Planetary Magnetic Fields
Planetary Magnetic Fields 1. 2. 3. 4. 5. 6.
Liam Farley David Kaufman Matthew Lawless Marc Veletzos
What is a Magnetic Field? How do we know about them? Different Types of M.F. Planetary Comparison Benefits of M.F. and Conclusions References
Specific Property of MF 1. What is a magnetic field? The region surrounding a magnet (or an electric current) which is endowed with specific properties. - Van Nostrand’s Scientific Encyclopedia
ÎFLOATING WATER!!!!??
Specific Property of MF
http://www.hfml.ru.nl/
Magnetic Field Lines (Bar Magnet Example) • Way to visualize the magnetic field • Vector field around magnet • Compass will point along M.F. lines
Î FLOATING FROGS!!!!??
http://www.hfml.ru.nl/
1
Planetary Magnetosphere The region surrounding a planet within which its own magnetic field dominates the behavior of electrically charged particles.
Maxwell’s Equations of Magnetism Differential Form
Gauss’ Law for Magnetism
Faraday’s Law of Induction
Ampere-Maxwell Law of Induction
ρ εo
∫E⋅d A = ε
∇⋅B = 0
∫B⋅d A = 0
∇⋅E =
Gauss’ Law for Electricity
∇× E = −
∇× B =
Integral Form
J
+
εoc 2
q o
∂B ∂t
∫ E ⋅ds = −
1 ∂E c 2 ∂t
dΦB dt
∫ B ⋅d s = µ i + µ ε o
o o
dΦ E dt
http://www.windows.ucar.edu
Gauss’ Law for Electricity
Gauss’ Law for Magnetism
q
∫B⋅d A = 0
∫E ⋅d A = ε
o
= Electric Field [V/m]
E
dA
q
= differential Area [m2]
The Electric flux through a Gaussian surface is related to the electric charges within that surface.
B
= charge [C]
εo
dA
= permittivity constant [F/m=C/V-m]
Faraday’s Law of Induction
∫ E ⋅ds = − E ds
= Electric Field [V/m] = differential length [m]
ΦB = ∫ B ⋅ d A
= Magnetic Flux [T-m2=V-s]
Î no magnetic monopoles.
= differential Area [m2]
Ampere-Maxwell Law of Induction
dΦB dt A changing magnetic flux produces an electric field.
The Magnetic Flux through a closed Gaussian surface must be zero.
= Magnetic Induction often called Magnetic Field, but this in not strictly correct [T=V-s/m2]
∫ B ⋅d s = µ i + µ ε o
B
= Magnetic Induction [T =V-s/m2]
ds
= differential length [m]
ΦE = ∫ E ⋅ d A
εo
µo
= Electric Flux [V-m]
o o
dΦE dt A changing electric field or a moving electric charge (i.e. a current) produces a magnetic field.
= electric permittivity constant [F/m=C/V-m] = magnetic permeability constant [H/m=V-s/A-m]
2
2. How do we know about M.F.? 2.1 Earth - magnetometer - volcanic flows - pottery 2.2 Other Planets - magnetometers on transmitters
3.1 Interplanetary Dynamos 9
Sources of energy for regenerative dynamos:
1. 2. 3. 4.
Decay of radioactive elements in the earth. Primordial heat remnant from the formation of the planet. Latent heat of solidification. Gravitational energy release from potential to kinetic of the solidified atoms. Magnetic fields have a tendency to decay over time. This decay time is in the order of approximately 3000yrs for the earth and varies with each planet. The fluid motion of the dynamo which regenerates the magnetic field is called the
3. Different Types of M.F. 3.1 Interplanetary Dynamo 3.2 Remanent Magnetic Fields 3.3 Induced Magnetic Fields 3.4 Atmospheric Magnetic Fields
9Parker 1995 Fluid inside planetary bodies tends to rotate differentially, with the inner most region spinning fastest. If an exterior North South magnetic field penetrates into conducting fluid then it will be round up into coils of toroidal magnetic field. This acts to concentrate and to amplify the magnetic field strength. If the conducing fluid convects by heat then the toroidal loops are twisted upwards and reinforce the original magnetic field.
Regenerative Dynamo Action
The dynamo equation 9 Why do large magnetic fields require energy sources? 9 A combination of Ohm’s law, Amperes law and Faraday’s law allows us to show why this is so. B= mag field V= Fluid motion relative to rotating frame of reference λ= magnetic diffusivity = 1/µoσ µo= permeability of free space σ= electrical conductivity T= free diffusive decay ~ 3000yrs ∆=differential
9 Dynamo equation: dB/dt= λ ∆2B + ∆x (vxB) What this allows us to show is that the timescale for non regenerative primordial mag fields is less than the age of our solar system showing energy sources are required to maintain these large mag fields.
9 In terrestrial planets electrical conductivity to liquid metallic iron core with alloys σ ~5x10·6 S/m λ ~ 2m2/second Gas giants have Hydrogen cores and Hydrogen attains the lowest conductivity appropriate to metals: σ ~2x105 S/m λ ~ 20-50 m2/second (pressure = 1.5Mbar and Temp = 2000+K) This corresponds to 0.8 of Jupiters’ core or 0.5 of Saturns’ core
3
9 9
The essence of a dynamo lies in the electromagnetic induction. This creates an EMF and associated current and field through the motion of the conducting fluid across magnetic field lines.
9
Dimensional analysis of the dynamo equation shows magnetic fields Reynolds number A magnetic Reynolds number is a measurement of the likelihood of the existence of a dynamo in a particular medium at a specified temperature and pressure.
Rm= vL/λ V= characteristic fluid velocity L = characteristic length scale of the motion Evidence from modeling suggest that a dynamo will exist if Rm exceeds 10 – 100 It is however dependant on a high Corriolis effect v/ΩL <1 Where Ω is the rotation rate of the planet. Two main parameters: At sufficiently low conductivity there is a size dependant cut off base on the need to exceed a critical magnetic Reynolds number. A n approximate size independent criterion for existence of convection as if conductivity too high=no convection
Different types of theorized dynamos in extraterrestrial planets Earth Mercury Moon Jupiter Saturn Neptune
-
-
Uranus Venus Mars
-
Mettallic iron core dynamo “ “ Gas giants Hydrogen dynamo “ planets containing a conductive layer of ice around a small silicate core “ No dynamo found “
See dia on board + explanation
Remanent Crustal Fields
3.2 Earth’s Magnetic Field Remanent crustal fields:
4 main types of permanent magnetizations:
Natural remanent magnetism (NRM) Thermorememanent magnetism (TRM) Chemical remanent magnetism (CRM) Depositional remanent magnetism (DRM)
9Types and processes responsible
Processes of magnetizations: 9 (NRM)Æ fosssil magnetism in rocks. Silicate minerals capable of acquiring a permanent magnetism. 9 i.e. iron oxides and iron sulfides are ferrimagnetic.
Paramagnetic (olivine, pyroxene, garnet, amphiboles) & Diamagnetic (quartz, feldspar) make up the bulk of silicate minerals and can’t be permanently magnetized.
Processes of magnetizations: o (TRM)Æ ferromagnetic minerals are weakly magnetized after being heated past the Curie temperature (previous magnetization lost) and allowed to cool below the blocking temperature in the presence of a magnetic field. o This allowed ancient pottery to become weakly magnetized, and provide a reference to the rate of decline of Earth’s recent magnetic field.
4
Processes of magnetizations: 9 (CRM)Æ Magnetic minerals formed by chemical processes at low temperatures allow crystals to grow to a size that is magnetically stable with the intensity of the applied magnetic field, they align with that field.
Post-formation magnetization 9 This type of magnetization can usually be removed or altered by subjecting the rock to a different magnetic field or by heating the rock to a significant portion of its Curie temperature. i.e. magnetite has a Curie temp = 851 K
Æ Must establish magnetization is remanent of formation time, and the declination (D) or magnetic azimuth of the remanent field must be known (positive clockwise 0-360 degree variance of field from true geographic north). Also, Inclination (I) = angle between horizontal and the field direction (measured positive downward).
Paleomagnetism Overview
Processes of magnetizations: 9 (DRM)Æ When a sedimentary rock acquires a remanent magnetism during formation. As small ferromagnetic particles settle out of water in the presence of a magnetic field their magnetic moments become partially aligned with the ambient magnetic field.
Magnetic magnitude (B) Some governing equations: B(horiz) = B cos I
(further resolved into northward component and eastward component)
B(vert) = B sin I Earth presently is ~ a dipole magnetic field Assuming a spherical Earth, vertical and horizontal components @ surface are governed by (show equations and diagram, Turcotte P.23 & 24)
Paleomagnetism A world map of paleomagnetic isochrons:
9 M.O.R.Æ
9 extrude hot new crustal material symmetricallyÆ
9 new material cools, locking in the paleomagnetic fieldÆ
9 creating symmetrical reversals of magnetic bands detectable by magnetometers Æ 9 until subduction recycles the oceanic crust
Figure from pbs.org/nova/magnetic
5
What are magnetic reversals?
Earth’s Polarity Time Scale (to 155Ma) Cretaceous normal anomaly??
9 Magnetic reversals *are evident in rocks of up to 170Ma
9 Earth’s magnetic field switches from positive (normal), like that of the last 720,000yrs (e- in at the N. pole and out at the S. pole), to negative (reversed), the exact opposite prior to that. 9 Measurements of Earth’s polarity time scale is highly resolved to ~5Ma, and especially the last 12Ka from pottery.
Figure from pbs.org/nova/magnetic
What are magnetic isochrons? 9 Isochrons are long parallel magnetic stripes, or +/- anomaly bands symmetrically located on each side of a spreading ridge, and can tell us the polarity of Earth’s field at certain times in the past. 9 K-Ar radiometric dating of volcanic flows like that of the Empire Chain is the choice calibration technique to provide dates for the isochrons.
3.3. Induced Magnetic Fields • Internal magnetic field caused by a temporally varying external field magnetic field • Need conductive material • Identified by distinctive time variability, phase and amplitude
What’s paleomagnetism good for? 9Can indicate the position of the magnetic pole as a function of time for rocks of different ages.
9 A measurement of a paleomagnetic pole can be used to deduce relative plate motions.
3.4 Atmospheric Magnetic Fields Ionosphere The Ionosphere is the part of the atmosphere that is ionized by solar radiation. It forms the inner edge of the magnetosphere. 50-95km-550km
• Recall Maxwell’s Equations of Magnetism
∫ E ⋅ds = −
dΦB dt
∫ B ⋅d s = µ i + µ ε o
o o
dΦ E dt
6
Plasma 9 Atoms high in the atmosphere are bombarded with particles from the solar wind. Often times if the atom is hit hard enough electrons can be lost, causing a net charge in the atoms. 9 Known as the fourth state of matter, and still being researched. More than 99% of all matter in the Universe is found in the plasma state. 9 Stars, solar wind, fluorescent lamps, lightning, Aurora borealis 9 Assumption of the Maxwell-Boltzmann distribution yield quantitatively wrong results and even prevent a correct qualitative understanding of the physics involved.
Solar Wind 9 Plasma flows along the Sun’s magnetic field lines, which flow radially from the sun. 9 Consists of mostly protons, with 5% helium and smaller fractions of oxygen and other elements. 9 Travels approximately between 400-800km/sec.
Atmospheric Magnetic Field
Solar Wind & Ionosphere 9 Some high energy particles from the solar wind are able to make it through the magnetosphere to reach the Ionosphere. 9 These particles react with molecules in the ionosphere, ionizing them, creating more plasma. 9 The plasma flows along the Earth’s Magnetic Field Lines. 9 Spiral, bounce, drift motions.
9 A dynamo is not needed though, as is seen in Mars and Venus. The tidal winds are able to cause enough motion to cause flow.
Earth’s Ionospheric Dynamo 9 Produced by movement of charged particles in Ionosphere across Earth’s main field lines. Motion driven by solar and lunar tides and tidal winds.
9 The flow of charged ions in the atmosphere is a moving conductor, which can produce electric currents and in turn, a magnetic field. 9 These fields are strongest on the dayside of a planet, where the interaction is occurring.
4. Planetary Comparison/What does M.F. tell us about Planets? Rotation Period
Diople
Angle
Typical
Moment Between Magnetopause
(days)
(Earth=1)
Axes
Distance
Mars
1.03
<.0002
-
-
Dyanmo Remanent Induced Atmospheric 0
+
0
+
Venus
243.02
<.0004
-
-
0
0
0
+
9Tidal winds are heating and expansion of the daytime side, and cooling and contraction on the nighttime side.
Mercury
58.65
0.0007
14
1.5
0?
?
0?
0
Earth
1
1
10.8
10
+
+
+
+
Uranus
0.72
50
58.6
20
+
0
0?
+
Electrons and Ions passing over magnetic field lines create electric currents which create magnetic fields of their own. This perturbs the Earth’s magnetic field locally.
Neptune
0.67
25
47
20
+
0
0?
+
Jupiter
0.41
20,000
9.6
80
+
0
0?
+
Saturn
0.44
600
<1
20
+
0
0?
+
Io
1.77
< 0.02
-
-
?
?
?
?
Ganymede
7.15
0.04
-
-
+
0?
0?
0?
Europa
3.55
< 0.002
-
-
0?
0?
+
?
Callisto
16.69
0.00008
-
-
0?
0?
+
0?
Moon
27.32
-
-
-
0
+
0?
0
7
Mars 9 9 9
Observed MF ~ 10^-9 to 10^-4 or <.0002 of Earth’s dipole moment Internal Structure similar to Earth’s Had a dynamo in the past, but no longer. 9 9 9
Core cooling until conductive heat loss dominated convection – no inner core formed Underwent convective change and became stagnant lid; no more cooling or convection Core froze enough that remaining fluid could not sustain a dynamo
9
Remanent fields found in the crust of Mars, mostly in the older crust in the southern hemisphere.
9
Solar wind is scouring the atmosphere away
9
Atmospheric Magnetic Fields are found in the upper atmosphere of Mars, in correspondence with crustal remanent fields.
9 9
9
9 9
Martian pressure balance obstacle model made from calculations of pressure contributions from crustal magnetic pressure, ionospheric thermal pressure, and solar wind dynamic pressure.
This is our main proof that Mars had a dynamo. It showed that the dynamo had a strength of ? More than Earth when it was functioning. Any water that was there, and the atmosphere it had has been swept away by the solar wind due to the lack of a magnetosphere.
The magnetic fields produced here keep some particles in the atmosphere concentrated These particles are ionized and flow, producing electric currents which also create local magnetic fields.
Venus 9 9
Observed MF ~10^-8 or <.0004 of Earth’s dipole moment Internal Structure thought to be similar to Earth’s
9
No dynamo at present. Most probable reason is that core does not convect.
9Has a liquid outer core (with or without an inner core)
9There are no plate tectonics on Venus, which makes cooling more efficient. 9Stagnant lid form of mantle convection is what is described here. 9Core may not be cooling, perhaps going through a transition in convection from the global resurfacing ~500 Mya.
9
No remanent magnetic fields detected.
9
Atmospheric Magnetic Fields are present on Venus.
9The temperature of the surface of Venus is above the Curie temperature for most materials, the temperature at which the minerals lose their magnetic signatures. 9The global resurfacing may or may not have had remanent magnetic signatures. 9Interactions between the solar wind and UV rays on the atmosphere of Venus create an ionosphere. 9Much like on Mars, the flow of ions from tidal winds and from the magnetized solar winds create the ionosphere to flow and electrical fields are created, in turn creating local magnetic fields.
Looking Forward Messenger Mission
Mercury’s Magnetic Field 9 Mariner 10 --> 1% of Earth’s field strength (220nT)
9 Dipolar magnetic field @ 7 degree inclination to its axis of rotation
9 Mercury’s magnetosphere is likely generated by a “dynamo effect” or is remanent of such in its younger ages. 9 Mercury’s density is 5.44g/cm^3 (Earth’s 5.52g/cm^3), suggests 70% metals to 30% silicates by weight, w/42% of volume being iron core, 1800-1900km thick (a portion must be molten for dynamo).
Neptune Neptune was first thought to have similar magnetic field to earth, however the 1989 Voyager mission showed otherwise The equatorial radius is 24800km and is equivalent to 17 earth masses. It is inferred that it has a large rocky core, a conductive iced based middle layer and a Hydrogen and Helium envelope The magnetic dipole of Neptune is tilted 47 degrees to the rotational axis and it this which gives rise to the large surface field of 1.42µT Although not much is known about Neptune it is thought to be very similar to Uranus due to their similar magnetic pole inclinations and sizes of the planets.
8
Uranus 9
Jupiter
The rotational axis of Uranus is nearly inline with its rotational plane orbiting the sun so a different mag field was expected on the voyager mission.
9 Jupiter is a gas giant planet and is the largest planet in our solar system 9 It also has the largest magnetosphere and actually produces a signal receivable on Earth 9 It is thought to produce this magnetic field
However due to the high inclination of its magnetic field relative to the rotation axis it had a similar magnetosphere to that of earth
by a highly conductive layer of pressurized Hydrogen in a dynamo affect. 9 The interactions of Jupiter with its especially
Radius = 25600km Surface field = 23µMT which is 50 times the expected field
Io has some interesting results with the two interacting causing visible aurora in he poles
This is again due to Uranus’ contribution of the quadrupole moment to the surface magnetic
of Jupiter. 9 Cassini will try to look into Jupiters’
field is large, almost comparable to the contribution from the dipole moment
magnetic field more closely.
Io
Saturn
• Observed M.F. Î < 0.02 * Earth?
9 Saturn is similar to Jupiter on a slightly smaller scale
• Complex (deeply imbedded in Jovian field)
9 Pressures of 1000000bar in the deep core of Saturn enable the liquid hydrogen to act as a conducting metal and for the dynamo effect to occur 9 Pionneer 11 detected the bow shock wave at 1.44million km from the planet 9 Sattellite revealed a magnetic field 600 times that of earth bt considerably weaker than that of Jupiter
• No convincing evidence of dynamo
9 The rings act as buffer zones absorbing electrons and charged particles 9 The moons of Saturn act as a source of plasma eapeciallyTitan which loses N2 from its atmosphere to produce plasma which causes the auroa in the poles of Saturn
• No simple inductive response • Metallic core
http://solarviews.com
Ganymede
Europa
• Observed M.F. Î 0.04 * Earth
• Clear signature of permanent dipole
• Observed M.F. Î < 0.002 * Earth
• Possible much smaller induction signal from water ocean
• Clear induction field signal Î strong likelihood of water with similar conductivity to Earth’s oceans below ice layer (~10 km deep)
• Dynamo likely in metallic core (Fe-S?), but surprising because due to difficulties of small body sustaining convection. Sulfur and large 40K heating will help.
• No evidence of permanent dipole
http://solarviews.com
http://solarviews.com
9
Callisto
Moon • Observed M.F. Î patchy; no global field
• Observed M.F. Î 0.00008 * Earth
• Impact generated?
• Clear induction field signal Î salty water ocean below ice layer (150-200 km deep)
• Ancient dynamo (may have arisen through mechanical stirring in inner core Î unique in our solar system)?
• Ocean is expected due to radioactive heating alone
• Likely has core that is at least partially liquid
http://solarviews.com
5. Benefits of M.F. and Conclusions
http://solarviews.com
Life!!! Dependent on and Adapted to magnetic fields
9Life! And adaptations 9Protection for solar wind/particles 9Atmosphere/Water
Protection from Solar Wind 9 Because the particles are charged, they can change molecular structures as they pass through them! Cancer, mutations! 9 Our atmosphere would be stripped away without magnetic fields, and water would not be sustainable.
Protection from Solar Winds
A computer model driven by science data shows Earth's bow shock -the leading, colored edge to the left -- stretching out toward the Sun as solar wind density drops. The magnetosphere (gray shading) changes from a windsock shape to a dipole. http://www.solarviews.com/cap/sun/bs-nasa.htm
10
Aurora?
Without MF?! 9Not much
6. References 1.
Halliday D. and Resnick R., “Fundamentals of Physics”, 3rd Edition, John Wiley & Sons, Inc., 1988.
2.
Stevenson D., “Planetary Magnetic Fields, Science and Nature”, Earth and Planetary Science Letters Frontiers, 2002.
3.
“Van Nostrand’s Scientific Encyclopedia”, 5th Edition, New York: Van Nostrand Reinhold Company, 1976.
4.
Buffett B., “The Thermal State of Earth’s Core”, Science, Vol. 299, March 14, 2003.
5.
Stevenson D., “Mars’ Core and Magnetism”, Nature, Vol. 412, July 12, 2001.
References 9 Windows to the Universe, www.windows.ucar.edu/windows.html 9 Fortes, A.D., (1997) Introduction to Planetary Magnetism, www.es.ucl.ac.uk/research/planetaryweb/undergraduate/dom /magrev/intromag.htm 9 Brain, D. (November 2003) The Influence of Crustal Magnetic
Sources on the Topology of the Martian Magnetic
Environment, http://sprg.ssl.berkeley.edu/~brain/rsrch.html 9 Russel, C.T., Vaisberg, O., (1983) The Interaction of the Solar Wind with Venus, http://wwwssc.igpp.ucla.edu/personnel/russell/papers/interact_solwind/ 9 The Solar Wind at Mars, http://science.nasa.gov/headlines/y2001/ast31jan_1.htm
http://www.pbs.org/wgbh/nova/magnetic/reversals.html
11
