The origin of the Earth's magnetic field Author: Stanislav Vrtnik Adviser: prof. dr. Janez Dolinšek March 13, 2007

Outline 1 Introduction 2 Structure of the Earth 3 The self-excited dynamo 4 An Earth-like numerical dynamo models 5 The approaching polarity reversal 6 Conclusions

1 Introduction Geomagnetic field is generated in Earth’s core Temperatures > 3000 K; above Curie point (T c (Fe) = 1043 K; T c (Ni) = 627 K ) Magnetic field is generated by electrical current Unsustained electrical current would dissipate within years Paleomagnetic records (ancient field recorded in sediment and lavas ) Earth’s magnetic field exists millions of years Mechanism that regenerates electrical currents (self-excited dynamo) The polarity reversal Earth will lose magnetic shield for high-energy particles

The mantle: 2900 km thick Silicate rocks (with Fe, Mg) Solid, but ductile can flow on large timescale Convection of the material moves tectonic plates Pressure increase with depth and change viscosity Lower mantle flow less easily 2 Structure of the Earth Crust Not to scale To scale Upper mantle Lower mantle Liquid outer core Solid inner core The Crust: 5-70 km tick < 1% Earth’s volume 100 millions years old Some grains are 4.4 billion years old Part of the lithosphere divided on tectonic plates The outer core: 2180 km tick Liquid Fe, Ni, some light elements The inner core: Radius of 1220 km Solid (Fe, Ni)

3 The self-excited dynamo Self-excited dynamo model was first proposed by Sir Joseph Larmor in 1919 Magnetic instability → (perturbation of the field is exponentially amplified) Simple experiment with mechanical disk device Faraday disk dynamo Magnetic flux through the disk: Induced voltage:

3 The self-excited dynamo Permanent magnet → replaced with solenoid Magnetic flux through the disk: Induced voltage: Electrical current is given by: R - electrical resistivity of the complete circuit Self-excited dynamo

3 The self-excited dynamo Electrical current is given by: Solution of the differential equation is: System becomes unstable when: (  <  C ) the resistivity will damp any initial magnetic perturbation (  <  C ) the system undergoes a bifurcation →an initial perturbation of the field will be exponentially amplified A) B)

4 An Earth-like numerical dynamo models Nonlinear three-dimensional model is needed Geodynamo operates in ‘strong field’ regime: nonlinear magnetic Lorentz force ≈ Coriolis force → Lorentz force cannot be treated as perturbation → nonlinear numerical computation is required Cowling’s theorem: self-sustained magnetic field produced by a dynamo cannot be axisymmetric → no 2D solution can be sought → problem has to be investigated directly in 3D

4.1 The magnetohydrodynamics Equations Induction equation: - magnetic field - velocity - the magnetic diffusivity interaction diffusion magnetic field decreases exponentially (  Earth = years) magnetic field is "frozen" into the conducting fluid A) B)

4.1 The magnetohydrodynamics Equations Navier-Stokes equation: - mass density - scalar pressure - viscosity - external forces: Lorentz force gravity force Coriolis force buoyancy force To simulate the geodynamo we also need equations for:the gravity potential the heat flow Model for geodynamo can have up to 10 equations

4.2 3D simulation of a geomagnetic field Glatzmaier-Roberts model: with the dimensions, rotate rate, heat flow and the material properties of the Earth’s core Time step: 20 days Simulation now spans more than years The simulation took several thousand CPU hours on the Cray C-90 supercomputer Yellow - where the fluid flow is the greatest. The core-mantle boundary - blue the inner core boundary - red G.A. Glatzmaier and P.H. Roberts

4.2 3D simulation of a geomagnetic field Magnetic field is similar to the Earth's field: Intensity of the dipole moment A dipole dominated structure Westward drift of the non-dipolar field at the surface (0.2° per year) G.A. Glatzmaier & P.H. Roberts

4.2 3D simulation of a geomagnetic field Middle of reversal years into the simulation magnetic dipole underwent polarity reversal over a period of a 1000 years. the magnetic dipole moment decreases down to 10% recovered immediately after consistent with the paleomagnetic records G.A. Glatzmaier & P.H. Roberts 500 yr before500 yr after a)b)c)

4.2 3D simulation of a geomagnetic field The longitudinal average of the 3D magnetic field (out to the surface) Left – lines of force of the poloidal part of the field Right – contours of the toroidal part of the field Red (blue) contours – eastward (westward) directed toroidal field Green (yellow) lines – clockwise (anticlockwise) poloidal field G.A. Glatzmaier & P.H. Roberts, Nature, 377, (1995) 5000 yr beforeMiddle of reversal4000 yr after

4.2 3D simulation of a geomagnetic field The radial component of the magnetic field (Hammer projection) Upper plots (surface); lower plots (core-mantle boundary) Red (blue) contours represent outward (inward) directed field Intensity at the surface is multiplied by 10 G.A. Glatzmaier & P.H. Roberts, Nature, 377, (1995)

4.2 3D simulation of a geomagnetic field Rotation of the inner core relative to the surface: In simulation rotates 2° to 3° per year faster than at the surface Motivated seismologists to search for evidence (0.3° to 0.5° year faster ) The field couples the inner core to the eastward flowing fluid analogous to a synchronous electric motor G.A. Glatzmaier & P.H. Roberts

5 The approaching polarity reversal Study of the geodynamo has received considerable attention in the press Concerns of an approaching polarity reversal The magnetic field protects Earth’s surface from high-energy particles Sun wind, cosmic rays from deep space When the field switches polarity, its strength can drop to below 10% for few 1000 years. with potentially disastrous consequences for: the atmosphere, the climate and life. These concerns are supported by observational facts

5 The approaching polarity reversal Date/PeriodDipole moment In x A m 2 In x A m 2 Over the last years7.5 ± 1.7 x A m 2 Over million years5.3 ± 1.5 x A m 2 The first term of the spherical harmonic expansion It can be recovered in the past (paleomagnetic records) Measurements show rapid and steady decrease of the geomagnetic dipole moment Primary motive for pondering the possibility of an approaching reversal The geomagnetic field amplitude is a fluctuating quantity The present dipole moment is still significantly higher than its averaged value Over the last polarity interval and the three preceding ones The dipole moment:

5 The approaching polarity reversal Tilt angle according to the axis of rotation The angle is rapidly increasing toward 90° Opposite of what is expected for a reversal Direction of the dipole moment:

5 The approaching polarity reversal The magnetic dip poles: North South The two places on Earth Horizontal component of the field is zero Local objects They are affected by all components in a spectral expansion Move independently of one another The northern magnetic dip pole velocity 40 km/year ( last few years) 15 km/year (last century) The southern magnetic dip pole velocity decreasing (now 10 km/year) The dip pole is simply an ill defined quantity

5 The approaching polarity reversal The last reversal dates back some years 7 reversal in last 2 million years The reversal rate is not constant Average over few million years is 1 per million years Maximum value is 6 reversals per million years Maximum: Superchrones (10 millions years) The overdue reversal:

6 Conclusions Numerical models are successful but: restricted to a very remote parameter regime viscous force is much larger than are in the liquid core Experimental fluid dynamos were created (1999 in Latvia and Germany) the flows were extremely confined Dynamo action works on a large variety of natural bodies planets in the solar system (Venus and Mars excepted) Sun (reverses with a relatively regular period of 22 years) galaxies exhibit their own large-scale magnetic field Evidence for an imminent reversal remains rather weak The typical timescale for a reversal is of the order of 1000 years

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