2.2. Dipolar-shaped Magnetic Field
Figure 2 shows a dipolar shape for the magnetic field around a natural bar magnet usually made from a ferrous oxyde. In theory, this would be the ideal unperturbed shape of the magnetic field of the Sun or most stars on a global scale, for some inner planets such as Earth and Mercury, as well as for some giant planets such as Jupiter, Saturn, Uranus, Neptune.
 |
Figure 2. Dipolar-shaped magnetic field lines of a bar magnet. An ideal shape for the magnetic field close to the surface (thick circle) of a star or a planet, as produced inside these bodies by fluid motions (dynamos). |
Outside the body's surface, the magnetic field of a dipole decreases roughly as the inverse cube of the distance,
 |
where Bsurf is the magnetic field strength at the surface of the object of radius rsurf. It is customary to define the 'dipole magnetic moment' as
 |
and to express its units as Gauss m3 .
Inside the body's surface, the three basic ingredients needed for a dynamo are a large volume of electrically conducting fluid in the body's interior, an energy source (such as convection) to circulate the fluid, and the body's overall rotation to organize the resulting fluid motions.
2.2.1. Big Moons With Dynamos (~ 103 to 104 km; ~ 10-10 pc) (~ 10-2 Gauss)
Big moons could be viewed as mini-planets.
2.2.1.1 Ganymede The discovery of the magnetic field of Ganymede (one of the moons of the planet Jupiter) by the spacecraft Galileo (e.g., Kivelson et al. 1996a) has shown that remanent magnetization is very unlikely. The internal magnetic field is strong enough to carve out a magnetosphere with clearly defined boundaries within Jupiter's own magnetosphere - Ganymede's magnetic field is several times larger than Jupiter's ambient magnetic field (120 nT = 1.2 milliGauss) at Ganymede's distance. Ganymede is at 15 Jupiter radii from Jupiter's center.
The data are consistent with an active Ganymede-centered magnetic dipole of ~ 1.4 × 1017 Gauss m3, tilted by about 10 degrees relative to the spin axis of the moon. The radius of Ganymede is ~ 2650 km. The magnetic field strength at the equatorial surface amounts to 750 nT = 7.5 mGauss (e.g. Kivelson et al. 1996a).
The source of Ganymede's magnetic field could be a dynamo action, located in a molten iron core (or a salty-water internal ocean). Ganymede is "almost certainly" operating its own dynamo, albeit altered by Jupiter's own magnetic field (Sarson et al. 1997).
2.2.1.2. Io Voyager I spacecraft detected magnetic fields from Jupiter's moon Io (e.g., Ness et al. 1979). The Galileo spacecraft confirmed this finding. A part of Io's magnetic field could be extrinsic, induced externally by a current-carrying ionosphere (Kivelson et al. 1996c), and a part could come from an internal dipole. The extrinsic part is maintained by Jupiter's own magnetic field (Sarson et al. 1997), via magnetoconvection processes induced by Jupiter's ambient field of strength ~ 1800 nT (= 18 mGauss). Io is at 6 Jupiter radii from Jupiter's center.
The data for Io are consistent with some kind of passive magnetic dipole, anti-aligned with Jupiter's magnetic dipole, of strength ~ 8 × 1016 Gauss m3. The radius of Io is ~ 1820 km. The magnetic field strength at the equatorial surface amounts to 1300 nT = 13 milliGauss (e.g., Kivelson et al. 1996b). The recent evidence suggests that Io has a large molten iron-sulfide core and that adequate tidal heating is present to drive a small dynamo field (e.g., Kivelson et al. 1996b).
2.2.2. Planet Earth (~ 104 km)
The Earth's interior can be subdivided into 4 main volumes. At the center one has the core, composed of (i) a 1200-km radius solid crystalline metallic 'inner core', (ii) which is surrounded by a 2300-km thick "liquid" molten (iron-alloy) metallic 'outer core'. On top of that one has the 2900-km solid oxide shell, composed of (iii) a 'lower mantle', and (iv) an 'upper mantle'.
Inside the Earth, the magnetic field may be generated and maintained somewhere in the outer core by dynamo action. The rough extent of the dynamo region is above 0.2 and below 0.5 Earth radii. It is motions in the "liquid" molten metallic 'outer core' that produce the Earth's magnetic field, through MHD processes in the electrically conducting fluid of the outer core, where the magnetic field there can reach 300 Gauss (e.g., Fig. 3 in Jeanloz & Romanowicz 1997). The temperature at the top of the outer core is near 4000 K, while it is about 5000 K at the top of the inner core. An important energy source for the dynamo is the crystallization of iron at the inner-outer core boundary, releasing latent heat and light constituents, driving convection in the liquid outer core (e.g., Olson 1997). Geo-dynamo theories have predicted the shape of the magnetic field inside the Earth, aligned along the rotation axis in the inner core, but more complex in the outer core due to convective fluid (Glatzmaier and Roberts, 1996).
The data for Earth are consistent with some kind of active magnetic dipole, of strength ~ 1.3 × 1020 Gauss m3. The radius of Earth is ~ 6400 km. The magnetic field strength at the equatorial surface amounts to about 0.5 Gauss (e.g., Lanzerotti & Krimigis 1985). The Earth's magnetic field has reversed polarity many times in the past, the last ones being 780 000 years ago and 990 000 years ago. The duration of the reversal is short, about 4000 years during which the average intensity of the Earth's field is not zero but small, decreasing to about a quarter of its usual value (e.g., Merrill 1997).
Outside the Earth, the magnetic field strength in the Earth's ionosphere (ionized atmosphere at 100 km above the surface of the Earth) is about 0.3 Gauss. The effects of the solar wind on the Earth's original dipolar-shaped magnetic field is to push or deform the Sun-facing side into a smaller lobe, and to pull/expand the opposite side into a long trailing lobe. The full length of the magnetotail on the extended/night side can reach as fas as 220 Earth radii. The Moon is at 60 Earth radii.
Figure 3 shows a sketch of the Earth's magnetic field (or shield), which has a roughly dipolar form and a surface strength of about 0.5 Gauss. The lines of force of the Earth's magnetic field come into the Earth's geographic North pole, and exit through the Earth's geographic South pole. When the needle from a compass points to the Earth's North, the needle's own North pole aligns itself with the Earth's geographic North pole direction. An "equivalent bar magnet" inside the Earth would be upside down (have opposite polarity) to the earth's geographic North and South poles.
 |
Figure 3. Earth's magnetic field, as deformed from its ideal bar-magnet shape by the ram-pressure effects of the solar wind. |
2.2.3. Planets (~ 104 to 105 km; ~ 10-9 parsec) (~ 0.1 Gauss)
Aside from Earth, planetary magnetic fields have been detected so far through in-situ spacecraft measurements, for Mercury and the giant planets Jupiter, Saturn, Uranus, Neptune (e.g., Fig. 5 in Kivelson et al. 1996b).
For a planetary dipolar-shaped magnetic dynamo, the time-variation of the magnetic field B follows the interaction between a diffusion term and an induction term
 |
where 
signifies a
partial differential operator, t is the
time, B is the global magnetic field,
is the magnetic
diffusivity (
< 107 cm2 sec-1) and V is the
velocity field relative to the rigidly rotating frame defined by the
external magnetic field (e.g., chapter 6 in
Hubbard 1984).
2.2.3.1 Mercury The data for Mercury are consistent with some kind of active magnetic dipole, of strength × 5 × 1016 Gauss m3. The radius of Mercury is ~ 2440 km. The magnetic field strength at the equatorial surface amounts to about 3.5 milliGauss (e.g. Lanzerotti & Krimigis 1985).
In Mercury, the magnetic field may be generated and maintained somewhere in the liquid outer core by dynamo action. The rough extent of the dynamo region is above 0.4 and below 0.6 Mercury radii (Schubert et al. 1988), and the dynamo is driven by release of gravitational energy and latent heat upon inner core growth.
2.2.3.2 Venus The data for Venus do not show a magnetic field, so the magnetic moment < 6.6 × 1016 Gauss m3. The radius of Venus is ~ 6050 km. The magnetic field strength at the equatorial surface is < 0.3 milliGauss (e.g. Lanzerotti & Krimigis 1985).
Dynamo theory does not predict much magnetism for Venus, due to the very slow rotation of ~ 243 days of Venus as a whole, < 0.6 milliGauss (e.g., chapter 20 in Parker 1979).
2.2.3.3 Mars The data for Mars show a very weak
magnetic field, about 800 times weaker than Earth's or about 0.6
milliGauss (e.g.,
Cohen 1997a;
Kerr 1997;
Lanzerotti & Krimigis
1985),
so the mean magnetic moment is
2.3 ×
1016 Gauss m3. Mars' radius is ~ 3370 km.
The Global Surveyor probe found some patchy magnetic areas on Mars' surface, showing a random distribution of rocky bar magnets scattered all over the surface, sometimes reaching a few milliGauss - this is not a global magnetic field. The random magnetic patches are thought to be the remnants of an ancient field (e.g., Cole 1997).
The planetary core of Mars may extend up to 0.5 Mars radius. Dynamo theory does not predict much magnetism for Mars, due to the current absence of thermal convection inside the core (e.g., Schubert et al. 1992). Such a very weak magnetism implies that the planetary core must have cooled quickly and the current magnetism may be the relic of a dead turn-off dynamo, a fossilized remnant left in crustal rocks of earlier interior activity.
2.2.3.4 Jupiter The data for Jupiter are consistent with some kind of active magnetic dipole, of strength ~ 1.5 × 1024 Gauss m3. The radius of Jupiter is 71,370 km. The magnetic field strength at the equatorial surface amounts to ~ 4.1 Gauss (e.g. Lanzerotti & Krimigis 1985).
Substantial polarized synchrotron radio emission comes from Jupiter, implying the presence of a strong dipolar magnetic field, rotating with the same period as for the planet as a whole. The position of the moon Io seems to affect the intensity of the radio emission coming from the magnetosphere of Jupiter, possibly due to the matter being spurned out from the volcanoes of Io.
A substantial dynamo can be sustained by a highly turbulent MHD flow inside Jupiter (e.g., Hubbard 1984), involving a convecting electrically conducting dynamo in the planet's interior.
2.2.3.5 Saturn The data for Saturn are consistent with some kind of active magnetic dipole, of strength ~ 9 × 1022 Gauss m3. The radius of Saturn is ~ 60330 km. The magnetic field strength at the equatorial surface amounts to ~ 0.4 Gauss (e.g., Lanzerotti & Krimigis 1985).
In Saturn, the magnetic field may be generated and maintained somewhere in the outer core by dynamo action. The rough extent of the dynamo region is above 0.4 and below 0.6 Saturn radii, in the outer core of liquid-metallic-hydrogen and semiconducting-molecular-hydrogen (Hubbard & Stevenson 1984).
2.2.3.6 Uranus The data for Uranus are consistent with some kind of active magnetic dipole, of strength ~ 5 × 1020 Gauss m3. The radius of Uranus is ~ 12800 km. The magnetic field strength at the equatorial surface amounts to about 0.23 Gauss (e.g., Table 3.2 in Lang 1992).
In Uranus, the magnetic field may be generated and maintained by dynamo action. The rough extent of the dynamo region is above 0.3 and below 0.7 Uranus radii, through nonuniform motions in a highly ionic conducting fluid (Podolak et al. 1991).
2.2.3.7 Neptune and Pluto The data for Neptune are consistent with some kind of active magnetic dipole, of strength ~ 2.5 × 1020 Gauss m3. The radius of Neptune is ~ 12380 km. The magnetic field strength at the equatorial surface amounts to about 0.13 Gauss (e.g., Table 3.2 in Lang 1992).
In the large planets Uranus and Neptune, it has been argued that the magnetic field could also be generated in a shell at intermediate depth in the planetary interior, not in the core (Kivelson et al. 1997).