Why does the magnetic field of the Earth reverse?

Transcription

1 IMPRS Solar System Seminar June 2002 Why does the magnetic field of the Earth reverse? Dieter Schmitt (Katlenburg-Lindau) 1. Geomagnetic field >99% of matter in universe is plasma: gas of electrons, ions and neutral particles moving charged particles electric currents magnetic fields basic process magnetic fields everywhere in cosmos: planets, stars, accretion disks, galaxies magnetic field of Earth oldest known magnetic field of a celestial body: compass, Gilbert (1600) Gauss (1838): spherical harmonics, sources in interior, mainly dipolar, E 0.3 G, P 0.6 G, tilt 11, offset 450 km 0.07 R E, D r 3 higher multipoles superposed secular variation westdrift of nonaxisymmetric components of 0.18 /yr pole wobble intensity variations polarity reversals, 10 3 yr yr

2 SINT-800 VADM (Guyodo & Valet, 1999) Ma Ma

3 2. Dynamo theory basics composition of Earth solid inner core, r 1200 km, Fe, Ni fluid outer core, r 3500 km, good electrical conductor, thermal and chemical convection, location of electric currents, which excite the geomagnetic field mantle, poorly conducting; thin crust decay time in core: yr electromagnetic induction: u j ( u) self-excitation, dynamo-electrical principle (Siemens 1867) disk dynamo: u ux homogenous dynamo, complicated flows, induction equation t = rot (u η rot), differential rotation = pol + tor helical convection (Parker 1955) Ω Ω θ Ω Ωcosθ θ Ω Ωcosθ uxω u uxω u u u j j

4 theory of mean fields (Steenbeck, Krause & Rädler 1966) = +, u = u + u average: ensemble, azimutal, spatial, temporal t = rot ( u + u η rot) u = α η T rot α = 1 u (t) rot u (t τ)dτ, η 3 T = 1 3 u (t) u (t τ)dτ η αω-dynamo gradω pol tor dynamo number C = R α R Ω = α 0 R/η T Ω 0 R3 /η T α stochastic helicity fluctuations δα of each convective cell α = α 0 (θ) + δα (θ, t) with δα = f rmsf (θ, t) α 0 2Nc sin θ correlation length Rθ c = Rπ/N c, correlation time τ c forcing parameter f 2 rmsθ 2 cτ c back reaction of magnetic field on velocity (u, u ) through Lorentz force, e.g. α()-quenching sign of free

5 3. 1D mean-field αω-dynamo model azimuthal averages, axisym. component of field = (θ, t) exp(ikr), = rot(p e φ ) + T e φ θ R dimensionless αω-dynamo equation ( ) ( ) ( ) P α/α = 0 P t T C( / θ) sin θ T diffusion operator dynamo number C α fluctuations and quenching: α = α 0 (θ, ) + δα (θ, t) mode structure: fundamental mode: monotonous dipole, supercritical, nonlinearly saturated t t overtones: dipolar and quadrupolar, oscillatory, decaying t

6 effect of α-fluctuations δα: variation of fundamental mode amplitude t stochastic excitation of higher modes t 4. Numerical results standard case: kr = 0.5, Ccrit = 57.9, C = 100, frms = 6.4, θc = π/10, τc = part of much longer run with 500 reversals secular dipole ampl. variation d v = h(a hai)2i/hai rapid reversals with Tr 100 τd

7 reversals through decay of fundamental mode and short-time dominance of oscillating overtones variation of stochastic forcing: top: f rms = 5.4 dv 0.07, T r 500 τ D bottom: f rms = 7.4 dv 0.3, T r 35 τ D linear increase of forcing from f rms = dv and T r τ D

8 variability / secular variation reversal rate 5. Theoretical analysis Fokker-Planck equation: expansion of into unperturbed eigenmodes b i (θ, t) = a i (t)b i (θ) i a i t = λ i a i + (1 a2 0 ) k N ik a k + k F ik (t)a k averaging over fluctuations p t = a Sa a Dp 2 p(a) probability distribution of fundamental dipole 2 amplitude a = a 0 drift term S = Λ(1 a 2 )a = du/da determined by dynamo model (supercriticality, nonlinearity) diffusion term D = D 0 a 2 + D 1 (a), D 1 (0) 0 depends on forcing f 2 rmsθ 2 cτ c variation of fundamental mode (F 00, D 0 ) influence of overtones (F 0k, D 1 )

9 bistable oscillator U(a) p(a) a 1 2 U(a) given by U/ a = S symmetry, central hill, side walls, wells reversals through overtones (D1) reversals fast Ra 1 1 amplitude distribution p(a) D exp 0 2SD dx y d v, Tr frms % y dv % y Tr ball in honey, reversal is random process, no specific cause 6. Comparison with SINT-800 data SINT-800 VADM secular VADM variation d v = ± dynamo model y Tr 500τD

10 VADM distribution comparison with dynamo 7. Diffusion time scale τ D VADM(t) and a(t) are essentially the same absolute time turbulent diffusion time adjust τ D until autocorrelation functions match τ D 10 4 yr