlais
et al., 2004; Mitchell et al., 2007; Lillis et al., 2004, 2008a). Similarly, the Moon does not presently have an active magnetic field,
but likely had one in the past. Crustal magnetization of lunar rocks
was first detected during the era of Apollo exploration (Coleman
et al., 1972), and has since been mapped in detail by Lunar Prospector in 1998 and 1999 (Binder, 1998; Purucker, 2008). The internal structures of these bodies are consistent with the inferred
dynamo mechanism since there is strong evidence that both objects have metallic cores. The exact radii and densities of the cores
are not well-known, but are constrained by the measured values of
the moment of inertia of both objects (e.g., Folkner et al., 1997;
Konopliv et al., 1998). The physical states of the cores are also largely unknown, although there is evidence that both cores are at
least partially molten (Yoder et al., 2003; Khan et al., 2004).
The crustal magnetic fields of Mars and the Moon are mapped in
Fig. 3. The Martian crustal field is essentially confined to the southern hemisphere of the planet and is further concentrated into a relatively small region of the southern highlands between about 120°
and 240° East longitude (Terra Cimmeria and Terra Sirenum).
Notably, many major impact basins lack magnetic signatures.
Intensities of local flux patches at spacecraft altitudes tend to be
one to two orders of magnitude larger than the Earth’s crustal magnetization of about 20 nT (Langlais et al., 2010). The lunar crustal
field is distributed unevenly across the surface with flux patches
that tend to be at least an order of magnitude weaker than those
of Mars (Langlais et al., 2010).
The timing of the onset and cessation of dynamo activity in
Mars and the Moon is debated. For Mars, it has been argued that
the dynamo was active in the early Noachian (first Martian geologic period) and ceased to operate prior to the formation of the
Hellas impact basin about four billion years ago (Acuña et al.,
1999; Acuña et al., 2001). However, Schubert et al. (2000) have
proposed that the onset of dynamo activity could have postdated
the formation of Hellas with continued operation into the Hesperian or Amazonian periods (see also Milbury and Schubert
(2010)). Still another possibility is that the Martian dynamo was
active for part of the Noachian prior to the Hellas impact and
was re-activated after the Hellas event (Lillis et al., 2005).
There are similar uncertainties for the lunar dynamo. Paleointensity data from Apollo samples imply that the dynamo was
long-lived and turned off about four Gyr ago (Garrick-Bethell
et al., 2009). This early dynamo scenario is supported by modeling
efforts. Stegman et al. (2003) propose that changes in mantle convection early in the Moon’s history enhanced core heat flux enough
to power a dynamo, although short-lived. In addition, Takahashi
and Tsunakawa (2009) argue that a heterogenous core-mantle
boundary heat flux due to hemispherically-asymmetric mantle
convection can also power an early lunar dynamo. Alternatively,
Dwyer et al. (2010) have suggested an early nutation-driven dynamo, while Russell et al. (1977) have proposed that the Moon’s
G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
dynamo turned on only when the body cooled sufficiently for a solid inner core to freeze out.
Why then did the dynamos in Mars and the Moon turn off? For
both bodies, one of two scenarios seems most likely. Either the
cores of these bodies cooled to the point where thermal convection
and dynamo action were no longer sustainable or they cooled to
the point of growing such large solid inner cores that dynamo action could no longer take place in the surviving liquid outer core.
2.3. No dynamos
2.3.1. Venus
Measurements by the Mariner spacecraft in the 1960s and Pioneer Venus Orbiter in 1978 showed that Venus does not have an
intrinsic magnetic field (Bridge et al., 1969; Russell et al., 1980;
Phillips and Russell, 1987). Why not? The planet likely has a molten metallic core similar in size to Earth’s core (Zhang and Zhang,
1995). Two plausible explanations have been discussed. One possibility is that Venus has not cooled sufficiently for an inner core to
have yet formed but enough that a purely thermally-driven dynamo cannot operate. This is consistent with Venus’ slightly smaller
size compared with Earth (Stevenson et al., 1983). It also attributes
a major role to compositional buoyancy release upon inner core
solidification in driving dynamo action. A second explanation is
that Venus has no plate tectonics and, therefore, is inefficient in
cooling its core (Nimmo and Stevenson, 2000). A small heat flow
out of Venus’ core could mean that the core is not convective, a
state without the possibility of dynamo action. Venus may have
had a dynamo in the past, perhaps if a sudden mantle overturn
resurfaced the planet and rapidly cooled the core as has been proposed for the Moon (Stegman et al., 2003). Venus’ high surface
temperature makes it unlikely (though not impossible) for crustal
magnetization to have preserved the signature of a past dynamo.
Absence of plate tectonics on Mercury and Ganymede, however,
has not inhibited these bodies from generating magnetic fields in
their cores.
2.3.2. Io
Io, a moon of Jupiter about the size of Earth’s Moon, does not
have a magnetic field (Jia et al., 2010). Yet it has a large metallic
core (Schubert et al., 2007). This is perhaps surprising in that its
close neighbor, Ganymede, has a magnetic field and a virtually
identical internal structure below its thick ice shell. What accounts
for the lack of dynamo activity in Io’s core? The answer appears to
be that the satellite is too hot. There is so much heat produced in
the mantle by tidal dissipation that it cannot cool its core. With
no core cooling, there is no core thermal convection and no dynamo activity (Wienbruch and Spohn, 1995; Khurana et al., 2011).
This is basically the same explanation as offered above for why Venus has no magnetic field, though the reason for inefficient cooling
of the core is different in the two cases.
2.3.3. Callisto and Titan
Callisto and Titan, satellites of Jupiter and Saturn, respectively,
might be expected to have magnetic fields based on their comparable sizes to Ganymede. However, they do not (Jia et al., 2010).
The lack of a magnetic field is easy to understand in the case of
these bodies because they are only partially differentiated, rock
from ice, and do not have metallic cores (Schubert et al., 2004; Iess
et al., 2010).
97
among the fields. Given the diverse spectrum, the fundamental
goal is to determine what controls the strength, morphology, and
evolution of the magnetic fields. Since dynamos are intimately
linked to convective fluid motions driven by thermal and compositional gradients, the coupling between magnetic fields, fluid flow,
and heat/mass transfer must also be understood.
Further, it is important to understand why some large terrestrial
bodies do not have, and may have not had, intrinsic magnetic fields.
This raises the question of whether a purely thermally-driven dynamo can exist or if compositional buoyancy accompanying inner
core freeze-out is needed. For example, Earth’s dynamo is at least
partially driven by compositional buoyancy associated with growth
of the solid inner core. Are the dynamos of Mercury or Ganymede
driven only by thermal gradients? Though this seems unlikely, we
will probably not be able to observationally confirm or deny the
existence of solid inner cores in these bodies for the foreseeable
future.
3. Fundamentals of dynamo theory
3.1. Basic equations
The governing equations of dynamo theory are the induction
equation, conservation of mass, conservation of momentum, conservation of energy, and the equation of state. The unknowns are
the magnetic field B, the velocity field u, and three thermodynamic
variables, e.g., pressure p, temperature T, and density q. There are
nine equations for these nine variables. The induction equation is
@B
¼ r ðu BÞ r ðgr BÞ
@t
ð5Þ
where g = 1/lor is the magnetic diffusivity, lo = 4p 107 H/m is
the permeability of free space, and r is the electrical conductivity.
The conservation of mass is
@q
þ r ðquÞ ¼ 0;
@t
ð6Þ
and the conservation of momentum is
q
Du
1
þ 2qX u ¼ rp qX ðX rÞ þ ðr BÞ B
Dt
lo
1
þ qg þ qmrðr uÞ þ qmr2 u;
3
ð7Þ
where X is the rotation rate of the reference frame, r is the position
vector, g is the acceleration of gravity, and m is the kinematic viscosity. In (7), terms from left to right are inertial acceleration, Coriolis
acceleration, pressure gradient, centrifugal force, Lorentz force,
buoyancy, and two viscous diffusion terms where the Stokes
assumption to neglect the bulk viscosity has been made. The conservation of energy equation is
DT
aT Dp U þ r ðkrTÞ
¼
;
Dt qC p Dt
qC p
ð8Þ
where a is the thermal expansivity, Cp is the specific heat at constant pressure, k is the thermal conductivity, and U is the dissipation function including both viscous and ohmic heating. The
second term on the left of (8) represents heating (cooling) due to
adiabatic compression (expansion). The equation of state relates
density to the temperature and/or pressure.
2.4. Comparative planetology
While there are outstanding questions about each planetary
magnetic field, it is also valuable to consider the comparative approach which attempts to explain the similarities and differences
3.1.1. Boussinesq approximation
In most geodynamo studies, Eqs. (5)–(8) are simplified using the
Boussinesq approximation. Here, the material properties are assumed to be constant and the density is treated as constant except
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G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
in the buoyancy force of the momentum equation. The induction
equation simplifies to
@B
¼ r ðu BÞ þ go r2 B;
@t
ð9Þ
the conservation of mass simplifies to
r u ¼ 0;
ð10Þ
and the conservation of momentum simplifies to
Du
1
þ 2X u ¼ rP þ
ðr BÞ B ao T 0 g þ mo r2 u:
Dt
lo q o
ð11Þ
The buoyancy force on the right side of (11) arises from density differences with respect to the density of the motionless background
state (usually assumed to be constant density qo). These perturbations, q0 , are produced by temperature variations, T0 , from the background state temperature profile. The equation of state is then given
by q = qo + q0 = qo(1 aT0 ), and the gravity term becomes
qg = qog qoaT0 g. The mean gravitational component is hydrostatic
and can be absorbed into the pressure gradient term. Since the centrifugal force can be written as the gradient of a potential, this term
is also incorporated into the pressure gradient. As a result, P represents the effective pressure relative to the hydrostatic pressure of a
motionless background state, i.e., P is associated with the velocity
field. The energy equation also simplifies in the Boussinesq approximation. Heating associated with adiabatic compression and due to
viscous and ohmic dissipation are assumed negligible (Hewitt et al.,
1975), and (8) becomes
DT
¼ jr2 T
Dt
been studied using the Boussinesq approximation with some success (e.g., Heimpel et al., 2005a; Stanley and Bloxham, 2006).
3.1.2. Anelastic approximation
The ratio of dynamo region thickness to density scale height is
not small in the outer planets; consequently, the Boussinesq
approximation is not valid. Instead, the anelastic approximation
should be adopted. This simplification involves replacing the continuity equation with
r ðquÞ ¼ 0;
ð13Þ
where q is the basic density state. Here and below, the overbar refers to the basic state which can vary with radius. Approximating
(6) by (13) essentially eliminates sound waves from the problem.
In this approximation, pressure variations from the basic state also
contribute to buoyancy in the momentum equation and adiabatic,
viscous, and ohmic heating must be accounted for in the energy
equation:
Du
1
þ 2X u ¼ rP þ
ðr BÞ B þ vp0 aT 0 g þ mr2 u; ð14Þ
Dt
lo q
DT a
U
ðu gÞT 0 ¼ jr2 T þ
:
ð15Þ
Dt C p
qC p
Here v is the isothermal compressibility and p0 is the pressure variation from the basic state. The induction equation is given by (5)
with g. For simplicity, a polytropic equation of state is often
adopted (e.g., Glatzmaier and Gilman, 1981; Clune et al., 1999;
Jones and Kuzanyan, 2009).
ð12Þ
where j is the thermal diffusivity.
The validity of the Boussinesq approximation requires that the
relative density perturbations produced by temperature and pressure variations be small compared with unity. The thermally induced relative density perturbations are proportional to aT0 ,
while the smallness of the pressure induced relative density perturbations requires that flow speeds be much less than the speed
of sound. These requirements are likely satisfied in planetary cores,
which are expected to be nearly-adiabatic with subsonic flows
(e.g., Smylie and Rochester, 1980; Guillot, 2005). In addition, this
approximation further requires that the thickness of the convecting region be small compared with the density scale height.
Schubert et al. (2001) give a more detailed analysis of the Boussinesq approximation and its applicability.
The Boussinesq approximation is likely reasonable for the cores
of the terrestrial planets and moons of the outer solar system, but
it is probably not adequate for the giant planets. In the Earth’s core,
the density increases by 23% across the fluid layer (Boehler, 1996),
and the layer thickness corresponds to 0.2 density scale heights.
The number of density scale heights in a layer is given by
Nq = ln(qbot/qtop), where qbot (qtop) is the density at the bottom
(top) of the region (e.g., Evonuk, 2008). Since the Earth is likely
more strongly stratified than the other terrestrial bodies, the Boussinesq approximation is also practical for the cores of terrestrial
planets and moons of the outer solar system. However, density increases rapidly with depth in the outer solar system planets. The
gas giant internal structure model of Guillot (1999b) predicts the
density to increase by a factor of about 100 between the 1 kbar
and 10 Mbar levels; this region then extends about 5 density scale
heights. The ice giant internal structure models of Hubbard et al.
(1995) predict their convecting regions to extend at least one density scale height. Because of the significant density stratification in
the outer solar system planets, it is likely necessary to adopt the
anelastic approximation for these bodies. However, we note that
deep convection and dynamo models of the giant planets have
3.1.3. Boundary conditions
The dynamo equations are usually solved in the spherical shell
geometry appropriate to planets. Velocity boundary conditions are
impenetrable and either stress-free or no-slip surfaces. No-slip
boundaries are relevant to the liquid cores in terrestrial planets,
while stress free boundaries may be more relevant to dynamos
in the outer planets. Temperature boundary conditions are either
isothermal or insulating surfaces. The magnetic field must satisfy
the continuity of the normal component of B and the continuity
of the tangential component of B on the spherical shell boundaries.
The latter condition assumes no surface currents and no change in
permeability across the boundaries. The magnetic field outside the
dynamo region must therefore be determined or specified consistently with the field in the dynamo region.
3.2. Non-dimensional parameters
Non-dimensional parameters are meaningful ways to simply
represent the dynamics and geometry of a system. Table 2 summarizes the parameters often used in the planetary dynamo community. The relative influences of the terms in the governing
equations can be evaluated by taking their ratios and assuming
typical scales for length D, velocity U, and magnetic field strength
B. For example, the Ekman number, E, estimates the ratio of the viscous to the Coriolis forces: E = (mr2u)/(2X u) (mU/D2)/
(XU) = m/XD2. The Rayleigh number, Ra = agDT D3/mj, characterizes the ratio of buoyancy to diffusion. The Prandtl numbers,
Pr = m/ j and Pm = m/g, characterize the ratio of viscous to thermal
and magnetic diffusivities, respectively. The Rossby number,
Ro = U/XD, characterizes the ratio of inertial to Coriolis forces.
The Reynolds number, Re = UD/m = Ro/E, characterizes the ratio of
inertial to viscous forces, and the magnetic Reynolds number,
Rm = UD/g = RePm, characterizes the ratio of magnetic induction
to magnetic diffusion. The Elsasser number, K = B2/qlog X, estimates the ratio of Lorentz to Coriolis forces. The depth of the dynamo region relative to the planet radius is given by RD/RP, and the
99
G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
Lee et al., 2006); these values are used for the ice giants. The characteristic rms magnetic field strengths at the tops of the dynamo
regions are calculated by downward continuing the measured radial magnetic fields using (2). This provides a lower bound for
the Elsasser number since the actual magnetic field strength will
be stronger than the estimated value due to the unresolved field
components. In addition, the Elsasser number will be larger still
within the dynamo region since toroidal field components are also
present. Dynamo action occurs only when the fluid velocities are
fast enough that magnetic induction overcomes magnetic diffusion; thus, the magnetic Reynolds number must exceed its critical
value: Rm J 102 (Christensen and Aubert, 2006). Using this criterion, we infer the minimum flow speeds in terms of the Reynolds
and Rossby numbers. In the Earth’s core, secular variations suggest
core speeds of U 0.5 mm/s (Bloxham and Jackson, 1991), yielding
Rm 103. Assuming this value is valid for all of the planets, the
flow speeds are likely at least an order of magnitude larger than
the lower bound estimate. It is difficult to determine the superadiabatic heat flux and, thus, the Rayleigh number. For the Earth’s
core, estimates range between 1022 < Ra < 1030 (Jones, 2000;
Gubbins, 2001). Additional complications arise since compositional
buoyancy should also be considered. Given this uncertainty, we do
not make Ra estimates for the other planets.
These parameters, given in Table 4, indicate that a range of dynamo region geometries and convective dynamics are possible. The
geometries can range from a sphere for Ganymede to a thick spherical shell for Earth to possibly a thin spherical shell for Mercury.
Ganymede also has the most deep-seated dynamo. This may explain the satellite’s strongly-dipolar surface magnetic field. However, recall that Ganymede consists of a water-ice shell, rocky
mantle, and metallic core. In order to compare against other terrestrial bodies, we also consider the radius ratio of the top of the core
to the top of the mantle. This ratio is about 0.5 assuming a mantle
thickness of 900 km (Schubert et al., 2007), similar to the RD/
RP = 0.55 ratio of the Earth. Interestingly, Uranus and Neptune appear to have different dynamo region geometries. Recent thermal
evolution models suggest that this difference occurs because Neptune is fully convecting, while Uranus may only be convecting in a
thin layer (Fortney et al., 2011). Both of the gas giants have thick
spherical shell geometries, assuming a central core is present. Further, the dynamo region of Jupiter extends up to a relatively shallow depth. This occurs because the electrical conductivity varies
strongly with radius and dynamo action can also occur in the
semi-conducting region overlying the metallic hydrogen layer
(Liu et al., 2008).
The low Ekman and Rossby numbers indicate that the Coriolis
force plays a strong role in the interiors of the planets, while viscous and inertial forces are substantially weaker. The inertial force
may not be negligible, however, since all of the planets are strongly
turbulent. This is especially evident for the ice giants since they
have the largest Reynolds numbers in the solar system. Inertial effects have also been linked to multipolar magnetic field generation
Table 2
Non-dimensional parameter definitions and physical interpretations. Symbols are
defined in the text.
Parameter
Definition
Physical
interpretation
Ekman Number
Rayleigh Number
E = m/XD2
Ra = agoDT
D3/mj
Pr = m/j
Pm = m/g
Viscous/Coriolis forces
Buoyancy/Diffusion
Ro = U/XD
Re = U D/m
Rm = U D/g
Inertial/Coriolis forces
Inertial/Viscous forces
Magnetic induction/Magnetic
diffusion
Lorentz/Coriolis forces
Dynamo region depth
Dynamo region geometry
Prandtl Number
Magnetic Prandtl
Number
Rossby Number
Reynolds Number
Magnetic Reynolds
Number
Elsasser Number
K = B2/qlogX
RD/RP
RDI/RD
Viscous/Thermal diffusivities
Viscous/Magnetic diffusivities
geometry of the dynamo region is given by RDI/RD. In these definitions, X is rotation rate, D = RD RDI is the thickness of the dynamo
region, RD is the outer radius of the dynamo region, RDI is the inner
radius of the dynamo region, m is kinematic viscosity, j is thermal
diffusivity, g is magnetic diffusivity, a is thermal expansion coefficient, g is gravitational acceleration, DT is superadiabatic temperature contrast, q is density, lo is magnetic permeability of free
space, U is characteristic rms velocity, and B is characteristic rms
magnetic field strength.
In order to estimate the non-dimensional parameters, we need
to make assumptions about the dynamo regions, the fluid properties, the flow speeds, and the magnetic field strengths. This is a difficult task since many of these values are poorly constrained; the
best estimates are given in Table 3. Dynamo region rotation frequencies are taken from Lodders and Fegley (1998). Note that
the giant planet rotation rates are assumed to coincide with the
rotation rates of their magnetic fields. The magnetic rotation rate
is inferred from the periodicity of radio emissions that result from
charged magnetospheric particles (e.g., Carr et al., 1981, 1983). Radii of the dynamo regions are taken from Williams et al. (2007) for
Mercury, from Dziewonski and Anderson (1981) for Earth, from
Nellis (2000) and Stevenson (1982) for the gas giants, from Schubert et al. (2007) for Ganymede, from Lee et al. (2006) and Podolak
et al. (1991) for Uranus, and from Lee et al. (2006) and Stevenson
(1982) for Neptune. The inner dynamo region radii especially have
a large degree of uncertainty. Based on the estimated physical
properties of the Earth’s core given in Stacey (2007), we assume
m 106 m2/s, g 1 m2/s, and j 105 m2/s for all bodies with liquid iron cores. Transport properties of metallic hydrogen are estimated to be m 107 m2/s and j 106 m2/s (Stevenson et al.,
1977) and g 1 m2/s (Nellis, 2000); these values are used for the
gas giants. Transport properties of high-pressure water are estimated to be m 106 m2/s (Abramson, 2005), j 107 m2/s
(Abramson et al., 2001), and g 102 m2/s (Cavazzoni et al., 1999;
Table 3
Summary of mean properties of the planets’ dynamo regions used to calculate the non-dimensional parameters given in Table 4. RP is planet radius given in Table 1. Molecular
transport properties are assumed. References are given in the text. RDI is particularly uncertain for all bodies other than Earth.
Dynamo
Mercury
Earth
Jupiter
Ganymede
Saturn
Uranus
Neptune
X
(s1)
RD
(RP)
RDI
(RP)
q
m
j
g
(kg/m3)
(m2/s)
(m2/s)
(m2/s)
jBr(r = RD)j
(lT)
1.2 106
7.3 105
1.8 104
1.0 105
1.6 104
1.0 104
1.1 104
0.75
0.55
0.95
0.3
0.5
0.8
0.8
0.5 ?
0.19
0.2 ?
0?
0.25 ?
0.6 ?
0.3 ?
8000
11,000
2000
6000
2000
2000
2000
106
106
107
106
107
106
106
105
105
106
105
106
107
107
1
1
1
1
1
102
102
0.6
270
625
32
45
75
73
100
G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
Table 4
Order of magnitude estimates of key dimensionless parameters for the planets’
dynamo regions. Rm = 102 is assumed to estimate lower bounds for Re = Rm/Pm and
Ro = ReE. The K values neglect contributions from the toroidal field and the
unresolved poloidal components, which likely increase the estimate by an order of
magnitude.
Dynamo
E
Pr
Pm
Rm
Ro
Re
K
RDI/
RD
RD/
RP
Mercury
Earth
Jupiter
Ganymede
Saturn
Uranus
Neptune
1012
1015
1019
1013
1018
1016
1016
0.1
0.1
0.1
0.1
0.1
10
10
106
106
107
106
107
108
108
102
102
102
102
102
102
102
104
107
1010
105
109
106
106
108
108
109
108
109
1010
1010
105
0.1
1
103
0.01
104
104
0.6
0.35
0.2
0
0.5
0.6
0.4
0.75
0.55
0.95
0.2
0.5
0.8
0.8
in dynamo models (e.g., Christensen and Aubert, 2006; Olson and
Christensen, 2006). As indicated by the Elsasser number, the Lorentz force is significant for the Earth and the gas giants, but may
be less so for the other planets. It is often assumed that the planets
are in magnetostrophic balance where the Lorentz and Coriolis
forces are comparable (e.g., Stevenson, 2003). The low K estimates
for Mercury, Ganymede, and the ice giants, however, do not support this hypothesis. Recent dynamo modeling results further dispute the prevalence of magnetostrophic balance (e.g., Christensen
and Aubert, 2006; Soderlund et al., in review). The magnetic Prandtl numbers much less than unity suggest a separation of scales
between the magnetic and velocity fields where the magnetic flux
patches are large compared to the flow eddies. However, the
dynamical implications of low viscosity and rapid rotation on convection and dynamo action are not well understood since it is difficult to study low Pm, low E systems.
3.3. Methods
Numerical models and laboratory experiments are valuable
tools to better understand the dynamics of planetary interiors.
Both approaches, however, are unable to reach the extreme planetary parameter values due to computational and technological limitations. Fortunately, many systems exhibit asymptotic behavior at
large or small values of the control parameters (e.g., Christensen
and Aubert, 2006; Aurnou, 2007; King et al., 2010). Large surveys
are carried out to map the behavioral regimes and to determine
how the control parameters influence the dynamics. With these
surveys, it is possible to develop scaling laws to quantify how
the dynamics (e.g., magnetic field strength, flow speeds, heat transfer efficiency) depend on the control parameters. Researchers then
attempt to develop asymptotic scaling laws which can be extrapolated to planetary conditions. For a recent review of scaling laws,
see Christensen (2010). Moreover, numerical models have shown
that convectively-driven dynamos in rotating spherical shells are
able to generate some of the key features of the planetary magnetic
fields (e.g., Stanley and Bloxham, 2004; Sakuraba and Roberts,
2009; Stanley and Glatzmaier, 2010). Recent planetary dynamo
models are summarized in the next section.
4. Planetary dynamo models
4.1. Terrestrial planets and Ganymede
In this section we discuss the modeling that has been carried
out to understand the dynamos in planets with molten iron-alloy
cores. The objects include the terrestrial planets, except for Venus,
and the outer planet satellite Ganymede. There is an enormous literature on the modeling of Earth’s dynamo and with our primary
focus being the magnetic fields of the other planets, we do not at-
tempt to review the geodynamo literature here. Instead we focus
on recent modeling attempts to explain the magnetic fields of Mercury and Ganymede. Models of the ancient Martian dynamo will
also be discussed. See Kono and Roberts (2002), Glatzmaier
(2002), and Wicht et al. (2009) for reviews of geodynamo models.
4.1.1. Mercury
Dynamo modeling of Mercury’s magnetic field has focused on
explaining why it is so weak. Mercury’s magnetic dipole moment
is about 3.3 4.2 1019 Am2 (Anderson et al., 2008). Compared
with Earth’s magnetic dipole moment of 7.8 1022 Am2, Mercury’s
moment is only about 5 104 that of Earth. Further, Mercury’s
magnetic dipole moment is about half that of Ganymede, which
is 1.32 1020 Am2, even though Ganymede, stripped of its ice
shell, has a radius only about 75% of Mercury’s radius. It has been
proposed that a stably-stratified layer at the top of the liquid part
of Mercury’s core might be responsible for weakening the external
dipole field (Christensen, 2006; Stanley and Mohammadi, 2008). In
the Christensen (2006) model, this weakening is due to attenuation
of the internally generated field by the electrically conducting stable layer. The Stanley and Mohammadi (2008) model emphasizes
the importance of thermal winds in the stable layer that induce
unfavorable zonal flows throughout the liquid part of the core. In
their models, the magnetic field is strongly time variable and the
external dipole can be either weak or strong. Another possible
explanation is the thickness of the liquid part of Mercury’s core
within which the dynamo operates. Dynamo action in a thin shell
can produce weak external dipole fields (Stanley et al., 2005;
Takahashi and Matsushima, 2006), while Heimpel et al. (2005b)
have produced single plume dynamos in a thick shell that are also
consistent with Mercury’s weak magnetic field.
Yet another explanation for Mercury’s weak magnetic field involves the self-interaction of its internal dynamo with the magnetosphere created around the planet by the dynamo itself, a type of
feedback effect (Glassmeier et al., 2007; Gomez-Perez and
Solomon, 2010; Gomez-Perez and Wicht, 2010). Mercury is effectively embedded in an external magnetic field generated by Chapman-Ferraro currents in its magnetopause. This self-generated
ambient magnetic field influences the dynamics of the internal
dynamo, similar to the way the Jovian magnetic field influences
dynamo action in Jupiter’s moon Ganymede (Sarson et al., 1997).
Chapman-Ferraro currents generate a magnetic field that enhances
the magnetospheric field and tends to cancel the field outside the
magnetosphere. In the dynamo region, the Chapman-Ferraro field
opposes the dynamo-generated field so that the dynamo is embedded in an ambient field of opposite polarity. Glassmeier et al.
(2007) use a kinematic a–X-dynamo model to show that the feedback dynamo indeed has a Mercury-type solution with a weak
magnetic field. Recent self-consistent dynamo models with imposed external magnetic fields also support strong magnetospheric
feedback on weak internal fields (Gomez-Perez and Solomon,
2010; Gomez-Perez and Wicht, 2010).
The possibility that solid iron precipitation in Mercury’s core occurs differently than it does in Earth’s core provides another feasible explanation for Mercury’s weak magnetic field (Vilim et al.,
2010). Laboratory experiments have shown that the Fe-S system
behaves in a non-ideal way at temperatures and pressures likely
encountered in Mercury’s core for sulfur concentrations between
about 7 and 12 wt% (Chen et al., 2008). As a consequence, iron
could precipitate at different places in the core depending on the
sulfur concentration; an Fe snowfall could originate from the top
or the mid-point of the core or from both locations. When Fe
freezes out at both the top and midway through the core, there
are two sources of compositional buoyancy, the heavy iron sinking
from the top of the core and from below mid-depth and the light Srich fluid rising above mid-depth. Vilim et al. (2010) modeled
G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
dynamo action driven by this unusual source of compositional
buoyancy, a double snow layer, and found separate dynamo regions above and below the mid-depth freezing layer that produce
magnetic fields of opposite sign with a consequent weakened surface field. Conditions in Ganymede’s core, as discussed below,
might also lead to a distinctly non-earthlike form of Fe precipitation (Hauck et al., 2006).
The generation of Mercury’s weak magnetic field is not yet
understood, although there is no lack of ideas to explain it. The
MESSENGER spacecraft is now in orbit around Mercury and data
from three flybys are published to date (Uno et al., 2009). With
careful analysis of these observations, particularly with respect to
separating the externally driven effects from the internally produced magnetic field, we may be able to distinguish among the
above explanations. For example, Fig. 4 compares the observed
surface magnetic spectra against the spectra predicted by dynamo
models. This comparison shows that the model of Christensen
(2006) is in best agreement, supporting his conclusion that an electrically conducting stable layer at the top of the dynamo region
may be responsible for the weak, dipole-dominated field at the planet surface.
4.1.2. Ganymede
Dynamo action in Ganymede’s core was first studied by Sarson
et al. (1997) who investigated how Jupiter’s magnetic field might
influence magnetic field generation in the satellite. The Jovian
magnetic field at Ganymede’s orbit is much weaker than the satellite’s intrinsic magnetic field and, therefore, is not expected to play
a significant role in the operation of Ganymede’s dynamo. The dynamo model of Sarson et al. (1997) confirmed this, but left open
the possibility that in the initial stages of dynamo activity, the Jovian magnetic field could provide a seed field that would explain
the anti-alignment of Jupiter’s and Ganymede’s dipole moments.
Similar to Mercury, Ganymede’s dynamo acts in a relatively low
pressure, low temperature environment compared with the Earth.
Solidification of Ganymede’s core and the associated compositional
driving of its dynamo might then be completely different from the
freezing out of Earth’s core and the compositional buoyancy driving the geodynamo. According to Hauck et al. (2006), Ganymede’s
dynamo can be driven in part by compositional buoyancy released
through the sinking of Fe snow formed below the core-mantle
boundary or by the upward flotation of solid FeS formed in the
Power / Dipole power
100
10-1
10-2
Uno et al., 2009
Heimpel et al., 2005a
Takahashi and Matsushima, 2006
Christensen, 2006
10-3
Vilim et al., 2010
10-4
1
2
3
4
5
6
Spherical Harmonic Degree, l
Fig. 4. Normalized surface magnetic power spectra for Mercury from Uno et al.
(2009) and select dynamo models: the v = 0.15 case of Heimpel et al. (2005b), the
Ra = 2 105 case of Takahashi and Matsushima (2006), case II of Christensen
(2006), and model 1 of Vilim et al. (2010).
101
deep core. These alternative scenarios for the thermochemical
state of the core arise because the eutectic melting temperatures
and eutectic sulfur contents in the binary Fe–FeS system decrease
with increasing pressure in the range of core pressures in Ganymede (14 GPa). Iron snow or flotation of solid FeS occur upon
cooling of Ganymede’s core depending on whether the core composition is more or less iron-rich than eutectic. Hauck et al.
(2006) did scaling calculations and concluded that for iron snow
cooling scenarios, typical Rossby and magnetic Reynolds numbers
are consistent with dynamo action occurring in the core and estimates of the generated magnetic field agree with the strength of
Ganymede’s field.
Though Ganymede is larger than Mercury, the silicate-metal
part of the satellite is only about the size of Io and the Moon,
and Ganymede’s core is at most about half that large (Schubert
et al., 2004). It is perhaps surprising that such a small core could
support dynamo action over a geologically long time. What supplies the energy to drive the dynamo? Why is the core not almost
completely solidified? Bland et al. (2008) and Kimura et al. (2009)
have investigated thermal history models for Ganymede with the
aim of identifying scenarios that allow for present day dynamo
activity. Bland et al. (2008) conclude that a present day dynamo
could exist only if the sulfur mass fraction in Ganymede’s core is
very low (<3%) or very high (>21%), and only if the silicate mantle
could cool rapidly (e.g., a mantle with a wet olivine rheology). Kimura et al. (2009) conclude that a Ganymede dynamo could currently be operative for a sufficiently large sulfur-rich metallic
core in which dynamo activity started late in the satellite’s evolution. In contrast, Hauck et al. (2006) inferred that a dynamo could
exist at present for a broad range of core sulfur concentrations.
Bland et al. (2008) also studied whether tidal heating during passage through an eccentricity pumping Laplace-like resonance in
Ganymede’s past could enable present day dynamo action in the
metallic core. They found that such an event would not facilitate
the operation of a present day dynamo. Of course, Ganymede does
have a dynamo at present which may indicate that its core formed
relatively late in the satellite’s thermal evolution.
To date, there are no published quantitative models of Ganymede’s dynamo. The studies of Hauck et al. (2006), Bland et al.
(2008), and Kimura et al. (2009) use scaling arguments and qualitative criteria to determine whether dynamo action could occur in
their Ganymede models. Progress in understanding how Ganymede generates its magnetic field requires at least the numerical
modeling of dynamo activity in Ganymede models derived consistently from thermal-orbital evolution models of the satellite.
4.1.3. Mars
Mars crustal magnetization preserves a record of its ancient dynamo. The record has been exploited to infer the nature of the Martian dynamo, but only a few attempts have been made to model
dynamo action in the special circumstances of ancient Mars. As
discussed in Section 2.2, one of the main questions about the Martian dynamo is the period in which it was active. When did dynamo action begin and when did it end? Why did the Martian
dynamo stop working? There is an observed absence of magnetic
anomalies over the major impact basins, perhaps due to impact
demagnetization (Hood et al., 2003; Mohit and Arkani-Hamed,
2004). This has led many investigators to the conclusion that the
Martian dynamo had an early onset and ceased before the formation of the major impact basins (Acuña et al., 1999; Frey, 2003;
Arkani-Hamed, 2004). The only constraint on the timing of the dynamo comes from the magnetized Allan Hills meteorite ALH84001.
This meteorite is the oldest known Martian rock, dated between
3.9 and 4.1 Ga (Weiss et al., 2002). The onset of dynamo activity
in Mars, therefore, occurred around 4 Ga or earlier. Bibring et al.
(2006) presented a global mineralogical map of Mars and
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concluded that a rapid drop in atmospheric pressure near the end
of the Noachian (first Martian geologic period) could have been
triggered by a rapid decrease in dynamo field strength. It has also
been suggested that the major impacts could have altered the
internal temperature and convective character of Mars and may
have led to the early demise of the dynamo (Frey et al., 2007; Lillis
et al., 2008b).
Early dynamo cessation has been challenged by Schubert et al.
(2000) (see Section 2.2). More recently it has been recognized that
some volcanic edifices which postdate the formation of the major
impact basins on Mars are magnetized. Hood et al. (2010) demonstrated that the Apollinaris Mons construct, dated at 3.7 Ga
(Werner, 2009), is the most likely source of the magnetic field
anomaly centered on the volcano. Milbury and Schubert (2010)
did a statistical analysis of the global magnetic field and found very
small differences between Noachian and Hesperian geologic units,
suggesting that the dynamo persisted into the Hesperian. Further,
volcanic edifices at both Hadriaca Patera and Tyrrhenus Mons were
built in the period 3.7–4.0 Ga and show signs of magnetization
(Greeley and Crown, 1990; Williams et al., 2008; Werner, 2009;
Robbins et al., 2011). Lillis et al. (2006) used the electron reflectometry data from Mars Global Surveyor and found a magnetic signature associated with Hadriaca Patera, an edifice located on the rim
of the Hellas impact basin that postdates basin formation. Milbury
et al. (2011) modeled a large number of magnetic anomalies collocated with gravity anomalies within the region surrounding Tyrrhenus Mons. They found a correlation of paleopole locations with
units of different geologic age showing a progression of pole positions from initial magnetization to pole reversal through polar
wander.
The numerical dynamo simulations of Kuang et al. (2008) suggest possible behaviors of the Martian dynamo toward the end of
its activity. Near its demise, the Martian dynamo could have reversed frequently, and it could have operated as a subcritical dynamo since the energy to sustain a dynamo is significantly less than
what is required to excite it. Subcritical dynamo activity would
lengthen the life of the magnetic field. In addition, it would enable
an abrupt termination of dynamo activity. Once turned off, it
would be difficult to reactivate the dynamo without a substantial
increase of the buoyancy force in the Martian core. Glatzmaier
et al. (1999) and Stanley and Glatzmaier (2010) suggest another
possible termination scenario for the Martian dynamo involving
a critical role of reversals. Mars’ dynamo could have ended by
going through a series of dipole reversals and not completely
recovering after each one. Evidence for dipole reversal in the Tyrrhenus Mons region of Mars (Milbury et al., 2011) might indicate
the termination of the Martian dynamo in the Hesperian.
The spatial distribution of Mars crustal magnetic field confronts
us with another major puzzle (Fig. 3). Is the southern hemisphere
confinement of the magnetic anomalies a consequence of post dynamo modification of the magnetized crust by endogenic processes
or impacts, or did the Martian dynamo produce a field that reflects
the current magnetization distribution? Since the asymmetry of
the crustal magnetic field coincides with the crustal dichotomy,
it is possible that whatever process created the dichotomy also destroyed the crustal magnetization in the northern hemisphere.
Plausible causes of the dichotomy include endogenic removal of
crust in the northern hemisphere or exogenic disruption of the
northern hemisphere crust by a giant impact (Wilhelms and Squyres, 1984; Frey and Schultz, 1988; Andrews-Hanna et al., 2008;
Marinova et al., 2008; Nimmo et al., 2008). An endogenic process
that could have removed crust from the northern hemisphere is
degree-1 mantle convection or overturn (Schubert and Lingenfelter, 1973; Lingenfelter and Schubert, 1973; Weinstein, 1995;
Harder, 1998; Breuer et al., 1998; Zhong and Zuber, 2001; ElkinsTanton et al., 2003; Elkins-Tanton et al., 2005; Roberts and Zhong,
2006; Ke and Solomatov, 2006). The endogenic and exogenic
mechanisms can both not only remove magnetized crust from
the northern hemisphere, but can also create conditions deep in
the Martian mantle that influence convection and dynamo generation in the Martian core (Watters et al., 2009). Both mechanisms,
upwelling in the northern hemisphere and energy deposition by
impact, imply a hotter deep mantle in the northern hemisphere
of Mars and, therefore, a reduced heat flux from the core into the
northern hemisphere mantle. Stanley et al. (2008) investigate the
effect of this core-mantle boundary heat flux dichotomy on magnetic field generation in the core by imposing a large outward
core-mantle boundary heat flux in the southern hemisphere of a
dynamo model and an inward core-mantle boundary heat flux in
the northern hemisphere. The heat flux pattern imposed on the
outer shell boundary of the model and the resulting magnetic field
upward continued to the planet surface are shown in Fig. 5. Their
dynamo model generates a magnetic field concentrated in and
strongest in the southern hemisphere. This largely occurs because
the core-mantle heat flux boundary condition made the northern
hemisphere of the core subadiabatic and focused core convection
in the southern hemisphere. Thus, it is possible that the concentration of Martian magnetization to its southern hemisphere could
have been the result of a peculiar southern hemisphere Martian
core dynamo or the destruction of magnetized northern hemisphere crust by post-magnetization processes.
While the hemispheric dynamo of Stanley et al. (2008) shows
that it is possible to confine the Martian magnetic field to the
southern hemisphere of the planet, it does not explain the further
concentration of the observed magnetization to the Terra Cimmeria-Terra Sirenum region of the southern highlands. It is not apparent that impact demagnetization of the southern hemisphere crust
can account for this localization of magnetization either. Perhaps
an even more restrictive condition on heat flow at the core-mantle
boundary or some azimuthal dependence of the condition could
explain the observation.
4.2. Giant planets
The magnetic fields of the giant planets are likely coupled to
their surface zonal flows and convective heat transfer patterns.
These planets have strong winds that are organized into zonal jets.
The wind velocities are measured with respect to the planet’s rotation rate, assumed to correspond with the rotation rate of the deep
interior and magnetic field (e.g., Russell et al., 2001; Giampieri and
Dougherty, 2004). Jupiter and Saturn have strong prograde (eastward) equatorial jets and multiple smaller-scale jets at higher latitudes (e.g., Porco et al., 2003; Sanchez-Lavega et al., 2000). The
high latitude jets of Jupiter alternate in direction, while those of
Saturn are exclusively prograde assuming the Voyager-derived
rotation rate (Desch and Kaiser, 1981) and alternate in direction
assuming the planetary rotation rate estimates of Anderson and
Schubert (2007) and Read et al. (2009). In contrast, the zonal winds
of Uranus and Neptune are retrograde (westward) at low latitudes
and prograde at high latitudes (e.g., Sromovsky et al., 2001; Hammel et al., 2005). The wind speeds, however, can vary up to 50% due
to uncertainties in the rotation rates (Helled et al., 2010). It is not
presently known to what depths the winds of the giant planets extend, although the Galileo probe suggested that the Jovian winds
penetrate to at least the 20 bar pressure level (Atkinson et al.,
1998). The latitudinal internal heat flux profiles peak in the polar
regions with a minimum near the equator on the gas giants (Pirraglia, 1984) and peak in the equatorial and polar regions with minima at mid-latitudes on Neptune (Pearl and Conrath, 1991). The
heat flux pattern of Uranus is not well constrained (Pearl et al.,
1990). Modelers attempt to self-consistently generate these observations, to understand the underlying mechanisms, and to explain
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G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
(a) Imposed Heat Flux
(b) Radial Magnetic Field
-15 µT
0 µT
15 µT
Fig. 5. (a) Imposed outer boundary heat flux pattern in the Stanley et al. (2008) model. Red (blue) indicates inward (outward) directed heat flux. (b) Simulated radial
magnetic field upward continued to the surface of Mars. Red (blue) indicates outward (inward) directed field.
the fundamental differences in behavior between the gas and ice
giants.
Deep convection modeling efforts are typically channelled into
non-magnetic rotating convection models and into planetary dynamo models. Non-magnetic models are also important to consider because the electrically insulating regions are likely coupled
to the dynamo region and the mechanisms responsible for driving
zonal flows and controlling the heat transfer are more easily
understood without the added complexity of the Lorentz force.
The results of recent gas giant-like and ice giant-like models are
summarized below.
4.2.1. Gas giants
Busse (1976) first proposed that deep convection in the molecular envelopes may be responsible for the zonal winds of Jupiter.
He envisioned that the alternating jets are the surface expressions
of differentially-rotating cylinders aligned with the rotation axis. In
this hypothesis, the fluid motions are quasigeostrophic and do not
strongly vary along the direction of the rotation axis, in agreement
with the Taylor–Proudman theorem (Taylor, 1917; Proudman,
1916). Gas giant-like zonal flows with multiple jets were first obtained in rapidly-rotating Boussinesq convection models by
Christensen (2001, 2002). More recently, Heimpel et al. (2005a),
Heimpel and Aurnou (2007), and Aurnou et al. (2008) have shown
that turbulent, rapidly-rotating convection in thin spherical shells
produces zonal flow and heat flux patterns that are consistent with
those observed on Jupiter. The simulated zonal winds of the
Heimpel et al. (2005a) model are shown in Fig. 6. The equatorial
jets in these models result from Reynolds stresses due to correlations between the fluctuating cylindrical and azimuthal velocity
components (e.g., Zhang, 1992). Outside the tangent cylinder, the
imaginary right cylinder tangent to the inner shell at the equator,
the height of the convection columns decreases with increasing
cylindrical radius. As a result, fluid moving away from the rotation
axis must speed up and fluid moving toward the rotation axis must
slow down in order to conserve potential vorticity. This leads to
spiraling convection cells in which cylindrically outward flows correlate with prograde azimuthal flows, and vice versa. These Reynolds stresses transport positive angular momentum outward
and negative angular momentum inward, driving zonal flows that
are prograde near the outer boundary and retrograde near the inner boundary. Inside the tangent cylinder, quasigeostrophic turbulence leads to multiple jets whose widths are determined by the
Rhines scale (Rhines, 1975; Heimpel and Aurnou, 2007). This style
of zonal flow inhibits equatorial heat transfer and promotes polar
Fig. 6. Instantaneous azimuthal winds on the inner and outer boundaries of the
Heimpel et al. (2005a) model. Red (blue) indicates prograde (retrograde) flow.
heat transfer (Aurnou et al., 2008). In the equatorial plane, the convective flows are less efficient at transferring heat outward since
they must compete with the strong azimuthal forcing. The convective flows in the polar regions are most efficient because the zonal
flows do not inhibit radial motions.
Density stratification must also be considered to accurately
simulate the dynamics of the gas giants. Flow speeds will tend to
decrease with increasing density and the convection will not tend
to manifest as axially-invariant columns (Glatzmaier et al., 2009).
Thus, the vortex-stretching mechanism of driving the zonal flow
is no longer appropriate. Rather, compressional torques produce
negative vorticity in the expanding, uprising plumes and positive
vorticity in the contracting, sinking plumes. Since fluid moving
radially outward will tend to become faster and fluid moving radially inward will tend to become slower due to density effects, the
plumes tilt and correlations again develop between the fluctuating
cylindrical and azimuthal motions (Glatzmaier and Gilman, 1981;
Evonuk, 2008; Glatzmaier et al., 2009). Reynolds stresses drive
the zonal flow by transporting positive angular momentum outward and negative angular momentum inward, resulting in equatorial zonal flows that have the same organization as models
without density stratification. Jones and Kuzanyan (2009) contrast
anelastic and Boussinesq convection in rotating spherical shell
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G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
models and find that the zonal flow pattern is not strongly affected
by the density stratification, but the convective flow speeds are
suppressed at depth in the anelastic models.
Electrical conductivity stratification makes the models even
more realistic since it allows coupling between the lower conductivity molecular envelope and the metallic mantle. Stanley and
Glatzmaier (2010) have carried out dynamo simulations with both
density stratification and radially-varying electrical conductivity.
Rapidly-rotating, turbulent convection in a thin shell geometry
produces zonal flows and a radial magnetic field that agree to first
order with the observations of the gas giants (Fig. 7). The zonal
flows are maintained by the compressional torque mechanism.
The magnetic field is dipole-dominated, but has significant power
in the higher order modes since the axisymmetric radial field
exhibits a banded structure with latitude. Additional measurements are needed to improve the spatial resolution of the planets’
magnetic fields in order to compare against the model predictions.
For Saturn, modelers must also attempt to explain the strong
axisymmetry of the magnetic field. Stevenson (1980, 1982) proposed that differential rotation in a stably-stratified layer created
by helium rain-out near the molecular-metallic hydrogen transition could diminish the non-axisymmetric components of the
magnetic field. Recent dynamo models support this hypothesis.
The kinematic dynamo models of Schubert et al. (2004) show that
the morphology of the dynamo is determined by the characteristics of the zonal thermal winds in the overlying stable layer.
Christensen and Wicht (2008) and Stanley (2010), respectively,
show that thick and thin stably-stratified layers overlying the dynamo region develop differential rotation through thermal winds;
4.2.2. Ice giants
Convection in the molecular envelopes of Uranus and Neptune
has also been proposed to drive their observed zonal flows and
to be dynamically coupled to their dynamo regions (Suomi et al.,
1991; Aurnou et al., 2007). Further, since the ice giants are estimated to have the most turbulent fluid flows in the solar system
(compare Re in Table 4), inertial effects may be important in these
planets. The non-magnetic Boussinesq models of Aurnou et al.
(2007), non-magnetic anelastic models of Brun and Palacios
(2009), and Boussinesq dynamo models of Soderlund and Aurnou
(2010) show that strongly-forced convection in rotating spherical
shells, regardless of shell thickness, can drive zonal flows that qualitatively agree with the observations of Uranus and Neptune. The
simulated zonal winds and radial magnetic field of the Soderlund
and Aurnou (2010) model are shown in Fig. 8. In these models,
the Taylor–Proudman constraint is not valid due to strong inertial
effects, leading to three-dimensional convection. This convective
turbulence strongly mixes the fluid and homogenizes the temperature and absolute angular momentum (Scorer, 1966; Gough and
Lynden-Bell, 1968; Bretherton and Turner, 1968). Aurnou et al.
(2007) find that retrograde equatorial jets and strong prograde jets
at high latitudes develop in order to conserve angular momentum.
Soderlund and Aurnou (2010) show that this convective regime
also generates heat flux patterns and magnetic field morphologies
that are consistent with observations of the ice giants. The importance of inertia for the transition from dipolar to multipolar
(b) Radial Magnetic Field
90
90
60
60
30
30
Latitude
Latitude
(a) Zonal Flows
this flow can suppress rapidly-varying, higher-order magnetic field
components through a skin effect mechanism.
0
0
-30
-30
-60
-60
-90
0
200
400
-90
-3000
0
3000
Intensity, µT
Velocity, m/s
Fig. 7. (a) Zonal flow and (b) radial magnetic field snapshots on the outer boundary of the Stanley and Glatzmaier (2010) model. In (a), red (blue) indicates prograde
(retrograde) flow. In (b), red (blue) indicates outward (inward) directed fields. The latitudinal profiles are averaged over all longitudes.
(b) Radial Magnetic Field
90
90
60
60
30
30
Latitude
Latitude
(a) Zonal Flows
0
0
-30
-30
-60
-60
-90
-90
-500
0
Velocity, m/s
500
-103
0
Intensity, µT
103
Fig. 8. Snapshots of (a) zonal flow and (b) radial magnetic field up to harmonic three on the outer boundary of the Soderlund and Aurnou (2010) model. In (a), red (blue)
indicates prograde (retrograde) flow. In (b), purple (green) indicates outward (inward) directed fields. The latitudinal profiles are averaged over all longitudes.
G. Schubert, K.M. Soderlund / Physics of the Earth and Planetary Interiors 187 (2011) 92–108
magnetic field generation has also been shown in the geodynamo
models of Grote et al. (1999, 2000), Kutzner and Christensen
(2000), Kutzner and Christensen (2002), Simitev and Busse
(2005), Aubert (2005), Sreenivasan and Jones (2006); and
Soderlund et al. (in review).
Other groups have also produced ice giant-like magnetic fields.
Gomez-Perez and Heimpel (2007) find that dynamo models tend to
become multipolar as the electrical conductivity is decreased and
as strong zonal flows develop. In addition, Stanley and Bloxham
(2004), Stanley and Bloxham (2006) find multipolar dynamos
when moderately strong convection occurs in a thin spherical shell
overlying a stably-stratified fluid. They suggest that solid, electrically conducting inner cores act to stabilize the magnetic field
and promote dipolar dynamos, while stably-stratified fluid cores
do not have this anchoring effect. While this model may be appropriate for Uranus, it is inconsistent with recent internal structure
models of Neptune (Fortney et al., 2011). Further, the zonal flows
in each group’s models have strong prograde equatorial jets, opposite to those observed.
5. Conclusions and outlook
Dynamo models yield a diverse spectrum of dynamical behaviors and are able to reproduce aspects of the planets’ magnetic
fields, fluid flows, and thermal emissions. Thus, through these
models, we learn about the dynamics and underlying mechanisms
that may be occurring in planetary interiors. Further modeling progress and additional constraints on the magnetic fields and the
internal structures and dynamics derived from upcoming spacecraft missions will likely allow us to develop sophisticated models
that capture the relevant physics and to make predictions about
the evolution of planetary magnetic fields. For example, technological advances will enable models to reach lower Ekman and magnetic Prandlt numbers, to develop asymptotic scaling laws, and
to incorporate significant stratification in density and electrical
conductivity. By understanding the dynamos of our solar system,
we may also use these models and associated scaling laws to predict the magnetic field strengths and morphologies of exoplanetary
dynamos.
As for observations, the MESSENGER and Bepi-Columbo missions will help constrain the structure of Mercury’s dynamo region
and the behavior of the body’s magnetic field. In addition, a possible future mission to the Jupiter system would help to characterize
Ganymede’s dynamo and internal structure. The upcoming Juno
mission will critically improve our understanding of Jupiter by
resolving the magnetic field up to spherical harmonic degree 14,
detecting short timescale secular variation, and constraining the
depth of the zonal winds (Connerney, private communication).
The Cassini spacecraft may closely orbit, and eventually impact,
Saturn in the possible extended-extended phase of the mission,
allowing the magnetic and gravitational fields to be mapped in further detail (Cassini Mission Plan, Revision N). Missions to Uranus
and/or Neptune are necessary to better constrain the internal
structures and dynamics of the ice giants and to map the magnetic
fields globally and with higher resolution.
Improved understanding of planetary dynamos will come not
only from additional observations of planetary magnetic fields by
future spacecraft missions, but also from new modeling efforts to
address the diversity of physical settings in which planetary dynamos operate. The release of compositional buoyancy in the cores of
Ganymede and Mercury can be fundamentally different from the
source of compositional buoyancy in the Earth’s core, and numerical dynamo models that focus on these different buoyancy distributions are needed. Strong density and electrical conductivity
stratifications occur in the interiors of the giant planets and dyna-
105
mo models that can account for these extreme property variations
need to be developed. To understand dynamos that operated in the
past, and even some presently active dynamos, connections with
thermal evolution models of the planets and satellites are required.
The internal structures of the outer planets are especially uncertain
and need to be better known if the dynamos in these planets are to
be modeled and understood. Even the rotation rates of the giant
planet interiors need to be determined with more confidence before we can really know the significance of the observed zonal circulations. This is especially true of Saturn and possibly the ice
giants. Gaps in our knowledge of planetary properties place serious
limitations on our ability to understand the variety of planetary
dynamos found in our solar system. Despite these obstacles, we
are optimistic about future discoveries and modeling efforts that
will progress the study of planetary magnetic fields.
Acknowledgments
G.S. was supported by NASA grant NNX09AB57G from the Planetary Atmospheres Program and by NSF Grant AST-0909206 from
the Planetary Astronomy Program. K.M.S. was supported by NASA
Grant NNX09AB61G from the Planetary Atmospheres program.
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