# Class 13 - Magnetic Fields

Notices:
Mid-term Tuesday Oct 15th
Thurs Oct 17th - Terrestrial Planet Formation & Evolution

Reading:

Hartmann pp 209-211
Optional - Chapter 4 of the New Solar System

### PLANETARY MAGNETIC FIELDS

Below is a table showing the magnetic fields of the planets - or lack thereof.

 Rotation Period (days) Magnetic Moment (Earth=1)a Field at Equator (gauss) Field Ratiob Maximum / Minimum Tilt of Dipolec (degrees) Typical Magnetopause Distance Plasma Sourcesd (Rplanet) (km) Mercury 59 0.0007 0.003 2 +14° 1.5 0.04 x 105 W Venus 243 (R)e <0.0004 <0.0003 ? - - - A, W Earth 1.00 1 0.305 2.8 +10.8° 11 0.7 x 105 W,A Mars 1.03 <2.5 x 10-5 f <5 x 10-5 f ? - - - A, W Jupiter 0.41 20,000 4.2 4.5 -9.6° 80 60 x 105 S, A, W Saturn 0.44 600 0.20 4.6 -<1° 20 12 x 105 S, A, W Uranus 0.72 (R)e 50 0.23 12 -59° 20 5 x 105 A, W Neptune 0.74 25 0.14 9 -47° 25 6 x 105 S, A, W

a Earth’s dipole moment = 7.906 x 1025 Gauss cm3 = 7.906 x 1015 Tesla m3

b Ratio of maximum surface field to minimum equals 2 for centered dipole field

c Angle between the magnetic and rotation axes

d W = solar wind, A = atmosphere, S = satellite(s) or rings

e (R) = retrograde

f These values are upper limits on a global magnetic field. The Mars Global Surveyor has shown Mars to have 2000 km x 200 km regions of strong, local magnetization, presumed to be remnant magnetization produced by an ancient (now inactive) dynamo.

Note the following characteristics: There is a HUGE range in planetary magnetic moments (blue column), but the range in surface fields (for those planets that have magnetic fields to speak of) are all on the order of ~1 Gauss (except tiny wee little Mercury). Nevertheless, there are also all sorts of interesting differences between these magnetic fields. For example, the range in values between the strongest and weakest surface fields (which should be a factor of 2 for a centered dipole) vary up to as much as 9 and 12 for the highly offest magnetic fields of Uranus and Neptune. This is a strong indication that the magnetic fields are really not dipoles (like bar magnets) but more complex structures. Next, let's look at the orientations of the magnetic fields:

Earth, Jupiter and Saturn have fields that are oriented within ~10 degrees of the spin axis. Uranus and Neptune, on the other hand, have highly tilted magnetic fields that are strongly offset:

How do these "iron filings" diagrams look like as maps of magnetic field on the surface?

Again, Earth and Jupiter's simple tilted dipoles look very similar (except that Earth is upside down - or is it Jupiter?!). But Uranus and Neptune have very irregular magnetic fields - with magnetic "equators" which do not even circle the planet.

### MAGNETIC DYNAMOS

How are these magnetic fields generated? First, they cannot be simple "bar magnets" - magnetic fields frozen in lumps of iron - because (a) the gas giants do not have lumps of iron inside them and (b) above a temperature of a few hundred K (the Curie temperature) iron and rock do not remain magnetized. This means that the planets with magnetic fields must have DYNAMOS inside. These are mysterious beasts - no one has modeled magnetic dynamos realistically (it is a major computational task) but we can say that there are

3 ESSENTIAL INGREDIENTS FOR A DYNAMO:

1. A volume of electrically-conducting fluid (e.g. liquid iron, metallic hydrogen or "oceans" of water with ions to carry charge)
2. A source of energy to drive convective motions
3. Rotation

Thus, the presence of a magnetic field surrounding a planet tells you that these 3 ingredients have to be present inside the planet. It turns out that #3 is satisfied by all solar system bodies - they all rotate sufficiently. So, the lack of a magnetic field suggests that there is either not a large volume of conducting liquid (e.g. that the conducting material has solidified) or that there is not enough heat source to drive convection.

To remind you, Jupiter and Saturn have large regions of metallic hydrogen - Jupiter much larger than Saturn (which probably is the main explanation for Jupiter having a much stronger magnetic field). Inside Uranus and Neptune the conductor is the liquid ocean - where "inpurities" allow the conductivity (just like salt - sodium and chlorine ions - in Earth's ocean).

But this poses a problem - why are Uranus and Neptune have such similar magnetic fields when they have such different heat sources? What drives the dyanamo motions (and atmospheric circulation) inside Uranus?

Dynamo theory is hard to express simply - and even with super-computers there are not yet very realistic models. But here is a cartoon of the process.

## SUMMARY OF GIANT PLANET INTERIORS

### Jupiter

• Mjupiter ~ 320 Mearth -> high pressures -> Large metallic hydrogen region -> strong magnetic field.
• Enhanced by ~3 in heavy elements over cosmic abundances
• Internal heat source (from formation and differentiation) -> heat output ~2.5 solar input
• Solid core? probably not cool enough, core material entrained in the metallic H

### Saturn

• Msaturn ~ 90 Mearth -> lower pressures -> moderate metallic hydrogen region -> moderate magnetic field.
• Lower pressures -> cooler interior -> helium rain downwards
• Internal heat source (from formation and differentiation) -> heat output ~2.5 solar input
• Cool enough for a colid core

### Uranus

• Tilted on side = high obliquity
• Muranus ~ 14Mearth -> much lower pressures -> no metallic H
• Density requires substantial amounts of Water, Ammonia, Methane -> liquid ocean -> magnetic dynamo region
• NO internal heat source - why?

### Neptune

• Mneptune ~ 17Mearth -> similar to Uranus
• Density requires substantial amounts of Water, Ammonia, Methane -> liquid ocean -> magnetic dynamo region
• Internal heat source (from formation and differentiation) -> heat output ~2.5 solar input