Planetary dynamos: Dipole-multipole transition and dipole reversals

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1 Planetary dynamos: Dipole-multipole transition and dipole reversals Ulrich Christensen Max-Planck-Institute for Solar System Research Katlenburg-Lindau, Germany in collaboration with Hagay Amit, Julien Aubert, Erik King, Carsten Kutzner, Kumiko Hori, Gauthier Hulot, Ajay Manglik, Peter Olson, Martin Schrinner, Andreas Tilgner, Johannes Wicht

2 The geodynamo Thermal /compositional convection in liquid outer iron core Electromagnetic induction by motion through the existing magnetic field sets up electrical current Currents produce magnetic field as needed for induction Selfsustained dynamo Fe,Ni +10% light element (Si, S, O) Fe,Ni + 2-4% light element

3 Dipole reversals A few reversals per million years Stochastic (vs. periodic at Sun) Mill. years Low magnetic field strength during reversal (but non-zero) Field during reversal dominated by multipole components

4 Field morphology Br Earth, Mercury, Jupiter and Saturn have dipoledominated magnetic fields Br Earth Uranus and Neptune have multipolar fields Picture 33 Neptune

5 Outline of geodynamo models Solve equations of thermal / compositional convection and magnetic induction in a rotating and electrically conducting spherical shell Direct numerical simulation of fundamental equations of magnetohydrodynamics Some parameters not Earthlike Tangent cylinder Solid inner core Fluid outer core

6 Governing equations u r 2 ( + u u ) + 2ez u + P = E u + Ra* T + ( B ) B t ro. Inertia Coriolis Viscosity Buoyancy T E + u T = 2T t Pr Advection Diffusion B E 2 + u B = B u + B t Pm Advection Induction u = 0 Diffusion B = 0 Lorentz

7 Magnetic field morphology Ra/Rac= 114 E=10-5 Pm=0.8 Rm = 914 Roℓ = 0.12 Ra/Rac= 161 E=10-5 Pm=0.5 Rm = 917 Roℓ = 0.21 Dipole dipolar dynamo multipolar dynamo Earth

8 Selection of dynamo regime Ratio inertia / Coriolis measured by dipolar reversing Rossby number multipolar Roℓ = U/Ωℓ critical point Roℓ 0.12 reversing dynamos near transition point

9 Dipole tilt Simulated reversals 2.5 million years Time

10 Geomagnetic reversal Magnetic field of dynamo model at Earth s surface

11 Generation of dipole field Ω-effect poloidal field α-effect toroidal field -effect

12 Differential rotation Reynolds stress: inverse inertial cascade from small eddies Thermal wind: Coriolis force acting on flow driven by temperature variation with latitude Non-magnetic Ra=22Rac Uϕ Reynolds Dipolar dynamo Uϕ Ra=22Rac Reynolds Geostrophic Ageostrophic Reynolds stress Thermal wind T Multipolar Uϕ Ra=29Rac Reynolds Largely geostrophic Aubert (2005); Simitev & Busse (2009) Zonal flow change passive reaction to different magnetic field? or Different zonal flow pattern causes breakdown of dipole field?

13 Forced zonal flow Uϕ Manipulate zonal flow in dynamo by imposing velocity condition on outer boundary Shape of forced flow similar to that driven by Reynolds stress.

14 Forced transitions Dipolarity Dipolarity 0% -40 % 16% 40% 8% 0% Time Time By forcing geostrophic differential rotation, an intrinsically dipolar dynamo can be turned multipolar Undoing the differential rotation by inverse forcing, an intrinsically multipolar dynamo turns dipolar

15 Change in Omega effect Ra = 11 Rac Ω-effect in forced dynamo (while field is still dipolar) Uϕ /s toroidal field Ω term Bϕ versus forced free Bϕ / t = s Bpol (Uϕ /s) + Ω - effect in free dynamo Geostrophic differential rotation: Ω-effect counterproductive for generating toroidal flux tubes

16 Forcing of reversing synamo unforced +4% -4% Reversal frequency increased by forcing differential rotation Reversal frequency decreased by suppressing differential rotation

17 Change in reversal frequency Dynamo models suggest reversals are sensitive to small change in parameters Is there evidence from geomagnetic field that this is so? Change of reversal frequency on 100 Mill.year time scale Possibly change in core heat flow by changes in mantle

18 Bistability and hysteresis multipolar dipolar Rol Simitev & Busse, EPL 2009 In other dynamo models, bistability of dipolar and multipolar solutions found over significant parameter range. For such dynamos, rapid dipole reversals by an excursion into the Ω multipolar mode would not be possible

19 Conclusions Geodynamo probably close to phase transition between strongly dipolar and multipolar regime Dipole reversals due to instability of dipolar dynamo. Fluctuations lead to brief lapse into multipolar phase. Phase transition occurs where inertial force relative to Coriolis force reach a critical limit Inverse inertial cascade transfers energy from small eddies to geostrophic differential rotation Anti-Ω-effect eliminates toroidal flux tubes of dipolar dynamo Open question: is Earth by chance near critical point, or is it self-organized criticality?

20 Hazard for satellites Geomagnetic field intensity 1990 Radiation damage events Topex/Poseidon Heirtzler, JASTP, 2002 Geomagnetic field particularly weak over South Atlantic and South America (South Atlantic Anomaly) Disruption of electronics on satellites by MeV protons Field intensity in SAA anomaly decreasing by 2% in 10 years